基于高斯光学齐次坐标变换的光机装调

Optical-mechanical assembly based on Gaussian optical homogeneous coordinate transformation

高性能光学系统装调的调整量与光机结构设计相关,而装调所用参考坐标系往往与光学设计所用的坐标系不同。为了精确描述调整量对高斯像位置的影响,本文在基准坐标系下建立了引入装调误差量的高斯光学齐次坐标变换模型。针对具体的光机结构,建立了高斯像像旋和离焦对调整变量的函数,据此计算小的结构变化导致的离轴三反望远物镜高斯像面的移动,结果显示其与光学设计软件对最佳像面位置优化结果的相对差小于4%。利用方差合成方法建立线性规划模型,对17个装调变量做了最宽松的误差分配方案。用Monte Carlo法验证了分配方案,结果表明,该方案在±300μm调焦能力下满足各视场±10μm的焦深要求。本文的方法忽略了复杂、微小像差的影响,适用于含多个已做内部精装的光学组件或平面反射镜的复杂成像光学系统的装调。

The assembly variables of a high performance optical system are dependent on the design of optical and mechanical structure, however, the reference coordinates used in the system assembly are mostly different from those used in optical design. To describe paraxial image motions due to adjust- ments precisely, the Gaussian optical homogeneous coordinate transformation model with assembly er- ror variables was established under a reference coordinate. According to specified optical-mechanical design, the Gaussian image rotation and defocus as functions of assembly variables were described. Then, the paraxial image motion induced by small deformation of a three-mirror off-axis telescope was calculated, which shows a relative difference less than 4% compared with that from the optical soft- ware optimized image location. By the variance combining method, a linear optimization model wassolved to get the loosest error budget for 17 variables and the Monte-Carlo simulation was used to ver- ify the error budget. It indicates that all fields meet the focus depth of ±10μm within the focusing a- bility of ±300μm. This method ignores subtle influences caused by aberration, and is favorable for optical systems consisting of plane optical components and near aberration-free components.