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where to is the integration time (s) of the measurement. Figure 9.6 illustrates graphically the effect of integrating the signal (i.e. reducing the bandwidth) in observations of the signal returned from a lidar (optical radar) system viewing the atmosphere vertically upwards from the ground. This is an example of an active system, that is, one that includes its own source. A real lidar system, used to observe the backscatter from thin cloud layers in the atmosphere, uses two lasers, one to generate the transmitted beam and the other as a local oscillator in a heterodyne detection system. The random noise is reduced by the square root of the number of pulses averaged, and the signal is clearly seen emerging from the noise as a result. In a single measurement, the information is nearly lost in the noise; after 100 pulses (an improvement of a factor 10 in SNR) it stands out clearly.

FlG. 9.6. Cloud backscatter measurements with an upward-viewing infra-red lidar, showing the reduction of noise by integrating signals for various times. The effect on the signal-to-noise ratio of varying the bandwidth can be seen clearly. With a dwell time of 100 s (top), the backscattered signal from layers of low and high cloud can be discerned; in a 1-s measurement, these are largely lost in the noise.

FlG. 9.6. Cloud backscatter measurements with an upward-viewing infra-red lidar, showing the reduction of noise by integrating signals for various times. The effect on the signal-to-noise ratio of varying the bandwidth can be seen clearly. With a dwell time of 100 s (top), the backscattered signal from layers of low and high cloud can be discerned; in a 1-s measurement, these are largely lost in the noise.

9.4 Photon detectors

There are two main categories of photon detector, photoconductive and photovoltaic. Photoconductive detectors are chips of semiconductor that rely for their operation on the excitation by incident photons of current carriers that flow in the external circuit under the influence of an applied bias voltage. Photovoltaic devices are usually semiconductor diodes of a design that allows carriers to cross the junction against the potential barrier when they are excited by absorbed photons. When this happens, a voltage appears across the terminals of the device, which can be measured directly and no bias is required.

Photovoltaic devices are generally superior to photoconductive ones for most applications because the bias voltage is an inconvenience, as well as a source of extra noise if it is not perfectly stable. Photoconductors also dissipate more power, obviously; this is a further disadvantage because the devices usually have to be cooled and the dissipation makes extra demands on the cryogen supply or refrigerator used for this. Furthermore, we shall see below that an ideal photovoltaic detector has a lower noise voltage than an ideal photoconductive device, by a factor of a/2- On the other hand, photovoltaic detectors (often called photodiodes) are in practice more prone to noise sources having their origin in imperfections introduced during manufacture, and, while the state-of-the-art of making them advances still further, photoconductors are still used extensively, especially at the longer infra-red wavelengths.

Both kinds of photodetector offer generally higher performance, in terms of re-sponsivity, NEP, and time constant, in comparison to even the best thermal detectors. However, they will not replace the latter entirely, because thermal detectors have the great advantage that they do not need to be cooled. They also have a nearly uniform performance over a very wide spectral range - essentially the whole of the infra-red in most cases - whereas photon detectors peak sharply at a particular wavelength and cut off altogether at the long wavelength side of this peak. There is also the practical consideration that thermal detectors are cheap and robust, and very high performance is not always essential anyway. As we continue with our analysis of the performance of different detector types in terms of their physical properties, we will build up the criteria that allow us to decide what detector type and characteristics are best for a given application.

9.4.1 Photoconductive detectors

These are semiconductors with bandgaps chosen to be smaller than, but close to, the energy of the photons to be detected. Incident radiation then excites transitions into the conduction band and a current flows when a bias voltage is applied. At infra-red wavelengths and room temperatures, hv is comparable to kT so thermal excitation into the conduction band also occurs, resulting in an additional noise source. The detectors are usually cooled to suppress this, often to around 77 K using a liquid-nitrogen reservoir, and the band-gap adjusted to the energy of the photons to be measured by using different types of material, intrinsic and with n-type and p-type doping.

Many photoconductive detectors are based on the properties of the 'solid solutions' lead tin telluride and mercury cadmium telluride (MCT). The wavelength at which the performance is maximized can be varied by adjusting the mixture of components. For HgCdxTe(i-x), for example, the gap energy (eV) is

Eg = -0.25 + 1.59x + 0.327x3 + 5.233 x 10-4T(1 - 2.08x), (9.21)

where x is the fraction of cadmium in the mixture, and T is temperature. Doped germanium is another commonly used material.

The basic setup for a photoconductive detector is similar to the generalized bolometer shown in Fig. 9.2, although a modest (but still accurately constant) bias voltage of a few volts now suffices. Let AS (cm-2) be the increase in conduction-band electron surface density produced by the photon flux of power P falling on a detector of active surface area A cm2 so that

where n is the efficiency of a photon for excitation and t\ the lifetime of a carrier in the conduction band. The current i that flows is i = -evlAS (9.23)

amps, where e is the charge on the electron, v its drift velocity, and l the distance across the active element (l2 = A, usually). Hence

G = vt/i is called the photoconductive gain, defined as the number of carriers that flow in the external circuit per successful photon. G can be greater than one, because once an excited state has been created many carriers can flow through the detector element in the conduction band until a transition in the reverse direction takes place.

There are three important sources of noise current in photoconductors, and each dominates at a different frequency. The noise at low frequencies is very high, due to a phenomenon called 1/f noise (or 'flicker' noise). The cause of this effect is not sufficiently understood to allow it to be calculated from any well-founded physical theory. From measurements, however, it has been found that the noise power is inversely proportional to the chopping frequency; and so for practical purposes it can be overcome simply by chopping fast enough. A few times 10 Hz is generally sufficient.

GR (generation-recombination) noise is due to statistical fluctuations in the number of carriers available to conduct at any given instant. A statistical analysis, assuming that generation and recombination are stochastic and independent gives

for an intrinsic detector at low temperatures. The current i has two components: that produced by the radiation of interest, and that produced by background radiation from the rest of the system and its surroundings. If the total power falling on the detector is P then

= v^L, „.„, hv and the noise equivalent power (W Hz-1/2) is

i.e. this is the signal power from the target required to produce an output equal to the noise induced by the total power falling on the detector. The condition

FlG. 9.7. Detectivity D* as a function of wavelength for several common detector materials used in photoconductive mode. These are (left to right) lead sulphide (PbS) at a temperature of 295 K; indium antimonide (InSb) at 77 K; mercury cadmium telluride (Hg0.sCd0.2Te) at 77 K; and germanium doped with cadmium, copper and zinc, respectively, all at liquid helium temperature (~4 K). The ideal (background limited) performance for a room-temperature target is also shown.

FlG. 9.7. Detectivity D* as a function of wavelength for several common detector materials used in photoconductive mode. These are (left to right) lead sulphide (PbS) at a temperature of 295 K; indium antimonide (InSb) at 77 K; mercury cadmium telluride (Hg0.sCd0.2Te) at 77 K; and germanium doped with cadmium, copper and zinc, respectively, all at liquid helium temperature (~4 K). The ideal (background limited) performance for a room-temperature target is also shown.

for the contribution from Johnson noise due to the resistance in the circuit to be negligible is

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