In view of the primary mirror of large optical system

with the statistical optics theory and Harvey-Shack scatter theory

the mathematical model between the root-mean square (RMS) errors of mid- and high-frequency errors and the ratio of scattering loss (RSL) was established by assuming that the surface error is a stationary Gaussian random process

and the numerical computation and actual surface profile data of the model was validated. It is found that the RSL increases almost in exponential form with the increasing of RMS and the mathematical model agrees with the simulation results very well within the focused radius. The influence of the mid- and high-frequency errors on the RSL is less than 1% when the RMS of the mid- and high frequency errors are less than λ/63 respectively and the analysis provides the support for the further finishing and figuring of the optical surface profile.