Use of point spread and beam spread functions for analysis of imaging systems in water

An accurate method of analysis of underwater imaging systems using optical spread functions and their transforms, the modulation transfer functions, is presented. The overall system spread function is obtained from the water spread functions and the spread functions of the system components. The water point spread and beam spread functions are defined, and measurements of these are presented for clear coastal water for distances up to nine attenuation lengths. Relationships between the spread functions and their dependence on range are also given. In addition, their relationships to the conventional optical oceangraphic parameters of beam attenuation, absorption, and scattering are described. Combined optics-water spread functions and their transforms are developed for illuminator and receiver geometries typically used in underwater imaging. These are then used to determine the system (optics plus water) response to the target reflectance. An analytic technique for accurate computation of backscatter signals is developed. Computed and measured signals compare favorably. It is concluded that the use of spread functions is a convenient and viable technique for analytic computation of underwater images.