Dr. Tiago Botari Profile

Dr. Tiago Botari

at ASML Netherlands BV

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Proceedings Article | 7 August 2023 Paper

New solutions to Cooke triplet problem via analysis of attraction basins

Kirill Antonov, Tiago Botari, Teuss Tukker, Thomas Bäck, Niki van Stein, Anna Kononova

Proceedings Volume 12624, 126240T (2023) https://doi.org/10.1117/12.2675836

KEYWORDS: Mathematical optimization, Evolutionary algorithms, Optical design, Education and training, Lenses, Optics manufacturing, Algorithm development, Reflection, Lithography, Imaging systems, Nonlinear optimization

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Optical systems in lithography machines play a significant role in their performance and, therefore, need to be optimized for specific applications. Artificial Intelligence (AI) and, in particular, metaheuristics are utilized in optimization algorithms for finding a diverse set of feasible and high-performing designs. The diversity requirement of the produced solutions is enforced to allow taking into account additional constraints that are difficult to formalize. In this work, we analyse the space of solutions previously produced by a niching evolutionary algorithm for the Cooke Triplet optical system and propose an approximation of the manifold where all high-performing designs exist. First, we show the existence of high-performing optical designs that are structurally different from the 21 previously known theoretical solutions. In order to do this, we develop a general computationally efficient methodology to create a partition of known high-quality points and their (accidentally found) improvements to their corresponding attraction basins, in the case when neither the exact number of landscape attractors nor their locations are known. We construct a manifold estimation which contains high-performing solutions by fitting a Gaussian Process-based classifier which predicts if an arbitrary design is close to high-performing. The proposed approach shows that AI-assisted optimization is beneficial, and it can be used to extend the capabilities of lithographic scanners and metrology equipment. Furthermore, it opens the possibility of studying other industrial applications.

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