Pupil filter design by using a Bessel functions basis at the image plane

Many applications can benefit from the use of pupil filters for controlling the light intensity distribution near the focus of an optical system. Most of the design methods for such filters are based on a second-order expansion of the Point Spread Function (PSF). Here, we present a new procedure for designing radially-symmetric pupil filters. It is more precise than previous procedures as it considers the exact expression of the PSF, expanded as a function of first-order Bessel functions. Furthermore, this new method presents other advantages: the height of the side lobes can be easily controlled, it allows the design of amplitude-only, phase-only or hybrid filters, and the coefficients of the PSF expansion can be directly related to filter parameters. Finally, our procedure allows the design of filters with very different behaviours and optimal performance.