Designing double freeform surfaces for point source and extended sources using a construction, iteration and optimization process

Abstract

In this paper, a construction-iteration-optimization method is developed to design a double freeform surface lens for point sources as well as extended sources to achieve uniform illuminance. In the construction process, the initial double freeform surfaces are first calculated by the variable separation method with preset source-target ray mapping to obtain the maximum utilization ratio with Fresnel loss. Then, the double freeform surfaces are fitted into a fourth-order XY polynomial surface considering both the coordinates and surface normals of the data points, which ensures the smoothness of freeform surfaces. To reduce the relative standard deviation of the illuminance distribution, an iteration process is required to reconstruct the two freeform surfaces by turns, and this process can be repeated several times to further decrease the deviation of the rays. The system after the construction-iteration process can be taken as a good starting point for further optimization with optical design software. Although the construction-iteration-optimization process is for a point source at first, with the advantage of multi-parameter representation of freeform surfaces we can further optimize the parameters for an extended source by replacing the point source. Simulation results for illuminance uniformity are demonstrated to verify the effectiveness of this method. The energy utilization ratios are above 86.5% and 82.3% with Fresnel loss, while the relative standard deviations of the illuminance distribution are less than 0.036 and 0.063 for a point source and an extended source, respectively.

A Noncontact Method for Calibrating the Angle and Position of the Composite Module Array

“…With the rapid development of computer and manufacturing technology, freeform surfaces are playing an increasingly important role in the fields of bionics, optics, precision machining, and measurement [1][2][3][4]. J Lai et al [5] developed a construction iteration optimization method to design a double freeform surface lens for point sources, as well as extended sources to achieve uniform illuminance. Gao et al [6] utilized a double-sinusoidal freeform surface to achieve 2-D displacement and angle measurement of machine tools.…”