Property Measurement Utilizing Atomic/Molecular Filter-Based Diagnostics

ARTICLE IN PRESS

Progress in Aerospace Sciences 41 (2005) 93–142 www.elsevier.com/locate/paerosci

Property measurement utilizing atomic/molecular ﬁlter-based diagnostics M. Boguszko, G.S. ElliottÃ

Department of Aerospace Engineering, University of Illinois Urbana Champaign, 306 Tabolt Laboratory, 104 South Wright Street, Urbana, IL 61801-2935, USA

Abstract

A variety of atomic/molecular filter diagnostic techniques have been under development for qualitative and quantitative flow diagnostic tools since their introduction in the early 1990s. This class of techniques utilizes an atomic or molecular filter, which is basically a glass cell containing selected vapor-phase species (e.g., I2, Hg, K, Rb). In filtered Rayleigh scattering (FRS), and techniques derived from it, the atomic/molecular filter is placed in front of the detector to modify the frequency spectrum of radiation scattered by flow-field constituents (i.e., molecules/atoms and/or particles) when they are illuminated by a narrow linewidth laser. The light transmitted through the filter is then focused on a detector, typically a CCD camera or photomultiplier tube. The atomic/molecular filter can be used simply to suppress background surface/particle scattering, and thereby enhance flow visualizations, or to make quantitative measurements of thermodynamic properties. FRS techniques have been developed to measure individual flow properties, such as velocity (when the scattered light is from particles) or temperature (when the scattered light is from molecules), and measure multiple flow properties simultaneously such as pressure, density, temperature, and velocity. This manuscript summarizes the background needed to understand FRS techniques, and gives example measurements that have been used to develop FRS, demonstrate its capabilities, and investigate flow fields (both non-reacting and combustion) of research interest utilizing the unique capabilities of FRS. In addition, FRS has been used in conjunction with other diagnostics to improve the technique or measure properties simultaneously such as temperature and velocity (measured with PIV), or temperature and species concentration (measured by Raman scattering or laser-induced fluorescence). Also, a brief discussion is given of similar techniques being developed which utilize atomic/molecular filters and Thomson scattering from electrons to measure the electron number density and electron temperatures in plasmas. r 2005 Elsevier Ltd. All rights reserved.

Contents

1. Introduction ...... 95 1.1. Motivation ...... 95 1.2. Background ...... 95 1.3. General description of molecular/atomic ﬁlter-based techniques for property measurement ...... 96

ÃCorresponding author. Tel.: +1 217 265 9211; fax: +1 217 265 0720. E-mail address: [email protected] (G.S. Elliott).

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Nomenclature Z fluid shear viscosity y scattering angle w.r.t. the laser propaga- a polarizability tion direction B background calibration coefficient j scattering wave vector c speed of light l laser wavelength cp specific heat at constant pressure r degree of polarization cv specific heat at constant volume s Rayleigh scattering cross section C dark current and offset constant ds=dO differential scattering cross section E radiant energy n optical frequency (GHz) gðy; T; nÞ scattering spectral distribution based on n0 laser central optical frequency Gaussian model n¯ frequency wave number (in cmÀ1) gðn¯Þ absorption line shape (assumed Gaussian) n¯j frequency line center of absorption transi- h Planck’s constant tion j (in cmÀ1) I transmitted radiant intensity through the f angle relative to the incident laser polar- filter ization I0 incident radiant intensity to the filter cell c angle between incident and detected polar- k Boltzmann’s constant ization vectors k^ l laser propagation direction unit vector k^ s scattering direction unit vector Subscripts K energy-to-grayscale conversion constant l filter cell optical path length cam camera filter cell L optical path imaged at detection element e electron m molecular mass i incident quantity n index of refraction iso isotropic N fluid number density j running index for multiple quantities Npe number of photo-electrons f filtered p pressure p polarization-sensitive quantity r(y) Rayleigh scattering spectral distribution pe photo-induced electrons (Cabannes line) photon relative to a photon RðfÞ Rayleigh scattering calibration coefficient ref reference condition S grayscale value (counts) s scattered quantity tðnÞ filter absorption function stp standard temperature and pressure T temperature u unfiltered quantity u, v, w Cartesian velocity components 0 polarization-insensitive quantity uk velocity component along j vector 1 undisturbed flow quantity V velocity vector x non-dimensional frequency Superscripts Xj mole fraction of gas species j y order parameter c spectral central line alone M total number of absorption transitions Greek letters Acronyms aj scattering angle with respect to horizontal plane ASE amplified spontaneous emission b background scattering cross section BBO beta barium borate crystal g anisotropy BUT buildup time Gj integrated absorption coefficient for ab- CARS coherent anti-stokes Raman scattering sorption transition j CCD charged coupled device DnD optical frequency Doppler shift CW constant wave DnT FWHM of the Rayleigh scattering spec- CMOS complimentary metal oxide semiconductor trum DC direct current Dn¯j FWHM of absorption line j DGV Doppler global velocimetry DO scattering solid angle FARRS filtered angularly resolved Rayleigh scat- optical efficiency constant tering z frequency function FRS filtered Rayleigh scattering ARTICLE IN PRESS

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FM-FRS frequency-modulated FRS PD photodiode FWHM frequency width at half-maximum PDV planar Doppler velocimetry HSRL spectral high-resolution LIDAR PIV particle image velocimetry ICCD intensified CCD PLIF planar laser-induced fluorescence KTP potassium titanyl phosphate crystal PMT photomultiplier tube LIDAR light detection and ranging QE quantum efficiency MFRS modulated FRS RF radio frequency Nd:YAG neodymium-doped yttrium aluminum gar- SBS stimulated Brillouin scattering net crystal STP standard temperature and pressure Nd:YVO4 neodymium-doped orthovanadate crystal

2. Rayleigh scattering from atomic and molecular species ...... 97 2.1. Intensity characteristics...... 97 2.2. Spectral characteristics ...... 100 3. Atomic/molecular absorption filter ...... 102 4. The FRS signal ...... 103 5. Equipment ...... 105 5.1. Typical atomic/molecular filter ...... 105 5.2. Illuminating lasers ...... 106 5.3. Laser frequency monitoring...... 109 6. FRS flow visualization ...... 111 7. Single property measurement ...... 115 7.1. FRS velocimetry ...... 116 7.2. Frequency-modulated filtered Rayleigh scattering ...... 120 7.3. FRS thermometry ...... 122 8. Multiple property measurements ...... 127 8.1. Average measurements (FRS frequency scanning technique) ...... 127 8.2. Instantaneous measurements ...... 131 9. Combined techniques and future trends ...... 134 10. Conclusion ...... 138 Acknowledgements ...... 139 References ...... 139

1. Introduction and in more than one spatial dimension. The perfect technique might be thought of as one that allows the 1.1. Motivation measurement of all the properties, everywhere, at all times. For example, properties in a compressible flow Recent advances in sensor and laser technologies have may vary significantly throughout the flow field (i.e., led many flow diagnostics previously utilized only in the through shock and expansion waves) and compressible development laboratory to gain widespread use as ‘‘off- turbulence quantities such as Reynolds stresses have the-shelf’’ diagnostics. Techniques such as particle image terms that involve multiple fluctuating variables that velocimetry (PIV) and spectroscopy are now more must be measured simultaneously and independently. widely available due to advances in camera, laser, The number of properties we desire to measure becomes computer, and sensor technologies and are common- even larger and more complex as we consider reacting place due to reduced costs and software integration flows and turbulent flames. Although as the subject of making them more ‘‘user friendly’’. This has led to a the current review article, atomic/molecular filter-based more complete understanding of many thermal/fluid techniques do not reach all these goals, they do provide systems and the ability to verify computer models of a unique means of measuring flow properties that few complex flows. As these techniques are more universally other techniques can achieve as effectively. applied to problems of research interest, there is still a need, however, to develop techniques that measure 1.2. Background properties non-intrusively without introducing artificial particles or substances into the flow being measured. In As an introduction to molecular/atomic filter-based addition, it is desirable to enhance current capabilities so techniques we consider first how these techniques came that multiple properties can be measured simultaneously to be utilized by the scientific research community. In ARTICLE IN PRESS

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1983, Shimizu et al. [1] proposed the use of atomic and a sheet of laser light from a frequency-doubled injection- molecular vapor filters for high spectral resolution seeded Nd:YAG laser and modified the spectrum of the LIDAR (HSRL). The purpose of the atomic and scattered light from the flow field using an iodine vapor molecular vapor filter was to eliminate the interference filter placed in front of the detector. By tuning the of particles and aerosols in atmospheric Rayleigh narrow linewidth laser to an absorption line of iodine, scattering measurements. Shimizu and colleagues pro- the scattering passing through the filter is spectrally posed that since the particle/aerosol spectrum has a modified. FRS was first demonstrated by Miles and bandwidth on the order of 100 MHz (due to the radial Lempert to improve flow visualizations by blocking wind velocities) and the Rayleigh scattering from strong background scattering from walls and windows, molecules, although much weaker, has a broader line- and later with Forkey the technique was developed to width (2 GHz for visible wavelengths due to Doppler measure flow quantities [10–14]. From these initial broadening), an atomic/molecular filter may be able to studies several investigators have further developed block the particle scattering, while passing much of the FRS techniques and applied them to study various flow Rayleigh scattering signal [1]. In their groundbreaking fields. This article will review the development and paper, they presented fundamental calculations demon- application of FRS, as well as techniques that utilize strating how the temperature (and backscatter ratio) similar technologies for flow property measurement. In could be measured using HSRL and atomic/molecular particular, we will highlight the applications of FRS vapor filters used in conjunction with the appropriate where molecules or particles small enough to be laser to an accuracy of 71 K if the signal-to-noise ratio considered in the Rayleigh scattering regime have been is 300. Later, utilizing a pulsed Nd:YAG laser and utilized iodine-vapor filter, Hair et al. [2] developed an HSRL system which measured the atmospheric temperature 1.3. General description of molecular/atomic filter-based over an average time span of about 6 h, and an altitude techniques for property measurement range of 2–5 km for eleven nights, yielding values accurate to within 72.0 K of balloon soundings. The In most FRS techniques, the laser beam is either authors also discussed the use of different molecular/ focused to a small volume or formed into a sheet that atomic filters and the upper limit of temperature interrogates the flow field to be measured. As the sensitivity with the technique. incident light encounters the particles or the gas From Shimizu’s initial LIDAR application, two molecules in the flow field, a portion of the light is research groups applied similar types of filters to the scattered. Whether from small particles or molecules in area of fluid mechanics. Komine, Brosnan and Meyers the flow field, the scattering intensity and spectral profile [3,4] introduced atomic/molecular filters to fluid me- contain information about the fluid properties. The chanics research in the 1990s to measure the velocity in a scattering from particles will be shifted in frequency due seeded flow in a technique they termed Doppler global to the Doppler effect (which will be presented shortly), velocimetry (DGV). With DGV (which also has been and the magnitude of the shift is a function of the termed planar Doppler velocimetry, PDV, by some velocity and observation direction. Since particles are investigators [5–7]) one records laser radiation scattered generally not affected as much by the microscopic from particles, when the laser optical frequency is tuned thermal motion (due to their relatively high mass to a gradual sloping edge of the filter absorption profile. compared to molecules) they generally have a spectral The shifts in frequency are thus detected as changes in linewidth approximately equal to that of the radiation iodine cell transmission, while rationing filtered and source, which is on the order of tens of megahertz when unfiltered images (taken simultaneously) removes seed- narrow-bandwidth lasers are used; this is represented in ing non-uniformities. The Doppler shift, and therefore Fig. 1(a). It should be noted that if the particles were the velocity, can be determined by converting the uniformly distributed within the interrogation volume measured cell transmission to frequency. Of course, the total scattered intensity would be also proportional since these initial efforts, much development has taken to the density, but often the process is affected by place, as summarized by Elliott and Beutner [8], and varying particle size, agglomeration, and formation/ Samimy and Wernet [9]. evaporation processes. If the scattered light is from gas At approximately the same time period Miles and molecules, as shown in Fig. 1(b), the shape of the Lempert [10,11] introduced another atomic/molecular molecular Rayleigh scattering spectrum is related to filter technique termed filtered Rayleigh scattering other flow properties in addition to the velocity-induced (FRS) based on the scattered light from atoms/ Doppler shift. As will be shown in detail in Subsection molecules (or even small condensation particles in the 2.1, the total intensity of the scattered light is related to Rayleigh scattering regime, in which case the technique the density, the width of the spectrum is related to the becomes similar to PDV without artificial seeding). In temperature, and the spectral line shape is related to FRS Miles and colleagues illuminated the flow field with both pressure and temperature. Therefore, the molecular ARTICLE IN PRESS

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1.0 Laser Particle scattering Laser Sheet spectrum spectrum Atomic/Molecular 0.8 Filter

0.6 Polarizer Interference filter 0.4 Camera or Detector

Fig. 2. General FRS optical arrangement. 0.2 ∆ν D(V)

0.0 –3 –2 –1 0 1 2 3 this paper will describe the background needed to (a) Optical Frequency ν understand FRS, and by extension, other diagnostic techniques that are based on similar principles. 1.0 Laser spectrum Molecular Rayleigh scattering spectrum 2. Rayleigh scattering from atomic and molecular species 0.8 I (N ) y (T, p) 2.1. Intensity characteristics 0.6 The process of light scattering by air molecules was presented by Lord Rayleigh [15] utilizing a simple 0.4 ∆ν T(T ) Intensity (a.u.) Intensity (a.u.) mechanical model. This model consists of a positively charged nucleus containing the majority of the mass 0.2 ∆ν D(V) surrounded by a negative shell of electrons. The binding forces between the nucleus and electrons are represented 0.0 by ideal springs. The system is assumed to be in –3 –2 –1 0 1 2 3 electrical equilibrium (i.e., non-ionized), with the nega- (b) Optical Frequency ν tive charge spherically distributed concentric to the Fig. 1. Characteristics of the spectral intensity profile from nucleus (i.e., non-polar). The binding forces are assumed particle (a) and molecular (b) scattering. to be linear and with the same spring constant in all directions (i.e., isotropic system obeying Hooke’s law). When the system is subjected to an electromagnetic field it will experience a redistribution of its electric Rayleigh scattering spectral intensity profile contains charges bringing the negative and positive charges to a information about the properties of the fluid (pressure, new equilibrium position, creating an induced dipole. density, temperature, and velocity) and a measurement The dipole, based on the assumption of isotropy will of these properties can be made if their contributions are align itself with the electric field and will try to separated. To accomplish this, FRS employs a mole- counteract its action, according to Lenz’s law. In the cular or atomic filter, which acts as a spectral absorption case of an electromagnetic wave, the induced dipole will notch. The filter is simply a glass cell that contains a follow the time-varying electric field with the same species in vapor form with absorption lines that are frequency, producing a secondary wave propagating accessible in frequency by the interrogating laser. The outwardly from the dipole. In general, scattering is scattered radiant energy is collected by a detector [e.g., considered to be in the Rayleigh regime when the photomultiplier tube (PMT), photodiode (PD), e´ talon] particle size is less than 1/10 of the wavelength of the or imaged by a CCD camera through the atomic/ incident wave [16]. In this regime the electric field of the molecular filter, which is placed in front of it. Fig. 2 primary wave can be safely considered uniform across illustrates the general optical experimental arrangement, the particle. Since visible light ranges between approxi- consisting of the three major components. By utilizing mately 400 and 700 nm, molecules (such as those this frequency notch filter, researchers have been able to: comprising air) are generally considered to be in the reduce background scattering from walls and windows Rayleigh scattering regime. in flow visualizations, measure individual flow proper- The ratio of the total scattered intensity to incident ties such as velocity and temperature, or deduce multiple irradiance is a measure of how much energy is being flow field properties simultaneously. The remainder of taken away from the primary wave and radiated in all ARTICLE IN PRESS

98 M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142 directions, and is known as the scattering cross section, and rotational Raman scattering, both of which reach generally denoted in the literature as s. A very clear and the detector as well. The vibrational manifold intensity is intuitive derivation of this quantity using the Rayleigh spectrally well separated (on the order of 103 cmÀ1) from mechanical spherical model is presented by McCartney the incident frequency and contains less than 0.1% the [16]. Detectors usually receive a fraction of the total total signal and thus can be neglected in most cases. The scattering over a limited solid angle DO, so a more useful rotational manifold is composed by the Stokes and anti- quantity is the differential scattering cross section Stokes bands (lines appearing at lower and higher ds=dOU The latter is defined as the intensity per unit frequency, respectively), and Q-branch (same frequency irradiance per unit solid angle, scattered at an angle f as the incident energy). All of these components are with respect to the incident polarization direction, and incoherent due to the random orientation of the for a perfectly isotropic gas it is expressed as molecules, which are averaged within the interrogation volume, and so, their scattering signal is partially or ds 4p2ðn À 1Þ2 iso ¼ stp 2 fully depolarized. 2 4 sin f, (1) dO Nstpl The polarizability tensor was expressed by Placzek [17] in terms of an isotropic part and an anisotropic part. where n and N are the index of refraction and stp stp Placzek introduced two invariant scalar quantities number density respectively, measured at STP (standard derived from them that completely characterize the temperature defined at 273.15 K), l is the wavelength of system, namely the polarizability a (equal to the trace of the incident radiation, and the subscript iso indicates the the isotropic tensor) and the anisotropy g (equal to the condition of isotropy. The scattering in this case is fully second invariant of the polarizability tensor). With this polarized in the same direction as that of the incident concept, the central portion (unshifted) molecular radiation and can be observed in monatomic gases such scattering can be thought of as originating from as helium, argon, etc, or spherical-top molecules such as perfectly spherical imaginary molecules (now referred methane, carbon fluoride, etc. The cross section depends to as the Placzek trace component [18]), and from Q- on the substance (through the index of refraction) and is branch rotational Raman. These two occur at the same inversely proportional to the fourth power of the frequency as that of the incident wave and are referred incident laser wavelength. The scattered light intensity to as the Cabannes line [18], which will be described in has a toroidal spatial distribution as seen in Fig. 3. For further detail in the next sub-section. The frequency- this reason, it is always preferable to align the shifted bands (Stokes and anti-Stokes rotational Ra- polarization direction perpendicularly to the measuring man) fall only a few cmÀ1 away from the Cabannes line direction (on the x2y plane in Fig. 3) so that the and are also referred to by many authors as the wings of detected signal is strongest. the scattering profile [21]. If the scattering medium is air More generally, gases such as air or many combustion and one uses linearly polarized incident light and byproducts are not isotropic, and therefore their polarization-insensitive detector, the wings contribute polarizability tensor is not spherical. The incident approximately 2.5% of the total scattering intensity (see radiation induces changes in vibrational and rotational [2,21]), and because they are so close to the Cabannes states of the molecules, and thus gives rise to vibrational line their contribution is often not negligible. Young [19] points out that ‘‘Rayleigh scattering consists of rotational Raman lines and the central Cabannes line’’. He z Polarization direction discourages the use of the term Rayleigh or Rayleigh– Brillouin line when referring to the central feature, and instead favors the term Cabannes line to avoid any confusion. This terminology has been recently adopted by Miles et al. [20], and Hair et al. [2] among others. The degree of depolarization of the detected scattering, usually expressed in the literature with the symbol r, is defined as the ratio of observed scattering with polarization perpendicular and parallel to the incident radiation vector. The depolarization takes different values depending on how it is measured. Kattawar et xyal. [21] tabulated relative scattering intensities, which provides the necessary information for the investigation of polarization effects in all circumstances. For instance, let us assume that the incident radiation propagates Fig. 3. Spatial distribution of the differential angular Rayleigh horizontally along the x-axis of a Cartesian coordinate scattering cross-section. system and the detector is on the horizontal plane in the ARTICLE IN PRESS

