Annular binary filters for controlling the axial behaviour of optical systems

The one-dimensional (1D) version of the iterative Fourier transform algorithm (IFTA) and a modified error diffusion algorithm are proposed for binarizing rotationally symmetric pupil filters designed to shape the axial impulse response of optical system. The resulting binary masks consist of a set of transparent and opaque annular zones of equal area or equal width. A numerical experiment in which we examine the performance of the binarization methods is carried out. In this experiment the resemblance between the axial diffractive behaviour of the binary version of an axially superresolving pupil filter, and that of the original continuous-tone filter is evaluated. It is shown that the performance of the binary mask obtained with 1D IFTA is much better than that of the annular binary filters obtained by other digital half-toning techniques which preserve the rotational symmetry of binarized pupils.