Enlarging the depth of focus by filtering in the phase-space domain

The ambiguity function was employed as a merit function to design an optical system with a high depth of focus. The ambiguity function with the desired enlargeddepth-of-focus characteristics was obtained by using a properly designed joint filter to modify the ambiguity function of the original pupil in the phase-space domain. From the viewpoint of the filter theory, we roughly propose that the constraints of the spatial filters that are used to enlarge the focal depth must be satisfied. These constraints coincide with those that appeared in the previous literature on this topic. Following our design procedure, several sets of apodizers were synthesized, and their performances in the defocused imagery were compared with each other and with other previous designs.