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z not consistent across the literature and may possibly lead to bias errors as noted by Young [25].An interesting technique that takes advantage of the Polarization different depolarization ratios was introduced by Field- direction Propagation ing et al. [22]. With it, they measured temperature, direction mixture fraction and species in flames, where the species are determined by detecting the depolarized Rayleigh signal. Although the intensity of the latter is about 10À2 π/2 with respect to the total Rayleigh scattering they point out that it still represents a gain in signal strength by a x factor of about 10 as compared with vibrational Raman scattering methods. Observation y The differential Rayleigh cross section from an direction anisotropic gas is presented by Penney [26] from the quantum mechanical formulation. Its value can be expressed in an equivalent but slightly different, form as ! Fig. 4. Schematic representation of the polarization, propaga- ds 4p2ðn À 1Þ2 3 tion and observation directions. ¼ spt ½r þð1 À r Þ cos2 c, 2 4 À p p dO p Nsptl 3 4rp y direction (see Fig. 4) then the depolarization is (4) 2 2 ! 3g 6g 2rp ¼ ¼ ¼ 2 2 rp 2 2 ; r0 2 2 and so r0 , ds 4p ðnspt À 1Þ 3 45a þ 4g 45a þ 7g 1 þ rp ¼ dO N2 l4 3 À 4r (2) 0 spt p Â½2r þð1 À r Þ cos2 c, ð5Þ where the subscript p and 0 indicate polarized (in the z p p direction) and unpolarized incident radiation, respec- where subscripts p and 0 on the left-hand side indicate a tively. Note that in this case the total Rayleigh scattering polarization-sensitive or polarization-insensitive detec- (Cabannes+wings) is detected. If the wings are spec- tion, respectively; c is the angle between the incident trally removed, for instance by means of an narrow- and detected polarization vectors. The only difference band filter (e.g., a spectrometer) before reaching the between the detection scheme of Eqs. (4) and (5) is the detector, only the Cabannes portion will be captured; use of a polarizer or a beam-splitting cube in front of the then the depolarization becomes detector. According to this definition we have cos c ¼ 3g2 6g2 2rc sin f; and so, for an isotropic gas, Eqs. (4) and (5) reduce c ¼ c ¼ c ¼ p rp 2 2 ; r0 2 2 and r0 c , to Eq. (1). Equivalent expressions have been derived and 180a þ 4g 180a þ 7g 1 þ rp presented by Miles et al. [20] in terms of r0. Using the (3) index of refraction formula given by Birch [27] at STP, where the superscript c makes it explicit that the ðn À 1Þ Â 108 ¼ 8342:54 þ 2; 406; 147½130 À n¯ðmmÀ1ÞÀ1 Cabannes line is the only contribution. However, except s þ 15; 998½38:9 À n¯ðmmÀ1ÞÀ1 ð6Þ for H2, which is very light and thus has the rotational bands spectrally separated, it is difficult to remove the and Fielding’s data for rp in air [22], we obtain a rotational Raman with ordinary interference filters, differential Rayleigh cross section of where 1 nm FWHM is considered very narrow. In typical laboratory Rayleigh scattering experiments ds ðair; l ¼ 532 nm; STP; c ¼ 0Þ the incident radiation is polarized, as it comes from a dO p laser source, and the total Rayleigh scattering is ¼ 5:986 Â 10À28 cm2=steradian: ð7Þ collected, and therefore rp is normally used. In atmospheric studies, however, r0 is preferred (as the source, The factor 3=ð324rpÞ in Eqs. (4) and (5) is a result of sun light, is unpolarized). Different research groups have assuming that the total Rayleigh scattering is detected, published data for both quantities. For example, including Q, S, and O branches of rotational Raman. As Fielding [22] reports values of rp for different species, was mentioned above, in general it is difficult to exclude while Bates [23] gives values of r0 for air. Also, it is the S and O branches for all but very light molecules worth noting that Bridge and Buckingham [24] pub- such as H2 (where rotational side bands are widely lished values of rp of different gases using a helium– separated) without significantly reducing the intensity of neon laser, but they chose to represent the results with the Cabannes line. In fact, one can use a molecular/ the symbol r0. This shows that the terminology used is atomic filter to block the latter and thus resolve the ARTICLE IN PRESS

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Stokes and anti-Stokes bands, as was done by Finkel- the central Cabannes line as a function of thermo- stein et al. [28]. In FRS thermometry (as will be dynamic properties. explained in Section 7) the scattering signal is reduced as the temperature increases. Also, the Cabannes line is 2.2. Spectral characteristics significantly attenuated by the absorption filter. How- ever, the Stokes and anti-Stokes wings remain present, In the previous section, we focused our attention on and may become important enough to impact the the fact that a molecule scatters light at the same results. frequency as that of the irradiating wave. As we The energy reaching the detector, scattered through a carefully analyze in more detail, however, we will solid angle DO can be expressed as show that the Rayleigh scattering central frequency X Z can be Doppler shifted, and second, we will discuss dsj Es ¼ NLEi X j dO, (8) that the characteristics of the Cabannes line spectral j dO DO profile are determined by the thermodynamic state of the gas. where Es is the scattered energy, Ei is the incident energy It is well known that when there is a relative motion on the probe volume, whose integration optical path between the source and the receiver the wave suffers along the viewing direction is L; N is the gas number a shift in frequency that depends upon the frame density, Xj is the mole fraction of species j, is the of reference in consideration. For our present Rayleigh optical efficiency constant, and dsj=dO is the appro- scattering discussion we consider a moving particle priate differential Rayleigh scattering cross section of that encounters incident light and scatters a portion species j. If the differential cross section variation over of it, which is observed at a given direction as the solid angle is negligible (as is typical), Eq. (8) can be shown in Fig. 5. In this case the Doppler shift is given approximated as by [30] X dsj 1 Es NLEiDO X j . (9) DnD ¼ V Áðk^ s À k^ lÞ, (11) j dO l where V is the velocity vector of the particle (or The scattered energy is equal to the number of molecule), k^ s is the observation unit vector (defined scattered photons times the energy of the photon, from the scatterer to the observer), and k^ l is the incident Es ¼ Nphc=l. Due to the finite efficiency of the detector, light unit vector defined from the laser to the scatterer. the number of photo-electrons (those created by the Often it is convenient to define a quantity called the scattered photons when they reach the detector) is going scattering wave vector as to be Npe ¼ Np, where e is the efficiency stemming from the quantum efficiency QE and transmission through the 2p j ¼ ðk^ s À k^ lÞ, (12) lens system and other minor losses. Then, in terms of l photo-electrons, Eq. (9) can be written as [29] which has a magnitude NLlE DO X ds 4p y N ¼ i X j . (10) k ¼ sin , (13) pe j l 2 hc j dO where y is the angle between the incident and observa- The significance of this is that detectors such as PMTs tion vectors as shown in Fig. 5. Therefore, another way and CCDs respond to the number of photons striking them (not, as such, to the energy or power reaching them). If one substitutes in Eq. (10) the value for the Particle differential scattering cross section, it becomes apparent Velocity (V) (kˆ – kˆ ) ~ κ that the detected signal (in counts, for example) is s l proportional to lÀ3. This strong wavelength dependence makes it attractive to work in the ultraviolet regime, where the scattering signal is greatly enhanced. How- ever, additional problems are encountered at ultraviolet wavelengths, such as higher cost of equipment and optics, diminished detector efficiencies, and possible Observed Incident fluorescence interferences. Due to these problems that Scattered Radiation Laser Radiation many times outweigh the benefits of working in UV, a ˆ ˆ (ks) (kl) large part of Rayleigh scattering investigations is done in the visible range. In the next section, we will Fig. 5. Geometry of velocity and light wave unit vectors for the further describe the spectral structure and position of Doppler shift equation. ARTICLE IN PRESS

M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142 101 of expressing the Doppler shift is which is given by rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 k 8kT ln 2 2 sinðy=2Þ 8kT ln 2 DnD ¼ V Á j (14) Dn ¼ ¼ , (17) 2p T 2p m l m or in scalar form where k is the Boltzmann constant, m is the molecular k mass, T is the temperature, and k the magnitude of the Dn ¼ u , (15) D 2p k wave vector, which was previously defined in Eq. (13). The FWHM of the Gaussian distribution as defined here where u is the velocity component along j (see Fig. 5). pffiffiffiffi k grows as T. It should be noted that the distribution is With this arrangement it is possible to measure the not only dependent on the thermodynamic properties velocity component along the sensitivity direction j. of the gas, but also dependent on the angle between From Eq. (13) it can be seen that the system is highly the incident and observation light vectors, y, through the dependent on the observation angle, being zero at y ¼ 0 magnitude of the wave vector (k factor). This is the and maximum at y ¼ p. It would be ideal to observe the distribution observed at low densities, when the mean flow at an angle as close to y ¼ p as possible (back- free path is large with respect to the wavelength, and is scatter arrangement). However, most of the work referred to as the Knudsen regime. presented here was performed on planar fields, making At the opposite extreme, when gas density is very the laser beam into a thin sheet of light. In order to high, the mean free path becomes small compared to the avoid image distortions the preferred observation wavelength. In this regime, referred to as the hydro- direction is generally close to y ¼ p/2. The Doppler dynamic regime, the motion of a molecule is not shift does not only play a roll in determining the random, but correlated to the motion of the rest of the frequency shift of the center of the Rayleigh scattered molecules in its vicinity. The spectral distribution is spectrum, but, is also used to describe the broadening of governed by the density fluctuations in the fluid [31]. the scattered spectrum. Also it is noted that the Doppler This phenomenon, which is specifically related to frequency shift affects both particles and molecules by adiabatic sound disturbances propagating in the med- changing the center of their respective spectral profiles ium, [32] produces two symmetrically displaced wings with respect to that of the incident beam. from the incident frequency n (the Mandel’shtam–Bril- Now that the major source of frequency shift has been 0 louin doublet). Kattawar et al. [21] and Young [19] point presented, we also need to determine the spectral profile out that the Brillouin doublet can be thought of as the of the Rayleigh scattered light. Owing to the fact it is translational Raman lines, while the central peak should difficult to model the Raman scattering lines and that be called the Gross line. Additionally, a central peak their contribution is relatively small, we will neglect occurs at the same frequency as that of the incident them, and only consider that the Rayleigh scattering line wave, which is due to the thermal diffusion [33,34].Itis shape is that of the Cabannes line. known that the ratio of the central peak to the displaced Let us assume the radiation is scattered by molecules peaks is equal to ðc 2c Þ=c [35]. The reader is referred from monochromatic and linearly polarized incident p v v to Crosignani [33] who presents the derivation of the light. In addition to the Doppler frequency shift due to spectral profile for a continuous liquid medium. the bulk fluid motion, the shape of the molecular For the intermediate regime, which corresponds to scattering spectral intensity profile is also affected by the standard atmospheric pressures and temperatures, the molecular thermal motion, which can be related to the continuum assumption cannot be made, since the thermodynamic properties (i.e., pressure, temperature, wavelength is of the order of the molecular mean free density) of the medium. On an atomic scale, the light path. A number of kinetic models have been developed scattered by each molecule is going to experience a to overcome this difficulty over the last 50 years. The Doppler shift due to its motion with respect to the most significant works related to the study of the source and the observer, also governed by Eq. (11). The Rayleigh scattering spectrum were put forth between macroscopic result of the thermal motion is a frequency 1966 and 1974 by Yip, Nelkin and co-workers [34–38], broadening of the scattering profile, which is referred to Hanson and Morse [39,40], and Tenti et al. [41]. All as thermal broadening. At a low gas density (or high these works are based on the study of the double Fourier temperature) the Rayleigh scattering spectral profile is transform of the density–density correlation function. Gaussian and is given by [20] The S6 model developed by Tenti [41] is generally rffiffiffiffiffiffiffiffi "# 2 2 ln 2 n À n0 utilized by researchers to describe the Rayleigh scatter- gðy; T; nÞ¼ exp À4ln2 , (16) ing distribution for diatomic molecules such as nitrogen. DnT p DnT It should be noted that the S6 model has also been where (n2n0) is the relative frequency from that of the verified for a variety of atomic, diatomic, and polya- irradiating beam (n0), and DnT is the full-width at half- tomic molecules [42]. Various curves using this model maximum (FWHM) of the thermally broadened profile are presented in Fig. 6. The Rayleigh scattering ARTICLE IN PRESS

102 M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142

1.0 tions through k. Also, the kinetic model satisfies, as is expected, both Knudsen and hydrodynamic regimes at y = 0.01 the two ends of its range of applicability. As observed 5 0.8 y = 0.50 for y 1 the spectral profile is essentially Gaussian and y = 1.00 the scattering can be considered to be in the Knudsen y = 2.00 regime, but as y increases the profile tends toward the 0.6 y = 4.00 hydrodynamic regime as evidenced by the three distinct ) y

, peaks described previously. One can now consider that x (

r since the shape of the scattering spectral distribution is 0.4 governed by the thermodynamic properties of the gas, it may be possible to obtain their values from the scattered light. 0.2

0.0 3. Atomic/molecular absorption filter –3 –2 –10 1 2 3 x In order to improve flow visualizations or obtain thermodynamic properties of the fluid flow, it is Fig. 6. Cabannes line in the over a range of y-parameters. necessary to spectrally modify the shape of the Rayleigh scattering spectrum. In FRS, this is accomplished with an atomic or molecular absorption filter. The absorption filter is created by introducing a gas of an atomic or distribution (only Cabannes line modeled, wings are molecular species in a glass cell, which is placed in front neglected) rðx; yÞ is generally expressed as of the detector (camera or photomultiplier tube) to Z Z 1 1 modify the scattered light collected from the flow field. rðx; yÞ dn ¼ rðn À n0; p; T; yÞ dn ¼ 1, (18) In general, the absorption lines that are used in FRS À1 À1 may be from single or multiple transitions (i.e., from which is a normalized distribution defined so that the hyperfine splitting) merged by Doppler or collisional integral over all frequencies is equal to one. The profile broadening. The transmission profile for the atomic/ is written in terms of two dimensionless parameters used molecular filter is generally derived from Beer’s law in the analysis, which are sufficient to describe the applied to each line making up the profile and is spectrum and are given by Tenti [41] as represented by Forkey et al. [43,44] for an iodine 2pðn À n Þ m 1=2 ðn À n Þl m 1=2 molecular filter as x ¼ 0 ¼ 0 , (19) () k 2kT 2sinðy=2Þ 2kT Iðn¯Þ XM tðn¯Þ¼ ¼ exp l ½ÀG g ðn¯Þ , (22) ð Þ j j p m 1=2 lp m 1=2 I 0 n¯ ¼ y ¼ ¼ , (20) j 1 kZ 2kT 4pZ sinðy=2Þ 2kT where l is the length of the absorption cell, j is the where p is the pressure in the medium, Z is the shear individual absorption line out of all those (M) relevant viscosity. The variable x is referred to as the dimension- to the absorption process (i.e., an absorption line within less frequency and the variable y is referred to as the the frequency range of interest), n¯ is the optical À1 order parameter or simply as the y-parameter. The latter frequency wave number (usually in units of cm ), Gj is the ratio of the effective wavelength (given by the is the integrated absorption coefficient for each applic- inverse of the scattering wave vector) and the mean free able absorption line, and gjðn¯Þ is the normalized line path. Utilizing empirical Sutherlan’s formula for visc- shape. The latter is determined by the broadening osity [1] the y-parameter for air is given by process governed by the conditions of the absorption cell with generally three considered to be significant; TðKÞþ110:4 pðatmÞlðnmÞ y ¼ 0:2308 . (21) natural broadening due to the lifetime of the excited 2ð Þ sinðy=2Þ T K energy state, pressure (collisional) broadening due to It can be observed from Fig. 6 that the shape of the collisions between species which cause dephasing of the Rayleigh scattered spectrum depends upon the y- wave function, and temperature broadening due to the parameter, which in turn, depends upon the thermo- random motion of the molecules as they absorb incident dynamic properties p and T. The width of the scattering, light. In general, temperature broadening is considered namely the FWHM grows with the square root of to be the most significant from order-of-magnitude temperature. Additionally, both x and y depend upon estimates of the lifetimes of the excited states and the angle between the incident and observation direc- because the absorption filters are normally operated at ARTICLE IN PRESS

M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142 103 low pressure, rendering collisional broadening small. surfaces. Also, from a data processing point of view, it is Therefore, in the absorption model developed by Forkey convenient to have lines utilized in the measurement et al. [43,44] for iodine (which has been used by several relatively separated from other absorption lines so that investigators) the normalized line shape is represented as more of the signal outside of the absorption line passes a Gaussian profile given by through the absorption filter and is recorded. It should rffiffiffiffiffiffiffiffi "# be noted that many of these same attributes are desirable 2 2 ln 2 n¯ À n¯j for other molecular filter velocimetry techniques, but the gjðn¯Þ¼ exp À4ln2 , (23) Dn¯j p Dn¯j main difference here is the desire to have sharp edges on the profile whereas DGV and PDV velocity techniques where Dn¯j is the FWHM linewidth due to thermal may favor gradual slopes for a higher bandwidth in broadening, which given for the absorption process as velocity measurements. rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 8kT ln 2 Dn¯ ¼ n¯ , (24) j j m 4. The FRS signal where m is the molecular mass, n¯j is the central frequency À1 wavenumber of transition j (in cm ), T is the Now that the characteristics of Rayleigh scattering temperature of the gas, and k is the Boltzmann constant. and the absorption filter have been described, we There are three primary characteristics that the consider the signal that would reach a detector viewing atomic/molecular filter must meet in order for it to be the molecular Rayleigh scattering from a flow field utilized in FRS experiments. First, the atoms or through an atomic/molecular filter as shown in Fig. 2. molecules must have absorption lines within the The equations for FRS data interpretation are presented wavelength range of the laser utilized to interrogate as developed in detail by Forkey [43]. When the the flow field. There are several different laser and scattering from the narrow-bandwidth laser is collected atomic/molecular filter combinations that have been by the camera through the absorption filter, the process utilized in FRS as listed in several previous articles, can be summarized as illustrated in Fig. 7. There are [1,8,13] the most common of which will be discussed essentially two sources of signal, which will be convolved shortly. Although as discussed earlier, the signal grows À3 with the absorption profile as a portion of the light proportionally to l , which makes it attractive to work is transmitted through the atomic/molecular filter; the in or near the uv range, other characteristics about the Rayleigh scattering from the flow, and background operation and efficiencies of the detector and laser often scattering from walls and windows. The intensity determine the wavelength to be utilized. For instance, of the transmitted light is then integrated in frequency the lasers typically have less energy per pulse, losses when it is imaged by the camera (since each camera pixel through windows and collection optics are higher, and will sum the intensity spectrum over its range of efficiencies of the detector are lower, particularly if CCD wavelength sensitivity). Following the expressions given detectors are utilized. Secondly, the absorption line by Forkey et al. [13,43], we consider the portion of utilized should have as sharp frequency cut-off edges as radiant energy due to Rayleigh scattering from air possible, in a range significantly narrower than the (considered as a single species) that reaches the camera Rayleigh scattering linewidth. This enables the greatest through the absorption filter from molecules in the flow frequency selectivity and highest frequency profile field [43] as resolution. Since one of the objectives of the technique is to produce velocity and property measurements, a E Rayleigh scattering Z cutoff edge with a gradual slope would require larger ds þ1 variations in the measurement quantities to be registered ¼ NL ðfÞDOEi tðnÞÀrðn À n0 À nD; p; T; yÞ dn; dO À1 as intensity changes by the detector. As a first-order ð25Þ approximation, the slope of the absorption line can be shown to be inversely proportional to the absorption where N is the fluid number density, ds=dOðfÞ is the thermal linewidth given in Eq. (24) above [12]. appropriate differential scattering cross section, Ei is the Additionally, the filter transmission outside of the filter laser radiant energy, DO (steradian) is the solid angle should be close to unity, to prevent signal attenuation, subtended by the illumination region to the camera lens while inside it should be low to achieve a good extinction or detector, and tðnÞ is the filter transmissionR at the ratio. Exactly how low depends on the particular optical frequency n. Recall that the integral r dn ¼ 1, application, so it is convenient that the extinction ratio so the filter produces a decrease in the energy collected can be variable to adapt the filter to a variety of which is dependent on the relative position of the conditions. High extinction ratios (deep absorption Rayleigh scattering (Doppler shift), shape of the lines) are desirable when it is necessary to block strong spectrum (thermodynamic properties) and viewing background reflections as is the case of flows near angle. ARTICLE IN PRESS

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Background scattering Molecular Absorption Rayleigh spectrum EFRS scattering × = Transmission × EBG Transmission Spectral intensity Intensity

∆ν Frequency Frequency Frequency D ν 0

Fig. 7. Illustration of the FRS signal created from molecular Rayleigh scattering and background scattering (from walls and/or windows). The figure on the left is the background and molecular Rayleigh scattering spectra, the middle plot is the transmission profile of the atomic/molecular filter, and to the right is an illustration of the convolution of the scattered light spectrum and transmission profile resulting in the FRS signal.

