CN100567932C - Fan-shaped off-axis aspheric mirror splicing measurement system - Google Patents
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Abstract
Description
技术领域 technical field
本发明属于先进光学制造与检测技术领域，涉及一种光学检测系统，特别涉及一种针对扇形离轴非球面镜的光学检测系统，The invention belongs to the technical field of advanced optical manufacturing and detection, and relates to an optical detection system, in particular to an optical detection system for fan-shaped off-axis aspheric mirrors.
技术背景 technical background
为了能观测到更多的早期宇宙事件，更进一步地研究太阳系外的类地行星，需要具备集光能力更强、分辨率更高、口径更大的空间和地面望远镜。我国天文学家提出了中国30m口径巨型望远镜(CFGT)建议，它的主镜是由17种不同类型的离轴非球面子镜呈圆环形排列拼接而成，具体描述可参考文献“一个巨型望远镜方案，苏定强，王亚男，崔向群，天文学报，45(1)：105-114，2004.”。扇形离轴非球面镜的制造需要相应的检测系统。然而，对扇形离轴非球面镜进行高精度检测仍然存在很多挑战。In order to observe more early cosmic events and further study the terrestrial planets outside the solar system, it is necessary to have space and ground telescopes with stronger light-gathering capabilities, higher resolution, and larger apertures. Chinese astronomers put forward the suggestion of the China 30m Aperture Giant Telescope (CFGT). Its primary mirror is composed of 17 different types of off-axis aspheric sub-mirrors arranged in a circular ring. For a detailed description, please refer to the document "A Giant Telescope Scheme, Su Dingqiang, Wang Yanan, Cui Xiangqun, Chinese Journal of Astronomy, 45(1): 105-114, 2004.". The manufacture of fan-shaped off-axis aspheric mirrors requires a corresponding inspection system. However, there are still many challenges for high-precision inspection of sector-shaped off-axis aspheric mirrors.
在扇形离轴非球面镜的抛光加工阶段，通常的定量检测方法有无像差点法和补偿器零检验法。无像差点法仅适用于二次曲面的检测，除凹椭球面不用辅助镜可实现独立检验和扁球面没有无像差点之外，其余二次曲面无像差点检验均要用一辅助镜；然而对于大口径扇形离轴非球面镜所需的高精度辅助镜通常制造困难，价格昂贵。In the polishing process of fan-shaped off-axis aspheric mirrors, the usual quantitative detection methods include the aberration point method and the compensator zero inspection method. The aberration-free point method is only applicable to the detection of quadratic surfaces. Except that the concave ellipsoid can be independently inspected without an auxiliary mirror and the oblate spheroid has no aberration-free points, the other quadratic surface aberration-free point inspections must use an auxiliary mirror; however The high-precision auxiliary mirrors required for large-aperture sector-shaped off-axis aspheric mirrors are usually difficult to manufacture and expensive.
补偿器零检验法是广泛使用的一种非球面镜检测方法，该方法的实质是借助补偿器把平面或球面波前转换为与被测非球面镜理论形状重合的非球面波前，其最大优点在于所适用的辅助元件(补偿器)的直径比被检验镜直径小得多。为了对被测非球面镜作出可靠结论，补偿器必须具有所要求的质量，并相对于被检非球面正确地安装。然而，随着被测扇形非球面镜口径和相对口径的增大，补偿器可能将具有的复杂的结构，并且对其制造和装调精度也将提出更苛刻的要求，对补偿器的精度标定存在一定困难。The compensator zero test method is a widely used aspheric mirror inspection method. The essence of this method is to use a compensator to convert a plane or spherical wavefront into an aspheric wavefront that coincides with the theoretical shape of the tested aspheric mirror. Its biggest advantage is that The diameter of the applicable auxiliary element (compensator) is much smaller than the diameter of the mirror under inspection. In order to draw reliable conclusions about the asphere under test, the compensator must be of the required quality and mounted correctly with respect to the asphere under test. However, with the increase of the caliber and relative caliber of the sector-shaped aspheric mirror to be tested, the compensator may have a complex structure, and more stringent requirements will be placed on its manufacturing and assembly accuracy, and there are certain limitations on the precision calibration of the compensator. difficulty.
