This chapter provides the information needed to evaluate the performance of an imaging spectrometer in terms of the signal output and the noise.
There are several ways to specify system sensitivity. One is surely the signal-to-noise ratio for a given object. Another, more normalized way, is to evaluate the noise-equivalent power on the detector or aperture. This is the power that gives a signal-to-noise ratio of one. The difference between the power on the detector and that on the aperture is just the system transmission. Another way is the noise equivalent flux density (NEFD), the flux per unit area that gives an SNR of one. Then there is the noise equivalent radiance (NEL or NER) and noise equivalent spectral radiance (NESR or NESL). These, like power, are constant through the system, except for transmission losses. Remember, however, that an SNR of one is not very useful. .
The specific detectivity is defined as D ∗ ==A d B √ Î¦ SNR. The expression can be inverted to obtain SNR=D ∗ Î¦ A d B √ . When the target is extended, that is, larger than the image of the detector (field stop) at the target, then Î¦=LA o A d f 2 , ignoring the cosine factors, and where A o is the area of the optics, A d is the area of the detector, L is the radiance, and f is the focal length. Therefore, the sensitivity equation in its defining form can be manipulated to the following form. It will be shown in other forms for spectral quantities and for photonic quantities.
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