Here focus on freeform lens design for irradiance tailoring on tilted target planes based on differentiable ray tracing. Leveraging the computational graph, we develop a differentiable Monte Carlo ray tracing framework featuring a 3D coordinate rotation operator. The forward calculation within this framework can simulate the irradiance distribution on a tilted target plane generated by a freeform lens, facilitating the assessment of deviations from the desired irradiance distribution. The back-propagation efficiently acquires surface parameter gradients for optimization through the Adam optimizer. The design example demonstrates that the proposed method can effectively generate a high-quality uniform irradiance distribution on a tilted receiver.
We previously proposed an iterative wavefront tailoring (IWT) method [Optics Letters 44(9): 2274-2277] to solve the freeform lens design problem for irradiance tailoring, where the entrance surface can be predefined as a spherical, aspherical or freeform surface. Here, this method is adapted to address a more challenging design problem where the exit surface is predefined. We design a freeform lens with a fixed aspherical exit surface to demonstrate the effectiveness of the modified method.
We previously optimized the freeform surfaces using extended polynomials in stereographic projection coordinates based on an automated workflow linking the optimization engine, 3D modeling software and ray tracing software [Optics Express 29(9), 13469–13485 (2021)]. However, this method is time consuming as it needs thousands of irradiance evaluations. Here, we speed up the optimization of spherical-freeform lenses for uniform illumination based on differentiable ray tracing. The freeform surface is still parameterized with the ‘uv’ extended polynomials under stereographic projection coordinates, which is suitable for generating simple illumination patterns. We implement differentiable ray tracing based on computation graph in MindSpore framework, which is efficient and effective by calculating derivatives of the surface parameters during a single backpropagation. We provide two design examples for generating uniform irradiance distributions with a point-like source and an extended light source, respectively.
Compared with traditional optical surfaces, freeform surfaces provide much more degrees of freedom to tailor the irradiance distributions of light sources, forming previously unimaginable illumination optical systems. However, the complexity of freeform surfaces presents a huge challenge to the design process, especially when the light source size is assignable. We achieved fast irradiance evaluation of freeform illumination lens based on deep learning methods, preparing for a rapid optimization for the lens design. These learned simulation results are similar to those of LightTools, while the computation time is greatly reduced. The representation of freeform surfaces, the generation of datasets, and the selection of neural network structures are introduced in this paper. In the future, we will further improve the neural network performance and use the back-propagation of the neural network to realize a rapid optimization of the freeform lens.
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