Comparison of signal collection abilities of different classes of imaging spectrometers

Although the throughput and multiplex advantages of Fourier transform spectrometry were established in the early 1950's (by Jacquinot(1,2,3) and Fellgete(4,5) respectively) confusion and debate(6) arise when these advantages are cited in reference to imaging spectrometry. In non-imaging spectrometry the terms throughput and spectral bandwidth clearly refer to the throughput of the entire field-of-view (FOV), and the spectral bandwidth of the entire FOV, but in imaging spectrometry these terms may refer to either the entire FOV, or to a single element in the FOV. The continued development of new and fundamentally different types of imaging spectrometers also adds to the complexity of predictions of signal and comparisons of signal collection abilities. Imaging spectrometers used for remote sensing may be divided into classes according to how they relate the object space coordinates of cross-track position, along-track position, and wavelength (or wavenumber) to the image space coordinates of column number, row number, and exposure number for the detector array. This transformation must be taken into account when predicting the signal or comparing the signal collection abilities of different classes of imaging spectrometer. The invariance of radiance in an imaging system allows the calculation of signal to be performed at any space in the system, from the object space to the final image space. Our calculations of signal - performed at several different spaces in several different classes of imaging spectrometer - show an interesting result: regardless, of the plane in which the calculation is performed, interferometric (Fourier transform) spectrometers have a dramatic advantage in signal, but the term in the signal equation from which the advantage results depends upon the space in which the calculation is performed. In image space, the advantage results from the spectral term in the signal equation, suggesting that this could be refer-red to as the multiplex (Fellgett) advantage. In an intermediate image plane the advantage results from a difference in a spatial term, while for the exit pupil plane it results from the angular term.; both of which suggest the throughput (Jacquinot) advantage. When the calculation is performed in object coordinates the advantage results from differences in the temporal term.