Halftoning (intensity-to-area modulation) is used to implement nonlinear gray-scale transformations in optical information processing and in the graphic arts. Dynamically variable halftoning can be achieved by recording the intensity distribution of cross-line grating diffraction patterns onto a high contrast photosensitive medium. The input image information thus becomes an array of opaque periodic structures whose areas are related to the input image intensity. To achieve a required halftone mapping from intensity to area, we pose an inverse problem: given the area of the periodic structures as a function of input intensity, synthesize an optical system that implements this function. This ill-posed problem is solved using a class of symmetric functions with separable variables.