Information-theoretic approach to Fourier transform spectrometry

We describe a specific bandpass sampling procedure that provides high efficiency for interferogram sampling. This new approach is able to mitigate the important radiometric and noise disadvantages of Fourier transform spectrometry that recent theoretical investigations have pointed out. Proof of concept is given using simulations and measurements performed with a Sagnac triangular interferometer. Adopting an information-theoretic approach to spectrometry, we demonstrate the existence of important limitations to the radiometric efficiency achieved by any interferential or dispersive multiplex spectrometers. We find an extension to optics of the well-known data processing inequality, confirming that the Fellgett (multiplex) advantage is an inappropriate expectation. We give evidence of radiometric disadvantages implicit in the coded aperture architecture typical of compressive sensing.