Hybrid refractive-diffractive lenses combine the light efficiency of refractive lenses with the information encoding power of diffractive optical elements (DOE), showing great potential as the next generation of imaging systems. However, accurately simulating such hybrid designs is generally difficult, and in particular, there are no existing differentiable image formation models for hybrid lenses with sufficient accuracy. In this work, we propose a new hybrid ray-tracing and wave-propagation (ray-wave) model for accurate simulation of both optical aberrations and diffractive phase modulation, where the DOE is placed between the last refractive surface and the image sensor, i.e. away from the Fourier plane that is often used as a DOE position. The proposed ray-wave model is fully differentiable, enabling gradient back-propagation for end-to-end co-design of refractive-diffractive lens optimization and the image reconstruction network. We validate the accuracy of the proposed model by comparing the simulated point spread functions (PSFs) with theoretical results, as well as simulation experiments that show our model to be more accurate than solutions implemented in commercial software packages like Zemax. We demonstrate the effectiveness of the proposed model through real-world experiments and show significant improvements in both aberration correction and extended depth-of-field (EDoF) imaging. We believe the proposed model will motivate further investigation into a wide range of applications in computational imaging, computational photography, and advanced optical design. Code will be released upon publication.

翻译：混合折射-衍射透镜结合了折射透镜的光学效率与衍射光学元件（DOE）的信息编码能力，展现出作为下一代成像系统的巨大潜力。然而，对此类混合设计进行精确模拟通常较为困难，特别是目前尚无足够精确的、适用于混合透镜的可微分成像模型。本研究提出了一种新的混合射线追踪与波传播（射线-波）模型，用于精确模拟光学像差与衍射相位调制，其中DOE被置于最后一个折射表面与图像传感器之间，即远离常被用作DOE位置的傅里叶平面。所提出的射线-波模型完全可微分，支持梯度反向传播，从而实现折射-衍射透镜优化与图像重建网络的端到端协同设计。我们通过将模拟的点扩散函数（PSF）与理论结果进行比较，以及仿真实验表明我们的模型比Zemax等商业软件包中的解决方案更为精确，从而验证了所提模型的准确性。我们通过真实场景实验证明了该模型的有效性，并在像差校正与扩展景深（EDoF）成像方面均显示出显著提升。我们相信，所提出的模型将推动计算成像、计算摄影与先进光学设计等领域中广泛应用的进一步研究。代码将在论文发表时开源。