【作者】 丁凌艳；

【导师】 李圣怡；

【作者基本信息】 国防科学技术大学 ， 机械工程， 2011， 博士

【摘要】 非球面光学零件在光学系统中的广泛应用,对现代光学加工和检测技术提出了挑战。因为光学制造的精度和效率很大程度上依赖于检测技术,所以高精度在位检测对于非球面尤其是大型非球面镜制造有着非常重要的意义。利用相位恢复技术测量镜面面形,结构简单,抗振动,测量量程较大,可以获得较高精度的定量检测结果,是实现非球面在位检测最有希望的方案之一。本论文从相位恢复原理出发,围绕非球面检测的特点及要求,充分利用计算机处理技术,对非球面在位测量问题进行了理论和实验研究。论文的研究工作包括以下几个部分:1、从相位恢复原理出发,研究了相位恢复面形检测中的一般性问题。在分析相位恢复检测中多解来源的基础上,提出先用两个离焦平面初步恢复相位以及人为构造不可分解支持域来保证检测结果的唯一性。基于二维抽样定理和空间带宽积不变性原理确定衍射光场的计算量,并分析相位恢复检测范围的限制因素。根据光线传播的几何模型,提出波前曲率对离焦光强分布的主导作用,总结光强图位置的选择原则。2、为扩展可测镜面f数范围提出了欠采样相位恢复算法。算法结合亚像素光场思想与非线性交替优化策略,利用远焦点光强图重构高分辨率的近焦点光强图,交替优化近焦点光强图和镜面光场相位,最终使之收敛到正确解。实验研究了欠采样算法的可行性及误差。3、针对初加工阶段波前像差较大的实际情况,设计了大动态范围测量算法,并用仿真和实验验证了算法的有效性。大动态范围算法融合了参数算法和数据点算法,先用参数算法循环恢复面形的低频轮廓,再将此轮廓作为已知相位,用数据点GS算法循环恢复高频面形信息,从而实现由粗到细的面形恢复。4、研究了相位恢复非球面直接检测方法。在继承非球面直接检测基本原理的基础上,明确了被测波前像差与面形误差的关系。为了处理大型数据,采用光场拼接计算方法实现非球面衍射光场计算。利用多幅同一位置不同曝光时间的光强图融合消除非球面光强图饱和区域的影响,并分析了光强误差。通过对焦散区的研究,明确划分了焦散区内光强图的有效区域。基于上述研究形成了较为完善的非球面检测算法。此外还提出将点光源和检验点分别置于被测镜面的近轴共轭点上,通过寻求适当的近轴共轭点位置减少测量过程中的系统像差。以双曲面和抛物面为例,用相位恢复在位检测各镜面的面形误差,并分别与干涉仪子孔径拼接和自准直测量结果对比,对相位恢复非球面直接检测的有效性进行了实验验证。5、利用无像差点光路构建了相位恢复离轴非球面测量系统。通过建立等效衍射模型,将非轴对称衍射光场的相位恢复问题转化成一般球面波相位恢复问题。探索了离轴镜相位恢复检测的光路调整方法。将测量光路调整归结为点光源相对被测镜三个坐标轴方向的平动,并利用线性误差模型分离调整误差。用离轴椭球镜进行测量实验,与干涉仪补偿器测量结果对比表明所提方法能有效实现离轴非球面的面形检测。更多还原

【Abstract】 Modern technology meets serious challenge in the manufacture and measurement of aspheric optics which are being used widely in optical systems. Because the accuracy and efficiency of manufacture much depends on the optical measurement technology, in-situ test with high accuracy is very useful to aspheric optics manufacture,especially to those with large aperture. Since it has advantages of simplicity, vibration insensitivity, broad testing range and capability of quantitative calculation, phase retrieval is promising to realize in-situ test of aspheric optics. This thesis is dedicated to applying phase retrieval to problems in aspheric optical metrology. Beginning with the phase retrieval theory, it presents theoretical and experimental study on the in-situ test problems for aspheres, combined with the characteristics of aspheres and computer technology. The major research efforts include the following points.1. Some common problems in wave-front metrology are investigated from the view of classical phase retrieval. In view of the existence of ambiguity solutions in phase retrieval, some steps are taken to ensure the uniqueness of the testing result. Those include iterative computations back and forth between two defocus positions and constructing an irreducibility support to enhance restriction on solutions. The number of sampling points is defined theoretically using two-dimensional sampling theorem and space-bandwidth product invariability, and the limits of measurement are analyzed. According to the geometric optics model of wave-front curvature and intensity distributions, some principles about how to select the defocus positions are presented.2. Under-sampled phase retrieval algorithm is presented to expand the f-number of measurement range. This approach arrives at correct solution by virtue of sub-pixel ideal and nonlinear alternating optimization technique. Super solution intensities close to the focus are reconstructed from intensities away from the focus by sub-pixel phase retrieval algorithm. Then super solution intensities and phases are alternating optimized. An experiment is presented to investigate the validity of this method.3. A high dynamic range algorithm is described and demonstrated, which retrieves the figure errors beyond one wavelength after the rough polish process. Parameter algorithm and point-by-point algorithm are combined in this algorithm to reconstruct the figure error from outline to details. The low frequency part of the figure error is obtained by parameter algorithm firstly, and treated as a known wave-front phase in the followed point-by-point GS algorithm. And the latter is used to retrieve the high frequency part of the figure error.4. The phase retrieval method that tests aspheric mirror without auxiliary optics has been developed and demonstrated experimentally. Based on the primary principle of aspheric testing without auxiliary optics, the relationship between tested wave-front aberrations and figure errors is identified. In order to process large-scale data, a stitching method is proposed to calculate the light field produced by aspheres. Due to significant departure from the spherical surface, the intensities are usually saturated which will lead to phase retrieval failure. In order to overcome the effect from saturation, multi-pictures of the same scene with various exposure times are fused and the error in this process is analyzed. Based on the understanding of the caustic region produced by aspheric surfaces, the valid areas of intensities are defined. An aspheric phase retrieval algorithm is then presented. In addition, the light point and test point are proposed to be placed at paraxial conjugate positions properly selected to reduce system aberrations in the test. Phase retrieval tests are performed with a hyperboloid mirror and a paraboloid mirror at in-situ status. The retrieval results are then compared with the stitching and auto-collimating interference tests respectively, which verified the validity of the phase retrieval test.5. The phase retrieval testing system for off-axis aspheres based on Hindle test has been designed. The problem of phase retrieval for non-axial symmetry wave-front is translated into general spherical wave-front retrieval based on equivalent diffraction model. Adjustment in the test is reduced to moving light point along the direction of coordinate axes of tested mirror, and the displacement errors are separated using linear model about misalignment gradients for each degree of freedom. An experiment about off-axis ellipsoid testing is conducted. The phase retrieval test result is compared with measurements by interferometer and compensator. The agreement demonstrates this approach is feasible and realistic for off-axis ellipsoid test.更多还原