Freeform mirror design for beam shaping by a combined approach using Poisson-based grid optimization and a discrete cosine transform

In this study, we have designed freeform mirrors capable of transforming uniform irradiance distribution into complicated irradiance distribution. The design methodology incorporates two key algorithms: Poisson-based grid optimization and a discrete cosine transform (DCT). The grids on the target plane were optimized using Poisson-based grid optimization while maintaining uniformity on the incident plane. By obtaining grids for both input and target planes, we derived the normal vector field and utilized the DCT to calculate the sags of the freeform surface. Several examples have been devised to substantiate the validity of the approach. For Case 1 and Case 2, the results demonstrate that these freeform surfaces produce high-contrast and complicated irradiance maps with a notable proportion exceeding 4:1 in terms of irradiation intensity ratio between the graphic area and the background. In Case 2, when compared to the prescribed irradiance distribution, the normalized cross correlation values for generated irradiance distributions by the freeform mirror, both with and without sag error, are 94% and 96%, respectively. Furthermore, Cases 3 and 4 demonstrate that incident beams with complex irradiance distributions can be transformed into uniform irradiance profiles by the freeform mirror designed using the proposed method, achieving uniformity levels of 93% and 95%, respectively. It is noteworthy that the incident beam aperture in Case 4 exhibits an elliptical shape.