Global Optimization of Freeform Design Using Simple Saddle Point Detection

Global optimization in optical design is particularly challenging for aspheric and freeform surfaces due to their complex, non-symmetric nature and the presence of numerous local minima in high-dimensional design spaces. Traditional optimization methods often struggle to efficiently escape these local minima, leading to suboptimal solutions. To address this, we propose the Simple Saddle Point Detection (SSPD) Algorithm, which enhances optimization by systematically identifying transition points that connect different design regions. By leveraging these pathways, the algorithm enables a more structured exploration of the design space, improving the convergence toward high-performance solutions. This study applies the SSPD approach to optimize complex optical systems, including catadioptric and multiple (folded) imaging mirror systems, where conventional methods face significant limitations. The results demonstrate that this approach is highly effective in refining aspheric and freeform optical designs, facilitating more efficient and reliable global optimization. Finally, we present the global search results as a closed network, highlighting the capability of SSPD to navigate complex design landscapes and achieve superior optical performance.