Abstract

Filters of the type exp(inθ)sgn Jn(zor) with θ the azimuthal angle and r the radial coordinate in the filter plane, are shown to maximize the energy content in a narrow annular image of radius zo with respect to incident energy. The simplest optimal filter, sgnJo(zor), is well approximated by the binary circular phase grating sgn cos(zorπ/4). The single lobe of the first order image of this filter contains 46% of the incident energy within the half-width 0.4λf/a, centered around the image radius Nλf/(2a), where Nzo/π is the number of filter sections.

© 1974 Optical Society of America

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