Non-scanning imaging spectrometry.

Abstract

The objective of imaging spectrometry is to collect three-dimensional data about object space. Two of the three dimensions are spatial. The third dimension is spectral. Current techniques rely on some form of scanning, causing instruments to include moving components and/or to be capable of imaging only static or slowly changing scenes. An interpretation of the problem in terms of computed tomography leads to a system design which can fulfill the objective of imaging spectrometry without scanning. The imaging spectrometer assumes the frame-rate and integration-time properties of its imaging array. The raw data collected by such an instrument must be processed to yield temporally coincident spectral images of the scene. The computed tomography imaging spectrometer is therefore an example of indirect imaging. The three-dimensional frequency-space viewpoint and the associated central slice theorem form the theoretical basis for an understanding of this technique and its limitations. As described here, computed tomography imaging spectrometry belongs to the class of limited-view-angle problems. The spectrometer is treated as a discrete-to-discrete mapping and described accordingly by the linear imaging equation g = Hf + n. The M-element vector g represents the data collected by the spectrometer. The purpose of the instrument and the subsequent processing is the acquisition of the object cube f. In the discrete-to-discrete model, f is approximated as a vector of N independent elements. The vector n represents measurement-computing noise. The M-by-N matrix H embodies the imaging properties of the instrument. We have developed and implemented an experimental method of characterizing H. Such an approach yields a description of the imaging spectrometer which is more accurate than techniques that model the instrument and compute H. Inversion of the imaging equation to find an estimate of f has been best performed by the Expectation-Maximization algorithm. This approach is based on a Poisson likelihood law and therefore the assumption of quantum noise dominating the measurements g.