WO2017107777A1 - Method for measuring surface shape error of rotary symmetrical unknown aspheric surface, and measurement device thereof - Google Patents

Method for measuring surface shape error of rotary symmetrical unknown aspheric surface, and measurement device thereof Download PDF

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WO2017107777A1
WO2017107777A1 PCT/CN2016/108999 CN2016108999W WO2017107777A1 WO 2017107777 A1 WO2017107777 A1 WO 2017107777A1 CN 2016108999 W CN2016108999 W CN 2016108999W WO 2017107777 A1 WO2017107777 A1 WO 2017107777A1
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aspheric
probe
measuring
aspherical
tested
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彭石军
苗二龙
高松涛
武东城
隋永新
杨怀江
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中国科学院长春光学精密机械与物理研究所
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01BMEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B11/00Measuring arrangements characterised by the use of optical means
    • G01B11/24Measuring arrangements characterised by the use of optical means for measuring contours or curvatures

Abstract

A high-precision measurement method for a rotary symmetrical unknown aspheric surface, and a measurement device. The measurement method comprises: enabling a target measurement head (1004) of an interferometer (10) to be perpendicular to a surface (15) to be measured and scan the surface (15) to be measured; after the scanning, obtaining a group of arrays that pass through a top point of an aspheric surface and that contain spatial coordinates; obtaining, according to an aspheric surface formula, the curvature radius of the top point of the aspheric surface and values of coefficients by using a least squares fitting method; and inputting the calculated aspheric surface parameters to carry out point-to-point scanning on the whole aspheric surface, and comparing an ideal aspheric surface to obtain a surface shape error of the aspheric surface. The measurement device comprises an interferometer (10), an interferometer actuating device, and an interferometer spatial position detection device.

Description

一种旋转对称未知非球面面形误差的测量方法及其测量装置Method for measuring rotationally symmetric unknown aspherical surface shape error and measuring device thereof 技术领域Technical field
本案涉及光学测量领域,特别提供了一种旋转对称未知非球面面形误差的测量方法及其测量装置。The present invention relates to the field of optical measurement, and particularly provides a method for measuring rotationally symmetric unknown aspherical surface shape error and a measuring device thereof.
背景技术Background technique
在光学系统中的透镜及反射镜,曲面形式多数为平面和球面,原因是这些简单形式的曲面加工、检测容易,能够做到批量化生产,也容易达到高精度的面形要求,尤其是各种高精度面形检测干涉仪的出现大大降低了高精度平面和球面面形检测的难度。尽管如此,在某些高精度成像系统中,如光刻物镜及核聚变系统,仅仅使用平面和球面镜难以达到预期的成像质量,然而非球面镜的引入成功解决了这一问题,而且非球面的应用增加了非球面设计的自由度,对改善光学系统的成像质量,提高光学性能,减小外形尺寸和重量几方面起着重要作用。采用非球面技术设计的光学系统,可消除球差、慧差、象散、场曲,减小光能损失,从而获得高质量的成像和高品质的光学特性。然而,非球面的加工和检测都要比球面困难很多,这是因为:球面有无数个对称轴,而非球面只有一个,所以非球面不能采用球面加工时的方法加工;非球面各环带的曲率半径不同,在抛光时难以修正。目前,非球面检测的主要方法是轮廓法和干涉法。In the optical system, the lens and the mirror are mostly in the form of plane and spherical surface. The reason is that these simple forms of surface processing and detection are easy, mass production can be achieved, and high-precision surface shape requirements are easily achieved, especially The emergence of a high-precision surface detection interferometer greatly reduces the difficulty of high-precision planar and spherical surface detection. However, in some high-precision imaging systems, such as lithography objectives and nuclear fusion systems, it is difficult to achieve the desired image quality using only planar and spherical mirrors. However, the introduction of aspherical mirrors has successfully solved this problem, and aspheric applications. The added freedom of aspheric design plays an important role in improving the imaging quality of optical systems, improving optical performance, and reducing the size and weight. Optical systems designed with aspherical technology eliminate spherical aberration, coma, astigmatism, field curvature, and reduce light energy loss for high-quality imaging and high-quality optical properties. However, the machining and inspection of aspherical surfaces are much more difficult than spherical surfaces. This is because spherical surfaces have an infinite number of symmetry axes, and there is only one spherical surface. Therefore, aspheric surfaces cannot be processed by spherical processing; aspherical rings The radius of curvature is different and it is difficult to correct during polishing. Currently, the main methods of aspheric detection are contouring and interferometry.
