Toraldo filters with concentric unequal annuli of fixed phase by evolutionary programming

The resolving power of an optical imaging system is limited by residual aberrations and diffraction effects. The Rayleigh-Abbe diffraction limit of resolution corresponds to radius of the central lobe of the point spread function of an aberration free diffraction limited system. An attempt to circumvent this limitation was proposed by Toraldo di Francia, who showed that suitable pupil plane filtering can overcome this resolution limit, albeit over a restricted field. This paper reports results of our investigations on the use of evolutionary programming to obtain globally or quasi-globally optimum solutions in synthesis of lossless Toraldo filters consisting of concentric unequal area zones of fixed phase.