Unified ray-wave model for end-to-end imaging in refractive–diffractive hybrid optics

End-to-end optical design has emerged as a promising paradigm in computational imaging, emphasizing the joint optimization of optical elements and computational algorithms. However, existing models struggle to simultaneously achieve efficiency, accuracy, and differentiability, which limits the development of refractive-diffractive hybrid systems. To address this challenge, we propose a unified ray-wave (UniRW) differentiable modeling framework that couples generalized Snell's law with wave propagation. By unifying geometric ray tracing and wave optics, the framework enables accurate and efficient simulation of arbitrary hybrid optical systems, and can be naturally embedded into end-to-end optimization pipelines to support joint learning of optical parameters and image reconstruction networks. We validate the proposed framework on aberration correction and extended depth-of-field (EDOF) tasks. In aberration correction, the proposed hybrid lens achieves improved image reconstruction quality enabled by more accurate PSF modeling and end-to-end optimization. Quantitative results show that UniRW improves the reconstructed image peak signal-to-noise ratio (PSNR) by approximately 3.4 dB. In the EDOF setting, the proposed framework achieves high-quality image reconstruction with a PSNR of approximately 31.9 dB across an extended axial defocus range of ±500<i>µm</i>. These results demonstrate that the proposed approach bridges physical modeling and deep learning optimization, providing an efficient, accurate, and general paradigm for hybrid optical design.