An airborne millimetre-wave radiometer at 183 GHz: receiver development and stratospheric water vapour measurements
Inauguraldissertation der Philosophisch-naturwissenschaftlichen Fakult¨at der Universit¨atBern
vorgelegt von
Vladimir Vasi´c von Serbien-Montenegro
Leiter der Arbeit: Prof. Niklaus K¨ampfer Institut f¨urAngewandte Physik -2 An airborne millimetre-wave radiometer at 183 GHz: receiver development and stratospheric water vapour measurements
Inauguraldissertation der Philosophisch-naturwissenschaftlichen Fakult¨at der Universit¨atBern
vorgelegt von
Vladimir Vasi´c von Serbien-Montenegro
Leiter der Arbeit: Prof. Niklaus K¨ampfer Institut f¨urAngewandte Physik
Von der Philosophisch-naturwissenschaftlichen Fakult¨at angenommen.
Der Dekan:
Bern, den 16.12.2004 Prof. Paul Messerli 0 Abstract
The subject of this Ph.D. thesis is the redesign of an airborne water-vapour radiometer AMSOS (Airborne Millimetre- and Submillimetre Observing Sys- tem) and measurements conducted with the new receiver. The thesis consists of three parts and four publications. The publications are placed within the thesis after appropriate chapters.
The first part is an introduction which addresses the scientific motivation of this thesis: why is water vapour in the stratosphere important and why are we studying it at all? An answer to this is made by emphasising the three main roles of stratospheric water vapour: its role in the ozone chemistry con- nected with ozone depletion, its greenhouse effect contributing to the global warming of the atmosphere and its long lifetime which makes H2O a good tracer. Another question arises logically: how can we measure water vapour in the stratosphere? This is also answered in the first part, where we discuss the physics behind absorption and emission in the millimetre-wave part of the spectrum, radiative transfer and line broadening and how they can be used for retrieval of vertical H2O-profiles. The principles of operation and calibration of a microwave radiometer are also presented here.
The second part of the thesis deals with experimental aspects and describes design of the AMSOS radiometer and especially of the radiometer’s qua- sioptics. After a short introduction to Gaussian optics, a new layout of the radiometer frontend is presented. All components are described according to their role in the quasioptics: first, a beam-shaping section which consists of a feed horn, a parabolic and an elliptic mirror; then a new quasioptical λ/4- isolator for reduction of internal reflections (which cause baseline ripple in observed spectra); and finally a Martin-Puplett interferometer for sideband filtering. The theoretical calculations and methods used in the design of ev- ery component are presented together with numerical simulations. However, special attention was paid to measurements of the quasioptical behaviour of every component and their artifacts. Measurements of the amplitude, phase and polarisation were done using the AB Millimetre vector network anal- yser, mainly at the radiometer’s operational frequency of 183 GHz. Several components were also tested at other frequencies. The beam-shaping section generated a regular output beam with a half power beam width of around 1◦, which was one of our main goals. The new λ/4-isolator performed well and ac- 2 cording to our theoretical predictions, attenuated internal reflections by more than 30 dB. Although it is a standard and simple component, widely used in mm- and submm-wave radiometers, the Martin-Puplett interferometer (MPI) and its rooftop mirrors showed very interesting quasioptical behaviour, differ- ent from theoretical expectations. The measured level of internal reflections in an MPI was always around -30 dB. The radiometer backend, system sta- bility, operational control and improvements are also presented. This part of the thesis includes three publications. Publication I (in press in Optics and Lasers in Engineering) addresses issues concerning the quasioptics of the frontend. Publication II (proceedings of the 28th International Conference on Infrared and Millimeter Waves, Otsu, Japan, 2003) deals with non-ideal quasioptical behaviour of a rooftop mirror. Publication III (submitted to IEEE Transactions on Geoscience and Remote Sensing) presents the whole radiometer and first results of water vapour measurements.
In the third part we present inversion methods that we used for the retrieval of water vapour altitude profiles, as well as the results from two measure- ment campaigns in November 2003 and February 2004. For the inversion we decided to switch to the retrieval software Qpack, that uses ARTS as for- ward model. Therefore we tested Qpack and ARTS in many simulations of a realistic retrieval which included instrumental parameters and artifacts. At the end we present the profiles obtained from the spectra recorded in the two campaigns. A comparison of AMSOS and balloon measurements from Febru- ary 2004 during the international LAUTLOS/WAVVAP campaign are also presented. In addition, AMSOS measurements were compared with satellite profiles.
The thesis ends with a summary of the results achieved and with an outlook towards further development of the receiver and its application. Contents
I Stratospheric water vapour and principles of mi- crowave radiometry 6
1 Water vapour in the atmosphere 7 1.1 Water vapour as a greenhouse gas ...... 7 1.2 Water vapour dynamics and ’Tape Recorder Effect’ ...... 10 1.3 Water vapour chemistry ...... 11
2 Microwave gas spectroscopy 13 2.1 Absorption and emission of gases ...... 14 2.2 Line broadening ...... 15 2.3 Radiative transfer ...... 19
3 Microwave radiometry 23 3.1 Heterodyne principle ...... 23 3.2 Calibration of a heterodyne receiver ...... 26
II AMSOS radiometer 28
4 Overview 29
5 The quasioptics of AMSOS radiometer 32 5.1 Principles of quasioptics ...... 32 5.2 Design of AMSOS’s quasioptics ...... 34 5.2.1 Feed horn antenna ...... 35 5.2.2 Parabolic mirror ...... 37 5.2.3 Radiometer’s output beam ...... 44
6 Quasioptical λ/4 isolator 51 6.1 Introduction ...... 51
3 4 CONTENTS
6.2 Theoretical description ...... 52 6.2.1 Detail analysis ...... 55 6.3 Measurements of the isolator ...... 63 6.3.1 Measurement setup and methods ...... 63 6.3.2 Results ...... 65 6.4 Isolator in AMSOS ...... 70 6.5 Isolator during flight campaigns ...... 72
7 Publication I 77
8 Martin-Puplett interferometer 93 8.1 Basics of the MPI ...... 93 8.2 Reflection measurements ...... 93 8.3 Sources of reflections ...... 98 8.4 Non-ideal polarisation rotation ...... 105 8.5 Lateral offsets of two beams ...... 106 8.6 Usage of the MPI ...... 111
9 Publication II 113
10 Signal down conversion and radiometer backend 117 10.1 Down conversion and amplifiers ...... 117 10.2 System stability ...... 118 10.3 Radiometer calibration and operation control ...... 121 10.3.1 Calibration cycle ...... 121 10.3.2 Operation control ...... 122 10.3.3 Control software and AMSOS database ...... 124 10.4 Aircraft window ...... 125
11 Publication III 127
III Inversion and Results of Stratospheric Water Vapour Distribution 137
12 Inversion 138 12.1 Introduction to inversion process ...... 138 12.2 Forward model: ARTS; inversion: Qpack ...... 141 12.3 Validation of retrievals with Qpack ...... 143 CONTENTS 5
13 Measurement campaigns and results 151 13.1 Ground-based measurements ...... 151 13.2 Airborne measurements ...... 151 13.2.1 Test campaign, November 2003 ...... 151 13.2.2 LAUTLOS/WAVVAP campaign, February 2004 . . . . 153 13.3 Validation of AMSOS: comparison with HALOE and POAM . 155
14 Publication IV 159
15 Conclusions and outlook 163 Part I
Stratospheric water vapour and principles of microwave radiometry
6 Chapter 1
Water vapour in the atmosphere
The Earth atmosphere consists mainly of nitrogen (N2, 78 %), oxygen (O2, 21 %) and argon (Ar, 0.93 %). Other gaseous species and particles make up the remaining 0.07 %. Although the amount of these remaining component (trace gases) is very small compared to the major ones, they play a crucial role in atmospheric chemistry and dynamics. One of the most important tracers is water vapour. The vertical distribution of water vapour, on contrary to e.g.
N2 and O2, decreases significantly with increasing altitude in the troposphere. Figure 1.1 shows the vertical distribution of water vapour according to the U.S. Standard atmosphere, [1]. The difference between the water vapour content at sea level and in the stratosphere is several orders of magnitude. The H2O-abundance in the stratosphere might look negligible compared to the troposphere. However, despite the concentrations that make water vapour a trace gas in the strato- sphere (concentrations similar to the ones of ozone), its role has a key influ- ence in several domains. There are three major fields where water vapour should be studied: its role in the ozone chemistry, its long lifetime affording studies of atmospheric dynamics and its major impact on the greenhouse effect.
1.1 Water vapour as a greenhouse gas
A yearly average of the power density radiated by the Sun to the Earth is 342 Wm−2. However, the whole energy will not be absorbed by the Earth sur- face. About 107 Wm−2 will be reflected from clouds, aerosols, air molecules
7 8 Water vapour in the atmosphere
120
100
80
60 Altitude [km]
40
20
0 −1 0 1 2 3 4 10 10 10 10 10 10 H O volume mixing ratio [ppm] 2
Figure 1.1: Vertical distribution of water vapour according to the U.S. Stan- dard Atmospheres. The abundance changes for several orders of magnitude from the lower troposphere to the stratosphere
(atmosphere) and from the Earth surface, and returned to space, [2]. Addi- tional 87 Wm−2 is absorbed in the stratosphere and troposphere by ozone, water vapour and clouds. The rest of the 148 Wm−2 is absorbed by the Earth surface. This power density would be enough for an Earth mean sur- face temperature of 255 K. However, the mean Earth temperature is 288 K, which is a result of the greenhouse effect. The surface temperature of the Sun is around 6000 K, which, according to Planck’s law on blackbody radiation gives a maximum radiation in the visible part of the EM-spectrum. This radiation propagates through the Earth’s atmosphere as described above. The radiation emitted by the Earth has its maximum, however, in the infrared domain, due to the Earth’s far lower surface temperature. Atmospheric gas molecules (mainly H2O, CO2, O3,N2O and CH4) absorb much more in the infrared region, compared to their absorption in visible and UV region. Therefore, the radiation emitted by the Earth surface will be absorbed much more by the atmosphere than the solar radiation. The difference between the radiative emission at the Earth’s surface of 390 Wm−2 (corresponding to the Earth’s actual mean 1.1 Water vapour as a greenhouse gas 9 surface temperature) and the emission to the space of 235 Wm−2 is 155 Wm−2 which remain in the atmosphere, [2]. This represents the greenhouse effect. Due to the greenhouse effect the surface temperature of the Earth is 288 K, which is around 33 K higher than the 255 K expected from the direct solar radiation. Such higher temperatures are crucial for life development on the Earth. However, human activities contribute to the changes in the green- house effect, indeed they lead to an increase of the amount of greenhouse gases in the atmosphere. The highest human contribution is visible on the increase of the CO2 abundance, due to fossil fuel burning. However, water vapour has the highest absorption in the infrared domain and is therefore the strongest greenhouse gas, [2]. To get the same increase in the green- house warming caused by a potential doubling of CO2, the amount of H2O would have to be increased by only 17 %, [3]. The increase of the CO2 is strongly human-related, but human activities do not greatly affect global water vapour distribution - it is mainly driven by physical processes.
Figure 1.2: Global-mean profiles of cooling (left side of the plot) and heating (right side). Contributions from individual active consitutens are also shown. Figure taken from [4] .
Only on a local scale can human activities cause stronger disorder in water vapour distribution, for instance through deforestation. Human activities can, however, indirectly increase the global H2O-amount through the increase 10 Water vapour in the atmosphere
of CO2 abundance (stronger greenhouse effect causes increased evaporation). A change in water vapour content can have more subtle consequences. The greenhouse gases have a local cooling effect in the troposphere as well as in the stratosphere due to their activity in the infrared region and inactivity in the visible and UV region (excluding ozone).
In the troposphere the strongest cooling effect is caused by the impact of H2O and CO2, and in the stratosphere by CO2,O3 and H2O, as shown in Figure 1.2. This means that an increase in the stratospheric water vapour would decrease temperatures in the stratosphere. Lower stratospheric temperatures would allow building of more polar stratospheric clouds, that are the main precondition for ozone depletion inside the polar vortex. Lower ozone content would lead to additional cooling of the stratosphere and to building of an even stronger polar vortex, [5]. This positive feedback caused by a potential water vapour increase can have long-term effects on the prolongation of ozone depletion.
1.2 Water vapour dynamics and ’Tape Recorder Effect’
The upper troposphere/lower stratosphere (UT/LS) exchange has a great influence on the global circulation of air masses. The exchange is initiated in the equatorial area, where the vast air masses go upwards due to strong convection caused by solar radiation. These air masses cross the tropopause, go into the stratosphere and afterwards spread pole-wards. This global trans- port is know as the Brewer-Dobson circulation, [6]. Due to low temperatures of the tropopause, the air masses are dehydrated and this dry air reaches the troposphere. However, it seems that small amounts of tropospheric wa- ter vapour are not frozen and washed down by the cold tropopause. They probably cross the tropopause and reach the lower stratosphere to some ex- tent, which is still a subject of scientific research. Due to Brewer-Dobson circulation, water vapour and other gases can reach polar areas, where they cool down adiabatically and drop to the lower layers. They can influence the ozone depletion there. These transport processes are still not well explored. The role of water vapour is therefore significant - due to its long chemical life- time it can be used as a tracer of dynamical motions of the air masses. The height and the temperature of the tropopause show seasonal fluctuations, and therefore the water vapour VMR that enters the stratosphere shows similar fluctuations. These fluctuations are also visible after 15 to 18 months when 1.3 Water vapour chemistry 11 this water vapour achieves altitudes of around 35 km. This effect is known as the ’taper recorder’ effect, [7]. This means that, under certain circumstances, we can estimate the air masses that crossed the tropopause in the past from the water vapour local abundance. Therefore measurements, estimation and understanding of the global distribution of stratospheric water vapour are very important.
1.3 Water vapour chemistry
Most of the water vapour in the stratosphere is supposed to come from methane oxidation. In recent years an increase of water vapour abundance have been observed by several authors, [8, 9, 10, 11]. Only around 50% of the H2O increase can be explained by the increase of (mainly anthropogenic) methane in the stratosphere. The rest remains not well explained. In the last couple of years H2O increases have been smaller then those previously observed.
The chemistry of CH4 and H2O is directly related to ozone depletion. Through methane oxidation the very reactive OH radical (hydroxyl) arises, which is active in ozone degradation. Hydroxyl is first created in reactions of H2O and H2 with the oxygen atom, and afterwards arises from oxidation of methane:
1 O( D) + H2O −→ 2OH 1 O( D) + H2 −→ OH + H 1 O( D) + CH4 −→ OH + CH3 (1.1)
−→ CH3O + H
−→ CH2O + H2
Water vapour in the stratosphere is the most important source of hydroxyl. Hydroxyl is included in many oxidation reactions in the stratosphere, pri- marily the ones involving dissociation of ozone:
OH + O3 −→ HO2 + O2
HO2 + O3 −→ OH + 2O2 (1.2) nett :2O3 −→ 3O2
An additional important role of hydroxyl is the activation of chlorine which is involved in ozone catalytic destruction, [2]. This process takes place on 12 Water vapour in the atmosphere a large scale in the presence of polar stratospheric clouds and is responsible for ozone destruction during the polar winter/spring inside the polar vortex. The initial reaction which activate chlorine is:
OH + HCl −→ Cl + H2O (1.3)
Atomic chlorine is very reactive and easily oxidates in reactions with ozone, decomposing a molecule of ozone into a molecule of oxygen. Chapter 2
Microwave gas spectroscopy
In the previous Chapter we explained to some extent the importance of water vapour. There are several methods for measurements of H2O in the atmo- sphere. The methods used for the measurements of tropospheric H2O are manyfold: balloon sounding, backscatter lidar, passive (radiometry) and ac- tive sensing (radar, GPS), spectroscopy. The methods used for the upper troposphere/stratosphere are more limited. There are two methods that are mainly used from the ground: balloon sounding and passive radiometry. By balloon sounding a probe is mounted on a balloon, and it measures water vapour content along the balloon’s flight track. The drawback of this method is that balloons have a limited altitude range, rarely above 35 km, and such experiments are often connected with high costs and logistical complexity. The two most commonly used type of probes used for balloon sounding are: the Lyman-α-hygrometer and the frost-point mirror. These two methods are very accurate and are used for calibration of other measurements techniques. However, it is obvious that large-scale global coverage is impossible by bal- loon sounding. They are mainly suitable for campaigns that are used for trend analysis. One of the best records of balloon H2O soundings come from the National Centre for Atmospheric Research (NCAR), Boulder, Colorado, [8]. Scientific rockets can achieve higher altitudes (up to 100 km), but are relatively rarely used due to their application complexity and expenses. A very cost-effective method for measurements of atmospheric species is pas- sive radiometry. A radiometer is a passive receiver that detects weak electro- magnetic radiation emitted by gaseous molecules from the atmosphere. Us- ing appropriate inversion methods, the vertical distribution of a species can be obtained from the measured spectrum. For detection of tropospheric/ stratospheric gaseous species (including water vapour) various observation
13 14 Microwave gas spectroscopy techniques, platforms and receiver types are used: ground based, airborne or satellite-borne. Most of them have sensors that detect signals in millimetre- and submillimetre part of the spectrum, also in far-infrared to infrared region (for instance HALOE on the UARS satellite). The mechanism of emission/absorption of the electromagnetic radiation of gases will be explained in the following chapters.
2.1 Absorption and emission of gases
We use electromagnetic radiation emitted by molecules of a specific gas to detect its abundance. A basic presumption that we use to explain this phe- nomenon is that radiation at a certain frequency f is generated by an electric dipole oscillating at the frequency f, [12]. There are three different types of absorption or emission transitions that generate such electromagnetic radia- tion. If we consider an isolated molecule of a gas, its total energy consists of three types of energy states:
rotational energy
vibrational energy
electronic energy.
According to quantum theory, these energy states can only be quantised and every state is described by an appropriate quantum number. Correspond- ing to every electronic state there is a number of possible vibrational states. Corresponding with every vibrational state there is a number of possible ro- tational states.
Rotational transitions (absorption or emission) occur when a molecule makes a transition between two different state of rotation. However, not every molecule can perform rotational transition - only the molecules with a permanent electric dipole moments can perform such a transition. The molecules without a permanent dipole have no rotational lines - like CO2, a linear molecule with a C-atom lying on the same line with two O-atoms. A similar situation occurs with the CH4 molecule: the molecule is symmetrical and can not generate rotational transition. The molecules with a permanent dipole are classified in three different groups, according to their geometry: a) Linear rotors - their atoms lie on a line and 2.1 Absorption and emission of gases 15 the moments of inertia along two (of three - x, y and z) spatial axes are equal. The moment of inertia along the main axis is negligible. The most important molecules for atmospheric chemistry in this group are HCl and ClO. b) Symmetric rotors - the two moments of inertia along two axes are again the same, but the third moment of inertia is not negligible. NH3 or CH3Cl are such molecules. c) Asymmetric rotors - all (of the three) moments of inertia are different. Some of the most important species for atmospheric research belong to asymmetric rotors: O3 and H2O.
The smallest possible difference between the energy levels are associated with differences between two rotational states, that belong to the same vibrational and electronic state. Transition between such pure rotational states have a result in emission (or absorption) of a line in microwave or far-infrared part of the spectrum. Only these lines are of the interest for microwave radiometry.
Vibrational transitions occur when atoms of a molecule oscillate along one axis of the molecule - the molecule is ’out-stretching’ and ’compressing’ along the axis. Vibrational transitions can be generated only by changing the vibrational energy state of an electric dipole. This means again that only those molecules with a permanent electric dipole generate vibrational lines. The molecules without a permanent electric dipole like H2,N2 or O2 are therefore inactive concerning vibrational transitions.
The energy changes by vibrational transitions are several orders of magni- tude larger then the energy changes by rotational transitions. Therefore, the vibrational transitions never occur alone - they are accompanied by many rotational transitions. These transitions occur between the red part of the visible spectrum and thermal infrared region. This group of lines lies in so called vibrational-rotational band.
Electronic transitions. The dipole moment of a molecule may change during an electronic distribution. If an electron redistribution occurs sym- metrically, there is no net change in the dipole and a transition is impossible. If the electron redistribution generates a dipole moment, electronic transition is possible. The energy differences between two electronic energy states are large and are always connected with vibrational and rotational transitions as well. Such complex transitions occur in the visible and ultraviolet part of the spectrum and involve simultaneous changes of all three types of energy. 16 Microwave gas spectroscopy
2.2 Line broadening
The transitional emission (or absorption) line of a gas should be infinitely narrow due to the strictly defined energy states of two transition levels. How- ever, in reality this is not the case. Lines generated by an atmospheric species have a broadened shape. There are three different mechanisms that lead to broadening of a emission line:
Natural broadening. According to the Heisenberg uncertainty principle, it is impossible to specify exactly the energy of molecule quantum levels. If an excited molecule lives for a time τ, then its energy instead of being exactly E, may be anywhere in a energy range δE around E, where δE ∼ ~/τ. Only if the lifetime τ was infinitely long, it would be possible to exactly deter- mine E. A transition line hasn’t therefore got an exact frequency. This line broadening is called natural broadening. Although physically important, this broadening effect is typically between ∆f = 10−6 and ∆f = 10−7 Hz which is negligible for atmospheric remote sensing.
Doppler broadening. Molecules of a gas are in a permanent motion. A quiet observer sees the radiation coming from a molecule that is moving with a velocity v as Doppler-shifted: v f = f 1 − cos θ) (2.1) l c where fl is the frequency in the local coordinate system and θ is the angle be- tween the axis of molecule’s propagation and the line of sight of the observer. Therefore, the Doppler-shift of the frequency will be: v ∆f = |f − f | = f cos θ (2.2) l l c For a system in thermodynamic equilibrium, the molecules’ velocities have a Maxwell-distribution. The number of molecules which have the x-component of the velocity between vx and vx + dvx is:
2 dN 1 vx = √ e u2 dv (2.3) N u π x where the most probable velocity u is given as: r 2kT u = (2.4) m 2.2 Line broadening 17
c Using (2.2) we can write vx = ∆f and therefore: fl c c dvx = d(∆f) = dv (2.5) fl fl The number of molecules which absorb or emit in domain v and v + dv:
c2∆f2 dN c u2f2 F (f, fl)dv = = √ e l dv (2.6) N u pifl The line shape of the Doppler-broadend line is:
2 2 c (f−fl) c u2f2 FD(f, fl) = √ e l (2.7) u pifl The halfwidth of the line is:
r r f u√ 2kN ln 2 T T ∆f = l ln 2 = A f = 3.58 · 10−7f (2.8) c c2 l M l M This makes an estimation of the Doppler broadening relatively easy. Typical values for Doppler-broadening at room temperature in mm-wave-range are several tenths to hunderds of kHz. As it is going be shown later, at lower altitudes (less then approx. 50 km) pressure broadening is much stronger than Doppler-broadening. However, at higher altitudes these two become comparable. By remote sensing, the Doppler broadening is therefore consid- ered only at higher altitudes, and is often limiting factor for the maximal altitude resolution of a radiometer.
Pressure broadening. Due to thermal motions of molecules in a gas, they collide permanently with other molecules. These collisions shorten the life- time of energy states of the molecules, which leads to broadening of the emis- sion/absorption line shape. The collisions rate depends on density, molecule velocity and collision cross-section. Since the density of the molecules de- pends on pressure, the line broadening of this kind is called pressure broad- ening. Pressure broadening plays the most important role in line shaping at lower altitudes (less then 50 km). There are two types of pressure broad- ening: a) Self broadening: the molecules collide with the molecules of the same species. b) Foreign broadening, where the molecules collide with the molecules of other species. The latter is indeed more important, for the molecules of the species interesting for radiometric observation (H2O, O3 18 Microwave gas spectroscopy etc.) collide mainly with the molecules of oxygen and nitrogen. The abun- dance of O2 and N2 is much higher then the one of the observed species and is uniformly distributed to the highest altitudes. Different theories have been developed to describe collision processes and the shape of absorption/emission lines. The simplest model is the one of Lorentz. The Lorentzian line-shape function is
1 γ FL(f, fl) = 2 2 (2.9) π (f − fl) + γ with γ being linewidth parameter
p T −x γ = ∆f0 (2.10) p0 T0 where fl is the frequency of the line centre, ∆f0 is approximately 1MHz/1mbar, x ∼ 0.5-1.0 [13]. This gives us values of line broadening of several MHz, which is, at lower altitudes, much larger then the Doppler frequency broadening. The Lorentzian line shape shows a good agreement with experimental results only for pressures between 1 and 17 mbar and for lower frequencies. For instance, the 22.2 GHz water vapour line can be well described by Lorentzian line shape. For other atmospheric conditions and other frequencies, a better line shape was proposed by Van Fleck and Weisskopf:
1 f h γ γ i Fvw(f, fl) = 2 2 + 2 2 (2.11) π fl (f − fl) + γ (f + fl) + γ There are also other models for different atmospheric conditions. An impor- tant one is the Voigt line shape which is used for the altitudes where the pressure broadening becomes comparable with Doppler broadening. Although the line shape has been modelled, for a full description of the line, the line strength remains to be defined. There are two main spectral line catalogues where the line strength can be obtained: the HITRAN [14] and the JPL [15] catalogues. Using the two parameters, line shape and line strength, an absorption spectrum can be simulated. For these purposes several software packages have been developed, one of which is ARTS, [16]. In Figure 2.1 the atmospheric spectrum from 0 to 900 GHz simulated with ARTS is presented, covering the whole millimetre- and the biggest part of the submillimetre wave range. Figure 2.1 shows numerous absorption (emission) lines in this frequency range. The most important species with the largest number of rotational transitions are ozone and water vapour. The two play, as already said, a 2.3 Radiative transfer 19
300
250
200
150
100 Brightness temperature [K] 50 aircraft at 10000 m Jungfraujoch Bern 0 0 100 200 300 400 500 600 700 800 900 Frequency [GHz]
Figure 2.1: Simulated spectrum (with ARTS software) of the atmospheric gaseous absorption in the mw-frequency-range in zenith angle. Three differ- ent lines are for different altitudes: 10000 m, 3600 m (which is the altitude of the ISS Jungfraujoch, Switzerland) and 550 m (the altitude of Bern) very important role in the Earth atmosphere and passive (radiometric) ob- servation of the two is a very useful and widely-used method. Figure 2.2 shows a simulated line of water vapour transition at 183.31 GHz. This line is being observed by AMSOS radiometer (in the upper sideband) and the simulation was done for realistic conditions of radiometer’s operation. At 175.5 GHz there is a weak ozone line (Figure 2.2) which is also observed by AMSOS in the lower sideband.
