Optimal Filter Design for Annular Imaging

Abstract

Filters of the type exp(in theta)sgn J(n)(z(o)r) with theta 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 z(o) with respect to incident energy. The simplest optimal filter, sgnJ(o)(z(o)r), is well approximated by the binary circular phase grating sgn cos(z(o)r - pi/4). The single lobe of the first order image of this filter contains 46% of the incident energy within the half-width 0.4lambdaf/a, centered around the image radins Nlambdaf/(2a), where N approximately z(o)/pi is the number of filter sections.