光学面形误差对环围能量比的影响

以发射光学系统为研究对象,假设面形误差为高斯平稳随机过程,建立了光学面形误差均方根梯度(GRMS)与远场靶面上环围能量比(EE)之间的数学关系模型,进行了仿真分析并对实际面形数据做了验证。研究表明,环围能量比随GRMS的增加呈指数衰减;同时面形误差低频和高频部分分别形成远场光强分布的中心核和边缘。在GRMS≤7 nm/mm时,理论计算与仿真结果非常吻合。与实际分析结果的比较表明,该数学关系模型是正确的,能够用来分析GRMS对EE的影响。

Influence of optical surface error on encircled energy

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.