Continuous freeform lens design and optimization based on proportional source-target mapping for prescribed illumination

A general and simple method for constructing a proportional source-target energy mapping in order to design a continuous freeform lens for an extended LED light source is proposed. This mapping has the characteristic that we can directly obtain the relationship between the angles of the emitted and incident rays in both the longitudinal and latitudinal directions. By applying this angular function in turn to the normal vector, the lighting situation on the target plane can be quickly determined. Simulation results motivate the proposal of a feedback optimization algorithm to compensate for the deterioration near the diagonal on the target surface caused by surface construction errors and the finite extent of a real source. Based on energy conservation theory and the edge-ray principle, the optimization algorithm is divided into three steps. Finally, the illumination effect on the irradiated surface is consistent with our expectations for an extended LED light source with dimensions of 4 mm x 4 mm. Simulation results show that the energy efficiency n of the freeform lens on the target surface is approximately 0.85 and that the uniformity exceeds 90%. We subsequently analyze the error tolerance of the designed freeform lens from two perspectives: translation and rotation. The minimum translational and rotational error tolerances are 0.3 mm 0.3 mm and 4 degrees, respectively, and the rotational error tolerance around the z-axis are greater than those around the x- and y-axes.