Vol. 15, issue 08, article # 10

Dubovik A.N. Differential and statistical invariants of a wavy surface. Part 1. General properties of invariants. // Atmospheric and oceanic optics. 2002. V. 15. No. 08. P. 645-650.
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Abstract:

The transformation and symmetry properties of surface derivatives, correlation functions, and spectral moments at rotation of coordinate axes are examined. The spectral moments and derivatives of the same order are shown to be transformed in the same manner and can be represented in terms of their rotational invariants. Recurrence relations are found for invariants of different orders. The properties of isotropic, homogeneous, and inhomogeneous surfaces are discussed.

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