2.3 Radiative transfer
Let us consider a radiometer that receives radiation from above (or below in case of a satellite) lying atmosphere. The radiation of higher (lower) atmo- spheric layers is transfered through the rest of the atmosphere downward (or upward) to the receiver. The physics of this energy transfer is described by radiative transfer theory, formulated by Chandrasekhar, [17]. The interaction between radiation and matter consist of two processes: absorption and emis- sion. If the intensity of radiation sinks by a transfer through a medium than we have absorption in this medium. If, however, the medium adds energy by 20 Microwave gas spectroscopy
100
90
80
70
60
50
40
30 Brightness temperature [K]
20
10
0 175 180 185 190 Frequency [GHz]
Figure 2.2: Simulated spectrum of the water vapour rotational line at 183.31 GHz. The simulation was done for realistic operational conditions of an airborne radiometer: the altitude was 12000 m and the observation elevation angle was 20◦ over the horizon. At 175.54 GHz there is a relatively weak ozone line (left side of the plot) radiation, we have emission. Both processes occur usually simultaneously in a gas. We consider this gas to be in local thermodynamic equilibrium. In addition we are neglecting scattering, because the wavelength of the radia- tion is several magnitudes of order larger than the cloud droplets (usually the largest droplets in the atmosphere). In a gas volume with length ds along the line of propagation (Figure 2.3) all sinks and sources are summed, and we get the radiative transfer equation in differential form [18]:
dI f = −αI + S (2.12) ds f where α is the absorption coefficient. The first term on the right side of Equa- tion (2.12) is absorption and the second represents the energy gain within the considered volume element (emission). In a thermodynamic equilibrium, the emission term is equal to the Planck radiation: 2.3 Radiative transfer 21
I (S ) f 0 s = s 0 s
τf (s)
s = 0 I (0) f
Figure 2.3: Radiative transfer through the atmosphere
S = αBf (T ) (2.13) where Bf (T ) is the Planck function at the temperature T and frequency f :
2hf 3 1 B (T ) = (2.14) f c2 ehf/kT − 1 The Planck constant is h = 6.626·10−36Js, c is the speed of light in the propa- gating medium (in a vacuum c = 2.997924 ·108m/s) and k is the Boltzmann’s constant (k = 1.38·10−23JK−1). If we substitute (2.14) into (2.12) we get a standard differential equation which can be solved by If :
Z s1 −τ(s1 −τ(s) If (s0) = If (s1)e + Bf (T (s))e α(s)ds (2.15) s0
In this case s0 is the observation point, If (s1) is the background radiation at the point s1, s is the optical path length and τ(s) is the atmospheric opacity:
Z s τ(s) = α(s0)ds0 (2.16) s0 If the background radiation, the absorption coefficients of the observed species and atmospheric temperature profile are known, the intensity radiated by the atmosphere can be calculated. For frequencies in the mw-region and for the temperatures in the range of atmospheric temperatures, hf kT and the Planck function can be reduced to: 22 Microwave gas spectroscopy
2kf 2 B (T ) ≈ T (2.17) f c2 This is known as Rayleigh-Jeans approximation. Brightness temperature is defined as follows:
λ2 T (f) = I (2.18) B 2k f Brightness temperature is a widely used unit in radiometry. In the frequency (and temperature) range where the Rayleigh-Jeans approximation is valid, it offers a simple mechanism to convert radiation intensity into ’temperature’ units. Brightness temperature of an object is linearly proportional to its radiation intensity and assuming the emitting object to be a blackbody, the brightness temperature is equal to its physical temperature. This is partic- ularly practical for calibration of a microwave radiometer. The strength of a transition line in the microwave region is almost exclusively expressed in brightness temperature units (Kelvin). The radiative transfer equation within Rayleigh-Jeans approximation be- comes:
Z s0 −τ(s0) −τ(s0) TB(f) = TB0 e + T (s)e αds (2.19) 0
Under above described conditions, the term TB0 is the cosmic background temperature of 2.7K. The absorption coefficient can be written as follows:
α(f, s) = α0n(s) (2.20) where α0 is absorption coefficient per volume mixing ratio (VMR) and n(s) is volume mixing ratio of the species of interest along the observation direction, [13]. The radiative transfer equation in that case is:
Z s0 −τ TB(f) = C + α0T (s)e n(s)ds (2.21) 0 −τ Quoting W (f, s) = α0T (s)e we get finally
Z s0 TB(f) = C + W (f, s)n(s)ds (2.22) 0 The weighting function W (f, s) is a measure of emission at the height z. From (2.22) follows that, if we are able to measure the brightness temper- ature of an atmospheric emission line, by solving the inverse problem it is 2.3 Radiative transfer 23 possible to determine the volume mixing ratio of this species along the line of observation. This is essential for microwave radiometry. However, the inverse problem is significantly harder then the direct problem. It is analytically not easily solvable (usually not at all). The inversion process for water vapour observations with the airborne radiometer AMSOS will be presented in the third part of this thesis. Chapter 3
Microwave radiometry
3.1 Heterodyne principle
The energy carried by the atmospheric signal detected by a radiometer is very small in the microwave region. The receiver has therefore to be very sensitive. The technology of semiconductor devices has progressed in recent years and HEMT amplifiers are available today at frequencies even higher than 100 GHz. In radiometers working below these frequencies some signal processing can already be done at radio frequencies (RF). However, devices used for the spectral analysis of atmospheric spectrum (acousto-optical spectrometers, chirp spectrometers, auto-correlators etc.) work only at far lower frequencies. Therefore, a down-conversion of the RF-signal is necessary at some stage in the receiver. Down-conversion is a process where a signal is translated from its original frequency to a lower frequency. Receivers that work on this principle are called heterodyne receivers. A typical heterodyne receiver is shown in Figure 3.1. The RF-signal is re- ceived by an antenna and sent into a mixer. The mixer is a key component of a heterodyne receiver and it does the actual frequency conversion, which will be explained later on. The signal at the intermediate frequency (IF) is further amplified, a part of the spectrum of interest is truncated by a filter and the signal is finally detected. Every component in this chain generates noise. Therefore, the detected signal does not look ’flat’ as shown in Figure 2.2 - it is contaminated by the receiver’s noise. The equivalent receiver noise temperature can be calculated as:
Tn2 Tn3 Tnm Trec = Tn1 + + + ... + (3.1) G1 G1G2 G1G2...Gm−1
24 3.1 Heterodyne principle 25
Mixer Antenna
Amplifier Bandpass Receiver filter
Local oscillator
Figure 3.1: A principal scheme of a heterodyne receiver
Where Tnx and Gnx are the equivalent noise temperature and gain of the x-th component. From Equation (3.1) we see that those components closer to the beginning of the receiver have a larger influence on the receiver noise temperature. The influence on the system noise temperature of every subse- quent component is divided by the gain of the component standing in front of it. Since every mixer is a noisy and lossy component (G < 1) and stands just behind the antenna, it has the biggest influence on the system noise tem- perature. For radiometers operating in lower frequencies of the microwave region, an amplifier can be placed between the antenna and the mixer. As already said, low-noise amplifiers are available in lower frequency range and the introduction of such an amplifier can reduce the system noise tempera- ture significantly, [19]. However, at frequencies above approx. 100 GHz, the first component after the horn has to be a mixer. The key element of a mixer is the mixer diode. The frequency conversion is performed using the non-linear impedances of the diode, whose dissipative and capacitive part are frequency-dependent, [20]. By mixing of the input signal (eg. atmospheric signal) and the signal of the local oscillator, the output current of the mixing diode will be [21]:
i(t) = i0
(1) jwst −jwst jwlt −jwlt + G (i0) Us(e + e ) + Ul(e + e ) 2 (2) jwst −jwst jwlt −jwlt + G (i0) Us(e + e ) + Ul(e + e ) (3.2) 3 (3) jwst −jwst jwlt −jwlt + G (i0) Us(e + e ) + Ul(e + e ) + ... 26 Microwave radiometry
i0 is the bias current and G(i0) are admittances of the diode that are fre- quency dependent; ws and wl are radian frequencies (w = 2πf) of the input signal and of the local oscillator respectively. The first term in Equation 3.2 is the bias. The second term in Equation 3.2 contains the signals at original frequencies, fs and fl. The third term, after transformations, contains four different elements:
2 2 2G(1)(Ul + Us ) DC component (1) 2 2 G (U cos 2wlt + U c cos 2wst) F reqeuncy doubling l s (3.3) (1) 2G UlUs cos(wl + ws) High frequency (1) 2G UlUs cos(wl − ws) Intermediate frequency The first term in Equation 3.3 is a DC component. The second and the third term in Equation 3.3 are not of interest and are filtered by the mixer itself or by one of the following components. The fourth term represents the desired signal at the intermediate frequency (IF), wi = |wl − ws|. The IF frequency appears by wl − ws as well as by ws − wl. This means that the two frequency bands from both sides of the local oscillator frequency will be downconverted to the same IF frequency. This is better illustrated in Figure 3.2.
IF LSB LO USB
¢ ¢ ¢ ¢ ¢
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¢ ¢ ¢ ¢ ¢
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£ £ £ £ £ ¡ ¡ ¡ ¡ ¡
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¢ ¢ ¢ ¢ ¢
£ £ £ £ £ ¡ ¡ ¡ ¡ ¡
¢ ¢ ¢ ¢ ¢
£ £ £ £ £ ¡ ¡ ¡ ¡ ¡ f 0 f f i s1 flo fs2
Figure 3.2: The principle of downconversion. Two frequency bands around the LO-frequency are downconverted to the same IF frequency
Figure 3.2 shows the mentioned effect: the frequency band around frequency fs1 and the band around fs2 (both at a distance fi from two sides of flo) are downconverted to the intermediate frequency fi. The frequency band at the frequency fs2 is called upper side band and the one at fs1 the lower side band. The operation of a radiometer that is designed to receive the signals from both side bands is called double-sideband operation. However, often one of the sidebands is undesirable. In atmospheric observations, it is not unusual for the spectra in the area of interest to contain numerous transition 3.2 Calibration of a heterodyne receiver 27 lines. It often happens that there are spectral lines in both sidebands. In that case the rejection of the other sideband is necessary. Such operation of a radiometer is called single-sideband operation. The mechanism of sideband filtering and rejection in AMSOS will be considered in detail in Chapter 8.
3.2 Calibration of a heterodyne receiver
In order to determine the unknown brightness temperature of the atmo- sphere, the radiometer has to be calibrated by two blackbodies at well known physical temperatures. Very often the two blackbodies are absorbers kept un- der stable conditions where the temperature is well defined. A typical cold load is an absorber soaked in liquid nitrogen. The boiling temperature of liquid nitrogen can be measured as well as calculated from the air pressure of the surroundings. An absorber at room temperature or a heated absorber is often used as a hot load. The important point is that the temperatures of the loads stay stable during a calibration cycle and that they are well defined. The (brightness) temperatures of the loads should also, if possible, cover the range of the measured brightness temperatures.
Output voltage
VH
VA
VC V0
−T T T N 0 C TA H Brightness temperature
Figure 3.3: The principle of a radiometer’s calibration. Knowing physical temperatures (and therefore the brightness temperatures) of the two calibra- tion loads, we can determine the brightness temperature of the atmosphere
As already pointed out, the principle on which the radiometer operates is that the brightness temperature of the detected signal is proportional to the output voltage of the receiver. From Figure 3.3 we see a linear dependence of 28 Microwave radiometry the output voltage on the brightness temperature of the atmospheric signal. Therefore:
VA − VC TA = (TH − TC ) + TC (3.4) VH − VC Such a calibration is called a total-power calibration. In many radiometers the output beam is subsequently pointed to the atmosphere, cold load and hot load, therefore defining a calibration cycle. The linearity can be used for determination of the receiver noise tempera- ture. The receiver noise temperature TN has the same linear influence on the output voltage as the detected atmospheric signal:
Vtotal = Gk(TN + TA)∆f (3.5) where G is the system gain, k is the Boltzman’s constant and ∆f is the radiometer frequency bandwidth. The system gain can be determined as the steepness of the calibration line from Figure 3.3:
V − V G = H C (3.6) TH − TC
The offset voltage V0 of the receiver is the voltage which is measured at the output with no signal at the input of the receiver. The voltage output when the receiver is looking at the cold and the hot load can respectively be calculated as:
VC − V0 = Gk(TN + TC )∆f (3.7) VH − V0 = Gk(TN + TH )∆f Dividing the second equation with the first one we get so called y-factor:
V − V T + T y = H 0 = N H (3.8) VC − V0 TN + TC The y-factor is used for practical determination of the system noise temper- ature. It is enough to measure the voltage output of the radiometer when the antenna beam is pointed to the hot and to the cold load (through inter- nal calibration of the measurement device V0 can easily be brought to zero) and the y-factor is determined using Equation (3.8). The equivalent noise temperature of the receiver is then:
T − yT T = H C (3.9) N y − 1 3.2 Calibration of a heterodyne receiver 29
The noise temperature of a receiver is reduced through integration. The sensitivity of a heterodyne receiver is therefore determined from its noise temperature, bandwidth and length of integration time (τ):
T + T ∆T = √N A (3.10) A ∆fτ Equation (3.10) is known as the radiometer formula. Part II
AMSOS radiometer
30 Chapter 4
Overview
The first version of an airborne 183 GHz radiometer was built by the IAP in the early eighties. At that time the instrument was flown on a Falcon aircraft. In 1992 a new radiometer was designed and the operation switched to a Swiss Air Force Lear jet (Figure 4.1). The receiver was used only at 183 GHz with a 1-GHz-wide filterbank-backend, [22]. Since then, the radiometer has undergone several upgrades, one of the major changes taking place in 1998, [23]. At that time, the AMSOS radiometer’s filterbanks were replaced by two acousto-optical spectrometers.
Figure 4.1: The Learjet T-781 aircraft of the Swiss Air Force. The Learjet is on IAP’s disposal on a campaign basis for about a week a year. The photo was taken in the arctic, during a refuelling stop in Rovaniemi, Finland
Also, a computer-controled positioning of a reflector in the Martin-Puplett
31 32 Overview interferometer introduced a possibility to measure in both sidebands alter- nately (H2O in the upper and O3 in the lower sideband). In 1998 and 1999 the radiometer was used by A. Murk with a submillimetre frontend for ClO,
HCl and O3 measurements at 625 GHz and 650 GHz, [24].
Figure 4.2: The AMSOS radiometer during laboratory testing
AMSOS consists of two major parts, frontend and backend, Figure 4.3. The frontend focuses the atmospheric radiation coming through the aircraft win- dow, does sideband filtering, directs it to a horn antenna where it is received and further downconverted in a mixer. It also uses a turning mirror which is pointed to the two reference loads, defining radiometer’s calibration cy- cle. The downconverted and amplified signal is then directed to the backend, where spectral analysis of the signal is performed by two acousto-optical spectrometers (AOS). These spectra, together with the aircraft position and other relevant data are recorded and later saved in AMSOS-database. Between 2001 and 2003 a mayor refurbishment of the 183 GHz-receiver took place. Several goals were defined, for every part of the radiometer:
Frontend:
Lower receiver noise temperature
Better beam shaping and a narrower output beam (∼ 1◦)
Reduction of baseline ripple 33
Better defined calibration cycle, primarily more accurate positioning of the turning mirror
Extended control over radiometer operation, better temperature mea- surements, higher reliability and flexibility
Calibration unit Radiometer Control System Data archive Quasi Optics Atmosphere Hotload AMSOS database Aircraft Lambda/4 window Isolator Mirror control Computer Roof top Software mirrors Rotating mirror Coldload AOS AOS Grids Absorber >1 GHz< >50 MHz< USB LSB Absorber
Heterodyn receiver Navigation system Subharmonic mixer USB: >182.4−184.4 GHz< LSB: >175.0−177.0 GHz< GPS IF 3.7 GHz
Synchro Focusing Preamp. 64 dB mirror LO PLL Temperature measuring system Tunable LO >89−90GHz< temperature measuring converter LO frequency control Sideband control
Figure 4.3: Schematic of the AMSOS radiometer. The atmospheric signal is focused and received in the quasioptics. After downconversion the signal is further analysed by the AOSs and the data are recorded by the computer which controls all functional processes. The left half of the scheme is located in the frontend, and the right half is in the backend
Backend:
Better control over both AOS (calibration, heating)
New software for radiometer control
Higher reliability of the backend operation, including a stabile com- puter operation
The changes were finished in autumn 2003 and the first flight campaign with the new frontend took place in November 2003. Chapter 5
The quasioptics of AMSOS radiometer
5.1 Principles of quasioptics
In the millimetre- and submillimetre wavelength range geometrical optics cannot be applied. One of the main assumption of geometrical optics is that the size of optical components is a lot larger then the wavelength. In mm- and submm range this is obviously not the case. On the other hand, losses in the classical mw-components (waveguides, couplers etc.) become too high at these frequencies for practical use. Therefore, wave propagation in free space is preferred. At these frequencies, propagating waves can have electric field with a Gaussian distribution. The optics in this domain is therefore often called Gaussian optics, or quasioptics. Assuming a source that launches radiation with a Gaussian distribution of the E-field (for instance a horn antenna, [25]), the Huygens-Fresnel diffraction integral for the E-field distribution of the basic Gaussian mode in free space can be relatively easily solved, [26]. We will assume a propagation in the z- direction, with a plain phase front at z=0. We also define a value w0 at z=0, called the beam waist, as the distance from the z-axis to the point where the E-field falls to 1/e of the maximum on the axis of propagation. As beam size we assume the distance from the z-axis to the point where the E-field falls to 1/e of the value on the axis, for an arbitrary plane perpendicular to the axis of propagation. Under these assumptions, it can be shown ([26], [27]) that the beam size at a certain frequency depends on only two parameters: the distance from the beam waist (z) and the beam waist size (w0):
34 5.1 Principles of quasioptics 35
s λz 2 w(z) = w0 1 + 2 (5.1) πw0
The phase front can similarly be described through the radius of curvature as:
πw2 R(z) = z(1 + 0 2 (5.2) λz From Equation (5.1) we see that the smaller the beam waist is, the faster the beam diverges. A useful parameter that describes how fast a Gaussian beam diverges is the Rayleigh distance and is defined as:
πw2 z = 0 (5.3) c λ
The Rayleigh√ distance is the distance along the z axis where the beam size w has grown to 2w0. Another parameter interesting for design of a quasiop- tical system is how fast the beam diverges in the far-field. It can be shown
([26], [27]) that the beam divergence-angle in the far-field (where z zc) can be estimated as:
λ θ0 ' (5.4) πw0 The divergence angle is the asymptotic beam growth angle. For a radiometer, it is of greatest interest to know how its output beam will look in the far-field, i.e. how narrow or wide it is. Therefore the divergence angle is important. Another parameter which describes the far-field divergence of a Gaussian beam is the half-power beam width (HPBW). This is the angle at which the power carried by a Gaussian beam falls to 1/2 of its maximal value (on the axis of propagation). The HPBW-angle can be calculated as:
θHPBW = 1.18θ0 (5.5)
The HPBW defines how wide the ’view angle’ of a radiometer is going to be. For some types of radiometers (limb-sounders, for instance) a very nar- row output beam is necessary. For some other radiometer types (salinity, soil moisture measurements etc.) a wider output beam might be preferred, depending on their application. 36 The quasioptics of AMSOS radiometer
5.2 Design of AMSOS’s quasioptics
One of the main goals of the new AMSOS-quasioptics was to generate a narrower output beam and to make its shape regular. The planned beam divergence angle of 1◦ at 183 GHz requires an output beam waist of 31 mm. In order to minimise diffraction effects, the beam size at the components was selected to be around 4.6 times the beam radius at that location (D/w), [28]. In this case the edge taper was small (99.99% of the power of the basic Gaussian mode is kept inside the system), and the cut-off ripple should be below 1 %. The achievment of an even narrower output beam was not possible in our case. We designed the output beam waist to be in the plain of the aircraft window, in order to maximise the D/w ratio. The diameter of the window is 15 cm and with a beam waist size of 31 mm the D/w ratio is around 4.8. A narrower output beam (a larger beam waist) could have been achieved only by decreasing this ratio, which was undesirable. Therefore the trade off ◦ resulted in a projection of a divergence angle of 1 (the corresponding θHPBW angle would be around 1.2◦). Figure 5.1 shows an elementary scheme of the quasioptics. It consists of a feed horn antenna and two beam-shaping components, a parabolic and an elliptic mirror.
AIRCRAFT WINDOW
W = 31 mm HORN ANTENNA
W = 5.5 mm Min D/W IS 4.4
W = 32 mm MPI + ISOLATOR W = 20.5 mm
ELLIPTIC MIRROR PARABOLIC MIRROR
Figure 5.1: The basic scheme of the quasioptics, that consist of two focusing mirrors, an MPI for sideband filtration and a quasioptical isolator for baseline reduction
Between the two mirrors a Martin-Puplett interferometer (MPI) and a λ/4- quasioptical isolator for baseline reduction are placed. The λ/4-isolator con- sists of a metal plate and a grid standing in front of it. The beam bending 5.2 Design of AMSOS’s quasioptics 37 angle at the isolator is 90◦. The MPI consists of two wire grids and two rooftop mirrors. A detail description of these devices will be given in sepa- rate chapters. The whole scheme of the instrument’s quasioptics is given in Figure 5.2.
Aircraft window
W0 = 31mm
Lambda/4 Isolator MP interf. LO Elliptic turning Absorber mirror Antenna W = 23.3mm W0 = 5.5mm
W0 = 20.5mm Absorber
Parabolic mirror
Figure 5.2: The principal scheme of AMSOS quasioptics with indications of the beam radius size
After defining the basic layout of the quasioptics our goal was to design every component to fit our needs. A description of every subsequent device follows.
5.2.1 Feed horn antenna We used a profiled corrugated feed horn antenna designed and produced by Thomas Keating Ltd, Figure 5.3. The aperture of the horn is 17 mm and the slant length 208.8 mm. Due to the long slant length we considered it to be an aperture limited horn, producing a beam waist of [25]:
w0 = 0.644a (5.6) which lay very close to the horn aperture. With a being the radius of the horn aperture, the beam waist was w0 = 5.5 mm. 38 The quasioptics of AMSOS radiometer
Figure 5.3: The corrugated profiled horn antenna for 183 GHz produced by Thomas Keating Ltd.
For verification of our calculations we performed a series of measurements of individual components at specific places in the optics. The antenna pat- tern was measured at 183 GHz using the ABmm vector network analyser, [29]. The first measurement (Figure 5.4) was an angular scan of the antenna pattern in the H-plane. It was done by turning the antenna around an axis going through the phase centre.
0 copolar crosspolar 150 −10 100 −20
50 −30
−40 0 Phase [deg]
Relative level [dB] −50 −50
−60 −100
−70 −150
−80 −60 −40 −20 0 20 40 60 −20 −15 −10 −5 0 5 10 15 20 Angle [deg] Angle [deg]
(a) Amplitude (b) Phase
Figure 5.4: The measured output of the horn antenna
The antenna diagram had a regular Gaussian beam shape in its upper part as illustrated in Figure 5.4. The crosspolar signal had a strong minimum, with a maximal difference of 50 dB to the copolar signal. In the main lobe the 5.2 Design of AMSOS’s quasioptics 39 crosspolar signal was always at least 30 dB below the copolar signal, which was very good. In the (b) part of the plot the phase measurement is shown. Around 0◦ the phase was regular and flat. This also confirms that the horn was really rotated around the phase centre during the measurements. The planar diagram of the antenna pattern shows its round and regular shape, Figure 5.5. This measurement was made with a sender antenna mounted on an xy-stage.
80 −20
60 −20 −5 −10
−20 40
−10 −10 20 −3
−10 −3
0 −10 −15
−20 y [mm] −20
−20 −20 −40 −3
−60 −10 −20 −10 −25
−80 −20 −80 −60 −40 −20 0 20 40 60 80 x [mm]
Figure 5.5: The measured output of the horn antenna - planar scan. The measurement shows the very regular round shape of the antenna pattern
5.2.2 Parabolic mirror It was necessary to have two focusing elements in order to transform the small beam waist produced by the horn into the larger beam waist needed at the output of the radiometer. On the other hand, the Gaussian beam should not diverge too fast inside the quasioptics in order to keep the size of the components reasonable. Considering designs of some other instruments built by IAP [30], the first idea was to use two elliptic mirrors. However, in our case an elliptic mirror as a first mirror was not desirable as the transfor- mation of a small input beam waist into a large output beam waist would have required a very strong surface curvature. We found out that for the given input and output parameters it would have been difficult to machine a 40 The quasioptics of AMSOS radiometer surface with such strong curvature. The curvature would also have produced stronger cross-polar effects. Therefore we used an offset parabolic mirror. Firstly, this mirror gave a larger output beam waist (in geometrical optics the output is parallel) and secondly was easily machined. The diameter of this parabolic mirror was 90 mm and it had an effective focal length of ρ = 216.5 mm (Figure 5.6). The beam propagation, theoretical analysis, test and simulations will be described in separate sub-sections. a) Beam transformation and propagation
The analysis of the propagation of the Gaussian beam launched by the cor- rugated horn antenna through the whole optics was performed with software modules based on the normal ABCD matrix method, [27]. The ABCD matrix of a focusing element is given by:
AB 1 0 ABCD = = 1 (5.7) CD − f 1 where f is the nominal focal length. For a parabolic mirror f = ρ (distance from the mirror centre to the focal point, Figure 5.6) and for an elliptic mirror R1R2 f = , R1 and R2 being the distances from the foci to the mirror centre. R1+R2
200mm horn
y
70 ρ = 216.5 mm x = 70 y = 6.125 45
x = 115 y = 16.531 45
x = 160 y = 32
x
Figure 5.6: The scheme of the parabolic mirror with relevant dimensions and the position of the horn
Defining an input beam waist for the parabolic mirror as w0in and its distance to the centre of the mirror as din, the distance of the output beam waist from the centre of the mirror along the axis of propagation is: 5.2 Design of AMSOS’s quasioptics 41
2 (Adin + B)(Cdin + D) + ACzc dout = − 2 2 2 (5.8) (Cdin + D) + C zc and its size is given by:
w0in w0out = (5.9) p 2 2 2 (Cdin + D) + C zc
Where zc is the Rayleigh distance defined earlier. The virtual beam waist of the horn (size 5.5 mm) was positioned in the focus of the mirror. After applying Equations (5.8) and (5.9) the output beam waist of the mirror was 20.5 mm large at a distance ρ from the mirror centre. b) Angular scans
Similar to the measurements of the horn antenna we the output of the horn- parabolic mirror module. The first measurement was an angular measure- ment of the module pattern in the H-plane. It was carried out by turning the module around an axis that goes through the mirror centre. The result is given in Figure 5.7, where the horn antenna diagram is also shown. Since the output beam waist of the module was larger then the beam waist of the antenna, the module-diagram was narrower. The shape was still very regular with small distortions, the shoulders of the side lobes were symmetric. This confirmed the good alignment of the horn-mirror system. c) Crosspolar signal and beam distortions
Another effect to be taken care of was cross polarisation produced by the parabolic mirror. For our purposes it was enough to estimate the average level and the maximal value of the crosspolar signal. According to [27], the fraction of power that remains in the copolar component after reflection is given by:
2 Kco = 1 − 2U (5.10) where U is defined as:
w tan θ U = m√ i (5.11) 2 2f 42 The quasioptics of AMSOS radiometer
0
−10
−20
−30
−40 Relative level [dB] −50
−60
horn −70 horn + parabolic mirrror
−40 −30 −20 −10 0 10 20 30 40 Angle [deg]
Figure 5.7: The antenna pattern of the module horn-parabolic mirror
Here wm is the beam radius at the mirror surface, θi is the incidence angle and f is the nominal focal length. For a parabolic mirror f = ρ, as previously described. The fraction of power carried by the copolar signal is now:
w2 K = 1 − m tan2 θ (5.12) co 4f 2 i In our case the bending angle of the beam at the parabolic mirror was ◦ ◦ 32 (θi = 16 ), f = 216.5 mm and the beam radius at the mirror was wm = 20.9 mm. When calculated, Kco = 0.9998. This means that the crosspolar component carried around 0.02% of the power of the incident ra- diation, which was satisfactory. Although the overall power cx/co ratio can be low, the peak electric field value of the crosspolar component can be rel- atively high, especially for mirrors with strong curvatures and for the case of a strongly diverging incident beam. The relative maximum of the cross polarised radiation compared to the copolar signal is [27]: cx w max = 0.43 tan θ m (5.13) co i f where all parameters are the same as above. When calculated from Equation 5.13, the maximal level of the crosspolar signal was 19.2 dB below the copolar 5.2 Design of AMSOS’s quasioptics 43 signal, over the whole mirror surface. The beam distortions due to the offset-character of the parabolic mirror [31] were negligible. This was mainly due to a small incidence angle and relatively large beam waists. d) Numerical simulations
In order to prove our theoretical calculations we also performed numerical simulations with the GRASP software. The GRASP software, developed by Ticra, Denmark, is a set of tools for analysing general reflector antennas and antenna farms. The tool uses two of the approximate source field methods: geometrical optics (ray tracing) and physical optics for the calculations of the scattered field of various reflecting objects. It is a very flexible tool which can calculate electromagnetic radiation for very complex system set-ups. We simulated the output of the parabolic mirror fed by our antenna. The mirror dimensions and all lengths were set to correspond to our real case. We have to stress that simulations were done using an ideal Gaussian beam without side lobes as input, which gave relatively optimistic results. e) Planar scans
Planar scans of the output were carried out for both copolar and crosspolar signals. All measurements of the module were made in the near field. The D2 far field distance 2 λ for this mirror would be 9.8 m, considering D = 90 mm. For our laboratory conditions it was impossible to achieve such a distance. The first planar scans were made at a distance of 48 cm. The results of the measurements are given in Figure 5.8. The left plot is the result of the measurements and the right plot is the result of the GRASP- simulations. In all figures the data sets were normalised. Parts (a) and (b) of Figure 5.8 show an agreement between the measurement and the numerical simulation, especially in the area up to -20 dB below the maximum. As this was the most important range, the agreement was sufficient for our needs. Parts (c) and (d) of Figure 5.8 show the measured values and the simula- tion of the crosspolar component. The simulation confirms the shape of the crosspolar signal expected from theory - the cross polarised component had two lobes around the horizontal axis of the mirror, [27]. Both the E01 and the E10 components of the Gauss-Hermite polynomials had the same ratio to E00 which resulted in the two-maximum shape of the crosspolar output ((d) 44 The quasioptics of AMSOS radiometer
60 60
−10 −10
40 40 −30 −30 −20 −20
−30 −20 −20 20 20 −30 −10 −30 −30 −20 −3 −20 −30 −10 −3
−10
0 −30 −3 0 −10 −40 −30 −30 −20 −3 y [mm] y [mm] −40 −30 −30 −30 −20 −10 −10 −20 −20 −50 −20 −20 −50
−40 −30 −30 −40 −30 −60
−30 −60
−30 −60 −60 −70
−70 −60 −40 −20 0 20 40 60 −60 −40 −20 0 20 40 60 x [mm] x [mm]
(a) Measurement - copolar (b) The GRASP simulation - copolar
0 0 −30 −30 −30 −30 −30 −30 −30 60 60 −30 −30 −30 −30 −20 −10 −30 −30 −30 −30 −10 −30 −20 −30 −30 −30 −20 40 −20 40 −10 −20 −20 −30 −20 −30 −30 −30 −20 −20 −10 −20 −3 −30−30 −10 −30 −20 20 −30 20 −10 −3 −3 −20 −30 −3 −30 −3 −30 −30 −10 −30 −40 −3 −30 −20 0 −3 0 −30 −30 −20 −20 −20 −20 −20 −10 −10 −10 −10 y [mm] −20 −40 y [mm] −3 −50 −10−10 −3 −30 −30−20 −30 −20 −30 −20 −20 −10 −30 −20 −60 −50 −30 −10 −20 −20 −20 −40 −40 −30 −30 −30−30 −30 −20 −30 −30 −20 −70
−30 −30 −20 −60 −30−30 −30 −20 −30 −20 −20 −30−20 −60 −30 −30 −30 −60 −80 −30 −30 −30 −60 −40 −20 0 20 40 60 −60 −40 −20 0 20 40 60 x [mm] x [mm]
(c) Measurement - crosspolar (d) The GRASP simulation - crosspo- lar
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(e) Measurement - cx/co ratio (f) The GRASP simulation - cx/co ra- tio
Figure 5.8: (a) and (b) - a comparison between the measurement of the copolar output of the parabolic mirror and the GRASP simulation. (c) and (d) - the crosspolar signal, measurement and the GRASP simulation. (e) and (f) - the ration between the co and cx signal, measurement and the simulation 5.2 Design of AMSOS’s quasioptics 45 in Figure 5.8) and a strong minimum towards the middle of the mirror. Our measurements did not show such an emphasised two-lobe shape. However, a slight minimum line can be seen in the middle of the mirror. This minimum was some 5-10 dB lower then the level of the crosspolar signal around it.
