非球面拼接测量中偏置误差作用机理与拼接方法研究
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摘要
大口径非球面光学元件是空间光学系统中起支撑作用的关键部件,对大口径非球面面型的精确测量则直接关系到大口径非球面的精密制造与有效应用。然而目前测量大口径非球面面型的普遍方法——接触式扫描法和零检测技术,由于受到测量范围、效率、成本的限制,制约了大口径非球面精密测量的进一步发展,因此迫切需要一种更快、更精确的测量手段解决上述问题。
课题“非球面拼接测量中偏置误差影响机理与拼接方法研究”的目的是:研究采用子孔径拼接干涉测量技术对大口径非球面面型进行精确测量,着重探讨一种实现大口径非球面面型精确拼接测量的拼接方法,通过分析三方向调整误差和拼接定位机构的偏置误差在子孔径干涉测量中的作用表现形式,完善了非球面的拼接干涉测量模型,提高了单次拼接测量的精度。本课题为大口径非球面的精密测量提供了一种技术方案,为最终实现大口径非球面的高精度拼接测量奠定理论基础。
本文首先基于波前像差理论,分析了三方向调整误差对干涉测量非球面影响机理及作用表现形式,结果表明,三方向调整误差使被测非球面波前分布各阶分量都发生变化,不仅包含低阶倾斜与二次离焦,而且还产生了三阶纵向球差、彗差等高阶偏差。因而在利用标准平面波前或球面波前干涉测量非球面时,目前传统三方向调整误差修正拼接法,由于在拼接过程中未修正高阶系统像差分量而产生残余误差累积,因此不适用于精确测量非球面面型。
为实现拼接测量中装调误差的分离,建立了拼接定位机构偏置误差与各运动自由度之间的函数关系模型。该模型的建立是以二次曲面为测量对象,通过分析拼接测量定位机构的空间复合运动机理,用量化的数学表达式完整地描述了拼接定位机构偏置误差对干涉测量结果的影响,该模型为拼接测量非球面的机构设计提供一定的理论分析基础。
基于三方向调整误差与拼接定位机构偏置误差对干涉测量非球面的作用表现形式,提出了系统像差修正的拼接测量非球面方法和技术。该方法通过建立系统像差修正模型实现拼接,为实现拼接,采用了求解多元线性回归方程来获得拼接系数,并利用统计分布的方法来评定子孔径重叠区的相位拟合精度与系统的拼接精度。仿真与对比实验表明,利用该拼接测量方法,其子孔径重叠区相位拟合精度与系统拼接精度均高于目前传统的三方向调整误差修正拼接测量法。
最后,对本文所研究的拼接方法进行了实验验证,主要内容有:1)平面的拼接测量实验,拼接结果与全孔径测量结果相比较,其PV值差值小于λ/10,RMS值差值小于λ/50,初步证明了所搭建的实验系统与开发的拼接测量软件的有效性;2)为验证所提系统像差修正拼接方法的优越性,进行了非球面拼接测量对比实验,实验结果表明,同传统三方向调整误差修正拼接测量法相比,本文方法明显提高了单次拼接的精确度;3)最后对子孔径拼接干涉测量系统的测量结果的不确定度进行了系统的分析。
Large aperture aspheric optical elements have become key parts in the area of space optics. Accurate measurements of large aperture aspheric surfaces associate with precise manufacture and effective application. However, The current aspheric surface testing methods, such as contact scanning testing method and null testing method are restricted by measurement range, efficiency and cost, which restricts the further development of accurate measurement of large aspheric surfaces. For this reason, it is urgent to find a faster and more accurate measurement method to solve the above key technology.
The subject,“study on the effect mechanism of structure bias error and the stitching method in the stitching interferometric measurement of aspheric surfaces”, which aims to research on measuring large aperture aspheric surfaces accurately using the stitching method. The paper mainly focuses on studying the realization of a stitching method for large aperture aspheric surface measurement. Both stitching interferometric measurement model of aspheric surface and the single stitching measurement precision have been improved according to analyzing the behavior of three-direction adjustment errors and stitching structure bias error in the sub-aperture interferometric measurement of aspheric surface. These researches offer a technology scheme for testing large aperture aspheric surface precisely, and settle the theoretical foundation ultimately for implementing the precise testing large aperture aspheric surface.
The behavior of three-direction adjustment errors and stitching structure bias error in the sub-aperture interferometric measurement of aspheric surface have been analyzed based on wavefront aberration theory. The analysis results show that all the components of aspheric surface wavefront distribution under test have been changed by three direction adjustment errors; these changes not only include the low order tilts and the second order defocus but produce the high order bias such as the third order longitudinal spherical, comatic aberration and so on. Therefore, the traditional correcting method of three direction adjustment errors will make the residual errors accumulated due to the high order aberrations uncorrected during the stitching process of interferometric measurement, and hence is not suitable for aspheric surface precise testing when using the standard planar and spherical wavefront in the interferometric measurement of aspheric surface.
