Phase image differentiation with linear intensity output

A heuristic development of the operation of a square root filter (one whose amplitude transmittance is proportional to the square root of position in frequency space) is presented. The output of a coherent optical processor utilizing this filter for phase image inputs is shown to be an intensity which is directly proportional to the derivative of the input phase function. The results of a digital filtering experiment which confirms this linear relationship are presented. The use of this filter in phase image visualization systems is also discussed.