Incidence-insensitive freeform reflector for arbitrary distributions

Freeform surfaces enable the transformation of a given light source into an arbitrarily specified intensity distribution. However, conventional designs, typically based on mappings between predefined sources and targets, exhibit high sensitivity to slight variations in the incident profile, thereby limiting their practical applicability. Here, we propose an integration-based freeform reflector design method that eliminates the requirement for prior incident specifications. The global freeform is composed of multiple sub-regions with original or flip-symmetry optimal-transmission mappings, constrained by the area-preserving principle through grid distortion. The boundaries of each sub-region exhibit curved features, ensuring C 1 -continuity across the entire surface. In contrast to conventional methods, our generated surface demonstrates excellent tolerance to changes in beam size, geometry, energy distribution, and wavelength. The mean relative error remains around 0.17 under diverse input conditions, indicating close agreement with the target distribution. Additionally, the smoothness of the surface enhances manufacturability and enables it to withstand higher input power with minimal output loss. Our work bridges the gap between theoretical design and practical deployment, facilitating its adoption in illumination and high-power laser systems and opening, to our knowledge, new directions in beam-shaping research.