The (e) and (f) parts of the Figure 5.8 show the ratio between the crosspolar and the copolar signal. The measurements of both signals were carried out one after another in order to keep the sender power constant. Again, the differences between the measured and simulated output were relatively high. However, in the region of the main lobe, the crosspolar signal was at least 20 dB lower then the copolar signal. This corresponded well to the approx- imation given in equation 5.13. Also, the level of the crosspolar component at the mirror centre was more then 30 dB lower then the copolar signal. f) Simulation of the output
To better characterise the output of the parabolic mirror in the far field, we repeated the scans in several planes at distances between 30 cm and 1 m. Four scans were made and the results are shown in Figure 5.9. The setup was re-aligned for every single scan separately, so that the beam-centre position was relative. The qualitative divergence of the Gaussian beam can clearly be seen from these plots. In order to quantify this propagation, we fitted the measured values to an ideal Gaussian beam using the least-squares method. First, at every measured plane we made a circular fit of the beam size (the contour where the power falls to 1/e2 of the maximum). Afterwards, using these circular fits of the beam sizes at different distances, we found the position and size of the beam waist of an ideal Gaussian beam that best fitted these beam sizes (again using the least-square criteria). The waist of this synthesised (fitted) beam was 20.56 mm which corresponded very well to our predicted value of 20.5 mm. The position of the waist should have been ρ = 21.65 cm away from the mirror centre. The fitted beam waist was positioned relatively far away from this point and lay 28.5 cm from the mirror centre. These values however should be taken with reserve, as only four measurements were made. On the other hand, instrumental and measurement set-up artifacts (mainly multiple reflections) could also have played a role. Anyway, it was a good starting point to evaluate the behaviour of the radiometer’s output. 46 The quasioptics of AMSOS radiometer
60 0 60 0
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(a) Distance 32 cm (b) Distance 60 cm
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(c) Distance 83 cm (d) Distance 96 cm
Figure 5.9: The planar scans of the parabolic mirror outputs
5.2.3 Radiometer’s output beam
The size and the position of the beam waist at the output of the parabolic mirror were used as input parameters for the elliptic mirror design. The input beam waist was located 966.5 mm in front of the centre of the elliptic mirror. The output beam waist (at the same time the radiometer’s output) was chosen to be 31 mm large and was positioned 470 mm from the mirror. This was chosen, for the aircraft window lies at this distance (470 mm) away from the mirror. Considering these parameters and the ABCD beam trans- formation method (Formulas 5.8 and 5.9) we determined the nominal focal 5.2 Design of AMSOS’s quasioptics 47
50 fit: wo=20.56 mm measurements
45
40
35
Beam radius [mm] 30
25
20 0 0.5 1 1.5 Distance from the mirror [m]
Figure 5.10: The synthesised ideal Gaussian beam that fits the measured values using the least-square fit
length for this elliptic mirror to be f = 1.3521 m. R1 and R2, the distances from the mirror centre to the foci, were 1.640 m and 7.706 m respectively. The predicted beam radius at the mirror was 31.9 mm. Therefore the diam- eter of the mirror was chosen to be 150 mm to keep the ratio D/w above 4.6. Thomas Keating Ltd. produced the mirror using these input parameters. According to Formulas (5.12) and (5.13) the power of the crosspolar compo- nent was 38 dB below the copolar signal. The peak value of the crosspolar signal should be at least 19.8 dB below the copolar. a) Planar scans of the output
Figure 5.11 shows the measured output scan of the complete instrument including the whole MPI and the quasioptical isolator. The shape of the diagram is relatively regular, but it exhibited an asymmetry along the x and y axes, which was assumed to come from the MPI. This effect will be discussed in Chapter 8. Parts (a) and (b) of Figure 5.12 show 3D plots of the output beam which illustrate these asymmetries along the x and y axes. Parts (c) and (d) of Figure 5.12 present a section through the X and Y 48 The quasioptics of AMSOS radiometer
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Figure 5.11: Output pattern of the complete AMSOS front-end measured at 128 cm from the elliptic mirror centre plane of the output beam. During the measurement the distance between the sender and the centre of the elliptic mirror was 128 cm. The plot in the (c) part of Figure 5.12 shows the angular pattern of the output beam. Since the measurement was made in the near field, the angular pattern should not be considered as finalised. There are different opinions. When trying to esti- mate the θHPBW from scans, the angle has to be calculated from the distance of the scan plane. As a valid axial distance to the plane in which the planar scanning was done, two different values can be taken into consideration: the distance to the centre of the elliptic mirror, but also the distance to the out- put beam waist plane. Using both methods it was estimated that the θHPBW was around 1◦. b) Simulation of the output beam
The estimation described above was obviously inaccurate. To determine the output beam propagation in the far field more precisely, we conducted the same procedure as for the parabolic mirror. This time scans were made in six planes with distances from the mirror centre ranging between 25 cm and 5.2 Design of AMSOS’s quasioptics 49
0
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(a) View I (b) View II
0 X−cut X−cut Y−cut 150 Y−cut −5 100 −10
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Relative level [dB] −50 −30
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−45 −4 −3 −2 −1 0 1 2 3 4 −3 −2 −1 0 1 2 3 Angle [deg] Angle [deg]
(c) Amplitude - X and Y cut (d) Phase - X and Y cut
Figure 5.12: (a) and (b) The 3D view of the AMSOS output antenna pattern. (c) and (d) A section through the X and Y plane of the planar scanned output diagram of the AMSOS radiometer
190 cm. The planar scans are presented in Figure 5.15. Again, the setup was re-aligned for every measurement and the position of the beam centre is relative. In every plane, the measured contour of 1/e2-power (beam size) was fitted with the least-square circular fit. These fitted beam sizes were used in the simulation of the output beam of the whole radiometer, as described earlier. An ideal Gaussian beam which best corresponds the measurements was then obtained, Figure 5.13. This time, the size of the fitted beam waist was 27.38 mm instead of the calculated 31 mm, which was a considerable difference. According to the fit, 50 The quasioptics of AMSOS radiometer
50 fit: wo=27.38 mm measurements
45
40
35 Beam radius [mm]
30
25 0 0.5 1 1.5 2 Distance from the mirror [m]
Figure 5.13: The synthesised ideal output Gaussian beam that corresponds the best to the measured values using the least-square fit it lay only 8 cm from the mirror centre, instead of more than 40 cm. One less likely reason for this discrepancy from could be the inaccuracy of the mirror production. A more probable reason could be position of the output beam waist of the parabolic mirror. As described, it lay further away then it should have. We recalculated the output of the elliptic mirror for this position of the parabolic mirror output beam waist. The output beam waist of the elliptic mirror should then be 28.9 mm, which corresponds better to the measurements and their fit. However, as already said for the parabolic mirror, both measured output beams diverge slowly and have large beam waists at these frequencies. There- fore it was relatively difficult to determine their positions. A series of planar scans should have been made in the planes close to the beam waist and then the corresponding fit should have (hopefully) given a more accurate result. Even with a size of 27.38 mm the output beam waist generates a pencil-like output antenna diagram and satisfies D/w requirements at the window. The ◦ θHPBW of the fitted output beam was 1.28 which satisfied very well the basic criteria of the quasioptics design. For retrievals with Qpack/ARTS (to be addressed in the third part) an an- 5.2 Design of AMSOS’s quasioptics 51
0 fit: gauss measurement
−5
−10
−15 Relative level [dB] −20
−25
−30 −2 −1 0 1 2 Angle [deg]
Figure 5.14: The output antenna diagram of AMSOS radiometer used for ◦ retrieval (solid line). The ideal Gaussian beam with a θHPBW = 1.28 is shown for comparison (dashed line) tenna diagram had to be defined. Since all our measurements lay in the near field, we decided to synthesise an output beam in the following manner: we took a 2D-section of the measured antenna pattern (at 190 cm) and matched it to the simulated ideal beam in the far field, Figure 5.14. This way the ap- proximate shape of the real antenna pattern (distortions and side lobes) was kept, and the half power beam width corresponds to the simulated behaviour in the far field. 52 The quasioptics of AMSOS radiometer
60 0 60 −30 0 −20 −20 −30 −20 −20
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(a) Distance 25 cm (b) Distance 32 cm
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(c) Distance 47 cm (d) Distance 80 cm
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(e) Distance 120 cm (f) Distance 190 cm
Figure 5.15: Planar scans of the AMSOS output pattern at different distances Chapter 6
Quasioptical λ/4 isolator
6.1 Introduction
Baseline is one of the problems which is often present in a microwave ra- diometer. Under the term ’baseline’ we consider multiple reflections in the quasioptics that lead to standing waves. Standing waves occur between the mixer and some other reflecting surface - mainly calibration loads, lenses and mirrors. In case of AMSOS, additional baseline comes from reflections between the mixer and the aircraft window. In order to prevent or to reduce baseline effects, a couple of methods have been developed so far, [32, 33, 34]. One of them, commonly used in a couple of radiometers built by IAP is the ’baseline wobbler’. This is a path length modulator that reduces baseline ripple by modulating sinusoidally the optical signal path. This method has got some drawbacks: the wobbling length has to be determined very accurately, otherwise the problem can be worsen, and the system’s optical path length is changing steadily by wobbling. A new method that we implemented in AMSOS radiometer was a quarter wave plate, also called λ/4-quasioptical isolator. The essential function of this plate is to transform a linear polarised input signal into a circular polarised output signal. A part of the atmospheric signal that should be received by the radiometer will be reflected from the mixer and returned in the quasioptics (see Figure 6.1) where it is re-reflected again thus producing standing waves. If this lin- early polarised signal (signal 1 in Figure 6.1) goes through the λ/4-isolator, it will be transformed into a circular polarised signal (2), right-hand oriented for instance. If it happens that this signal is reflected by a component stand- ing perpendicular to the propagation direction (plane of reflection in Figure
53 54 Quasioptical λ/4 isolator
PLANE OF 2 ISOLATOR REFLECTION 3
1 4
Ein Eout
HORN
MIXER Figure 6.1: Principle of work of the λ/4 isolator
6.1), it will turn back still circular polarised (3), but this time left-hand ori- ented. Another passage through the λ/4-isolator makes the output signal linear polarised, but this time orthogonally to the initial one (4). This signal will not be detected by the mixer. Theoretical principles of this device will be described in detail, as well as results of measurements.
6.2 Theoretical description
Physics behind a λ/4-isolator is relatively simple. The isolator that we are describing consists of a metal reflecting plate and a grid that stands in front of it at a constant distance d. Between the grid and the plate a slab of dielectric could be placed as described in [27], but we decided to design an isolator without dielectric because of its simplicity and adjustability. In both cases the principle is the same. The radiation that comes to the isolator is polarised by the gird. A part of the signal with the electrical field vector parallel to the gird wires is reflected from the grid. The other part with E-vector perpendicular to the wires goes through the grid and is reflected from the metal plate (Figure 6.2). The second signal has a longer optical path which introduces a phase delay in comparison to the signal reflected form the grid. From the triangle ABD: 6.2 Theoretical description 55
1 2
o A D
d L1 o C L2 B
Figure 6.2: The two signals polarised by the grid have a path difference, which introduces a phase difference
d L1 = (6.1) cos θ Further, if we consider the triangle ABC:
L2 cos 2θ = (6.2) L1
L2 = L1 cos 2θ (6.3) The path difference between the two signals is:
d d L1 + L2 = + cos 2θ cos θ cos θ d = (1 + cos 2θ) cos θ (6.4) d = 2 cos2 θ cos θ =2d cos θ
Now we have the path difference between the two signals:
∆L = L1 + L2 = 2d cos θ (6.5) 56 Quasioptical λ/4 isolator with θ to be the angle of incidence. The phase delay φ introduced this way is:
4πd Φ = k∆L = cos θ (6.6) λ At the exit of the isolator the two signals are recombined and if their phase π π difference is 2 , the output radiation will be circular polarised. To have Φ = 2 , ∆L has to satisfy:
π k∆L = (6.7) 2 λ which gives ∆L = 4 . Therefore the name ’λ/4-isolator’. The isolator can π be built to introduce a phase change of not necessarily a 2 , but any uneven π π product of 2 , i.e. (2n + 1) · 2 . The output characteristic of such an isolator would be narrower, but distortions caused by a lateral walk-off offset of the π beams would increase. We built an isolator with a phase delay of 2 . π The signal frequency where the isolator should give a 2 phase delay is 183.3 GHz. Therefore, the distance between the grid and the reflector plate can be calculated from:
4πd π Φ = cos θ = (6.8) λ 2
λ d = (6.9) 8 cos θ In our case the incident angle was θ = 45◦. Wavelength for 183.3 GHz is 1.64 mm, making d to be:
d = 289µm (6.10)
Figure 6.3 shows the λ/4-isolator made by IAP. It consists of a round frame with a grid fixed on a metal construction. The inner part of the construction fits to the grid frame’s shape and is so designed that the flat metal surface stands at the constant distance d = 289µm off the grid. The grid wires had a 20 µm diameter, 40 µm spacing and were made of tungsten. This theoretical consideration and description of the component’s work is basically all what is needed to understand its functionality. However, some features have to be understood further and are important for practical ap- plications. 6.2 Theoretical description 57
Figure 6.3: The λ/4 isolator made by IAP
6.2.1 Detail analysis
Let us consider an isolator and its grid to be placed in the coordinate system like the one in Figure 6.4. We will assume that the incoming signal comes along z axis towards the isolator. The whole isolator grid lies in a plane x’y that stands perpendicular to the xz plane. This plane builds an angle ϕ with the xy plane - the angle between the x and x’ axes is ϕ. Inside the x’y plane the wires of the grid stand under an angle γ to the horizontal x’ axis. In Figure 6.4, the dashed lines lie in the xy plane and they are projection of the gird on this xy plane along the z axis.
When it comes to (undesired) reflections from the mixer, the reflected signal will hit the isolator. In most practical cases the physical position of the mixer is such to make the polarisation of the reflected signal either horizontal or vertical. This is often the case, for many instruments have additional quasioptical components built to work when the polarisation is vertical or horizontal. One of the most used ones is the Martin-Pupplet interferometer, whose roof mirrors are normally designed for either horizontal or vertical polarisation. We assume radiation that comes to the isolator to be vertically polarised and spreading along z axis. We will also assume this signal to be a plane wave in order to simplify mathematics. However, this is not always the case, for real propagation is Gaussian-beam propagation. Therefore some corrections have to be introduced, which will be done later. Vector ~n is the normal on the grid-plain x’y, as shown in Figure 6.4. The 58 Quasioptical λ/4 isolator
y
α x ϕ γ n
z Ein x’ Figure 6.4: The position of the wires of the isolator and the incident radiation projection of the grid on the xy plane (when projecting along z axis) gives a grid in the xy plane whose wires stand under an angle α to the x axis, like in
Figure 6.5. The vectors i~p and i~n are projections of the unity vectors ~x and ~y (unity vectors parallel and perpendicular to the wires). i~p is the projection parallel to the grid, and i~n is the projection perpendicular to the grid wires:
i~p = ~x cos α + ~y sin α (6.11)
i~n = −~x sin α + ~y cos α (6.12) and
~n = −~x sin ϕ + ~z cos ϕ (6.13) ~ The incident electric field vector is Ein = E0~y and propagates along the z axis. In the xy plane we will decompose this vector into two vector- components: a vector parallel to the grid wires projection and a vector per- pendicular to the wires. The unity vectors i~p and i~n denote directions of these two vectors (Figure 6.5). The vector-component parallel to the wires ~ is Ep. This component will be reflected from the grid, and the component ~ perpendicular to the wires, En will pass the grid. We get the length of these ~ ~ two vectors as a scalar product of Ep and En with i~p and i~n respectively. 6.2 Theoretical description 59
y
in ip
α
x
Figure 6.5: The projection of the grid wires on the xy plane
~ ~ ~ Ep = Ein · ip = E0 sin α (6.14) and the E-field vector that is to be reflected from the grid is:
~ ~ ~ 2 Ep = Ep ip = ~xE0 sin α cos α + ~yE0 sin α (6.15) ~ The Ep vector will be fully reflected from the grid. The reflected vector we ~ denote as ERp. We can calculate it according to the Snell-Descartes law [35]:
~ ~ ~ ERp = −Ep + 2(Ep · ~n)~n (6.16) which gives:
~ ERp = −E0 sin α · (~x cos α cos 2ϕ + ~y sin α + ~z cos α sin 2ϕ) (6.17) ~ Similarly we can get En. As said, this vector is perpendicular to the projec- tion of the wires and will pass the grid.
~ ~ ~ En = Ein · in = E0 cos α (6.18)
~ ~ ~ 2 En = En in = −~xE0 sin α cos α + ~yE0 cos α (6.19) After passing the grid, it is reflected from the metal plate. We will call the ~ reflected vector ERn1: 60 Quasioptical λ/4 isolator
~ ~ ~ ERn1 = − En + 2(En · ~n)~n (6.20) ~ ERn1 =E0 cos α · (~x sin α cos 2ϕ − ~y cos α + ~z sin α sin 2ϕ)
However, as already described, this signal has a longer path then the signal reflected from the grid. When it reflects from the plate and comes back to recombine with the signal reflected from the grid, it has a phase delay of φ. We will keep φ as a parameter. The output E-field vector reflected from the ~ metal plate, at the place where it recombines with ERp is:
~ ~ jφ ERn =ERn1e (6.21) ~ jφ ERn =E0e cos α · (~x sin α cos 2ϕ − ~y cos α + ~z sin α sin 2ϕ)
The whole output signal will be:
~ ~ ~ ER = ERp + ERn (6.22) This is the signal that goes off the isolator and propagates further along its propagation axis. Very often we have an object in the quasioptics that stands perpendicular to the axis of signal propagation, mainly calibration loads or lenses. The signal reflects from one of these objects and comes back towards the isolator along the same axis. We assume the signal to be fully reflected:
~ ~ jπ EB = ERe (6.23) and this is the signal that returns to the isolator:
~ ~ ~ EB = −ERp − ERn (6.24)
~ jφ EB = ~xE0 sin α cos α cos 2ϕ(1 − e )+ 2 jφ 2 jφ + ~yE0(sin α + e cos α) + ~zE0 sin α cos α sin 2ϕ(1 − e ) (6.25)
This result should be discussed. We can use the analogue method to cal- culate the signal after the second passage through the isolator. We need a projection of the grid in the yz plane along the x axis, in order to decompose ~ vector EB into a component parallel to the wires’ projection and a compo- nent perpendicular to the wires’ projection. The angle between the wires’ 6.2 Theoretical description 61
projections and the z axis will be α1 as shown in Figure 6.6. Considering the geometry form Figure 6.4 and Figure 6.6 we get: tgγ tgα = (6.26) 1 sin ϕ As we already know from the projection in the xy plane: tgγ tgα = (6.27) cos ϕ
y
i2n i2p
α1
z
Figure 6.6: The projection of the grid wires on the yz plane
If we want the output signal of the isolator to be linear polarised and orthog- ~ ~ onal to Ein, the angle of the wires α1 that signal EB ’sees’ in the yz plane has to be equal to α. Practically it means that the signal that comes to the isolator from both directions has to ’see’ the grid under the same angle. This is only possible if sin ϕ = cos ϕ, giving ϕ = 45◦. Even more, from the geometry of the system it can be seen that α1 and α will be equal only if they are 45◦ each. Under these circumstances the real angle of the grid γ in the isolator in the x’y plane is tgγ = tgα cos ϕ. This gives an already known value of γ = 35.26◦.
This leads to some important conclusions: i) if the signal that comes for the first time to the isolator is vertically or horizontally linear polarised, we have to implement the isolator so that the bending angle between its input and output beam is 90◦. The most of the 62 Quasioptical λ/4 isolator quasioptical set-ups are built to have a physical position of the mixer and the horn to be either horizontal or vertical. If this is the case, the real angle of the wires in the grid has to be γ = 35.26◦. Under this condition the radiation ’sees’ the grid under the same angle of 45◦ from both directions. ii) if the grid of the isolator is vertical or horizontal the projection of the grid will be also vertical or horizontal, no matter under which azimuth angle we look at it. This would mean that we can apply such an isolator under any angle of incidence. However, the polarisation of the signal that comes to the isolator has to be linear and under 45◦ then. Such quasioptical systems are more rare. They must have unusual forms of some components (for instance rooftop mirrors under 45◦) or, more probable, additional polarisation grids. An example of such a system is the JEM/SMILES receiver, [36].
In AMSOS the orientation of the horn/mixer and the Martin-Puplett inter- ferometer give a vertically liner polarised signal. The incident angle in the ◦ ◦ ◦ isolator is 45 and this gives ϕ = 45 and α = α1 = 45 . This simplifies Equation 6.25 and we canconduct our analysis further. The E-field vector ~ EB that comes for the second time to the isolator is:
E E E~ = ~y 0 (1 + ejφ) + ~z 0 (1 − ejφ) (6.28) B 2 2 From Figure 6.6 we see that the projections of the unity vectors ~y and ~z in the yz plane, along and perpendicular to the wires are respectively: √ √ 2 2 ~i = ~y + ~z (6.29) 2p 2 2 √ √ 2 2 ~i = ~y − ~z (6.30) 2n 2 2 ~ ~ Similarly we can get the E2p component of the EB vector which is parallel with the wires’ projection that is going to be reflected from the grid: √ 2E |E~ | = E~ ·~i = 0 (6.31) 2p B 2p 2 √ √ 2|E~ | 2|E~ | E~ = |E~ |~i = ~y 2p + ~z 2p (6.32) 2p 2p 2p 2 2 The vector that is reflected from the grid we get as: 6.2 Theoretical description 63
~ ~ ~ ER2p = −E2p + 2(E2p · ~n)~n (6.33) which gives: √ √ 2|E~ | 2|E~ | E~ = −~x 2p − ~y 2p (6.34) R2p 2 2 The vector component that goes through the grid we get again as a scalar product: √ 2E |E~ | = E~ ·~i = 0 ejφ (6.35) 2n B 2n 2 √ √ 2|E~ | 2|E~ | E~ = |E~ |~i = ~y 2n − ~z 2n (6.36) 2n 2n 2n 2 2 This vector is reflected from the plate and analogue:
~ 0 ~ ~ E R2n = −E2n + 2(E2n · ~n)~n (6.37) Once again, this signal has a longer path then the signal reflected from the grid and additional phase delay of φ will be introduced: √ √ 2|E~ | 2|E~ | E~ = E~ 0 ejφ = ~x 2n ejφ − ~y 2n ejφ (6.38) R2n R2n 2 2 The vector of the whole output signal that comes back to the horn/mixer will be a sum of the two reflected vectors:
~ ~ ~ Eout = ER2p + ER2n (6.39)
√ √ 2 2 E~ = ~x (|E~ |ejφ − |E~ |) − ~y (|E~ |ejφ + |E~ |) (6.40) out 2 2n 2p 2 2n 2p The x-component of this signal will not be detected by the mixer. It is of interest to get the y-component: √ 2 |E~ | = (|E~ |ejφ + |E~ |) (6.41) y 2 2n 2p Considering (6.31) and (6.35) we obtain
E E~ = 0 (1 + e2jφ) (6.42) y 2 64 Quasioptical λ/4 isolator
The fraction of power that will be received by the mixer can be calculated ~ ~ comparing squares of the intensities of Ey and of the input signal Ein:
E2 |E~ |2 0 (1 + cos 2φ)2 + sin2 2φ y = 4 (6.43) ~ 2 2 |Ein| E0 which finally gives
|E~ |2 y = cos2 φ (6.44) ~ 2 |Ein| The theoretical characteristic can be seen in Figure 6.7. It is plotted in the π log scale and for the frequency region of interest. For a phase delay of 2 the signal will be totally suppressed and mixer will not receive it, which confirms our assumptions. For other frequencies (and therefore other φ), the distance d will represent another fraction of λ and the isolation will be finite.
−10
−15
−20
−25
−30
−35
−40 Attenuation [dB]
−45
−50
−55
−60 170 175 180 185 190 195 Frequency [GHz]
Figure 6.7: The theoretical frequency dependence of the λ/4 isolator transfer function, plotted on a log-scale
From Figure 6.7 we see that already at frequencies eg. 5 GHz away from the central frequency, the isolation falls to values of approx. 25 dB. Since AMSOS works in both side bands, at 183.3 GHz (water vapour line) and 176 GHz 6.3 Measurements of the isolator 65
(ozone line), we had to make a choice at which frequency to set the maximum of the isolation. We decided to make it at 183.3 GHz due to importance of water vapour measurements. The isolation of the baseline in the lower side- band should be around 20 dB. This device is very narrow-banded which limits possibilities of its application. However, most radiometers are built to operate at a certain, exact frequency or a narrow range of frequencies. That makes application of such an isolator very suitable for radiometers.
6.3 Measurements of the isolator
6.3.1 Measurement setup and methods We used the ABmm vector network analyser to measure the isolator’s charac- teristics. The setup is shown in Figure 6.8. For frequency sweeps between 170 GHz and 195 GHz we used the 11th harmonic of the transmitter. The same horn antenna was used to send the signal as well as to detect the reflected one. This was possible by using a directional coupler, Figure 6.8.
Metal reflector
Source ∆ z
10 dB Isolator Coupler Grid ABMM Absorber TK RAM
Detector
Eliptic mirror
Figure 6.8: The scheme of the measurement setup for determination of the isolator characteristics
It was possible to turn the horn under different angles: −45◦, 0◦, +45◦ and +90◦. First we had to establish a reference signal. It was done by making the polarisation of the sent signal so that it reflects fully from the isolator grid, 66 Quasioptical λ/4 isolator which was done by placing the horn under an angle of +45◦. The signal was sent, then reflected from the isolator grid, then from the metal reflector, once again from the grid and got back to the horn. After the reference signal had been established, the horn was positioned under 0◦, so that the transmitted signal (horizontally linear polarised) hit the wires of the isolator under an angle of 45◦. In that case the isolator really worked as previously described. The output of the isolator was supposed to be circular polarised, it reflected from the metal reflector, hit again the isolator and went back towards the horn. This signal should have been vertically linear polarised. Although the horn should not have detected this signal, it would have been reflected from once again, would have made another passage through the isolator and come back again to the horn. The polarisation would be horizontal and the horn would detect this signal. To avoid such multi-reflections-effects, we placed a grid in the signal path as shown in Figure 6.8. The orientation of the grid was vertical - the signal sent out of the horn did not see it, but the reflected signal that had gone twice through the isolator was reflected from this grid and ended up in a RAM absorber. The grid was also placed in order to avoid crosspolar effects of the elliptic mirror and the horn.
Figure 6.9: A photo of the measurement setup
A single frequency sweep in both antenna positions would have contained errors as the directivity of the coupler was not ideal and was frequency de- pendent. Figure 6.11 illustrates the frequency dependence of the coupler for two observed signals. 6.3 Measurements of the isolator 67
−15
−20
−25
−30 Isolation [dB]
−35
isolator − measured −40 theory
170 175 180 185 190 195 Frequency [GHz]
Figure 6.10: The measured characteristics of the IAP-made isolator. The isolation at the central frequency of 183 GHz is more then 35 dB
6.3.2 Results
Also, when establishing a reference signal, multiple reflections between the horn and the metal reflection occurred and detracted the accuracy of the measurement. Therefore we repeated measurements at different lengths of the signal path. The metal reflector plate was mounted on a stepping motor that moved it over approximately one-λ-length in 80 steps. By measuring the phase we were able to distinguish the real reflected signal from the sig- nals originating from the coupler’s imperfection and from multiple reflections. The finally measured characteristics of the isolator is shown in Figure 6.10. We see that measurements stand in a good agreement with the theoretical predictions. The shape of the measured curve and properties of the measured setup are worth of a more detail discussion. a) Reference signal and analyser’s sensitivity
We used the grid of the isolator as a perfect reflector for establishing a refer- ence level. To prove that, we conducted a measurement where two reference levels were established: one as before, using the grid of the isolator and an- 68 Quasioptical λ/4 isolator
60
50
40
30 Relative level [dB]
20
10 reference signal reflected (isolated) signal
170 175 180 185 190 195 Frequency [GHz]
Figure 6.11: A reference frequency sweep (circles) together with the corre- sponding isolated signal other one when a plan metal reflector was placed instead of the isolator. The average difference between the reference levels was 0.054 dB which made us consider the grid a reflector close to ideal. In Figure 6.12 there are plotted both isolator characteristics for two established reference levels, one with the isolator grid and the other with a metal plate. The differences were very small. The ripple that can be seen around the area of the maximal isolation, Figure 6.10, might have come from a certain lower sensitivity of the mixer receiver in the narrow band between 182 and 186 GHz, which could be seen in Fig- ure 6.11. Similar effects occurred by some other independent measurements. This ripple should have been compensated by subtracting the measured val- ~ ◦ ues (the angle of Ein = 0 ) from the reference level values when the angle of ~ ◦ Ein = 45 . However, we allow a possibility that irregularities in that area of the characteristic came from the mixer receiver. b) Beams’ walk-off
Another assumption that we already stated, was that the incident wave that hits the isolator was a plane wave. However, in the real quasioptics of AMSOS 6.3 Measurements of the isolator 69
−15
−20
−25
−30 Isolation [dB]
−35
grid as reference plate as reference −40 theory 170 175 180 185 190 195 Frequency [GHz]
Figure 6.12: The isolator characteristics for two reference levels. The charac- teristics look very similar, which means that the grid acts as an almost ideal reflector this was not the case, where propagation is quasioptical. This was also the case for our measurement setup. The beam waist that the elliptic mirror produced was 10 mm large and lay 5 cm in front of the isolator. One of the main effects that occur in such an isolator is the walk-off of the two output beams. The analysis of this effect is described by Goldsmith, [27]. One beam was reflected from the grid and the other from the metal plate that was at the distance d behind. The propagation axes of these two beams√ were parallel but had an axial offset of l = 2d cos θ, and in our case l = 2d = 409µm. The two beams with a lateral offset derived from a single beam with a common beam waist - only one beam came to the isolator. However, to conduct a correct analysis, we had to consider these two beams as if they had separate beam waists. The beam reflected from the metal mirror had a longer path then the beam reflected from the grid. As result, beam radius of this beam was larger at the output of the isolator then the radius of the beam reflected from the grid. This effect can be described if we assume this beam to have a beam waist of the same size, but further back then the beam waist of the beam reflected from the grid. It can be shown that the axial difference of the two beam waists that produces such a difference in the beams at the 70 Quasioptical λ/4 isolator output of the isolator was ∆z = ∆L. The two-dimensional power coupling coefficient between two offset beams is, [27]:
2 2 2 −2x0(w0a+w0b) (w2 +w2 )+(λ∆z/π)2 Koffset = Kax · e 0a 0b (6.45)
Where w0a and w0b are the beam waists of two beams that have a lateral offset of x0. ∆z is the axial offset of the two beam waists. As said ∆z = ∆L and w0a = w0b. Kax is defined as:
4 Kax = 2 2 (6.46) (w0a/w0b + w0b/w0a) + (λ∆z/πw0aw0b) For assumed positions of the beam waists, we got the power coupling coeffi- cient of more then 0.999, which was very good. This was expected since the beam waist was relatively large for this frequency and the lateral offset was small. c) Mechanics
From the theoretical description we saw that the isolator was sensitive to the changes of the angles. Especially it was sensitive to the change of the angular position of the grid. The other significant imperfection of the component was the position of the grid in respect to the metal reflector plate. It could have happened that it was not constant over the whole area of interest. It was technically difficult to produce both metal reflector’s surface and the grid and to fit them together so that they stand at a very accurately determined distance. The accuracy of the metal reflector’s surface made by a high precise CNC machine goes down to 5 µm. The accuracy of the grid position was a bit worse. Fitting the two together could have introduced a distance variation of more then 10 µm. This corresponds to a frequency drift of several GHz. These effects were difficult to control, as they depended on the isolator’s machining. In reality the isolator showed high sensibility. The adjustment of the dis- tance d had to be done in several iterations. The distance between the the grid and the plate could be changed by placing thin foils between the grid frame and the plate. After every of them the characteristic was measured as described above. We finally found the setup that corresponded to our needs after several relatively complex and difficult iterations. 6.3 Measurements of the isolator 71 d) Tests of another isolator
Figure 6.13 shows another λ/4-isolator made by Thomas Keating Ltd. which was used for test purposes.
