## Variational principles and the one-dimensional profile reconstruction

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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