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为满足各类复杂光学镜面轮廓的测量需求,该测量方法应用通用性较强的坐标测量技术,通过非接触式光学测头对待测光学元件面形轮廓进行逐点扫描测量。扫描测量过程中,光学测头应始终沿非球面表面上任意待测曲线的等距线移动,角度始终保持与曲线上任意一点的法线方向保持平行。以非球面的子午截面曲线为例,图1为光学测头对凸/凹非球面的子午线扫描轨迹示意图。
非球面子午截面曲线具有一定特殊性,曲线上各点的曲率半径均不相同,因此需利用被测点与图1中构造的几何关系求得光学测头实际位置。设子午面曲线上任一待测点为Pi(xi, yi),L为已知的光学测头长度,沿曲线过Pi(xi, yi)点的法线方向距离为L的点设为Ki,每一个待测点在扫描一侧均有唯一对应的Ki点,全部Ki离散点集合即为测头的实际运动轨迹。
已知通用的轴对称高次非球面曲线方程表达式为:
$$ {x}=\frac{C{y}^{2}}{1+\sqrt{1-(1+K){C}^{2}{y}^{2}}}+d{y}^{4}+e{y}^{6}+g{y}^{8}+\dots $$ (1) 式中:C=1/R0为非球面子午截面曲线顶点曲率,R0为曲线顶点的曲率半径;K=–e2为曲线常数,e2为曲线形状系数;d,e,g,···为系数。
曲线过任一Pi(xi,yi)点的法线方程为:
$$ {{y - }}{{{y}}_i} = - \frac{1}{{y'}}(x - {x_i}) $$ (2) 对公式(1)求导数可得:
$$ {{y}}' = \frac{1}{{f + 4a{y^3} + 6b{y^5} + 8c{y^7} + 10d{y^9} + ...}} $$ (3) $$ \begin{split} {{f}} = &\frac{{2Cy}}{{1 + \sqrt {1 - (1 + K){C^2}{y^2}} }} + \\& \frac{{(1 + K){C^3}{y^3}}}{{{{(1 - \sqrt {(1 + K){C^2}{y^2}} )}^2}\sqrt {1 - (1 + K)C{y^2}} }} \end{split} $$ (4) 曲线上过Pi(xi, yi)点的法线(或法线延长线)与X轴交点为Qi ,由公式(2)可知该点坐标Qi(yiy'+xi,0),此时法线与X轴夹角θi为:
$$ {\theta _{\text{i}}} = \arctan \frac{{\left| {{y_i}} \right|}}{{\left| {{x_i} - {y_i}y' - {{{x}}_{\text{i}}}} \right|}} = \arctan \left| {\frac{1}{{y'}}} \right| $$ (5) 扫描轨迹关于Y轴对称,当非球面镜面为凸镜面时,第一象限内扫描轨迹点Ki (xi+L·cosθi,yi+L·sinθi);当非球面面形为凹面镜时,第一象限内扫描轨迹点Ki (xi−L·cosθi,yi+L·sinθi)。即测量过程中,任一时刻光学测头的空间位置主要与被测面形尺寸及法线方向有关。理论上,当扫描装置X、Y方向有足够的运动空间,光学测头可转动角度大于等于90°时,即可对各类连续性轴对称非球面面形进行测量。
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以传统的三坐标测量机扫描结构为例,三个运动轴共计21项运动误差,测量过程中的振动以及环境变化误差均有可能会耦合到扫描测头上,严重限制了坐标扫描测量系统的测量精度[13]。为避免运动机构造成的各项误差累积,提出一种运动回路与计量回路相互独立的分离式计量框架结构如图2所示。
图 2 分离计量框架式坐标扫描装置示意图
Figure 2. Schematic diagram of coordinate scanning device with separate metrology frames
测量时,运动框架支撑跟踪扫描模块进行X、Y方向运动,配合工件台的回转运动保证镜面轮廓的完整扫描;计量框架上不承担任何运动机构负载,仅用于计量回路内干涉定位系统获取位移信息,实时确定跟踪扫描模块的空间位置以及被测点位信息。该分离式计量框架结构具有以下特性:(1)计量框架与运动框架相互独立,可以保证计量框架的相对稳定性。有效避免在测量过程中,扫描模块运动引起支撑框架内部发生形变、振动以及环境热变化等误差因素对测头造成影响,保证系统整体测量精度;(2)计量回路内应用激光干涉测量系统,能够实时高精度地获取扫描模块X、Y方向运动位移信息,保证测头运动轨迹的准确性,最大程度满足阿贝原则。
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非接触坐标测量系统能对形状比较复杂的非球面元件进行三维测量,主要通过光学测头来拾取点位信号,因此测量系统的功能、效率、精度等均与测头密切相关。目前常见的各类非接触式扫描测头的特性参数[14-18]见表1。
表 1 各类非接触式扫描测头的特性参数
Table 1. Characteristic parameters of different non-contact scanning probes
Probe type Resolution Range Characteristics Differential confocal 10 nm (Vertical resolution) Micron-scale Must be matched with the actuator to
