光学自由曲面的表征方法与技术研究
发布时间：2018-08-11 08:47
【摘要】：随着现代光学精密制造和检测技术的发展与提高,自由曲面光学元件的加工和使用逐步成为现实。光学自由曲面具有非旋转对称性,以其丰富的自由度和较强的像差校正能力,使光学系统向着小型化、轻量型、大视场、小F数和高性能等高要求方向发展。自由曲面光学在现代智能家居、先进工业制造、绿色能源和航空航天等领域,有着重要的作用和价值。光学自由曲面的表征方法与技术是自由曲面光学领域中基础且关键的研究内容,其表征方法与技术的提高能够进一步促进自由曲面光学的发展。近十年来,对光学自由曲面的表征方法与技术的研究已经成为热点,其中某些关键问题亟需解决。本文围绕光学自由曲面的表征方法与技术展开深入研究。从正交和非正交函数两个方面,总结了现有多类可用于表征光学自由曲面的函数,分析了各自的优点和局限性。正交多项式如泽尼克圆域正交多项式等,以其优良的数学特性,在自由曲面表征、波前分析和系统像差评价等方面具有广泛的应用;非正交函数如XY多项式等,以其较强的像差校正能力,常用于设计离轴非对称自由曲面光学系统。针对解析型正交函数在实际应用场合(如实际检测或光线追迹等方面得到的是离散数据点)会失去其正交特性,以及现有正交多项式具有一定的孔径选择性等问题,本文提出了适用面广、表征精度高的数值化正交多项式表征光学自由曲面的方法,克服了当前解析型正交函数表征光学自由曲面存在的不足。通过数值分析和实验研究,将数值化正交多项式与正方形域正交多项式(如二维切比雪夫多项式、二维勒让德多项式、泽尼克正方形域正交多项式)在表征正方形域自由曲面的效果等方面,做了详细地对比分析。结果表明,数值化正交多项式表征光学自由曲面具有明显优势。同时,对数值化正交多项式用于动态孔径变化的自由曲面或波前实时表征进行了研究。针对局部大梯度自由曲面的高精度表征问题,本文提出了基于泽尼克多项式和径向基函数相结合的光学自由曲面表征方法。该方法采用"化整为零,合零为整"的表征策略,其表征精度达到纳米量级,能够高精度地反映复杂自由曲面的局部特性,克服了全孔径单次表征法的局限性。详细分析了相邻子孔径间距和子孔径半径大小两个重要参数,对局部大梯度自由曲面表征误差的影响。结果表明,子孔径半径大小对表征精度的影响程度更大,需在合理确定相邻子孔径间距的基础上,通过优选子孔径半径大小,以满足实际检测中局部大梯度自由曲面的表征精度要求。针对由梯度离散数据点反演自由曲面或波前,现有区域法或模式化法存在的局限性,本文提出了一种非迭代的二次数值化正交变换法。通过推导得到了数值化正交梯度多项式,用于直接表征测得的梯度数据。根据梯度与矢高之间的关系,反演出自由曲面或波前。该方法适用于任意孔径形状或动态孔径变化的基于梯度测试的光学自由曲面表征。结果表明,二次数值化正交变换法由离散梯度数据点反演自由曲面时,因数值化正交梯度多项式具有正交特性,对圆形孔径、正方形孔径、长方形孔径、六边形孔径和环形孔径等规则孔径区域都有很高的表征精度;对存在无效梯度数据点的不规则孔径区域或动态孔径区域,其反演精度仍然很高;对基于梯度测试的局部大梯度复杂自由曲面,该方法也具有较好的反演效果。在自适应光学或眼视光学等领域具有重要的应用价值和前景。
[Abstract]:With the development of modern optical precision manufacturing and testing technology, the fabrication and application of free-form optical elements have gradually become a reality. Optical free-form surfaces have non-rotational symmetry, with its rich degree of freedom and strong aberration correction ability, so that the optical system toward miniaturization, lightweight, large field of view, small F number and high performance. Freeform surface optics plays an important role in the fields of modern smart home, advanced industrial manufacturing, green energy, aerospace and so on. The representation method and technology of optical free form surface is the basic and key research content in the field of free form surface optics, and its characterization method and technology can be further improved. Promote the development of free-form optics. In the last decade, the research on the representation methods and techniques of optical free-form surfaces has become a hotspot. Some key problems need to be solved urgently. This paper focuses on the representation methods and techniques of optical free-form surfaces. The advantages and limitations of orthogonal polynomials, such as Zernike circle orthogonal polynomials, are analyzed in terms of the functions that characterize optical free-form surfaces. Orthogonal polynomials, such as Zernike circle orthogonal polynomials, are widely used in the characterization of free-form surfaces, wavefront analysis and system aberration evaluation due to their excellent mathematical properties; non-orthogonal functions, such as XY polynomials, are calibrated by Positive ability is often used to design off-axis asymmetric free-form surface optical systems. In view of the fact that analytic orthogonal functions lose their orthogonal properties in practical applications (such as actual detection or ray tracing, etc.) and that existing orthogonal polynomials have certain aperture selectivity, an applicable surface is proposed. The method of numerically orthogonal polynomials with wide range and high precision for characterizing optical free-form surfaces overcomes the shortcomings of analytic orthogonal functions for characterizing optical free-form surfaces. By numerical analysis and experimental study, orthogonal polynomials in square domain (such as two-dimensional Chebyshev polynomials, two-dimensional Legendre polynomials) are numerically and experimentally characterized. The results show that the numerical orthogonal polynomial has obvious advantages in characterizing the optical free-form surface. At the same time, the numerical orthogonal polynomial is used to characterize the free-form surface with dynamic aperture change or wavefront real-time. In this paper, an optical free-form surface characterization method based on Zernike polynomial and radial basis function is proposed for high-precision characterization of locally large gradient free-form surfaces. Based on the local characteristics of the surface, the limitation of the full aperture single characterization method is overcome. The influence of the distance between adjacent sub-apertures and the radius of sub-apertures on the characterization error of the local large gradient free form surface is analyzed in detail. On the basis of subaperture spacing, the size of subaperture radius is optimized to satisfy the requirement of local large gradient free-form surface characterization accuracy in practical detection. Aiming at the limitation of existing regional method or modelling method for inversion of free-form surface or wavefront from gradient discrete data points, a non-iterative quadratic numerical orthogonal transformation is proposed in this paper. A numerical orthogonal gradient polynomial is derived to directly characterize the measured gradient data. According to the relationship between gradient and vector height, the free-form surface or wavefront is inverted. The method is suitable for the gradient-based characterization of optical free-form surfaces with arbitrary aperture shape or dynamic aperture change. Because the numerical orthogonal gradient polynomial has orthogonal property, it has high precision in characterizing the regular aperture regions such as circular aperture, square aperture, rectangular aperture, hexagonal aperture and annular aperture, and has irregular aperture regions with invalid gradient data points. Or in the dynamic aperture region, the inversion accuracy is still very high, and the method has a good inversion effect on the local large gradient complex free form surface based on gradient measurement.
