改进的灵敏度矩阵法在离轴望远镜装调中的应用

为了在较大失调范围内准确求解离轴梅逊式无焦卡塞格林望远镜元件的失调量,提出了基于改进的灵敏度矩阵模型的计算机辅助装调方法。分析了传统灵敏度矩阵法的原理及局限性,并在传统方法的数学模型中加入二次修正项,对传统计算机辅助装调技术进行了改进。针对离轴望远镜系统,分析了次镜失调状态下系统的像差特性,分别采用改进模型和传统模型对系统失调量与像差间的映射关系进行近似,并对失调望远镜系统进行仿真装调。仿真装调结果表明:在次镜偏心为±8mm、倾斜为±1.5°的失调范围内,传统方法计算得到的次镜x、y、z偏心量和α、β倾斜量均方根误差分别是:2.689mm、2.494mm、0.194mm和0.500°、0.525°;而改进方法对应的计算结果为:0.404mm、0.323mm、0.047mm和0.064°、0.065°,显示改进后的灵敏度矩阵方法的失调量求解准确度大幅优于传统方法。最终,采用改进方法对望远镜进行装调,得到了轴上视场波像差(均方根值RMS)为0.056λ(λ=632.8nm),边缘视场波像差RMS均优于0.1λ的良好装调结果。得到的结果满足设计要求。

Application of modified sensitivity matrix method in alignment of off-axis telescope

To calculate the misalignments of optical elements accurately in an off-axis Mersenne afocal Cassegrain telescope, a computer-aided alignment method based on modified sensitivity matrix model was proposed. The principle and limitations of conventional sensitivity matrix method were analyzed. By means of adding a quadratic correction term to conventional sensitivity matrix model, the conventional computer-aided alignment technology was improved. For the off-axis telescope, the aberration characteristics were analyzed when the secondary mirror was misaligned. The modified model and conventional model were used to approximate the mapping relationships between misalignments and aberrations. Then the alignment of misaligned telescope was simulated. The simulation results in the range of decenter ±8 mm and tilt ±1.5° for a secondary mirror show that the root mean square error of x-,y-,z-decenters and α-,β-tilts of the secondary mirror calculated by conventional method are 2.689 mm, 2.494 mm, 0.194 mm and 0.500°, 0.525° respectively, and the corresponding calculations by modified method are 0.404 mm, 0.323 mm, 0.047 mm and 0.064°, 0.065° respectively. The calculation accuracy of the modified sensitivity matrix method is much higher than that of the conventional method. Finally, the telescope is well aligned with the modified method, and the results give that the Wavefront Errors(WFEs) RMS on axis is 0.056λ(λ=632.8 nm),while the WFEs RMS(Root Mean Square) in marginal field of view are better than 0.1λ.The results meet the design requirements.