应用Collins公式和像差的Zernike展开分析激光光束在实际光学系统传输特性

Analysis of laser beam propagation through optical system using Collins formula and Zernike polynomials

在Collins公式基础上,将像差项用Zernike多项式展开后加入衍射积分,获取实际激光光束通过光学系统后的光强分布。对相关理论进行仿真,验证了理论的正确性。同时针对实际激光聚焦光学系统,从统计规律角度分析了系统公差引入对Gaussian光束聚焦光斑带来的影响。计算结果表明聚焦光斑总体随波像差RMS值增大而增大,不同像差分布形式对聚焦光斑特性影响较大。未分配系统公差时,激光聚焦光斑半径为1.520 mm;引入系统公差后,聚焦光斑半径有90%概率小于2.085 mm,平均值为1.700 mm,标准偏差为0.238 mm。

The method to obtain the intensity distribution of laser beam after propagation through practical optical systems was proposed by combining the Collins formula and the Zernike polynomials for aberrations. The simulations were given to prove the correctness of the theory. Using this theory, the statistical change of the focus spots of Gaussian beams affected by the tolerance aberrations was presented. As a result, it shows that the spot radii increase with the RMS wave front aberrations and the detail forms of tolerance aberrations are important for the issue of laser beam focusing. Detail analysis of a practical system demonstrates that the spot radius is 1.520 mm without the tolerance aberrations. After the tolerance is introduced, the spot radius has an average of 1.700 mm, a standard deviation of 0.238 mm and it is smaller than 2.085 mm with a probability of 90%.