Abstract

A pupil coating PN(β) 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 PN(β) to image theory, we find that (1) the scalar wave equation has a point like solution; (2) a modification of PN(β) causes an arbitrarily narrow depth of focus; (3) an arbitrary point amplitude response may be optically produced; and (4) coating PN(β) 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 PN(β) are discussed.

© 1970 Optical Society of America

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