Theoretical description and numerical simulations of a simplified Hadamard transform imaging spectrometer

摘要

A familiar concept in imaging spectrometry is that of the three dimensional data cube, with one spectral and two spatial dimensions. However, available detectors have at most two dimensions, which generally leads to the introduction of either scanning or multiplexing techniques for imaging spectrometers. For situations in which noise increases less rapidly than as the square root of the signal, multiplexing techniques have the potential to provide superior signal-to-noise ratios. This paper presents a theoretical description and numerical simulations for a new and simple type of Hadamard transform multiplexed imaging spectrometer. Compared to previous types of spatially encoded imaging spectrometers, it increases etendue by eliminating the need for anamorphically compressed re-imaging onto the entrance aperture of a monochromator or spectrophotometer. Compared to previous types of spectrally encoded imaging spectrometers, it increases end-to-end transmittance by eliminating the need for spectral re-combining optics. These simplifications are attained by treating the pixels of a digital mirror array as virtual entrance slits and the pixels of a 2-D array detector as virtual exit slits of an imaging spectrometer, and by applying a novel signal processing technique.