Figure 6.13: The isolator made by TK with a vertical polarising grid
This isolator was also built to operate at 183 GHz. It consists of a metal frame and a metal plate that is exactly 290 µm thinner then the frame. Around the frame a wire grid was wound. The orientation of the grid was vertical. Due to some production imperfection we had to place several thin foils in order to adjust the distance between the grid and the plate again. The measurement setup was the same as the one described before. The reference signal was established by the horn elevation angle of 0◦ and the measurement of the characteristic by an angle of 45◦. Once more the metal reflector was moved over an area of approximately one λ in 80 steps. The isolation characteristic is shown in Figure 6.14. Compared with the characteristic of the IAP-made isolator we see that the maximal isolation is around 5 dB less. Also, there is a bigger overall noise in the characteristic. One of the reasons for that could have been the non- constant distance between the plate and the grid again. After several foils that had to be placed to reduce the distance grid-plate, it was again difficult to keep d constant. The metal reflector was longer and bigger then the one at IAP-made isolator. The whole construction was more complicated and this could have been the reason of bigger irregularities in the distance d over a bigger area of reflection. 72 Quasioptical λ/4 isolator
−15
−20
−25
−30 Attenuation [dB]
−35
isolator − measured −40 theory 170 175 180 185 190 195 Frequency [GHz]
Figure 6.14: The measured characteristics of the isolator made by TK. the isolation is slightly smaller and the overall characteristic is more noisy
6.4 Isolator in AMSOS
The measurements presented were done with the isolator as stand-alone. However, the major interest was to check if the isolator worked well in the radiometer. a) Measurement setup
We prepared another setup for measurements inside the AMSOS quasioptics, Figure 6.15. We used the same mixer-receiver combination and the coupler as in the earlier experiment. The rest of the system was the one from AMSOS. We had tried to measure the isolator with the original setup, but soon we noticed some problems that came from the MPI (next chapter). Therefore, the measurements of the isolator were conducted with a slightly changed setup of the quasioptics - the rooftop mirrors and the second grid of the MPI were replaced by a plain metal reflector. The moving plane reflector was placed at the position of the aircraft window (and the output beam waist) - 470 mm away from the elliptic mirror. The other sources of reflections in AMSOS, namely calibration loads, lay also at 6.4 Isolator in AMSOS 73
∆ z REFLECTOR ABmm
LAMBDA/4 ISOLATOR
ELLIPTIC TURNING MIRROR
ABSORBER A METAL PLATE (instead of the MPI) AMSOS ANTENNA
ABSORBER
PARABOLIC MIRROR
Figure 6.15: The measurement setup for measurements of isolator’s charac- teristics inside the AMSOS radiometer. The MPI was replaced by a metal plate approximately the same distance, which gave a realistic note to this test. The role of the grid from the stand-alone setup (Figure 6.8) took the first grid of the MPI. When establishing the reference signal this grid was placed under 45◦. The signal coming from the horn was polarised and the component that was reflected from this grid was parallel to the grid of the isolator and was reflected. The signal that should be isolated was produced by placing the grid under 90◦. In that case the signal coming to the isolator hit the wires under an angle of 45◦ and the isolator worked. The signal was further re- flected from the plain metal reflector, came back for the second time through the isolator and should have been linear polarised at the output, but this time with a horizontal polarisation. This signal went through the grid and ended in an absorber. b) Results
By establishing the reference signal, a half of the signal launched by the horn was lost at the polarising grid. When this signal came back once again only a half of the signal being linear polarised under 45◦ would be detected by the horn. Therefore the level of the final isolator characteristic had to be corrected by -6 dB. The metal reflector was again moved by a stepping motor 74 Quasioptical λ/4 isolator over a approximately one-λ-length. The measured characteristic is given in Figure 6.16.
−15
−20
−25
−30 Isolation [dB]
−35
isolator alone theory −40 isolator in AMSOS
170 175 180 185 190 195 Frequency [GHz]
Figure 6.16: The characteristic of the isolator inside the AMSOS radiometer, together with the theoretical characteristic and the stand-alone isolator
The characteristic of the isolator measured in the stand-alone setup is also given on the same plot. The agreement between the two curves is good which confirms that the reduction of the reflections in the quasioptics was relatively high, around 35 dB. The slight frequency drift of the isolation characteristic (Figure 6.16) after building the isolator in AMSOS could have come from its high mechanical sensitivity. After attaching the balky holders to it and fixing it on the front-plate, the grid-plate distance could have slightly changed.
6.5 Isolator during flight campaigns
The campaign conducted in November 2003 was used mainly for test pur- poses. The goal was to test the functionality of the radiometer. After analysis of the campaign results, we found out that some of the calibrated spectra had a relatively strong baseline. More astonishing was the fact that the baseline came and went suddenly during a flight with no obvious reason. This could not be connected with the state of the window or the cold load - there was 6.5 Isolator during flight campaigns 75 no ice, either on the window or in the cold load, which caused baseline some- times. In Figure 6.17 are presented several spectra from different time of the same flight. The baseline amplitude variated with the time from almost 5 K to a negligible value and back.
lat: 52.0, time: 2003−11−18 10:24:46 lat: 54.1, time: 2003−11−18 10:43:59 80 80
70 70
60 60
50 50
40 40
30 30
20 20 Brightness temperature [K] 10 10
182.8 183 183.2 183.4 183.6 183.8 182.8 183 183.2 183.4 183.6 183.8
lat: 56.1, time: 2003−11−18 11:21:59 lat: 52.7, time: 2003−11−18 11:56:10
80 80
70 70
60 60
50 50
40 40
30 30
20 20 Brightness temperature [K] 10 10 182.8 183 183.2 183.4 183.6 183.8 182.8 183 183.2 183.4 183.6 183.8 Frequency [GHz] Frequency [GHz]
Figure 6.17: Four different AMSOS spectra, recorded at the same flight dur- ing 1.5 hours. The baseline visible at the spectra appeared and disappeared quickly
A logical reason for this baseline-fluctuations could have been possible changes in the λ/4-isolator characteristics. Since the transfer characteristic of the iso- lator was highly frequency selective, we supposed that the temperature fluc- tuations in the cabin could have caused isolator’s frequency drifts. We found that the ring that held the grid was made of steel, and the back-plate and mounting of aluminium. Due to different expanding coefficients of the two metals, the distance between the grid and the plate could have changed with 76 Quasioptical λ/4 isolator
−18 Frequency = 184.5 GHz; t = 21.7 deg −20 Frequency = 186.7 GHz; t = 37.0 deg
−22
−24
−26
−28
Isolation [dB] −30
−32
−34
−36
−38 175 180 185 190 Frequency [GHz]
Figure 6.18: The isolation characteristics at two temperatures. When the isolator was at a higher temperature, the distance between the grid and the plate reduced, shifting the characteristic to higher frequencies the temperature fluctuations. The distance where the expansion differences occurred was indeed the thickness of the ring, l=10 mm. Thermal expan- µm sion coefficient of stainless steel used for the ring is αsteel = 16 m·◦C . The µm expansion coefficient of aluminium is considerably higher: αAl = 23.8 m·◦C . In order to prove this we conducted an experiment with the isolator in the laboratory - we measured the characteristic at two different temperatures. The same setup as in Figure 6.8 was used. First we measured the char- acteristic of the isolator at room temperature. Temperature was measured at the ground plate very close to the isolator’s holders and changed very slightly between 21.7◦C and 21.9◦C during the measurement. Afterwards, the holder and the isolator were heated with an air-heater from the back side until its temperature stabilised at 37◦, and the measurement was repeated. The characteristics at two temperatures are shown in Figure 6.18. The frequency drift of the isolation characteristic is obvious. The sensitiv- ity of the analyser receiver had worsen since earlier measurement (technical problems) - the characteristics were therefore not very sharp. It is easier to see the drifts from the theoretical cos2 Φ-fit, Figure 6.18. 6.5 Isolator during flight campaigns 77
The ∆d is the difference in the grid-plate distance caused by temperature change:
∆d = ∆lAl − ∆lsteel (6.47) where ∆lAl is the temperature-caused relative change of the length of the region of interest (l=10 mm) in aluminium and ∆lsteel is the same for steel. Since ∆lAl = lαAl∆t and ∆lsteel = lαsteel∆t we get the relative change of the distance between the grid and the plate as:
∆d = l(αAl − αsteel)∆t (6.48) For expansion coefficients of aluminium and steel given above and a temper- ature change of ∆t = 15.2◦C
∆d = 1.19µm (6.49) The dependence of the isolator’s central frequency (where the isolation is the strongest) on the distance d is: c f = √ (6.50) 4 2d In Figure 6.18 the solid line is the frequency characteristic at the room tem- perature that corresponds to a distance d = 288.2µm. With heating, this distance reduced for the calculated ∆d = 1.19µm and the new distance grid- plate was 287.01µm. The frequency that corresponds (6.50) to this distance would be f = 185.3 GHz. As we see from the measurements, the frequency drift was even larger and was around 2 GHz. This could be probably ex- plained by the isolator construction and the measurement setup. When heat- ing the isolator, the air-blower was directed to the back side of the isolator. The back aluminium plate was heated more then the steel frame. Also, be- tween the steel frame and the aluminium plate there were mylar foils used for the isolator’s fine tuning. The heat transfer from the back plate to the frame was worse due to these foils. All these effects probably made the temperature of the steel frame to be lower then the temperature of the aluminium back plate. This probably caused larger frequency drifts that we measured. Therefore, we made the back plate new and of the same steel used for the grid frame.
Chapter 7
Publication I
Quasioptical characterisation of a mm-wave receiver for atmospheric remote sensing
V. Vasi´c,N. K¨ampferand A. Murk
Optics and Lasers in Engineering, Volume 43, Issues 3-5, March-May 2005, Pages 303-315 http://www.sciencedirect.com/science/article/B6V4G- 4CYNR5Y-2/2/7fce745fab6abfa3aebcaef3f9630270
79
ARTICLE IN PRESS
Optics and Lasers in Engineering 43 (2005) 303–315
Quasioptical characterisation of a mm-wave receiver for atmospheric remote sensing
V. Vasic*,! N. Kampfer,. A. Murk Institute of Applied Physics, University of Bern, Sidlerstrasse 5, 3012 Bern, Switzerland
Received 5 December 2003; received in revised form 10 March 2004; accepted 17 March 2004 Available online 28 July 2004
Abstract
In this paper, we present the quasioptics of a millimetre wave radiometer for the remote sensing of atmospheric water vapour. The presented work addresses the design of the quasioptics with special emphasis on the verification of theoretical aspects by measurements of phase, amplitude and polarisation. The optical behaviour of a quasioptical isolator and a Martin–Puplett interferometer for the suppression of the undesired sideband is discussed in detail. It is shown that the optical behaviour of a rooftop mirror is different from what is theoretically expected. r 2004 Elsevier Ltd. All rights reserved.
Keywords: Quasioptics; Baseline reduction; Internal reflections; Rooftop mirror
1. Introduction
Investigation of the Earth atmosphere by remote sensing techniques is of fundamental importance for atmospheric and climatological sciences. Microwave radiometry offers an ideal tool in this context. It is possible to infer the altitude profile of atmospheric constituents by measuring pressure-broadened emission spectra of the species under investigation. Using proper retrieval schemes information on the distribution of the species can be inferred. However, instrumental artifacts may significantly affect system ability to achieve this goal. Therefore all means have to be taken to characterise the optics of the instrument. At the Institute
*Corresponding author. Tel.: +41-31-631-89-58; fax: +41-31-631-37-65. E-mail address: [email protected] (V. Vasic).!
0143-8166/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlaseng.2004.03.007 ARTICLE IN PRESS
304 V. Vasic! et al. / Optics and Lasers in Engineering 43 (2005) 303–315 of Applied Physics, University of Bern, microwave radiometers have been built and successfully operated from the ground, aircraft and from space. More recently, a new instrument for the detection of water vapour at 183.31 GHz and ozone at 175.45 GHz has been developed which will be flown from a Learjet aircraft. Altitude profiles of water vapour and ozone between approx. 20 and 70 km can be obtained with this radiometer. Phase and amplitude properties of the quasioptics system are first analysed for individual optical elements and then also for the complete system.
2. Beam shaping throughout the quasioptics
The atmospheric species which were to be retrieved put some tight requirements on the design of the quasioptics. For optimal retrieval of the atmospheric water vapour and ozone content the radiometer output beam should be as narrowas possible. Therefore a YHPBW (half power beam width angle) of around 1 was set as a first goal of the design. Secondly, a good suppression of the baseline was required. The internal reflections that occur between the mixer and other components produce standing waves (baseline) and can seriously degrade the radiometer sensitivity. Finally, in order to reduce diffraction loss, the ratio of the diameter of quasioptical components to beam waist (D/w ratio) should be equal or higher than 4.6 keeping the edge taper well below 40 dB. Furthermore, with a D/w ratio of 4.6, the cutoff ripple of the signal should be below1% [1, 2]. However, several boundary conditions had to be taken into account when designing the quasioptics. Since the radiometer is an airborne device, observation of the atmosphere is conducted through a specially designed aircraft window which is transparent to microwaves at these frequencies. The diameter of the window is limited to 15 cm due to safety reasons. This is a major constrain, as it limits the width of the output beam waist. To meet the D/w ratio requirement at the window, a maximal output beam waist of 32 mm was allowed. The other factor to be taken into account was that space was limited by the size of the aircraft cabin and thus a very compact design for the quasioptics and the distribution of the components was required. This problem also constrained on the size of every component. After considering different possibilities we chose the basic quasioptics design shown in Fig. 1. For beam launching and shaping we use a corrugated feed horn and two focusing mirrors, a parabolic and an elliptic one. Between the two a Martin– Puplett interferometer acts as a sideband filter and a l/4 quasioptical isolator is implemented for baseline suppression. Such a configuration of the mirrors was chosen for several reasons. Since the beam waist between the mirrors has to be relatively large the first mirror after the horn has to transform the horn’s small beam waist into a relatively large one. This requirement is best met by an offset parabolic mirror whose output beam waist is used as the input beam waist for the elliptic mirror. The elliptic mirror determines the size of the beam waist at the aircraft window and thus the output of the radiometer. The feed we use is a profiled, corrugated horn antenna with an aperture diameter of 17 mm and a slant length of 208.8 mm. It is therefore an aperture limited horn, ARTICLE IN PRESS
V. Vasic! et al. / Optics and Lasers in Engineering 43 (2005) 303–315 305
Aircraft window W = 31mm
Lambda/4 Isolator MP interf. LO Elliptic turning Absorber mirror Antenna W = 23.3mm W = 5.5mm W = 20.5mm Absorber
Parabolic mirror Fig. 1. Schematic of the quasioptics. The beam-shaping section consists of a feed horn and two focusing mirrors (parabolic and elliptic).
0 -20 20- -10 50 - 20 -20 -10
10 - - 3 - 20 3-
-40 0 -3 y [mm] -10
20 - - 20
Relative level [dB] -3 -60 - 50 0 1- copolar -10 crosspolar - 20 -80 -20 -60 -40 -20 0 20 40 60 -50 0 50 (a)Angle [deg] (b) x [mm] Fig. 2. The measured output of the horn antenna. The angular and the planar scan showa regular shape with low crosspolar signal: (a) angular scanning; (b) planar scanning. producing a virtual beam waist of [3]:
w0 ¼ 0:644a ð1Þ which lies very close to the horn aperture. With a being the radius of the horn aperture, the virtual beam waist is w0 = 5.5 mm. For the verification of our calculations we performed a series of measurements of individual components at specific places in the optics. The antenna pattern was measured at 183 GHz using an ABmm vector network analyser [4]. The measurements shown in Fig. 2 are the results of an angular and planar scan of the antenna pattern. The shape of the copolar signal is regular with a side lobe level of less than 25 dB and the crosspolar signal is lower than 30 dB. The planar scanning shows that a very regular shape of the horn output beam. The focusing elements were designed using the ABCD-matrix method [1]. Using the known distance d0in and the size w0in of the input beam waist, the position and ARTICLE IN PRESS
306 V. Vasic! et al. / Optics and Lasers in Engineering 43 (2005) 303–315 the size w0out of the output beam waist is given by 2 ðAdin þ BÞðCdin þ DÞþACzc d0out ¼ ; ð2Þ 2 2 2 ðCdin þ DÞ þ C zc
w0in w0out ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi: ð3Þ 2 2 2 ðCdin þ DÞ þ C zc The elements of the ABCD matrix are defined by ! AB 10 ¼ 1 ; ð4Þ CD f 1 where for an offset parabolic mirror f is equal to the effective confocal distance ( f = r), and for an elliptic mirror f =(R1R2)/(R1+R2). R1 and R2 are the distances of the mirror centre to the foci. The offset parabolic mirror has a nominal focal length of 200 mm and the effective confocal distance r = 216.5 mm (the distance between focus and the centre of the mirror). Knowing the position and size of the horn’s virtual beam waist and using Eqs. (2) and (3) we obtain the position and the size of the parabolic mirror output beam waist. It is located at a distance r off the mirror centre and has a size of 20.9 mm which satisfies the given pre-conditions. As the crosspolar signal from the mirrors is a source of internal reflections in the quasioptics causing baseline ripples it is important to estimate the average and the maximal value of the crosspolar signal produced by the mirrors. According to [1], the fraction of the power that remains in the copolar component after reflection is given by w2 K ¼ 1 m tan2 y ; ð5Þ co 4r2 i where wm is the beam radius at the mirror surface, yi is the incidence angle and r is the effective confocal distance, as described. In our case, the beams at the parabolic mirror are reflected at an angle of 32.6 giving yi=16.3 . Given r=216.5 mm and a beam radius at the mirror of wm=20.9 mm, we get Kco=0.9998. This means that the crosspolar component carries around 0.02% of the power of the incident radiation. However, in many cases it is more important to calculate the maximum value of the electric field of the crosspolar component. Although the overall ratio crosspolar to copolar power can be low, the peak electric field value of the crosspolar component can be relatively high, especially for mirrors with strong curvature and for strongly divergent incident beam. The relative maximum of the cross polarised to the copolar signal is [1] cx w max ¼ 0:43 tan y m; ð6Þ co i r where all parameters are the same as above. According to (6) the maximal level of the crosspolar signal should be at least 19.2 dB belowthe copolar signal over the whole mirror surface, which is sufficient for our purposes. The calculated beam ARTICLE IN PRESS
V. Vasic! et al. / Optics and Lasers in Engineering 43 (2005) 303–315 307
0
50 - 20 -30 -30 -30 20
20 40 0 - -3
- -
10 y [mm] - - 30 10
Relative level [dB] 60 50 -20 - - -30 horn+parabolic mirror - horn 30 - 80 - 60 - 40 - 20 0 20 40 60 -- 100 50 0 50 100 (a) Angle [deg] (b) x [mm] Fig. 3. The measured output diagrams of the parabolic mirror—angular and planar scans. The distortions in the upper part of the planar scan are due to the measurement setup: (a) angular scanning; (b) planar scanning.
100 0 X cut Y cut 30 -20 50 - - 5 -10 10
3 20 - - - - 30 0 2 - 3 15 y [mm] - - 30 - 0 -10 - 20 - 50 - 30 Relative level [dB] - 25 -100 - 30 - 100 - 50 0 50 100 - 5 0 5 (a)x [mm] (b) Angle [deg] Fig. 4. The measured output diagram of the radiometer. The asymmetries along the x- and y-axis are assumed to come from the rooftop mirrors: (a) radiometer output; (b) X- and Y-cut. distortion due to offset effects of the mirror [10] is negligible due to a large beam waist and a relatively small incidence angle. Extensive laboratory tests confirmed the above theoretical calculations. Fig. 3 shows the angular and planar measurements from the parabolic mirror fed by the horn. As expected, due to a larger output beam waist, the horn–mirror antenna diagram is narrower than that for the horn alone. Planar scans show that the copolar signal has a relatively regular shape down to 20 dB. The planar scans of the crosspolar signal showvalues at least 20 dB lowerthen the copolar signal, whichis in good agreement with the theoretical prediction above. The beam distortions that can be seen in the upper part of the planar diagram in Fig. 3 are due to the measurement setup, and not from the mirror itself. The final element of the quasioptics is the elliptic mirror which uses the output beam waist from the parabolic mirror as input. Given the output beam waist of 31 mm (YHPBW=1 ) and using Eqs. (2) and (3), the R1 and R2 parameters of the mirror are calculated to be 1.640 and 7.706 m, respectively. The radius of the beam at the mirror is 31.9 mm and therefore the diameter of the mirror is chosen to be 150 mm. The total reflection angle for the input and output beams is 90 . Fig. 4 shows the planar scan of the elliptic mirror output which is at the same time the radiometer output. Again, the diagram has a regular shape down to 20 dB. However, it exhibits slight asymmetries along the x- and y-axis, which is better ARTICLE IN PRESS
308 V. Vasic! et al. / Optics and Lasers in Engineering 43 (2005) 303–315 illustrated in the Fig. 4b showing the X and Y cuts of the output. This effect of asymmetry is assumed to come from the non-ideal behaviour of the rooftop reflectors in the Martin–Puplett interferometer, an interesting issue discussed in a later section. The measurements had to be done in the near field for technical reasons. Therefore it is difficult to determine the HPBW angle. The estimated yHPBW is around 1 and the major goal of the quasioptical design has been achieved.
3. k=4 quasioptical Isolator
Internal reflections producing baseline ripple may significantly decrease the sensitivity of a radiometer and are therefore one of the main problems in a heterodyne receiver. A part of the atmospheric signal can be reflected from the mixer and sent back in the quasioptics. After another reflection from a component standing perpendicular to the beam propagation axis, standing waves between the mixer and this component can be generated. Several methods to decrease baseline have so far been developed [5–7], but none of them have completely solved the problem. We have tried a relatively newmethod using a quarter waveplate that acts as a quasioptical isolator. This method has already been applied [8], however it is still not widely used. The essential function of this plate is to transform a linearly polarised input signal into a circularly polarised output signal.
3.1. Theoretical description
The isolator we are describing consists of a metal reflecting plate and a grid that stands in front of the plate at a constant distance d, Fig. 5. Radiation coming to the isolator is polarised by the grid. A part of the signal with the electrical field vector parallel to the gird wires is reflected from the grid. The other part with E-vector perpendicular to the wires goes through the grid and is reflected from the metal plate. This isolator is designed for an angle of incidence of y =45 . The analysis for an arbitrary angle of incidence is given by [9]. As the second signal has a longer optical path a phase delay is introduced in comparison with the first signal reflected from the grid. The path difference between the signals is DL, as can be seen in Fig. 5: pffiffiffi d DL ¼ ¼ d 2; ð7Þ cos y
1 2
θ θ = 45 deg
d ∆L
Fig. 5. The two reflected signals have a path difference that produces a phase difference. ARTICLE IN PRESS
V. Vasic! et al. / Optics and Lasers in Engineering 43 (2005) 303–315 309 where d is the distance between the grid and the plate. The phase delay F introduced this way is pffiffiffi 2 2pd F ¼ kDL ¼ : ð8Þ l As they exit from the isolator the two signals are recombined and if their phase difference is p/2, the output radiation will be circularly polarised. Obviously, a path difference of l/4 will produce a phase difference of p/2. Therefore the name ‘l/4 isolator’. Putting F = p/2 in Eq. (8)pffiffiffi we calculate the required distance between the grid and the plate to be d ¼ l=4= 2: In the case of the AMSOS radiometer, the operating frequency is 183.3 GHz giving l/4=409 mm. Therefore the required distance d is d=289 mm. After another reflection in the quasioptics, the returned signal will still be circularly polarised, but the sense will have changed from left- to right-hand or vice versa. After a second passage through the isolator the output signal will be linearly polarised, but nowthe polarisation willbe orthogonal to the initial one. Under these conditions, the unwanted reflected signal causing the baseline will not be detected in the mixer. However, the l/4 isolator is a frequency-selective component. Only at a frequency where F =p/2 will the suppression of the baseline be optimum. At the other frequencies, the distance d corresponds to another fraction of l and the suppression of the reflected signal will be proportional to cos2 F [9]. Care has also to be taken about howsuch an isolator is used in the optical beam. The radiation coming from both directions must ‘see’ the isolator–grid at the same angle. If the horn launches a linear vertical or horizontal polarised signal, we have to implement the isolator in order that the reflection angle between its input and output beam is 90 . The analysis above was done assuming a plane wave as input signal for the isolator. However, this is not the case in the quasioptics of our radiometer. The Gaussian beam spreads out of the horn, is reflected from the parabolic mirror and the output beam waist is 20.5 mm wide and lies 31 cm in front of the isolator. The main effects of the Gaussian propagation is the walk-off of the two output beams. The analysis of this effect has been described by [1]. After calculation of the coupling coefficients between the two offset beams [9], we obtain a power coupling coefficient for the two beams with an axial offset of 409 mm of more than 0.999. Doing a further analysis and taking into consideration the second passage through the isolator and another axial offset of the beams, the resulting power coupling coefficient remains high, above 0.998.
3.2. Measurement results
We used the vector network analyser (of AB Millimetre) to measure the isolator’s characteristics. The setup was as shown in Fig. 6. We performed frequency sweeps in order to get the isolator’s characteristics between 170 and 195 GHz. The same horn antenna was used to transmit the signal as well as to detect the reflected one. This was achieved by using a directional coupler. ARTICLE IN PRESS
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Metal reflector
Source ∆ z
10 dB Isolator Coupler Grid Absorber TK RAM
Detector Eliptic mirror Fig. 6. The setup for the measurement of the isolator frequency characteristics.
The linear vertically polarised test signal launched by the horn, after a first passage through the isolator is transformed into a circularly polarised signal and after the reflection from the metal plate at the output and another passage through the isolator the signal is linearly horizontally polarised. Therefore it is reflected by the grid (Fig. 6) and sent into an absorber. The grid is placed into the beam for that reason. This is however the case only for the central frequency. At other frequencies, the reflected signal should be attenuated by a factor of cos2 F with respect to the reference signal. The reference signal was established by replacing the isolator with a plane reflector and repeating the same frequency sweep. In order to decrease the effect of multiple-reflections that can occur (especially when establishing the reference signal) and to avoid the effects of the limited directivity of the directional coupler, the plain reflector at the output was moved by a stepping motor in 80 steps over an approximate distance of one l. By following the phase of the detected signal, we were able to distinguish the signal reflected from the plate from that leaking from the source due to the limited directivity of the coupler and also from that caused by multiple-reflections. The results are presented in Fig. 7 as a solid line. The measurements are in good agreement with the theoretical expectations (dashed line). A final measurement was conducted but this time with the isolator built into the radiometer [9], Fig. 7 (dash-dot line). Again it is in good agreement with theory, but with a small frequency drift. This difference could be explained by the isolator’s high mechanical sensitivity. Small changes in the distance between the grid and the plate can cause relatively large frequency drifts. After attaching the mechanical holders of the isolator and building it into the radiometer, it is possible that the distance d has changed slightly. However, these measurements show that at the central frequency the isolator attenuates internal reflections by more than 30 dB, which would strongly reduce the baseline. ARTICLE IN PRESS
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−15 isolator alone theory isolator in AMSOS −20
−25
−30 Isolation [dB]
−35
−40
170 175 180 185 190 195 Frequency [GHz] Fig. 7. The measured characteristics of the isolator: alone and in the AMSOS radiometer. At the central frequency the internal reflections are reduced by more than 30 dB.
4. The Martin–Puplett interferometer
The down conversion of the water vapour RF signal at 183.3 GHz is done by a subharmonically pumped Shotky mixer. The frequency of the local oscillator is 89.8 GHz (its second harmonic is used) and the IF frequency is 3.7 GHz. The upper side band is used for the observation of the water vapour line. Coincidentally, in the lower side band there is a weak ozone line at 175.45 GHz. Therefore the radiometer is designed to observe alternatively both side bands. When measuring in one of the side bands, the signal from the other one has to be efficiently suppressed. This is done by using a Martin–Puplett interferometer, Fig. 1. The Martin–Puplett interferometer (MPI) is a two beam polarisation-rotating interferometer with a basic transfer function [11]: pðz z Þ P ¼ A cos2 1 2 ; ð9Þ Vout l where PVout is the output power of one polarisation (e.g. vertical) and z1 and z2 are distances from the first and the second rooftop mirror to the polarising grid. By changing one of these distances, the output characteristics change and a successful suppression of one of the side bands can be achieved. Theoretically, the whole signal input to the MPI should go to the output and none of it should return towards the source. This, however, is not the case in reality as was discovered by reflection measurements of the AMSOS quasioptics. The experimental setup is shown in Fig. 8. To make the data analysis easier, the case with one single rooftop mirror is analysed. For reference purposes a metal reflector was placed at the ARTICLE IN PRESS
312 V. Vasic! et al. / Optics and Lasers in Engineering 43 (2005) 303–315
Metal reflector Lambda/4 isolator Detector Source
10 dB Coupler Antenna
Parabolic mirror Fig. 8. The measurement setup for reflection measurements in the quasioptics of the AMSOS radiometer.
