Enabling freeform optics design for extended light source

Designing compact freeform optics for extended light sources requires explicit treatment of the source extent in both space and angle, where point-source formulations are no longer valid. We present a new direct design method for this problem. The method establishes a mathematical framework in which extended-source freeform design is cast as a coupled Monge–Ampère system with a nonlinear boundary condition. The extended source is discretized into subsources, and the irradiance contribution of each subsource is evaluated deterministically, so the freeform surface is obtained directly from the numerical solution. The formulation is examined in singlesource on-axis, single-source off-axis, and array-source configurations. In all three cases, the computed irradiance patterns reproduce the prescribed target structures.