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The Ultimate Detectors for Cmb Measurements

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The Ultimate Detectors for Cmb Measurements 31 BOLOMETERS : THE ULTIMATE DETECTORS FOR CMB MEASUREMENTS ? Jean-Michel Lamarre Institut d'Astrophysique Spatiale CNRS- Universite Paris-Sud, Orsay, France. Abstract The noise of an optimized bolometer depends mainly on its temperature, on its re­ quired time constant, and on the incoming power. It can be made less than the photon noise of the sky in the millimeter range provided that: ( 1) the bolometer frequency re­ sponse required by the observation strategy does not exceed a few tens of hertz; (2) the temperature of the bolometer is low enough, i.e. 0.3 Kor even 0.1 K; (3) The bandwidth of the observed radiation is large, in order to maximize the detected flux. Then, the best available bolometer technology allows photon noise limited photometry of the Cosmic Mi­ crowave Background. These conditions are met in current projects based on bolometric detection for the measurement of CMB anisotropy, and especially for COBRAS/SAMBA. The space qualification of the needed cryogenic systems has been demonstrated for 0.3 K temperatures and is in preparation for 0.1 K. For this type of wide band photometry, bolometers are the best type of detectors in the 200 µm - 5 mm wavelength range. 1 Introduction Bolometers are used in a very wide range of frequencies, fromX rays to millimeter waves. This results fromthe principle of thermal detection. Photons have only to be transformed in phonons, which is a very common process at nearly all frequencies. The temperature changes of the radiation absorber are then measured by a thermometer. Historically, the discovery of infrared radiations has been made with a simple mercury-glass thermometer used as a detector. The submillimeter range {200 µm - mm is now the domain of predilection of bolometric detection. 5 ) At shorter wavelengths, photons are energetic enough to efficiently trig the photoconductor effect in low noise detectors that prove to be more sensitive. At longer ones and at high 32 Electrical and thermal connection radiative) �W ( Heat capacity � ( / J ===;;;;i;::::=::;::::i Heat conduction C fY'/ K) -::=-----� G / 3>i� /J.T = /J.W I G � �1��,��I Figure 1: Representation of a conventional composite bolometer and of the simplifiedassociated thermal scheme. The absorber insures the coupling with the radiation, while the thermometer allows to measure of the temperature changes. It must be larger than one wavelength to achieve a good coupling with the radiation field. The absorber is thermally attached to a thermometer and to a heat leak towards a heat sink at temperature If G is the thermal conductance of the heat leak, the steady state temperature T0 • change induced by an increased absorbed power is: AT AW AW (1) AT = G is measured thanks to the thermometer, usually doped silicon or germanium. A wide variety AT of techniques are now considered for new developments. The resistance R of the thermometer changes with its temperature, and may be measuredby applying a constant biascurrent I, and 33 measuring the voltage change. Taking into account the electrical power in the thermometer, the power balance can be written: (2) where a . The responsivity, i.e. the voltage change per unit of power, is = � dV a l (3) dW G-aJ2 a is negative for semi-conductors. We do not consider here thermometers working at the supraconductive transient, although promising researches are currently done in this field. From (3), we can deduce that there is an optimal current, and that high responsivities can be obtained with low values of G. The thermal time constant of a bolometer is: c (4) T=-G Its apparent time constant when operating is modified by the feedback effect of the power deposited by the bias current, but its general behaviour follows that of equation (4) : it varies as f. Sources of noises 2.2 In his nonequilibrium theory of bolometer noise (Mather, 1982], John Mather identifiesfive main sources of noise of independent origin: Johnson noise in the thermometer, thermal fluctuations of the bolometer, photon noise of the radiation, noise in the load resistor, and noise in the amplifier. In addition, he gathers other sources, especially low frequency electrical noise, under the denomination of excess noise. The total noise is the quadratic sum of all these contributors. A way to improve the sensitivity of a bolometer is to increase its responsivity by decreasing the heat leak G (see equation 3). Electrical noises will not increase, and the thermal noise will only increase as the square root of 1/G. In theory, it is possible to build infinitely sensitive bolometers by reducing G values to zero. Two phenomena will limit this search forlow G values: G must be large enough to obtain a reasonably short thermal time constant (see equation 4) and also large enough to prevent excessive heating by the incident radiative power (see equation 1). Consequently, two main requirements will limit the sensitivity of a bolometer: the required frequency response /0 , which depends on the observation strategy, and the background power, i.e. the steady part of the optical power Wbg · These two requirements determine the two terms of a semi-empirical formula giving the Noise Equivalent Power (NEP, in W H z-112) of a perfectly optimized bolometer (Mather, 1982]. 