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Proceedings Paper

Comparison Of The Inverse Source Problem For Quasihomogeneous, Partially Coherent Sources In Two And Three Dimensions
Author(s): Ivan J. LaHaie
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Paper Abstract

The nature of the uniqueness of the inverse source problem for quasihomogeneous, partially coherent sources is investigated. Comparisons are made between the formulations for two-dimensional and three-dimensional source distributions. It has recently been shown that the inverse source problem for the former is unique, while that of the latter is known to be nonunique; however, the derivations were performed using significantly different approaches. A unified approach is presented herein by considering the two-dimensional source distribution as a three-dimensional distribution with delta-function support in one dimension. The problem is then formulated such that the known data provide a measure of the three-dimensional spatial Fourier transform of the cross-spectral density of the source (the desired unknown) on a surface in the Fourier domain. It is shown that these data are sufficient to reconstruct the unknown source cross-spectral density for two-dimensional sources, while they are insufficient for three-dimensional sources. Finally, the use of a priori information and its effect on the uniqueness of the three-dimensional inverse source problem is discussed. In particular, a set of supplemental data is described which guarantees uniqueness of the three-dimensional inverse and which is less restrictive than that previously identified. An inversion algorithm which makes use of these data is also presented.

Paper Details

Date Published: 25 October 1985
PDF: 8 pages
Proc. SPIE 0558, Inverse Optics II, (25 October 1985); doi: 10.1117/12.949570
Show Author Affiliations
Ivan J. LaHaie, Environmental Research Institute of Michigan (United States)


Published in SPIE Proceedings Vol. 0558:
Inverse Optics II
Richard H.T. Bates; Anthony J. Devaney, Editor(s)

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