The "Shenguang-II" Facility laser uses an 8-beam double-pass architecture capable of delivering several KJ of infrared or ultraviolet energy in a temporal pulse format of an approximately 1ns quasi-square. Ideally the output wavefront of each beam from the main spatial filter should be a plane wave. But a real output wavefront of the laser light beam with a 200 mm section diameter in our facility is always a complex superimposed one. On its cross section, it has a distribution of curvature radius, which is called "local curvature radius" here. But the quality level of the output wavefront is mainly marked by its "global curvature radius", which is an assessing result based on the local ones. To meet the requirements of enhancing the conversion efficiency of the KDP crystal, each beam of wavefront out of the main spatial filter should resemble a plane wave as possibly as it can. Because only in this way can we achieve an optimal match between the injection direction of the laser beam and the functioning angle of the KDP crystal. In other words, the global curvature radius of each beam wavefront should be as large as possible. We have assessed the global curvature radiuses of eight beams, wavefronts by measuring their local curvature radii using Hartmann method. Finally, we have acquired better frequency conversion efficiencies by correcting each output wavefront to a better level according to the measurement results.