Fully coherent laser beams are very sensitive to the turbulence medium. Studies have shown that using partially coherent
beams is an effective method to reduce this unsatisfactory feature. Unfortunately partially coherent beams are more
expanded when they propagate thought turbulence medium. In this paper we have determined a special degree of global
coherency, which optimizes beam propagation with respect to limiting factors (sensitivity to the turbulence and broadening)
The quality factor of laser beams has attracted considerable attention and some different approaches have been reported to treat the problem. In this paper we analyze quality factor of laser beam and compare the effect of different aberrations on beam quality by expanding pure phase term of wavefront in terms of Zernike polynomials. Also we analyze experimentally the change of beam quality for different Astigmatism aberrations, and compare theoretical results with experimentally results. The experimental and theoretical results are in good agreement.