高斯光束整形非球面透镜的粒子群优化设计方法

提出了一种设计激光光束整形系统的新方法粒子群优化算法。根据能量守恒定律，推导出光束整形系统中任意光线与入射面和出射面交点坐标之间的变换关系，并把用此变换关系得到的光线与出射面的交点坐标作为目标值。把追迹光线在输出面上的交点坐标与目标值差的绝对值作为光束整形系统的能量分布变换评价函数，把出射光线方向矢量的y分量绝对值作为准直评价函数，并将能量分布变换评价函数与准直评价函数的和作为光束整形变换系统的总评价函数，依此函数作为粒子群算法中的适应度函数，对适应度函数进行极小值操作，便可得到了一个既能把光强高斯分布转换为光强均匀分布，又能近似实现光束重新准直的非球面整形透镜系统。用这种方法设计了一个单非球面凹平透镜，可以把光强高斯分布、光斑半径30 mm的红光激光光束整形为光强均匀分布、光斑半径为36 mm的平顶光束，且准直出射。证明这种设计方法简单有效。

Particle swarm optimization method for designing aspheric lens Gaussian beam shaping

A new method, the particle swarm optimization algorithm for designing the laser beam shaping system was put forward. According to the law of conservation of energy, the transformation relation of the coordinates of two intersection points between an arbitrary ray and the input and output plane can be deduced, and the coordinates of an intersection point between a ray and the output plane achieved based on this relation will be used as the target coordinates. Absolute values of differences between the target coordinates and the corresponding coordinates obtained from the ray tracing will be used as the evaluation function of transformation of energy distribution, the absolute value of the y-component of the direction vector of outgoing ray will be used as the evaluation function of the collimation, and the sum of the evaluation function of energy distribution transformation and the evaluation function of collimation was the total evaluation function of a beam shaping system. Taking this function as the fitness function of the particle swarm optimization algorithm and manipulating it to the minimum value, an aspheric lens can be gotten, which can not only convert an Gaussian intensity distribution into a uniform distribution but also approximately r-collimate the output beam. A single aspheric concav-flat lens was designed by using this method, it can transform red laser beams with a spot radius of 30 mm and a Gaussian intensity profile into flat-topped beams with a spot radius of 36 mm, and output beams can be r-collimated.