−10 1 2 3
−20
−30
−40
−50 FFT Amplitude [dB]
−60 no isolator isolator −70 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5 3 Distance [m] Fig. 9. The reflection measurements of the quasioptics. We can distinguish three reflection peaks from the three reflection sources: (1) directional coupler (2) rooftop mirror (3) metal reflector at the output. output. The test signal is launched through the horn into the quasioptics and the amplitude and phase of the reflected signal is detected via a directional coupler. We performed 10 GHz wide frequency sweeps around the central frequency of 183 GHz. The first sweep was with the isolator in place and the second one with the isolator replaced by a plain reflector. An additional frequency sweep for calibration purposes was made with an aluminium plate at the horn aperture. To distinguish between different sources of reflection the calibrated measurements were analysed using the Fast Fourier Transform method. In Fig. 9, reflections as a function of distance between the reflection plane and the reference plane at the horn aperture are illustrated. We can clearly distinguish three peaks. The first one behind the horn aperture comes from the limited directivity of the coupler. The third peak comes ARTICLE IN PRESS
V. Vasic! et al. / Optics and Lasers in Engineering 43 (2005) 303–315 313 from the reflection plate at the output. It differs significantly depending on the position of the isolator. The reflection peak when the isolator is present (dashed line, Fig. 9) is heavily suppressed compared to the situation when there is no isolator (solid line). The attenuation of the reflection is more than 30 dB and is another good proof of the isolator’s functionality. However, the second reflection peak originates from the position where the MPIs rooftop mirror is located. The level of the reflection is around 30 dB. A similar measurement was conducted with another MPI using frequency sweeps and an alternative technique which involves shifting the rooftop mirror at a fixed frequency instead of the FFT [12]. Both measurements showreflections from the rooftop mirror at a level of around 30 – 35 dB. The obvious reason for these reflections could be the crosspolar leakage of the beam-splitting grid. However, at these frequencies and for the spacing and diameter of the wire grid that we use [13], the cross-polar leakage is below 40 dB. This indicates that the residual reflections of the MPI originate from the rooftop mirror. The rooftop mirror is a retroreflector that rotates the polarisation of the incoming signal by 90 . However, it has been noted that the cross-polar pattern of the reflected signal does not correspond to what is theoretically expected. In order to investigate such an effect we performed the following experiment, Fig. 10. This time the source was mounted on a planar scanner. The copolar output of the signal reflected by the rooftop mirror is sent out and the cross-polar component is focused by an elliptic mirror and detected by the detector. Planar scans 100 100 mm were done for the two physical orientations of the rooftop mirror: first with the rooftop line vertical and afterwards with the rooftop line horizontal. The reference copolar signal was established by a scan with a plane reflector instead of the rooftop mirror. The crosspolar patterns in Fig. 11 showa clear structure which is dependent on the physical alignment of the rooftop mirror. The symmetry axis is parallel to the rooftop line. The amplitude maxima of the crosspolar signal are again around 30 dB lower than the copolar signal maxima. This indicates that the rooftop mirror exhibits a non-ideal polarisation rotation. A small part of the reflected signal has got the same polarisation as the incoming signal and causes residual reflections of the Martin–Puplett interferometer which may affect the sensitivity of a radiometer. The reason for such behaviour of the MPI can be the non-ideal shape of the rooftop
Rooftop mirror Detector Grid 2 45 deg Source Planar scanner Grid 1 0 deg
Fig. 10. Measurement setup for the two physical orientations of the rooftop mirror, vertical and horizontal. ARTICLE IN PRESS
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100 100
50 50
0 0 y [mm] y [mm]
−50 −50
−100 −100 −100 −50 0 50 100 −100 −50 0 50 100 (a) x [mm] (b) x [mm] Fig. 11. Pattern of the cross-polar signal of the rooftop mirror for the two orientations of the rooftop line: (a) vertical; (b) horizontal. mirror. Even small deviations from the 90 angle can cause irregularities in the beam pattern. Also, the crosspolar pattern is sensitive to the angle of the polarising grid. These issues are the subject of separate ongoing research.
5. Conclusions
The quasioptics of a millimetre wave radiometer for the remote sensing of atmospheric trace gases have been analysed in detail. Measurements of amplitude, polarisation and phase have been made for single elements as well as for the whole instrument. Although most optical components propagate the fundamental Gaussian beam mode at this wavelength, it turned out that some components exhibit unexpected behaviour. Rooftop mirrors as used in a Martin–Puplett interferometer affect the polarisation of the reflected signal depending on the roof line. Internal reflections causing baseline effects are suppressed using a l/4 quasioptical isolator inserted in the beam, thus decreasing reflected signals by 35 dB at 183.3 GHz.
Acknowledgements
This work has been supported through the Swiss National Science foundation under Grants 2000-063793.00 and 2000-063897.00. The authors would like to thank Dr. June Morland and Dr. Stephan Nyeki for language corrections.
References
[1] Goldsmith P. Quasioptical systems—gaussian beam quasioptical propagation and applications. NewYork: IEEE Press/Chapman & Hall Publishers series on microwavetechnology and techniques; 1998. [2] Siegman AE. Lasers. California: University Science Books, Sausalito; 1986. p. 663–9 [chapter 17]. ARTICLE IN PRESS
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[3] Wylde RJ, Martin DH. Gaussian beam-mode analysis and phase-centers of corrugated feed horns. IEEE Trans Microwave Theory Tech 1993;41(10):1691–9. [4] Goy P, Caroopen S, Gross M. Vector measurements at millimeter and submillimeter wavelengths: feasibility and applications. Proceedings of the Second ESA Workshop on Millimeter Wave Technology and Applications: Antennas, Circuits and Systems, Millilab, Espoo, Finland, May 1988. p. 89–94. [5] Gustincˇ ic! JJ. A quasi-optical radiometer. Digest of the Second International Conference on Submillimeter Waves and their Applications, San Juan, Puerto Rico, December 6–10, 1976. [6] Goldsmith PF, Scoville NZ. Reduction of baseline ripple in millimeter radio spectra by quasi-optical phase modulation. Astron Astrophys 1980;82:337–9. [7] Deuber B, Kampfer. N. Minimized standing waves in microwave radiometer balancing calibration. Radio Sci 39: RS1009, doi:10.1029/2003RS002943. [8] Manabe T, Inatani J, Murk A, Wylde RJ, Seta M, Martin DH. A newconfiguration of polarization- rotating dual-beam interferometer for space use. IEEE Trans Microwave Theory Tech 2003; 51(6):1696–704. [9] Vasic! V, Murk A, Kampfer. N. The l/4 quasioptical isolator for baseline reduction. Research report, Nr. 2003-7, Institute of Applied Physics, University of Berne, June 2003, http://www.iapmw.unibe.ch/ publications/publication.php?type=TechReport. [10] Murphy JA, Withington S. Perturbation analysis of Gaussian-beam-mode scattering at off-axis ellipsoidal mirrors. Infrared Phys Technol 1996;37:205–19. [11] Martin DH, Puplett E. Polarised interferometric spectrometry for the millimetre and submillimetre spectrum. Infrared Phys 1970;10:105–9. [12] Vasic! V, Murk A, Kampfer. N. Non-ideal quasi optical characteristics of rooftop mirrors. In: Hiromoto N, (editor), Conference Digest of the 28th International Conference on Infrared and Millimeter Waves, Otsu, Japan, 2003. p. 261–3. [13] Manabe T, Murk A. Transmission and reflection characteristics of slightly irregular wire-grid for arbitrary angles of incidence and grid rotation. 14th International Symposium on Space TeraHertz Technology, Tucson, USA, April 2003.
Chapter 8
Martin-Puplett interferometer
8.1 Basics of the MPI
The Martin-Puplett interferometer (MPI) is a two beam polarisation-rotating interferometer. The incoming signal is firstly polarised by the first grid that stands under 0◦ or 90◦. The second grid acts as a beam splitter, for the angle of the wires that the beam ’sees’ is 45◦. A half of the signal is sent to the first rooftop mirror which acts as a retroreflector that changes the polarisation of the incoming signal for 90◦. This signal returns towards the grid and goes through it. The second half of the signal goes through the beam-splitting grid towards the second rooftop mirror. Once again, after reflection and polarisation rotation this signal returns to the beam-splitting grid and is sent to the output. The two beams recombine at the output of the MPI. The output of the interferometer is [37]:
π(z − z ) P = A cos2 1 2 (8.1) V out λ where PV out is the output power of one polarisation (e.g. vertical) and z1 and z2 are the distances from the first and the second rooftop mirror to the polarising grid. By changing one of these distances the output characteristic changes and a successful filtration of one of the side bands can be achieved. In AMSOS, a mirror is moved by a computer controlled motor.
8.2 Reflection measurements
In an MPI, theoretically, the whole input signal should go to the output and none of it should return towards the source. However, this was not the case
95 96 Martin-Puplett interferometer
ROOFTOP MIRROR 1 GRID 1 0 deg or 90 deg Z 1
input Z2
GRID 2 45 deg ROOFTOP MIRROR 2 output
Figure 8.1: The basic scheme of the Martin-Puplett interferometer in reality as discovered by reflections measurements of the AMSOS quasiop- tics. a) Measurement setup and methods
The setup is shown in Figure 8.2. To make the data analysis easier, the case with one rooftop mirror was analysed. For reference purposes a metal reflector was placed at the output. A test signal (linear vertical polarised) was launched through the horn into the quasioptics and the amplitude and the phase of the reflected signal were detected by the detector head using a directional coupler. The 10 GHz wide frequency sweeps were made around a central frequency of 183 GHz. The first sweep was with the λ/4-isolator and the second one also with the isolator, but when it acted as a plain reflector. This was done by turning the first grid of the MPI to stand under 45◦. The whole incoming signal was fully reflected from the isolator grid and the isolator really acted as a plain reflector, [38]. Additional frequency sweep for calibration purposes was made with an aluminium plate at the horn aperture. b) Results
To distinguish between different sources of reflection, the calibrated mea- 8.2 Reflection measurements 97
Metal reflector Lambda/4 isolator Detector Source
10 dB Coupler Antenna Grid 1 Grid 2
Parabolic mirror
Figure 8.2: The measurement setup for reflection measurements in the AMSOS-quasioptics surements were analysed using the Fast Fourier Transform. In Figure 8.3 the abscissa of the plot shows the distance between the reflection plane and the reference plane at the horn aperture. We can clearly distinguish three peaks. The first one behind the horn aperture came from the limited directivity of the coupler. The third peak came from the reflection plate at the output. By this peak there were two clearly different situations - with a functional iso- lator and without it. The reflection peak when the isolator worked (dashed line, Figure 8.3) was heavily suppressed compared to the situation when the isolator did not work (solid line). The reflection was attenuated by more then 30 dB and it was another good proof of the isolator’s functionality. The level of the peak in case with the non-functional isolator was about 10 dB below the reference level. This was due to losses on polarisation grids (three times 3 dB) during the signal propagation and due to non-ideal beam coupling. The second reflection peak was however at the position where the MPI’s rooftop mirror was. The level of the reflection was around -30 dB. c) Measurements of another MPI
In order to validate this result, similar reflection measurements were per- 98 Martin-Puplett interferometer
−10 1 2 3
−20
−30
−40
FFT Amplitude [dB] −50
−60 no isolator isolator −70 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5 3 Distance [m]
Figure 8.3: The reflection measurements of the quasioptics. We can distin- guish three reflection peaks from the three reflection sources: (1) directional coupler (2) rooftop mirror (3) metal reflector at the output formed with another MPI. This MPI was originally built in the EMCOR radiometer [39], and was later used for test purposes. The measurement setup is shown in Figure 8.4. The horn launched a test signal (linear polarised under −45◦), which went through the first grid (+45◦) without losses, as well as through the second grid. After reflection and polarisation-rotation the signal went out. In case of an absorber at the output, ideally, none of the signal should return towards the detector. On the other hand, in case of a metal plate at the output, the whole signal would be returned and detected in the detector head. The FFT analysis showed also a level of reflections coming from the rooftop mirror to be again around -30 dB, Figure 8.5. When the mirror was moved along the axis of propagation (different positions for new scans), the peak also moved appropriately. This was another confirmation of the peak’s origin. A similar measurement was performed by A. Murk with another MPI using frequency sweeps and an alternative technique which involved shifting of the rooftop mirror at a fixed frequency instead of the FFT, [40]. The both measurements showd reflections from the rooftop mirror in a level of around 8.2 Reflection measurements 99
ROOFTOP ROOFTOP MIRROR MIRROR
SOURCE SOURCE METAL REFLECTOR GRID 2 GRID 2 45 deg ABSORBER 45 deg
GRID 1 GRID 1 45 deg 45 deg
DETECTOR DETECTOR
(a) Vertical (b) Horizontal
Figure 8.4: Measurement setup for the reflection measurements in another MPI (from EMCOR). (a) with an absorber at the output (b) as a reference a plane reflector was positioned at the output
-30 dB to -35 dB.
0 1 2 3
−10
−20
−30
−40 FFT Amplitude [dB]
−50
metal reflector −60 absorber
−0.2 0 0.2 0.4 0.6 0.8 1 Distance [m]
Figure 8.5: The reflection measurements of EMCOR MPI. Again we can distinguish three reflection peaks from the three reflection sources: (1) direc- tional coupler (2) rooftop mirror (3) metal reflector at the output 100 Martin-Puplett interferometer
8.3 Sources of reflections
An obvious reason of such relatively strong reflection could be the cross-polar leakage of the beam-splitting grid. However, at these frequencies and for the spacing and diameter of the wire grid we used, the cross-polar leakage should be below -40 dB, [41]. This indicated that residual reflections of the MPI derived from the rooftop mirror. a) Theory
Another reason which can lead to reflections is the angular position of the beam-splitting grid. The grid should stand under 45◦ and only then there should be no return signal. However, if the angle is different from 45◦ a part of the signal will, after retroreflection and polarisation-rotation from the rooftop mirror, go back through the grid towards the source. This effect will be analysed in more detail. Let us consider the part of the MPI with one rooftop mirror and a beam-splitting grid, Figure 8.6.
ROOFTOP MIRROR
Output 2 Output 1
GRID
Ein
Figure 8.6: The geometry for analysis of the angular position effects of the beam-splitting grid. The input signal is linear polarised with vertical orien- tation
The input signal is a plane wave which comes along the symmetry axis and ~ it is supposed to be linear vertical polarised (Ein). If we consider the angle of the grid that incoming radiation sees to be θ (θ is the angle between the 8.3 Sources of reflections 101 projection of the wires and vertical line), the returned signal (towards the source) can be determined using Jones-matrices, [26, 27]. The output E-field vector in that case will be:
~ ~ Eout = AT,π−θRAT,θEin (8.2) ~ AT,θ is a matrix that determines which part of Ein will be transmitted through the beam-splitting grid:
sin2 θ − cos θ sin θ A = (8.3) T,θ − cos θ sin θ cos2 θ The matrix that determines retro-reflection and polarisation rotation pre- formed by the rooftop mirror is:
−1 0 R = (8.4) 0 −1
Another passage through the beam splitting grid is determined by AT,π−θ:
sin2(π − θ) cos(π − θ) sin(π − θ) A = (8.5) T,π−θ cos(π − θ) sin(π − θ) cos2(π − θ) After mathematical calculations we get the ratio between the vertical E-field component of the signal at the output, and Ein, to be:
E V,out = − sin2 θ(sin2 θ − cos2 θ) (8.6) Ein As said, θ is the grid angle that the incoming signal ’sees’ along its axis of propagation. This angle is a projection of the physical angle of the grid wires:
tan β θ = arctan( √ ) (8.7) 2 In this case, β is the real angle of the grid wires when we look at the grid under an incidence angle of 90◦. Let us remind: if the grid is well aligned, in order to get a projection of the wires to be 45◦, β should be 54.73◦ (the complementary angle γ is 35.27◦, as described in the theory of the λ/4- isolator). In the real case, due to bad angular alignment, β can be different and we can expect then reflections towards the input. The fraction of the E-field intensity of the input signal that returns towards the source is 102 Martin-Puplett interferometer
E tan β tan β tan β V,out = − sin2(arctan( √ )) sin2(arctan( √ ) − cos2(arctan( √ ) Ein 2 2 2 (8.8) E The appropriate power-ratio Pr = ( V,out )2 is plotted on dB-scale in Figure Pin Ein 8.7.
0
−10
−20
−30
−40
−50
−60 Reflected signal [dB] −70
−80
−90
−100 0 10 20 30 40 50 60 70 80 90 Wires angle [deg]
Figure 8.7: The fraction of the power of the input signal that will be returned towards the source as a dependence of the wires angle
Figure 8.7 shows nicely this dependence on the wire gird angle. In the case β = 0◦ (vertical polarising grid) the signal will be reflected by the grid and sent to the Output 1, Figure 8.6, none of it will go through it and of course none of it will return. In the other extreme situation with β = 90◦ (horizontal polarising grid) the whole input signal passes the grid, is reflected by the rooftop mirror without changing the polarisation, passes the grid once again and returns to the source. We can see that for β = 54.73◦ (projection 45◦) there should be no reflections towards the source - the whole signal is sent to the Output 2. Figure 8.8 shows the same ratio as in Figure 8.7 but plotted for a narrower area of wire angles. We can notice that already for a relatively small inac- curacies of β we have relatively strong reflections. For an angle inaccuracy 8.3 Sources of reflections 103
−20
−30
−40
−50
Reflected signal [dB] −60
−70
−80 50 52 54 56 58 60 Wires angle [deg]
Figure 8.8: The fraction of the power of the input signal that will be returned towards the source as a dependence of the wire grid angle (narrower area of the possible wire-grid angle misalignment) of around 1.5◦ we already have reflections with a level of -30 dB. This could possibly explain discovered residual reflections in an MPI. On the other hand, the mechanical tolerance should be certainly much better then 1.5◦. But, it is relatively difficult to measure the wire angle when they are already built in a radiometer. b) Measurement setup and methods
In order to prove the influence of the grid-alignment we did the following ex- periment with a setup given in Figure 8.9. The Grid 2 was rotated in small steps around a central position of the physical grid-angle of β=54.73◦ (pro- jection 45◦), in a range 54.73◦ ± 6◦. The key element of this setup was a me- chanical construction on which the Grid 2 was mounted. It was a frame with a very fine mechanical reductor that had a resolution of 1:43200 (0.008333◦). Turning of reductor’s wheel resulted in rotation of Grid 2. The high trans- mission factor of the reductor allowed very accurate angle positioning around the chosen central position. 104 Martin-Puplett interferometer
ROOFTOP MIRROR
ABSORBER GRID 2
DETECTOR GRID 1 SOURCE 90 deg
antenna polarization 0 deg antenna polarization 90 deg
Figure 8.9: The setup for measurements of dependence of the reflected signal from angular position of the polarising grid. The Grid 2 can be rotated with an accuracy of 0.008333◦
The sender was the ESA1 module of ABmm network analyser. A signal sent by the sender was reflected from the Grid 1 (vertical grid wires) and sent towards the Grid 2 and the rooftop mirror. Theoretically, when the wires stand under 45◦ (projection), the whole signal should end up in the absorbers. Similarly as earlier, detector head was positioned after a focusing elliptical mirror and picked up the crosspolar artifacts of the mirror.
The transfer function of this system (Ereflected/Ein) is a bit different from the ratio shown in Equation 8.8, for there was another grid (Grid 1) in the system. In this case, the output E-vector will be:
~ ~ Ereflected = VTAT,π−θRAT,θEin (8.9) where all matrices are the same as above, with VT being the transfer matrix of a vertical grid:
0 0 V = (8.10) T 0 1
After matrix-multiplication, the ratio between the horizontal component of the E-field vector which is detected by the detector and the input signal is: 8.3 Sources of reflections 105
E H,detector = − sin θ cos θ(sin2 θ − cos2 θ) (8.11) Ein
Figure 8.10 shows theoretical dependence the appropriate power ratio ( EH,detector )2 Ein on wires’ angle of Grid 2. The x-axis represents the physical angle of the grid wires β.
0
−10
−20
−30
Reflected signal [dB] −40
−50
−60 0 10 20 30 40 50 60 70 80 90 Wires angle [deg]
Figure 8.10: The theoretical dependence of the reflected signal level from the angular position of the grid. Around 54.73◦ (45◦ projection) there should be no reflections towards the source
We can see again that for a grid’s physical angle of 54.73◦ (projection 45◦) there should be no reflected signal towards the detector. The measurements were done by turning Grid 2 from 48.7◦ to 60.7◦ in around 160 steps, each step being 0.075◦. The absolute ’zero’-position of the grid (real 54.73◦) was determined experimentally, where the signal measured by the detector was the lowest. We did narrow frequency sweeps from 182.5 GHz to 183.5 GHz for every angular position of the Grid 2. The reference signal was established doing the same frequency sweep without Grid 2, with Grid 1 replaced by a grid under 45◦, and with the detector head standing under -45◦. 106 Martin-Puplett interferometer
−20 measured theory
−25
Reflected signal [dB] −30
−35 50 52 54 56 58 60 Wires angle [deg]
Figure 8.11: The measured characteristic shows a reflected signal which was always above -33 dB for any angular position of Grid 2
c) Results
The measured curve was obtained by calculating a mean value of the differ- ence between the reference signal and the detected signal, for every angular position of Grid 2. Figure 8.11 shows the results - the measured reflected signal and theoretical curve. The differences between the two are relatively large in the right part of the characteristics centre (between 55◦ and 56◦). The source of this deviation is still unknown. However, a more important fact: the reflected signal did not fall below roughly -33 dB around the central position of 54.73◦. We repeated the same measurement, but in a narrower range and this time with the highest angular resolution of 0.008333◦. The result in Figure 8.12 shows that reflected signal was always above -33 dB, no matter how fine the grid was positioned around the ’zero’-point. These measurements excluded a possible bad aliment of the MPI’s beam- splitting grid as a source of internal reflections. It strengthened our assump- tion that the reflections came from the rooftop mirror, not from the rest of the MPI. 8.4 Non-ideal polarisation rotation 107
−32
−32.5
−33 Reflected signal [dB]
−33.5
53.5 54 54.5 55 Wires angle [deg]
Figure 8.12: The same measurement as in Figure 8.11, but with a lot higher resolution and in a narrower band. The level of reflections remained higher then -33 dB for every angular position of the Grid 2
8.4 Non-ideal polarisation rotation
The rooftop mirror is a retroreflector that rotates the polarisation of the incoming signal by 90◦. In order to validate the crosspolar artifacts of polar- isation rotation we conducted the following experiment, Figure 8.13. The source was mounted on a planar scanner. The copolar output of the
Rooftop mirror Detector Grid 2 45 deg Source Planar scanner Grid 1 0 deg
Figure 8.13: Measurement setup for the two physical orientations of the rooftop mirror, vertical and horizontal 108 Martin-Puplett interferometer signal reflected by the rooftop mirror was sent out and the crosspolar com- ponent was focused by an elliptic mirror and detected by the detector. Planar scans 100 x 100 mm were done for the two physical orientations of the rooftop mirror: first with the rooftop line vertical and afterwards with the rooftop line horizontal.
100 100
50 50
0 0 y [mm] y [mm]
−50 −50
−100 −100 −100 −50 0 50 100 −100 −50 0 50 100 x [mm] x [mm]
(a) Vertical (b) Horizontal
Figure 8.14: Pattern of the cross-polar signal of the rooftop mirror for the two orientations of the rooftop line
The reference copolar signal was established by a scan with a plane reflector instead of the rooftop mirror. Several later repetitions for different rooftop mirrors under similar conditions gave very similar results. The cross-polar patterns in Figure 8.14 show a clearly visible structure which is dependent on the physical alignment of the rooftop mirror. The symmetry axis was however parallel to the rooftop line. The amplitude maxima of the cross-polar signal were again around 30 dB lower then the copolar signal maxima. This indicates that the rooftop mirror preformed non-ideal polarisation rotation. A small part of the reflected signal got the same polarisation like the incoming signal and caused residual reflections in the Martin-Puplett interferometer.
8.5 Lateral offsets of two beams
During the tests of the radiometer’s output diagram, we noticed slight dis- tortions in the beam pattern. In order to investigate that, we did two mea- surements of the output beam with only one of the two rooftop mirrors in the 8.5 Lateral offsets of two beams 109
MPI. The other one was replaced by an CV-3 absorber. First we measured with the first mirror (the upper mirror in Figure 5.2) and afterwards with the second mirror (the mirror on the right side in Figure 5.2). The results are shown in Figure 8.15.
60 60 0 −20 −20 −30 −30 −30 −20 −5 −30 −10 −10 −10 40 40 −10
−20 −10 −15 −20 −20 −10 20 20 −10
−3 −20 −3 −3
−3 −20 −10 −20 −30 −30 −25 0 −10 0
−30 y [mm] −30 y [mm] −20 −40 −3 −20 −20 −3 −35 −20 −10 −10 −10 −50 −10 −40 −30 −20 −30 −30 −40 −20 −40 −45 −20 −20 −30 −60 −30 −30 −50 −60 −60 −60 −40 −20 0 20 40 60 −60 −40 −20 0 20 40 60 x [mm] x [mm]
(a) With rooftop mirror 1 (b) With rooftop mirror 2
Figure 8.15: The output of the radiometer with one of the rooftop mirrors in the MPI
We can see a lateral offset of 5.5 mm between the centres the two beams. First logical idea was that one of the rooftop mirrors was laterally misaligned. However, a series of further measurements with different lateral positions of the mirrors did not give aligned beams. This was also a strong indication that the rooftop mirror did not reflect as expected. Some other authors experienced similar problems, [42]. Another also logical assumption was that there was axial misalignment of the two mirrors. In other words, the mirrors might have not ’looked’ in the same directions, their axes might have not been parallel. In that case, output beams of the two would diverge, which would result in a lateral beam offset in the scanning plane. This would have also given tilted phase fronts. However, this was not the case in the measured phase scans. We made further measurements, together with the output beam scans of the whole radiometer, as described in Chapter 5. We scanned in six planes, with the distances between the scanning plane and the elliptic mirror centre ranging between 25 cm and 190 cm. We made scans with both rooftop mirrors in the MPI (Figure 5.15), but also scans with single mirrors where the other one was replaced by an absorber. Such additional scans (a scan for every 110 Martin-Puplett interferometer
0 −30 0 50 −20 −30 50 −20
−10 −20 −10 −20 −3 −3 0 0
y [mm] −10 −30 −30 −40 −10 −20 −40 Relative level [dB] −20 −50 −50 −30 −30 −60 −60 −50 0 50 −50 0 50 x [mm] x [mm] 0 0 50 50 −20 −20 −30 −30 −10 −10 −20 −3 −20
0 −20 0 −3 y [mm] −10 −40 −40 −20 −10 Relative level [dB] −20 −30 −30 −50−30 −30 −50 −60 −30 −60 −50 0 50 −50 0 50 x [mm] x [mm] 0 0 50 −20 50
−30 −10 −30 −10 −30
−20 −30 −20
−20 −3 −20 0 0
−3 −20 y [mm] −10 −40 −10 −40 −20 Relative level [dB] −30 −30 −50 −30 −50 −30 −60 −60 −50 0 50 −50 0 50 x [mm] x [mm]
Figure 8.16: Planar scans at distances 25 cm, 31 cm and 47 cm. On the left side are beams for rooftop mirror 1, on the right side for rooftop mirror 2 rooftop mirror) were made in all six planes, keeping the setup alignment. The normalised diagrams of the scans at 25 cm, 31 cm and 47 cm distance are presented in Figure 8.16 and the scans at 80 cm, 120 cm and 190 cm in Figure 8.17. Again, the positions of the beam centres in a scanning plane were relative, due to re-alignment for every scanning distance. What is important are the lateral offsets between the beams of the two rooftop reflectors in every scanning plane. The lateral offset of the two beams ranged 5 mm ± 1.5 mm for all scans, and did not increase significantly with increasing distance of the 8.5 Lateral offsets of two beams 111
−30 0 0 −20 −30 50 50 −10
−10 −20 −20 −20
−10 −3 0 −3 0 −30 −10 −30
y [mm] −30 −30 −30 −20 −30 −40 −40 −30 −20 Relative level [dB] −30 −50 −50 −30 −60 −60 −50 0 50 −50 0 50 x [mm] x [mm]
−30 0 0 −10 50 −30 −10 50
−30
−20 −30 −20
−20
−3 0 −20 0 −30 −3
y [mm] −30 −20 −40 −10 −40 −10 −20 Relative level [dB]
−30 −30 −50 −30 −30 −50 −60 −60 −50 0 50 −50 0 50 x [mm] x [mm] 0 0 −20 50 −30 50 −20 −20 −20 −10 −10 −3 −3 −20 −10 −20
0 −10 0 −3 y [mm] −40 −10 −40 −3 −20 −10 −20 −20 Relative level [dB] −20 −50 −50 −30 −60 −60 −50 0 50 −50 0 50 x [mm] x [mm]
Figure 8.17: Planar scans at distances 80 cm, 120 cm and 190 cm. On the left side are beams for rooftop mirror 1, on the right side for rooftop mirror 2 scanning plane. For instance, the offset at the 31 cm scanning distance was the same as for 120 cm. Figure 8.18 shows phases of the beams in first three scanning planes. Contours of the amplitudes are also plotted over phase scans in order to emphasise the positions of the beams. The scans show relatively constant phase fronts for each mirror for these scans. This, again, means that the beams did not diverge, they lateral offset increased only slightly with the increased distance of the scanning plane. Also, as said above, a mechanical lateral offset of 5 mm is excluded. Mechanical tolerances of all components in the MPI in AMSOS were better than 20µm. 112 Martin-Puplett interferometer
50 50 −30 −20 −20 −10 −30 100 −10 100 −3
0−10 0 0−10 0 −3 y [mm] −30 Phase [deg] −100 −100 −20 −20 −50 −30 −30 −50 −30 −50 0 50 −50 0 50 x [mm] x [mm]
50 −20 50 −20 −30 100 100 −10 −30 −10 −3 0 0 0 0 −20 −20 −10 y [mm] −20
−3 Phase [deg] −30 −10 −100 −100
−50 −30 −30 −50 −30 −30 −50 0 50 −50 0 50 x [mm] x [mm]
50 −20 50 −30 −10 −30 −10 100 −30 100
−30
−20
−20 0 0 0 0 −10 −3 y [mm] −10 −3 −20 Phase [deg]
−20 −100 −100 −30 −30 −50 −30 −50 −30 −50 0 50 −50 0 50 x [mm] x [mm]
Figure 8.18: Phase scans for first three scanning planes. The amplitude contours from Figure 8.16 are plotted over phases
Similar lateral beam offsets were measured in the MPI from EMCOR ra- diometer. Measurement artifacts could have also played a role, mainly mul- tiple reflections between the sender and the receiver. Therefore, we would take the measured offsets rather qualitatively. The observed effect was very interesting, but we will not make speculations on its origin yet. Further measurements have to be done, as well as an analysis on the influence of the rooftop line. 8.6 Usage of the MPI 113
8.6 Usage of the MPI
Our measurements showed that a MPI produced internal reflections with a level of around -30 dB. This could be critical for potential applications where the highest sensitivity is required, eg. for observation of atmospheric species with very weak lines. In our case this issue was not that critical for the observed water vapour line is strong. Therefore the usage of the MPI was well-founded. Its easy adjustability was a strong advantage because the observation in both sidebands was preformed. However, care about these non-ideal properties of the MPI has to be taken and will be a subject of fur- ther research. First, the other mechanical inaccuracies have to be excluded, like possible inaccuracy of the 90◦-angle of the mirror, or roughens of the mirror surface. Thereafter, a detail electromagnetic analysis of the mirror’s corner should be done, in order to investigate if the reflections come from the rooftop line and a narrow area around it. The analysis described in [43, 44, 45] might be used as a starting point. These and similar analysis use geometrical and physical optics for backscatter calculations, and the GRASP software works on the same principle. However, simulations with GRASP did not show disturbances around the rooftop line. The diffraction theory of geo- metrical optics was not enough to explain the effects mentioned above. Also, physical optics, as used in GRASP, has accuracy problems in a range of 1-2 λ round the rooftop line. This is indeed the area we are most interested in. A deeper electromagnetic analysis of the corner should probably be applied. This will also be a subject of our further research.