Additionally, background scattering due to wall therefore given by [43] reflections will be imaged by the detector. The spectral Sðn ; Dn ; p; T; N; y; fÞ distribution of the background scattering is not broa- 0 D Z þ1 dened and has a spectral profile similar to that of the ds ¼ KNL ðfÞDOEi tðnÞrðn À n0 À nD; p; T; yÞ dn incident laser. The energy due to background scatter- dOZ À1 ing reaching the camera through the filter is therefore þ KbE tðnÞlðn À n Þ dn þ C, ð27Þ given by i 0 Z where K is the conversion constant from energy to E ¼ bE tðnÞlðn À n Þ dn, (26) Background i 0 grayscale, including camera and lens efficiencies, and C is the pedestal value due to dark current and signal where b is the analogous to the Rayleigh differential offset. In general it can be assumed that the signal cross section, that is, how much of the primary wave is follows a linear relationship with energy, but this should scattered [43]. always be confirmed experimentally in the normal range As the radiation passes through the camera lens of operation of the camera. The constant C is easily and reaches the detector (e.g., CCD array) losses measured by taking images with the camera covered, so occur from optical transmission and CCD quantum it will be removed from the analysis and we will assume efficiency. The latter is the number of photoelec- that it has been subtracted out. For convenience, all the trons produced per photon. In intensified cameras variables that multiply the integrals of the first and (ICCD), the photons reach a photocathode and produce second term are grouped into two optics calibration the release of electrons, which are accelerated through parameters [43] microchannels where by collisions on the walls release thousands other electrons, and each of those releases ds RðfÞ¼KL ðfÞDOE , (28) thousands more in subsequent collisions, an effect dO i known as cascaded secondary emission. At the end of the intensifier the electrons hit a phosphor-coated B ¼ KbEi (29) screen where they are converted back to photons yielding the equation for the recoded signal given by [44] and are finally detected by the CCD array. In this way, very weak signals are dramatically strengthened Sðn0; DnD; p; T; N; y; fÞ Z although quantum efficiency is much lower. The þ1 photoelectrons created in one sensing element over the ¼ RN tðnÞrðn À n0 À DnD; p; T; yÞ dn ZÀ1 entire duration of the frame exposure are collected at þ1 readout, amplified and digitized and sent to the þ B tðnÞlðn À n0Þ dn. ð30Þ computer for storage as an image file. Each image À1 pixel is represented by an integer whose value is This equation represents the value of the signal at a proportional to the energy collected at that resolution single resolution element (pixel) in the image, which we element. It is usual to find that the camera produces will refer to as the FRS signal in our discussions to a non-zero output even in the absence of light due follow. The same process occurs at all the other elements to dark current and offset. The signal recorded is of the CCD and it is assumed that each one of them is ARTICLE IN PRESS

M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142 105 independent. It should be noted that the formalism of T = 373 K this derivation is credited to Miles, Lempert, and Forkey cell 0.9 Tcell = 393 K T = 413 K who were the initial developers of FRS with the 0.8 cell nomenclature presented following Forkey’s dissertation 0.7 where additional details are given [13,43]. 0.6

0.5

5. Equipment 0.4

Transmission 0.3

Before discussing applications of FRS, we note that 0.2 there is variety of equipment (i.e., cameras, detectors, 0.1 lasers, etc.) with characteristics that may be somewhat unique to FRS techniques. The equipment and their 0.0 attributes relevant to FRS include: experimental char- -2 -1 0 1 2 acteristics of the atomic/molecular vapor filter, unique (a) Relative Frequency (GHz) characteristics of the illuminating laser, and methodologies for monitoring the laser frequency accurately. It T = 308 K 1.0 I2 should be noted that slightly more emphasis is placed on TI2 = 313 K 0.9 T = 318 K the equipment utilizing the iodine molecular filter and I2 TI2 = 323 K Nd:YAG laser since this is the most common filter/laser 0.8 TI2 = 328 K combination utilized to date. 0.7

5.1. Typical atomic/molecular ﬁlter 0.6 0.5

At the heart of any FRS system is the atomic/ Transmission 0.4 molecular vapor filter. Fig. 8 gives a schematic of a 0.3 typical filter cell utilized in various FRS experiments. It is basically a glass cylinder with flat optical-quality 0.2 windows generally welded on each end. A stopcock on 0.1 the top of the cell allows it to be evacuated. Since many 0.0 of the species utilized in FRS are liquid or solid at room -2 -1 0 1 2 (b) Relative Frequency (GHz) temperatures and pressures, the cell is generally operated under vacuum and wrapped with heating tape main- Fig. 9. Experimentally obtained iodine absorption profile À taining it an elevated temperature. The side wall (centered around a wave number of 18789.28 cm 1)asa temperature prevents the crystallization of the species function of cell-wall temperature (a) and side-arm temperature on the cell walls and windows which are also heated by (b). From Mosedale et al. [7] reprinted with permission. conduction, or may have a multiple pane design so that the temperature of the inner window is elevated. Elevating the temperature of the cell walls (assuming increases the temperature of the species, which will that only atomic/molecular vapor is present in the cell) change the thermal broadening of the absorption lines and therefore should be regulated. Fig. 9a gives an example of the effect of cell-wall temperature for an iodine molecular vapor cell (length ¼ 22 cm, n¯j ¼ 18789:28 cmÀ1, sidearm temperature ¼ 313 K). As observed, the effect of cell wall temperature is not Cell body significant since it governs the thermal broadening Temperature (Tcel ) process only. In most atomic/molecular cell designs, a side-arm contains the liquid or solid species, which is Iodine Side-Arm Temperature (T ) maintained at a lower temperature than the cell body. I2 Often the temperature is maintained by a temperature- controlled water bath since it generally requires a more constant temperature. This arrangement allows the partial pressure (i.e., number density) of the filter species Fig. 8. Schematic of a typical atomic/molecular filter. From to be regulated since it will deposit as a liquid/solid at Boguszko and Elliott [106]; reprinted by permission of the the coldest point of the cell. Fig. 9b gives an example of American Institute of Aeronautics and Astronautics, Inc. the effect of the sidearm temperature for the iodine ARTICLE IN PRESS

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3 þ 1 þ molecular filter described previously. As observed, the namely the bound-bound Bð P0uÞ Xð S0gÞ and the 1 1 þ sidearm temperature has a much greater effect on bound-unbound P1u Xð S0gÞ states [45]. At room the absorption profile. Often for a given species temperatures there are approximately 150 rotational the temperature/partial pressure relationship is avail- levels and 3 vibrational levels populated [47]. Absorp- able. For example the relationship for iodine is given tion lines will occur only when the molecule is excited by [43,44] with the exact energy to produce a transition to a higher 2867:028 energy level allowed by the ro-vibrational selection rules. log pðTorrÞ¼9:75715 À , (31) As noted by Hiller and Hanson [47], there are 10 T ðCÞþ254:180 I2 approximately 50 higher possible energy levels, which T where I2 is the cold point temperature of the sidearm. give rise to approximately 45,000 absorption lines Since the latter must be controlled more accurately, and between 500 and 650 nm. For the unbound state, the may lead to uncertainties in the FRS measurement, equilibrium inter-nuclear distance of the molecule some cell designs incorporate a valve to isolate the requires a higher energy than that of dissociation. A liquid/solid species from the cell body. This ensures that transition to this state produces the brake-up of the the density (or partial pressure) of the species remains molecule where there are no longer rotational or constant, and is therefore termed a starved vapor cell vibrational states, thus producing continuum absorption design. Although it is generally more desirable to have at all frequencies [45]. an absorption profile with sharp sloping edges, non- The absorption lines of interest are those near the absorbing species may be added to the absorption cell to laser emission wavelength, which is produced by a provide pressure broadening resulting in a convolution frequency-doubled, injection seeded Nd:YAG laser at of Gaussian and Lorentzian profile, which is equivalent 532 nm. There are several manufactures of injection- to the real part of the complex error functional and seeded Nd:YAG laser systems, which is one of the is also known as the Voigt function. The addition of the reasons this filter species/laser combination is so widely non-absorbing species is found to greatly decrease used. The laser is tuned in frequency by applying a bias the slope of the absorption line and thus greatly increase voltage to the injection seeder temperature control the FWHM. This is also why one must ensure that the circuit. This changes the temperature and index of cell is free of contaminants that may vaporize, so that refraction of the Nd:YAG (or Nd:YVO4) crystal which the most optimum controllable profile can be realized. slightly varies the output frequency (over approximately 80 GHz). The injection seeder laser beam is then 5.2. Illuminating lasers introduced into the Nd:YAG host laser cavity where it is amplified over spontaneous noise emission if it is Several different atomic/molecular filter and laser within the bandwidth of the longitudinal mode of the combinations have been proposed or actually used in host laser [52]. In order to optimize the output, the host FRS measurement techniques as will be seen shortly resonator is mechanically translated by mounting the [1,8,20]. An applicable system generally is a combination rear mirror on a piezoelectric tuning element which is of a laser, which is relatively available and well dithered to provide a feed back signal to produce the characterized by industry, with an atomic/molecular frequency overlap with the seed laser frequency. This species, which is easily handled, has characterized typically results in slow frequency changes to prevent the absorption properties, and has lines which are sharp laser from unlocking. One indicator of how well the and form relatively isolated absorption profiles simulat- frequency of the host laser overlaps with the injection ing a frequency notch filter. Due to their common use in seeder is to monitor the Q-switch Build-up Time (BUT), FRS applications to be described shortly, there are three which is a voltage output proportional to the time absorption species and laser combinations discussed in between the firing of the Q-switch and the occurrence of some detail here. the laser pulse. The BUT is minimized for optimized The most utilized filter species/laser combination is frequency overlap indicating that most of the energy is the iodine molecular filter, generally used in conjunction going into the frequency associated with the seed laser with a Nd:YAG pulsed laser (although it is noted that and not spontaneous emission. Generally the resulting iodine also has absorption lines accessible by cw argon- linewidth is quoted as having a frequency linewidth on ion lasers). At ambient temperature and pressure, iodine the order of 150 MHz. The downside of utilizing is a solid substance of a dark blue/black color and injection seeding is that the laser is typically susceptible sublimates forming a violet color diatomic gas. Spectro- to vibrations, and may unlock (support multiple cavity scopic studies of the iodine molecule [43–51] show that modes, thus becoming broadband) unexpectedly. For- in the visual range absorption lines occur due to tunately, the BUT can be monitored so that data is not electronic transitions with associated rotational and taken when the laser is not seeded. Another practical vibrational states. In the literature it is recognized that aspect to the laser is that it has been observed to have only two of these transitions affect the visual range, frequency variations across the beam of up to 100 MHz ARTICLE IN PRESS

M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142 107

1.2 [53] sometimes termed a frequency chirp. This has been 1.1 reported to be due to manufacturing limitations in the 1.0 Nd:YAG rods and may be fairly stable, but can be 0.9 reduced by limiting the useable portion of the laser to 0.8 0.7 the center of the beam [53,54]. 0.6 Fig. 10a shows a portion of the absorption spectrum 0.5 as modeled by Forkey [13,44], corresponding to the

Transmission 0.4 vicinity of the tunable range of the Nd:YAG laser (it 0.3 should be noted that this model does not include the 0.2 unbound state). The absorption lines are calculated 0.1 from published data of ro-vibrational transitions of the 0 2 18787 18788 18789 18790 18791 18792 B X system. As can be observed, there are several (a) Wavenumber (cm–1) optically thick absorption features within the tunable frequency range of the Nd:YAG laser that have the 1.2 characteristics mentioned previously and thus can be utilized for FRS. The absorption feature located near 1 Experiment 18789.28 cmÀ1 is often chosen as the ﬁlter band used for Theory FRS experiments, since it satisﬁes requirements stated 0.8 above. Fig. 10 shows a comparison between the iodine

0.6 absorption lines modeled and the absorption proﬁle experimentally measured in the vicinity of this absorp-

Transmission 0.4 tion feature. As demonstrated here the agreement between the model and measured profiles is very good 0.2 with almost all the features having similar magnitudes and positions. 0 0 5 10 15 20 25 Another pulsed laser system which utilizes iodine (b) Frequency [GHz] molecular filters in FRS techniques is the pulse-burst laser, first proposed and developed by Lempert et al. and Fig. 10. Portion of the iodine absorption spectra within the Wu et al. [55,56]. Fig. 11 gives a general schematic of the frequency tuning range of a Nd:YAG laser (a) and comparison system developed and utilized by Thurow et al. [57] in of modeled (using the model provided by Forkey et al. [44]) and measured profiles in the vicinity of the feature at their PDV studies and is similar in concept to those 18789.28 cmÀ1 (b). utilized by the other researchers [57,58]. The goal of this

To Application (532 nm) λ/2 CW Harmonic Laser Telescope λ Crystal λ/2 λ/4 /4 Fast Pockel Cells Telescope λ/2

λ/2 λ/4 Telescope λ/2 λ Focusing /2 λ PCM /4 Assembly Lens

Amp Optical Isolator Waveplate Focal / Expanding Lens

Polarizer Mirror

Fig. 11. Schematic of a Nd:YAG pulse-burst laser utilized by Thurow et al. [57], Reprinted with permission. ARTICLE IN PRESS

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Burst Repitition Rate 5 to 10 Hz (0.2 to 0.1 sec.) Micro-pulses 1 to 100 µs pulse separation

Time Burst 1 to 99 Pulses

Fig. 12. Illustration of the output of a pulse-burst laser. laser is to provide relatively low frequency (5–10 Hz) burst laser has been reported by Thurow et al. [59] to be bursts of packets of micro-pulses at a higher frequency approximately 65 MHz before frequency doubling. The (1 MHz) as illustrated in Fig. 12. This allows the energy of each micro-pulse varies depending on such micro-pulses to have much higher individual pulse quantities as the leakage through the pulse slicer, energy than if the laser were continually pulsed at the number of amplifiers in the system, and number, and high frequency. The laser is initiated with a CW distribution of pulses, as well as other factors, but Nd:YAG ring laser which serves as the primary typically ranges from 10 to 100 mJ/pulse. amplifier. Next the beam is double-passed through a A second laser and filter combination that has been flash-lamp pumped preamplifier. The 200-ms pulse is utilized by researchers is the cavity-locked, injection- then chopped into a predetermined number of micro- seeded titanium:sapphire (Ti:Al2O3) laser and mercury pulses using a Pockels cell pulse slicer. Generally, the vapor cells. Application to flow diagnostics with this pulse slicer allows micro-pulse spacing of 1 to 100 ms combination was first introduced by Finkelstein et al. with the number of pulses determined by how many can [60]. Their Ti:Al2O3 laser which was operated in the be fit into the 200 ms manifold of the Nd:YAG ultraviolet range based on the system described by Rines amplification. This micro-pulse train is then passed and Moulton [61]. Considering the Rayleigh scattering through multiple Nd:YAG flash lamp amplification cross section, it is apparent that utilizing ultraviolet stages (some with a double pass configuration) to wavelengths will result in more scattering signal increase the energy of the resulting beam. The individual compared to the visible wavelengths described pre- pulse energies are made relatively equal by adjusting the viously. It should be kept in mind, however, that the energy and delay of each amplification stage, as well as gain actually achieved may not be as great due to optical the transmission through the Pockels cell pulse slicer. and sensor efficiencies and available laser energies at Spatial filters and telescope optics are generally used at ultraviolet wavelengths [62]. The pulsed, injection- one or more locations in the pulse-burst laser system to seeded laser developed by Finkelstein et al. [60] consists improve the beam profile, and optical Faraday isolators of two Ti:Al2O3 crystals pumped by a frequency- are utilized to prevent feedback. In addition, a phase- doubled Nd:YAG laser operating at 10 Hz. The laser conjugate mirror is added to the system to reduce the is cavity-locked to its seed source which is a CW amplified spontaneous emission and eliminate the DC Ti:sapphire (modified Schwartz Electro-Optics titan CW pedestal, which decreases the energy available in each ring laser) which is pumped by the 514 nm line of an micro-pulse [57]. Before the laser beam exit, a potassium argon-ion laser and tunable over a range from 680 to titanyl phosphate (KTP) crystal doubles the frequency 1100 nm. For FRS measurements utilizing mercury, the resulting in a wavelength of 532 nm that can be tuned in seeded laser is tuned to 761 nm and introduced into the frequency to the iodine absorption features described unstable resonator cavity of the host laser. The pulsed previously. The pulse burst laser is tuned in a similar cavity’s high reflector is mounted on a custom piezo- manner to the injection seed laser by adjusting the electric transducer with a unique ‘‘Ramp and Lock’’ temperature of the Nd:YAG crystal in the CW ring methodology to allow the laser frequency to be rapidly laser. The advantage of the pulse-burst laser design is scanned and the frequency to be locked between the seed that it does not require injection seeding to the host laser and pulsed laser before every pulse [60]. In order to which results in a much more stable frequency without a attain the ultraviolet wavelengths, the near infrared need to lock onto a host laser cavity mode using a output is frequency-tripled by passing the single-mode dithered mirror. The frequency linewidth of the pulse- pulsed beam through a pair of beta barium borate ARTICLE IN PRESS

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(BBO) crystals. This laser developed for FRS had a temporal linewidth of 22.5 ns and frequency linewidth of approximately 20 MHz. It should be noted that, other than the mercury absorption lines described below, the seed laser has been used in conjunction with potassium absorption cells in frequency-modulated studies which will be described shortly [63]. Fig. 13 shows the mercury lines in the vicinity of 253.7 nm, accessible by the Ti:sapphire laser utilized in FRS studies by Yalin et al. [62]. The transmission profiles using the CW seed laser are shown for a cell length of 5 cm evacuated to minimize collisional broadening. The cell wall body temperature is set slightly above the cold side-arm temperature which is varied from 20 to 200 1C in the scan shown resulting in vapor pressures of 0.003, 0.48 and 2.89 Torr. The transmission profiles shown are from the 3P-1S mercury transition with the absorption features due to the naturally occurring isotopes of mercury [60]. Aside from the advantages provided to the Rayleigh scattered signal by Fig. 13. Mercury absorption profiles over a range of vapor cell ultraviolet illumination, several features of mercury partial pressures accessible by a tirsapphire laser operating at a wavelength of 253.7 nm. From Yalin and Miles [62]; reprinted filters make them an excellent choice for FRS applica- by permission of the American Institute of Aeronautics and tions [62]. First is the fact that the absorption profiles Astronautics, Inc. have steeply sloping edges due to the relatively high atomic weight of mercury. The low melting point allows the vapor pressure to be attained at reasonable reported by Mach and Varghese, must be placed in a dry temperatures. As shown in Fig. 13 the absorption nitrogen environment so that excessive condensation is profile changes greatly due to the increase in mercury avoided on the diode [64]. vapor density and collisional broadening that combines the individual lines into a single feature by 2.89 Torr. 5.3. Laser frequency monitoring Probably the greatest advantage of using mercury vapor filters, however, is the fact that mercury has much Another equipment item that is somewhat special to deeper absorption features than iodine and does not FRS systems is motivated by the need to monitor (and suffer the continuum absorption from unbound transi- adjust) the pulse-to-pulse laser frequency. There are two tions as the number density is increased. Instead, away methods that are commonly employed to monitor the from the absorption features, the mercury filter has a laser frequency. The first method, illustrated in the transmission of almost unity with losses due only to schematic of Fig. 14, has been used by a variety of windows and broadening from the adjacent lines. research groups for FRS and PDV measurements that Although the previously described laser systems employs a second atomic/molecular filter sometimes utilized in FRS have all been solid-state lasers, another termed the reference filter [6,7,65–69]. As seen in Fig. 14, laser system utilized in FRS technologies described a portion of the laser beam is directed to the laser below are diode lasers. These can be much less expensive frequency monitoring system (or wavemeter) with an than the systems previously discussed and can have a optical wedge and divided again to be directed to modest cw output with a rapid and continuous tuning multiple photodiode locations. Generally, at least three capability within their operational range [64]. Due to measurement locations are utilized, one to measure the their lower intensities leading to weaker Rayleigh intensity directly, one to measure the transmission scattering, however, diode lasers are more commonly through the iodine reference filter, and a third location utilized in frequency-modulated FRS techniques [63,64] used to calibrate other filters used in the experiment. that incorporate lock-in amplifiers so that the low signal Before passing the light through the filters, the beam is levels can be measured. One diode laser and atomic filter generally expanded and collimated to a larger diameter combination utilized in modulated FRS techniques is a (28 mm). After emerging from the filters, the beams GaAlAs diode operated at a wavelength of 794 and were refocused onto diffusing elements before being 780 nm to access the D1 and D2 lines of a rubidium collected by the photodiodes. This allowed for the vapor filter [64]. In order to be utilized in FRS these highest intensity to be sent through the filter without diode lasers typically require ultra-low current sources, saturating the transition. To ascertain whether or not cooled thermoelectric temperature controllers and, as the transition is saturated, measurements could be ARTICLE IN PRESS

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M W Injection-seeded Nd:YAG laser To flow field

BS BS CL BI : Boxcar Integrator PD1 BS : Beam splitter M CL : Collimating lenses FMS : Freq. Monitoring system ND S BI ND FC : Iodine filter cell M : Mirror RC FC Computer ND : Neutral density filter PD2 PD3 RC : Reference iodine cell S : Shutter FMS W : Wedge

