Abstract: In the paper,the power in the bucket(PIB), β and η parameters are chosen as criteria to characterize the laser beam quality in the far field,then the beam quality of super Gaussian beams passing through a spherically aberrated lens with an annular rectangular aperture is studied.It is shown by a great number of numerical calculation results and physical analyses that the beam quality depends on the obscure ratio of the rectangular aperture,spherical aberration of the lens and the order of the super Gaussian beam.If a suitable lens with negative spherical coefficient is selected,a better beam quality at the real focal plane can be obtained.Namely,larger PIB and η,smaller β,even β smaller than 1.