光學自由曲面的表征方法與技術研究
發(fā)布時間：2018-08-11 08:47
【摘要】：隨著現(xiàn)代光學精密制造和檢測技術的發(fā)展與提高,自由曲面光學元件的加工和使用逐步成為現(xiàn)實。光學自由曲面具有非旋轉對稱性,以其豐富的自由度和較強的像差校正能力,使光學系統(tǒng)向著小型化、輕量型、大視場、小F數(shù)和高性能等高要求方向發(fā)展。自由曲面光學在現(xiàn)代智能家居、先進工業(yè)制造、綠色能源和航空航天等領域,有著重要的作用和價值。光學自由曲面的表征方法與技術是自由曲面光學領域中基礎且關鍵的研究內容,其表征方法與技術的提高能夠進一步促進自由曲面光學的發(fā)展。近十年來,對光學自由曲面的表征方法與技術的研究已經成為熱點,其中某些關鍵問題亟需解決。本文圍繞光學自由曲面的表征方法與技術展開深入研究。從正交和非正交函數(shù)兩個方面,總結了現(xiàn)有多類可用于表征光學自由曲面的函數(shù),分析了各自的優(yōu)點和局限性。正交多項式如澤尼克圓域正交多項式等,以其優(yōu)良的數(shù)學特性,在自由曲面表征、波前分析和系統(tǒng)像差評價等方面具有廣泛的應用;非正交函數(shù)如XY多項式等,以其較強的像差校正能力,常用于設計離軸非對稱自由曲面光學系統(tǒng)。針對解析型正交函數(shù)在實際應用場合(如實際檢測或光線追跡等方面得到的是離散數(shù)據(jù)點)會失去其正交特性,以及現(xiàn)有正交多項式具有一定的孔徑選擇性等問題,本文提出了適用面廣、表征精度高的數(shù)值化正交多項式表征光學自由曲面的方法,克服了當前解析型正交函數(shù)表征光學自由曲面存在的不足。通過數(shù)值分析和實驗研究,將數(shù)值化正交多項式與正方形域正交多項式(如二維切比雪夫多項式、二維勒讓德多項式、澤尼克正方形域正交多項式)在表征正方形域自由曲面的效果等方面,做了詳細地對比分析。結果表明,數(shù)值化正交多項式表征光學自由曲面具有明顯優(yōu)勢。同時,對數(shù)值化正交多項式用于動態(tài)孔徑變化的自由曲面或波前實時表征進行了研究。針對局部大梯度自由曲面的高精度表征問題,本文提出了基于澤尼克多項式和徑向基函數(shù)相結合的光學自由曲面表征方法。該方法采用"化整為零,合零為整"的表征策略,其表征精度達到納米量級,能夠高精度地反映復雜自由曲面的局部特性,克服了全孔徑單次表征法的局限性。詳細分析了相鄰子孔徑間距和子孔徑半徑大小兩個重要參數(shù),對局部大梯度自由曲面表征誤差的影響。結果表明,子孔徑半徑大小對表征精度的影響程度更大,需在合理確定相鄰子孔徑間距的基礎上,通過優(yōu)選子孔徑半徑大小,以滿足實際檢測中局部大梯度自由曲面的表征精度要求。針對由梯度離散數(shù)據(jù)點反演自由曲面或波前,現(xiàn)有區(qū)域法或模式化法存在的局限性,本文提出了一種非迭代的二次數(shù)值化正交變換法。通過推導得到了數(shù)值化正交梯度多項式,用于直接表征測得的梯度數(shù)據(jù)。根據(jù)梯度與矢高之間的關系,反演出自由曲面或波前。該方法適用于任意孔徑形狀或動態(tài)孔徑變化的基于梯度測試的光學自由曲面表征。結果表明,二次數(shù)值化正交變換法由離散梯度數(shù)據(jù)點反演自由曲面時,因數(shù)值化正交梯度多項式具有正交特性,對圓形孔徑、正方形孔徑、長方形孔徑、六邊形孔徑和環(huán)形孔徑等規(guī)則孔徑區(qū)域都有很高的表征精度;對存在無效梯度數(shù)據(jù)點的不規(guī)則孔徑區(qū)域或動態(tài)孔徑區(qū)域,其反演精度仍然很高;對基于梯度測試的局部大梯度復雜自由曲面,該方法也具有較好的反演效果。在自適應光學或眼視光學等領域具有重要的應用價值和前景。
[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.
【學位授予單位】：南京理工大學
【學位級別】：博士
【學位授予年份】：2016
【分類號】：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.
【學位授予單位】：南京理工大學
【學位級別】：博士
【學位授予年份】：2016
【分類號】：O43
【參考文獻】
相關期刊論文 前10條
1 周向東;白劍;;Q-Type非球面小畸變全景環(huán)帶光學系統(tǒng)設計[J];光學學報;2015年07期
2 孫文卿;陳磊;李金鵬;烏蘭圖雅;何勇;;非圓孔徑離散采樣點正交多項式波前擬合[J];紅外與激光工程;2015年03期
3 葉井飛;高志山;劉曉莉;王偉;張聰e，
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