Vol. 15, issue 08, article # 11

Dubovik A.N. Differential and statistical invariants of a wavy surface. Part 2. Properties of a Gaussian surface . // Atmospheric and oceanic optics. 2002. V. 15. No. 08. P. 651-655.
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It is shown that the spectrum of a Gaussian surface has only the second-order rotational axis, and its moments of higher than the second order are degenerated in such a way that only three of them are independent and only two invariants are nonzero. The conditions for decomposition of the spectrum into one-dimensional systems are revealed, and the joint statistical distribution of the mean and differential curvatures at horizontal surface points is found. Within the framework of the Gaussian model, a simple optical method is suggested for simultaneous remote measurement of the second- and fourth-order invariants of spectral moments.