Chapter 9
Publication II
Non-Ideal Quasi Optical Charac- teristics of Rooftop Mirrors
V. Vasi´c,A. Murk and N. K¨ampfer
The 28th International Conference on Infrared and Mil- limeter Waves, Proceedings, Editor N. Hiromoto, Vol. JSAP 031231, No. W4-2, Pages 261-262, October 2003, Otsu, Japan
115
Non-Ideal Quasi Optical Characteristics of Rooftop Mirrors
V. Vasic´∗, A. Murk and N. Kampfer¨ University of Bern, Inst. of Applied Physics (IAP), Switzerland
Abstract: Rooftop mirrors are widely used as ideal po- was done with a planar mirror at the aperture of the horn. larisation rotating devices in Martin-Puplett Interferome- A further measurement with a plane reflector at the output ters at millimetre and submillimetre wavelengths. But they of the MPI was also done for reference purposes. also have a significant non-ideal behaviour which can lead to standing waves. We present measurements of these non-ideal Rooftop Mirror properties and dicuss the consequences for quasi-optical re- Absorber ceivers. Source
I Introduction Grid 2 45 deg The Martin-Puplett Interferometer (MPI) is a low loss polarisation-rotating two-beam interferometer which is Grid 1 45 deg often used as single sideband filter and diplexer for hetero- dyne receivers in the millimetre and submillimetre wave Detector range [1]. The MPI makes use of a wire grid, which acts as a beam Figure 1: Setup for reflection measurements of a rooftop mir- splitter and combiner for the two orthogonal polarisations ror between 130 GHz and 140 GHz. For calibration purposes a of a beam, and of two rooftop mirrors, which act as po- plane mirror was placed at the position of the horn aperture or of larisation rotating retroreflectors. If these components are the absorber. not an ideal polariser or ideal polarisation rotators a cer- tain fraction of an incoming signal will be reflected at the To distinguish between different sources of reflection MPI. This will result in standing waves between the re- the calibrated measurements were analysed with a Fast ceiver and the rooftop mirrors which can limit the sensi- Fourier Transform. Figure 2 shows the FFT Amplitudes tivity of astronomical or atmospheric observations. of two different frequency sweeps from 130 to 140 GHz. An obvious reason for reflections from the MPI is the The abscissa of that plot gives the distance between the re- cross-polar leakage of the wire grid. Depending on the flecting element and the reference plane at the horn aper- wire diameter and spacing, but also on the irregularities ture. The first of the three peaks in this figure appears be- of the spacing, it can be around -40 dB for frequencies up hind the reference plane (negative distance) and is caused to 200 GHz and considerably higher at submm wave fre- by the limited directivity of the waveguide coupler. Peak quencies [2]. Another possible reason for standing waves number 2 in the MPI measurement is at about -32 dB and from the MPI can be the non-ideal polarisation rotation of the rooftop mirror which is discussed in this paper. 0 1 2 3
II Reflection Measurements of an MPI −10 The internal reflections of a MPI were measured using a vector network analyser from AB-Millimetre. The trans- −20 mit and the receive channel for these S11 measurements −30 were combined with a D-band waveguide coupler and launched through the same corrugated horn antenna. An FFT Amplitude [dB] −40 elliptical mirror produced a Gaussian beam with a beam −50 Ref waist of w0 = 10mm close to the grid of the MPI. To sim- MPI −60 plify the data analysis only half of the MPI was tested at −0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 a time by injecting the signal with ±45◦ polarisation and Distance [m] covering the unused rooftop mirror with absorber. Fig- Figure 2: FFT spectra of two reflection measurements of a ure 1 shows the principal setup for these measurements. rooftop reflector (solid) and of the reference mirror (dashed). To calibrate phase and amplitude of the typically 10 GHz The x-axis gives the distance of the reflecting elements from the wide frequency sweeps additional reference measurement reference plane at the horn aperture. The dotted lines indicate ∗Correspondence: [email protected]. This work has the position of the waveguide coupler (1), the rooftop reflector been supported through the Swiss National Science foundation under (2) and the reference mirror (3). grant 200020-100153
261 corresponds to the distance between the reference plane alignment of the rooftop mirror with respect to the optical an the rooftop reflector, while the third peak of the 0 dB axis. The symmetry axis of these pattern, however, was reference measurement shows the distance to the flat mir- always parallel to the roofline of the mirror which indi- ror. cates that the non-ideal polarisation rotation is caused by The same type of reflection measurements were done this corner. in an 183 GHz radiometer [3] module. The sweeps were in a narrower frequency band between 181 and 185 GHz. The setup was very similar to the one in Figure 1 but with the components from the radiometer quasioptics: the horn 50 50 antenna, polarising grids and the rooftop mirror. The re- sults of the FFT analysis have shown a very similar level 0 0 z [mm] z [mm] of reflection from the rooftop mirror, with a peak value of −50 −50 -30 dB, Figure 3.
−100 −100 −20 −50 0 50 100 −50 0 50 100 1 2 x [mm] x [mm]
−25 (a) Rooftop mirror vertical (b) Rooftop mirror horizontal −30
−35 Figure 4: The crosspolar output of the rooftop mirror for two different orientations (2 dB contours from -45 dB to -30 dB). −40 FFT Amplitude [dB] −45 IV Conclusions −50 Martin-Puplett Interferometers can produce a signif- −55 icant level of standing waves in quasi-optical systems. −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5 3 Distance [m] Their reflectivity can be above -35 dB, which is consider- ably higher than the reflections from good calibration tar- Figure 3: FFT spectra of the reflection measurements of a gets or well designed Cassegrain Antennas. The reasons rooftop reflector in the 183 GHz radiometer module. The dotted are the crosspolar leakage of the polarising grids, which lines indicate the position of the waveguide coupler (1) and the becomes worse with increasing frequency, as well as the rooftop reflector (2). non-ideal polarisation rotation of the rooftop reflectors. The latter will be determined by the ratio of wavelength to beamwidth. Also similar results were obtained when further testing To reduce the impact of these standing waves during the MPI of the receiver at 183 GHz. An alternative mea- the observation the pathlength between the MPI and surement technique, which involves shifting the rooftop the receiver should be kept as stable as possible, which mirror at a fixed frequency instead of the FFT, also showed can put very tight constraints on the allowed thermal reflectivities of about -35 dB. drift of a system. Another solution is to use alternative designs of the dual beam interferometer which are free of III Non-ideal polarisation rotation residual reflections, e.g. the one which will be used in the The reflection measurements in the previous chapter submillimetre limb sounder SMILES [4]. can be explained by a small fraction of the signal which is returned from the rooftop reflector with the same polarisa- References tion as the incoming beam. This can be expected from the [1] D. H. Martin, E. Puplett: ’Polarised interferometric spec- geometry because the roofline of the mirror corresponds trometry for the millimetre and submillimetre spectrum’, In- to a one-dimensional singularity for the field. To investi- frared Physics, Vol. 10, p. 105-109 (1970) gate this effect the cross-polar pattern of a beam reflected [2] T. Manabe, A. Murk: ’Transmission and reflection char- acteristics of slightly irregular wire-grid for arbitrary angles of by a rooftop mirror was measured in a similar setup as incidence and grid rotation’, 14th International Symposium on shown in Fig. 1. In this case, however, the source was Space TeraHertz Technology, Tucson, USA, April 2003 mounted on a planar scanner in front of the first grid at [3] V. Vasic,´ A. Murk and N. Kampfer:¨ ’An Optimised Quasi horizontal polarisation. An additional co-polar beam pat- Optical Design of an Airborne Radiometer’, 3rd ESA Workshop tern measurement with a flat mirror instead of the rooftop on Millimetre Wave Technology and Applications, Espoo, May reflector was used as 0 dB reference. 2003. Proceedings, p. 337-342 Figure 4 shows the results of such measurements for [4] T. Manabe, J. Inatani, A. Murk, R. J. Wylde, M. Seta and two different orientations of the rooftop mirror. The D. H. Martin: ’A New Configuration of Polarization-Rotating amplitude maxima of these cross-polar pattern are again Dual-Beam Interferometer for Space Use’, IEEE Transactions about -30 dB below the maximum of the co-polar sig- on Microwave Theory and Techniques, Vol. 51, No. 6, p. 1696- 1704, June 2003 nal. The position of these maxima depended on the lateral
262 Chapter 10
Signal down conversion and radiometer backend
10.1 Down conversion and amplifiers
The RF signal is received by the corrugated horn and lead to a sub-harmonically pumped uncooled Schottky mixer made by Virginia Diodes Inc. The PLL stabilised local oscillator (LO) pumps the mixer with a 89.8 GHz signal. The second harmonic of the LO signal was used for the down conversion of the atmospheric signal to an IF frequency of 3.7 GHz. The measured double-side band noise temperature of the mixer was around 700 K, and the conversion loss was 6 dB. The measured noise temperature of the radiometer was around 1950 K, which was slightly higher then expected from theory. However, this was a good result considering the ambient temperature operation. Required simplicity of an on board usage, power and space limits of the Learjet ex- cluded cryogenic operation.
The first amplifier after the mixer had a high gain of more then 65 dB in frequency range between 3 and 4.5 GHz and a noise temperature of 66 K. The characteristics of this amplifier is shown in Figure 10.1. The second amplifier had a gain of around 25 dB and very good flatness in the range 3 - 4.5 GHz, Figure 10.1. Its contribution to the noise temperature was negligible due to very high gain of the first amplifier. Together both amplifiers have more then 90 dB amplification and a 20 dB attenuator was put between them.
119 120 Signal down conversion and radiometer backend
80
70
60
50
40
30 Amplification [dB]
20
10 First amplifier Second amplifier 0 2.5 3 3.5 4 4.5 5 Frequency [GHz]
Figure 10.1: The characteristics of the first amplifier after the mixer (solid line) and the second amplifier (dotted-diamond line)
10.2 System stability
The IF signal is amplified by two amplifiers and analysed in two acousto- optical spectrometers (AOS). The first one is a wide-band AOS made by Meudon Observatory Paris, with a bandwidth of 1 GHz and 1725 channels. The second one is a narrow-band AOS made by Elson Research Lab, with 2048 channels that cover a bandwidth of 50 MHz. Such high resolution of the narrow-band AOS is required for retrievals of water vapour profiles at highest altitudes, between 60 and 70 km. The offset of both AOSs was automatically recorded at the beginning of every measurement. Both AOSs are laboratory devices. At the beginning of a flight, especially in polar regions, temperature inside the aircraft can fall below 0◦C. Therefore, additional automatically controlled heating was built in around the laser block of both AOSs. It brought the AOSs to their operational temperature while the aircraft reached its cruising altitudes. In earlier versions of the radiometer, we had losses of measurement time due to a long heat-up phase of the AOSs. The main sources of the system instability are variations of system gain due 10.2 System stability 121 to amplifier fluctuations and the AOS thermal instability. The system gain should remain stabile during a calibration cycle. This also depends on the length of pre-integration time τ (time needed to record one spectrum). The τ has to be short so that gain remains stabile, but also long enough for reduc- tion of thermal noise. The Allan-variance has become a standard method for determination of heterodyne receiver’s gain stability and the optimal length of integration time. To determine the Allan-variance we did several thousands (around 6000) uncalibrated measurements. The measurements were done with the whole system including the quasioptics, mixer, IF chain and the Meudon wide-band AOS. The turning mirror looked at the cold load, due to its temperature stability. The pre-integration time τ was chosen to be 1.42 s. We chose three of 1725 channels to observe their stability - channel 150, 1200 and 1500. In order to get the Allan-variance, mean values of k successive measurement were determined, [46]:
kj 1 X X = x (10.1) k,j=1...m k j i=1+k(j−1) where x1...n are data from separate channels and m is the number of such mean values m = n/k. The Allan-variance σk is calculated using the differences between the two subsequent mean values ∆Xk,j = Xk,j − Xk,j+1 as:
m−1 m−1 1 X 1 X 2 σ2 = (∆X )2 − ∆X (10.2) k m − 1 k,j m − 1 k,j j=1 j=1
2 2 where the first part on the right side is ∆Xk and the second part is (∆Xk) . 2 This way of calculation is valid only if the time mean-value (∆Xk) is zero. However, due to the time-dependent drifts of the AOS this value was not always zero which would have overestimated system stability. Therefore we calculated the Allan-variance as:
m−1 1 X σ2 = (∆X )2 (10.3) k m − 1 k,j j=1 Figure 10.2 shows the Allan-variance for the three chosen channels. We see that the integration time had an optimum around 10 sec, which was also channel-depending. It was interesting to check the Allan-variance in the first part of the measurements (first 500 spectra) when the temperature of the 122 Signal down conversion and radiometer backend
AOS was not stabilised. This corresponds to real operational conditions at the beginning of a flight.
−2 10 ch 150 ch 1200 ch 1500 k σ
−3 10 Allan−variance
−4 10 0 1 2 10 10 10 Integration time [s]
Figure 10.2: The Allan-variance for the whole time of measurement of around 6000 spectra. The optimal integration time lies about 10 sec.
Figure 10.3 presents the Allan-variance for the first 500 spectra which approx- imately corresponds to the first 20 minutes of measurements. The optimal integration time in that case was around 3.5 sec. Such a decrease was due to temperature-dependence of the system gain in the heat-up phase. In the rest of the measurement time (spectra 500-6000), the system stability was higher and the integration time was around 13 sec, Figure 10.3. This comparison was useful for one reason: in the aircraft, with a maximal length of the flight of around 4 hours, the heat-up-phase can not be avoided. However, thank to the new heating, the AOS were always temperature stabilised until we reached altitudes where we measured. No spectra were recorded during the heat-up phase. The pre-integration time for Meudon-AOS in AMSOS was chosen to be 1.42 sec. 10.3 Radiometer calibration and operation control 123
−1 10 ch 150: stabile ch 1200: stabile ch 1500: stabile ch 150: warming phase ch 1200: warming phase
k −2 ch 1500: warming phase
σ 10
−3 10 Allan−variance
−4 10 0 1 2 10 10 10 Integration time [s]
Figure 10.3: The Allan-variance for the measurement 500-6000 spectra (lines): integration time when the AOS temperature is stabile is up to 13 sec. For the spectra 1-500 during the warming-up-phase (circles): the maxi- mal integration time is significantly shorter, around 3.5 sec.
10.3 Radiometer calibration and operation con- trol
10.3.1 Calibration cycle
AMSOS is a total power radiometer calibrated by beam-switching. The turning mirror focuses the radiometer’s beam in three deferent position one after another: cold load (C) - atmosphere (A) - hot load (H). The calibration cycle is C-A-H-A-C. Both calibration loads were made of CV-3 absorber that acts as blackbody. In earlier versions of AMSOS radiometer a heated hot load was used, where the absorber was heated from the back side. Since the heating lasted several tents of minutes, we were suspicious about a possible temperature gradient inside the absorber’s body. Therefore the new version of the radiometer used an unheated hot load, well isolated from the cabin air. The temperature mea- surements during the flights showed that the absorber’s temperature varied 124 Signal down conversion and radiometer backend very slowly in time. The cold load was realized with a CV-3 absorber soaked in liquid nitrogen in a special dewar. Boiling temperature of liquid nitrogen in the flying aircraft differs from the one at the see-level pressure. The measured temperature of the absorber in the cold load varied during the flight between approx. 74 K and 77 K. In both cold and hot load the absorbers were treated similarly to other qua- sioptical components (regarding their diameter): their size was determined using the beam size at the absorber. The ratio D/w (absorber diameter versus beam size) was kept above 4.6 to avoid spillover.
10.3.2 Operation control Due to very limited space available in the cabin of the Lear jet aircraft, the operation of the radiometer had to be possibly highly automated, which was also useful for ground-based measurements at Jungfraujoch. Also, the instru- ment should be modular, so that a repair could be done quickly. Numerous parameters had to be coordinated and observed during a measurement: cal- ibration cycle of the turning mirror, side-band control, PLL stability of the local oscillator, GPS data and various temperatures. a) Mirror positioning
The elliptic mirror was turned by a computer-controlled brushless DC mo- tor and positioning of the motor axis was determined by an optical encoder. Since the moment of inertia of the elliptic mirror was relatively large, posi- tioning time was around 1.3 s. An accurate positioning of the mirror was essential for a good retrieval and one of our pre-conditions was pointing bet- ter then 0.1◦. The data from the last flight showed that mirror held the exact position in around 57 % of measurement time. In the rest of 43% of time the mirror position was only ±0.045◦ around central position, Figure 10.4. In only 0.7% of time the mirror was 0.09◦ off the central position and the rest was negligible. Pointing was indeed better then originally supposed. The actual observation angle of the atmosphere depends on the aircrafts roll angle as well. The data with the roll angle were taken directly from the aircraft control. The accuracy of this angle was better then 0.05◦.
The observation in both side bands (alternately) requires very accurate po- sitioning of this mirror as well. A similar type of driving as for the turning 10.3 Radiometer calibration and operation control 125
60
50
40
30
20 % of measurement time
10
0 19.85 19.89 19.93 19.98 20.02 20.07 Elevation [deg]
Figure 10.4: The time distribution of the turning mirror position. In more then 99% of time is the mirror at the exact position or within 0.045◦ off the central position mirror was used for the movements of the rooftop mirror in the MPI. We also used a combination of a brushless DC motor and an optical encoder for this purpose. The accuracy of achieved positioning was better then 0.4 µm which was very good. b) Temperatures
Since the cabin conditions varied and changed relatively quickly, numerous temperatures had to be controlled. During operation of the radiometer ten different temperatures were observed and saved. Accuracy of all sensors was better then 0.2 K. Cabin pressure changed rapidly and was usually between 600 and 700 mb. Temperature of liquid nitrogen was therefore measured with two sensors placed in the cold load dewar. Two sensors measured also temperature of the absorber in the hot load. Temperature in the 4 cm-thick high-density polyethylene window changed with a high gradient. The outside temperature could fall below −60◦C and the cabin temperature raised above +25◦C. The window temperature was therefore measured with two sensors in 126 Signal down conversion and radiometer backend two different layers of the window. In both AOSs there were built-in sensors for monitoring of laser-block temperatures. Two additional sensors measured temperatures of cabin air and of the quasioptical front plate. The latitude and altitude of the aircraft were acquired using a standard GPS- receiver. The antenna of the receiver was fixed on an aircraft window. The data delivered by the GPS-receiver were saved in every calibration cycle.
10.3.3 Control software and AMSOS database a) Control computer and software
The software that controls processes in the radiometer was written by S. M¨uller,[47] in LabVIEW and under Linux as operating system. Modular features of LabVIEW allowed high flexibility and extended control over all processes. Both LabVIEW-based software and Linux showed very high reli- ability without any failures, either during laboratory tests or flights. Additional reliability was achieved using a Raid system with two hard discs operating simultaneously. In case of failure of one of the hard discs the other one continues operation without interrupting the measurement. For the on board operation this was an advantage, but we did not experience problems in the aircraft during flight campaigns. However, during ground-based mea- surements on Jungfraujoch in period March-May 2004, a hard disk crashed. This is an already known phenomenon for high-altitude sites, where hard disks crash probably due to low air density. At the beginning of May 2004 the primary hard disk crashed, but the radiometer continued operation with- out interruption until the end of the campaign. a) AMSOS database
A significant progress in data storage was made introducing the AMSOS- database (realised by D. Feist). The database is realised in mySQL. The spectra were directly recorded in sql format and immediately added to the data base after a day of measurements. The advantage of such data storage is really immense during retrieval process. The way the spectra can be sorted out from the database are manyfold: we can chose and integrate spectra depending on time they were recorded, on the flight altitude, the roll angle of the aircraft etc. Additionally, diverse flags can be placed in spectra in case of artifacts. All these features allowed a really dynamical integration. The AMSOS-database consist of five table structures. The table header 10.4 Aircraft window 127 contains the most important parameters around a spectrum: date and time of recording, altitude, latitude, longitude, roll angle, LO-frequency, ten tem- peratures from sensors etc. The tables level0 counts AOS F1 and level0 counts AOS E1 contain the raw data - the AOS counts from wide-banded Meudon-AOS (’F1’) and narrow-banded Elson-AOS (’E1’). The level0- offset AOS F1 and level0 offset AOS E1 contain the AOS-offsets that are recorded at the beginning of every measurement. The level0 frequency AOS F1 and level0 frequency AOS E1 contain channel frequencies of the AOSs. And, finally, level1 intensity AOS F1 and level1 intensity AOS E1 contain calibrated spectra, which are used for retrievals later on.
10.4 Aircraft window
As already mentioned, the atmosphere is observed through a specially de- signed aircraft window. During campaigns, a normal aircraft window was replaced by a high-density polyethylene window, transparent at microwave frequencies. However, it had a certain opacity which had to be considered in retrievals. We included it in the forward model. Brightness temperature of the observed spectrum after the window Bout is:
Bout = Bint + Bwin(Twin)(1 − t) (10.4) where Bin is the brightness temperature before the window and Bwin(Twin) is the brightness temperature of the window itself at a temperature Twin. The t is the window transparency. Let us remained that the window temperature is being measured with two sensors in two layers. Although the temperature gradient in the window was large during a flight, we considered the window as a single slab with an average temperature which was the mean temperature from two sensor. Therefore, the needed brightness temperature before the window is:
B − B (T )(1 − t) B = out win win (10.5) in t The window transparency was already determined to be 0.94 by L. Zalesak, [23]. We repeated the measurement of the window transparency using ad- ditional cold load as a source. The window was placed between the source and the radiometer input. Since the brightness temperature of the source was known (Bout), and Bin was measured by the radiometer, t was easily 128 Signal down conversion and radiometer backend calculated. The result was similar to the previous measurement, we obtained t = 0.941 which was further used in retrievals. The window reflectivity r can also be included in the Equation 10.4, as done by A. Murk for the submillimetre frontend, [24]. We tried to measure the reflectivity of the window, in a similar manner as characteristics of the λ/4-isolator, by moving the window in small steps over 1-λ-distance. By observing the phase of the returned signal, the real reflections could have been distinguished from the artifacts. However, this measurement did not give satisfactory results (r was too small) and the window reflectivity was let out from the forward model. Chapter 11
Publication III
An airborne radiometer for strato- spheric water vapor measurements at 183 GHz
V. Vasi´c,D. G. Feist, S. M¨uller and N. K¨ampfer
Submitted to IEEE Transactions on Geoscience and Re- mote Sensing, October 2004
129
SUBMITTED TO IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING 1 An airborne radiometer for stratospheric water vapor measurements at 183 GHz Vladimir Vasic,´ Dietrich G. Feist, Stefan Muller¨ and Niklaus Kampfer¨ Member, IEEE,
Abstract— The Airborne Millimeter- and Submillimeter Ob- this frequency are possible, but they are difficult and relatively serving System (AMSOS) is a total-power radiometer for observa- inefficient due to the high absorptivity of the tropospheric tion of 183.3 GHz water vapour rotational line, operated on board water vapor [11], [12]. An aircraft flying above the troposphere a Learjet aircraft of the Swiss Air Force. The neatly designed quasioptics provide a regular and narrow output beam with a half is therefore a much better platform for a 183 GHz-radiometer. power beam width angle of 1.2◦ and efficient sideband switching. It also provides a far better spatial coverage. Therefore, the A λ/4-quasioptical isolator is used for baseline reduction securing Airborne Millimeter- and Submillimeter Observing System attenuation of internal reflections by more then 30 dB. A low AMSOS was built to observe stratospheric water vapor at noise temperature of the ambient-temperature-operating system 183 GHz from a Learjet that belongs to the Swiss Air Force. (1900 K) and excellent target pointing (better then 0.1◦) provide a stabile duty cycle and reliable calibration. A good control over From the measured spectra, altitude profiles of water vapor the radiometer’s operational parameters, like system stability and from roughly 20 to 70 km can be derived along the flight track. system temperatures, and higher automatization were required The instrument has been used in seven yearly flight campaigns to come up with high demands of an on board operation. The since 1998, where an earlier version of the radiometer was retrieved profiles look typical for the region and time where they used between 1994 and 1998, [6]. A typical campaign took were observed. The winter arctic-profiles show an emphasized maximum at lower altitudes of around 30 km, while the profiles about one week and covered a maximum latitude range of ◦ ◦ from tropics have a maximum at much higher altitudes of 7 N to 90 N over Europe and Africa. approximately 45-50 km. When not in flight, the radiometer was placed at the ◦ Index Terms— Microwave remote sensing, quasioptics, water International Scientific Station Jungfraujoch (ISSJ, 46.5 N, ◦ vapor, stratosphere 7.5 E, 3580 m altitude) during three winters [12]. Due to the high altitude of the site, the low tropospheric opacity in winter allowed ground-based measurements at 183 GHz. The results I.INTRODUCTION of these measurements will be presented separately. Water vapor enters the stratosphere either directly from the troposphere or as a product of the methane oxidation cycle. II.TECHNICALDESCRIPTION The typical photochemical life time of H2O molecules in the The aircraft operation put some specific requirements on middle atmosphere is in the range of months to years which the design of the AMSOS radiometer. A compact design, makes water vapor an excellent tracer for atmospheric trans- simple operation and high reliability were basic requirements. port. Besides that, water vapor is an important greeenhouse In this chapter a detailed description of the radiometer is given gas. The interest for measurements of stratospheric water with special emphasis on the quasioptics, system stability, vapor has been growing in recent years, especially because radiometer control and system calibration. of the yet unexplained increase in stratospheric H2O, [1], [2]. Microwave radiometry offers a relatively simple way to A. Measurement principle derive altitude profiles of various stratospheric constituents including water vapor. The Institute of Applied Physics (IAP) The radiometer frontend of the AMSOS instrument is of the University of Bern, Switzerland, has built numerous based on a conventional uncooled heterodyne receiver using a microwave radiometers over the last years and operated them Schottky diode mixer. The atmosphere is observed through a from the ground, from aircraft and from space, [3], [4], [5], specially designed aircraft window made of polyethylene. The [6], [7]. One of the possibilities to measure water vapor is window is highly transparent at millimeter wave frequencies, from the ground at 22 GHz, [8], [9], [7], [10]. Radiometers with a measured transparency of 0.941 at 183 GHz. Figure 1 of this type have become relatively easy to build since many shows a schematic of the instrument components. The at- components can be bought off-the-shelf today. However, the mospheric signal is sent into the quasioptics by an elliptic 22 GHz line is weak and requires a long integration time in the mirror. This mirror is turned by a computer controlled motor range of several hours. There is a much stronger water vapor into three different positions that define the calibration cycle. rotational line at 183.31 GHz. Ground based measurements at For the calibration purposes we used two loads: an ambient- temperature hot load and a liquid-nitrogen cold load. Manuscript received 21st October 2004. This work has been supported The quasioptics define the shape of the beam, perform the through the Swiss National Science foundation under grant 200020-100153 side-band filtering and reduce baseline effects that originate and under grant 200020-100167 Authors are with the Institute of Applied Physics, University of Bern, from mismatches and reflections in the frontend optics. The Switzerland (e-mail: [email protected]) 183.31 GHz water vapor line is observed in the upper side SUBMITTED TO IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING 2
Atmosphere 1 2 Aircraft window Hotload
Mixer QUASIOPTICS θ focusing Turning SB filter mirror PLL LO Coldload d L1 L2 AOS AOS
Fig. 3. The two reflected signals have a path difference L1 + L2 which Mirror control SB control Computer introduces a phase difference Φ.
