A Differentiable Ray–Wave Framework for Hybrid Refractive–Diffractive System Modeling and Optimization

Abstract

Hybrid optical systems combining refractive and diffractive optical responses have the potential to support new types of optical behavior, but they are difficult to model and optimize due to the disparate spatial scales and physics exhibited by ray and wave phenomena. In this work, we present a differentiable ray–wave framework for modeling hybrid refractive–diffractive optical systems that operates as a plug-and-play module within standard ray tracing pipelines. Our model uniquely applies to both planar and curvilinear diffractive surfaces and accommodates arbitrary scalar holographic profiles with high spatial frequency responses, with each simulation evaluated at a single wavelength. We analyze ray–wave modeling regimes that optimally account for the spatial frequency properties and spatial curvature of the diffractive surfaces, and we demonstrate the gradient-based end-to-end optimization of hybrid refractive–diffractive systems featuring planar and conformal diffractive surfaces. We anticipate that these modeling capabilities will enable new classes of hybrid optical systems relevant to computational imaging and display applications.