The Problem of Reconstructing the Profile of the Sea Surface from the Video Image of Laser Beams

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Currently, there are no remote methods for recording the instantaneous two-dimensional profile of the sea surface Z(x, y, t) in field conditions. There are no methods for recording capillary wave profiles directly on the sea surface. The short-wave component of sea waves plays a very important role in radiometry in the formation of the surface's own radiation and in solving inverse radar problems. This article proposes an optical measurement technique that makes it possible to measure the parameters of the entire wave spectrum, including capillary waves with amplitude of less than 0.1 mm. However, the author has not yet been able to fully solve the inverse problem of reconstructing the two-dimensional wave profile. The author considered it expedient to formulate this problem and involve the scientific community in its successful solution. Obtaining the profile of sea waves Z(x, y, t) in natural conditions with a high update rate will allow obtaining complete information about the characteristics of waves, temporal and spatial spectra of elevations, spectra of slopes, and studying the evolution of waves when the wind changes. Of particular value is the possibility of recording and studying the short-wave components of waves, including capillary waves.

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作者简介

V. Sterlyadkin

MIREA-Russian Technological University

编辑信件的主要联系方式.
Email: sterlyadkin@mail.ru
俄罗斯联邦, Moscow

参考

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2. Fig. 1. Schematic of wave measurements from an offshore platform. Scanner 1 directs the needle laser beam 2 along the specified trajectory 3. The radiation scattered by the surface is recorded on a digital video camera 4.

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3. Fig. 2. Two pairs of consecutive video images of laser beams obtained at night and daytime from the offshore platform. In the lower photos capillary waves are registered in the daytime.

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4. Fig. 3. Results of field measurements: a - distribution of surface slopes for a rectangular triangle with sides 283×253 mm [23]; b - spectrum of elevations in a separate point of the profile in logarithmic scale for the developing wave 26.08.2021, Katsiveli. The degree indices at the first, second and third (capillary) sites are 4.5 ± 0.3, 4.0 ± 0.2 and 2.6 ± 0.3.

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5. Fig. 4. Path of rays through the agitated sea surface: a - lateral view, ray projections on the xz plane; b - top view, xy section.

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6. Fig. 5. Dependence of coordinates of point A on sea surface slopes: a) curve 1 - dependence of coordinate x of luminous point A on slope γx of sea surface at LED depth zc = 0.2 m and absence of slope along y-axis, curve 2 - the same at γy = 10°; b) dependence of displacement of point A along y-axis on slope γy along y-axis. The slopes along the x-axis are indicated in the legend on the graph.

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7. Fig. 6. Displacement of the image of the luminous diode located at a given depth zc during the passage of a harmonic wave λ = 50 cm; a - at the wave amplitude of 7.5 mm, the depth of the LED zc = 0.3 m and different directions α relative to the x-axis: 1 - α = 1°, 2 - α = 10°, 3 - α = 45°, 4 - α = 80°, 5 - α = 89°; b - at the wave direction α = 45° and different amplitude A of the wave and depth of the LED zc (indicated in the legend).

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8. Fig. 7. Dependence of displacement of point A along y-axis on slope γy: a - for these plots A = (0.124, y, 0), slope γx of the sea surface is indicated in the legend; b - the same, but the x-coordinate at point A is further away - A = (0.187, y, 0)

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9. Fig. 8. Laser beam shape on the sea surface at a capillary wave λ = 15 mm, A = 0.2 mm, which propagates at an angle α = 45° with respect to the x-axis.

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10. Fig. 9. Plots of video frames with magnification: a - night measurements, image scale on two axes is represented by 50 mm segments, thin vertical line - beam shape at undisturbed surface, curve ab - average beam shape at absence of capillary wave; b - capillary waves registered in the daytime.

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11. Fig. 10. Geometry of two-dimensional sea surface profile measurements, top view: 1, 2 - orthogonally located video cameras; 3 - two sets of laser beams incident on the surface; 4 - area of the measured sea surface.

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