Computed-tomography imaging spectrometer: experimental calibration and reconstruction results

A temporally and spatially nonscanning imaging spectrometer is described in terms of computed-tomography concepts, specifically the central-slice theorem. A sequence of three transmission sinusoidal-phase gratings rotated in 60 deg increments achieves dispersion in multiple directions and into multiple orders. The dispersed images of the system's field stop are interpreted as two-dimensional projections of a three-dimensional (x, y, lambda ) object cube. Because of the size of the finite focal-plane array, this imaging spectrometer is an example of a limited-view-angle tomographic system. The imaging spectrometer's point spread function is measured experimentally as a function of wavelength and position in the field of view. Reconstruction of the object cube is then achieved through the maximum-likelihood, expectation-maximization algorithm under the assumption of a Poisson likelihood law. Experimental results indicate that the instrument performs well in the case of broadband and narrow-band emitters.