To simplify the analysis of a typical underwater imaging system--illuminator, target, and receiver adjacent to the illuminator--the combined optics-water response to a point reflectance is treated as a system response function. This is shown to be the product of the separate transmitter and receiver response functions. Each of these may be expressed as a convolution of the optics and water response functions. The latter are the point and beam spread functions. By an expansion of the principles derived, the backscatter arising from points in the region between the illuminator-receiver assembly and the target is characterized analytically. Then the total backscatter from the water is obtained by a simplified three dimensional integral. Values of the total backscatter obtained by this method are compared with values obtained by other means and with measured values. Finally an assessment of the utility of various analytical descriptions of underwater optical imaging is given.