In view of a optical transmitting system

the mathematical model between the Root-Mean-Square Gradient (GRMS) error of optical elements and Encircled Energy (EE) was established by assuming that the surface error is stationary Gaussian random process

and the numerical computation and actual surface profile data of the model was validated. It is found that EE declines in exponential form with the increasing of GRMS

and that the low and high-spatial frequency errors form the centre and the edge of the far-field intensity distribution respectively. The theoretical analysis matches numerical computation very well when GRMS is less than 7 nm/mm. The mathematical model agrees with the actual results well

which can be used to analyze the influence of GRMS on EE and can provide the support for the evaluation criterion of the surface profile of the optical elements.