Fig. 14. Reference filter based FRS frequency monitoring system. compared with a neutral density filter inserted in the reference CW beam path in front and behind the filter. If the former Nd:YAG laser portion of measurement showed greater attenuation than the latter, seed beam M the filter was saturated and the irradiance of the beam KTP needed to be reduced. Boxcar Integrators sampled the crystal photodiode signals over the 10 ns duration of the laser pulsed Nd:YAG pulse and transferred their signals to a personal laser 1064nm computer. The ratio of the outputs from the integrators BS is a measure of the transmission of the incident light HBS through the filter and, with the use of a calibrated filter/ BD 532nm frequency profile can establish the laser frequency. A frequency shutter is sometimes added to the system, which is counter stabilized reference capable of closing and obtaining a background reference iodine cell any time the filters are calibrated or the reference Mach 2 nozzle intensified frequency is measured. Additionally the seeder BUT CCD PD voltage is measured with each pulse to ensure that the camera laser is locked to single-mode operation. Generally, the laser frequency offset voltage, photodiode values, BUT, test iodine section lock-in are recorded for each camera image and stored in a log cell file. Successful operation of the frequency monitoring computer - amplifier A/D board and and feed back system has been shown to have an ability to accurately frame grabber circuitry measure the laser frequency within 4 MHz [7]. Improved reference filter frequency monitoring systems (utilizing Fig. 15. Optical heterodyne beat frequency detection utilized fiber optics, and energy meters instead of Boxcar for FRS laser frequency measurement. From Forkey et al. [13]; Integrators) are now commercially available. reprinted by permission of the American Institute of Aero- nautics and Astronautics, Inc. The second method of monitoring the laser frequency utilized in a variety of FRS applications is to incorporate a heterodyne technique, combining the beam of the through a KTP crystal, passing it through the absorp- laser interrogating the flow field with a second laser tion cell, and focusing it on an amplified photodiode. which is frequency stabilized. The signal from the photodiode is used to lock the laser Fig. 15 illustrates the system, first utilized by Forkey frequency using a first-derivative nulling technique. A et al. [13]. The system starts by redirecting a small portion of the CW reference laser beam (before portion of the CW injection seed laser, which sets the frequency doubling) is also sent through the fiber optic frequency of the Nd:YAG pulsed laser. This portion of overlapping the beam from the injection seed laser. The the CW seed laser beam is sent through a single mode interference of the two beams generates a heterodyne polarization-preserving optical fiber passing onto a high- beat signal, which is measured by a microwave speed detector. A second CW Nd:YAG laser (termed the frequency counter. The system developed by Forkey et reference laser) is frequency stabilized onto the mini- al. [13] is quoted to allow frequency measurements over mum of an optically thin absorption feature of a 80 GHz with an accuracy of 72 MHz. It should be controlled reference cell (iodine in the present case). noted that similar heterodyne methodologies in FRS This is accomplished by frequency doubling the beam techniques have been used by other researchers who ARTICLE IN PRESS

M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142 111 employ other types of CW lasers (e.g., diode lasers, mercury filters. In general, the reason that only Ti:sapphire lasers). qualitative flow visualizations are accomplished is due to the fact that the number density of the scattered particles is unknown (or not measured separately) and 6. FRS flow visualization therefore the transmission ratio is unknown, which could be used to measure the velocity in techniques One of the first utilizations of FRS in fluid dynamics discussed shortly. research was to improve qualitative flow visualizations. Miles and Lempert [11] were the first to employ FRS There are two distinct advantages of FRS when applied to flow visualizations in studying a Mach 2.0 supersonic to flow visualizations depending on the characteristics of jet and supersonic boundary layers [12,71]. The scattered the scattered light, as illustrated in Fig. 16. First, if the light from the supersonic boundary layer images was source of the scattered light is from solid particles seeded from condensation particles (estimated to be on the or naturally occurring (i.e., condensation from CO2, order of 30 nm in diameter), which mark the cold water, or ethanol) in the flow, the linewidth of the supersonic free stream and evaporate in the warmer particulate Rayleigh scattered light will experience little boundary layer near the wall. This method of seeding for broadening, often being approximately the same as the flow visualizations is sometimes referred to as passive interrogating laser beam. However, if the particles are scalar seeding or vapor screen technique. Additionally, moving with the fluid and the incident and observation the free stream provides sufficient Doppler shift to move directions are set appropriately [according to the the frequency of the condensation outside of the Doppler shift, given in Eq. (11)] the scattered light from absorption filter. The resulting signal effectively marks the moving particles will be shifted in frequency. The the free-stream fluid separately from the boundary layer, scattered light from walls or windows in the test section which has a significantly lower or no signal at all. The will also have a narrow linewidth similar to the advantage of FRS for boundary layer flow visualizations illuminating laser, but it will observe no shift in is clearly evident in that almost all of the surface frequency. Therefore, when a sharp atomic/molecular scattering is absorbed by the filter, which would filter is placed in front of the camera and the laser is otherwise saturate the detector and obscure the flow adjusted in frequency to be in the absorption well of the features. atomic/molecular filter, the unshifted background scat- Extensive FRS flow visualizations of Mach 3.0 tering from the walls and windows is strongly absorbed, supersonic boundary layers were also conducted by while the Doppler shifted light from the flow field is Samimy et al. [72] and Arnette et al. [73,74] to transmitted and imaged by the camera. For Nd:YAG characterize the large scale structures. Since FRS allows laser and iodine filter combinations the extinction ratio measurements to be made close to surfaces, they were has been improved when an e´ talon has been added to the able to characterize the presence of streamwise long- oscillator cavity [70], and extinction ratios over 5 orders itudinal structures present in planar views. Also, Arnette of magnitude are reported for Ti:sapphire lasers and et al. [73,74] attained FRS flow visualizations of the large-scale structures for a Mach 3.0 boundary layer. They compared the flat plate boundary layer with Background that formed after passing through a centered expansion. Signal Absorption Fig. 17 shows the FRS flow visualizations from water Profile condensation obtained in those works, where a Mach 3.0 supersonic boundary layer on a flat plate, on a 71, and on a 141 centered expansion are shown. The large- scale structures are clearly observed as the signal is reduced due to the lower Doppler shift and the Doppler Shifted evaporation of the seeding existing in the warmer Scattering From boundary layer. After analyzing several instantaneous Particles Background images, it was found that as large-scale structures pass Signal Transmitted through the expansion wave, they increase in scale and Through Filter angular orientation. Quite striking, however, is the fact that the laser sheet, which is directly hitting the surface visualized, does not saturate the Rayleigh scattering Spectral Intensity and Transmission signal. This is one of the main advantages of using FRS ∆ν Freq in flow visualizations. D FRS flow visualizations have also been utilized in Fig. 16. Illustration of the scattered spectra and transmission investigations on shock/shock boundary layer interac- profile for FRS particulate-based flow visualizations. tions in a Mach 3.0 flow by Forkey et al. [75]. Forkey ARTICLE IN PRESS

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Fig. 17. FRS flow visualizations of a Mach 3.0 boundary layer formed on a flat plate (a), and as it propagates through a 71 (b) and 141 (c) expansion as presented by Arnette et al. [74]. The flow direction is from right to left. Reprinted with the permission of Cambridge University Press. and colleagues were not only able to conduct planar the formation of large scale structures in supersonic FRS measurements, but they where able to construct a shear layers and their change in characteristics as the volumetric FRS flow visualization image by combining compressibility is increased. Also, Finkelstein et al. [60] multiple planes together of averaged images. Again FRS utilized Mercury atomic vapor filters and a Ti:Sapphire was necessary to minimize the overwhelming scattering laser to demonstrate the utility of this system for UV from the walls, near where the images of the flow field flow visualizations. were desired. Also the shock waves were clearly visible Aside from single-shot condensation-based FRS flow as a discrete increase in the intensity due to the density visualizations, investigators have also utilized multiple increase across the shock or total elimination of the laser pulses to investigate the temporal evolution of signal as the droplets evaporated due to the significant large-scale structures in supersonic boundary layers. temperature rise across stronger shock interactions. Baumgartner et al. and Erbland et al. investigated a Elliott et al. [76] have also utilized FRS to investigate Mach 8 supersonic boundary layer using what they ARTICLE IN PRESS

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termed CO2-enhanced FRS imaging [77–79]. Liquid compression (again utilizing CO2 condensation to CO2 was introduced into the stagnation chamber of the enhance the Rayleigh scattering signal). The images blowdown wind tunnel which initially vaporizes at the show the temporal evolution of the large-scale structures stagnation conditions, but later forms small particles and their clear interaction with the oblique shock wave (cited in their paper to be less than 100 nm, although formed from the compression process. Also, they no standard deviation is given) as the flow cools and is demonstrated that the flow visualizations in different expanded through the converging diverging nozzle. regions of the flow field can be enhanced by tuning the Initially, single-shot instantaneous FRS flow visualiza- frequency of the laser to overlap different regions of the tions were taken [77,78], but later tests incorporated a iodine absorption feature utilized in their study. double Q-switched Nd:YAG pulsed laser and two Additionally, Huntley et al. [81] conducted several cameras so that images could be taken at two successive experiments on an elliptic cone placed in a Mach 8 flow times varying from 15 to 200 ms [79]. This allowed to investigate boundary layer transition using mega- qualitative information about the evolution of the large- hertz-rate imaging FRS and a pulse-burstlaser. By scale structures to be calculated from spatial correlations taking temporal span-wise images at 500 kHz, Huntley between successive frames to determine the size, and colleagues were able to construct volumetric images coherence, and convective velocity of the large-scale indicating the shape of the boundary layer/free-stream structures. Erbland reported that structures convect with interface (as represented by the CO2 sublimation). the free-stream velocity at the top of the boundary layer, Fig. 18 shows the volumetric FRS flow visualizations decreasing to approximately 95% to 98% inside the created from span-wise plane imaging with a Reynolds boundary layer for the Mach 8 flow studies [79]. number (based on the stream-wise distance from the With the advent of Nd:YAG pulsed burst-lasers cone tip) of 1.53 Â 106 for a 4:1 cone. The x0-axis in the described previously and high framing rate (at or volumetric image is constructed assuming the average exceeding 1 MHz) CCD and CMOS cameras, FRS convective velocity measured by plan-view images and temporal flow visualizations are possible, allowing ten calculating the distance, based on the time separation to thirty images to be taken in sequence. Utilizing the between sequential images. The frozen-field hypothesis Nd:YAG pulse-burst laser with iodine molecular filters was then investigated for a range of conditions by taking to reduce surface scattering, Lempert et al. [80] and Wu simultaneous plan-view images and determining if the et al. [56] presented FRS time-sequenced flow visualiza- structures could be identified in the volumetric image. tions of a Mach 2.5 boundary layer over a 141 centered For the upstream location, the large-scale structure is

Fig. 18. Volumetric reconstruction (from 28 spanwise images taken at 500 kHz) of the centerline region of a 4:1 elliptic cone placed in a Mach 8 freestream. The X0-axis is scaled using the convective velocity and the streamwise location of the imaging plane results in a Reynolds number of 1.57 Â l06. From Huntley et al. [81]; reprinted by permission of the American Institute of Aeronautics and Astronautics, Inc. ARTICLE IN PRESS

114 M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142 characterized by a hemispherical bulge followed by pairs scattered light is from molecular scattering, it may be of smaller-scale ‘‘arms’’ which wrap around either side. Doppler shifted, but more importantly, is broadened The train of characteristic structures may represent due to the thermal motions of the molecules present in hairpin vortices as observed in subsonic boundary layers. the flow field. Therefore, background scattering from Other images taken further downstream indicate that walls and windows are again strongly suppressed, since the structures become smaller and their evolution is the linewidth of the scattering is narrow and unshifted in more pronounced. Structures of the boundary layer for frequency. One might consider why only qualitative flow a 2:1 elliptic cone show similar results [81]. visualizations are obtained, until Eq. (30) is fully The second type of flow visualization that can be considered and it is observed that there are many enhanced by FRS is illustrated in Fig. 19. Again, if the thermodynamic and optical arrangement variables which govern the intensity of the scattered light taken. If these quantities are not measured, can be assumed to Background be negligible, or are not modeled, then there will be more Signal Absorption Profile unknowns than equations or measurements to solve them and only qualitative measurements can be made. Even though quantitative measurements are not possible, qualitative flow visualizations still serve a useful purpose having led to many discoveries and descriptions Doppler Shifted of flow phenomena. Thermally Broadened As an example of molecular FRS flow visualizations, Scattering From Fig. 20 shows instantaneous and averaged images of an Background Molecules Signal Transmitted underexpanded jet formed from a converging nozzle Through Filter operated at an equivalent Mach number (Mach number realized if the flow was expanded isentropically from stagnation conditions) of Me ¼ 2:0 as presented by Spectral Intensity and Transmission Elliott et al. [82]. The laser sheet and camera are oriented ∆ν Freq for a stream-wise view of the jet as shown so that the D Doppler shift due to the dominant velocity component is Fig. 19. Illustration of the molecular Rayleigh scattering minimized and the intensity changes are more represen- spectra and transmission profile for FRS molecular based flow tative of density variations. As observed, the shock/ visualizations. expansion diamonds and Mach disk are clearly visible

Fig. 20. Instantaneous (a) and average (b) molecular FRS ﬂow visualization of an underexpanded jet with an equivalent Mach number of 2.0. The ﬂow is from left to right as depicted in the setup shown to the right [82]. ARTICLE IN PRESS

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Fig. 21. Molecular FRS image of the evolution of a laser induced spark from a 200 mJ Nd:YAG laser interacting with a Mach disk formed from a Mach 2.0 underexpanded jet (From Adelgren et al. [83] reprinted with permission).

and well defined from the change in the density/ the Mach disk formed in an under-expanded jet with an pressure/temperature to the scattering profile. Also the equivalent Mach number of 1.7 using molecular FRS instantaneous image clearly illustrates the presence and flow visualization. By taking images at successive time character of the turbulence in the shear layer created delays from the initiation of the laser-induced spark, the between the jet core and ambient air. In this experiment evolution of the heated region and shock interaction can the jet was slightly heated so as to avoid condensation. be characterized as shown in Fig. 21. As observed, the The effect of velocity is reduced by orientation of the distortion of the Mach disk (normal shock) due to the laser sheet and camera 901 to the major (streamwise) initial blast wave is minimal (t ¼ 8 ms), but as the heated velocity direction. Therefore, to a first-order approx- region interacts with the Mach disk (t ¼ 12–16 ms) it imation, the flow visualization represents the density distorts upstream in a process sometimes referred to as changes in the flow. Secondly, it is noted that the effect thermal lensing. At later times, a vortex ring is formed, of particles present in the ambient air is negligible, since consistent with the interaction of density variations with they have a narrow linewidth and remain in the the induced curvature of the shock wave. absorption profile of the filter. In similar measurements, Miles et al. [71] utilized molecular FRS flow visualization technique in an over-expanded Mach 5 jet to 7. Single property measurement compare the use of iodine filters to decrease the background scattering with unfiltered images taken at Returning to Eq. (28), it is clearly evident that the lower (266 nm) wavelengths. Also, investigations have scattered signal is a function of optical quantities, and been conducted by Adelgren et al. [83] and Yan et al. the thermodynamics properties and species concentra- [84] to investigated the flow resulting from laser-induced tion (through the Rayleigh scattering cross section), and optical breakdown in air using FRS. They were able to flow velocity. One can imagine that the optical characterize the formation of the ringed vortex and quantities can be eliminated by normalizing the signal induced jet in the heated region, and also to provide by that from known conditions (e.g., ambient condi- time-sequenced visualizations of the resulting blast tions) and the effect of the background scattering can be wave. In addition, Adelgren et al. [83] characterized eliminated through calibration (so long as the latter is the effect and evolution of laser induced breakdown on not so high as to overwhelm the Rayleigh signal). As ARTICLE IN PRESS

116 M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142 observed in Eq. (30), however, the thermodynamic term FRS velocimetry would also be accurate since the quantities are still unknowns. Before describing how to cases to be presented here collect the scattered light from resolve all the thermodynamic properties using FRS we particles at or near the Rayleigh scattering regime. As will first demonstrate that individual quantities can be illustrated, the laser sheet is imaged by one camera, resolved through a combination of assumptions, model- which views the illuminated plane through the atomic/ ing the quantities’ interaction, or through careful molecular filter, termed the signal camera (or signal arrangement of the optics. Following is a description image), and a second camera which views the light sheet of the methodologies and applications of various without a filter, termed the reference camera (or research groups to measure single or a reduced set of reference image). A polarizer is placed before the beam flow properties utilizing FRS. splitter to insure that there are no polarization- dependent optical distortions between the signal and reference images. Also, a neutral density filter is utilized 7.1. FRS velocimetry in the reference camera leg so that the two cameras have approximately the same intensity range. The atomic/ Similar to FRS flow visualizations from particulate- molecular filter is similar to those described previously based scattering discussed previously, velocity measure- containing an atomic or molecular species having an ments can be obtained from condensation particles, absorption line in the frequency tuning range of the which generally place the scattering in or near the illuminating laser, but as mentioned, the slope of the Rayleigh scattering regime. Although previous review absorption profile may be broadened with the addition articles have been written on utilizing molecular filters to of a non-absorbing species. This results in a filter that measure velocity [8,9], our emphasis will be on reviewing has a transmission profile with finite sloping edges, as recent work where Rayleigh scattering was employed. shown in Fig. 23a. The term In=I0 is the spectral When utilizing FRS for velocity measurements from transmission of the molecular filter, with I n; defined as condensation particles there are two differences from the the spectral intensity (intensity at frequency n) after the molecular Rayleigh scattering. First, the scattered signal cell, and I0 defined as the spectral intensity before from particles is not greatly broadened due to thermal entering the cell. The spectral intensity of the light motions of the gas and therefore we can assume it has a passing through the molecular filter is the integral of the constant linewidth determined by the spectral linewidth product of the scattered spectral intensity from the of the laser used to illuminate the flow field. Secondly, particles illuminated in the flow field, and the absorption when utilizing FRS for velocity measurements based on profile of the atomic/molecular filter as illustrated. As an condensation particles an absorption filter with more example, consider a case where the laser frequency, n0,is gradual sloping profile is sometimes needed, so that the tuned to the midpoint of the transmission profile. The Doppler shift does not move the scattered signal entirely scattered light experiences a change in frequency, due to out of the filter profile. This can be accomplished by the Doppler shift [Eq. (11)], causing the transmission introducing a non-absorbing gas into the atomic/ from the scattered light to either increase or decrease molecular filter. This will pressure-broaden the absorp- depending on whether the frequency increases or tion profile [7]. decreases. Note, also, that there is no ambiguity in the Fig. 22 gives a general arrangement of the laser, direction of the shift: positive and negative frequency cameras and atomic/molecular filter when making FRS shifts are distinguished by the increase or decrease in velocimetry measurements. This technique is also transmission, respectively. The pixels of the signal commonly referred to as DGV, or PDV although the camera CCD array, record the integrated spectral intensity transmitted through the molecular filter’s Laser absorption profile and is given by I. The second Sheet Reference reference camera (or a separate portion of the same camera camera) images the flow field without the molecular filter and is used to account for intensity fluctuations due to Filtered laser energy variations (and/or sheet energy distribution) Imaging Molecular camera or seed-concentration variations. The reference camera Filter Region records the integrated spectral intensity of the unfiltered Beam Splitter light I0. Cube After appropriately calibrating the reference and Polarizer signal camera images so that they have the same intensity scale and spatial position on a pixel-to-pixel Fig. 22. Schematic of the dual camera configuration for FRS basis, the integrated transmission through the cell is velocimetry (also termed DGV or PDV) measurements made obtained by dividing the intensities of the signal (I) and from condensation particles. reference (I0) cameras at corresponding pixels. Several ARTICLE IN PRESS

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using this measured Doppler shift in accordance with vector relationships given in Eq. (10). As may be noted, the measured Doppler shift is dependent on the difference between the illumination and observation ∆ν D directions, respectively. This fact may be exploited in order to make multi-component velocity measurements either by viewing the flow field from more than one direction (changing the direction of the observed vector), or by illuminating the flow field from multiple directions (changing the direction of the incident light wave vector) [87]. In addition, it has been shown that the laser and camera vectors can be optimized to minimize effects on

Spectral Intensity and Transmission laser frequency ﬂuctuations and accuracy of the velocity components [88,89]. Several works provide the details of (a) Frequency molecular ﬁltered velocimetry (or DGV, PDV) systems [5–7,85,90], detailed error analysis [86,90,91] and many practical considerations in implementing a system 0.5 [92–94]. Utilizing FRS velocimetry offers two advan- 0.4 tages. First, particles are small, and therefore more

(Ghz) 0.3 accurately track the ﬂow, particularly in turbulent

cam 0.2 regions and ﬂows around shock waves where there can

ζ ∆ν 0.1 D be abrupt changes in velocity. Gustavsson and Segal [95] 0 theorized that for their axisymmetric supersonic Mach 2.2 jet studies, the decay time of 10 to 100 nm particles –0.1 were 2.6 ns and 55 ns respectively, clearly illustrating the –0.2 advantages of utilizing smaller particles to more –0.3 accurately measure the velocity of the gas. Second, the –0.4 Frequency function scattering characteristics in the Rayleigh scattering –0.5 regime from polarized coherent light sources are more uniform, lacking the intensity lobes characteristic of 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 larger particles. The latter may cause uncertainties (b) Transmission ratio through the optical train particularly if beam splitters Fig. 23. Illustration of the transmission profile and particle are utilized or the optics of the signal and reference scattering for FRS velocimetry measurements (a) and resulting cameras are different. Doppler shift frequency function (b) used to determine the Previously, investigators have utilized condensation velocity from the transmission ratio measured by the calibrated particles in the Rayleigh scattering regime to make velo- signal (filtered) and reference (unfiltered) cameras. city measurements in supersonic flows [12,71], supersonic shear layers [91], supersonic jets [6,7,90,94,95], and works have been published where the details of this supersonic boundary layers [96]. Since the publication of calibration process are described [5,6,7,85,86]. The trans- a review article on molecular filtered based velocimetry mission profile is transformed so that the integrated techniques of Elliott and Beutner [8] several studies have transmission is the independent variable and the frequency utilized Rayleigh scattering from condensation particles shift is the dependent variable as shown in Fig. 23b.Inan to obtain velocity measurements. FRS velocimetry experiment, once the integrated trans- Crafton et al. [97] applied PDV (or FRS velocimetry) mission is determined from the two cameras at each to measure three velocity components in a small-scale corresponding pixel, the Doppler shift can be found using supersonic Mach 1.36 jet. Fig. 24 shows the experi- the frequency function (Fig. 23b). This process may be mental arrangement used for the jet study. The arrange- represented by the equation ment utilizes two-camera systems and two laser light positions so that all three velocity components could Dn ¼ z ðS=S ÞÀn (32) D cam ref 0 be resolved. In order to obtain three mean velocity where DnD is the Doppler shift, zcamm is the frequency components from two camera systems, two orientations function of the filter placed in front of the signal camera, of the incident laser directions were used in the study. S=Sreff is the transmission calculated at a given camera The camera positions were kept the same for both pixel after proper calibration, and n0 is the relative laser sheet arrangements. The combination of these data frequency of the laser, measured by the wavemeter. The results in three independent system sensitivity vectors. velocity is then calculated at each pixel of the image The jet was seeded with ethanol vapor, which condensed ARTICLE IN PRESS

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Reference Camera Laser Sheet Position #1 Mirror Signal Excitation Laser Camera Beam Laser Sheet Molecular Filter Position #2 Z PDV Polarizer Component #2 Beam X Mirror Splitter Polarizer Cube Reference Camera Y Jet Beam Splitter Cube Molecular Filter PDV Component #1 Signal Camera

Fig. 24. FRS velocimetry (PDV) arrangement utilized by Crafton et al. [97] to measure multiple velocity components of a Mach 1.34 supersonic jet force using laser energy deposition.

