Computational modeling of the imaging system matrix for the CTIS imaging spectrometer

Imaging systems such as the Computed Tomographic Imaging Spectrometer (CTIS) are modeled by the matrix equationg = Hf , which is the discretized form of the general imaging integral equation.. The matrix H describes the contributionto each element of the image g from each element of the hyperspectral object cube f. The vector g is the image of thespatial/spectral projections of f on a focal plane array (FPA). The matrix H is enormous, sparse and rectangular. It isextremely difficult to discretize the integral operator to obtain the matrix operator H .NormallyH is constructedempirically from a series of monochromatic calibration images, which is a time consuming process. However we havebeen able to synthetically construct H by numerically modeling how the optical and diffractive elements in the CTISproject monochromatic point source data onto the FPA. We can evaluate a CTIS system by solving the imagingequation for f using both the empirical and synthetic H from some test data g. Comparison between the two resultsprovides a means to evaluate and improve CTIS system calibration procedures noting that the synthetic system matrix Hrepresents a baseline ideal system.Keywords: Hyperspectral Imaging, Tomographic Imaging Systems, Diffractive Optics