光學(xué)自由曲面的表征方法與技術(shù)研究
發(fā)布時間：2018-08-11 08:47
【摘要】：隨著現(xiàn)代光學(xué)精密制造和檢測技術(shù)的發(fā)展與提高,自由曲面光學(xué)元件的加工和使用逐步成為現(xiàn)實(shí)。光學(xué)自由曲面具有非旋轉(zhuǎn)對稱性,以其豐富的自由度和較強(qiáng)的像差校正能力,使光學(xué)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(xué)在現(xiàn)代智能家居、先進(jìn)工業(yè)制造、綠色能源和航空航天等領(lǐng)域,有著重要的作用和價值。光學(xué)自由曲面的表征方法與技術(shù)是自由曲面光學(xué)領(lǐng)域中基礎(chǔ)且關(guān)鍵的研究內(nèi)容,其表征方法與技術(shù)的提高能夠進(jìn)一步促進(jìn)自由曲面光學(xué)的發(fā)展。近十年來,對光學(xué)自由曲面的表征方法與技術(shù)的研究已經(jīng)成為熱點(diǎn),其中某些關(guān)鍵問題亟需解決。本文圍繞光學(xué)自由曲面的表征方法與技術(shù)展開深入研究。從正交和非正交函數(shù)兩個方面,總結(jié)了現(xiàn)有多類可用于表征光學(xué)自由曲面的函數(shù),分析了各自的優(yōu)點(diǎn)和局限性。正交多項(xiàng)式如澤尼克圓域正交多項(xiàng)式等,以其優(yōu)良的數(shù)學(xué)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(yīng)用;非正交函數(shù)如XY多項(xiàng)式等,以其較強(qiáng)的像差校正能力,常用于設(shè)計離軸非對稱自由曲面光學(xué)系統(tǒng)。針對解析型正交函數(shù)在實(shí)際應(yīng)用場合(如實(shí)際檢測或光線追跡等方面得到的是離散數(shù)據(jù)點(diǎn))會失去其正交特性,以及現(xiàn)有正交多項(xiàng)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(xiàng)式表征光學(xué)自由曲面的方法,克服了當(dāng)前解析型正交函數(shù)表征光學(xué)自由曲面存在的不足。通過數(shù)值分析和實(shí)驗(yàn)研究,將數(shù)值化正交多項(xiàng)式與正方形域正交多項(xiàng)式(如二維切比雪夫多項(xiàng)式、二維勒讓德多項(xiàng)式、澤尼克正方形域正交多項(xiàng)式)在表征正方形域自由曲面的效果等方面,做了詳細(xì)地對比分析。結(jié)果表明,數(shù)值化正交多項(xiàng)式表征光學(xué)自由曲面具有明顯優(yōu)勢。同時,對數(shù)值化正交多項(xiàng)式用于動態(tài)孔徑變化的自由曲面或波前實(shí)時表征進(jìn)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(xiàng)式和徑向基函數(shù)相結(jié)合的光學(xué)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(dá)到納米量級,能夠高精度地反映復(fù)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(xì)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(jié)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(chǔ)上,通過優(yōu)選子孔徑半徑大小,以滿足實(shí)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(diǎn)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(dǎo)得到了數(shù)值化正交梯度多項(xiàng)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(guān)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(xué)自由曲面表征。結(jié)果表明,二次數(shù)值化正交變換法由離散梯度數(shù)據(jù)點(diǎn)反演自由曲面時,因數(shù)值化正交梯度多項(xiàng)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(diǎn)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(fù)雜自由曲面,該方法也具有較好的反演效果。在自適應(yīng)光學(xué)或眼視光學(xué)等領(lǐng)域具有重要的應(yīng)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(xué)位授予單位】：南京理工大學(xué)
【學(xué)位級別】：博士
【學(xué)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(xué)位授予單位】：南京理工大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2016
【分類號】：O43
【參考文獻(xiàn)】
相關(guān)期刊論文 前10條
1 周向東;白劍;;Q-Type非球面小畸變?nèi)碍h(huán)帶光學(xué)系統(tǒng)設(shè)計[J];光學(xué)學(xué)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(diǎn)正交多項(xiàng)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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