Computed tomography imaging spectrometer (CTIS) technology is introduced and its use is discussed. An iterative method is presented for CTIS image-reconstruction in the presence of both photon noise in the image and post-detection Gaussian system noise. The new algorithm assumes the transfer matrix of the system has a particular structure. Error analysis, performance evaluation, and parallelization of the algorithm is done. Complexity analysis is performed for the proof of concept code developed. Future work is discussed relating to potential improvements to the algorithm. An intuitive explanation for the success of the new algorithm is that it reformulates the image reconstruction problem as a constrained problem such that an explicit closed form solution can be computed when the constraint is ignored. Incorporating the constraint leads to an inverse matrix problem which can be dealt with using a conjugate gradient method. A weighted iterative refinement technique is employed because the conjugate gradient solver is terminated prematurely. This dissertation makes the following contributions to the state of the art. First, our method is several orders of magnitude faster that the previous industry best (multiplicative algebraic reconstruction technique (MART) and mixed-expectation reconstruction technique (MERT)). Second, error bounds are established. Third, open source proof of concept code is made available.

A Computed Tomographic Imaging Spectrometer (CTIS) is an imaging spectrometer which can acquire a hyper-spectral data set in a single snapshot (one focal plane array integration time) with no moving parts. A specially designed dispersing element, which separates light from the three-dimensional object cube into a grid of two-dimensional prismatic diffraction orders, is the key element in the instrument. The capabilities of the CTIS instrument can be improved by employing a more optimized grating design.There were two main goals to this research: (1) to design a novel CTIS disperser that will improve CTIS capabilities over the previous 5x5 disperser and (2) to integrate the new disperser into the CTIS and evaluate its performance compared to the 5x5 disperser. Six new disperser ideas were evaluated based on their performance in a number of computer simulations to determine the most optimal dispersion pattern. A new CTIS disperser incorporating a novel radial design pattern was developed and tested. Reconstruction results of various spatial and spectral targets are presented. Capabilities of the new CTIS instrument incorporating the radial grating are compared to the previous instrument employing a 5x5 disperser. While both dispersers perform similarly for point-source objects, the radial grating performs better than the previous disperser for extended sources.