Generalized signal-to-noise ratio for spectral sensors with correlated bands

Traditional spectral sensors are intentionally designed to minimize overlap among spectral response functions of different bands. In contrast, some emerging classes of spectral sensors exhibit significant band overlap. An effect introduced by such band overlap is that the photodetector noise of one band is coupled into the others in subsequent data processing steps. Because of this, the traditional band-by-band definition of signal-to-noise ratio (SNR) cannot fully describe the detector's noise level. We devise a general definition of SNR in spectral space based on a recently developed geometrical spectral imaging model [J. Opt. Soc. Am. A24, 2864 (2007)]. With this model, we can find an orthogonal basis of the spectral response functions for the spectral sensor with decreasing instrument SNRs. We can also define the average instrument SNR for the whole sensor, which makes it possible to characterize quantitatively the photodetector noise of a spectral sensor with correlated bands.