Signal to noise ratio of a coded slit hyperspectral sensor

In recent years, a wide range of hyperspectral imaging systems using coded apertures have been proposed. Many implement compressive sensing to achieve faster acquisition of a hyperspectral data cube, but it is also potentially beneficial to use coded aperture imaging in sensors that capture full-rank (non-compressive) measurements. In this paper we analyse the signal-to-noise ratio for such a sensor, which uses a Hadamard code pattern of slits instead of the single slit of a typical pushbroom imaging spectrometer. We show that the coded slit sensor may have performance advantages in situations where the dominant noise sources do not depend on the signal level; but that where Shot noise dominates a conventional single-slit sensor would be more effective. These results may also have implications for the utility of compressive sensing systems.