## Vo Vs Vn

V0 can be determined by noting the voltage across the detector when the incoming flux is zero, i.e. by calibration of the detector or instrument using a shutter or, on a satellite, a view of cold space.

Most detectors take a finite time to reach a steady output after being exposed to a flux of radiation. The time constant for this process t, which determines how rapidly measurements can be repeated, is defined by the expression

so t = t is the time taken to reach 63% (= 1-1/e) of the steady-state output Vss after the detector is first exposed to the radiation stream.

The importance of the time constant, apart from reminding us that detectors cannot respond instantaneously (especially thermal detectors, which need time to warm up to their equilibrium temperature), is because the incoming flux is usually modulated or chopped, making V an a.c., not a d.c., signal. If t is significantly greater than the reciprocal of the chopping frequency f, then the reponsivity of the detector will be less than its value for t = 0 because the output will not have time to respond to the fluctuating input. We discuss below why chopping is a good idea, even though it can cause problems for 'slow' detectors. Assuming that the rate of chopping is not so fast that the detector cannot follow the fluctuations, the responsivity will normally be independent of the chopping frequency over a wide range, and is defined in terms of the peak (or r.m.s) value of the output voltage.

Generally, the signal that emerges from a detector is not the main concern -what matters is the ratio of the information-carrying signal to the meaningless fluctuations or noise that always accompany it. The sources of noise are different for different types of detector, and will be discussed in the relevant context below. For now, the crucial thing to recognize is that, in many practical infrared systems of interest, the signal is often not much greater than the noise, even though great trouble may have been taken to eliminate as many sources of noise as possible. Noise originating in the detector, which gets amplified along with the signal, is the most fundamental of all. To characterize this, we use a parameter called the noise equivalent power or NEP, which is simply the amount of power that has to fall on the detector before the signal output voltage is exactly equal to the noise voltage Vn. Then

where Af (Hz) in eqn (9.4) is the bandwidth in which the signal, and the noise, are measured. The bandwidth is usually defined inside the amplifier, which boosts the small signal from the detector. Intuitively, it makes sense to have a small bandwidth because it excludes some of the noise (which is often present at all frequencies) while the signal (at a single frequency f at the centre of Af) need hardly be attenuated at all. In fact, it is shown later in this chapter that Af is determined by the integration time to, such that Af = 1/2to.

The physical meaning of to is simply the time the amplifier spends summing the signal (and averaging out the random component of the noise) from the detector output. For this reason it is sometimes called the dwell time. It is the amount of time a radiometer spends dwelling on one scene before it is available to switch to another, or in the case of a scanning spectrometer, before it steps to the next wavelength. In practice, to will be set by an R-C circuit in the amplifier. The larger the value of the time constant of the amplifier, the longer it sums the signal voltage and the smaller is Af. Now, the reason why Af appears to the half power in eqn (9.4) can be appreciated; the noise, if random, is reduced by the square root of the number n of independent samples taken, and clearly n is proportional to to and hence to Af.

Generally, NEP is used to describe the performance of a given, individual detector. The user buying a detector for a specific application will decide what NEP

is needed, and expects the value to be included in the specification of the device. Nominally identical detectors often have quite different values of NEP, since small flaws introduced in the manufacturing process introduce additional noise in ways that are often obscure to manufacturer and user alike. The detectivity (W-1 Hz1/2), defined by

is preferred by some manufacturers because better detectors have higher values of D. However, a more useful and better-known parameter is the specific detectivity D* (W-1 cm Hz1/2) defined by

D* is approximately independent of detector area, since most (but not all) sources of Vn are proportional to A1/2, while Vs is proportional to A. Hence D* is used to compare different types of detectors.

### 9.3 Thermal detectors

Thermal detectors work by measuring the heating effect of a beam of radiation. The three main types available commercially are thermocouples, normally with multiple junctions (hence thermopiles), thermistor bolometers, and pyroelectric bolometers.

Thermocouples use the thermoelectric effect in the junction between dissimilar metals, traditionally copper and constantan, which have a very large value of the thermoelectric coefficient that determines the responsivity. Thermopiles have had something of a renaissance recently because modern micromachining techniques allow large numbers of small junctions in a given detector size, leading to a fairly rapid response and high D* in a robust and reliable device that does not require cooling. A recent design (Foote et al. 1998) uses 2—um widths and 2—um spacings between conductors to place about 50 thermocouples in a 100 ¡m wide detector element. This has a resistance of ^250 kQ and achieves a responsivity of 1.5 kV/W, response time of 1.7 ms, and detectivity D* of 2.4 x 108 W-1 cm Hz1/2.

A thermistor is a resistor with a high temperature coefficient of resistance, a. The word bolometer strictly refers to anything that measures radiation: here, it does this by measuring the change in the resistance of the detector element due to the heating effect of the radiation. Platinum has a high coefficient of resistance (a ~ 0.003 Q K-1) and used to be the commonest thermistor material, but in recent years this has been deposed by a sintered semiconductor mixture of manganese, nickel and cobalt oxides that achieves a ~ 0.056 Q K-1. A steady bias voltage must be applied to maintain a current through the detector element, which is normally in series with a load resistance, as shown in Fig. 9.2. The latter can be a second detector element, identical to the first, but shielded

Radiation

Radiation

Bias voltage

FlG. 9.2. A bolometer detector consists of an element with a high temperature coefficient of resistance, a fixed load resistor, and a bias voltage to provide a current through both. Changes in the current due to the heating effect of the radiation are detected as a change in the voltage across the load resistor.

from the radiation, an arrangement that provides additional stability should the background temperature vary.

The change in the signal voltage, AVS across the load resistor produced by a change in detector resistance, ARD, induced by the incoming radiation from the target is given by

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