可调支撑装置是高精度光学元件的常用支撑结构。分析了可调支撑装置支撑力调节对光学元件面形的影响规律。建立可调支撑装置的力学模型，利用有限元法计算光学元件的变形，并对光学元件面形进行Zernike 多项式拟合。不同工况下分析结果表明：均匀支撑时光学元件面形均方根(RMS)最小，可调支撑力变化时，引入的光学元件面形RMS 以及主要Zernike 多项式系数均与支撑力线性相关，与光学元件的初始支撑状态无关。建立FringeZernike 系数随任意支撑力变化的敏感度矩阵，采用该矩阵预测随机工况下光学元件支撑力调整后面形，预测调节面形与有限元仿真调节面形基本一致，RMS 误差优于0.3%，为可调支撑装置的设计与装调提供理论依据。

Adjustable optic mount is commonly used in the structure design of high precision optical system. Surface shape of optical element influenced by the supporting force adjustment is researched. Mechanical model of the adjustable mount is established, deformation of optical element is calculated with finite element method, and the surface shape is fitted with Zernike polynomials. The analysis results in different working conditions show that the root mean square (RMS) of surface shape is minimized when optical element is under uniform support; when supporting force changes, it causes linear variety of RMS and main Zernike polynomial coefficients of surface shapewhich is independent at the initial working condition of optical element. Finally, sensitivity matrix of Zernike polynomial coefficients changed by every supporting force is established, then estimation of surface shape due to support force adjustment in a new random working condition is made, the estimated result is similar to the finite element analysis surface shape, and the error of RMS is less than 0.3%, so the estimating method is able to guide the design and assembly of adjustable optic mount.