Fig. 25. Three components of velocity measured using FRS velocimetry (PDV) in a Mach 1.34 jet with laser excitation at 170 and 220 ms. The convective velocity (200 m/s) has been subtracted from the velocity vectors (based on date reported by Crafton et al. [97]). in the free stream, forming small particles, which could perturb the shear layer at the exit of the nozzle with accurately follow the ﬂow features. The jet was operated approximately 30 mJ in a 10 ns pulse from a second at Mach 1.34 with a stagnation temperature and exit Nd:YAG laser. The interrogation laser beam is then velocity (based on isentropic theory) of 300 K and delayed (by 170 and 220 ms) from the perturbation pulse. 399 m/s, respectively. In addition to measuring the This allows the formation of a large-scale structure in perfectly expanding supersonic jet using the three the shear layer that can be phase-averaged. The ﬁgure component PDV system, measurements were also taken shows the resulting three-component velocity measure- of the large-scale structures induced in the supersonic ments obtained in this manner. This not only is a good shear layer using laser energy perturbation (see Fig. 25). laboratory-scale experiment to test the FRS velocimetry This is accomplished by focusing a second laser beam to system and data reduction routines, but also is an ARTICLE IN PRESS

M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142 119 interesting flow field to quantify the evolution of the gular jet with an exit height of just 1 mm and aspect ratio large-scale structure as it convects downstream. The of 5 to investigate the ability of PDV to measure the color contours indicate the out-of-plane velocity com- velocity at small scales. FRS velocimetry techniques ponent while the vectors indicate streamwise and have a great advantage in micro-flows over PIV spanwise velocity components (with the convection techniques since individual particles need not be velocity subtracted from the streamwise component). resolved, and so the particles mark the fluid continu- Clearly visible is the large-scale structure that is formed ously instead of at discrete points. Although previously on the shear layer shown to the right. The PDV researchers had been able to combine signal and technique had the required sensitivity to capture the reference images on a single camera, after several optical change in the core velocity due to the growing structure. arrangements were attempted they found that separate Additionally, one can observe the change in the signal and reference cameras were needed to prevent spanwise component of velocity, which indicates that a significant cross-talk (light from the signal and reference vortical structure is present. For the later time, the images overlapping) between images. Similar to other velocity field shows the effect of the large-scale structure studies an injection seeded frequency-doubled Nd:YAG as it convects downstream and grows as it encompasses laser was used in conjunction with a pressure-broadened more fluid from the jet core and atmosphere. An iodine vapor cell. With a dual camera arrangement they uncertainty analysis was conducted indicating that the were able to construct a system which had a spatial random plus total uncertainty for the three-component resolution of as little as 20 mm and measured a single test was 17 m/s. This uncertainty is dominated by component of the velocity within 15% of theoretical speckle noise, with an uncertainty in the mean measure- isentropic values in the micro jet core [98]. ments reduced by about 10 m/s from this level. The error Going beyond MHz-rate FRS flow visualizations and reported in the mean measurements compared to single-shot velocity measurements, Thurow et al. have isentropic theory was approximately 7.2 m/s, which is utilized a Nd:YAG pulse-burst laser (described pre- less than 2% of the jet core velocity [97]. viously) to obtain temporally resolved FRS velocimetry One recent work which again took advantage of the (or PDV) measurements from condensation particles in naturally occurring condensation particles in the Ray- the Rayleigh regime [57,59]. They used two high-speed leigh scattering regime to measure the velocity using CCD cameras at framing rates of 250 kHz with atomic/molecular filters was conducted by Sethuram et accuracies in measuring the velocity reported to be al. [98]. They used an FRS velocimetry technique (PDV) within 16–24 m/s for single-(combined signal and to measure the velocity field in supersonic micro flows. reference images on a single camera) and two-camera Sethuram and colleagues constructed a Mach 2 rectan- systems, respectively. Fig. 26 presents a sequence of 21

Fig. 26. Movie of the velocity ﬁeld of the shear layer and large-scale structures created by a Mach 2 jet issuing into ambient air and measured using pulse-burst laser based PDV. The scattered signal is collected from condensation particle and the data was acquired at 250 kHz with the high-speed jet core at the top of the images and ambient air at the bottom (From Thurow et al. [59] reprinted with permission). The ﬂow direction is from left to right. ARTICLE IN PRESS

120 M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142 frames taken at 4 ms time intervals for the shear layer created by a Mach 2.0 supersonic jet issuing into ambient air [59]. The high-speed supersonic core of the jet is at the top of the image with the ambient air at the bottom. The images capture the details of a large-scale structure starting at the left of the first image and the evolution of the structure and the resulting velocity field as it is entrained and stretched by the faster moving fluid. The velocity measured was reported to be within 5% of the expected value in the supersonic core of the jet. This represents the first time in which the temporal evolution of the compressible turbulence could be quantified through velocity measurements at rates high enough to track the spatial velocity field changes due to individual turbulent structures at supersonic speeds.

7.2. Frequency-modulated ﬁltered Rayleigh scattering

As utilized by the FRS velocimetry techniques Fig. 27. Frequency-modulated laser spectrum (100 MHz mod- presented here, the frequency of the scattered light ulation frequency) for a titanium:sapphire laser operating at collected from particles in the flow is changed by the 770 nm. From Grinstead et al. [99]; reprinted with permission. Doppler shift. Instead of a direct measurement of the transmission profile to deduce the velocity, as described above, Grinstead et al. [63,99,100] proposed and developed a technique they termed frequency-modulated filtered Rayleigh scattering (FM-FRS). In FM-FRS the Doppler shift is determined utilizing frequency-modulated absorption spectroscopy. Similar frequency-modulated FRS techniques have been developed by Mach and Varghese [101] and Jagodzinski and Varghese [102,103] who investigated the feasibility of utilizing single diode lasers, as will be described shortly. As a first step in FM-FRS, Grinstead et al. utilized a narrow-frequency linewidth CW titanium:sapphire laser, which was modulated using a resonant electro-optic modulator driven at 100 MHz by a phased-lock oscillator [63,99,100]. The resulting laser beam has a power spectrum, which is reproduced in Fig. 27. Side bands representing the first harmonic (at the modulation Fig. 28. Direct and first-harmonic FM absorption spectra of a frequency) and second harmonic (at twice the modula- potassium vapor filter (Dl absorption line of potassium 39 tion frequency) appear symmetrically to the central line. occurring at 769.9 nm) as measured by Grinstead et al. [100]. These side bands are equal, but 1801 out of phase and at Reprinted with permission by the Optical Society of America. a reduced intensity from the center frequency [99]. Grinstead and colleagues utilized absorption lines of potassium in their atomic vapor filter (at wavelengths Fig. 28 shows the direct and FM absorption spectra of around 770 nm), which had a Gaussian transmission the D1 absorption line of potassium 39 occurring at profile. When the modulated laser profile (shown in 769.9 nm as modeled and measured by Grinstead et al., Fig. 27) is scanned through the filter, the direct utilizing a CW Ti:Sapphire laser [100]. Even a qualita- absorption spectrum is also Gaussian. However, if the tive comparison of the direct and FM absorption transmitted laser light is detected at the modulation profiles reveals that the FM absorption profile is frequency (100 MHz in the present case), the spectrum representative of the first derivative or slope of the obtained, referred to as FM absorption spectrum,is direct absorption profile. As part of the FM-FRS approximately proportional to the first derivative of the system, Grinstead and colleagues utilized the FM filter transmission profile. For a detailed mathematical absorption signal to form a closed-loop feedback treatment of the FM spectrum the reader is referred to controller, locking the laser frequency to the cross-over the work by Hils and Hall [104]. point of the FM absorption profile. If the laser ARTICLE IN PRESS

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flow facility high-speed photodiode

vapor filter vapor filter

E/O modulator E/O modulator optical heterodyne/ high-speed photodiode photomultiplier tube

frequency counter

feedback feedback Real-time Doppler shift phase-sensitive reference measurement probe phase-sensitive detector/amplifier laser laser detector/amplifier

Reference laser frequency Probe laser frequency

Fig. 29. Schematic of the FM-FRS to measure velocity in real time. The FM-FRS system shown here utilizes two titanium: sapphire lasers one locked directly to the potassium FM absorption line and one locking the Doppler shifted scattering from the ﬂow ﬁeld to the FM absorption line. The frequency difference between the two lasers represents the Doppler shift, which is measured using an optical heterodyne technique. From Grinstead et al. [99]; reprinted with permission.

frequency drifts to either side of the zero-crossing laser was directly frequency-locked onto the potassium frequency of the FM absorption spectra the closed-loop FM absorption profile and the second laser was adjusted controller was developed to return the laser frequency to in frequency until the Doppler shifted signal from the the zero-crossing frequency (a complete description of flow field was locked onto an identical potassium FM the details of the innovative closed-loop controller is absorption profile. A schematic of the FM-FRS system given by Grinstead et al. [99]). developed by Grinstead et al. is illustrated in Fig. 29 In order to make velocity measurements using FM- [99]. The frequency difference between the two lasers FRS, Grinstead and colleagues demonstrated that not therefore represented the Doppler shift frequency, which only could the modulated laser light be obtained from could be used to calculate the velocity from Eq. (11). the laser directly, but also it can be obtained from the Ginstead et al. utilized an optical heterodyne technique scattering signal, as the modulated signal is preserved (similar to that employed by Forkey) to measure the when scattered light is collected from particles (CO2 frequency difference (and therefore the Doppler shift) condensation particles) seeded into a flow field. If the between the two lasers. In their initial work, they flow is moving, however, the modulated laser light will constructed the mathematical model to analyze the be Doppler-shifted in frequency [Eq. (9)] due to the measurement capabilities and uncertainty of the system. optical arrangement and flow velocity. In FM-FRS the They also performed rotating disk velocity measure- scattered light from the flow field is collected at the ments obtaining a Doppler shift of 164.472.1 MHz, in modulation frequency using a high-speed photodetector very good agreement with the 16573 MHz measured by viewing the light through a potassium absorption filter. a conventional system. Also, they evaluated the bias Similar to using the direct laser light described above, error introduced in the measurements by background the scattering based FM absorption signal can be scattering (not Doppler shifted), and proposed methods utilized in a closed-loop control system to lock the to account for or eliminate this error. Grinstead et al. scattered signal (which represents the laser frequency [63,100] also demonstrated that a single titanium:sap- plus the Doppler shift frequency) onto the cross-over phire laser could be utilized by obtaining the reference point of the FM absorption spectra. The advantage of frequency from direct absorption measurement of a utilizing this signal detection at RF is that the noise is second potassium reference cell instead of utilizing a minimized making detection at low light levels possible second laser and the optical heterodyne technique [99]. Originally, Grinstead et al. developed a system (which was unavailable at the time of the test). They utilizing two separate Ti:sapphire laser systems; one performed experiments in an underexpanded supersonic ARTICLE IN PRESS

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Fig. 30. Real-time velocity measurement in a supersonic jet taken using FM-FRS. The FM-FRS system is locks the Doppler shifted scattering from the jet to the potassium FM absorption feature and monitors the frequency with a second reference ﬁlter. The regions indicated by B, C, and D represent the measurement as the stagnation pressure (i.e. exit velocity) is changed. From Grinstead et al. [100]; reprinted by permission of the Optical Society of America.

jet collecting the scattered light from condensation measured to be 280725 m/s using their laser diode particles of CO2 seeded into the flow. Fig. 30 demon- based MFRS system and sources of uncertainties were strates the ability of the single laser FM-FRS system to evaluated. Jagodzinski and Varghese later extended measure the flow velocity in real time as the jet MFRS to measure the velocity in unseeded flows [102], stagnation pressure (and therefore exit velocity) was and improved the temporal resolution of the MFRS varied. Fig. 30 shows the relative laser frequency (which velocimeter [103]. was locked to the Doppler shifted signal from the flow field) measured by the potassium reference cell as the 7.3. FRS thermometry stagnation pressure of the jet was changed as indicated at the top of the graph. This plot clearly indicates that Another thermodynamic property measurement, which the velocity can be measured in real time with an has been measured using FRS is temperature. To begin estimated error of less than 3% in a 10-Hz bandwidth. our discussion let us consider again the FRS signal Mach and Varghese [101] proposed an alternative equation [Eq. (28)]. In general, there are three assumptions, system composed of a single GaAlAs diode laser tuned that are needed to reduce the number of unknowns so that in frequency to the absorption lines of Rb isotopes the collected signal is only a function of temperature: (either the D1 or D2 lines at 794 and 780, respectively) to produce and detect modulated filtered Rayleigh scatter- 1. The Doppler frequency shift (DnD) due to the flow ing (MFRS). They highlighted the low-cost, reliability, velocity is negligible. As observed in Eq. (11), this can and ruggedness of diode lasers, which are beneficial for be accomplished when the flow velocity is negligible use in flight instrumentation and industrial applications. or by aligning the laser and camera directions so that The arrangement modulated the laser at 50 MHz they do not have a sensitivity to major (e.g., stream- sinusoidally and detected the second harmonic (see wise) velocity directions. Fig. 27) of the scattering. In this way, the signal detected 2. The scattered light is from a single species whose through a Rubidium cell is approximately proportional concentration is constant. This allows us to assume to the second derivative of the absorption spectrum. The that the Rayleigh scattering cross section [found in spectrum was realized by mounting a second modulation the R calibration parameter; Eq. (30)] is constant and of a 10-Hz ramp current to the laser tuning circuit, known at every camera sensing element. which caused the laser to scan linearly in optical 3. The pressure is relatively constant, which for an ideal frequency over 10.5 GHz. In their experiments, the gas allows the temperature and density to be directly authors obtained the Doppler shift by comparing the related. peaks of the second-harmonic FM scans from the flow scattering to that from a reference cell. A jet of CO2 gas With these assumptions, and the ideal gas law operating at high pressure was utilized to test their given by system, forming condensation particles when expanding into the atmosphere. The core velocity of the jet was p ¼ NkT. (33) ARTICLE IN PRESS

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Eq. (30) can be represented as of simplifying the setup and also has the added benefit of incorporating slight variations that may occur in the Sðn ; p; T; y; fÞ 0 Z computational model into the calibration coefficients. þ1 The last method and most simplified way to calibrate the ¼ RðfÞp=kT tðnÞrðn À n0; p; T; yÞ dn FRS thermometry system is to assume that the back- À1 ground signal S is small compared to the Rayleigh þ S ðn Þ, ð34Þ Back Back 0 scattered signal or is constant and can be subtracted where SBackk is the background signal which includes from the collected signal. At first this may seem any scattered light transmitted through the cell in unrealistic, but since the background scattering from addition to the dark-current signal of the camera [term solid objects has a narrow spectral linewidth (on the C in Eq. (27)]. Although the signal is represented as order of the laser) it will be significantly absorbed when function of multiple parameters, it is noted that many of the laser is tuned near the center of the absorption line of these are optical parameters such as the angle between the atomic/molecular filter. With this simplifying the incident and observation direction, y, the polariza- assumption Equation (32) can now be written as Z tion direction, f, and laser set-point frequency, n0. These þ1 can be assumed constant, are known, or can be Sðn0; p; T; y; fÞ¼RðfÞp=kT tðnÞrðn À n0; p; T; yÞ dn, measured separately for a given experimental arrange- À1 ment. If we tune the laser frequency to a specific (35) frequency in the absorption line of the atomic/molecular where SBack has been neglected or is a constant filter (which is known) and also by knowing the subtracted from the collected signal at each pixel. pressure, the FRS signal is only a function of the Therefore, we can now normalize the signal from the temperature and optical calibration parameters R and flow at test conditions we wish to measure with the SBackk. Therefore, if we can measure these two optical signal at known thermodynamic condition and laser calibration parameters, the signal is only a function of frequency. The equation results in the form of the unknown temperature of the flow (since the pressure R þ1 is assumed to be known). The method of solution is Sðn ; TÞ T tðnÞrðn À n ; p; T; yÞ dn 0 ¼ Rref À1 0 realized by considering that the FRS signal (S) given in S ðn ; T Þ þ1 ref 0 ref T À1 tðnÞrðn À n0; pref ; T ref ; yÞ dn Eq. (32) not only can be measured experimentally, but T f ðTÞ can also be computationally modeled. The computation ¼ ref , ð36Þ Tf ðT Þ of the FRS signal utilizes a model of the Rayleigh ref scattering spectral profile [r: found by Tenti’s six- where Sref, Tref, and pref are, respectively, the signal, moment model, or assuming a Gaussian distribution at temperature and pressure at the known flow reference low densities, Eq. (16)] overlapped with the measured condition. For the form of the equation shown on the transmission profile of the atomic/molecular filter (t) right-hand side, the pressure has been assumed to be and then integrated as shown in Eq. (32). Therefore the approximately constant with the flow at test and temperature is found by comparing the measured signal reference conditions identical. By normalizing the signal with the modeled signal (using values for the optical in this fashion the optical calibration does not need to be constants, pressure, and laser frequency from the found explicitly since it is divided out in the normal- experimental arrangement), which is computed over a ization procedure. This method of solving for the range of temperatures. When the modeled and experi- temperature from a FRS signal has been used by mentally determined FRS signals agree, the temperature various investigators, but it should be kept in mind that of the flow is found. To use this method of solution, even a slight amount of background scattering passing however, R and SBack must be known at each camera through the filter can lead to large measurement sensing element (i.e., pixel). uncertainties [105,107]. There are various methods for determining R and Fig. 31a gives the measured temperature as a function SBack. One method is to measure SBack directly by of the normalized FRS signal as represented in Eq. (34) eliminating all Rayleigh scattering. This can be done by for a range of laser set-point frequencies. These curves evacuating the test region or filling it with a gas of small were created using Tenti’s six-moment model of the Rayleigh scattering cross section [13,105]. R can then be spectral Rayleigh scattering profile of nitrogen at solved by collecting the signal at a known laser atmospheric pressure assuming the detector is located frequency and thermodynamic flow condition (e.g., 901 to the incident light direction. An iodine molecular ambient conditions). Another method is to scan the filter and a frequency-doubled injection-seeded Nd:- laser frequency through several locations in the absorp- YAG laser were utilized in these simulations. Fig. 3b tion line for known flow field thermodynamic conditions represents the location of the laser set-point relative to and use a curve-fitting routine to solve for the only the line center of the iodine absorption filter. As can be unknowns R and SBack [106,107]. This has the advantage observed from these curves the shape of the temperature ARTICLE IN PRESS

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1.2 1.2 ν1=0.30 ν2=0.0

1 ν3=0.30 1 ν4=0.75 ν5=1.19 0.8 0.8 ν6=1.74

0.6 0.6 Transmission 0.4 0.4 Normalized FRS Signal [S/Sref] 0.2 0.2

0 0 200 400 600 800 1000 1200 1400 -5 -4 -3 -2 -1 0135 2 4 Temperature [K] Frequency [GHz]

Fig. 31. Normalized FRS signal versus ﬂow temperature curves (shown on the left) for a range of laser set-point frequencies relative to an iodine absorption ﬁlter (shown on the right).

