The characterization of optical anisotropy in thin van der Waals (vdW) materials is crucial for both fundamental studies and nanophotonic applications. However, conventional techniques such as spectroscopic ellipsometry face significant limitations in measuring out-of-plane anisotropy and require large-area, uniform films. In this work, we present a novel framework based on coherent Fourier scatterometry (CFS) combined with deep learning for the rapid, label-free characterization of in-plane and out-of-plane refractive indices of anisotropic thin films. We designed a specialized deep neural network, AnisoVision, and trained it on simulated far-field angular spectra from multilayer stacks using the 4 × 4 Berreman matrix formalism. To efficiently capture the directional dependence of anisotropy, we utilize radially polarized light and extract only three far-field azimuthal cross sections (0, 45, 90°), enabling robust retrieval while minimizing data requirements. Our method demonstrates accurate index retrieval for both isotropic and anisotropic materials, including uniaxial h-BN and biaxial α-MoO3 flakes of varying thickness. We further validate the model’s stability by testing multiple flakes of the same material across a range of thicknesses, yielding consistent optical constants. Our approach is single-shot, nondestructive, and applicable to localized sample regions, making it suitable for heterogeneous or exfoliated samples. Additionally, the technique can be readily extended to broadband operation for spectroscopic analysis. Our work establishes CFS coupled with deep learning as a powerful platform for high-throughput optical metrology of low-dimensional materials.

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.