We analyze the uniqueness of the solutions of inverse lithographical problems, stated as optimization problems, and optical images. By considering a band-limitedness argument, examples of ill-posed problems are constructed with multiple solutions in the domain of real non-negative passive masks. We conclude that the necessary condition for the solution m to be unique is to touch (or to pass infinitely close to) the boundary of the constraint 0 ≤ m ≤ 1. In the domain of binary masks, we propose a procedure to construct two nonunique solutions from a possibly unique one. We prove the existence of unique binary solutions in some class of optical systems and suggest a thresholding procedure to generate a unique solution from a possibly nonunique one.
"On the uniqueness of optical images and solutions of inverse lithographical problems," Journal of Micro/Nanolithography, MEMS, and MOEMS 8(3), 031405 (1 July 2009). https://doi.org/10.1117/1.3158613