干涉测量法是测量光学元件的重要方法,既能实现高精度测量,又不会对待测面产生损伤。但是这种干涉仪要实现对非球面的测量,需要特殊的方法或装置。在干涉测量法中常用的测量方法有无像差点法、补偿镜法、计算全息图法、环带拼接法、子孔径拼接法、长波长法等。虽然这些方法均能实现高精度测量,但是前提是必须知道非球面的所有几何参数,且补偿镜法、计算全息图法所使用的补偿装置只能针对一种非 球面,无像差点法只针对二次曲面。Interferometry is an important method for measuring optical components, enabling high-accuracy measurements without damage to the measuring surface. However, such an interferometer requires a special method or device to achieve measurement of the aspheric surface. The commonly used measurement methods in interferometry include the aberration point method, the compensation mirror method, the computational hologram method, the ring stitching method, the subaperture stitching method, and the long wavelength method. Although these methods can achieve high-precision measurement, the premise is that all geometric parameters of the aspheric surface must be known, and the compensation device used in the compensation mirror method and the computational hologram method can only target one type of non-spherical Spherical, no aberration method is only for quadric surfaces.
轮廓测量法采用接触式或非接触式的测量方式,直接测量非球面的矢高,然后利用非球面方程,减去理想非球面的轮廓线,从而得到非球面的面形轮廓线。接触式测量仪器采用探针直接与非球面接触,通过横向移动探针,并记录探针的高度变化,从而获得非球面的轮廓,这种设备存在测量行程与测量精度矛盾的特点,且容易划伤被测表面;三坐标测量机也是接触式测量仪器,通过对空间坐标的测量,可以获得被测表面的外形轮廓,这种设备测量范围大,但是测量精度相对较低,且容易对被测表面造成损伤。The profilometry method uses a contact or non-contact measurement method to directly measure the azimuth of the aspheric surface, and then uses the aspherical equation to subtract the contour of the ideal aspheric surface to obtain an aspherical contour. The contact measuring instrument adopts the probe to directly contact the aspherical surface, and moves the probe laterally and records the height change of the probe to obtain the aspherical contour. The device has the characteristics of contradiction between the measuring stroke and the measuring precision, and is easy to draw. The measured surface is injured; the coordinate measuring machine is also a contact measuring instrument. By measuring the space coordinates, the contour of the measured surface can be obtained. The measuring range of the device is large, but the measuring accuracy is relatively low, and it is easy to measure. The surface causes damage.
因此,研发一种在完全未知被测面的几何参数的情况下,实现无损伤检测,成为人们亟待解决的问题。Therefore, the development of a non-damage detection in the case of completely unknown geometric parameters of the measured surface has become an urgent problem to be solved.
发明内容Summary of the invention
鉴于此,本案的目的在于提供一种旋转对称未知非球面面形误差的测量方法及其测量装置,以至少解决以往在非球面测量过程中需要已知非球面对应的几何参数,以及测量方法精度不高,对待测非球面造成损伤等问题。In view of this, the purpose of the present invention is to provide a method for measuring rotationally symmetric unknown aspherical surface shape error and a measuring device thereof, so as to at least solve the geometric parameters required for the known aspherical surface in the aspherical measurement process, and the accuracy of the measurement method. Not high, causing damage to the aspheric surface.
