Scattering from Moderately Rough Surfaces

  • Soon K. Cho

Abstract

Electromagnetic scattering from a moderately rough surface model will be studied here. By a moderately rough surface we mean one whose height and slope variations are moderate as described by
  • kz(x,y) < 1

  • \( \tfrac{{\partial z}}{{\partial x}},\tfrac{{\partial z}}{{\partial y}} < 1, \)

  • l x ,l y << L

where z is the surface height at (x, y), l x , l y , and L denote respectively the x-and y-component of the roughness correlation length l and the dimension of the illuminated area. The surface is also restricted to be highly conducting so that the assumption of perfect conductivity is approximately valid. For this type of the surface model, we will describe a method of estimating the stochastic radar cross section in bistatic scattering by carrying out in detail the mathematical procedures, based on the S-matrix formulation developed in the preceding chapter. It is generally believed that the random variations of the surface height and the surface slope of this type of rough surface obey the Guassian statistics. Our discussion is based on this belief (cf. for example, W. Hoffman [5.4], P. Beckmann and A. Spizzichino [5.1], J. Kong, et al. [5.5], A. Fung, et al. [5.3]). The material of this chapter is an outgrowth of joint work with C. M. Chu of the Radiation Laboratory of the University of Michigan.

Keywords

Microwave Covariance Radar Remote Sensing ptAP 

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References

  1. 5. 1
    P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces, Pergamon Press, New York, NY, 1963.MATHGoogle Scholar
  2. 5. 2
    H. Cramér, Mathematical Methods of Statisitcs, Princeton University Press, 1946.Google Scholar
  3. 5. 3
    A. Fung, R. Moore, and F. Ulaby, Microwave Remote Sensing, Volumes II and III, Addison-Wesley, Reading, Mass., 1981.Google Scholar
  4. 5. 4
    W. C. Hoffman, Scattering of electromagnetic waves from a ran- dom surface, J. of Appl. Math., XIII, 3, /1955; pp. 291–304.Google Scholar
  5. 5. 5
    J. Kong, L. Tsang, and R. Shin, The Theory of Microwave Re- mote Sensing, Interscience Publisher, New York, NY, 1985.Google Scholar
  6. 5. 6
    J. E. Moyal, Stochastic processes and statistical physics, J. Royal Sta. Soc., Series B, XI, no. 2, 1949; pp. 150–210.MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag New York Inc. 1990

Authors and Affiliations

  • Soon K. Cho
    • 1
  1. 1.YpsilantiUSA

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