In order to separate the adjustment errors in the stitching measurement, functional relationship model between the bias error of stitching positioning mechanism and corresponding movement freedom is established. The presented model with quadratic surface as its testing object, describes integrally how the stitching positioning mechanism affects the interferometric measurement results with quantified mathematical expression by analyzing the spatial combined motion mechanism of stitching positioning structure. Moreover, the model provides the basis of theoretical analysis for the mechanism design of the stitching interferometric measurement of aspheric surface.
Aberration correction method and technology for stitching measurement of aspheric surfaces have been proposed based on the influences of three-direction adjustment errors and the bias error of stitching positioning mechanism on interferometric measurement of aspheric surfaces. In this method, the stitching measurement has been successfully accomplished by established mathematical model of aberration correction. In order to implement stitching, the multiple linear regression equation has been solved to obtain the stitching coefficients, and phase fitting precision of overlapping area of sub-apertures and stitching precision of the measurement system are evaluated utilizing the statistical distribution method. The simulations and comparable experimental results show that both phase fitting precision of overlapping area of sub-apertures and stitching precision of the measurement system are higher than the current stitching measurement method based on three-direction adjustment error correction by using this proposed stitching measurement method. At last, the proposed stitching method has been validated by experiments: 1)
For the stitching interferometric measurement of plane surfaces, the difference of PV values is less thanλ/10, and the difference of RMS values is less thanλ/50 comparing with full-aperture measurement results, which preliminarily verifies the validity of the experimental system and the developed software for stitching interferometric measurement. 2) A contrast experiment has been implemented to validate the superiority of the presented aberration correction stitching method. The experimental results show the single stitching measurement precision has been obviously improved by the proposed method comparing with the stitching measurement method of three-direction adjustment error correction. 3) The uncertainty of sub-aperture stitching interferometric measurement results is analyzed systematically in the last chapter of this thesis.
课题“非球面拼接测量中偏置误差影响机理与拼接方法研究”的目的是:研究采用子孔径拼接干涉测量技术对大口径非球面面型进行精确测量,着重探讨一种实现大口径非球面面型精确拼接测量的拼接方法,通过分析三方向调整误差和拼接定位机构的偏置误差在子孔径干涉测量中的作用表现形式,完善了非球面的拼接干涉测量模型,提高了单次拼接测量的精度。本课题为大口径非球面的精密测量提供了一种技术方案,为最终实现大口径非球面的高精度拼接测量奠定理论基础。
本文首先基于波前像差理论,分析了三方向调整误差对干涉测量非球面影响机理及作用表现形式,结果表明,三方向调整误差使被测非球面波前分布各阶分量都发生变化,不仅包含低阶倾斜与二次离焦,而且还产生了三阶纵向球差、彗差等高阶偏差。因而在利用标准平面波前或球面波前干涉测量非球面时,目前传统三方向调整误差修正拼接法,由于在拼接过程中未修正高阶系统像差分量而产生残余误差累积,因此不适用于精确测量非球面面型。
为实现拼接测量中装调误差的分离,建立了拼接定位机构偏置误差与各运动自由度之间的函数关系模型。该模型的建立是以二次曲面为测量对象,通过分析拼接测量定位机构的空间复合运动机理,用量化的数学表达式完整地描述了拼接定位机构偏置误差对干涉测量结果的影响,该模型为拼接测量非球面的机构设计提供一定的理论分析基础。
基于三方向调整误差与拼接定位机构偏置误差对干涉测量非球面的作用表现形式,提出了系统像差修正的拼接测量非球面方法和技术。该方法通过建立系统像差修正模型实现拼接,为实现拼接,采用了求解多元线性回归方程来获得拼接系数,并利用统计分布的方法来评定子孔径重叠区的相位拟合精度与系统的拼接精度。仿真与对比实验表明,利用该拼接测量方法,其子孔径重叠区相位拟合精度与系统拼接精度均高于目前传统的三方向调整误差修正拼接测量法。
最后,对本文所研究的拼接方法进行了实验验证,主要内容有:1)平面的拼接测量实验,拼接结果与全孔径测量结果相比较,其PV值差值小于λ/10,RMS值差值小于λ/50,初步证明了所搭建的实验系统与开发的拼接测量软件的有效性;2)为验证所提系统像差修正拼接方法的优越性,进行了非球面拼接测量对比实验,实验结果表明,同传统三方向调整误差修正拼接测量法相比,本文方法明显提高了单次拼接的精确度;3)最后对子孔径拼接干涉测量系统的测量结果的不确定度进行了系统的分析。
Large aperture aspheric optical elements have become key parts in the area of space optics. Accurate measurements of large aperture aspheric surfaces associate with precise manufacture and effective application. However, The current aspheric surface testing methods, such as contact scanning testing method and null testing method are restricted by measurement range, efficiency and cost, which restricts the further development of accurate measurement of large aspheric surfaces. For this reason, it is urgent to find a faster and more accurate measurement method to solve the above key technology.
