Optimizing freeform lenses for extended sources with algorithmic differentiable ray tracing and truncated hierarchical B-splines

We propose a method for optimizing the geometry of a freeform lens to redirect the light emitted from an extended source into a desired irradiance distribution. We utilize a gradient-based optimization approach with MITSUBA 3, an algorithmic differentiable non-sequential ray tracer that allows us to obtain the gradients of the freeform surface parameters with respect to the produced irradiance distribution. To prevent the optimizer from getting trapped in local minima, we gradually increase the number of degrees of freedom of the surface by using Truncated Hierarchical B-splines (THB-splines) during optimization. The refinement locations are determined by analyzing the gradients of the surface vertices. We first design a freeform using a collimated beam (zero-etendue source) for a complex target distribution to showcase the method's effectiveness. Then, we demonstrate the ability of this approach to create a freeform that can project the light of an extended Lambertian source into a prescribed target distribution.