Extended-source light distribution design method based on discrete generatrix set envelope fitting and optimization

Optical lens design based on an ideal point-source mathematical model suffers from performance degradation as the source size increases. In practical engineering applications involving extended LED sources, this results in issues such as poor irradiance uniformity and significant edge diffusion. To address this issue, we propose an extended-source light distribution design method based on discrete point-source generatrix set envelope fitting and optimization. The extended source is first discretized into a series of ideal point sources. The outer envelope of a set of generatrix curves-each obtained from the exact mathematical model of a point source-is then extracted and fitted to serve as the generatrix of the initial structure. In the optimization process, the fitting coefficients are iteratively adjusted through a coordinated framework that integrates three program modules: the optimization routine, the envelope fitting and restoration routine for the initial structure generatrix, and the two-dimensional ray-tracing routine. When the optimization metric, namely the root-mean-square error of the irradiance distribution, falls below a prescribed threshold, the restored generatrix coordinate data are used to construct a 3D lens model suitable for extended-source light distribution, which is then validated through ray tracing. The validation results show that the irradiance uniformity is improved from 76.8% for the initial structure to 92.7% after optimization; the RMSE of the irradiance distribution decreases from 1.625 to 0.827; and the edge irradiance gradient increases from 0.27 to 0.45, indicating that the edge diffusion problem is effectively mitigated. Furthermore, the robustness of the proposed method is verified through comparisons with the optimization method in commercial software and engineering tolerance analysis.