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dc.contributor.authorAllen, Joseph
dc.date.accessioned2011-02-07T23:32:31Z
dc.date.available2011-02-07T23:32:31Z
dc.date.issued2011-02-07
dc.date.submittedDecember 2010
dc.identifier.urihttp://hdl.handle.net/1928/12021
dc.description.abstractThe Zernike polynomials are an infinite set of orthogonal polynomials over the unit disk, which are rotationally invariant. They are frequently utilized in optics, opthal- mology, and image recognition, among many other applications, to describe spherical aberrations and image features. Discretizing the continuous polynomials, however, introduces errors that corrupt the orthogonality. Minimizing these errors requires numerical considerations which have not been addressed. This work examines the orthonormal polynomials visually with the Gram matrix and computationally with the rank and condition number. The convergence of the Fourier-Zernike coefficients and the Fourier-Zernike series are also examined using various measures of error. The orthogonality and convergence are studied over six grid types and resolutions, polynomial truncation order, and function smoothness. The analysis concludes with design criteria for computing an accurate analysis with the discrete Zernike polynomials.en_US
dc.language.isoen_USen_US
dc.subjectzernikeen_US
dc.subjectpolynomialen_US
dc.subjectcondition numberen_US
dc.subjectgram matrixen_US
dc.subjectorthogonalen_US
dc.subjectopticsen_US
dc.subjectdiscreteen_US
dc.subject.lcshOrthogonalization methods.
dc.subject.lcshOrthogonal polynomials--Asymptotic theory.
dc.titleOrthogonality and convergence of discrete Zernike polynomialsen_US
dc.typeThesisen_US
dc.description.degreeApplied Mathematicsen_US
dc.description.levelMastersen_US
dc.description.departmentUniversity of New Mexico. Dept. of Mathematics and Statisticsen_US
dc.description.advisorEmbid, Pedro
dc.description.committee-memberEmbid, Pedro
dc.description.committee-memberPereyra, Cristina
dc.description.committee-memberDenham, Hugh


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