横向剪切干涉二维波前重建技术研究
文献类型：学位论文
| 作者 | 戴凤钊 |
| 学位类别 | 博士 |
| 答辩日期 | 2013 |
| 授予单位 | 中国科学院上海光学精密机械研究所 |
| 导师 | 王向朝 |
| 关键词 | 波前测量 横向剪切干涉 波前重建 模式法 区域法 |
| 其他题名 | Research on two-dimensional wavefront reconstruction techniques for lateral shearing interferometry |
| 中文摘要 | 波前测量技术在现代物理学、天文学、生物医学以及工程技术等领域发挥着越来越重要的作用。横向剪切干涉波前测量技术具有不需要参考面、对振动不敏感、测量动态范围大等优点，在高能激光技术、天文观测、眼科学、光学测试等领域得到了广泛的应用。与普通的干涉法波前测量技术直接测量待测波前不同，横向剪切干涉技术直接测量的是待测波前在剪切方向的差分（差分波前），因此需要从差分波前中重建待测波前。波前重建是横向剪切干涉波前测量的关键环节，其研究和发展对横向剪切干涉技术的发展和应用起着重要的促进作用。波前重建技术一直是横向剪切干涉波前测量技术领域的研究热点。 模式法和区域法是横向剪切干涉波前重建的两类重要方法，本文针对基于Zernike多项式的模式法和区域法在实际应用中存在的一些问题开展理论与仿真实验研究，主要包括以下几项工作： 1.对Rimmer-Wyant重建方法进行理论分析，基于分析结果提出一种数值正交变换Zernike多项式模式法。Rimmer-Wyant方法是一种典型的基于Zernike多项式的模式法，该方法以Zernike多项式作为差分波前基函数。本文通过对Rimmer- Wyant方法进行理论分析，研究残余高阶项对低阶项重建的耦合影响。根据耦合分析结果，提出一种新的基于Zernike多项式的模式法，即数值正交变换法。该方法以Rimmer-Wyant方法为基础，以在差分波前离散测量点上正交的数值多项式代替Zernike多项式作为差分波前基函数，降低残余高阶项对低阶项的耦合影响，提高波前重建精度。 2.对四种典型的基于Zernike多项式的模式法开展比较研究。Rimmer-Wyant方法、椭圆正交变换法、数值正交变换法和差分Zernike多项式拟合法是四种典型的基于Zernike多项式的模式法，四种方法的主要区别在于差分波前基函数不同。本文首次对这四种方法的重建精度、噪声性能、适用范围等进行综合量化分析。分析结果表明差分Zernike多项式拟合法最有效，因为其重建精度最高、实现难度最低，并且适用于一般光瞳形状。该结论为实际应用中横向剪切干涉波前重建技术的选择提供了量化依据。 3.提出一种新的基于线性插值法赋初始值的高空间分辨率区域法波前重建方法。现有区域法存在重建空间分辨率低或测量过程复杂等问题，本文通过与剪切量相关的系数矩阵建立离散的差分波前和待测波前之间的关系方程组，以给待测波前赋初始值的方式将系数矩阵拓展为列满秩矩阵，通过对测量的差分波前进行线性插值计算初始值，并通过最小二乘法求解拓展后的线性方程组。该方法重建波前的抽样间隔不受剪切量的限制，并且只需要在正交方向上分别进行一次测量，因此在实现高空间分辨率波前重建的同时简化了测量过程。 4.提出一种新的模式法与区域法的混合重建方法，并将其与模式法和区域法进行综合性能比较研究。以线性插值法计算初始值的高空间分辨率区域法在剪切率较大时重建误差较大，所提出的混合重建方法以模式法的部分重建结果作为初始值进行高空间分辨率的区域法重建。该方法与模式法相比，不损失待测波前的高频分量；与区域法相比，重建对剪切率的变化不敏感；而且，混合方法的重建精度以及Zernike系数精度高于模式法和区域法。 |
| 英文摘要 | Wavefront measurement technology plays an increasingly important role in field of physics, astronomy, biomedical sciences, engineering technology, just to name a few. Lateral shearing interferometry (LSI), as a kind of self-reference wavefront measurement technology, does not need a separate high-precision reference wavefront and has the capability of insensibility to vibration, and large measurement dynamic range. Owing to these advantages, LSI has been applied extensively in many fields, such as high-energy laser technology, astronomical observation, ophthalmology, optical testing and so on. The optical path difference in LSI measurement is directly related to the wavefront difference (i.e. differential wavefront) in the shearing direction rather than the test wavefront itself as that in the conventional interferometry. Therefore, it is naturally necessary to have a further mathematical treatment to reconstruct the test wavefront from its differential wavefront. However, the research and development of wavefront reconstruction has important stimulating effects on the development and application of lateral shearing interferometry. Wavefront reconstruction technology is always the hot area of research in the field of lateral shearing interferometry. Existing wavefront reconstruction techniques for LSI can be generally categorized into modal method and zonal method. In order to solve some problems existed in practical applications of Zernike-polynomials-based modal method and zonal method, the theoretical and simulation experiment research are performed in this dissertation. The main contributions are summarized as follows. i.We theoretically analyze the Rimmer-Wyant reconstruction method, and based on the results of which, we propose a new numerical orthogonal transformation Zernike-polynomials-based modal method. The Rimmer-Wyant method is a typical Zernike-polynomials-based modal method. In this method, the differential wavefront is expanded on the base of Zernike polynomials. Through theoretical analysis