中文摘要：

环境载荷引起的光机系统变形会严重影响光学系统性能。光机热集成分析是评估这种影响的有效手段。在光机热集成分析中，为减小光学系统刚体位移对变形后镜面拟合的影响，采用齐次坐标变换及最小二乘算法来分离光学镜面变形所包含的刚体位移。该方法首先用齐次坐标变换表示出变形数据中的刚体位移；其次利用最小二乘法求解刚体位移参数。利用该方法对一个低温环境下离轴抛物面镜进行了分析，其刚体偏转量都小到txrad量级。同时，对该方法求解刚体位移的精度进行了分析。当刚体偏转量小于0．01rad求解误差小于l％，结果表明该方法满足光学镜面变形中的刚体位移求解精度要求。

英文摘要：

The deformation of opto-mechanical system caused by environmental load has a serious effect on the performance of the optical system. Thermal-structural-optical integrated analysis is an effective method to evaluate this kind of effect. To reduce the impact of the rigid body displacement of optical system on the deformed optical face fitting, a method based on homogeneous transformation and least square method was studied in optical-structural-thermal integrated analysis. Firstly, the homogeneous transformation was employed to express rigid-body displacement in deformed surface data. Then, least square method was adopted to resolve the rigid-body displacement parameters. An off-axis parabolic mirror under cryogenic environment was analyzed by this method. The deflections of the mirror were small to the magnitude of μrad. Also, analysis of the resolving precision was made. The results indicate that the resolution error is less than 1% with the rigid rotation less than 0.01 rad and it meets the demand of precision in optical-structural-thermal integrated analysis.