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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. 2, Iss. 11 — Nov. 1, 1985
  • pp: 1922–1930

Accurate one-dimensional inverse scattering using a nonlinear renormalization technique

D. L. Jaggard and Y. Kim  »View Author Affiliations


JOSA A, Vol. 2, Issue 11, pp. 1922-1930 (1985)
http://dx.doi.org/10.1364/JOSAA.2.001922


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Abstract

A nonlinear method based on the inversion of the Riccati equation is presented here for the one-dimensional nondispersive inverse-scattering problem. This method avoids the significant errors in both amplitude and phase that plague most linearized (e.g., Born or its varients) inversion schemes. Instead, a nonlinear approximation to the Riccati equation is used for the accurate determination of the refractive-index amplitude from reflection data. This information is subsequently used to stretch the coordinates so as to remove the phase-accumulation error. The resulting refractive-index reconstructions are therefore accurate both in amplitude and in longitudinal placement as evidenced by the excellent comparison with exact theory. The method is applicable to both continuous and discontinuous refractive profiles and is supported by experimental measurements.

© 1985 Optical Society of America

History
Original Manuscript: May 30, 1985
Manuscript Accepted: July 25, 1985
Published: November 1, 1985

Citation
D. L. Jaggard and Y. Kim, "Accurate one-dimensional inverse scattering using a nonlinear renormalization technique," J. Opt. Soc. Am. A 2, 1922-1930 (1985)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-2-11-1922


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References

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  15. Note that r(p) must satisfy energy conservation and causality. However, r̂(p) is a mathematical transformation that does not necessarily satisfy the restriction |r̂(p)|<1.
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  19. See, e.g., D. L. Jaggard, K. E. Olson, “Numerical reconstruction of dispersionless refractive profiles,” J. Opt. Soc. Am. A 2, 1931–1936 (1985). [CrossRef]
  20. D. L. Jaggard, P. V. Frangos, “Profile reconstruction for dispersionless layered dielectrics with imprecise and band-limited data,” IEEE Trans. Antennas Propag. (to be published).
  21. H. D. Ladouceur, A. K. Jordan, “Renormalization of an inverse-scattering theory for inhomogeneous dielectrics,” J. Opt. Soc. Am. A 2, 1916–1921 (1985). [CrossRef]

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