Liu.Y.M等(“Subaperture testing of aspheres with annular zones”，Ying-Moh Liu，GeorgeN.Lawrence，Christ L.Koliopoulos，Applied Optics，27(21)：4504-4513，1988)提出了一种无需辅助元件就能检测大口径非球面镜的环形子孔径测试技术，该检测技术大大降低了检验成本。但是对于大口径非球面镜，所需环形子孔径数目较多，测量时间较长，在检测过程中容易受到环境因素等的影响，同时多个子孔径的“拼接”处理会造成误差的累积和传递，影响到最终的检测精度。值得说明的是，该技术仅仅能应用于旋转对称非球面的检测。Liu.Y.M et al. ("Supaperture testing of aspheres with annular zones", Ying-Moh Liu, GeorgeN.Lawrence, Christ L.Koliopoulos, Applied Optics, 27(21): 4504-4513, 1988) proposed a method without auxiliary components The annular sub-aperture testing technology for large-diameter aspheric mirrors can be detected, which greatly reduces the inspection cost. However, for large-aperture aspheric mirrors, the required number of annular sub-apertures is large, and the measurement time is long, and it is easily affected by environmental factors during the detection process. At the same time, the "stitching" of multiple sub-apertures will cause error accumulation and transmission. affect the final detection accuracy. It is worth noting that this technique can only be applied to the detection of rotationally symmetric aspheric surfaces.
侯溪等在中国专利申请号“200510116819.5”“一种大口径深型非球面镜检测系统”中的实施方案中提出一种基于环形子孔径法和部分补偿法的大口径深型非球面镜检测系统，但该系统不能检测离轴非球面镜。Hou Xi et al. proposed a large-diameter deep aspheric mirror detection system based on the annular sub-aperture method and the partial compensation method in the implementation of the Chinese patent application number "200510116819.5" "A Large-Aperture Deep Aspheric Mirror Detection System". However, this system cannot detect off-axis aspheric mirrors.
发明内容 Contents of the invention
本发明要解决的技术问题：克服现有技术的不足，提供一种针对扇形轴非球面镜的扇形子孔径拼接检测系统，可以有效地解决现有定量检测技术中的辅助元件(大口径高精度反射镜、零补偿器)制造困难、成本高、装调误差灵敏等问题，并且结构简单、检验成本低、具有一定的动态测试范围。The technical problem to be solved by the present invention is to overcome the deficiencies in the prior art and provide a fan-shaped sub-aperture splicing detection system for the fan-shaft aspheric mirror, which can effectively solve the problem of auxiliary components in the existing quantitative detection technology (large-aperture high-precision reflection Mirror, zero compensator) manufacturing difficulties, high cost, sensitive assembly and adjustment errors, etc., and has a simple structure, low inspection cost, and a certain dynamic test range.
