Geometric waveguides are a promising architecture for optical see-through augmented reality displays, but their performance is severely bottlenecked by the difficulty of jointly optimizing non-sequential light transport and polarization-dependent multilayer thin-film coatings. Here we present the first end-to-end differentiable optimization framework for geometric waveguide that couples non-sequential Monte Carlo polarization ray tracing with a differentiable transfer-matrix thin-film solver. A differentiable Monte Carlo ray tracer avoids the exponential growth of deterministic ray splitting while enabling gradients backpropagation from eyebox metrics to design parameters. With memory-saving strategies, we optimize more than one thousand layer-thickness parameters and billions of non-sequential ray-surface intersections on a single multi-GPU workstation. Automated layer pruning is achieved by starting from over-parameterized stacks and driving redundant layers to zero thickness under discrete manufacturability constraints, effectively performing topology optimization to discover optimal coating structures. On a representative design, starting from random initialization within thickness bounds, our method increases light efficiency from 4.1\% to 33.5\% and improves eyebox and FoV uniformity by $\sim$17$\times$ and $\sim$11$\times$, respectively. Furthermore, we jointly optimize the waveguide and an image preprocessing network to improve perceived image quality. Our framework not only enables system-level, high-dimensional coating optimization inside the waveguide, but also expands the scope of differentiable optics for next-generation optical design.

翻译：几何波导是实现光学透视增强现实显示的一种有前景的架构，但其性能受到非序列光传输与偏振相关多层薄膜涂层联合优化难题的严重制约。本文提出了首个用于几何波导的端到端可微分优化框架，该框架将非序列蒙特卡洛偏振光线追迹与可微分传输矩阵薄膜求解器相耦合。可微分蒙特卡洛光线追迹避免了确定性光线分裂的指数级增长，同时支持从眼动框指标到设计参数的梯度反向传播。借助内存节约策略，我们在单个多GPU工作站上优化了超过一千个层厚度参数以及数十亿次非序列光线-表面交点。通过从过参数化的堆栈开始，并在离散可制造性约束下驱动冗余层厚度趋于零，实现了自动化的层剪枝，这实质上执行了拓扑优化以发现最优涂层结构。在一个代表性设计中，从厚度边界内的随机初始化开始，我们的方法将光效率从4.1%提升至33.5%，并将眼动框和视场角的均匀性分别提高了约17倍和约11倍。此外，我们联合优化了波导和一个图像预处理网络，以改善感知图像质量。我们的框架不仅实现了波导内部系统级、高维度的涂层优化，而且拓展了可微分光学在下一代光学设计中的应用范围。