Thin freeform lens design for irradiance tailoring based on differentiable ray tracing

Freeform optics enable effective irradiance tailoring of light sources. However, conventional design methods often produce relatively thick lenses, limiting their use in emerging compact optical systems. In this work, we propose an optimization method based on a differentiable ray tracing (DRT) framework for thin freeform lens design. Its central mechanism is multi-subregion cooperative control, in which spatially separated surface regions jointly shape the target irradiance distribution, thereby reducing the required surface sag. For collimated beam design, this mechanism is explicitly induced by a cosine-based initial surface containing convex, concave, and saddle-shaped sub-regions. A periodic hard constraint is further introduced for far-field applications to ensure strict periodicity, improve machinability, and enable scalable replication, while a a surface regularization term promotes smooth surface variations. For extended source tailoring, the same cooperative-control mechanism is realized in two different ways: direct optimization of a freeform surface with high degree of design freedom, which automatically forms irregular sub-regions, and control assisted by a relay lens, which enables regularly distributed sub-regions. The framework is validated in progressively complex scenarios, including collimated-beam control for far-field and near-field targets, direct extended source control, and relay-lens-assisted extended source control. The resulting freeform lenses exhibit reduced thickness, continuous curvature distributions, and improved robustness against local disturbances, providing a systematic solution for thin freeform lens design under diverse optical conditions.