本发明解决其技术问题所采用的技术方案：扇形离轴非球面镜拼接测量系统，其特征在于：包括菲索型干涉仪、被测扇形离轴非球面镜、电控平移台、数字驱动器及计算机系统；被测扇形离轴非球面镜采用侧支撑系统支撑，菲索型干涉仪放置在电控平移台上，计算机系统通过数字驱动器与电控平移台相连，通过计算机系统控制电控平移台移动菲索型干涉仪，所产生的一系列不同曲率半径参考球面波前将与被测扇形离轴非球面镜相应的扇形区域相匹配，在所匹配的扇形区域里的参考球面波前与被测扇形离轴非球面镜的表面之间的偏离量将减小到菲索型干涉仪的测量范围内，产生一系列可分辨的干涉条纹，通过安装在计算机系统上的菲索型干涉仪的数据处理软件把可分辨干涉条纹对应的相位数据提取出来，由扇形子孔径拼接算法将所得到的子孔径测试数据送入计算机系统进行全孔径波前重构，从而获得被测非球面面形信息。The technical solution adopted by the present invention to solve the technical problems: sector-shaped off-axis aspheric mirror splicing measurement system, characterized in that it includes a Fizeau-type interferometer, a sector-shaped off-axis aspheric mirror to be measured, an electronically controlled translation stage, a digital driver and a computer system The measured fan-shaped off-axis aspheric mirror is supported by a side support system. The Fizeau type interferometer is placed on the electronically controlled translation platform. Type interferometer, a series of reference spherical wavefronts with different curvature radii will be matched with the corresponding fan-shaped area of the measured fan-shaped off-axis aspheric mirror, and the reference spherical wavefront in the matched fan-shaped area and the measured fan-shaped off-axis The deviation between the surfaces of the aspheric mirrors will be reduced to the measurement range of the Fizeau-type interferometer, and a series of resolvable interference fringes will be generated. The data processing software of the Fizeau-type interferometer installed on the computer system will The phase data corresponding to the resolution interference fringes is extracted, and the obtained sub-aperture test data is sent to the computer system by the fan-shaped sub-aperture splicing algorithm for full-aperture wavefront reconstruction, thereby obtaining the measured aspheric surface shape information.
本发明与现有技术相比的优点在于：The advantage of the present invention compared with prior art is:
(1)本发明的系统中无需制造特殊的辅助光学元件，降低了检测成本和检测准备周期，且本发明的检测系统结构简单、易于操作；(1) In the system of the present invention, there is no need to manufacture special auxiliary optical elements, which reduces the detection cost and detection preparation period, and the detection system of the present invention is simple in structure and easy to operate;
(2)本发明所使用的子孔径测量范围为扇形子孔径，而环形是扇形的特例，圆形是环形的特例；因此基于在单位扇形域里正交Zernike多项式的拼接算法是基于环形和圆形Zernike多项式拼接算法的推广；(2) The sub-aperture measuring range used in the present invention is a fan-shaped sub-aperture, and the ring is a special case of a fan, and the circle is a special case of a ring; therefore, based on the splicing algorithm of the orthogonal Zernike polynomial in the unit fan domain, it is based on the ring and the circle Generalization of shape Zernike polynomial splicing algorithm;
(3)本发明将拼接技术应用到离轴非球面镜的测量，主要用于扇形离轴非球面镜的面形误差检测。(3) The present invention applies the splicing technology to the measurement of off-axis aspheric mirrors, which is mainly used for surface error detection of fan-shaped off-axis aspheric mirrors.
附图说明 Description of drawings
图1为扇形离轴非球面镜拼接测量系统的示意图；Figure 1 is a schematic diagram of a sector-shaped off-axis aspheric mirror splicing measurement system;
图2为扇形子孔径示意图；Fig. 2 is a schematic diagram of fan-shaped sub-aperture;
图3为对大口径非球面镜环形子孔径检测的模拟干涉图；Fig. 3 is the simulated interferogram of the annular sub-aperture detection of the large-aperture aspheric mirror;
图4为圆形、环形、扇形相互关系图；Fig. 4 is a circular, circular, fan-shaped interrelationship diagram;
图5为测量系统所涉及到的全孔径波前重构数据处理流程图。Fig. 5 is a flowchart of data processing of full-aperture wavefront reconstruction involved in the measurement system.
具体实施方式 Detailed ways
下面结合附图及具体实施例详细介绍本发明。The present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments.