of Rimmer-Wyant method, we study the coupling influence of the remaining high-order terms on the reconstruction of the lower-order terms. Based on this result, we propose a novel Zernike-polynomials-based modal method, namely the numerical orthogonal transformation method. The main advance is that the numerical polynomials are used instead of the Zernike polynomials as the orthogonal bases of the differential wavefront at the measuring points and thus reducing the coupling of the remaining high-order terms on the lower-order terms. As a result the reconstruction accuracy is significantly improved. ii.We perform a comparative study of four typical Zernike-polynomials-based modal methods, the Rimmer-Wyant method, elliptical orthogonal transformation method, numerical orthogonal transformation method, and differential Zernike polynomials fitting method. They identify themselves mainly by the bases on which the differential wavefront expansion. These four methods are analyzed quantitatively and comprehensively in this dissertation in terms of reconstruction accuracy, noise performance, and scope of application. The analysis results show that differential Zernike polynomials fitting method is the most effective, because it has the highest reconstruction accuracy, the least implementation difficulty, and can be applied to arbitrary pupil shapes. This result provides a quantitative basis for the choice of the wavefront reconstruction techniques in practical LSI measurement. iii.Based on linear-interpolation-based initialization, we propose a new zonal method for high spatial resolution wavefront reconstruction. Existing zonal method have the problems of either low spatial resolution or high spatial resolution with a complicated measurement process. Here we develop a set of linear equations that depict the relationship between the discrete differential wavefronts and the test wavefront through the coefficient-matrix associated with the shear amount. The coefficient matrix (and so the equations set) is extended to be of full column rank by initializing with the original test wavefront. Then the extended equations set can be solved using the least square method after the measured differential wavefront is initialized by linear interpolation. The wavefront reconstructed in this way does not have the restriction of the sampling interval on the shear amounts, and only needs two measurements in the orthogonal shear directions. Therefore, we justify a high spatial resolution reconstruction method with a simplified measurement process. iv.We propose a new hybrid modal-zonal method, and present comprehensive comparative study between the hybrid method and the modal method, and the zonal method. For the high-spatial-resolution linear-interpolated-based zonal method, the reconstruction error is large when the shear amount is large. The proposed hybrid method uses the results in a subgrid reconstructed with the modal method as the initial values for the high-spatial-resolution zonal reconstruction. The hybrid method does not lose the high frequency components of the test wavefront in comparison to the modal method, and is not sensitive to the change of the shear ratios in contrast to the zonal method. Furthermore, the hybrid method is superior to both modal and zonal method in terms of reconstruction and Zernike coefficients accuracy. |
| 语种 | 中文 |
| 源URL | [http://ir.siom.ac.cn/handle/181231/15739]  |
| 专题 | 上海光学精密机械研究所_学位论文 |
| 推荐引用方式 GB/T 7714 | 戴凤钊. 横向剪切干涉二维波前重建技术研究[D]. 中国科学院上海光学精密机械研究所. 2013. |
入库方式： OAI收割
来源：上海光学精密机械研究所
浏览0
下载0
收藏0
其他版本
除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。