The design and analysis of computed tomographic imaging spectrometers (CTIS) using Fourier and wavelet crosstalk matrices

The properties and imaging performance of the computed tomographic imaging spectrometer (CTIS) have been investigated with Fourier and wavelet crosstalk matrices. These matrices and their corresponding datacube reconstruction algorithms explicitly used sensitivity equations describing the CTIS imaging system. These equations derived from Franhofer diffraction theory of the computed generated hologram (CGH) disperser, serve as the mathematical model of the CTIS.;A key to this dissertation was the efficient computation of these crosstalk matrices and from them, the means to evaluate the CTIS performance. These matrices are derived from the physical model of the CTIS and the concept of the object cube being a three-dimensional (3D) continuous object. This object cube, in this dissertation, is treated as an expansion of 3D Fourier functions cut off to zero at the object cube boundary or an expansion of dyadic wavelet functions. Here the physics of CTIS describes and determines imaging system performance.;The Fourier and wavelet system matrices that are used to generate their respective crosstalk matrices and expansion function coefficients for the reconstructed datacube were found to be too large to store and too inflexible for any real CTIS system design studies contemplated for future work. In their place the CTIS model was encoded into lookup tables, which are expansion function independent, and which could compute selected subsets of elements of crosstalk matrices without the computation and storage of the entire corresponding system matrix. These lookup tables enabled the crosstalk matrices to be evaluated using massively parallel computing systems.;In this research, the Fourier and Wavelet crosstalk matrices had separate (but often overlapping) roles.;The Fourier crosstalk matrix (FCTM) was primarily used to analyze the CTIS imaging system. The FCTM describes which spatial and spectral frequencies contribute to object cube data entering the system and whether or not these frequencies give distinct contributions with respect to each other. Furthermore, since the CTIS is a limited angle tomographic imaging system the missing cone of frequencies which is a feature of this instrument is clearly shown using the FCTM. Subsequently, Fourier-based estimates of the reconstructed object cube (i.e. the datacube) will be missing this frequency information even if the CTIS is a perfect optical system. However, for objects that are non-compact the Fourier expansion function system is still useful for datacube estimation.;The wavelet crosstalk matrix (WCTM) was used for datacube reconstruction only. The datacube reconstruction calculations are primarily proof-of-concept and reproduce the Fourier results with some absence of Fourier related artifacts. The wavelet decomposition of the object cube is useful for studying multiple objects in a parallel processing environment without reconstructing the entire datacube. Furthermore the type of wavelet transform used here enables efficient reconstruction algorithms to be used, which are also well suited for parallel processing. Using wavelets the lookup tables were especially useful in estimating localized subsets of the wavelet expansion coefficients that reduces computational complexity.;Datacube reconstructions of actual astronomical observations with the CTIS, using the techniques of this research, were consistent with previous independent datacube estimates from the same data using existing conventional techniques. Furthermore these objects furnish natural point-spread functions that supplement computational simulations of the CTIS by describing actual imaging system performance.;The computational mechanisms of the lookup table formulation of the CTIS imaging system provide the additional bonus of an analysis of object detectability by the computation of receiver operator characteristic (ROC) curves. We used a synthetic binary star to simulate this in the presence of both detector and object noise.;Some suggestions for future research directions are given.