Information-based optical design for binary-valued imagery

Applications such as optical data storage, optical computing, and optical interconnects require optical systems that manipulate binary-valued images. Such an optical system can be viewed as a two-dimensional array of binary communication channels. This perspective is used to motivate the use of pagewise mutual information as a metric for optical system analysis and design. Fresnel propagation and coherent imaging both are analyzed in terms of mutual-information transmission. An information-based space-bandwidth product is used to analyze the trade-off between the numerical aperture and the number of image pixels in a coherent 4f system. We propose a new merit function to facilitate information-based optical system design. Information maximization and bit-error-rate minimization both are possible with the new radially weighted encircled-energy merit function. We demonstrate the use of this new merit function through a design example and show that the information throughput is increased by 8% and the bit-error rate is reduced by 36% when compared with systems designed with traditional criteria.