Zone plates with black focal spots

Computer-designed linear and circular zone plates are considered that utilize a pi ;-phase jump in order to create destructive interference in the focus. Intensity distributions in the focal plane as well as along the optical axis are calculated for a few examples. A significant decrease of the black spot diameter in comparison with the dimensions of the ordinary focal spot is obtained. Further reduction is achieved when the central region of the zone plate is obstructed. Some applications to alignment and the schlieren technique are suggested. Experimental results that confirm the calculated distributions are presented.