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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. 16, Iss. 9 — Sep. 1, 1999
  • pp: 2213–2218

Remarks on the Born and Rytov scatter approximations and related exact models and probability distributions

David Middleton  »View Author Affiliations


JOSA A, Vol. 16, Issue 9, pp. 2213-2218 (1999)
http://dx.doi.org/10.1364/JOSAA.16.002213


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Abstract

It is shown with the help of an operational formulation of scattering processes (in linear media) that the Rytov approximation, although limited to weak scattering, contains all orders of single and multiple scatter, unlike the Born approximation, which neglects multiple scatter. This explains the often observed superiority of the former vis-à-vis the latter, when compared with empirical data. These results are quite general and apply to scattering from random interfaces as well as volumes, including combinations of surface and volume interactions. It is also noted that probability density functions (pdf’s) consisting of Gauss (or Rayleigh) scatter and non-Gaussian Class A components, under various conditions, sometimes involving intensity fluctuations, provide essentially exact pdf’s for all intensities and orders of multiple scatter. [IEEE J. Ocean. Eng. 24, 261 (1999); Proceedings of the Third International Conference on Theoretical and Computational Acoustics (World Scientific, Singapore, 1999), p. 679].

© 1999 Optical Society of America

OCIS Codes
(000.5490) General : Probability theory, stochastic processes, and statistics
(030.6600) Coherence and statistical optics : Statistical optics
(070.6020) Fourier optics and signal processing : Continuous optical signal processing
(280.5600) Remote sensing and sensors : Radar
(290.0290) Scattering : Scattering
(290.4210) Scattering : Multiple scattering

History
Original Manuscript: October 30, 1998
Revised Manuscript: April 29, 1999
Manuscript Accepted: April 29, 1999
Published: September 1, 1999

Citation
David Middleton, "Remarks on the Born and Rytov scatter approximations and related exact models and probability distributions," J. Opt. Soc. Am. A 16, 2213-2218 (1999)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-16-9-2213


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References

  1. D. Middleton, “New physical–statistical methods and models for clutter and reverberation: the KA-distribution and related probability structures,” IEEE J. Ocean Eng. 24, 261–284 (1999). [CrossRef]
  2. D. Middleton, “The first and higher order probability densities and distributions of ocean acoustic reverberation from combined surface, bottom, and volume interactions,” in Proceedings of the Third International Conference on Theoretical and Computational Acoustics, 1997 (World Scientific, Singapore, 1999), pp. 679–694.
  3. J. W. Goodman, Statistical Optics (Wiley, New York, 1985), Secs. 8.4.3, 8.4.4, and the comments in Sec. 8.9; cf. p. 458 and Refs. 8–48 and 49 therein.
  4. A. Ishimaru, Wave Propagation and Scattering in Random Media, I and II (Academic, New York, 1978), Sec. 17-2-2.
  5. J. M. Rytov, A. Kravtsov, V. I. Tatarskii, Principles of Statistical Radio Physics 3, Wave Propagation Through Random Media (Springer-Verlag, New York, 1989); cf. Sec. 1.7.
  6. J. B. Keller, “Accuracy and validity of the Born and Rytov approximations,” J. Opt. Soc. Am. 59, Part 1, pp. 1003–1004 (1969).
  7. H. T. Yura, C. C. Sung, S. F. Clifford, R. J. Hill, “Second-order Rytov approximation,” J. Opt. Soc. Am. 73, 500–502 (1983). [CrossRef]
  8. U. Frisch, “Wave propagation in random media,” in Probabilistic Methods in Applied Mathematics, A. T. Barucha-Reid, ed. (AcademicNew York, 1968), Vol. 1, pp. 75–198.
  9. P. M. Morse, H. Feshbach, Methods of Theoretical Physics, I and II (McGraw-Hill, New York, 1953), Sec. 7.3.
  10. Corresponding to the dominant (far) E-field component of EM radiation.
  11. V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation (U.S. Department of Commerce, National Technical Information Service, Springfield, Va. 22151, 1971), cf. Chap. 5.
  12. D. Middleton, “Canonical and quasi-canonical non-gaussian noise models of Class A interference,” IEEE Trans. Electromagn. Compat. 25, 96–106 (1983).
  13. D. Middleton, “Channel modeling and threshold signal processing in underwater acoustics: an analytic overview,” IEEE J. Ocean Eng. 12, 4–28 (1987). [CrossRef]

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