Design of high-compactness freeform optical surfaces via energy accumulating optimization

Energy accumulating optimization based on dynamic programming is proposed to design non-rotational 3D high-compactness freeform optical surface for extended source. Each small piece which constructs the freeform optical surface is treated as a stage, and the normal vectors of the small pieces are treated as the decision variables. Then each small piece with a normal-vector-selection-range is calculated stage-by-stage, which is different to the common used loop-iterations-optimization-strategy. The state of the accumulated light distribution on the target plane is varied with the evolvement of the calculations. The optimal decisions are ascertained in a retrospective way only after all the calculations are finished, which are ensured by the principle of optimality. Moreover, several treatments are proposed to confine the normal vector selection range, and the feedback adjustment is developed as well. The effectiveness of this method is demonstrated by designing the 20 mm height freeform optical surfaces for 10 mm diameter Lambertian sources to achieve uniform illuminance distributions with dual-axial symmetry and single-axial symmetry, respectively. The energy utilization ratios are above 82% with Fresnel loss, while the relative standard deviation of the illuminance distribution can be less than 0.2.