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Journal of Micro/Nanolithography, MEMS, and MOEMS

On the uniqueness of optical images and solutions of inverse lithographical problems
Author(s): Yuri Granik
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Paper Abstract

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.

Paper Details

Date Published: 1 July 2009
PDF: 6 pages
J. Micro/Nanolith. 8(3) 031405 doi: 10.1117/1.3158613
Published in: Journal of Micro/Nanolithography, MEMS, and MOEMS Volume 8, Issue 3
Show Author Affiliations
Yuri Granik, Mentor Graphics Corp. (United States)


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