In view of the primary mirror of large optical system

with the relation between full frequency errors and fractional encircled energy (FEE)

the mathematical model between the root-mean square gradient (GRMS) errors of mid- and high-frequency errors and FEE was established by assuming that the surface error is stationary Gaussian random progress

and the numerical computation and actual surface profile data of the model was validated. It is found the FEE almost declines in exponential form with the increasing of GRMS of the mid- and high-frequency errors and the various frequency errors transform the edge energy of the ideal intensity distribution to the centre and wider domain of the intensity distribution and the energy transfer curve vibrates again and again with the increasing of GRMS. And the influences on FEE are less than 5% when the GRMS of the mid- and high-frequency errors are less than 12nm/mm and 30nm/mm respectively under the special optical diameter and can be used to control the influence of mid- and high-frequency error on FEE and provide the support for the further finishing and figuring of the optical surface profile.