Skip to main content Accessibility help

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

  • M. S. Longuet-Higgins (a1)


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.



Hide All
(1)Kendall, M. G. and Stuart, A.The advanced theory of statistics, vol. I. (London, 1958).
(2)Longuet-Higgins, M. S.The statistical distribution of the curvature of a random Gaussian surface. Proc. Camb. Phil. Soc. 54 (1958), 439–53.
(3)Longuet-Higgins, M. S.The distribution of the sizes of images reflected in a random surface. Proc. Camb. Phil. Soc. 55 (1959), 91100.
(4)Lowan, A.N. Tables of normal probability functions. N.B.S. Appl. Math. Ser., 23 (Washington, 1953).
(5)Whittaker, E. T. and Watson, G. N.A course of modern analysis, 4th ed. (Cambridge, 1952).


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed