Title: Lens design as multi-objective optimisation

Authors: Shaine Joseph; Hyung W. Kang; Uday K. Chakraborty

Addresses: Department of Mathematics and Computer Science, University of Missouri – St. Louis, One University Boulevard, St Louis, MO 63121, USA ' Department of Mathematics and Computer Science, University of Missouri – St. Louis, One University Boulevard, St Louis, MO 63121, USA ' Department of Mathematics and Computer Science, University of Missouri – St. Louis, One University Boulevard, St Louis, MO 63121, USA

Abstract: This paper demonstrates the computational advantages of a multi-objective framework that can overcome the generic and domain-related challenges in optical system design and optimisation. Non-dominated sorting genetic algorithms-II (Deb, 2003) is employed in this study. The optical systems studied in this paper are Cooke triplets, Petzval lens systems and achromatic doublets. We report the results of four studies. In the first study, we optimise the optical systems using computationally efficient image quality objective functions. Our approach uses only two paraxial rays to estimate the objective functions and thus improves the computational efficiency. This timesaving measure can partially compensate for the typically enormous number of fitness function evaluations required in evolutionary algorithms. The reduction in reliability due to the computations from a single ray pair is compensated by the availability of multiple objective functions that help us to navigate to the optima. In the second study, hybridisation of evolutionary and gradient-based approaches and scaling techniques are employed to speed up convergence and enforce the constraints. The third study shows how recent developments in optical system design research can be better integrated in a multi-objective framework. The fourth study optimises an achromatic doublet with suitable constraints applied to the thicknesses and image distance.

Keywords: lens design; optical design; multi-objective optimisation; evolutionary algorithms; genetic algorithms; Petzval lens; NSGA-II; optical systems.

DOI: 10.1504/IJAAC.2011.042851

International Journal of Automation and Control, 2011 Vol.5 No.3, pp.189 - 218

Received: 05 Feb 2011
Accepted: 08 Feb 2011
Published online: 17 Apr 2015 *

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