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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 19 — Sep. 18, 2006
  • pp: 8837–8848

A family of approximations spanning the Born and Rytov scattering series

Daniel L. Marks  »View Author Affiliations


Optics Express, Vol. 14, Issue 19, pp. 8837-8848 (2006)
http://dx.doi.org/10.1364/OE.14.008837


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Abstract

A new hybrid scattering series is derived that incorporates as special cases both the Born and Rytov scattering series, and includes a parameter so that the behavior can be continuously varied between the two series. The parameter enables the error to be shifted between the Born and Rytov error terms to improve accuracy. The linearized hybrid approximation is derived as well as its condition of validity. Higher order terms of the hybrid series are also found. Also included is the integral equation that defines the exact solution to the forward scattering problem as well as its Fréchet derivative, which is used for the solution of inverse multiple scattering problems. Finally, the linearized hybrid approximation is demonstrated by simulations of inverse scattering off of uniform circular cylinders, where it is shown that the hybrid approximation achieves smaller error than either the Born or Rytov approximations alone.

© 2006 Optical Society of America

OCIS Codes
(100.3190) Image processing : Inverse problems
(110.2990) Imaging systems : Image formation theory
(290.3200) Scattering : Inverse scattering

ToC Category:
Scattering

History
Original Manuscript: June 26, 2006
Revised Manuscript: August 18, 2006
Manuscript Accepted: August 19, 2006
Published: September 18, 2006

Citation
Daniel L. Marks, "A family of approximations spanning the Born and Rytov scattering series," Opt. Express 14, 8837-8848 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-19-8837


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