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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 15, Iss. 7 — Jul. 1, 1998
  • pp: 1867–1876

Variational principles and the one-dimensional profile reconstruction

M. A. Hooshyar  »View Author Affiliations


JOSA A, Vol. 15, Issue 7, pp. 1867-1876 (1998)
http://dx.doi.org/10.1364/JOSAA.15.001867


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Abstract

The problem of finding the dielectric constant of a slab from the reflection data is considered. It is shown that a recently developed method by Trantanella [J. Opt. Soc. Am. A 12, 1469 (1995)], which is based on an interesting extension of the Born approximation, is intimately related to the Schwinger variational solution. This remarkable relation enables one to extend the class of profiles that can be reconstructed, evaluate analytically some of the quantities that were found approximately by Trantanella et al., thus simplifying the numerical computations, and also arrive at a systematic development of a sequence of more accurate extensions of the Born inversion method. To illustrate the proposed inversion procedures, an exactly solvable analytical example is presented.

© 1998 Optical Society of America

OCIS Codes
(290.1350) Scattering : Backscattering
(290.3030) Scattering : Index measurements
(290.3200) Scattering : Inverse scattering

History
Original Manuscript: October 30, 1997
Revised Manuscript: February 26, 1998
Manuscript Accepted: March 5, 1998
Published: July 1, 1998

Citation
M. A. Hooshyar, "Variational principles and the one-dimensional profile reconstruction," J. Opt. Soc. Am. A 15, 1867-1876 (1998)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-15-7-1867


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