FRS signal curve is greatly affected by the laser set-point the excitation laser beam. Also, one can observe the and as shown here can become double-valued for some decrease in temperature as the flow field convects and absorption lines (due to the varying width and weaker mixes with the cooler ambient air. Temperature mea- neighboring lines) if the laser frequency is not carefully surements have also been made by Boguszko and Elliott selected. This obviously creates a problem if the flow in natural convection above a heated cylinder [82], being evaluated approaches these double-valued tem- natural convection from heated bars placed between two peratures and should be avoided. It should be noted, insulated flat plates [114] relevant to electrical compo- however, that other absorption profiles do not show this nent heat transfer studies. In addition, Kearney et al. problem. [105] demonstrated the use of FRS in measuring the Also, it can be seen in Fig. 31a that as temperature thermal development of a forced heated jet. Again, they increases the FRS normalized signal decreases. At high utilized the iodine filter with a Nd:YAG laser and were temperatures it is approximately proportional to T À1. able to capture average and instantaneous measurements Thus, when the temperature range is large the decrease of the heated air jet as it entrained cooler ambient air. in signal strength with T produces a proportionally They report uncertainties on the order of 20 K in their higher measurement uncertainty than at near ambient measurements of the 800 K heated jet. temperatures. The technique loses sensitivity as the In addition, several investigators have utilized FRS to temperature increases because the density decreases and measure the temperature field in flames. For flame p ¼ const. This makes it difficult to measure high- temperature measurements, Eq. (32) and the assump- temperature flows or flames, and it is usually replaced by tions associated with it are still applied. Again, one can emission spectroscopy or filtered Thomson scattering. generally assume that the pressure is constant, and the As an example of the utilization of FRS thermometry, effect of the velocity leading to a Doppler shift is Fig. 32 gives representative images of the temperature negligible (due to velocities encountered in the flow or field resulting from laser-induced breakdown in air as the direction of the incident and observation directions presented by Boguszko and Elliott [106,114]. The laser- selected). A slightly more difficult assumption in making induced breakdown creates a plasma, formed by focusing measurements in flames, however, is that the Rayleigh the second harmonic of a 200 mJ/pulse Nd:YAG laser differential cross section and molecular mass are using a lens with a focal length of 50 mm. After the constant (which is a similar problem encountered when plasma forms, a blast wave propagates from the center of utilizing unfiltered Rayleigh scattering in flames). For the laser spark, and by 30 ms computations and experi- example the Rayleigh scattering cross section of a fuel ments indicate that the pressure remains constant [67]. such as methane is over twice that of air. Therefore, in Therefore, the resulting temperature field can be non-premixed flames, regions dominated by fuel lead to measured by FRS using the assumption 3, as outlined measurement inaccuracies if not corrected. Unknown previously. Observed in Fig. 32 is a sequence of FRS species concentrations affects the thermal broadening temperature images taken at successive delay times and the y-parameter which governs the spectral shape of measured from the instant of the excitation pulse. the Rayleigh scattering. Clearly shown is the formation of a vortex ring and The most simple method of minimizing this problem induced jet, which propagates in a direction opposite to is to apply FRS thermometry in premixed fuel-air flames ARTICLE IN PRESS

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Fig. 32. FRS temperature measurements of the flow field created from a Nd:YAG laser beam (net energy of 145 mJ) focused in quiescent air taken at four delay times from the initiation of the laser spark. The focused laser beam is propagating from the top to bottom of each image From Boguszko and Elliott [106]; reprinted by permission of the American Institute of Aeronautics and Astronautics, Inc. or in non-premixed flames, where the Rayleigh scatter- some cases. Again, a Nd:YAG laser and iodine filter ing cross section is nearly equal between fuel and air, were utilized in these studies. Uncertainties were and thus may be assumed to be relatively constant. This evaluated assuming equilibrium species concentrations. method was employed by Hoffman et al. [108] who first For the premixed methane/air experiments the uncer- utilized FRS to make temperature measurements in tainty in temperature for the reactants region of the premixed methane-air flames. They were even able to flame zone was approximately 11–34% depending on extend the FRS temperature measurements to slightly the equivalence ratio (the higher the equivalence ratio sooting flames, since the scattering from soot particles the higher the uncertainty) due to the high Rayleigh has a narrow linewidth and is absorbed by the iodine scattering cross section of methane present in the flow. molecular filter. In their experiments, they compared In reacting regions of the flame, however, the uncer- results from kinetic and hydrodynamic models of the tainty reduced to 2.5–4.4% since the molecular mass and Rayleigh scattering spectra and were able to make Rayleigh scattering cross section of species were more average measurements with a standard deviation of consistent. In general, in the flames investigated by 7150 K in the hot regions of the flame. Elliott et al. [109] there was significantly less uncertainty Elliott et al. [109] investigated the premixed methane/ in the reacting regions of the premixed flames studied. air and hydrogen/air flames created above various Even when a fuel such as hydrogen is utilized in a burners (i.e., holed array, McKenna, and Hencken Hencken burner configuration, the measured tempera- burners) and were able to resolve instantaneous and ture can be relatively accurate in the product region, average temperature fields in buoyancy-driven flames which was verified by comparisons of temperature and very near the burner surface (within 0.3 mm) in profiles with CARS measurements. The CARS and ARTICLE IN PRESS

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Fig. 33. Average (a) and instantaneous (b & c) temperature ﬁeld measurements using FRS of a methane/air stagnation-ﬂame. From Elliott et al. [110]; reprinted by permission of IOP Publishing Limited.

FRS measured temperatures almost completely overlap, tions from the multiple species found in the product but do deviate slightly as the equivalence ratio is region of the flame. They compared three approaches to increased. correct the FRS signal analysis for multiple species Additionally, Elliott et al. [110] utilized FRS to make which included: (1) utilizing a NASA equilibrium code measurements near surfaces in studying the flow field to obtain species concentration, (2) using the species of a stagnation flame created below a cooled substrate. concentrations at stoichiometric conditions, and (3) Fig. 33 shows a premixed methane-air stagnation flame assuming that all of the Rayleigh scattering is from and associated instantaneous and average temperature nitrogen. Fig. 34 shows the results of these tests with fields for an equivalence ratio of 1.08. It is clear that the comparisons with CARS measurements and the adia- instantaneous flames show the temperature fluctuations batic flame temperature. As observed utilizing the due to the vortices rolling up on the edge of the flame. computational model the FRS results are within 50 K Also, one can see that due to the elimination of near- of the CARS measurements. Assuming that the scatter- surface scattering, temperature measurements were ing is only from nitrogen, the measured temperature possible very near the cold substrate. The study not using FRS can be up to 150 K lower as shown in only investigated variations in flame conditions, separa- Fig. 34b. If even a simple species correction is utilized tion distance, and substrate diameter, but also compared assuming stoichiometric conditions, the temperatures results with a computation. An uncertainty analysis was can be measured by FRS to within 50 K. It was conducted utilizing the computational model that suggested that much of the bias due to the ‘‘nitrogen- indicated uncertainties of less than 5% for average only’’ assumption can be corrected by adding the measurements and 6.5% for instantaneous measure- contribution of CO2 to the FRS scattering signal since ments shown in the products region of the flames it has a Rayleigh scattering cross section 2.2 times studied. Axial profiles were compared to computations greater than that of nitrogen [105]. using a one-dimensional detailed chemistry model (GRI- In addition, FRS has also been utilized to measure the Mech 1.2 model with 32 species, 177 reactions) showing temperature field in plasmas. Yalin and Miles utilized generally good agreement. It should be noted that in all ultraviolet FRS to measure the temperature in a weakly the studies listed above, the mix of species was assumed ionized discharge [62,111,112]. Unlike the Nd:YAG to be dominated by nitrogen in the measurement laser and iodine molecular filter combination, which has regions. been employed in the previous studies, Yalin and Miles Kearney et al. [42,105] utilized FRS to measure utilized a mercury filter and a Ti:saphire laser system, temperature fields in a heated calibration jet, premixed described previously [60], operating at a wavelength of flat flame, and acoustically forced diffusion flame (which 253.7 nm.Although there is significant signal improve- will be discussed shortly). Similar to the previous ment in the UV stemming from the higher Rayleigh studies, Kearney utilized a Nd:YAG laser and iodine scattering cross section, they also evaluated other filter for the FRS experiments. A Hencken burner benefits and weaknesses of using the lower wavelength geometry was utilized in this study with a methane/air in this study (i.e., quantum efficiency of the detector, flame created over a range of equivalence ratios. For this available energy in lower wavelength sources, tempera- controlled experiment, Kearney and colleagues studied a ture measurement sensitivity of mercury versus iodine variety of assumptions to correct for scattering varia- vapor cells). Although in many ways the temperature ARTICLE IN PRESS

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measurement error due to velocity Doppler shift in the sensitivity direction is negligible. However, when the velocity is important, such as in highly turbulent flows, supersonic combustion, or plasma jets, the investigation of temperature by FRS must include an error analysis in which Doppler shift is included as a source of bias error. Some knowledge (or estimation) of the largest velocity in the flow is necessary so that the error based on some DV is computed. This error can be calculated by finding the derivative of the total signal with respect to a change in velocity and using the customary laws of error propagation.

8. Multiple property measurements

8.1. Average measurements (FRS frequency scanning technique)

In the previous sections we have reviewed studies indicating that single properties (i.e., velocity or temperature) can be measured using FRS. Now we would like to investigate and review the research extending FRS to simultaneously measure multiple properties. In order to solve for the pressure, density, temperature, and velocity it is necessary to resolve their individual effects on the characteristics of the Rayleigh Fig. 34. Comparison of FRS-and CARS-measured flame scattering line shape. Miles et al. [12,71] and Forkey et temperatures from the Hencken burner and the calculated equilibrium product temperature for varying fuel-air stoichio- al. [13,14,43,112] developed a method from which the metries as measured by Kearney et al. Part (a) shows the FRS convolution of the Rayleigh spectrum and the absorp- temperatures deduced by using the calculated major product tion filter can be used to obtain these unknown compositions. Part (b) shows FRS temperatures calculated properties. Again, the setup is similar to Fig. 2, with a assuming a stoichiometric mixture (solid symbols) and assum- narrow linewidth laser formed into a sheet passing ing that all scattering arises from nitrogen (open triangles). through the flow field to be investigated. The Rayleigh From Kearney et al. [105]; reprinted by permission of the scattering from molecules in the flow is collected with a American Institute of Aeronautics and Astronautics, Inc. detector (generally a CCD or ICCD camera) viewing the light through an atomic or molecular vapor filter. In the sensitivity of iodine and mercury filters was similar, FRS frequency scanning method, the FRS is recorded Yalin and Miles indicated that the optical depth of the over a range of laser frequencies as the latter is tuned latter is much greater (over 105) without the background across an absorption line, as illustrated in Fig. 36a. The continuum absorption observed with iodine. In their camera then collects the transmitted light integrated initial study, they presented FRS point measurements in over all the frequencies, within the range of the detectors a 50 Torr, 20 mA weakly ionized (o10À6 ionization sensitivity. This results in a convolution of the Cabannes fraction) argon glow-discharge with unfiltered Rayleigh line and the filter function, described by Eq. (30). scattering data having an uncertainty of 3–4%. In later Note that various thermodynamic properties are experiments they measured the two-dimensional tem- clearly evident in the FRS convolution profile as perature fields in diffuse and contracted discharges using illustrated in Fig. 36b [43]. First, the density is directly FRS thermometry [111]. Fig. 35 gives an example of the proportional to the signal collected when the laser is temperature field of a diffuse discharge (50 Torr) in tuned outside of the filter since the Rayleigh scattered argon (20 mA) and in argon plus 1% nitrogen; the small intensity is not modified spectrally. The lowest point in amount of Nitrogen causes a decrease in temperature the convolution curve of Fig. 36(b) is an indication of even though the mixture is at a higher current. An the shape of the Rayleigh scattering profile which is a uncertainty analysis indicated that the temperature field function of pressure (through the y parameter) and could be measured in these glow discharges within 5%. temperature. As the temperature increases, the thermal In general, flames occur at low velocity and the broadening will increase, causing a greater portion of orientation of the interrogating beam is such that the the spectrum to be transmitted. Forkey [43] also ARTICLE IN PRESS

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methods described previously the laser frequency n0 is also known. Therefore, the unknowns are the flow properties (pressure, temperature, number density, and velocity) and the calibration parameters (R and B), which must be found for each pixel, similarly to the temperature measurements. In addition (as described previously in Section 8.2) R and B can also be obtained by performing a frequency scan with the flow off at a known thermodynamic reference condition (ambient). Generally, several instantaneous images are averaged together at each laser frequency to obtain the FRS spectral profile. For the reference condition the signal is then given by

S ðn ; Dn ; p ; T ; N ; y; fÞ ref 0 D refZ ref ref þ1 ¼ RðfÞNref tðnÞrðn À n0 À DnD; pref ; T ref ; yÞ dn À1

þ Btðn0Þ, ð37Þ

where Nref, pref, Tref, are the known thermodynamic conditions, and therefore DnD is also known (since the velocity is zero). All other parameters are known except R and B. After experimentally measuring the FRS spectral profile at the reference condition, the reference signal expressed in Eq. (35) is calculated at each probed laser frequency n0 using a computer model of the Rayleigh scattering (r: calculated using Tenti’s S6 Fig. 35. The temperature field of a diffuse discharge (50 Torr) model) at the reference conditions, multiplied by the in argon (20 mA) (a) and in argon plus 1% nitrogen (b) absorption filter profile tðnÞ, and integrated over the measured using a mercury filter and ultra-violet FRS. From frequency domain. R and B are determined using a Yalin and Miles [62]; reprinted by permission of the Optical curve-fitting routine (e.g., Levenberg–Marquardt algo- Society of America. rithm [113]) and adjusting these two quantities until the error between the computational model and the measured FRS spectral profile is minimized. Note that suggested that the side slopes of the FRS profile can also R and B must be determined for each pixel. be used to determine shape, which is also a function of Once measurements have been made to determine the pressure and temperature. In addition, the frequency calibration parameters, the laser is again tuned in shift of the minimum relative to the peak absorption is a frequency through the absorption profile of the atom- measure of the Doppler shift of the profile. Even ic/molecular filter, but this time the flow is on. Several utilizing only these general characteristics, the thermo- instantaneous images are taken at each laser frequency dynamic properties can be measured [82], but not as and averaged together resulting in an FRS spectral effectively as the method described below utilizing profile for ‘‘flow-on’’ conditions. Again, the FRS curve-fitting algorithms that employ more points to fit spectral profile is calculated using the computational the FRS spectral profile. model of the Cabannes line convolved with the As observed in Eq. (30) the convolution of the absorption filter, as is described by Eq. (28). In a similar Rayleigh scattering spectrum with the absorption manner, the computational model of the FRS spectrum feature chosen depends upon such quantities as the is fit to the function determined experimentally using the thermodynamic properties of the gas (p,T,N), viewing non-linear Levenberg-Marquardt algorithm [113]. With angle (y), angle of polarization (f), laser frequency (n0) the calibration factors and geometry known, the only and the Doppler shift DnD, which is proportional to the unknowns are the pressure, temperature, density, and flow velocity as defined by Eq. (9). Note that the Doppler shift (i.e., flow velocity), which become the constant C has been eliminated since this background is fitting parameters to the algorithm. Note that the ideal assumed to be already subtracted from the signal. gas law [Eq. (31)] is also used to reduce the number of Similar to single-property measurement techniques, thermodynamic unknowns by solving the density from from a knowledge of the optical geometry, y and f are the pressure and temperature. The thermodynamic known, and if the frequency is measured using the properties and velocity are determined by their values ARTICLE IN PRESS

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I 8000

7000

ν ν 6000 0 I ) φ ,

θ 5000 ,

T ~T , p , D 4000 ~ρ

ν ∆ν ,

ν 0 0 ν 3000

I ( S 2000 ∼∆ν ν 1000 D ν 0 I 0 –2 –1 012

ν0 (GHz) ν ν 0 I T = 150K T = 200K T = 250K T = 300K ν T = 350K –212–1 0 ν 0

Fig. 36. Illustration of the FRS frequency scanning technique developed by Forkey et al. [13] and utilized to measure multiple flow properties (i.e. temperature, density, pressure, and velocity) simultaneously. The illustration on the right depicts the resulting FRS signal when scanning the Rayleigh spectral profile from a flow field through the iodine absorption feature. when the quantities minimize the error between the one should filter out particles upstream of the inter- computed and experimentally obtained FRS spectral rogation region and block strong wall reflections. profile. Forkey et al. [13,14] was the first to utilize the FRS Fig. 37 gives a sample experimental and computed frequency scanning methodology to obtain multiple FRS spectra from a free-jet experiment for reference and thermodynamic properties and the velocity field of a ‘‘flow-on’’ conditions at a single camera pixel. The Mach 2 jet. A Nd:YAG laser and iodine filter combina- symbols indicate the grayscale values obtained experi- tion was utilized in their study. It should be noted that mentally, and the solid lines are the computationally their iodine absorption model has been used by a great modeled profiles obtained by solving the properties number of researchers. In order to measure the using the curve fitting algorithm of the FRS spectral frequency of the Nd:YAG laser, Forkey and colleagues profile. As shown, the agreement between the modeled utilized the optical heterodyne beat signal with a second and experimental profiles is quite good, and the shift in frequency stabilized CW Nd:YAG laser described frequency due to the velocity is clearly quantified. previously. Additionally, they were able to evacuate Unlike the temperature FRS measurement, the fre- the test chamber to determine the calibration factors R quency scanning technique is especially susceptible to and B by direct measurement. The velocity measured stray light and particle scattering. Reflections from within the Mach 2 jet was within an uncertainty of surfaces and large particle scattering may be orders of approximately 75 m/s (out of a measured velocity magnitude larger than Rayleigh scattering. These between 192 and 221 m/s in the direction of system sources may mask the Rayleigh signal, particularly sensitivity. Pressure measurements were within expected when the scattering frequency is outside of the absorp- levels for this initial study, but the temperature had a tion line. If the flow field investigated is near walls, has variation of 717 K across the jet, but the average of naturally occurring particles such as soot, a solution 142 K was within 1 K from the theoretical isentropic may be to reduce the scanning range only to the region value. In a later study, Forkey and colleagues conducted where the absorption band sufficiently attenuates these a detailed uncertainty analysis of the FRS system [14]. contributions, or use multiple absorption lines with They reported the uncertainty of the velocity, tempera- different characteristics. Of course, whenever possible ture, and pressure to be 72to73%, 72%, and 74to ARTICLE IN PRESS

