Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-26T02:08:46.282Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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.

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Kendall, M. G. and Stuart, A.The advanced theory of statistics, vol. I. (London, 1958).Google Scholar
(2)Longuet-Higgins, M. S.The statistical distribution of the curvature of a random Gaussian surface. Proc. Camb. Phil. Soc. 54 (1958), 439–53.CrossRefGoogle Scholar
(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
(5)Whittaker, E. T. and Watson, G. N.A course of modern analysis, 4th ed. (Cambridge, 1952).Google Scholar