Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Scattering of eletromagnetic waves from a random surface

Author: William C. Hoffman
Journal: Quart. Appl. Math. 13 (1955), 291-304
MSC: Primary 78.0X
DOI: https://doi.org/10.1090/qam/72702
MathSciNet review: 72702
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Abstract: Suppose $ Z\left( {x,y} \right)$ is a real random process, continuous in the mean over a finite region $ D$, and with mean value zero and covariance function $ r\left( {x,y;x',y'} \right)$. As such $ Z\left( {x,y} \right)$ defines a random surface (provided certain differentiability conditions are satisfied). Then, by Karhunen's theorem on the representation of a random function, $ Z\left( {x,y} \right)$ has an expansion in terms of an orthogonal process and the eigenfunctions and eigenvalues of the covariance function. Introducing this expression into the far-zone form of the Stratton-Chu solution of the electromagnetic field equations then leads to an approximate expression for the radiation scattered from the random surface, from which mean and covariance of the scattered field can be determined.

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DOI: https://doi.org/10.1090/qam/72702
Article copyright: © Copyright 1955 American Mathematical Society

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