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75%, respectively. Evaluating several sources of error, Boguszko and Elliott also utilized the FRS frequency they determined that significant uncertainties were due scanning technique to investigate the flow field created to frequency variations across the laser sheet, long-term by a converging nozzle operated at subsonic and drift of the reference laser frequency, and the measured underexpanded supersonic conditions [108,114]. The scattering angle [13,14,112]. FRS setup is presented in Fig. 38. A laser sheet from a Nd:YAG laser (532 nm, 10 ns pulse length) was used to illuminate the measurement region along the jet axis. 1.0 Perpendicular to the sheet an ICCD camera captured 0.9. the scattered radiation through the molecular iodine filter cell. A co-flow of clean dry air was used to prevent 0.8 particles from reaching the test section. The viewing 0.7 region started 10 mm (or about 1.5 diameters) down- 0.6 stream to avoid surface scattering from the nozzle exit. Since the experiments were performed in ambient air, it 0.5 was not possible to use evacuation techniques to 0.4 determine the calibration factors R and B. Instead, the Transmission 0.3 FRS frequency scanning technique was applied to a reference condition (ambient with zero velocity) and R 0.2 and B were solved for at each camera pixel using the 0.1 non-linear curve fitting algorithm as described pre- 0 viously. The reference condition was taken by acquiring –3 –2 –1 0123 images while performing a 120-point scan through the ν (GHz) absorption line, each point being an ensemble average of 50 instantaneous frames. After acquiring the calibration Filter cell Flow condition parameters, the FRS spectral profile is measured again Reference condition Model fit 2 by tuning the laser across the iodine absorption line p = 1.62 atm Model fit 1 (120-points), but now with the flow on. Fig. 38 shows p = 1 atm T = 338.76 K T = 291.65 K u = 373.7 m/s the properties measured using FRS with the jet operated u = 0 m/s with a stagnation pressure of 364 kPa. For these conditions the converging nozzle produced an under- Fig. 37. Experimental and modeled FRS spectral profile from expanded jet with an equivalent Mach number of frequency scanning measurements of ambient air and an Me ¼ 1:5. The shock-expansion diamond patterns char- underexpanded jet (Me ¼ 1:5) at a single pixel element. The symbols indicate the grayscale values obtained experimentally, acteristic of an underexpanded jet are apparent in the and the solid lines are the computationally modeled profiles figure. As the flow propagates downstream, pressure and obtained with properties solved for by the non-linear Leven- temperature decrease as the velocity increases. The berg–Marquardt algorithm. oblique shocks cause a rapid increase in thermodynamic

Fig. 38. Pressure, temperature, and velocity fields of an underexpanded jet (Me ¼ 1:5) measured using the FRS frequency scanning technique. The flow direction is oriented from the bottom to the top of the image. From Boguszko and Elliott [114] figures reprinted by permission of Springer Verlag. ARTICLE IN PRESS

M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142 131 properties and a reduction of flow velocity. Several in a discrete region after the shock. Comparisons other flow conditions were studied using FRS rang- between the FRS result and those from a computational ing from subsonic to supersonic Mach numbers. A model developed by Yan et al. are also shown in Fig. 39. detailed uncertainty analysis conducted indicated that The experimental results show good agreement and have the pressure, temperature, and velocity had uncertain- been used to refine the model (in the way the initial ties on the order of 70.07 atm, 74.1 K, and 77 m/s energy is deposited into the flow and the time and respectively, which was in general agreement with grid scale of the problem), to use in more complex measured errors of known (subsonic and sonic) flow flow geometries [115]. Comparing the property changes fields. with the expected changes which would occur across The FRS frequency scanning technique has also been a moving normal shock, the density change was within applied to study the flow field created by laser induced 5%, temperature change was within 1%, and the optical breakdown by Boguszko and Elliott [106] and velocity induced by the shock was within 75 m/s of Yan et al. [67], using a similar experimental arrangement expected values. as given in Fig. 38. Although the emission prevented the measurement of the thermodynamic properties at early 8.2. Instantaneous measurements times in the region of the formation of the laser spark, Boguszko and Elliott were able to capture the property The FRS frequency-scanning method is suitable for changes across the blast wave. Fig. 39 shows curves fluid flows, which are statistically steady or are of flow properties in the radial direction (tempera- repeatable so that phase-sampling is possible. Therefore, ture, density, and pressure) and velocity behind the the method does not capture fluctuating quantities or resulting blast wave in air 20 ms after a laser induced inherently unsteady flows, but only the average of the optical breakdown event. The initiating laser beam fluctuating properties. Early in the development of (Ei ¼ 18373 mJ) is focused by a lens with a focal length FRS however, Miles and Lempert [11] proposed that of 50 mm. The property changes due to the blast wave multiple filters adjusted to have slightly different are clearly recorded and are characterized by an increase absorption profiles could be used to measure the FRS in density, pressure, temperature, and induced velocity signal simultaneously on multiple detectors and the

1.4 1.3 Experiment Experiment 1.3 Simulation Simulation 1.2

1.2 1.1 ∞ ∞ ρ p /

/ 1.1 ρ p 1 1

0.9 0.9

0.8 0.8 01015202555010152025 (a)r/R0 (b) r/R0

1.125 0.25

1.1 Experiment 0.2 Experiment Simulation Simulation 1.075 0.15

∞ 1.05 0.1 T a / / T 1.025 u 0.05

1 0

0.975 –0.05

0.95 –0.1 0101520255 0 510152025 (c)r/R0 (d) r/R0

Fig. 39. Comparison between the properties measured using FRS and simulated for the ﬂow ﬁeld resulting from laser-induced energy deposition in quiescent air with a net energy absorption of 14572 mJ taken 20 ms after the discharge as reported by Yan et al. [67]. Reprinted with permission. ARTICLE IN PRESS

132 M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142 instantaneous property measurements could be realized. of interrogation region. This is followed by a spherical Boguszko [116] proposed the use of multiple viewing and a cylindrical lens, which allow the light to be angles of synchronized detectors so that turbulence or imaged onto the detector so that different pixel elements unsteady flow measurements of multiple properties in the vertical direction represent a point on the laser could be achieved. So far, however, none of these beam waist viewed from different angles. The lenses are techniques has been successfully used to conduct also arranged so that different pixels horizontally measurements. represent different horizontal points along the beam Another possible arrangement for measuring proper- waist. After passing through the lenses the light is divided ties and velocity instantaneously takes advantage of the by a beam splitter and imaged with a signal camera, angular variation of the scattering spectrum and was recording the light passing through an iodine molecular introduced by Shirley and Winter in 1993 [117]. They filter, and a second reference camera, which is unfiltered. proposed an anamorphic optical arrangement utilizing a In order to make preliminary measurements of low f-number lens to collect rays from different fluctuating quantities and demonstrate the concept of scattering angles and record them separately in a linear FARRS, Boguszko [116] assumed that the Doppler shift array of pixels on a CCD camera. Each individual from the flow velocity was predominantly in the resolution element provides the intensity from a point in streamwise direction, the background scattering was space as viewed from a different angle. Therefore, as negligible, and considered imaging to occur from only governed by Eq. (11), the Doppler shift frequency is the vertical column in the center of the lens (it should be slightly different for each pixel (or viewing angle). In noted that in processing the actual data this assumption essence, the different viewing angles represent the is not needed, but greatly simplifies the explanation of intensity from the Rayleigh scattering transmitted how the technique works). Defining aj, as the viewing through the atomic/molecular filter at different frequen- angle for each pixel j located in the vertical center of the cies due to the different Doppler shift components. lens, two main equations can be formulated, one for the Originally Shirley and Winter proposed this pointwise filtered (Sf) and one unfiltered (Su) camera pixels that technique to measure mass flux distributions. Elliott and are given by Samimy [118,119] in 1996 further developed this idea, S ½n ; Dn ðaÞ; p; T; N; f; a which they termed filtered angularly resolved Rayleigh f 0 D Z j þ1 scattering (FARRS) and demonstrated that with addi- ¼ Rf ðajÞN tðnÞr½n À n0 À DnDðajÞ; p; T; aj dn, tional cameras the average and instantaneous flow À1 properties of velocity, density, temperature, and pres- ð38Þ sure could be measured. Furthermore, Boguszko and

Elliott [116] extended this system to measure the mean SuðN; ajÞ¼RuðajÞN, (39) and turbulence quantities of the core flow and shear where R and R are optical calibration factors and a is layer created by a Mach 1.36 perfectly expanded jet. f u j the observation direction of the jth camera pixel in the The anamorphic optical arrangement used in their imaged column (from the previous equation y is now study is illustrated in Fig. 40. The system starts with a replaced by a function of a ). The Doppler shift equation low f-number lens (f/1.2), which is placed relatively j at each viewing angle can then be written for the close to the point focused on by the lens of the laser used assumptions given previously as to interrogate the flow (the second harmonic of an injection-seeded Nd:YAG laser). The collection lens 1 Dn ða Þ¼ ½u cosðp=2 À a Þ. (40) is followed by a field stop, which limits the size D j l j

Laser polarization direction Cylindrical lens Filter Á 1 o s Laser beam Field Camera 50-50 propagation stop lens Mirror (into page) 2 Spherical Flow lens

Fig. 40. FARRS optical arrangement. ARTICLE IN PRESS

M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142 133

The ﬁrst parameter that can be solved for using 1.7 FARRS is the density, which is readily obtained by 1.6 r/D = 0 dividing S by a reference condition (ﬂow off) 1.5 u 1.4 SuðN; ajÞ N 1.3

¼ (41) ) 1.2 φ

S ðN ; a Þ N ))

u ref ref j ref (

φ 1.1 u S u1.0 ref S

in this way, the calibration constant is eliminated. Now, ( 0.9 normalizing the filtered camera by the same no-flow 0.8 Reference case Flow-on case condition, the filtered calibration factor is also elimi- 0.7 Exper. Exper. nated and the signal is given by 0.6 Model Model 0.5 –20 –10020 10 Sf Snorm½DnDðaÞ; p; T; N; aj¼ (a) α (degrees) Sfref R ρ 3 þ1 ref = 1.20±0.008 kg/m N tðnÞr½n À n0 À DnDðajÞ; p; T; aj dn R À1 3 ¼ þ1 . ð42Þ ρ = 1.52±0.015 kg/m Nref À1 tðnÞr½n À n0 À DnDðajÞ; pref ; T ref ; aj dn 1.3 In Eq. (40) the unknowns are T, p, and DnD (or the u velocity after the Doppler shift equation is applied) 1.2 where it is assumed that N has been calculated from the normalized unfiltered camera and Eq. (39). The number 1.1 of unknowns is further reduced since in general the ideal 1.0 ref f ref N gas law can be applied and the pressure can be written as / /( ) N f 0.9 a function of temperature and density. Since we are S obtaining the normalized signal at each resolution 0.8 element, the number of known intensities and equations, 0.7 which can be written far exceeds the number of 0.6 unknowns. The solution must be evaluated to ensure –20 –10020 10 the values are not ill-defined (e.g., negative pressure), (b) α (degrees) which can occur when a stray dust particle is imaged or u = 1.80±3.47 m/s T = 300.8±0.7 K when the algorithm fails to converge. Similar to the FRS ref ref u = 234.3±39.5 m/s T = 229.1±5.0 K frequency scanning technique, the experimental FARRS signal-observation angle profile can be compared to the Fig. 41. Normalized FARRS signal over the range of viewing profile calculated from the computational model con- angles for ambient reference conditions and conditions with the structed for the experiment using the Tenti model of the jet running. Experimentally obtained (open symbols) and Cabannes line and knowing the absorption profile, computationally modeled (solid symbols) profiles are shown angles, laser frequency, density (from the direct mea- with the calculated properties from the least-squares curve fit: surement of the unfiltered signal), and ideal gas law (a) density calculation; (b) temperature and velocity calculation. relating the pressure and temperature. The Levenberg- Marquardt algorithm [113] was again used with the of the FARRS-observation angle profile for the computational model of the FARRS signal with u, T, unfiltered (Fig. 42a) and filtered (Fig. 42b) cameras, (the pressure is found knowing the temperature and with the flow off (ambient) and flow on conditions. The density using the ideal gas law) as fitting parameters. experimentally obtained profiles are shown with the More details of this procedure can be found in the works computed profiles and properties that were solved using of Elliott et al. and Boguszko [82,116,118,119]. the procedure outlined above. As can be observed in To evaluate the capability of FARRS to measure these graphs, the agreement between the experimental instantaneous flow properties, a preliminary experiment and computational profiles is quite good indicating that was conducted on a pressure-matched free jet with exit the model captures the relevant physics of the scattering diameter of D ¼ 12.7 mm, running at an exit Mach process. In order to resolve the turbulence profiles in the number of Me ¼ 1:36 by Boguszko [116]. The inter- jet, seven hundred instantaneous images were taken at rogation point was located at a distance x=D ¼ 5 each radial position, from which average and fluctuating downstream and data was collected at thirteen radial quantities were calculated. Fig. 42 shows the streamwise locations from the centerline r=D ¼ 0tor=D ¼ 1:4. velocity, temperature, and density obtained from Instantaneous values of the properties and stream-wise FARRS. As expected, the mean profiles show an velocity were found and used to calculate mean and increase in velocity and density in the jet core and fluctuating turbulence profiles for every laser pulse. In decrease in temperature with properties returning to Fig. 41 are sample data of an instantaneous realization ambient levels as the interrogation point is moved ARTICLE IN PRESS

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440 xD/ =4.0 300 1.8 390 3 1.6 340 250 LDV 1.4 290 FARRS 200 1.2 240 1 190 150 0.8 140 100 0.6 90 0.4 Mean Velocity (m/sec) Mean Velocity 40 (K) Mean Temperature 50 Mean Density (kg/m ) Mean Density (kg/m –10 0.2 0 0 –2.5 –1.5 –0.50 0.5 1.5 2.5 0 0.51.0 1.5 0 0.51.0 1.5 r/D r/D r/D 80 30 0.15 70 60 25 3 50 20 0.1 40 15 30 10 0.05 20 RMS Velocity (m/s) RMS Velocity 5

10 ) RMS Density (kg/m RMS Temperature (K) RMS Temperature 0 0 –2.5 –1.5 –0.50 0.5 1.5 2.5 0 0.51.0 1.5 0 0.51.0 1.5 r/D r/D r/D

Fig. 42. Mean and RMS profiles of streamwise velocity, temperature, and density as a function of radius through the shear layer of a Mach 1.36 axisymmetric jet measured using FARRS. Velocity results are compared to those from previous obtained by LDV. radially outward. The RMS fluctuations in all properties portion of the scattered light is transmitted through the are shown to increase in the shear layer region as filter and imaged by the camera. Utilizing the tempera- expected. The velocities were compared to LDV ture measurement technique described previously (Sec- measurements reported by Mosedale [7]. While the tion 7.3), the laser does not need to be scanned; average values seem to agree well, there is a discrepancy instantaneous measurements of velocity and instanta- of about 25% in the maximum RMS velocity, most neous measurements of temperature are possible. In likely due to the simplifying assumption that all the these preliminary experiments an injection-seeded Doppler shift is due to streamwise velocity only. Nd:YAG laser and iodine absorption filter were used, The uncertainty of the results for u, r, and T are and the FRS was imaged with an intensified CCD estimated to 7%, 3%, and 6%, respectively using this camera. The PIV measurements utilized a second technique. double-pulse Nd:YAG laser synchronized to give two pulses slightly delayed from the FRS laser pulse. An interline transfer camera (with the same field of view as 9. Combined techniques and future trends the ICCD camera used in FRS) recorded the two images of the particle scattering separately. Using cross- Now that various FRS techniques have been pre- correlation algorithms, particle shifts between the two sented, it is noted that many of these arrangements can images are determined and the velocity field can be be used in conjunction with other methods to improve calculated. Elliott et al. [110,120] presented preliminary the accuracy of the property measurement or measure results of the PIV/FRS technique for premixed stagna- additional properties (such as species concentration or tion-flow flames showing the simultaneous instanta- velocity) simultaneously. One of the combined techni- neous velocity and temperature field even near the ques utilizing FRS was demonstrated by Elliott et al. cooled substrate. [110,120] to measure the temperature field while The simultaneous FRS/PIV technique was also simultaneously measuring the velocity field with PIV. demonstrated by Most and Leipertz [121] who measured This was accomplished by seeding small particles into the instantaneous temperature and velocity field above a the flow field, which could be utilized for the PIV wire stabilized premixed methane-air V-shaped flame. measurement; particle scattering was greatly attenuated Instead of utilizing a double-pulse Nd:YAG laser for the when the laser is tuned in frequency near the peak PIV measurement, however, they were able to use the absorption of the filter. The Rayleigh scattered signal FRS laser as the initial pulse needed for PIV and use a from molecules, however, is thermally broadened and a second Nd:YAG laser for the second PIV pulse. ARTICLE IN PRESS

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Fig. 43. Instantaneous temperature and velocity fields in a lean premixed methane-air flame measured using simultaneous FRS and PIV. The dot in the bottom center of each image represents the position of the flame stabilization wire. From Most and Leipertz [121]; reprinted by permission of the Optical Society of America.

Additionally, they showed that for temperatures above variation using a flamelet-based model. Utilizing an 600 K, the Rayleigh scattering is in the kinetic regime, injection-seeded Nd:YAG laser with an iodine vapor which greatly simplifies the spectral profile calculation filter, Kearney et al. [68] made joint FRS/Raman since it is represented by a Gaussian distribution. measurements (shown in Fig. 44) in a methane- Additionally Most and Leipertz utilized the CHEMKIN nitrogen-air Wolfhard–Parker slot diffusion flame per- combustion code to account for various species con- iodically forced at 90 Hz. Since the structure of the flame centrations and their effect on the FRS signal due to could be phased-locked, 100 FRS and 200 Raman variable molecular mass and Rayleigh scattering cross images were averaged at each delay time taken relative section. Fig. 43 shows instantaneous images of the to the acoustic forcing. The Raman images were simultaneous temperature and velocity field that they obtained by replacing the iodine filter with an appro- obtained with this combined FRS/PIV technique. As priate interference filter and recording the CH4 vibra- shown, the local flame structure is clearly evident tional Raman shift, occurring at 2917 cmÀ1 relative to revealing characteristics of the temperature and velocity the incidence radiation. From the FRS signal and fuel fields and their interaction in the turbulent flame. An concentrations measured with the Raman signal, other uncertainty analysis indicated that the velocity could be major product species were determined using the model measured within 0.2 m/s, but the temperature may have in an iterative procedure so that the species dependent a maximum deviation of 23% in the worst case; this Rayleigh scattering cross section variations could be uncertainty seems to be quite conservative, however, corrected. Fig. 44 shows the temperature and simulta- since comparisons with the adiabatic flame temperature neous CH4 mole fraction at various delay times (phase show a discrepancy of only 4% and a deviation from angles) from the periodic forcing of the slot flame using ambient temperatures of 9% [121]. Most and Leipertz the joint FRS/Raman imaging technique. The evolution [122] also published a paper with some improvements of the temperature and fuel mole fraction fields is clearly over the original work by Hoffman. observed as the vortices interact to produce a strain- Another combined technique utilizing FRS for induced extinction event. Measurements in a laminar temperature measurements was proposed by Kearney diffusion flame indicate that the FRS corrected tem- et al. [68,105]. Their goal was to solve uncertainties peratures are within 5% of point-wise measurements associated with varying Rayleigh cross sections when made using CARS [68]. making FRS temperature measurements in non-pre- Another method of measuring species concentration mixed flames with unknown species concentrations. with temperature was demonstrated by Jacobsen et al. Previously, investigators used premixed flames and [123] and Boguszko [116]. They utilized FRS to measure assumed that a majority of the Rayleigh scattering was the temperature field and laser-induced fluorescence from a single species (i.e., nitrogen) or utilized combus- (instead of Raman imaging) to measure species con- tion models to adjust the molecular mass and Rayleigh centration. Jacobsen et al. [123] demonstrated the scattering cross sections in the model used to deduce the combined FRS/PLIF technique to measure the tem- temperature from the Rayleigh scattered signal. Kearney perature and nitric oxide fluorescence in a DC plasma- first proposed that Raman imaging of the fuel could be torch. Again the Nd:YAG laser and iodine filter were used to correct for the Rayleigh scattering cross section utilized at a wavelength of 532 nm for the temperature ARTICLE IN PRESS

136 M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142

Fig. 44. Joint FRS/Raman scattering measurements of temperature (color) and CH4 mole fraction (line contours) from a CH4–N2–air Wolfhard–Parker slot ﬂame that is periodically forced at 90 Hz. Measurements were taken at successive phase time delays synchronized to the forcing. From Kearney et al. [42]; reprinted with permission.

