Abstract

Filters of the type exp(inθ)sgn J_n(z_or) 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 z_o with respect to incident energy. The simplest optimal filter, sgnJ_o(z_or), is well approximated by the binary circular phase grating sgn cos(z_or − π/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 N ≃ z_o/π is the number of filter sections.

© 1974 Optical Society of America

Far Field Diffraction Patterns of Circular Gratings

Andre Fedotowsky and Kurt Lehovec
Appl. Opt. 13(11) 2638-2642 (1974)

Imaging Performance of Annular Apertures

Hubert F. A. Tschunko
Appl. Opt. 13(8) 1820-1823 (1974)

Method for Optimized Design of Dielectric Multilayer Filters

H. S. Hou
Appl. Opt. 13(8) 1863-1866 (1974)

Optical-Waveguide Band-Rejection Filters: Design

Masanori Matsuhara and K. O. Hill
Appl. Opt. 13(12) 2886-2888 (1974)

Comparison of superresolution effects with annular phase and amplitude filters

Hongxin Luo and Changhe Zhou
Appl. Opt. 43(34) 6242-6247 (2004)