【作者】 马鑫雪；

【导师】 王建立；

【作者基本信息】 中国科学院研究生院(长春光学精密机械与物理研究所) ， 机械电子工程， 2014， 博士

【摘要】 随着对大口径成像望远镜的需求日益紧迫，望远镜的口径增大和非球面光学元件的增加都给光学加工和检测带来很大的挑战。如何在加工过程中在位及时检测出高阶面形误差进行修正，如何在光学系统装调过程中在线检测像差变化，以便及时调整主镜支撑方案和光学系统装调方案；如何在光学系统使用过程中动态检测出系统波像差，以进行故障诊断和图像清晰化。基于焦面图像信息的波前解算系统也称为焦平面波前探测器（WS, Wavefront Sensing），有着光瞳面WS一些不可替代的优势，它通过采集多帧给定离焦像差的短曝光图像，解算得到光学系统的波前相位信息，并可以利用Zernike多项式拟合得到各单项像差。常见的相位解算技术主要有相位恢复法（PR, Phase Retrieval）和相位差异法（PD, Phase Diversity）。焦平面WS可用于光学系统的在位检测，即不用改变光学系统，直接测量出整个系统的传递函数和波前畸变，在轨定量检测，拼接镜的共焦共像检测等领域。本文在分析国内外研究进展的基础上，进行了大量的计算机仿真实验和实际光路实验工作，对PR和PD技术的原理、性能改进和实际应用进行了深入的探讨和分析，并对其在光学检测方面进行了大量的验证，具体开展的工作如下：1、通过理论分析和仿真，分析了PR的各种算法、建立和完善了PR数学模型。重点研究了PR技术中的Gerchberg-Saxton算法和梯度搜索算法，推导了当任意多帧输入图像及它们的离焦量作为输入时，梯度搜索算法的目标函数分别关于广义光瞳、波前以及泽尼克系数的偏导数。揭示了GS算法与梯度搜索算法之间的关系。针对单幅和多幅图像作为输入时分别用GS算法和梯度搜索算法设计了仿真实验，实验结果显示：对于单幅图像作为输入时，梯度搜索算法明显优于GS算法，对于多帧不同离焦量的图像作为输入时，GS算法和梯度搜索算法都能很好的解算出波前，但梯度搜索算法的收敛速度明显优于GS算法。2、对PD法的目标函数进行了改造，解决了自适应光学系统非共光路像差检测中的离焦量测不准问题，并利用多通道约束波前的解集和像差检测与变形镜调整互相迭代最终收敛的办法。使得改进后的方法理论上对波前求解精度更高。3、搭建了PRWS和ZYGO干涉仪对不同波前畸变进行比较测量的实验平台。采用液晶空间光调制器产生的单项差来验证PRWS对各种像差的检测能力，把PR测量结果与高精度的ZYGO干涉仪测量结果进行比较分析，结果表明在面形误差分布及误差的峰谷值（PV）和方均根值（RMS）上，两者具有一致性，对于波前RMS的测量精度达到3/1000波长左右，这说明PR测量方法的可行性和准确性。4、为了验证PRWS和PDWS波前检测的能力，分别利用PRWS和PDWS检测球面镜面形的实验平台。将PRWS测量结果和PDWS测量结果分别与ZYGO干涉仪测量结果进行比较，实验结果表明在面形误差分布及误差的峰谷值(PV)和方均根值(RMS)上，两者具有极大的相似性，验证了PRWS测量方法和PDWS测量方法的准确性，所以利用PRWS技术和PDWS技术能有效地检测出球面镜的面形误差。更多还原

【Abstract】 Along with the increasingly urgent demand for large diameter imagingtelescope, increasing the caliber of the telescope and the increase of the asphericoptical element has posed great challenges to the optical processing and testing.How to timely detect the high-order surface shape error correction, how in theprocess of the optical system with adjustable on-line detection aberration changes, inorder to adjust the primary mirror supporting plan, and the optical system withadjustable how dynamic detecting system in the process of optical system usingwave aberration to carry out fault diagnosis and the image clearer. The system ofwavefront solutions based on the focal plane image information, also known as thefocal plane detector, has some irreplaceable advantages comparing to a pupil surfacewave detector, by gathering multi-frames from a given focal aberration of shortexposure images and obtain phase information wavefront of the optical system bycalculating the wavefront, and can use Zernike polynomial fitting of each individualaberrations. The realizations of phase solver technology mainly include PhaseRetrieval (PR) and Phase Diversity (PD). Focal plane wave detector can be used inthe optical system in-line detection, namely directly measure of the transfer functionof the system of a whole system and wavefront aberration without changing theoptical system; On-orbit quantitative detection; Mosaic mirror image of confocal detection field, etc.Based on the analysis of domestic and foreign research progress, we have donea large number of simulation and the actual optical experimental work, in this paper,and have carried on the deep discussion and analysis of the principle of the PR andPD technology, performance and practical application, and on the a large number ofverification in optical detection, specific work is as follows:1. Through theoretical analysis and simulation, this paper analyzes the variousalgorithms of PR, establish and perfect the PR mathematical model. Phase retrievaltechnique is mainly studied the Gerchberg-Saxton algorithm and gradient searchalgorithm, when any amount of input images and their defocus amount as input, thispaper educes the objective function of the gradient search algorithm respectively ongeneralized pupil, wavefront and Nick coefficient of partial derivative, and revealsthe relationship between the GS algorithm with gradient search algorithm. For singleand multiple images are used as input, designs simulation experiment with GSalgorithm and gradient search algorithm, the experimental results show that for asingle image as input, the gradient search algorithm is superior to GS algorithm, formulti-frame different defocus amount of images as input, GS algorithms andgradient search algorithm can be a good solution calculated wavefront, but thegradient search algorithm convergence speed significantly better than the GSalgorithm.2. The objective function of the phase difference algorithm was modified tosolve the adaptive optics system of non-common path aberration detection ofinaccurate defocus and use the multi-channel constrained wavefront solution set andthe aberration detection with deformable mirror adjustment each iterationconvergence ultimately. The betterment method has higher accuracy in solving thewavefront theoretically.3. Build an experimental based on the PRWS method comparing with ZYGOinterferometer. This paper utilizes liquid crystal space light modulator (LC-SLM) toproduce single aberration and random aberration, and validates the ability of PRWS measurement for any aberrations. Experimental results demonstrate that agreementis obtained among the errors distribution, PV value and RMS value of ZYGOinterferometer. The measurement precision of wavefront is3/1000wavelength RMS.Therefore, the feasibility and accuracy of the proposed method can be confirmed.4. In order to verify the performance of phase retrieval wavefront sensingdemonstration system and the phase difference wavefront detector demonstrationsystem by using its own light source to complete the wavefront detection taskindependently. This paper sets up two detection mirror surface shape of experimentplatforms with the method of PRWS and PDWS, and compares both PRWSmeasurement results and PDWS measurement results with ZYGO interferometermeasurement results, experimental results demonstrate that good agreement isobtained among the errors distribution, PV value and RMS value of ZYGOinterferometer, so as to realize the estimation of large mirror aberration, whichvalidates the accuracy of PRWS and PDWS. PRWS technology and PDWStechnology can effectively estimate the aberration of spherical mirror.更多还原