The Extrapolating Pupil, Image Synthesis, and Some Thought Applications

Abstract

A pupil coating P(N)(beta) exists whose point amplitude response over a specified range of its argument is asymptotic (with N) to a Dirac delta function. Investigating the implications of coating P(N)(beta) to image theory, we find that (1) the scalar wave equation has a point like solution; (2) a modification of P(N)(beta) causes an arbitrarily narrow depth of focus; (3) an arbitrary point amplitude response may be optically produced; and (4) coating P(N)(beta) effectively extrapolates outward beyond the pupil margin one class of pupil functions. Some amusing analog devices based on property (4) are developed. The severe limitations on the practical use and fabrication of pupil P(N)(beta) are discussed.