Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-24T13:13:22.377Z Has data issue: false hasContentIssue false
  • English
  • Français

The distribution of the sizes of images reflected in a random surface

Published online by Cambridge University Press:  24 October 2008

M. S. Longuet-Higgins
M. S. Longuet-Higgins
Affiliation:
National Institute of OceanographyWormley
Get access Rights & Permissions [Opens in a new window]

Extract

It has been shown recently that a fruitful method of studying the formation of waves on the sea surface is through the average intensity of reflected sunlight, as seen from different angles ((3), (4)). This gives, in effect, the statistical distribution of the components of surface slope.

Following the same line of thought, we may inquire what information could be derived from the distribution of the sizes of the reflected images of the sun. The size of an image depends essentially on the total curvature of the surface at the point of reflexion (see § 2).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 55 , Issue 1 , January 1959 , pp. 91 - 100
Copyright
Copyright © Cambridge Philosophical Society 1959

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)Cartwright, D. E. and Longuet-Higgins, M. S.The statistical distribution of the maxima of a random function. Proc. Roy. Soc. A, 237 (1956), 212–212.Google Scholar
(2)Catton, Diana and Millis, B. G.Numerical evaluation of the integral Proc. Camb. Phil. Soc. 54 (1958), 454–454.CrossRefGoogle Scholar
(3)Cox, C. and Munk, W.Measurement of the roughness of the sea surface from photographs of the sun's glitter. J. Opt. Soc. Amer. 44 (1954), 838–838.CrossRefGoogle Scholar
(4)Cox, C. and Munk, W.Slopes of the sea surface deduced from photographs of sun glitter. Bull. Scripps Instn Oceanogr. 6 (1956), 401–401.Google Scholar
(5)Longuet-Higgins, M. S.The statistical analysis of a random, moving surface. Phil. Trans. Boy. Soc. A, 249 (1957), 321–321.Google Scholar
(6)Longuet-Higgins, M. S.Statistical properties of an isotropic random surface. Phil. Trans. Roy. Soc. A, 250 (1957), 157–157.Google Scholar
(7)Longuet-Higgins, M. S.The statistical distribution of the curvature of a random gaussian surface. Proc. Camb. Phil. Soc. 54 (1958), 439–439.CrossRefGoogle Scholar
(8)Primakoff, H. and Keller, J. B.Reflection and transmission of sound by thin curved shells. J. Acoust. Soc. Amer. 19 (1947), 820–820.CrossRefGoogle Scholar
(9)Rice, S. O.Mathematical analysis of random noise. Bell. Syst. Tech. J. 23 (1944), 282–282.CrossRefGoogle Scholar
(10)Weatherburn, C. E.Differential geometry of three dimensions, vol. 1 (Cambridge, 1939).Google Scholar