Backend
Fig. 1. The block scheme of the radiometer. The atmospheric signal is component) ratio providing low edge taper on the other [13]. directed and focused in the quasioptics and down-converted by a heterodyne The basic design of the quasioptics is shown in Figure 2. For receiver. The IF signal is analyzed in the two AOSs. beam launching and shaping we used a corrugated feed horn Aircraft window and two focusing mirrors: a parabolic one and an elliptic one. Between the two mirros a Martin-Puplett interferometer (MPI) W0 = 31mm acts as a sideband filter. A λ/4 quasioptical isolator suppresses Lambda/4 reflections that could lead to standing waves inside the quasi- Isolator optical path. The system layout and the component parameters MP interf. LO were calculated using the propagation of the basic mode of the Elliptic Gaussian beam. turning Absorber mirror Antenna 1) Suppression of baseline effects with a quasioptical iso- W = 23.3mm W0 = 5.5mm lator: Internal reflections can produce baseline ripple which significantly decrease the sensitivity of a radiometer. These W0 = 20.5mm Absorber reflections can be generated between the mixer and some other component standing perpendicular to the propagation direction. We tried a new method for baseline reduction using Parabolic mirror a quarter-wave plate that acts as a quasioptical isolator. The isolator consists of a reflecting metal plate and a grid Fig. 2. Scheme of the quasioptics. The beam-shaping section consist of a corrugated horn, a parabolic and an elliptic mirror. The MPI acts as a sideband in front of the plate at a constant distance d (see Figure 3). filter and a λ/4 isolator reduces baseline. An electromagnetic wave entering the isolator is polarized by the grid. The part of the signal with the electrical field vector parallel to the gird wires is reflected from the grid. The other band of the heterodyne receiver. In the lower side-band a part with the E-vector perpendicular to the wires goes through relatively weak ozone line at 175.45 GHz is visible. The the grid and is reflected by the metal plate. radiometer was built to observe both atmospheric species Since the second signal has a longer optical path a phase alternately by switching between the two side-bands. The delay Φ is introduced relative to the first signal that is reflected radio-frequency (RF) signal is down-converted by a sub- π by the grid. A phase difference of 2 produces a circular harmonically pumped mixer and the intermediate-frequency polarized output signal. After a reflection at a component (IF) signal is further amplified and analyzed in two acousto- standing perpendicular to the propagation axis and another optical spectrometers (AOS). The measured spectra are pre- passage through the isolator, the output signal becomes lin- processed and stored by the computer which also controls early polarized, however, this time orthogonal to the initial the calibration cycle, the sideband filter and other parameters one. Such a signal is not detected by the mixer. important for the radiometer operation. 2) The Martin-Puplett interferometer: The AMSOS ra- diometer was designed to observe two atmospheric species: B. Quasioptics water vapor at 183.3 GHz and ozone at 175.5 GHz. The spec- The quasioptics define the antenna pattern and feed the tral lines of the two species could be observed alternatively incoming radiation to the receiver. When the quasioptics for in the upper and the lower side band. When observing one the instrument were designed, two main goals had to be of these side bands, the other one had to be suppressed. A achieved: a narrow output beam with a half power beam width Martin-Puplett interferometer (MPI) is used in AMSOS for ◦ ΘHPBW = 1 and reduction of internal reflections that cause this purpose, Figure 2. so-called baseline. This however had to be realized taking into The Martin-Puplett interferometer (MPI) is a two beam consideration the limited aircraft cabin space on one side and polarization-rotating interferometer with a basic transfer func- a need for a good D/w (component diameter/beam size at the tion [14] of SUBMITTED TO IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING 3
E. Calibration cycle ¡ ¢ 2 π(z1 − z2) AMSOS is a total power radiometer calibrated with two PV out = A cos (1) λ loads. The turning mirror focuses the beam to three distinct positions: cold load (C), atmosphere (A), and hot load (H). where PV out is the output power of one polarization (for The calibration cycle was C-A-H-A-C. The cold load was a example vertical) and z1 and z2 are distances from the first and the second rooftop mirror to the polarizing grid. By changing CV-3 absorber soaked in liquid nitrogen in a special dewar. one of these distances the output characteristics change and a The boiling temperature of the liquid nitrogen depended on suppression of one of the two side bands can be achieved. In the cabin pressure and varied between approx. 74 K and 77 K AMSOS, this was done by moving one of the rooftop mirrors during the flights. Therefore we measured the temperature of with a computer-controlled motor. the absorber with two sensors. For the hot load we used a non-heated well-insulated CV-3 absorber at cabin temperature. Theoretically, the whole input signal in the MPI should go The temperature of the hot load was also measured with two to the output and none of it should return towards the source. sensors. However, reflection measurements of the AMSOS quasioptics In both cold and hot load the diameter of the absorber was [13] showed that this was not the case. In reality, a part of determined by the size of the beam radius at the absorber, very the signal reflected by the rooftop mirror returns in the same much like it was done for the other quasioptical components. polarization towards the input and causes internal reflections. The ratio D/w was kept above 4.6 to avoid spillover. The level of these reflections in the MPI can achieve up to -30 dB and they can seriously reduce the sensitivity of a radiometer when observing weak lines. In our case, however, F. Operation control the observed rotational lines were quite strong. Therefore using The space in the cabin of the Learjet aircraft was very an MPI was well founded, especially due to its ability to easily limited, thus making manual operation of the instrument switch between the two sidebands. difficult. Therefore, the operation of the radiometer had to be highly-automated, which was also useful for the ground-based operation at Jungfraujoch. Besides the spectra numerous pa- C. Down-conversion rameters were controled and recorded during the measurement: The corrugated horn receivers the RF signal and leads it to position of the turning mirror, side-band control, PLL stability a subharmonically pumped uncooled Schottky mixer made by of the local oscillator, GPS data and various temperatures. Virginia Diodes Inc. The phase-locked-loop (PLL) stabilized Since the cabin conditions varied and changed relatively local oscillator (LO) pumps the mixer with a 89.8 GHz quickly, ten different temperatures were observed and saved: signal. The second harmonic of the LO signal is used for two sensors in the hot load, two in the cold load, temper- the down-conversion of the atmospheric signal to a central atures of both AOSs, cabin temperature, temperature of the intermediate frequency (IF) of 3.7 GHz. The single-sideband quasioptics plate and two sensors in the aircraft window. noise temperature of the radiometer was around 1900 K. The temperature in the 4-cm-thick high-density polyethylene ◦ This was a good result for a mixer that operates at ambient window changed with a high gradient between −60 C outside ◦ temperature. Cryogenic operation of the mixer would have and +25 C inside. The window temperature was therefore exceeded the space and power limitations of the small aircraft. measured with sensors in two different layers of the window. The absolute accuracy of all temperature sensors was better than ±0.2 K. The data of the latitude and altitude positions D. Acousto-optical spectrometers of the aircraft were acquired using a standard hand held GPS receiver (Garmin GPS 12XL) with an external antenna The IF signal is amplified by two amplifiers and analyzed in attached to the inside of an aircraft window. The position two acousto-optical spectrometers (AOS). The first one, made and altitude measurements of this receiver were saved in by Meudon Observatory, Paris, has a bandwidth of 1 GHz with every calibration cycle. The time measurements were used to 1725 channels. The second one, made by Elson Research Lab, stabilize the PC’s internal clock. has a narrow bandwidth of 50 MHz with 2048 channels. Such The control software was written in Lab View under Linux high resolution of the narrow-banded AOS was required for as operating system. Both Lab View software and Linux retrieval of the water vapor content at the highest altitudes, showed very high stability and no failures. Additional reli- roughly above 60 km. ability was achieved by using a Raid system with two hard Both AOS were laboratory devices and not built for the discs operating simultaneously. In case of failure of one of rough operating conditions of an aircraft campaign. At the hard discs the other one would continue the operation without beginning of a flight the cabin temperature could be as low as interrupting the measurement. 0◦ C. Therefore, an additional automatically controlled heating was built around the laser blocks inside the AOS. It quickly III.RESULTS brought the AOS to their operational temperature while the aircraft reached its operation altitude. In earlier campaigns, a A. Beam size and shape lot of measurement time was lost because the AOS needed too To validate the theoretically calculated beam characteristics, much time to warm up. a series of laboratory tests were conducted. The measurements SUBMITTED TO IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING 4
−15 100 0 X−cut −20 −30 Y−cut −20 50 −5 −10
−3 −20 −30 −10 −30 0 −25 −20 −3 y [mm] −15 −30 −10 −20 −50
−30 Relative level [dB] −25 −30 Isolation [dB] −100 −30 −100 −50 0 50 100 −5 0 5 x [mm] Angle [deg] −35
(a) Radiometer output (b) X- and Y-cut isolator −40 theory
Fig. 4. The measured output diagram of the radiometer. The slight asymmetry 170 175 180 185 190 195 below -20 dB is supposed to come from the rooftop mirrors from the MPI Frequency [GHz]
50 fit: wo=27.38 mm Fig. 6. The measured characteristics of the isolator. Comparison with the 2 measurements theoretical cos Φ characteristic shows a good agreement.
45 beam was then fitted to the measured beam sizes. This is
40 illustrated in Figure 5. The fitted output beam had a beam waist of 27.4 mm which was less than the theoretically predicted 31 mm. The output 35 beam waist was large and its exact position was difficult to
Beam radius [mm] determine. To do that, a long series of scans in the area of the beam waist would have to be done. However, we found 30 the six scans to be enough to characterize the antenna pattern. ◦ The ΘHPBW of this synthesized output beam was 1.2 which
25 fulfilled the predefined criteria. The synthesized output beam 0 0.5 1 1.5 2 was used in the retrieval later on. Distance from the mirror [m]
Fig. 5. A Gaussian beam was fitted to the beam size of six planar scans of B. Performance of the quasioptical isolator the radiometer output beam The quasi-optical isolator only works perfectly at the central frequency where the phase difference is exactly λ/4. At other at 183 GHz were done in amplitude, phase and polarization frequencies, where the path difference between the two signals using a vector network analyzer from AB millimetre [15]. does not exactly correspond to λ/4, the suppression of the We measured the characteristics of every component at reflected signal is proportional to cos2 Φ. This characteristic relevant places inside the quasioptics [13]. The measured frequency dependence was also examined in the laboratory. horn antenna diagram and parabolic mirror output were in a The measurements of the isolator characteristics were done good agreement with the theoretical expectations. The copolar using the same vector network analyzer as above. In Figure diagrams had regular shapes down to -25 dB. The crosspolar 6 the theoretical and measured characteristics showed a good signal did not exceed the value of -20 dB below the copolar agreement. The reflected signal was attenuated by more than signal. The final component in the system that defines the 30 dB at the central frequency. output of the whole radiometer is the elliptic mirror. The In the laboratory tests the isolator performed very well. output of the radiometer was also scanned and is shown in However, after analysis of the measured calibrated spectra Figure 4. Again, the diagram had a regular shape down to - from the flight in November 2003, a relatively strong baseline 20 dB. However, it exhibited slight asymmetries along the x- was found in some of the spectra. An unusual effect was that and y-axis. This is better illustrated in the (b) part of the same the baseline came and went during a flight. We found that there figure showing the X- and Y -cuts of the output. This effect of was a correlation between the appearance of baseline and the asymmetry is supposed to come from the non-ideal behavior fluctuation of the cabin temperature. Further tests showed that of the rooftop reflectors in the Martin-Puplett interferometer. the frequency characteristic of the isolator was drifting with For technical reasons the measurements had to be done in the the change of the ambient temperature. The explanation was near field. that different materials were used in the first version of the In order to better characterize the radiometer antenna pat- isolator. The ring that held the grid was made of steel while the tern, six planar scans of the output beam at different distances reflector plate was made of aluminum. The different expansion off the elliptic mirror were done. The beam size (using 1/e coefficients of the two metals caused changes in the distance d criteria) was determined at each scan and an ideal Gaussian between the grid and the plate. In a laboratory test the distance SUBMITTED TO IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING 5
−2 60 10 ch 150 ch 1200 50 ch 1500 k
40 σ
−3 30 10
20 Allan−variance % of measurement time
10
−4 10 0 1 2 0 10 10 10 19.85 19.89 19.93 19.98 20.02 20.07 Integration time [s] Elevation [deg]
Fig. 7. The time distribution of the turning mirror position. In more than Fig. 8. The Allan-variance for the whole time of measurement of around 99% of time is the mirror at the exact position or within 0.045◦ off the central 6000 spectra. The optimal integration time lies about 9 sec. position −1 10 ch 150: stabile ch 1200: stabile d was changed by 1.2-1.3 µm by a temperature change of ch 1500: stabile 15◦ C. This caused a drift of the frequency characteristic of ch 150: warming phase ch 1200: warming phase almost 1.5 GHz. The typical changes of the cabin temperature k −2 ch 1500: warming phase during a flight were even larger. The cabin temperature varied σ 10 between 0◦ C (takeoff in the arctic) to almost 30◦ C (during the flight) and was difficult to stabilize. Therefore the holder plate had to be remade from the same steel as the grid ring. −3 10 Allan−variance C. Target pointing The elliptic mirror was turned by a computer-controlled brushless DC motor and the positioning of the motor axis −4 10 0 1 2 was determined by an optical encoder. Since the moment of 10 10 10 inertia of the mirror was relatively large, the positioning time Integration time [s] between the two positions could not be reduced below 1.3 s. Fig. 9. The Allan-variance for the measurement 500-6000 spectra (lines): One of the pre-conditions when designing the radiometer was the integration time when the AOS temperature is stable is up to 13 sec. a positioning accuracy of the mirror of better than ±0.1◦. For the first 500 spectra during the warming-up-phase (circles): the maximal integration time is significantly shorter, around 3.5 sec. The results from a three-day campaign in November 2003 showed an excellent positioning of the mirror (see Figure 7). It remained within ±0.045◦ around the central position in 99.3% that the gain remains stable, but also long enough so that of measurement time, which was better than planned. the statistical variations in the signal level out. The Allan- The actual observation angle of the atmosphere depended variance has become a standard method for determination of on the aircrafts roll angle as well. The data with the roll the heterodyne receiver gain stability and the length of the angle were taken directly from the aircraft’s inertial navigation integration time [16]. system. The accuracy of the angle was better than 0.005◦. A similar driving mechanism was used for the movement To determine the Allan-variance σk we did around 6000 of the rooftop mirror in the MPI. Again a DC-motor/encoder uncalibrated measurements with the wide-band spectrometer system showed an positioning accuracy better than 0.4 µm (in and a pre-integration time of 1.42 s (time needed to record comparison to a zero point determined by a reference switch) one spectrum). Figure 8 shows the Allan-variance for three which was very good. chosen channels out of the 1725 available. The figure shows that the optimum integration time was around 10 s, where σk has a minimum. This optimum time was, however, not the D. System stability same for all channels. The main sources of system instability are variations of the It is also interesting to consider the Allan-variance in the system gain due to amplifier fluctuations and the AOS thermal first part of the measurement when the temperature of the AOS instability. The system gain should remain stable during a has not been stabilized. calibration cycle. However, this depends on the length of Figure 9 shows the Allan-variance for the first 500 spectra the integration time τ. This time has to be short enough so which approximately corresponds to the first 20 minutes of SUBMITTED TO IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING 6
100 H O profiles: 19−2−2004 (north) to 24−2−2004 (south) latitude: 67N 2 latitude: 52N 90 50 latitude: 19N
80 45 70
60 40
50 35
40 Altitude [km] 30 Brightness temperature [K] 30
latitude: 67N 20 25 latitude: 52N latitude: 19N 10 a priori 182.8 183 183.2 183.4 183.6 183.8 20 Frequency [GHz] 2 3 4 5 6 7 8 9 H O Volume Mixing Ratio [ppm] 2 Fig. 10. Three spectra obtained at different latitudes: 67◦ N, 52◦ N and ◦ 19 N. The difference in the shapes of the arctic- and of the tropics-spectrum Fig. 11. Water vapor profiles retrieved from the spectra from the arctic, mid is obvious. latitudes and tropical latitudes. The profile from the arctic show a maximum at around 35 km altitutde, while the tropical profile has a maximum at around 55 km. There is no emphasized maximum in the mid-latitude profile. the measurement. The optimal integration time in that case profile: 67N was around 3.5 s. Such low value was due to temperature- 50 a priori dependence of the system gain in the heat-up phase. After- 1σ error bars wards, when the system gain was more stable, the optimal 45 integration time was around 13 s (see Figure 9). This com- parison of the Allan-variance for the two phases in the AOS- 40 heating was necessary because of the radiometer’s operating conditions. In this aircraft, with a typical flight time of 4- 35 5 hours, the heat-up-phase could not be avoided. Therefore, the pre-integration time for the Meudon-AOS in AMSOS was Altitude [km] 30 chosen to be 1.42 s.
25 E. Retrieved water vapor profiles 20 The end product of our data analysis are altitude profiles 1 2 3 4 5 6 7 8 9 10 H O Volume Mixing Ratio [ppm] of water vapor that are derived from the measured spectra. 2 The following profiles are examples from a flight campaign that took place in February 2004. The area covered in this Fig. 12. The profile from the arctic with error bars. campaign ranged from northern Scandinavia (around 67◦ N) over the Canary Islands to the African west coast (to 18◦ N). Figure 10 shows three typical spectra from the arctic arctic had a maximum at an altitude of around 35 km. In the (67◦ N), mid latitudes (52◦ N) and the tropics (19◦ N). upper part, above 40 km, the water vapor abundance decreased. All spectra were recorded at similar flight altitudes (between This corresponds to the trend of downward motions of the air 12600 m in Scandinavia and 13150 m in the south). Each masses during the arctic winter [19], [20]. On the other hand, spectrum was obtained by integrating 20 spectra of the broad- the profile from the tropics showed a maximum at a higher band AOS while the aircraft was flying level with roll angle altitude, around 45 km. At the mid latitudes there was no within ±0.1◦. The different shapes of the spectra, especially emphasized maximum between 30 and 45 km altitude. the ones from the arctic and from the tropics, are clearly Figure 12 shows the vertical H2O profile from the arctic visible. The arctic spectrum was recored on February 19, the with estimated error bars. OEM, like all other linear inversion mid-latitude spectrum on the February 21, and the tropical methods, requires a-priori information to provide meaningful spectrum on February 24, 2004. solutions. We used a water vapor profile from the U.S. standard atmosphere [21] to retrieve all profiles. We used the software package Qpack by [17] to retrieve profiles with the Optimal Estimation Method (OEM) [18]. This retrieval software allows a good characterization of IV. CONCLUSIONS instrumental parameters and artifacts and provides useful tools The refurbishment of our airborne radiometer AMSOS gave to automatize the retrieval process. us a chance to improve its performance and data quality and try The profiles of vertical water vapor distribution of the three new techniques at the same time. The main design goals were measurements are shown in Figure 11. The profile from the to improve the instrument parameters that have been found SUBMITTED TO IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING 7 to be critical for water vapor retrievals in earlier missions: a [2] S. J. Oltmans, H. Vomel,¨ D. J. Hofmann, K. H. Rosenlof, and D. Kley, narrow beam, effective side band suppression, standing wave “The Increase in Stratospheric Water Vapor from Baloonborne Frost- point Hygrometer Measurements at Washington, D. C., and Boulder, reduction, short integration time, stable pointing, good stability Colorado,” Geophysical Research Letters, vol. 27, no. 21, pp. 3453– under adverse operating conditions, and a robust calibration 3456, Nov. 2000. scheme. [3] D. G. Feist, C. P. Aellig, N. Kampfer,¨ P. M. Solomon, J. W. Barrett, S. Zoonematkermani, P. Hartogh, C. Jarchow, and J. W. Waters, “Val- The redesign of the quasioptics fulfilled several of the goals idation of stratospheric ClO measurements from the Millimeter-wave above. It provides a narrow beam with an antenna pattern Atmospheric Sounder (MAS),” Journal of Geophysical Research, vol. that turned out better than expected in the laboratory measure- 105, no. D7, pp. 9053–9062, 2000. [4] Y. Calisesi, “The Stratospheric Ozone Monitoring Radiometer ments. The side band filter was left mostly unchanged since SOMORA: NDSC Application Document,” Institut fur¨ angewandte there was little need for improvements. The most experimental Physik, Universitat¨ Bern, Bern, Switzerland, IAP Research Report 2003- component was the quasi-optical isolator which worked well 11, July 2003. [5] D. Gerber, I. Balin, D. Feist, N. Kampfer,¨ V. Simeonov, B. Calpini, and in the laboratory but caused unexpected problems during the H. van den Bergh, “Ground-based water vapour soundings by microwave first test flight in November 2003. Fortunately, these problems radiometry and Raman lidar on Jungfraujoch (Swiss Alps),” Atmospheric could be solved before the first major flight campaign in Febru- Chemistry and Physics Discussions, vol. 3, pp. 4833–4856, Sept. 2003. [6] R. Peter, “Stratospheric and mesospheric latitudinal water vapor distri- ary 2004. Switching to a passive calibration hot load without butions obtained by an airborne millimeter-wave spectrometer,” Journal internal heating greatly simplified the calibration process. At of Geophysical Research, vol. 103, no. D13, pp. 16 275–16 290, July the same time, calibration accuracy was improved by using 1998. [7] B. Deuber, N. Kampfer,¨ and D. G. Feist, “A new 22-GHz Radiometer more and better temperature sensors. The pointing accuracy, for Middle Atmospheric Water Vapour Profile Measurements,” IEEE which is a large error source in the water vapor retrievals, Transactions on Geoscience and Remote Sensing, vol. 42, no. 5, pp. was greatly improved through a new motor control system. 974 – 984, May 2004. [8] G. E. Nedoluha, R. M. Bevilacqua, R. M. Gomez, D. L. Thacker, W. B. However, since the new quasi optics required a much heavier Waltman, and T. A. Pauls, “Ground-based measurements of water vapor elliptic mirror, the pointing time also increased by a factor of in the middle atmosphere,” Journal of Geophysical Research, vol. 100, 4-5, thus reducing the duty cycle of the instrument effectively no. D2, pp. 2927–2937, 1995. [9] P. Forkman, P. Eriksson, and A. Winnberg, “The 22 GHz radio-aeronomy by a factor of 2. Fortunately, the overall system stability receiver at Onsala Space Observatory,” Journal of Quantitative Spec- and improved noise temperature were able to compensate the troscopy & Radiative Transfer, vol. 77, no. 1, pp. 23–42, Feb. 2003. resulting loss in net measurement time. The flight speed of [10] C. Seele and P. Hartogh, “A case study on middle atmospheric water vapor transport during the February 1998 stratospheric warming,” Geo- the Lear jet lies normally between 700 km/h and 900 km/h. physical Research Letters, vol. 27, no. 20, pp. 3309–3312, Oct. 2000. Integrating 20 spectra, we got a spatial resolution of around [11] J. R. Pardo, J. Cernicharo, E. Lellouch, and G. Paubert, “Ground-based 150 km. measurements of middle atmospheric water vapor at 183 ghz,” Journal of Geophysical Research, vol. 101, no. D22, pp. 28 723–28 730, 1996. The individual water vapor profiles that have been derived [12] A. Siegenthaler, O. Lezeaux, D. G. Feist, and N. Kampfer,¨ “First from the measured spectra of the first flight campaign look water vapor measurements at 183 GHz from the high alpine station typical for the time and region where they were observed. Re- Jungfraujoch,” IEEE Transactions on Geoscience and Remote Sensing, vol. 39, no. 9, pp. 2084–2086, Sept. 2001. trieval of profiles on a larger scale and an extensive validation [13] V. Vasic,´ N. Kampfer,¨ and A. Murk, “Quasioptical characterisation of a of the profiles is still going on. mm-wave receiver for atmospheric remote sensing,” Optics and Lasers Stratospheric water vapor measurements are still very sparse in Engineering, 2004, in press. [14] D. H. Martin and E. Puplett, “Polarised interferometric spectrometry for and we are confident that our results will be very useful for the the millimetre and submillimetre spectrum,” Infrared Physics, 1970. scientific community, for example for satellite or model vali- [15] M. G. P. Goy, S. Caroopen, “Vector Measurements at Millimeter and dation as well as trend analyses. The yearly flight campaigns Submillimeter Wavalengths: Feasibility and Applications,” in 2rd ESA Workshop on Millimetre Wave Technology and Applications: Antennas, will be continued and possibly extended during the next years. Circuits and Systems, May 1998, pp. 89–94. All future activities will be coordinated with the European [16] P. Hartogh, “High Resolution Chirp Transform Spectrometer for Middle SCOUT-O3 project and other international campaigns. Atmospheric Microwave Sounding,” in Satellite Remote Sensing of Clouds and the Atmosphere II, J. D. Haigh, Ed., vol. 3220. SPIE proceedings, 1998, pp. 115–124. [17] P. Eriksson, C. Jimenes,´ and S. A. Buehler, “Qpack, a general tool ACKNOWLEDGMENT for instrument simulation and retrieval work,” Journal of Quantitative Spectroscopy & Radiative Transfer, 2004, in press. This work has been supported through the Swiss National [18] C. D. Rodgers, Inverse Methods for Atmospheric Sounding: Theory and Science foundation under grant 200020-100153 and under Practice. New Jersey: World Scientific, 2000. grant 200020-100167. We would like to thank Swiss Air Force [19] W. J. Randel, F. Wu, J. M. Russell, A. Roche, and J. W. Waters, “Seasonal Cycles and QBO Variations in Stratospheric CH4 andH2O and especially their pilots for the support during this project. Observed in UARS HALOE Data.” Journal of Atmospheric Sciences, Thanks are due to the British Atmospheric Data Centre for vol. 55, pp. 163–185, Jan. 1998. providing access to the Met Office Stratospheric Assimilated [20] D. G. Feist, V. Vasic,´ and N. Kampfer,¨ “Changes in the distribution of stratospheric water vapor observed by an airborne microwave radiome- Data that we used in the retrieval. ter,” in Proceedings of the 16th ESA Symposium on European Rocket and Balloon Programmes and Related Research, B. Warmbein, Ed., no. SP-530. St. Gallen, Switzerland: ESA Publications Division, ESTEC, REFERENCES Nordwijk (NL), June 2003, pp. 401–404. [21] U.S. Committee on Extension to the Standard Atmosphere, U.S. Stan- [1] R. M. Bevilacqua, M. E. Summers, D. F. Strobel, J. J. Olivero, dard Atmosphere, 1976. Washington, D.C., U.S.A.: U.S. Government and M. Allen, “The seasonal variation of water vapor and ozone in Printing Office, 1976. the upper mesosphere - implications for vertical transport and ozone photochemistry,” Journal of Geophysical Research, vol. 95, pp. 883– 893, Jan. 1990. SUBMITTED TO IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING 8
Vladimir Vasic´ obtained a M.Sc. in electrical en- gineering (electronics and telecommunications) at the at the Faculty of Electrical Engineering, Uni- versity of Belgrade, Serbia in 1999. Since 2001 he has been working on his Ph.D. at the Institute of Applied Physics, University of Bern, in the fields of microwave remote sensing of stratospheric water vapour and millimeter-wave optics.
Dietrich G. Feist studied physics at the Ruprecht- Karls-Universitat¨ in Heidelberg, Germany, and re- ceived a Master’s degree in 1994. In 1995, he started his work on his Ph.D. thesis at the University of Bern, Switzerland, and finished in 1999. His main research interests are measurements of stratospheric water vapour from the ground and from aircraft as well as microwaver spectroscopy and radiative transfer simulation.
Stefan Muller¨ studied physics at the University of Bern, Switzerland where he received a Masters degree in 2004. Afterwards he started work at the Institute of Applied Physics, University of Bern towards his Ph.D. in microwave remote sensing of the atmosphere.
Niklaus Kampfer¨ studied physics and astronomy at the University of Bern. He got a master in physics in 1979 and a Ph.D. in 1983 for the analysis and interpretation of solar flares. Thereafter he changed his field of interest and pursued research in microwave radiometry of the atmosphere where he was involved in the development of the Millimeter waver Atmospheric Sounder, a space shuttle experiment. Since 1994 he is a professor for applied physics and head of the microwave department at the University of Bern. His research interests are microwave remote sensing of the atmosphere and optics in the millimeter and submillimeter range. Part III
Inversion and Results of Stratospheric Water Vapour Distribution
139 Chapter 12
Inversion
12.1 Introduction to inversion process
The result of measurements with AMSOS radiometer is an emission spec- trum from the atmosphere. The spectrum itself, although being a result of the state of the atmosphere during observations, as well as instrumental ar- tifacts, is not what we want as a final product. We are interested only in the information ’printed’ in the spectrum: the state of the atmosphere at the time of measurements, more precisely in the vertical distribution of water vapour molecules. In order to obtain this vertical distribution, we have to solve the inverse problem: to get a vertical H2O-profile from the measured spectrum. This is only possible, if we know relationships between the quan- tity to be retrieved and the measured signal. This relationship is known as the forward model:
y = F (x) (12.1) where y is a vector of the measured spectrum with length m, and x is the vertical distribution of the quantity to be retrieved, with length n. In our case it is water vapour. The forward model presented by Equation 12.1 is indeed an ideal case: the observed spectrum depends only on the vertical distribution of water vapour. In other words, in order to apply such a forward model, we have to have an ideal instrument which does not influence the spectrum. This is, unfortunately, not the case in reality. Another deviation from the ideal forward model are our estimates of atmospheric state parameters, for instance absorption coefficients or temperature and pressure profiles. Therefore, we have to introduce these effects in our forward model:
140 12.1 Introduction to inversion process 141
y = F (b, x) + y (12.2) where b is a vector which contains model parameters (observation angle, temperature and pressure profiles, spectral parameters, line shape), as well as instrumental parameters (sideband filter, attenuation by the aircraft win- dow, baseline etc.) and y is measurement error (due to thermal noise, for instance).