measurements. Relative species concentrations were Before concluding our review of FRS, it is worth measured of nitric oxide utilizing a second Nd:YAG- mentioning that similar methodologies are being utilized pumped dye laser operating at a wavelength of 573 nm, to measure properties from electrons instead of mole- which was frequency-doubled through a KDP crystal cules. Thomson scattering is the scattering of radiation and combined with the residual 1064 beam in a second by free electrons. In plasma flows such as those observed crystal to produce an output beam near 226.1 nm to in high-speed fluid dynamics, there is an interest in being access the NO fluorescence lines. Using the FRS able to measure key parameters such as the electron temperature and NO fluorescence system, Jacobsen et number density and electron temperature. Analogous to al. [123] and Boguszko [116] were able to obtain Rayleigh scattering, the electromagnetic wave intro- instantaneous temperature relative NO fluorescence duces an oscillating motion to the electrons, which intensity measurements in the plasma torch over a range reradiate the energy at the same frequency. Thomson of gas flow rates and plasma arc discharge powers. scattering has a much larger linewidth than Rayleigh Fig. 45 shows an instantaneous image of the tempera- scattering but is extremely weak and therefore is usually ture (taken using FRS) and NO fluorescence intensity masked by background scattering. Similar to FRS fields (taken using PLIF) in a plasma jet. Visible is the investigations, an atomic filter with a spectrally narrow increase in the NO fluorescence intensity, and gas absorption line is incorporated to block the unwanted temperature, in the high temperature regions of the sources of scattering, while allowing a portion of the heated gas. Although instantaneous temperature mea- Thomson radiation to be detected [124–129]. surements are possible using fluorescence signals (which In essence, electron temperature Te, and number are several orders of magnitude greater than the Raman density Ne are obtained by spectrally resolving the signal), the extra complexity of the system and data filtered Thomson scattering spectrum and measuring its processing may make it more difficult to implement, intensity. Its spectral width is sufficiently large that since it requires an additional camera and dye laser and commercial spectrometers have sufficient resolution for the fluorescence process is non-linear. this application. A Thompson scattering model is used ARTICLE IN PRESS

M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142 137

Fig. 45. Instantaneous images of relative NO concentration and temperature ﬁelds measured with LIF and FRS, respectively, in a 2 kW plasma torch igniter. From Jacobsen et al. [123]; reprinted with permission.

to fit the spectrum line shape and intensity with Te and react with the cell materials, including the glass Ne as fitting parameters. Generally, prior calibration is windows. The spectrometer captured the radiation from needed to determine quantitative values, which is usually the plasma luminescence and stray and filtered Thomson done by performing rotational Raman scattering on a scattering combined. The first two were removed by known species, such as N2. The rotational transition taking a measurement with the laser off, and subtracting strengths of the reference substance are used to find the it from the data. The remaining is a product of the detector sensitivity, probe region length, solid angle Thomson spectrum with the absorption filter profile, captured, and optical efficiency [124]. convolved with the instrument resolution. The filtered There are several difficulties in obtaining successful scattering model was applied and the solution was quantitative measurements with filtered Thomson scat- reached when it best fit the data [124]. tering technique. The most important is the interference Zaidi et al. [126] utilized a Ti:Sapphire laser at 780 nm, with elastic scattering, which is circumvented by the high combined with a rubidium atomic filter to measure rejection ratio (1:105) that can be achieved with the electron density and temperature from Thomson back- atomic filter. Another important problem is the residual scatter in an argon plasma at atmospheric pressure. broadband spontaneous emission of the laser, usually They described the construction and operation of the referred to as amplified spontaneous emission (ASE). rubidium filter, which was capable of producing a When the laser does not have a high level of spectral rubidium density gradient in one direction. This was purity due to ASE, it can induce unwanted fluorescence achieved by diffusion of the metal through He (buffer in the plasma, which masks the Thomson signal. To gas) between the heated lower surface (source) and the solve this problem Bakker et al. [124,130] proposed an cooled upper surface (trap). In an earlier work [125], ASE spectral filter consisting of a sequence of 20 they demonstrated the dispersion capabilities of this dispersion prisms with a pinhole field stop at each end. filter near the D2 absorption line and obtained rotational The system achieved a reduction in spectral impurity of Raman spectra of CO2. Using the filter as a notch filter, seven orders of magnitude, and has been widely in conjunction with a CW Ti:Sapphire seeded laser in a adopted. The interference with the luminescence from cavity-locked arrangement, and a 20-prism dispersion the plasma also can cause measurement problems when filter (ASE filter) they measured an electron density of 16 À3 its spectrum falls near the measurement wavelength. Ne ¼ (1.6170.05) Â 10 cm and electron temperature Care must be taken to choose an interrogation of T e ¼ 0:82 0:06 eV (T ¼ 9500 700 K) in an atmo- frequency sufficiently separate from plasma emission. spheric pressure argon plasma [126]. In recent works a number of different combinations of Lee and Lempert [127–129] constructed a system lasers and filters have been tested to measure the consisting of a diode laser injection-seeded, narrow Thomson scattering. Bakker et al. [124] utilized an spectral bandwidth Ti:Sapphire laser at 780.24 nm and a excimer dye laser emitting at 589 nm and a sodium vapor rubidium vapor filter for Raman/Thomson scattering absorption cell (exciting its D2 transition at 589.0 nm) to measurements in weakly ionized argon DC discharge obtain measurements of electron density and electron plasmas. Their contribution was significant in demon- temperature on a fluorescent lamp. They also presented strating how to improve the spectral purity of the a thorough description of the filter cell construction, laser with the objective of measuring lower electron given that sodium is a highly reducing agent that may density and electron temperatures. They demonstrated ARTICLE IN PRESS

138 M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142 improvements progressively: First, by using a config- works were reviewed that utilized particle scattering in uration of injection seeding alone, then by coupling the the Rayleigh regime for flow visualizations by leading- seed laser through the cavity output using a Faraday edge research groups. These investigations include rotation optical isolator, then by using the 20-prism volumetric visualizations, turbulent compressible flows dispersion monochromator (ASE filter), and lastly by at MHz rates, and boundary layer imaging. In the addition of a stimulated Brillouin scattering phase- quantitative velocity measurements a technique called conjugate cell (SBS cell) [131]. The latter reduced the DGV or PDV was described with filters of absorbing residual elastic scattering present after the filter due to species and also with mixtures of absorbing/non- an unlocked component of the output intensity. Using absorbing species. The literature reviewed describes the this system they successfully measured an electron study of single and multiple velocity components based density and electron temperature of (3.770.08) Â on the Doppler shift in environments ranging from 1013 cmÀ3 and 0.6370.025 eV (T ¼ 7300 290 K), re- large-scale flows to microflows, and studies of accuracy spectively, in a 100-mA, 30-torr argon DC constricted limits of this velocimetry technique. glow discharge [130]. In a following work they incorpo- In addition to utilizing direct absorption, researchers rated a feed-back loop between the Ti:sapphire laser have also demonstrated frequency-modulated FRS cavity and the CW seed laser increasing the laser spectral techniques (utilizing first or second harmonic absorption purity to above 0.99999 [128]. This allowed them to spectra). The basis of the technique is that when the operate the rubidium absorption cell at a lower scattering is demodulated at the frequency of the nth temperature (270 1C) resulting in a much narrower harmonic, the absorption spectrum recovered corre- absorption line. In this way a narrower Thomson sponds approximately to that of the nth derivative of the scattering spectrum (product of a lower electron filter absorption function. This allows the system to be temperature) was resolved. Measurements using this locked into a reference frequency via a closed-loop 13 À3 system yielded Ne ¼ (6.7570.04) Â 10 cm with an controller, having the FM absorption spectrum as the electron temperature of T e ¼ 0:27 0:036 eV (T ¼ 3100 error signal. The advantages of the method are 420 K) in the same argon discharge described pre- discussed, such as velocity measurements in real time, viously [128]. It should be noted that although Thomson even at low scattered light intensities. scattering represents a different regime than that of the If the scattered light collected from the flow field Rayleigh filtered techniques presented in the majority of originates from molecules, other thermodynamic prop- this review article it represents the next step in applying erties can be measured by determining their individual atomic/molecular filtered-based techniques to measure effect on the FRS signal. FRS-based temperature the properties of a species making up a fluid medium. measurements have been demonstrated for flows rele- The reader is referred to the book chapter by Lempert vant to heat transfer studies, and has even been extended [132] for an in-depth treatment of plasmas and Thomson to make instantaneous measurements in flames and scattering. plasmas with uncertainties less than 75%. Also, FRS techniques have been extended to measure multiple properties (pressure, density, temperature, and velocity) 10. Conclusion simultaneously by scanning the laser in frequency across the filter absorption profile, or utilizing anamorphic Several applications of FRS have been presented optical systems, which allow detection over a range of demonstrating the capabilities of atomic/molecular filter angles resulting in a different Doppler shift at each based techniques. A comprehensive description of the image element. Uncertainties in making measurements theoretical and mathematical basis of the scattering/ of velocity, temperature, and pressure have been absorption processes governing FRS and derivate reported to be as low as a few percent. FRS can be techniques is presented. The model equations including combined with other techniques to measure additional particle and molecular scattering, absorption spectro- properties (velocity or species concentration) or improve scopy, and detection methods are also illustrated the accuracy of the FRS measurement. qualitatively with figures so that a reader unfamiliar Going beyond the utilization of Rayleigh scattering, with these techniques can comprehend the fundamental research groups have also demonstrated the use of concepts. The mathematical model is explained with similar atomic/molecular filter technologies utilizing each application so that the method of solution is clearly Thomson scattering from electrons to make measure- understood. ments of electron temperature and electron number When the scattered light is based on condensation density. In essence, the filtered Thomson scattering particles, atomic/molecular filters can be utilized to technique is not much different from FRS thermometry, improve flow visualizations so that boundary layer except the fact that signals are much weaker, and the characteristics can be described and multi-component line width of the scattering is much broader. A very velocity field measurements are possible. A number of large rejection ratio is needed for the elastic scattering, ARTICLE IN PRESS

M. Boguszko, G.S. Elliott / Progress in Aerospace Sciences 41 (2005) 93–142 139 thus sodium, potassium, or mercury filters are normally [11] Miles RB, Lempert WR. Flow diagnostics in unseeded used. air. Paper 90-0624, AIAA, January 1990. FRS techniques have been proven to provide a [12] Miles RB, Lempert WR, Forkey JN. Instantaneous powerful tool in investigating fluid flow fields and velocity fields and background suppression by filtered obtaining quantitative properties from it. As the Rayleigh scattering. Paper 91-0357, AIAA, January 1991. technology progresses, they are becoming more and [13] Forkey JN, Finkelstein ND, Lempert WR, Miles RB. Demonstration and characterization of filtered Rayleigh more widely used and will continue to evolve and they scattering for planar velocity measurements. AIAA J will likely become commercially available as an off-the- 1996;34:442–8. shelf product in the near future. [14] Forkey JN, Lempert WR, Miles RB. 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[69] Roehle I, Schodl R, Voigt P, Willert C. Recent [86] Meyers JF, Lee JW, Schwartz RJ. Characterization of developments and applications of quantitative laser light measurement error sources in Doppler global velocime- sheet measuring techniques in turbomachinery compo- try. Meas Sci Technol 2001;12(4):357–68. nents. Meas Sci Technol 2000;11(7):1023–35. [87] Roehle I, Willert CE. Extension of Doppler global [70] Seasholtz RG, Buggele AE. Improvement in suppression velocimetry to periodic flows. Meas Sci Technol 2001; of pulsed Nd:YAG laser light with iodine absorption cells 12:420–31. for filtered Rayleigh scattering measurements. NASA [88] Clancy PS. Development and application of three- Technical Memorandum 113177. Cleveland: Lewis Re- component planar Doppler velocimetry for high speed search Center; 1997. flows. Ph.D. dissertation, The Ohio State University, [71] Miles RB, Forkey JN, Lempert WR. 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Exp supersonic boundary layer. J Fluid Mech 1998;367: Fluids 1994;18:107–18. 67–105. [92] Kuhlman J, Naylor S, James K, Ramanath S. Accuracy [75] Forkey JN, Lempert WR, Bogdaonoff SM, Miles RB, study of a 2-component point Doppler velocimeter. Paper Russell G. Volumetric imaging of supersonic boun- 98-2607, AIAA, January 1998. dary layers using filtered Rayleigh scattering back- [93] Beutner T, Elliott G, Williams G, Baust H, Crafton J, ground suppression. Paper 94-0491, AIAA, January Carter CD. Forebody and leading edge vortex measure- 1994. ments using planar Doppler velocimetry. Meas Sci [76] Elliott GS, Samimy M, Arnette SA. Study of compres- Technol 2001;12:378–94. sible mixing layers using filtered Rayleigh scattering [94] Beresh SJ, Kearney SP, Bourdon CJ, Grasser TW. based visualizations. AIAA J 1992;30(10):2567–9. Development of a Doppler global velocimeter for high- [77] Erbland PJ, Baumgartner ML, Yalin AP, Etz MR, overexpanded supersonic jet. Paper 2003-0915, AIAA, Muzas B, Lempert WR, Smits AJ, Miles RB. Develop- January 2003. ment of planar diagnostics for imaging Mach 8 flowfields [95] Gustavsson JPR, Segal C. Filtered Rayleigh scatter- using carbon dioxide and sodium seeding. Paper 97-0154, ing velocimetry-accuracy investigation in a M ¼ 2.22 AIAA, January 1997. axisymmetric jet. Paper 2004-0021, AIAA, January [78] Baumgartner ML, Erbland PJ, Etz MR, Yalin A, Muzas 2004. BK, Smits AJ, Lempert WR, Miles RB. Structure of a [96] Arnette SA, Samimy M, Elliott GS. Two component Mach 8 turbulent boundary layer. Paper 97-0765, AIAA, planar Doppler velocimetry in the compressible turbulent January 1997. boundary layer. Exp Fluids 1998;14:232–332. [79] Erbland PJ, Murray R, Etz MR, Huntley M, Miles RB. [97] Crafton J, Carter CD, Elliott GS. Three-component Imaging the evolution of turbulent structures in a phase-averaged velocity measurements of an optically hypersonic boundary layer. Paper 99-0769, AIAA, perturbed supersonic jet using multi-component planar January 1999. Doppler velocimetry. Meas Sci Technol 2001;12(4): [80] Lempert WR, Wu PF, Miles RB. Filtered Rayleigh 409–19. scattering measurements using a MHz rate pulse-burst [98] Sethuram S, Samimy M, Lempert W. Planar Doppler laser system. Paper 97-0500, AIAA, January 1997. Velocimetry in supersonic micro flows. Paper 2002-0690, [81] Huntley MB, Wu P, Miles RB, Smits AJ. MHz rate AIAA, January 2002. imaging of boundary layer transition on elliptic cones at [99] Grinstead JH, Finkelstein, ND, Lempert WR, Miles RB. Mach 8. Paper 2000-0379, AIAA, January 2000. Frequency-modulated filtered Rayeigh scattering (FM- [82] Elliott GS, Boguszko M, Carter C. Filtered Rayleigh FRS): a new technique for real-time velocimetry. Paper scattering: Toward multiple property measurements. 96-0302, AIAA, January 1996. Paper 2001-0301, AIAA, January 2001. [100] Grinstead JH, Finkelstein ND, Lempert WR. Frequency- [83] Adelgren RG, Elliott GS, Knight DD. Energy deposition locked light scattering: real-time Doppler velocimetry in supersonic flows. Paper 2001-0885, AIAA, January with closed-loop feedback control. Appl Opt 1998;37(9): 2001. 1617–25. [84] Yan H, Adelgren R, Boguszko M, Elliott GS, Knight [101] Mach J, Varghese PL. Velocity measurements by DD. Laser energy deposition in quiescent air. AIAA modulated filtered Rayleigh scattering using diode lasers. Paper 2003-1051. AIAA J 1999;37(6):695–9. [85] Meyers JF. Development of Doppler global velocimetry [102] Jagodzinski J, Varghese PL. Diode laser velocity mea- as a flow diagnostic tool. Meas Sci Technol 1995;6: surements in unseeded flows using modulated filtered 769–83. Rayleigh scattering. Paper 2000-2297, AIAA, June 2000. ARTICLE IN PRESS

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[103] Jagodzinski J, Varghese PL. Velocity measurements by thermodynamic properties. Paper 96-0304, AIAA, Jan- modulated filtered Rayleigh scattering using diode lasers. uary 1996. Paper 2001-0848, AIAA, January 2001. [119] Elliott GS, Samimy M. A Rayleigh scattering technique [104] Hils D, Hall JL. Response of a Fabry–Perot cavity to for simultaneous measurements of velocity and thermo- phase modulated light. Rev Sci Instruments 1987;58: dynamic properties. AIAA J 1996;34(11):2346–52. 1406–12. [120] Elliott GS, Glumac N, Carter CD. Molecular Rayleigh [105] Kearney SP, Beresh SJ, Grasser TW, Schefer RW, scattering applied to combustion and turbulence. Paper Schrader PE, Farrow RL. A filtered Rayleigh scattering 99-0643, AIAA, January 1999. apparatus for gas-phase and combustion temperature [121] Most D, Leipertz A. Simultaneous two-dimensional flow imaging. Paper 2003-0584, AIAA, January 2003. velocity and gas temperature measurements by use [106] Boguszko M, Elliott GS. Measurements in fluid flows of a combined particle image velocimetry and filtered using molecular filter-based techniques. Paper 2004-0018, Rayleigh scattering technique. Appl Opt 2001;40(30): AIAA, January 2004. 5379–87. [107] Boguszko M, Elliott GS, Carter CD. Filtered Rayleigh [122] Most D, Dinkelacker F, Leipertz A. Direct determina- scattering for fluid/thermal systems. Paper 2002-3233, tion of the turbulent flux by simultaneous application AIAA, June 2002. of filtered Rayleigh scattering thermometry and [108] Hoffman D, Munch KU, Leipertz A. Two-dimensional particle image velocimetry. Proc Comb Inst 2002;29: temperature determination in sooting flames by filtered 2669–77. Rayleigh scattering. Opt Lett 1996;21(7):525–7. [123] Jacobsen LS, Carter CD, Jackson TA, Schetz JA, O’Brien [109] Elliott GS, Glumac N, Carter CD, Nejad AS. Two- WF, Elliott GS, Boguszko M, Crafton JM. An experi- dimensional temperature field measurements using a mental investigation of a DC plasma-torch igniter. Paper molecular filter based technique. Comb Sci Tech 1997; 2002-5228, AIAA, 2002. 125:351–69. [124] Bakker LP, Freriks JM, de Hoog FJ, Kroesen GMW. [110] Elliott GS, Glumac N, Carter CD. Molecular filtered Thomson scattering using an atomic notch filter. Rev Sci Rayleigh scattering applied to combustion. Meas Sci Instr 2000;71(5):2007–14. Technol 2001;12(4):452–66. [125] Tang Z, Zaidi SH, Miles RB. Density gradient rubidium [111] Yalin AP, Ionikh Y, Mechchanov A, Miles R. 2-D dispersive absorption filter for low wavenumber Raman temperature fields in glow discharges measured with ultra and Thomson scattering. Paper 2000-0644, AIAA, violet filtered Rayleigh scattering. Paper 2000-0375, January 2000. AIAA, January 2000. [126] Zaidi SH, Tang Z, Yalin AP, Barker P, Miles RB. [112] Forkey JN, Lempert WR, Miles RB. Accuracy limits for Filtered Thomson scattering in an argon plasma. AIAA J planar measurements of flow field velocity, temperature 2002;40(6):1087–93. and pressure using filtered Rayleigh scattering. Exp [127] Lee W, Lempert WR. Rubidium vapor filter spectrally Fluids 1998;24:151–62. filtered Raman/Thomson scattering. Paper 2002–0394, [113] Marquardt DW. An algorithm for least-squares estima- AIAA, January 2002. tion of nonlinear parameters. J Soc Ind Appl Math [128] Lee W, Lempert WR. Rubidium vapor filter spectrally 1963;11:431–41. filtered Thomson scattering. Paper 2002–3236, AIAA, [114] Boguszko M, Elliott GS. On the use of filtered Rayleigh June 2002. scattering for measurements in compressible flows and [129] Lee W, Lempert WR. Spectrally filtered Raman/Thom- thermal fields. Exp Fluids 2005;38(1):33–49. son scattering using a rubidium vapor filter. AIAA J [115] Yan H, Knight D, Candler G, Kandala R, Elliott G, 2002;40(12):2504–10. Glumac N. Control of normal shock in Mach 2 flow by [130] Bakker LP, Freriks JM, Kroesen GMW. A new ASE pulsed laser energy. Paper AIAA 2005-785, AIAA, filter: the 20-fold prism monochromator. Meas Sci January 2005. Technol 1999;10:L25–8. [116] Boguszko MG. Measurements in fluid flows using filtered [131] Ni CK, Kung AH. Effective suppression of amplified Rayleigh scattering. Ph.D. dissertation, Rutgers Univer- spontaneous emission by stimulated Brillouin scattering sity, October 2003. phase conjugation. Opt Lett 1996;21(20):1673–5. [117] Shirley JA, Winter M. Air-mass flux measurement system [132] Lempert W. Non-equilibrium air plasmas at atmospheric using Doppler-shifted filtered Rayleigh scattering. Paper pressure. In: Becker K, Kogelschatz U, Schoenbach KH, 93–0513, AIAA, January 1993. editors. Plasma Diagnostics. Series in Plasma Physics. [118] Elliott GS, Samimy M. A molecular filter based tech- Bristol, UK: Inst. of Physics Pub. Inc.; November 2004 nique for simultaneous measurements of velocity and [Chapter 8, ISBN 0750309628].