The subject,“study on the effect mechanism of structure bias error and the stitching method in the stitching interferometric measurement of aspheric surfaces”, which aims to research on measuring large aperture aspheric surfaces accurately using the stitching method. The paper mainly focuses on studying the realization of a stitching method for large aperture aspheric surface measurement. Both stitching interferometric measurement model of aspheric surface and the single stitching measurement precision have been improved according to analyzing the behavior of three-direction adjustment errors and stitching structure bias error in the sub-aperture interferometric measurement of aspheric surface. These researches offer a technology scheme for testing large aperture aspheric surface precisely, and settle the theoretical foundation ultimately for implementing the precise testing large aperture aspheric surface.
The behavior of three-direction adjustment errors and stitching structure bias error in the sub-aperture interferometric measurement of aspheric surface have been analyzed based on wavefront aberration theory. The analysis results show that all the components of aspheric surface wavefront distribution under test have been changed by three direction adjustment errors; these changes not only include the low order tilts and the second order defocus but produce the high order bias such as the third order longitudinal spherical, comatic aberration and so on. Therefore, the traditional correcting method of three direction adjustment errors will make the residual errors accumulated due to the high order aberrations uncorrected during the stitching process of interferometric measurement, and hence is not suitable for aspheric surface precise testing when using the standard planar and spherical wavefront in the interferometric measurement of aspheric surface.
In order to separate the adjustment errors in the stitching measurement, functional relationship model between the bias error of stitching positioning mechanism and corresponding movement freedom is established. The presented model with quadratic surface as its testing object, describes integrally how the stitching positioning mechanism affects the interferometric measurement results with quantified mathematical expression by analyzing the spatial combined motion mechanism of stitching positioning structure. Moreover, the model provides the basis of theoretical analysis for the mechanism design of the stitching interferometric measurement of aspheric surface.
Aberration correction method and technology for stitching measurement of aspheric surfaces have been proposed based on the influences of three-direction adjustment errors and the bias error of stitching positioning mechanism on interferometric measurement of aspheric surfaces. In this method, the stitching measurement has been successfully accomplished by established mathematical model of aberration correction. In order to implement stitching, the multiple linear regression equation has been solved to obtain the stitching coefficients, and phase fitting precision of overlapping area of sub-apertures and stitching precision of the measurement system are evaluated utilizing the statistical distribution method. The simulations and comparable experimental results show that both phase fitting precision of overlapping area of sub-apertures and stitching precision of the measurement system are higher than the current stitching measurement method based on three-direction adjustment error correction by using this proposed stitching measurement method. At last, the proposed stitching method has been validated by experiments: 1)
For the stitching interferometric measurement of plane surfaces, the difference of PV values is less thanλ/10, and the difference of RMS values is less thanλ/50 comparing with full-aperture measurement results, which preliminarily verifies the validity of the experimental system and the developed software for stitching interferometric measurement. 2) A contrast experiment has been implemented to validate the superiority of the presented aberration correction stitching method. The experimental results show the single stitching measurement precision has been obviously improved by the proposed method comparing with the stitching measurement method of three-direction adjustment error correction. 3) The uncertainty of sub-aperture stitching interferometric measurement results is analyzed systematically in the last chapter of this thesis.
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74 Chen J.B., Song D.Z., and Zhu R.H.et.al. Large-aperture high-accuracy phase-shifting digital flat interferometer. In: Proc. SPIE(Interferometry VI), 1993, 2003: 367～375
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102 http://www.gedrnrf.com/
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90 Michael Bray. Stitching interferometry: how and why it works. SPIE. 1999,3739:259~273
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97 J. Fleig, P. Dumas, P. E. Murphy, G. W. Forbes. An automated subaperture stitching interferometer workstation for spherical and aspherical surfaces. Proc. SPIE. 2003, 5188: 296~307
98 Jon Fleig, Paul Dumas. An automated subaperture stitching interferometer workstation for spherical and aspherical surfaces. Proc of SPIE. 2003, 5188: 296~307
99 Jon Fleig, Paul Dumas, Paul E. Murphy, and Greg W. Forbes An automated subaperture stitching interferometer workstation for spherical and aspherical surfaces. Proceedings of SPIE. November 2003, 5188: 296~307
100 Greg Forbes and Marc Tricard. Subaperture approaches to finishing and testing astronomical optics. Proceedings of SPIE. 2004,5382: 440~448
101 Paul E. Murphy, Jon Fleig, Greg Forbes, Marc Tricard. High precision metrology of domes and aspheric optics. Proc SPIE. 2005, 5786: 112~121
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