Computational Modeling of the Imaging System Matrix for the CTIS Imaging Spectrometer

摘要

Imaging systems such as the Computed Tomographic Imaging Spectrometer (CTIS) are modeled by the matrix equation g = Hf, which is the discretized form of the general imaging integral equation. The matrix H describes the contribution to each element of the image g from each element of the hyperspectral object cube f. The vector g is the image of the spatial/spectral projections of f on a focal plane array (FPA). The matrix H is enormous, sparse and rectangular. It is extremely difficult to discretize the integral operator to obtain the matrix operator H. Normally H is constructed empirically from a series of monochromatic calibration images, which is a time consuming process. However we have been able to synthetically construct H by numerically modeling how the optical and diffractive elements in the CTIS project monochromatic point source data onto the FPA. We can evaluate a CTIS system by solving the imaging equation for f using both the empirical and synthetic H from some test data g. Comparison between the two results provides a means to evaluate and improve CTIS system calibration procedures noting that the synthetic system matrix H represents a baseline ideal system.