Algorithmic differentiable ray tracing is a new paradigm that allows one to solve the forward problem of how light propagates through an optical system while obtaining gradients of the simulation results with respect to parameters specifying the optical system. Specifically, the use of algorithmically differentiable non-sequential ray tracing provides an opportunity in the field of illumination engineering to design complex optical system. We demonstrate its potential by designing freeform lenses that project a prescribed irradiance distribution onto a plane. The challenge consists in finding a suitable surface geometry of the lens so that the light emitted by a light source is redistributed into a desired irradiance distribution. We discuss the crucial steps allowing the non-sequential ray tracer to be differentiable. The obtained gradients are used to optimize the geometry of the freeform, and we investigate the effectiveness of adding a multi-layer perceptron neural network to the optimization that outputs parameters defining the freeform lens. Lenses are designed for various sources such as collimated beams or point sources, and finally, a grid of point sources approximating an extended source. The obtained lens designs are finally validated using the commercial non-sequential ray tracer LightTools.

算法可微光线追踪是一种新的范例，它允许人们解决光如何通过光学系统传播的正向问题，同时获得相对于指定光学系统的参数的模拟结果的梯度。具体来说，算法上可微分的非顺序光线追踪的使用为照明工程领域提供了设计复杂光学系统的机会。我们通过设计将规定的辐照度分布投射到平面上的自由曲面透镜来展示其潜力。挑战在于找到合适的透镜表面几何形状，以便将光源发出的光重新分布成所需的辐照度分布。我们讨论了使非序列光线追踪器可微分的关键步骤。获得的梯度用于优化自由曲面的几何形状，并且我们研究了将多层感知器神经网络添加到输出定义自由曲面的参数的优化中的有效性。透镜设计用于各种光源，例如准直光束或点光源，最后是近似扩展光源的点光源网格。最终使用商业非序列光线追踪器 LightTools 验证所获得的镜头设计。