2 2 9 25 36Wb9 NEP kTo(/oCTo)( ) 4kTo (5) = ;;: A + A2 + -----:::i Where is Boltzmann's constant, and other variables have been previously defined. k A = - Depending on Wbg and f0 , the first or the��!�, second term dominate and are the main source of the NEP. The main parameter that can help is the temperature of the heat sink. Both terms depend on T0 , but the speed term is much more sensitive, since the heat capacity C of most materials is an increasing function of temperature. Ideally, the bolometer intrinsic NEP, given by formula should be significantlysmaller (5), than the photon noise, which is the fluctuationof the measured radiation itself. This determines 34 the ultimate sensitivity that can be obtained with any detector for a given source and with a given optical system. The photon noise with power sensitive detectors can be written [Lamarre, 1986]: (6) where his Planck's constant, the optical power, the optical frequency, and U the beam W n etendue in m2sr). The first term is the shot noise produced by the detection of photons as ( individual events and is dominant at short wavelengths, while the second one is produced by the interference of photons and appears when the photon occupation number is large, therefore in the Rayleigh-Jeans regime. In this case, and if the frequency term in (6) can be neglected, it is possible to derive, from equations (5) and (6) , a condition on the bolometer cooling temperature to obtain a photon noise limited sensitivity while observing a blackbody at T temperature 0 Ts : T. < ATs (7) 0 - 18 If we assume a realistic value of equal to 3 and a source temperature 3 K, it comes: A Ts = 0.5 K. From this first approach, it can be concluded that sub-Kelvin temperatures are T0 :::; needed forthe observation of the cosmic background limited by photon noise. 2.3 Frequency requirements and actual performances Equation (7) is independent of the technology and of the frequency requirement. Other con­ ditions may result from the actual heat capacity and of the scanning speed needed for a given project. For example, COBRAS/SAMBA is designed to be a spin stabilized satellite rotating at 1 round per minute, and to make measurements with an angular resolution down to 4.5 minutes of arc. The resulting maximum frequency of the signal arriving on the bolometer is 95 Hz. For the best conventional bolometers, frequency is the driving requirement for the five channels and photon noise limited photometry is achievable only for two of them, even with a cooling temperature of 0.1 K. Lower heat capacities must be looked at to solve this problem. The "Spider Web" bolometer uses a resistive grid instead of a continuous metallic layer to absorb the radiation [Lange, 1996]. Simultaneous work on the thermometer size has proven to significantlydecrease the heat capacity. Both improvements allow to reach bolometer NEPs not larger than twice the photon noise forall the channels. To give orders of magnitudes, the heat capacity of such a bolometer may be as low as 12 K, and its NEP may not exceed a few 10- J/ 1 z-112. These new bolometers have also the advantage of presenting a smaller cross 10- 7 W H section for the unavoidable interaction with particles, which decreases the rate of glitches on the bolometer signal. Other developments in the similar directions are undertaken by several teams in the world [Lamarre, 1995]. For projects less demanding than COBRAS/SAMBA in term of frequency, such as FIRE or SAMBA, temperatures significantly larger than 0.1 K can be accepted. For example, 0.3 K has been considered as a baseline for FIRE as being technically simpler than 0.1 K while not compromising significantly the finalsensitivity of the instrument. It can be considered that the available technology of bolometers at 0.3 K and 0.1 K covers the need fornearly photon noise limited sensitivities for the measurement of the cosmic background radiation. 35 3 Associated technologies 3.1 Optics The absorber of bolometers, unlike coherent detectors, can detect radiation fromany direction. Coupling a bolometer with the incoming radiation needs an efficient feed horn able to select, among all possible radiations, those coming from thetelescope. This light concentrator usually feeds an integrating cavity housing the bolometer and enhancing the efficiency of the absorber by allowing multiple reflection of photons. this cavity is usually at the temperature of the bolometer, in order to prevent its self emission from being significant.
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