2000 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.

IEEE Transactions on Antennas and Propagation
Volume 48 Number 3, March 2000

Table of Contents for this issue

Complete paper in PDF format

Effect of Correlation Between Shadowing and Shadowed Points on the Wagner and Smith Monostatic One-Dimensional Shadowing Functions

Christophe Bourlier, Joseph Saillard and Gérard Berginc

Page 437.

Abstract:

The Wagner [1] and Smith [2], [3] classical monostatic one-dimensional (1-D) shadowing functions assume that the joint probability density of heights and slopes is uncorrelated, thus inducing an overestimation of the shadowing function. The goal of this article is to quantify this assumption. More recently,Ricciardi and Sato [4], [5] proved that the shadowing function is given rigorously by Rice's infinite series of integrals. We observe that the approach proposed by Wagner retains only the first term of this series,whereas the Smith formulation uses the Wagner model by introducing a normalization function. In this article, we first calculate the shadowing function based on the Ricciardi and Sato work for an uncorrelated process. We will see that the uncorrelated results do not have any physical sense. Next, the Wagner and Smith formulations will be modified in order to introduce the correlation. Correlated and uncorrelated results are compared with the reference solution,which is determined by generating a surface [8] for a Gaussian autocorrelation function. So, we will show that the correlation improves the results for values µ<= 2, where µ represents the slope of incident ray and the slopes variance of the surface. Finally, our results will be compared to those given in [9], determined from the first three terms of Rice's series, but the shadowing function used is not averaged over the slopes.

References

  1. R. J. Wagner, "Shadowing of randomly rough surfaces", J. Opt. Soc. Amer., vol. 41, no. 1, pp.  138-147, June  1966.
  2. B. G. Smith, "Lunar surface roughness, shadowing and thermal emission", J. Geophys. Res., vol. 72, no. 16, pp.  4059-4067, Aôutut  1967.
  3. B. G. Smith, "Geometrical shadowing of a random rough surface", IEEE Trans. Antennas Propagat., vol. AP-15, pp.  668-671,  Sept.  1967.
  4. L. M. Ricciardi and S. Sato, "On the evaluation of first passage time densities for gaussian processes", Signal Processing, vol. 11, pp.  339-357, 1986.
  5. L. M. Ricciardi and S. Sato, "A note on first passage time problems for gaussian processes and varying boundaries", IEEE Trans. Inform. Theory, vol. IT-29, May  1983.
  6. M. I. Sancer, "Shadow-corrected electromagnetic scattering from a randomly rough surface", IEEE Trans. Antennas Propagat., vol. AP-17, pp.  577-585, Sept.  1969.
  7. P. Beckman, "Shadowing of random rough surfaces", IEEE Trans. Antennas Propagat., vol. AP-13, pp.  384-388, May  1965 .
  8. R. A. Brokelman and T. Hagfors, "Note of the effect of shadowing on the backscattering of waves from a random rough surface", IEEE Trans. Antennas Propagat., vol. AP-14, pp.  621-627, Sept.  1967.
  9. D. A. Kapp and G. S. Brown, "Effect of correlation between shadowing and shadowed points in rough surface scattering", IEEE Trans. Antennas Propagat., vol. 42, Aug.  1994.