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

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%.