如图1所示，本实施例的一种扇形离轴非球面镜拼接测量系统由菲索型干涉仪1、被测扇形离轴非球面镜2、计算机系统6、电控平移台4和数字驱动器5组成，3为被测扇形离轴非球面镜2的正面视图，菲索型干涉仪1的主机放置在电控平移台4上，计算机系统6通过数字驱动器5与电控平移台4相连，由计算机系统6控制电控平移台4在菲索型干涉仪1的光轴方向进行精确移动，被测扇形离轴非球面镜2采用侧支撑系统支撑。As shown in Figure 1, a sector-shaped off-axis aspheric mirror splicing measurement system in this embodiment consists of a Fizeau-
本发明扇形离轴非球面镜拼接测量系统的工作过程及检测步骤如下：The working process and detection steps of the fan-shaped off-axis aspheric mirror splicing measurement system of the present invention are as follows:
第一步：如图1所示，对被测扇形离轴非球面镜2进行扇形子孔径检测，其子孔径配置如图2所示；图3为对大口径非球面镜环形子孔径检测的模拟干涉图，可以看出仅有部分干涉条纹具有很好的对比度而且密度较小，可以被安装在菲索型干涉仪1内的CCD所分辨，扇形非球面的子孔径检测干涉图为其模拟干涉图中对应扇形部分；通过安装在计算机6上的菲索型干涉仪1数据处理软件将可以分辨的干涉条纹部分的相位值提取出来，然后由计算机系统6通过数字驱动器5控制电控平移台4在菲索型干涉仪1光轴方向移动，让不同曲率半径的参考球面波前来匹配被测扇形离轴非球面镜2上不同的扇形区域，在所匹配的扇形区域里的入射参考球面波前与被测扇形离轴非球面镜2的表面之间的偏离量将减小到菲索型干涉仪1的测量范围内，使得在不同的区域产生可以分辨的干涉条纹；以上测试过程可以从被测扇形离轴非球面镜2内侧开始向边缘进行，一旦取得了所有扇形子孔径测试数据，就可由扇形子孔径“拼接”算法重构出全孔径波前信息；具体的数据提取方法与环形子孔径检测方法中类似，可以参考文献“环形子孔径检测技术中测量数据的准确提取方法，侯溪，伍凡，杨力，吴时彬，陈强，光电工程，2006，33(8)：113-116，131.”。Step 1: As shown in Figure 1, the fan-shaped sub-aperture detection is performed on the measured sector-shaped off-axis aspheric mirror 2, and its sub-aperture configuration is shown in Figure 2; It can be seen that only some interference fringes have good contrast and low density, which can be resolved by the CCD installed in the Fizeau
第二步：全孔径波前重构；重构方法如下：每个子孔径测试数据均可以表达为正交的Zernike多项式的线性组合形式。这样各个子孔径测试数据就简化为一系列的子孔径Zernike拟合系数。这里所使用的Zernike多项式在单位扇形区域内具有正交性(“Gram-Schmidtorthonormalization of Zernike polynomials for general aperture shapes，”W.Swantner，WengW.Chow，Appl.Opt.33(10)：1832-1837，1994)，而环Zernike多项式(“Zernike annular polynomialsfor imaging systems with annular pupils，”V.N.Mahanjan，J.Opt.Soc.Am 71：75-85，1981)和圆Zernike多项式(“Principles of optics”，Born M，Wolf E，464-468，1980)是扇形域正交的Zernike多项式的特殊表现形式。扇形、环和圆相互之间的关系如图4所示，单位扇形域可以定义为(ε0≤r≤1，0≤θ≤α，α＝θ2-θ1)，单位环域可以定义为(ε0≤r≤1，0≤θ≤α，α＝2π)，单位圆域可以定义为(ε0≤r≤1，0≤θ≤α，α＝θ2-θ1，ε0＝0)；当α＝θ2-θ＝2π时，单位扇形域变换为单位环域，当α＝θ2-θ1＝2π且ε0＝0时，单位扇形域变换为单位圆域。因此本发明中所采用的基于扇形域正交Zernike的拼接算法为基于圆Zernike多项式拼接算法(“Subaperture testing ofaspheres with annular zones”，Ying-Moh Liu，George N.Lawrence，Christ L.Koliopoulos，AppliedOptics，27(21)：4504-4513，1988)和基于环Zernike多项式拼接算法(“Full-aperture wavefrontreconstruction from annular subaperture interferometric data using Zernike annular polynomials andmatrix method for testing large aspheric surfaces”，Xi Hou，Fan Wu，Li Yang，Shi-bin Wu，QiangChen，Applied Optics，2006，45(15)：3442-3455.)的扩展。