Nonlinear optical processing: analysis and synthesis

Coherent optical systems are of interest in image or data processing because of their ability to handle rapidly large bandwidth data in parallel. They have been restricted to performing linear operations such as Fourier transformation and convolution due to the inherent linear nature of an optical system at low power levels. In this paper, the combination of a nonlinear halftoning step followed by bandpass spatial filtering to yield a specific nonlinear intensity transfer function is explored. A general analysis of the problem assuming infinite copy film gamma and saturation density is made. A constructive algorithm for designing a halftone cell shape and selecting the diffraction order to yield very general types of nonmonotonic nonlinearities is presented. Numerous examples of the synthesis procedure are given. Experimental results with general halftone screens made on a plotting flatbed microdensitometer are presented. Logarithmic, exponential, and level slice characteristics are achieved with monotonic cells.