increase the range, and increased sources of errorsDispersion confocal 0.5 nm (Vertical resolution) Micron-scale White-light interference <0.1 nm (Vertical resolution) Micron-scale Multi-wavelength interference Sub-nanometer Millimeter-scale Large working distance Self-focused sensing 0.2 μm Millimeter-scale Large working distance but insufficient precision Laser triangulation 2 μm Millimeter-scale Scanning tunnel microscope 5 nm <1 nm Low scanning efficiency and only metal parts can be measured 对比发现,现有的光学测头量程大则精度较低;精度高则量程小,高精度测头常受其执行机构的运动精度影响使整体测量系统精度降低。因此,该测量方法采用测量精度较高的激光干涉测量,结合上文提出的分离式计量框架结构,可在获得较高测量精度的同时有效降低执行机构引入的各项运动误差。
激光干涉测头原理如图3所示。光矢量与入射平面成45°夹角的线偏振光,经光纤传输至光纤准直器FC后垂直入射PBS,被分光成两束相互垂直的线偏振光。其中:(1)水平线偏振光穿透PBS照射至探测器作为干涉参考光;(2)垂直线偏振光经PBS折射至凸透镜L1,焦点汇聚于标准球圆心上原路返回至PBS,途中经过λ/4波片QWP1两次,使原本垂直的线偏振光变为水平偏振光,此时该路光束能够直接透过介质分束膜,再一次经过凸透镜L2,焦点汇聚于待测曲面的测量点上,光路二次返回PBS,经过两次λ/4波片QWP2恢复为垂直线偏振光,经PBS折射后,作为干涉测量光最终与干涉参考光汇合。重合后光束经分束镜SP等分为四路,照射至四通道光电探测器上得到相对位移信息。
该干涉测头应用笔者课题组研制的集成阵列式波片的四象限干涉测量系统[19],适用于测量反射元件的相对位移。该系统应用NI-5734数字化适配器模块,能够同时对四通道的信号进行采集,采样率120 MHz,实际AD采集分辨率大于12.1位,静态分辨率优于1 nm,2 000 mm测量范围内,标准差为48.58 nm;针对非球面反射镜动态测量时,在30 μm的测量范围内,系统测量偏差在±3 nm之间,分辨率约为1 nm[20]。较传统的单频干涉系统集成度更高、光学测头的体积更小,能够起到增大光学测头旋转角度、减小测头对扫描执行机构的负载、提升测头的动态性能的作用,更有利于进行复杂面形轮廓的测量。
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跟踪扫描模块作为干涉光学测头运动的执行机构,是测量系统的核心运动部件,负责对被测轴对称光学元件的面形轮廓进行扫描跟踪运动,其空间定位的准确性直接影响测量结果的正确性。为保证其运动轨迹的的准确性,提出一种运动执行机构与多路激光干涉共基准的空间定位方法,图4为跟踪扫描模块的空间定位与测量原理图。
跟踪扫描模块内安装ϕ25 mm基准球作为跟踪扫描模块的运动基准,同时,该基准球还是模块内干涉定位系统和干涉测头共同的参考测量基准。其中:
(1)干涉定位系统由X、Y轴两套相对位置垂直的干涉系统组成,其原理均如图3所示,通过测量基准球与计量框架上定位参考镜M1、M2的相对位移变化量△X、△Y,确定参考基准球在XY平面内的实时空间坐标,即跟踪扫描模块运动的实时坐标信息;
(2)干涉测头始终围绕基准球做等距圆周转动,测得基准球与被测点的相对位移变化量△L后,结合基准球的空间位置与干涉测头转角即可确定该测量点的准确空间坐标。
跟踪扫描模块的运动基准与各干涉系统测量基准的统一,保证了扫描模块自身空间定位的准确性与运动精度,可以将测得的非球面面形信息直接溯源至光波长“米”定义上,为非球面镜面形轮廓测量量值统一和溯源提供一种有效的技术方案。
High-precision profile measurement method for axisymmetric aspheric mirror (invited)
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摘要: 为实现轴对称非球面反射镜轮廓的高精度、可溯源测量,建立了非球面测量轨迹的数学模型,提出了一种基于独立计量回路的非接触式坐标扫描测量方法。该方法采用分离式计量框架结构,有效减少了跟踪扫描模块运动对测量精度的影响;测头采用集成阵列式波片的四象限干涉测量系统,保证测头精度的同时更有利于实现复杂面形轮廓的跟踪扫描运动;设计扫描执行机构与多路激光干涉系统共基准的运动模块,实时跟踪扫描运动机构的位置信息,提高测头空间定位精度并使其测量值能溯源到“米”定义。搭建测量装置测试该方法的准确测量精度,试验结果表明,测量误差小于0.2 μm,重复性精度为70 nm,测量精度达到亚微米级。