本案一方面提供了一种旋转对称未知非球面面形误差的测量方法,包括以下步骤:In one aspect, the present invention provides a method for measuring a rotationally symmetric unknown aspherical surface shape error, comprising the following steps:
使用干涉仪沿待测非球面表面一经线方向进行逐点扫描采样,获得一组关于待测非球面空间坐标的数组L(x,z,t),其中,所述数组L(x,z,t)中包含待测非球面的顶点空间坐标;Using an interferometer to perform point-by-point scanning sampling along the aspherical surface of the aspherical surface to be tested, obtaining a set of arrays L(x, z, t) with respect to the aspherical space coordinates to be tested, wherein the array L(x, z, t) contains the vertex space coordinates of the aspheric surface to be tested;
依据所述数组L(x,z,t),利用最小二乘拟合法计算获得所述待测非球面的顶点曲率半径R0、二次项系数K和高次项系数AnCalculating, according to the array L(x, z, t), obtaining a vertex curvature radius R 0 , a quadratic coefficient K and a high-order coefficient A n of the aspheric surface to be tested by using a least squares fitting method;
依据所述待测非球面的顶点曲率半径R0、二次项系数K和高次项系数An,计算获得所述待测非球面的理想矢高面; Obtaining an ideal sagittal plane of the aspheric surface to be tested according to a vertex curvature radius R 0 , a quadratic coefficient K, and a high-order coefficient A n of the aspheric surface to be tested;
使用干涉仪对所述待测非球面整个表面进行逐点扫描采样,获得所述待测非球面的测量矢高面;Performing point-by-point scanning sampling on the entire surface of the aspheric surface to be tested using an interferometer to obtain a measured sagittal plane of the aspheric surface to be tested;
将所述待测非球面的测量矢高面与所述待测非球面的理想矢高面进行比较,获得所述待测非球面的面形误差。Comparing the measured sagittal plane of the aspheric surface to be tested with the ideal sagittal plane of the aspheric surface to be tested, and obtaining a surface shape error of the aspheric surface to be tested.
本案另一方面还提供了一种旋转对称未知非球面面形误差的测量装置,用于执行前述的旋转对称未知非球面面形误差的测量方法。In another aspect of the present invention, a measuring device for rotationally symmetric unknown aspherical surface shape error is provided for performing the aforementioned measurement method of rotationally symmetric unknown aspherical surface shape error.
该测量装置优选地包括干涉仪致动装置,用于使干涉仪的目标测头对待测物体的未知非球面进行扫描,并在扫描过程中使所述目标测头始终垂直于所述未知非球面且保持固定的距离。The measuring device preferably comprises interferometer actuating means for causing the target probe of the interferometer to scan an unknown aspheric surface of the object to be measured and to cause the target probe to be perpendicular to the unknown aspheric surface during the scanning process And keep a fixed distance.
该测量装置优选地还包括干涉仪空间位置检测装置,用于在所述扫描过程中实时获得所述目标测头的空间位置。The measuring device preferably further comprises interferometer spatial position detecting means for obtaining the spatial position of the target probe in real time during the scanning process.
该测量装置优选地还包括处理装置,用于获取所述目标测头的空间位置以计算待测非球面空间坐标的数组及执行所述的旋转对称未知非球面面形误差的测量方法。The measuring device preferably further comprises processing means for acquiring a spatial position of the target probe to calculate an array of aspherical space coordinates to be measured and a method of measuring the rotationally symmetric unknown aspherical surface shape error.
本案提供的旋转对称未知非球面面形误差的测量方法,可以在完全未知非球面方程的情况下,依据待测非球面的一组经线方向空间坐标数组(即一条经过顶点的矢高曲线),通过最小二乘拟合计算获得待测非球面的几何参数,依据该参数获得被测非球面的几何参数,获得理想矢高面,再依据逐点检查获得被测非球面的测量矢高面,通过比较测量矢高面和理想矢高面获得面形误差,完成非球面面形的测量,测量方法简单,方便。The measurement method of the rotationally symmetric unknown aspherical surface shape error provided by the present case can be passed according to a set of spatial coordinate arrays of a warp direction (ie, a vector curve passing through the apex) of the aspheric surface to be tested in the case of a completely unknown aspheric equation. The least squares fitting calculation is used to obtain the geometric parameters of the aspheric surface to be tested. According to the parameters, the geometric parameters of the aspheric surface to be measured are obtained, the ideal vector height surface is obtained, and the measured azimuth surface of the measured aspheric surface is obtained according to the point-by-point inspection. The sagittal plane and the ideal sagittal plane obtain the shape error, and the measurement of the aspherical surface shape is completed, and the measurement method is simple and convenient.
本案提供的旋转对称未知非球面面形误差的测量装置,通过多波长干涉仪作为测量头,测量精度高,可测量的非球面种类多,而且为非接触测量,能够满足加工阶段和最后的镀膜阶段的检测,不会对非球面表面产生任何损伤。 The measuring device for rotationally symmetric unknown aspherical surface shape error provided by the present invention uses a multi-wavelength interferometer as a measuring head, has high measurement precision, and has many types of measurable aspheric surfaces, and is non-contact measurement, which can satisfy the processing stage and the final coating. Stage detection does not cause any damage to the aspheric surface.
