The root-mean-square (RMS) phase distortion and the strehl ratio in the far-field influenced by the thermal distortion of mirrors in the propagation of high power lasers were calculated. Calculations with different CO<sub>2</sub> laser beam intensity distribution indicate that compare with stable cavity whose output is Gaussian, unstable cavity’s beam quality influenced by the thermal deformation depends on the slope of the intensity distribution, that is, contents of H<sub>2</sub>O, and the obscuration. Among the mirror materials such as SiO<sub>2</sub>, BeO, CaF<sub>2</sub> and Si, CaF<sub>2</sub> provides the steadiest thermal character in the high power laser irradiance. When the SiO<sub>2</sub> mirror is cooled, the RMS phase aberration brought by the thermal deformation would be less. For a high power mirror, cooled by the water is more efficacious than cooled by the wind.
The different definitions of the beam quality factor are introduced, including Strehl Ratio, times diffraction limited factor
β,power in the bucket, the root-mean-square (RMS)of wavefront error,etc. The contribution of the phase aberration to the
irradiance distribution in the far-field is calculated. The relationships between the wavefront error and theβfactor , the
wavefront error and the Strehl Ratio are analyzed.