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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: 1931–1936

Numerical reconstruction for dispersionless refractive profiles

D. L. Jaggard and K. E. Olson  »View Author Affiliations


JOSA A, Vol. 2, Issue 11, pp. 1931-1936 (1985)
http://dx.doi.org/10.1364/JOSAA.2.001931


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Abstract

An efficient method is presented here for reconstructing dispersionless refractive profiles from scattering data. This procedure makes use of known reflection data to determine the refractive index of a semi-infinite slab. The numerical method presented here avoids matrix inversion, successive differentiation, and the solution of auxiliary algebraic or differential equations. Instead, the method relies on leapfrogging through space and time to solve a recently developed integral equation. Results for several new profiles are displayed, and evidence of the robustness of the technique with respect to noise is exhibited.

© 1985 Optical Society of America

History
Original Manuscript: February 6, 1984
Manuscript Accepted: May 7, 1985
Published: November 1, 1985

Citation
D. L. Jaggard and K. E. Olson, "Numerical reconstruction for dispersionless refractive profiles," J. Opt. Soc. Am. A 2, 1931-1936 (1985)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-2-11-1931


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References

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  9. This is obtained from Eq. (2.8) of Ref. 8 with a change of variables and subsequent reordering.
  10. This is found by combining Eqs. (3.5) and (3.8) of Ref. 8.
  11. Here ΔK indicates the difference between the kernel function at any point and its value at an adjacent lattice point.
  12. H. N. Kritikos, D. L. Jaggard, D. B. Ge, “Numerical reconstruction of smooth dielectric profiles,” Proc. IEEE 70, 295–297 (1982). [CrossRef]
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  15. P. B. Abraham, H. E. Moses, “Exact solutions of the one-dimensional acoustic wave equations for several new velocity profiles: transmission and reflection coefficients,” J. Acoust. Soc. Am. 71, 1391–1399 (1982). [CrossRef]
  16. D. L. Jaggard, P. Frangos, “The inverse scattering problem for layered dispersionless media with incomplete and imprecise data,” submitted to IEEE Trans. Antennas Propag.

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