附图说明DRAWINGS
图1为旋转对称未知非球面面形误差测量装置的结构示意示意图;1 is a schematic structural view of a rotationally symmetric unknown aspherical surface shape error measuring device;
图2为测量装置的多波长干涉仪的前视结构示意图;2 is a schematic front view of a multi-wavelength interferometer of a measuring device;
图3为测量装置的多波长干涉仪的侧视结构示意图;3 is a side view showing a structure of a multi-wavelength interferometer of a measuring device;
图4为测量装置的多波长干涉仪中目标测头扫描待测非球面时运动轨迹示意图;4 is a schematic diagram of a motion trajectory of a target probe in a multi-wavelength interferometer of a measuring device when scanning an aspheric surface to be tested;
图5为测量装置的多波长干涉仪中目标测头扫描待测非球面时坐标变化示意图。FIG. 5 is a schematic diagram of coordinate changes when a target probe scans an aspheric surface to be tested in a multi-wavelength interferometer of a measuring device.
具体实施方式detailed description
下面结合具体的实施方案对本案进行进一步解释,但是并不用于限制本案的保护范围。The present invention is further explained below in conjunction with specific embodiments, but is not intended to limit the scope of protection of the present case.
为了解决以往在非球面测量过程中需要已知非球面对应的几何参数以及还存在测量方法精度不高等问题,本实施方案提供了一种旋转对称未知非球面面形误差的测量方法,包括以下步骤:In order to solve the problem that the geometric parameters corresponding to the known aspherical surface are required in the aspheric measurement process and the accuracy of the measurement method is not high, the present embodiment provides a method for measuring the rotationally symmetric unknown aspherical surface shape error, including the following steps. :
S1:使用干涉仪沿待测非球面表面一经线方向进行逐点扫描采样,获得一组关于待测非球面空间坐标的数组L(x,z,t),其中,所述数组L(x,z,t)中包含待测非球面的顶点空间坐标,即测量获得的数组L(x,z,t)为一条经过待测非球面顶点的矢高曲线。其中,x,z,t分别是X向、Z向和T向的坐标,所述X向一个水平方向、Z向为竖直方向,T向是绕XZ平面的法线的旋转方向,X、Z、T共同构成一个空间坐标。S1: using an interferometer to perform point-by-point scanning sampling along a warp direction of the aspheric surface to be tested, and obtaining a set of arrays L(x, z, t) about the aspherical space coordinates to be tested, wherein the array L(x, z, t) contains the vertex space coordinates of the aspheric surface to be tested, that is, the measured array L(x, z, t) is a vector height curve passing through the aspheric vertices to be tested. Where x, z, t are the coordinates of the X direction, the Z direction, and the T direction, respectively, the X direction is a horizontal direction, the Z direction is a vertical direction, and the T direction is a rotation direction of a normal around the XZ plane, X, Z and T together form a spatial coordinate.
S2:依据上述测量获得的数组L(x,z,t),利用最小二乘拟合法计算获得待测非球面的顶点曲率半径R0、二次项系数K和高次项系数AnS2: calculating, according to the above-mentioned measurement, an array L(x, z, t), obtaining a vertex curvature radius R 0 , a quadratic coefficient K and a high-order coefficient A n of the aspheric surface to be tested by using a least squares fitting method;
S3:上述计算获得的待测非球面的顶点曲率半径R0、二次项系数K和高次项系数An,计算获得待测非球面的理想矢高面; S3: the curvature radius R 0 , the quadratic coefficient K and the high-order coefficient A n of the aspheric surface to be tested obtained by the above calculation are calculated, and the ideal sagittal plane of the aspheric surface to be tested is calculated;
S4:使用干涉仪对待测非球面整个表面进行逐点扫描采样,获得待测非球面的测量矢高面;S4: using an interferometer to perform point-by-point scanning sampling on the entire surface of the aspheric surface to be measured, and obtaining a measured sagittal plane of the aspheric surface to be tested;
S5:将步骤S4获得的测量矢高面与步骤S3获得的理想矢高面进行比较,获得待测非球面的面形误差,完成非球面的面形测量。S5: Comparing the measured sagittal plane obtained in step S4 with the ideal sagittal plane obtained in step S3, obtaining a surface error of the aspheric surface to be tested, and completing the aspherical surface measurement.
