The Design and Analysis of Computed Tomographic Imaging Spectrometers (CTIS) Using Fourier and Wavelet Crosstalk Matrices
AuthorScholl, James Francis
AdvisorDereniak, Eustace L.
MetadataShow full item record
PublisherThe University of Arizona.
RightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
EmbargoEmbargo: Release after 4/22/2012
AbstractThe properties and imaging performance of the computed tomographicimaging spectrometer (CTIS) have been investigated with Fourierand wavelet crosstalk matrices. These matrices and theircorresponding datacube reconstruction algorithms explicitly usedsensitivity equations describing the CTIS imaging system. Theseequations derived from Franhofer diffraction theory of thecomputed generated hologram (CGH) disperser, serve as themathematical model of the CTIS.The Fourier crosstalk matrix (FCTM) was primarily used to analyzethe CTIS imaging system. The FCTM describes which spatial andspectral frequencies contribute to object cube data entering thesystem and whether or not these frequencies give distinctcontributions with respect to each other. Furthermore, since theCTIS is a limited angle tomographic imaging system the missingcone of frequencies which is a feature of this instrument isclearly shown using the FCTM. Subsequently, Fourier-basedestimates of the reconstructed object cube (i.e. the datacube)will be missing this frequency information even if the CTIS is aperfect optical system.The wavelet crosstalk matrix (WCTM) was used primarily for efficient datacubereconstruction only. The datacube reconstruction calculations areprimarily proof-of-concept and reproduce the Fourier results withsome absence of Fourier related artifacts. The waveletdecomposition of the object cube is useful for studying multipleobjects in a parallel processing environment withoutreconstructing the entire datacube, thus reducing overall complexity.Datacube reconstructions of actual astronomical observations withthe CTIS, using the techniques of this research, were consistentwith previous independent datacube estimates from the same datausing existing conventional techniques. Furthermore these objectsfurnish natural point-spread functions that supplementcomputational simulations of the CTIS by describing actual imagingsystem performance.The computational tools for the study ofthe CTIS imaging system provide the additional bonus of ananalysis of object detectability by the computation of receiveroperator characteristic (ROC) curves. We used a synthetic binarystar to simulate this in the presence of both detector and objectnoise.Some suggestions for future research directions are given.
Degree ProgramGraduate College