In a surrounding of an atmospheric state x0, it is possible to linearise the forward model function using the Taylor’s expansion:
∂F y = y + | = y + K (x − x ) (12.3) 0 ∂x x0 0 x 0 The rows of the matrix K are called weighting functions. They show what influence a change of the atmospheric state xj has got on the signal yi at a certain frequency fi. Therefore the elements of the weighting function matrix are defined as:
∂yi Kij = |x0 (12.4) ∂xj The goal of the inverse model is indeed to solve x. But, the inverse problem is much more difficult than the forward model. The linearised equation system is often both under and over-determined and F is not a bijective function. Therefore a direct solution of the inverse problem does not exist and an esti- mation of the atmospheric state xˆ has to be made. The Optimal Estimation Method (OEM) [48] has become a widely used inversion technique. It of- fers a better control over the inversion process and error budget. In OEM we assume that the a priori state of the atmosphere is known before doing a retrieval, as well as an a priori-covariance-matrix Sa. Using these infor- mation, as well as measurement vector y and the covariance matrix Sy, the OEM tries to get the most probable solution of x by minimising the so-called cost-function χ2, [18]:
2 T −1 T −1 χ = y − F(x) Sy y − F(x) + (x − xa) Sa (x − xa) (12.5) The χ2 is a cost-function for a weighted least-square fit of the measurement function parameters, together with weighted least-square fit of the same pa- rameters of the a priori profile. In order to minimise the χ2 we require:
∂χ2 = 0 (12.6) ∂x 142 Inversion
This leads to an approximate solution of the wanted atmospheric state xˆ:
ˆx = xa + Dy y − y0 − Kx(xa − x0) (12.7) where
T T −1 Dy = SaKx (Sy + KxSaKx ) (12.8)
The columns of Dy are called contribution functions. Contribution functions show the sensitivity of the retrieved profile xˆ to the measurement y. They represent indeed a generalised inverse of weighting functions Kx. Combining (12.10) and (12.3) we get the following expression:
ˆx = xa + DyKx(x − xa) = xa + A(x − xa) (12.9)
The matrix A = DyKx is called averaging kernels matrix. The rows of this matrix represent the sensitivity of the retrieval ˆx to the changes in the ∂ˆxi true profile x,Aij = . The averaging kernels matrix A is a convolution ∂xj of Kx which determines how well the measurements can be predicted given the model parameters, with Dy, which determines how well the true model parameters can be resolved when the measurement is given, [49]. This way we can obtain an approximate solution xˆ for the atmospheric state x. However, this is only valid in a surrounding of the state x0, where the errors of the Taylor-linearisation are negligible. For non-linear problems, where the deviation from the linearisation around the state x0 is larger, which is the case with H2O, the solution can be found using Gauss-Newton iterations. First we obtain one approximation of xˆ, which is used as the reference profile in the next iteration. The n+1-st iteration towards the solution of the wanted atmospheric state is:
ˆxn+1 = xa + Dy,n y − F(ˆxn) − Kx,n(xa − ˆxn) (12.10) ∂F T T −1 with Kx,n = ∂x |ˆxn and Dy,n = SaKx,n (Sy + Kx,nSaKx,n ) . Normally, the iteration process starts taking xn=0 = xa. In every following iteration xn is replaced by xn+1, but xa must be kept unchanged until the end of the retrieval. Otherwise, the solution tends to converge and oscillates around the fictive true state in infinite loops. As an a priori profile is usually taken a realistic state of the atmosphere, for instance, existing atmospheric models, such as US standard atmospheres, MODTRAN etc. Detail information (on which this section was mainly based) on OEM, retrieval parameters, error characterisation and retrieval characterisation can be found in Rodgers’ book, [48]. 12.2 Forward model: ARTS; inversion: Qpack 143
12.2 Forward model: ARTS; inversion: Qpack
As the main activity of the microwave group of the IAP Bern is passive remote sensing of the atmosphere, inversion has been widely used in our department. Different authors have used their own retrieval routines for dif- ferent instruments, [49, 50, 24, 51, 52, 53, 54]. Although several radiometers work similarly, there was no standardised inversion method and software that could comprehend various instruments, their properties and artifacts. The most often used method was though the OEM. An automatisation of the retrieval process, and a modular software that includes forward modelling as well as inversion, would certainly be an advantage. Such software packages have been developed in recent years, firstly in a close cooperation between the University of Bremen and Chalmers Institute of Technology, and further also by various groups under the GNU Licence. The forward model soft- ware is called ARTS [16, 55] and the inversion software is Qpack [56]. We decided to switch from our earlier retrieval to ARTS/Qpack, for several rea- sons. Firstly, Qpack allows good instrumental characterisation. Secondly, retrieval with Qpack is modular, changes in model or instrumental parame- ters can be done efficiently and simply. Thirdly, Qpack is highly flexible and retrievals can be automatised to a high extent. ARTS is a software for atmospheric radiative transfer simulations. The number of instruments and observation geometries has been growing in re- cent years. For data analysis of these numerous sensors, a modular and fast forward model was needed. That pushed the authors [16] to develop a forward model able to comprehend different observation platforms (together with re- trieval software Qpack) and that would be fast and efficient. The ARTS allows quick and user-friendly changes of model parameters - PTZ profiles, platform altitude, observation angle, line shape, or spectral catalogues. At the present one can choose between ARTS internal spectral catalogue, HI- TRAN, JPL or Myran spectral catalogues. Also, continuum absorption can be calculated according to several models. The overall application of ARTS is relatively simple and logical, with output data saved in the own ’arts’ for- mat. The AMI (ARTS Matlab interface) is a set of Matlab-routines that make usage of ARTS very efficient. Qpack is the inversion software, that uses ARTS as forward model. The two softwares are closely linked. One of the major advantages of Qpack is good instrumental characterisation. Qpack allows implementation of the real, measured antenna pattern, sideband suppression characteristics, mixer’s down conversion, AOS’s channel function. All these parameters are stored 144 Inversion in separate files in ’arts’ format, which are easily read by ARTS or by the user. After a possible change of some parameter or observation geometry (in our case, for instance, the roll angle) Qpack simply and time-efficiently recalculates sensor transfer matrix H. Basically, it is possible to automatise the retrieval process so much that it can work automatically in our case for every flight altitude and roll angle. Another advantage of Qpack is its flexi- bility with input parameters. The input parameters, including instrumental or model parameters, or covariance matrices can be defined on separate, not necessarily compatible grids. For instance, PTZ profiles can be given on a much more (or less) dense pressure grid than e.g. a priori profile. Qpack does the appropriate interpolation of all parameters, so that the actual ma- trices and vector formats agree. This is a considerable advantage for the end-user. For a definition of covariance matrices, the user has to create a file with the input axis (pressure, frequency, altitude etc.), known diagonal elements and correlation lengths. Qpack interpolates the rest and calculates the covariance matrix automatically.
AMSOS-modeling for Qpack
Before doing the actual retrieval, the radiometer parameters had to be defined as well. For the antenna diagram, we used the synthesised output beam pattern as shown in Figure 5.14, Chapter 5.2. One of the biggest problems, that we became aware unfortunately only after the measurement campaigns, was the sideband filter adjustment. For the mission in November 2003 the sideband filter was aligned in the laboratory using a transmitter of the ABmm network analyser. The sideband suppression of the opposite sideband both in upper-sideband- and lower-sideband-operation looked quite good, with around 20 dB attenuation. However, after the missions, we found out that a small ozone line was visible in the upper sideband. We did the test with another transmitter that was placed in the far field, and saw an effect where the lower side band was imaged in the upper sideband. More accurate tests showed that the suppression of the lower sideband was only 5-6 dB. The sources of these problems are still being investigated. Anyway, we had to retrieve these spectra and we needed the sideband-filter characteristic. The measured characteristics was fitted with the corresponding ideal function of the MPI, Equation 8.1. The fit was done because the noise-like fluctuations of the real (measured) characteristic were too strong. Figure 12.1 shows the function of the sideband filter which is used in retrievals. For the channel response in the backend, we used measurements of A. Murk, 12.3 Validation of retrievals with Qpack 145
1
0.9
0.8
0.7
0.6
0.5
Filter function 0.4
0.3
0.2
0.1
0 170 175 180 185 190 Frequency [GHz]
Figure 12.1: The characteristics of the sideband filter (upper sideband oper- ation) during the measurement campaigns in November 2003 and February 2004. Due to problems by the setup, the lower sideband was attenuated by only 3-4 dB
[24]. He measured the channel response for both Meudon AOSs that have been operated at IAP, one of them being used in AMSOS. A Gaussian fit of the channel response is used in retrievals. The agreement between the measured values and the Gauss-fit were very good. The other instrumental parameter needed for the retrieval were written in the appropriate files during the execution of the retrieval routine. The spectrum to be inverted is read from the database, with all necessary parameters - flight altitude, observation elevation, frequency vector, latitude, longitude and time of measurement, temperatures of the aircraft window etc. Before doing the actual retrieval, all these parameters were stored in files, that were later read by Qpack. This simplified and automatised the retrieval process.
12.3 Validation of retrievals with Qpack
In order to prove the accuracy of retrievals with Qpack, we did a series of re- trieval tests. Firstly, an artificial spectrum was synthesised with ARTS for a 146 Inversion
given atmospheric H2O vertical distribution (for a so-called ’true-state’ pro- file), given instrumental and climatological parameters. More precisely, the spectrum was generated from Qpack, which was able to call ARTS-functions. Afterwards, noise was added and the spectrum was retrieved by Qpack with the same climatological and instrumental parameters. The retrieved profile was then compared with the ’true-state’ profile.
1 10 a priori true state retrieved 1σ errors
2 10 Pressure [Pa] 3 10
4 10 0 1 2 3 4 5 6 7 8 9 H O Volume Mixing Ratio [ppm] 2
Figure 12.2: The ’true-state’ profile and the retrieved profile for the simplest simulation of AMSOS-retrieval. An ideal sideband filter was assumed, and no baseline added to the simulated spectrum a) Model parameters and ’true-state’ profiles
As ’true-state’ profiles we used the global monthly mean stratospheric water vapour distributions (based on UARS MLS and HALOE climatology) by William Randel, [57]. These profiles are available for twelve months and for latitudes from 80◦S to 80◦N. The advantage of using these profiles was twofold. Firstly, they were realistic profiles, so that expected scenarios could be tested. Secondly, the variety of profile shapes was also very useful to test the retrieval reactions on changes and to observe the retrieval parameters at the same time. The profiles are available for an altitude range from approx. 12.3 Validation of retrievals with Qpack 147
18 to 60 km. We interpolated these profiles below and above these altitudes to the U.S. standard profile, and finally put them on points of the U.S. standard pressure grid.
4
3
2
1
0
Residual [K] −1
−2
−3
−4 182.8 183 183.2 183.4 183.6 183.8 Frequency [GHz]
Figure 12.3: Residuals for the simplest simulation - ideal sideband filter and no baseline
As PTZ profiles we used the U.S. standard values, both for synthesis of the spectrum and for the retrieval later on. As a priori profile we also used the
U.S. standard H2O-profile. The used retrieval pressure grid had a resolution of around 2 km. The a priori-covariance matrix was self-defined, with diag- onal elements ranging between approx. 40% deviation from a priori in the altitude range 25-40 km, to roughly 70% below and above these altitudes. The measurement noise covariance matrix was recalculated for each spec- trum. The spectrum was divided into 20-30 parts, and the noise standard deviation was calculated for each part giving the elements of the noise covari- ance matrix. The observation geometry was a realistic one, with an assumed flight altitude of 12000 m and an observation elevation of 20◦. The fitted AMSOS antenna pattern was used, as described earlier. The same way we used the real backend characteristics - the channel response and a frequency vector from a real measurement. b) Case I: ideal radiometer 148 Inversion
The first test was done for a relatively ’simple’ case, assuming an ideal side- band filter and no baseline. The artifical sideband filter was created to have a factor 1 in the upper sideband and -40 dB otherwise. The ’true-state’ profile was the mean value for October and 68◦N latitudes. Figure 12.2 shows the ’true-state’ profile, retrieved profile, as well as the a priori profile. In the whole altitude range (on the plot approx. 16-64 km) the agreement between the retrieved profile and the ’true-state’ profile was very good, with differ- ences not exceeding 5%. Figure 12.3 shows residuals, which was practically only the introduced noise. In the retrieval, we did only the sine-baseline-fit (SINFIT option of Qpack). This was the case because the only known base- line effect in real measurements with AMSOS was a sinusoidal baseline that came from reflections (either in the optics between the mixer and the win- dow or in the cable connecting the frontend and backend - both path lengths being almost exactly 2 m). c) Case II: radiometer with non-ideal sideband filtering
1 10 a priori true state retrieved 1σ errors
2 10 Pressure [Pa] 3 10
4 10 0 1 2 3 4 5 6 7 8 9 H O Volume Mixing Ratio [ppm] 2
Figure 12.4: The ’true-state’ profile and the retrieved profile for the second simulation of AMSOS-retrieval. The real sideband filter was used and no baseline used 12.3 Validation of retrievals with Qpack 149
100 simulated 90 fitted corrected 80 baseline
70
60
50
40
30 Brightness temperature [K] 20
10
0 200 400 600 800 1000 1200 1400 1600 AOS channels
Figure 12.5: The simulated spectrum to be retrieved (blue, almost covered by red), corrected spectrum (red), fitted (the last iteration of the retrieval process, green) and found baseline (bright green/blue) for the real sideband filter and no baseline. On the right side of the spectrum the ozone line is visible
The second test was done for a more realistic situation, with the real sideband filter, as it was in the missions in November 2003 and February 2004 and is shown in Figure 12.1. We kept the same ’true-state’ water vapour-profile. Since the suppression of the lower sideband was not ideal, a ’true-state’ profile for ozone was also required (for the 175.45 GHz ozone line). We took an ozone profile in the same manner as for water vapour from Randel-climatology, for the same latitude and month. As a priori ozone profile we took the U.S. standard profile again. This test was very important to see how the retrieval would react on the ozone line at the wing of the spectrum. This was a simulation of a real AMSOS measurement from November 2003 and February 2004, however without baseline. Once again, the retrieved profile corresponded very well to the ’true-state’ profile, within 5%, as shown in Figure 12.4. Figure 12.5 shows some of re- trieval results. The retrieval fitted the spectrum well, and the baseline found by Qpack was very close to zero, as expected. Residuals looked quite the 150 Inversion same as in Figure 12.3. The result of this test means that even with a prob- lematic sideband filtering, Qpack was able to retrieve water vapour profiles within more then 5% accuracy. The simulation of the weak ozone line (from the ozone a priori profile) was good enough not to influence retrieval of the strong water vapour line. The same tests were repeated for numerous differ- ent ’true-state’ profiles, and retrievals were always within an accuracy of 5%, at least for an altitude range of 18-50 km.
simulated 25 fitted corrected baseline 20
15
10
5 Brightness temperature [K]
0
1350 1400 1450 1500 1550 1600 1650 1700 AOS channels
Figure 12.6: Zoomed right part of the spectrum from Figure 12.5. The ozone line is well fitted and the overall fit of the spectrum is very good d) Case III: realistic radiometer with baseline
The next step in the retrieval test was to introduce a baseline. Since the AMSOS-baseline as observed in the two measurement campaigns had a clear sinusoidal form, a similar baseline was introduced in the simulated spectra. The baseline was created by adding three sinusoidal signals with a zero mean value, a random amplitude (between 0 and 5 K) and a random phase. The number of periods over a 1 GHz wide spectrum was random between 10 and 13 for every sine-wave, which was close to real AMSOS-measurements. In Figure 12.7 we see that the retrieval was good, although a strong sinusoidal baseline was introduced. Figure 12.9 shows how well the baseline was fitted by Qpack. Figure 12.8 shows the simulated, corrected and fitted spectrum, together with the fitted baseline. The same test was repeated for numerous 12.3 Validation of retrievals with Qpack 151
1 10 a priori true state retrieved 1σ errors
2 10 Pressure [Pa] 3 10
4 10 0 1 2 3 4 5 6 7 8 9 H O Volume Mixing Ratio [ppm] 2
Figure 12.7: The ’true-state’ profile and the retrieved profile for the third simulation of AMSOS-retrieval. The real sideband filter was used and a synthesised baseline
’true-state’ profiles, and more importantly, for numerous simulated baselines. Qpack was always able to fit baseline very well. However, the SINFIT option of Qpack was only available after September 2004. Before that, we tried a sine-fit using FFT analysis. The FFT analysis of residuals was done and first several sinusoidal baselines were detected and afterwards subtracted from the spectrum. The corrected spectrum was retrieved, and the resulting profiles were quite good in several tests we did. However, the introduction of the SINFIT option in Qpack brought a more accurate sinusoidal baseline fit and an appropriate error budget analysis. Since the Qpack-fit needs approximate periods of baseline to be fitted, we kept the FFT analysis to determine base- line periods. They were further submitted to Qpack in order to make the SINFIT more accurate. 152 Inversion
100 simulated 90 fitted corrected 80 baseline
70
60
50
40
30 Brightness temperature [K] 20
10
0 200 400 600 800 1000 1200 1400 1600 AOS channels
Figure 12.8: The simulated spectrum to be retrieved (blue), corrected spec- trum (red), fitted (the last iteration of the retrieval process, green) and base- line found by Qpack (bright green/blue) for a realistic situation - real side- band filter and baseline
4 simulated 3 fitted
2
1
0
−1
−2 Brightness temperature [K] −3
−4 200 400 600 800 1000 1200 1400 1600 AOS channels
Figure 12.9: The synthesised baseline introduced in the spectrum and the baseline found by Qpack. The agreement between the two is very good Chapter 13
Measurement campaigns and results
13.1 Ground-based measurements
The radiometer is normally operated on board a Learjet of the Swiss Air Force during one week a year. At other times, the radiometer was placed at the ISS Jungfraujoch (46.5◦ N, 7.5◦ E, 3580 m a.s.l.) during three winters, [58]. Due to the high altitude of the site, atmospheric conditions (low tro- pospheric opacity) in winter allow ground-based measurements at 183 GHz. Statistically, in approximately 10% of time in winter the tropospheric trans- mittance was above 0.3, which was good enough to retrieve H2O profiles. A validation campaign of stratospheric water vapour measurements LAUTLOS was held in February 2004, which delayed placing AMSOS on Jungfraujoch. The results of the ground based measurements will therefore not be presented in this thesis. Due to the late start of measurements (April 2004), very few spectra were recorded at a good atmospheric transparency.
13.2 Airborne measurements
13.2.1 Test campaign, November 2003
The work on the radiometer was finished in late summer 2003 and as a preparation for an important international campaign (LAUTLOS/WAVVAP, February 2004) we conducted a test flight between 18th and 20th November 2003. The flight track covered the area form southern Scandinavia (57◦N)
153 154 Measurement campaigns and results to Gran Canaria (26◦N) and along the African coast to 22◦N. Integrating 20 spectra (around 5-6 min) we got a latitude resolution of 1◦ (∼ 100 km).
18th and 19th November 2003 55 a priori AMSOS, 55o N 50 AMSOS, 23o N
45
40
35 Altitude [km]
30
25
20 0 1 2 3 4 5 6 7 8 9 H O Volume Mixing Ratio [ppm] 2
Figure 13.1: Two profiles from the test-mission in November 2003. They are typical for the time of year and latitudes where they were observed
We present two representative profiles from this mission. Figure 13.1 shows the northernmost (55◦N) and the southernmost profile (23◦N). The differ- ences in their shapes are obvious, and they are typical for the time of year and latitudes where they were recorded, [57]. Despite the very successful tests of retrievals with Qpack/ARTS, the inversion of real spectra obtained during the two campaigns did not work as expected. Some features worked quite well, for instance, fitting of the sinusoidal base- line. We applied the same covariance matrices as in the tests, however, the obtained profiles (example: Figure 13.1) always showed a very strong mini- mum at an altitude of around 20 km. In the tropics, such low values could have probably been explained by a high hygropause, but in the arctic the hygropause was at least 7-8 km lower. As these deviations were at lower altitudes and looked always very similar, we supposed that a problem might have been at the spectrum wings, probably connected with the sideband fil- tering and the ozone line in the spectrum. However, this was not the case, 13.2 Airborne measurements 155 the retrieval worked well despite these problems and residuals were always in a range of ± 1K. We discovered that averaging kernels had a strong peak at the lowest altitudes, indeed at the point of the pressure grid just above the flight altitude. This problem is still being investigated. Therefore, the results presented here are a β-version. The retrieval has to be investigated in detail, and afterwards a re-retrieval of the spectra will be done.
13.2.2 LAUTLOS/WAVVAP campaign, February 2004 The LAUTLOS/WAVVAP campaign (Lapbiat Upper Tropospheric Lower Stratospheric Water Vapour Validation Project) took place in Sodankyl¨a in Finland (67◦N), Ny Alesund (Spitsbergen) and Lindenberg (Germany) between 29th January and 28th February 2004.
Flight 17−02−2004 18:00:59 − 19:21:30 Balloon start: 17−02−2004 17:45:02 70 Rovaniemi Sodankyla LearJet AMSOS Balloon ascent 69 Balloon descent
68
67 Latitude [°]
66
65
64 22 23 24 25 26 27 28 29 30 Longitude [°]
Figure 13.2: The flight route on 17th February 2004. The aircraft flew around predicted balloon’s trajectory in several loops, sometimes at different altitudes. The other flight routes looked quite similar
The goal of the campaign was an inter-comparison of balloon-borne water vapour probes, as well as comparison of these probes with other techniques (microwave radiometers). There were several institutes involved with dif- ferent types of sensors: Vaisala (types RS-80, RS-82, RS-90, that measure 156 Measurement campaigns and results the dielectric constant of a polymer), Snowwhite (frost point mirror, [59]), FLASH-B (Lyman-α-probe, [60]) and NOAA (frost point mirror, [61]). The probes were launched in the evening, on two balloon types, with bigger and smaller payloads. The NOAA and FLASH-B probes were able to reach alti- tudes of 23-25 km. The other probes had lower altitude ranges. IAP participated in the campaign with two radiometers: the ground-based radiometer MIAWARA was placed in Sodankyl¨aduring the whole campaign and AMSOS was flown on board the Learjet between 16th and 21st February. The base of the AMSOS-team was around the airport in Rovaniemi, around 120 km south of Sodankyl¨a. Flights were conducted simultaneously with the balloon launches on a daily basis, with the aircraft doing circuits (2-3 loops at different altitudes) around the area of the balloon’s predicted flight. In three days (16th-18th February) the overlap of the measurements of the four instruments (FLASH-B, NOAA, MIAWARA and AMSOS) were well correlated, spatially and temporally. On the other days of the campaign we tried to validate AMSOS with other instruments. On 19th February we measured in the same area as the POAM satellite and on 20th February we tried to measure simultaneously with the balloon probes from Ny Alesund. This flight was not successful as we were not able to reach Spitsbergen due to technical problems in the aircraft navigation system.
2004−02−16 2004−02−18 50 50 AMSOS 17:14 MIAWARA FLASH 45 45 NOAA AMSOS a priori AMSOS 1σ err. AMSOS 19:06 40 40 AMSOS 19:31 AMSOS 19:42 AMSOS 19:45 35 AMSOS 19:46 35 MIAWARA
Altitude [km] FLASH Altitude [km] NOAA 30 AMSOS a priori 30 AMSOS 1 σ err.
25 25
20 20 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 H O Volume Mixing Ratio [ppm] H O Volume Mixing Ratio [ppm] 2 2
(a) 16th February (b) 18th February
Figure 13.3: Profiles obtained on 16th and 18th February 2004. AMSOS profiles are plotted together with profiles of the ground-based radiometer MIAWARA and with the balloons In (a) part of Figure 13.3 profiles obtained with AMSOS on 16th February 13.3 Validation of AMSOS: comparison with HALOE and POAM 157
2004 are shown. On the same plot the profiles of the 22 GHz ground based radiometer MIAWARA and NOAA and FLASH balloons are given. Due to the problems with our retrieval at the lower altitudes, a serious comparison with the balloons is not possible yet. Discrepancies between the AMSOS- and MIAWARA-profiles were also large. MIAWARA delivered a relatively flat profile, with no strong maximum. On the other hand, AMSOS-profiles from the arctic had an distnictive maximum around 30-35 km altitude. A maximum at these altitudes is also visible in the profile from 18th February, (b) part of Figure 13.3. Again, comparison with balloons was not possible.
13.3 Validation of AMSOS: comparison with HALOE and POAM
19−11−2003, AMSOS lat: 43.0o N, long: 8.0o E 50 AMSOS AMSOS 1σ errors HALOE 45 HALOE 1σ errors AMSOS a priori
40
35 Altitude [km]
30
25
1 2 3 4 5 6 7 8 9 H O Volume Mixing Ratio [ppm] 2
Figure 13.4: Comparison of the AMSOS-profile with HALOE sunrise profile on 19th November 2003 at mid-latitudes
In order to validate our measurements done at the test flight, some AMSOS profiles were compared with appropriate HALOE measurements. The flight to Gran Canaria took place in the morning of 19th November 2003. At 158 Measurement campaigns and results that time, the HALOE sunrise measurements were done in the area (44.4◦N, 12.8◦E) close to our flight track. Figure 13.4 shows a comparison between AMSOS profile obtained at 42.9◦N and 7.9◦E. The distance between the two measurements was 427 km. Both profiles are plotted on their original altitude grids. Due to irregular shape of AMSOS’ averaging kernels, we did not convolute the HALOE profile with AMSOS averaging kernels and a priori profile. The overall shape of the AMSOS profile agrees well with HALOE profile, especially in the altitude range 25-50 km.
19−02−2004, AMSOS lat: 67.2o N, long: 18.9o E 50 AMSOS POAM AMSOS a priori 45
40
35 Altitude [km]
30
25
20 1 2 3 4 5 6 7 8 9 H O Volume Mixing Ratio [ppm] 2
Figure 13.5: On 19th February 2004 was the AMSOS-flight coordinated with the overpass of the POAM satellite over the northern Sweden. Comparison of the two profiles show a reasonable agreement
As earlier mentioned, another comparison with satellite profiles was con- ducted during the LAUTLOS campaign. On 19th February we flew to north- ern Sweden (67◦N, 19.9◦E) where the overpass of the POAM satellite was expected. Results of this comparison is shown in Figure 13.5. Both profiles are again plotted on their original altitude grids. Agreement between the two is relatively good, with an average difference of 10-15 % for the altitude range between 20 and 50 km. 13.3 Validation of AMSOS: comparison with HALOE and POAM 159
These two comparisons were relatively encouraging, for they show that the absolute values delivered by AMSOS were in a good agreement with the satellite profiles. However, as already mentioned, the retrieval process has to be improved. Thereafter, a serious validation of the measurements from both missions will be carried out.
Chapter 14
Publication IV
The Distribution of Stratospheric Water Vapour Observed by an Airborne Microwave Radiometer
V. Vasi´c,D. G. Feist, S. M¨uller and N. K¨ampfer
Proceedings of the XX Quadrennial Ozone Symposium, Editor Christos S. Zerefos, Vol. II, Pages 953-954, June 2004, Kos, Greece
161
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952 Proceedings Quadrennial Ozone Symposium, 1-8 June 2004, Kos, Greece 953 ����� �� ���� ��� ������������ �� ��� ������������� ����� ������
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954 Proceedings Quadrennial Ozone Symposium, 1-8 June 2004, Kos, Greece 955 Chapter 15
Conclusions and outlook
The goals set before the beginning of the AMSOS refurbishment were sum- marised in Chapter 4: lower receiver noise temperature; better beam shaping and a narrower output beam; reduction of the baseline ripple; better target pointing within a calibration cycle; extended control over the radiometer pro- cesses, better temperature measurements, higher reliability and flexibility. Some of these goals were achieved very satisfactorily. The noise temperature was reduced by a half in comparison to the old receiver, used before 2003. The pointing of the turning mirror showed excellent results in both measure- ments campaigns. The pointing accuracy was better then the planned 0.1◦ and the stability of the calibration cycle was disturbed very little during the radiometer’s operation. This result is particularly valuable considering diffi- cult operation conditions in the small aircraft. The new radiometer control, including the new software, temperature measurements, AOS heating and calibration, are very positive improvements. The radiometer had no major operational failures during 15 flights and more then 50 days of ground-based operation. The quasioptics performed mainly according to our expectations. The mea- sured antenna diagram of the whole radiometer was narrow, well-shaped and with relatively low side-lobes. The new quasioptical isolator performed very well in the laboratory. However, measured spectra showed a strong baseline which came and went irregularly and suddenly. The first suspicion was di- rected towards the isolator, and a relatively complex and costly modification was carried out. The measured spectra in the next flight had however a baseline. Additional analysis showed that the source of baseline was proba- bly a cable connecting the frontend with the AOSs. Therefore such a minor problem did not allow full evaluation of our quasioptical isolator in the ra-
165 166 Conclusions and outlook diometer. Very new and interesting non-ideal properties of Martin-Puplett interferometer were discovered during our tests. A reflection level of around -30 dB could not be eliminated with a better alignment of the components, indicating that the source of reflections could be more basic and came prob- ably from the rooftop line of the retroreflector. Research on this field has not be finished and will continue in the near future. The new retrieval procedures and software proved to be highly flexible and allowed a higher automatisation of the inversion process. The LAUTLOS campaign gave us an opportunity to compare our retrieved H2O profiles with the ones obtained with other techniques: balloons, ground based radiometer and satellite-borne sensors. However, the retrievals of the profiles obtained from the aircraft during the two missions did not go smoothly. Our profiles showed always a strong minimum at lower latitudes (around 20 km), which made comparisons with the balloons difficult. But, available satellite profiles and AMSOS-measurements agreed quite well above 25 km altitude, which was encouraging. As soon as we have improved the retrieval procedures (still on the run), a new inversion of the spectra will be carried out. Of course, the work on radiometer improvements has not ended. There are several areas where the performance could be improved. The elliptic form of the turning mirror required special and expensive manufacturing. The mirror remained though relatively balky. A fixed elliptic mirror and a turning flat mirror could be considered. The duty cycle could be substantially shortened if the turning mirror was made to have a lower moment of inertia. Also, the overall alignment of the quasioptics could be improved. Very fine positioning of sensitive components, like isolator or MPI, could easily be spoiled by even a small misalignment of the horn-parabolic mirror section. Other methods of sideband filtering could also be considered. Further, the narrow-banded AOS, being a laboratory device, was unstable and very difficult to handle in the aircraft. A lighter spectrometer with a higher stability would be very desirable. Comparisons of AMSOS with other instruments will also be welcome in fu- ture. The experience from the LAUTLOS campaign showed that partici- pation at such international campaigns was essential for validation of our radiometer and comparison with other measurement techniques. Bibliography
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Acknowledgements
I would like to attribute my gratitude to the following people, who supported me during my work on this thesis: Prof. Niklaus K¨ampfer for giving me the opportunity to work on this most interesting project. The full support he has given me, scientific and personal, was essential in bad and good days of my work. Dr. Dietrich G. Feist and Dr. Axel Murk deserve special thanks. Dietrich for the coordination of my work and for being a reference in atmospheric physics, and Axel for his support in our quasioptics- researches. Lots of original ideas came from him. My colleagues from the atmospheric physics group: Beat, Stefan, Alexan- der, Cristina, Daniel, Sigi for a true cooperation, and to other colleagues from the microwave department. Also, I thank Aleksandar Duri´cfor doing the simulations with GRASP and Stefan for producing several nice plots. June, Eddie and Ailsa for reading the manuscript and for language corrections. Our mechanics (B. Hiltbruner, S. Studer and W. L¨uscher) and electron- ics department (M. W¨utrich, D. Weber and N. Jaussi). Special thanks are to Daniel and Nik for their willingness to repair all the electronic- mess I have been producing and for being a helpful and nice company in the aircraft-missions. The pilots of the Swiss Air Force: Peter Hauser, Kurt N¨ani, Martin Jerg, Erich Hugi and Hansueli B¨anziger. Without their personal en- gagement the flights couldn’t have certainly been possible. They were also good and cheerful friends in the bars and restaurants around the globe... The staff and wardens of the ISS Jungfraujoch, Mr. and Mrs. Staub, Jeni and Fischer, for their hospitality and help during my stays at the Sphinx laboratory. Last, but not least: to my wife Mirjana for all her support. To my parents and my brother for their patience, support and readiness to see me once a year at most.
Biography
Vladimir Vasi´cwas born in Uzice, Serbia on March 18th, 1974. He grew up in Valjevo, where he visited primary school and later on the secondary school ’Valjevo Gymnasium’. In 1993 he majored in mathematics and physics and started his studies at the Faculty of Electrical Engineering, University of Belgrade. In October 1999 he obtained a M.Sc. in electrical engineering (electronics and telecommunications). After a year in telecommunication in- dustry, he started his work towards a Ph.D. thesis at the Institute of Applied Physics (IAP), University of Bern, Switzerland in January 2001. At IAP, he has been working in microwave remote sensing and millimetre-wave optics.