Analysis and Compensation of Geometric Distortions, Appearing when Observing Objects under Water

Abstract

In the paper, the analytical description of visual geometric distortions appearing when observing objects under water is performed. The problem of finding a virtual image of a point underwater light source is solved. Three results are derived from the solution of this problem. The first is an equation for a set of virtual images of a point light source, which is formed under all possible positions of the observer. The second is an equation for the observed image of an underwater plane under a stationary observer. The third is the transformation of coordinates simulating the underwater distortion of an optical system, and the inverse transformation, allowing the compensation of the underwater distortion without an underwater calibration procedure. The experimental confirmation of the derived laws is given.