First-Order Iterative Illumination Design and Simulation of Freeform Surface–Microlens Array Systems

For light sources with a prescribed intensity distribution, the design of complex customized illumination systems is challenged by limited control degrees of freedom and nonlinear coupling in the source–target mapping. Existing mainstream methods are mostly based on optimal transport theory, in which source–target mapping and lens modeling generally involve second-order implicit partial differential equations (PDEs), leading to complex formulations and difficult solutions. To address this issue, this paper proposes a first-order iterative illumination design and simulation method based on a freeform surface–microlens array. The method adopts a two-stage “collimation–shaping” stepwise energy mapping strategy, sequentially performing beam direction normalization and irradiance distribution reconstruction. This reduces the mathematical complexity of the system model and requires only a first-order explicit iterative formulation for mathematical modeling. By virtue of the stepwise decoupling mechanism, the lens surface profiles can be directly solved through analytical mapping without relying on numerical iterative optimization. This mechanism avoids the over-constraint of degrees of freedom that readily occurs in existing methods, which must simultaneously handle beam control and irradiance reconstruction, thereby enabling complex target irradiance distributions. Simulation results show that under full-angle illumination, the system achieves an optical energy utilization efficiency of 90% and an irradiance uniformity of 87% on the target plane.