The second step: full-aperture wavefront reconstruction; the reconstruction method is as follows: each sub-aperture test data can be expressed as a linear combination of orthogonal Zernike polynomials. In this way, the test data of each sub-aperture is simplified into a series of sub-aperture Zernike fitting coefficients. The Zernike polynomials used here have orthogonality in the unit sector ("Gram-Schmidtorthonormalization of Zernike polynomials for general aperture shapes," W.Swantner, WengW.Chow, Appl.Opt.33(10):1832-1837, 1994), while ring Zernike polynomials (“Zernike annular polynomials for imaging systems with annular pupils,” VN Mahanjan, J.Opt.Soc.Am 71:75-85, 1981) and circular Zernike polynomials (“Principles of optics”, Born M, Wolf E, 464-468, 1980) is a special representation of Zernike polynomials that are orthogonal in sector fields. The relationship among sectors, rings and circles is shown in Figure 4. The unit sector domain can be defined as (ε 0 ≤ r ≤ 1, 0 ≤ θ ≤ α, α = θ 2 -θ 1 ), and the unit ring domain can be defined as is (ε 0 ≤r≤1, 0≤θ≤α, α=2π), and the unit circle domain can be defined as (ε 0 ≤r≤1, 0≤θ≤α, α=θ 2 -θ 1 , ε 0 =0); when α=θ 2 -θ=2π, the unit sector field is transformed into a unit ring field; when α=θ 2 -θ 1 =2π and ε 0 =0, the unit sector field is transformed into a unit circle field. Therefore the splicing algorithm based on sector-shaped domain orthogonal Zernike used in the present invention is based on circular Zernike polynomial splicing algorithm ("Supaperture testing ofaspheres with annular zones", Ying-Moh Liu, George N.Lawrence, Christ L.Koliopoulos, AppliedOptics, 27(21): 4504-4513, 1988) and based on ring Zernike polynomial stitching algorithm ("Full-aperture wavefront reconstruction from annular subaperture interferometric data using Zernike annular polynomials and matrix method for testing large aspheric surfaces", Xi Hou, Fan Wu, Li Yang , Shi-bin Wu, Qiang Chen, Applied Optics, 2006, 45(15): 3442-3455.) extension.
因为菲索型干涉仪1与被测扇形离轴非球面镜2在相对移动过程中存在调整误差，每个子孔径测量主要有不同的相位常数、倾斜和离焦量。具有调整误差的全孔径波前W(P，Θ，ε0)可以按照Zernike环多项式的形式分解为具有全局面形信息和局部子孔径调整误差分析，Because the Fizeau-
其中(ρk，θ)为第k个子孔径归一化的局部像素坐标，(P，Θ)为全孔径归一化的全局坐标。K表示子孔径数目，L为所用Zernike环多项式项数，bki为第k个子孔径第i项Zernike调整误差系数，Bi为第i项Zernike全孔径系数。全孔径和第k个子孔径的中心遮拦比分别为ε0和εk，子孔径和全孔径中α＝θ2-θ1为恒定值；Zki(ρk，θ，εk，α)为第k个子孔径第i项Zernike环多项式，zi(P，Θ，ε0，α)为全孔径第i项Zernike环多项式。这里所使用的Zernike多项式的排序与Zygo开发的数据处理软件MetroPro中所采用的排序相同。Where (ρ k , θ) is the local pixel coordinate normalized by the kth sub-aperture, and (P, Θ) is the global coordinate normalized by the full aperture. K represents the number of sub-apertures, L is the number of Zernike ring polynomial items used, b ki is the Zernike adjustment error coefficient of the i-th item of the k-th sub-aperture, and Bi is the i-th Zernike full-aperture coefficient. The central obscuration ratios of the full aperture and the kth sub-aperture are ε 0 and ε k , and α=θ 2 -θ 1 is a constant value in the sub-aperture and the full aperture; Z ki (ρ k , θ, ε k , α) is The i-th Zernike ring polynomial of the kth sub-aperture, z i (P, Θ, ε 0 , α) is the i-th Zernike ring polynomial of the full aperture. The ordering of the Zernike polynomials used here is the same as that used in the data processing software MetroPro developed by Zygo.
