Generating freeform surface polynomial for beam shaping by adaptive weighted particle swarm optimization

With the application of freeform surface, beam shaping can achieve greater flexibility and precision. Ray mapping is an efficient geometric method for freeform surface design. However, the mapping may not always be integrable, which will result in actual performance falling short of expectations. Additionally, this method often relies on fitting the surface through the calculated coordinates of discrete points, and the fitting accuracy can also affect actual performance. In this study, adaptive weighted particle swarm optimization (AWPSO) is employed to optimize freeform polynomial coefficients to improve beam shaping performance. The initial freeform structure is obtained by non-integrable ray mapping method and fitted into a surface polynomial. Then, the process of optical design is transformed into a multi-dimensional optimization problem within mathematical models. Therefore, performance improvements do not depend on time-consuming ray tracing. A challenging beam shaping example of circle to regular hexagon is given to prove the effectiveness of the method. The results show a significant improvement in the uniformity of the ray spot on the target surface, with the contour becoming sharper and smoother after optimization. From the numerical results, the potential of this method is shown to be used in more irregular beam shaping conditions.