k-space design of methods for optical and imaging hardware

M. A. Fiddy; M. E. Testorf

doi:10.1117/12.683397

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5 September 2006 k-space design of methods for optical and imaging hardware

M. A. Fiddy, M. E. Testorf

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Proceedings Volume 6316, Image Reconstruction from Incomplete Data IV; 63160H (2006) https://doi.org/10.1117/12.683397
Event: SPIE Optics + Photonics, 2006, San Diego, California, United States

Abstract

Multiple scattering imposes severe challenges for inverse scattering and inverse synthesis applications. We have been pursuing a relatively simple nonlinear filtering technique that could provide an estimate of the scattering structure from scattered far-field data. This cepstral filtering method assumes that one can obtain an estimate of the secondary source distribution and that under certain conditions this is well approximated by a product of the scattering potential and terms representing the total internal field. Preprocessing of this estimated function can render it a minimum phase function, and its logarithm is then well behaved and amenable to spectral filtering that allows an estimate of the scattering potential to be obtained. We have applied this to real and simulated scattering data with some success. The deliberate manipulation of scattered field data mapped into in reciprocal or k-space allows one to define certain scattering characteristics at specific wavenumbers and scattering angles. Inversion of these data using the inversion method described generates a possible structure that exhibits these properties in practice. We show some examples of this and consider its usefulness for the design of rough surfaces with prescribed optical properties.

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M. A. Fiddy and M. E. Testorf "k-space design of methods for optical and imaging hardware", Proc. SPIE 6316, Image Reconstruction from Incomplete Data IV, 63160H (5 September 2006); https://doi.org/10.1117/12.683397

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