Effect of spherically aberrated lens on the quality of super-Gaussian beams

Based on the beam propagation equation,the hyperbolic-fit mothed is used to calculate the M2 factor of super-Gaussian beams passing through a spherically aberrated lens.The power in the bucket(PIB) at the geometrical and real focal planes of super-Gaussian beams with spherically aberration is also studied.With M2 factor and PIB as the criteria for laser beam quality,detailed numerical calculations are performed to illustrate the effects of the spherically aberrated lens on the beam quality of super-Gaussian beams.The result is useful for some practical application.