类似于分段函数，全孔径波前也可以表示为如下形式，Similar to the piecewise function, the full-aperture wavefront can also be expressed as follows,
其中aki表示第k个子孔径和第i项Zernike多项式的子孔径系数。where a ki represents the k-th sub-aperture and the sub-aperture coefficient of the i-th Zernike polynomial.
既然非球面自身不会改变，等式(1)与等式(2)必然相等，即Since the aspheric surface itself will not change, Equation (1) and Equation (2) must be equal, namely
将方程(3)进行数学处理，将其改写为矩阵形式并进行一些变换和运算，全孔径Zernike系数Bi可以被计算出。更详细的计算过程可参考文献根据全孔径Zernike系数，即可进行全孔径面形重构，可以绘制出全孔径波前图，并计算其PV(峰谷值)、RMS值(均方差值)。具体的计算过程可以参考基于圆Zernike和环Zernike多项式的拼接算法。Mathematically process equation (3), rewrite it into a matrix form and perform some transformations and operations, and the full-aperture Zernike coefficient B i can be calculated. For a more detailed calculation process, please refer to the literature. According to the full-aperture Zernike coefficient, the full-aperture surface shape can be reconstructed, and the full-aperture wavefront map can be drawn, and its PV (peak-to-valley value), RMS value (mean square error value) can be calculated. ). For the specific calculation process, please refer to the splicing algorithm based on circular Zernike and ring Zernike polynomials.
测量系统所涉及到的数据处理流程如图5所示，从内向外依次读入扇形子孔径测试数据，并进行正交Zernike多项式拟合，直到完成对所有子孔径测试数据的拟合，由上述全孔径重构算法将子孔径Zernike系数转化为全孔径Zernike系数，减去非球面理论面形并去除调整误差后，所获得的结果为全孔径面形误差信息。可以计算出PV(峰谷值)和RMS(均方根)值，并绘制二维和三维图形。The data processing flow involved in the measurement system is shown in Figure 5. The fan-shaped sub-aperture test data is read in sequence from the inside to the outside, and orthogonal Zernike polynomial fitting is performed until the fitting of all sub-aperture test data is completed. The full-aperture reconstruction algorithm converts the sub-aperture Zernike coefficients into full-aperture Zernike coefficients, subtracts the theoretical surface shape of the aspheric surface and removes the adjustment error, and the result obtained is the full-aperture surface shape error information. PV (peak-to-valley) and RMS (root mean square) values can be calculated, and two-dimensional and three-dimensional graphics can be drawn.
如果被测非球面的非球面度较大，该测量系统可在菲索型干涉仪1和被测扇形离轴非球面镜2之间放置部分补偿器，剩余波像差由扇形拼接测量技术处理。部分补偿器的设计参考朱秋东、郝群、刘惠兰在中国专利申请号“200410068823”“一种用部分补偿透镜实现非球面面形的干涉测量方法”中的实施方案。If the asphericity of the measured aspheric surface is large, the measurement system can place a partial compensator between the Fizeau-
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