OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • 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)

View Full Text Article

Acrobat PDF (286 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



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 <i>et al.</i> [J. Opt. Soc. Am. A <b>12</b>, 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 <i>et al.</i>, 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

M. A. Hooshyar, "Variational principles and the one-dimensional profile reconstruction," J. Opt. Soc. Am. A 15, 1867-1876 (1998)

Sort:  Author  |  Year  |  Journal  |  Reset


  1. K. Chadan and P. C. Sabatier, Inverse Problems in Quantum Scattering Theory, 2nd ed. (Springer-Verlag, New York, 1989).
  2. S. Coen, “Inverse scattering of a layered and dispersionless dielectric half-space. Part 1: Reflection data from plane waves at normal incidence,” IEEE Trans. Antennas Propag. AP-29, 726–732 (1981).
  3. M. A. Hooshyar and L. S. Tamil, “Inverse scattering theory and the design of planar optical waveguides with the same propagation constants for different frequencies,” Inverse Probl. 9, 69–80 (1993).
  4. J. Xia, A. K. Jordan, and J. A. Kong, “Electromagnetic inverse scattering theory for inhomogeneous dielectrics: the local reflection model,” J. Opt. Soc. Am. A 11, 1081–1086 (1994).
  5. R. Clayton and R. Stolt, “A Born-WKBJ inversion method for an acoustic reflection data,” Geophysics 46, 1559–1567 (1981).
  6. R. G. Keys and A. B. Weglein, “Generalized linear inversion and the first Born theory for acoustic stratified media,” J. Math. Phys. (New York) 24, 1444–1449 (1983).
  7. A. J. Devaney and M. L. Oristaglio, “Inversion procedure for inverse scattering within the distorted-wave Born approximation,” Phys. Rev. Lett. 51, 237–240 (1983).
  8. H. D. Ladouceur and A. K. Jordan, “Renormalization of an inverse-scattering theory for inhomogeneous dielectrics,” J. Opt. Soc. Am. A 2, 1916–1921 (1985).
  9. A. K. Jordan and H. D. Ladouceur, “Renormalization of an inverse-scattering theory for inhomogeneous dielectrics,” Phys. Rev. A 36, 4245–4253 (1987).
  10. M. A. Hooshyar, T. H. Lam, and M. Razavy, “Inverse scattering problem and the Schwinger approximation,” Can. J. Phys. 70, 282–288 (1992).
  11. T. M. Habashy, R. W. Groom, and B. Spies, “Beyond the Born and Rytov approximations: a non-linear approach to electromagnetic scattering approximation,” J. Geophys. Res. 98, 1759–1775 (1993).
  12. C. J. Trantanella, D. G. Dudley, and A. Nabulsi, “Beyond the Born approximation in one-dimensional profile reconstruction,” J. Opt. Soc. Am. A 12, 1469–1478 (1995).
  13. C. Duneczky and R. E. Wyatt, “Lanczos recursion, continued fractions, Padé approximants, and variational principles in quantum scattering theory,” J. Chem. Phys. 89, 1448–1463 (1988).
  14. J. R. Taylor, Scattering Theory (Wiley, New York, 1972).
  15. J. H. Mathews, Numerical Methods for Mathematics, Science, and Engineering, 2nd ed. (Prentice-Hall, London, 1992).
  16. H. E. Moses, “Calculation of the scattering potential from reflection coefficients,” Phys. Rev. 102, 559–567 (1952).
  17. M. Razavy, “Determination of the wave velocity in an inhomogeneous medium from reflection coefficient,” J. Acoust. Soc. Am. 58, 956–963 (1975).
  18. R. T. Prosser, “Formal solutions of inverse scattering problems. IV” J. Math. Phys. (New York) 23, 2127–2130 (1982).
  19. A. J. Devaney and A. B. Weglein, “Inverse scattering using the Heitler equation,” Inverse Probl. 5, L49–L52 (1989).
  20. A. K. Jordan and H. D. Ladouceur, “Renormalization of an inverse-scattering theory for Gaussian distributions,” in Multiple Scattering of Waves in Random Media and Random Rough Surfaces, V. K. Varadan, ed. (The Pennsylvania State University, University Park, Pa., 1985), pp. 233–240.

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited