Optimal binary image design based on the branch and bound algorithm

Mathematical programming techniques for systematic determination of optimal binary masks for precompensation in incoherent optical systems are developed. The feasibility of applying combinatorial optimization techniques to binary mask design for optical lithography is demonstrated. The mask is optimized in such a way as to precompensate the distortions due to optical diffraction of the system. The problem is formulated as a binary linear programming problem and solved with the branch and bound algorithm. Two different formulations corresponding to two optimization criteria are proposed and evaluated. Variation of the optimal mask as a function of the optical system bandwidth is discussed. One- and two-dimensional examples involving bars and a corner are presented