The lowest temperature that can be measured is that which produces SNR = 1; this is known as the noise equivalent temperature or NET and is given by
A more useful quantity is the noise equivalent temperature change (NEAT), given by
The NEAT is the amount by which T has to change to produce the smallest detectable change in the detector output, which is by definition equal to the NEP. It is therefore a measure of the sensitivity of the radiometer, and of the uncertainty in any measurement. For a given instrument and target, it can be improved only by integrating the measurement for a longer time, which reduces Af proportionately.
A more practical optical system is one where only the detector and band-limiting filters are cooled and beam modulation has been introduced. The background is often much more intense than the stream from the scene and its fluctuations often limit the sensitivity of the radiometer to the latter. Given that the objective is to measure the strength of the photon stream from the scene a problem this immediately presents is how to distinguish this stream from the background. The technique usually employed is to label the scene radiation by mechanical modulation or chopping of the radiation beam to convert the signal from d.c. to a.c., making it easier to amplify and filter, and reducing some sources of detector noise, particularly those that are most important at low frequencies (§184.108.40.206).
In a chopped system, the photon flux entering the optical system then alternates between that originating in the scene and the reference flux originating from or reflected by the chopper. The resulting flux at the detector can be regarded as the superposition of a steady flux equal to the mean of the scene flux and the reference flux and a square wave flux of peak-to-peak amplitude equal to their difference. Corresponding steady and square wave currents will be present in the detector output. The steady component is rejected. The square waveform may or may not be filtered in the amplifiers so that only the fundamental component is retained. In either case the signal is then synchronously rectified at the chopping frequency and then integrated to produce the output. The output of such a system will be zero when the reference flux is the same as the scene flux and maximum when these fluxes are most different.
The fluctuations in the background flux that give rise to noise at the output are those that lie in a frequency band centred on the chopping frequency that has a width of the order of the reciprocal of the integration time. The similar fluctuations in the reference flux also contribute to the noise level. In critical applications the optical system and its surroundings will be cooled, in extreme cases to helium temperatures. If a black chopper is used it will be cooled also, as will the source of reference flux used with a mirror chopper. A good example of this latter technique is the 'chopping to cold space' often employed in satellite-borne infra-red radiometers. As noted above, the necessary use of choppers to label the scene radiation flux leads to at least half the photons emitted from the scene being wasted.
Chopping alone will not guarantee good performance if the background flux is very large and/or variable compared to the signal. This leads to a requirement to cool, not only the detector itself, but its surroundings and key elements in the optical chain. The detector has a view to its surroundings of solid angle 2n around the beam cone. For infra-red wavelengths, the Planck function is very much smaller at 77 K and at 220 K than it is at 290 K and the contribution to the background falling on the detector from its cold surround and the fluctuation due to the signal flux are both negligible. It is therefore the fluctuation in the background lying in the beam cone (due to emission from the optical components and their surroundings the latter entering the beam via reflections and scattering at the surfaces of the components), which is the dominant source of noise.
Of the parameters of the system, ^ may well be fixed by the spatial resolution required, t0 by the required response time and the linear dimensions of aperture A and the ability to cool the whole optical system will be limited by cost. Obtaining a good optical transmission is obviously always desirable.
In practice, the realistic system described above would also be modified to include at least some of the following refinements:
(i) A band-limiting filter that passes a spectral range Av centred on v cm-1. Measurements that attempt to integrate over too wide a range of wavelengths may maximise the signal-to-noise ratio, but are generally more difficult to interpret, except in situations where the integrated radiance from the target is the essential measurement, for example in energy-balance studies. Narrow-band measurements are essential for radiometric temperature sounding, or for spec-troscopic composition measurements, for example.
(ii) A method of radiometric calibration, to account for the uncertainties and changes in the values of key instrument parameters such as background flux, optical system throughput, and detector response.
(iii) Thermal control. The detector performance is generally temperature dependent; if the temperature of the radiometer housing is not held constant the gain, offset and noise will drift.
(iv) Electromagnetic shielding and vibrational isolation. Sensitive radiometers need protection against extraneous noise sources, such as electromagnetic interference and microphonic noise induced by vibration.
The noise equivalent radiance (NER) of a realistic system can be written
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