【学位授予单位】：南京理工大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O43
[Abstract]:With the development of modern optical precision manufacturing and testing technology, the fabrication and application of free-form optical elements have gradually become a reality. Optical free-form surfaces have non-rotational symmetry, with its rich degree of freedom and strong aberration correction ability, so that the optical system toward miniaturization, lightweight, large field of view, small F number and high performance. Freeform surface optics plays an important role in the fields of modern smart home, advanced industrial manufacturing, green energy, aerospace and so on. The representation method and technology of optical free form surface is the basic and key research content in the field of free form surface optics, and its characterization method and technology can be further improved. Promote the development of free-form optics. In the last decade, the research on the representation methods and techniques of optical free-form surfaces has become a hotspot. Some key problems need to be solved urgently. This paper focuses on the representation methods and techniques of optical free-form surfaces. The advantages and limitations of orthogonal polynomials, such as Zernike circle orthogonal polynomials, are analyzed in terms of the functions that characterize optical free-form surfaces. Orthogonal polynomials, such as Zernike circle orthogonal polynomials, are widely used in the characterization of free-form surfaces, wavefront analysis and system aberration evaluation due to their excellent mathematical properties; non-orthogonal functions, such as XY polynomials, are calibrated by Positive ability is often used to design off-axis asymmetric free-form surface optical systems. In view of the fact that analytic orthogonal functions lose their orthogonal properties in practical applications (such as actual detection or ray tracing, etc.) and that existing orthogonal polynomials have certain aperture selectivity, an applicable surface is proposed. The method of numerically orthogonal polynomials with wide range and high precision for characterizing optical free-form surfaces overcomes the shortcomings of analytic orthogonal functions for characterizing optical free-form surfaces. By numerical analysis and experimental study, orthogonal polynomials in square domain (such as two-dimensional Chebyshev polynomials, two-dimensional Legendre polynomials) are numerically and experimentally characterized. The results show that the numerical orthogonal polynomial has obvious advantages in characterizing the optical free-form surface. At the same time, the numerical orthogonal polynomial is used to characterize the free-form surface with dynamic aperture change or wavefront real-time. In this paper, an optical free-form surface characterization method based on Zernike polynomial and radial basis function is proposed for high-precision characterization of locally large gradient free-form surfaces. Based on the local characteristics of the surface, the limitation of the full aperture single characterization method is overcome. The influence of the distance between adjacent sub-apertures and the radius of sub-apertures on the characterization error of the local large gradient free form surface is analyzed in detail. On the basis of subaperture spacing, the size of subaperture radius is optimized to satisfy the requirement of local large gradient free-form surface characterization accuracy in practical detection. Aiming at the limitation of existing regional method or modelling method for inversion of free-form surface or wavefront from gradient discrete data points, a non-iterative quadratic numerical orthogonal transformation is proposed in this paper. A numerical orthogonal gradient polynomial is derived to directly characterize the measured gradient data. According to the relationship between gradient and vector height, the free-form surface or wavefront is inverted. The method is suitable for the gradient-based characterization of optical free-form surfaces with arbitrary aperture shape or dynamic aperture change. Because the numerical orthogonal gradient polynomial has orthogonal property, it has high precision in characterizing the regular aperture regions such as circular aperture, square aperture, rectangular aperture, hexagonal aperture and annular aperture, and has irregular aperture regions with invalid gradient data points. Or in the dynamic aperture region, the inversion accuracy is still very high, and the method has a good inversion effect on the local large gradient complex free form surface based on gradient measurement.
【学位授予单位】：南京理工大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O43
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