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The focusing of radiation by a random surface when the source is at a finite distance

Published online by Cambridge University Press:  24 October 2008

M. S. Longuet-Higgins
M. S. Longuet-Higgins
Affiliation:
National Institute of Oceanography, Wormley, Surrey
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Extract

Imagine a nearly horizontal, statistically uniform, random surface ζ(x, y), Gaussian in the sense that the second derivatives , , have a normal joint distribution. The problem considered is the statistical distribution of the quantity

where J and Ω denote the mean curvature and total curvature of the surface, respectively, and ν is a constant parameter.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 56 , Issue 1 , January 1960 , pp. 27 - 40
Copyright
Copyright © Cambridge Philosophical Society 1960

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References

REFERENCES

(1)Kendall, M. G. and Stuart, A.The advanced theory of statistics, vol. I. (London, 1958).Google Scholar
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(3)Longuet-Higgins, M. S.The distribution of the sizes of images reflected in a random surface. Proc. Camb. Phil. Soc. 55 (1959), 91–100.Google Scholar
(4)Lowan, A.N. Tables of normal probability functions. N.B.S. Appl. Math. Ser., 23 (Washington, 1953).Google Scholar
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