Retrieval of the Vector of Water Surface Slopes by Use of It’s Image under Quasi-Nadir Observation

Turlaev D. G.

A new method for retrieving the slopes of a rough water surface from its imaging under the conditions of daylight illumination and clear cloudless sky is proposed. The traditional method uses the approximation, within the framework of which the distribution of the sky radiance can be considered linear. The new method uses more realistic approximation, in which the distribution of the sky radiance is not linear but has an axial symmetry with respect to the Sun direction. To implement any of these methods, one should not only image the water surface but also know the distribution of the sky radiance in the “mirror” area of the celestial sphere. An important part of the new algorithm is the operation of retrieving the second component of the surface slope vector by the component directly determined by spatial image processing. Mathematically, this operation is nothing but a problem of finding the gradient of a smooth function of two variables by one of its components. In this paper, this problem is solved by means of the Fourier transform. An improved (from the viewpoint of the computing speed) version of the algorithm and a formula for calculating the error are given.

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