Abstract: In order to achieve the goal of high-precision and traceable aspheric surface profile measurement, a mathematical model of the measurement trajectory is established for the surface profile measurement of axisymmetric aspheric mirrors, and a non-contact coordinate scanning measurement method with independent metrology loop is proposed. The method applies a separated metrology frame, which effectively reduces the influence of each motion module on the measurement accuracy of the system during the measurement process; the probe adopts a four-quadrant interferometry system with integrated array waveplates, which improves the dynamic performance of the probe and is more conducive to the measurement of complex aspheric surface shapes; the motion module with a common reference between the scanning actuator and the multiplexed laser interferometry system is designed to track the position information of the scanning motion mechanism in real time, which improves the accuracy of the scanning motion and enables the measurement of the surface shape. The scanning actuator is designed to track the position information of the scanning motion mechanism in real time to improve the accuracy of the probe motion and make its measurement value traceable to the definition of "meter". The measurement device is built and the surface profile of the standard sphere and aspheric mirror are measured separately. The test results show that the measurement error is less than 0.2 μm and the repeatability accuracy was 70 nm, and the system measurement accuracy reaches submicron level.
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Key words:
- surface inspection /
- aspheric /
- non-contact measurement /
- interferometric probe
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表 1 各类非接触式扫描测头的特性参数
Table 1. Characteristic parameters of different non-contact scanning probes
Probe type Resolution Range Characteristics Differential confocal 10 nm (Vertical resolution) Micron-scale Must be matched with the actuator to
increase the range, and increased sources of errorsDispersion confocal 0.5 nm (Vertical resolution) Micron-scale White-light interference <0.1 nm (Vertical resolution) Micron-scale Multi-wavelength interference Sub-nanometer Millimeter-scale Large working distance Self-focused sensing 0.2 μm Millimeter-scale Large working distance but insufficient precision Laser triangulation 2 μm Millimeter-scale Scanning tunnel microscope 5 nm <1 nm Low scanning efficiency and only metal parts can be measured -
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