A Multi-Objective Local Optimization Method for Imaging Optical Systems

Abstract

Addressing the inherent limitations of conventional local optimization methodologies such as damping least squares (DLS) and adaptation algorithms, this study proposes a novel approach to multi-objective optimization for imaging optical systems. The proposed method entails the formulation of a multi-objective optimization mathematical framework, where the objectives are established upon lateral aberration and wave aberration criteria. Subsequently, enhancements are made to the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) by implementing a directional initial population strategy and parallel optimization with multiple-trajectory planning. The genesis of the initial population is rooted in the gradient direction information extracted from the starting positions. This strategic foundation precludes potential efficiency limitations in subsequent optimization stages arising from undesirable initial population quality. By employing mechanisms such as differentiation and mutation to sustain population diversity, the trajectory of evolution is guided by the first- and second-order derivatives of the optimal individual, thereby elevating the quality of the evolutionary offspring population. The fusion of the parent and offspring populations yields a composite population, which undergoes rapid and non-dominated sorting, crowding calculation, and elite strategies. Empirical results illustrate the validation of the proposed methodology. The proof-of-concept paradigm demonstrates high efficiency in multi-objective local optimization for imaging optical systems.