Water Surface Topography Retrieved from Color Images

Abstract

ubmerged objects viewed through wavy water surfaces appear distorted by refraction. An imaging system exploiting this effect is implemented using a submerged planar light source designed so that color images reveal features of small-amplitude waves in a wind-wave tank. The system is described by a nonlinear model of image formation based on the geometry of refraction, spectral emission from the light source, radiative transfer through the water and surface, and camera spectral response. Surface normal vector components are retrieved from the color image data using an iterative solution to the nonlinear model. The surface topography is then retrieved using a linear model that combines surface normal data with a priori constraints on elevation and curvature. The high-resolution topographic data reveal small-amplitude waves spanning wavelength scales from capillary through short gravity wave regimes. The system capabilities are demonstrated in the retrieval of test surfaces, and of a case of wind-driven waves, using data collected at high spatial and temporal resolution in a wave tank. The approach of using a physical model of image formation with inverse solution methods provides an example of how surface topography can be retrieved and may be applicable to data from other similar instruments.