其中,步骤S2对应的计算过程为:将步骤S1扫描采样获得的数组L(x,z,t)中各采样点对应的x向和z向值代入到下面公式(a)中,当公式(a)的值最小时,计算得到待测非球面相应的顶点曲率半径R0、二次项系数K和高次项系数AnThe calculation process corresponding to step S2 is: substituting the x-direction and the z-direction value corresponding to each sampling point in the array L(x, z, t) obtained by scanning and sampling in step S1 into the following formula (a), when the formula ( When the value of a) is the smallest, the curvature radius R 0 , the quadratic coefficient K and the high-order coefficient A n of the corresponding aspheric surface are calculated.
公式(a)具体为,Formula (a) is specifically
Figure PCTCN2016108999-appb-000001
Figure PCTCN2016108999-appb-000001
其中,N为采样点个数,c=1/R0为顶点曲率,R0为顶点曲率半径,K为二次项系数,M为非球面系数的总阶数,An为高次项系数。Where N is the number of sampling points, c=1/R 0 is the curvature of the vertex, R 0 is the radius of curvature of the vertex, K is the coefficient of the quadratic term, M is the total order of the aspherical coefficients, and A n is the coefficient of the high order term .
步骤S3对应的计算公式为:The calculation formula corresponding to step S3 is:
Figure PCTCN2016108999-appb-000002
Figure PCTCN2016108999-appb-000002
其中,z为非球面的矢高,c=1/R0为顶点曲率,R0为顶点曲率半径,K为二次项系数,ρ为非球面的径向坐标,M为非球面系数的总阶数,An为高次项系数。Where z is the azimuth of the aspherical surface, c=1/R 0 is the curvature of the vertex, R 0 is the radius of curvature of the vertex, K is the coefficient of the quadratic term, ρ is the radial coordinate of the aspherical surface, and M is the total order of the aspherical coefficient Number, A n is the high order coefficient.
由于以往的接触式测量,容易给待测非球面造成损伤,为了解决该问题,在本实施方案中,干涉仪进行扫描采样过程中,干涉仪的测量头始终保持与待测非球面垂直,且测量头到待测非球面的距离保持恒定,优选,测量头到被测非球面的距离大于测量头的焦距,由于在测量头的焦点处容易受灰尘颗粒及表面瑕疵的干扰,通过大于焦距的设计能够提 高了测头抗环境干扰的能力。In order to solve the problem, in the present embodiment, during the scanning and sampling process of the interferometer, the measuring head of the interferometer is always perpendicular to the aspheric surface to be tested, and The distance from the measuring head to the aspheric surface to be tested remains constant. Preferably, the distance from the measuring head to the aspheric surface to be measured is greater than the focal length of the measuring head. Since it is easily disturbed by dust particles and surface flaws at the focus of the measuring head, it is greater than the focal length. Design can mention The ability of the probe to resist environmental interference is high.
本案还提供一种旋转对称未知非球面面形误差的测量装置,用于执行前述的旋转对称未知非球面面形误差的测量方法。The present invention also provides a measuring device for rotationally symmetric unknown aspherical surface shape error for performing the aforementioned measurement method of rotationally symmetric unknown aspherical surface shape error.
该测量装置至少包括干涉仪致动装置,用于使干涉仪的目标测头对待测物体的未知非球面进行扫描,并在扫描过程中使所述目标测头始终垂直于所述未知非球面且保持固定的距离。这样,通过检测干涉仪的扫描时的运动轨迹即可计算出待测物体的面形。此外,该测量装置还可包括干涉仪空间位置检测装置,其用于在所述扫描过程中实时获得所述目标测头的空间位置。The measuring device includes at least an interferometer actuating device for causing a target probe of the interferometer to scan an unknown aspheric surface of the object to be measured, and causing the target probe to be perpendicular to the unknown aspheric surface during the scanning process and Keep a fixed distance. In this way, the shape of the object to be tested can be calculated by detecting the motion trajectory of the interferometer during scanning. Furthermore, the measuring device may further comprise interferometer spatial position detecting means for obtaining the spatial position of the target probe in real time during the scanning process.
该测量装置还可包括处理装置,用于获取所述目标测头的空间位置以计算待测非球面空间坐标的数组及执行所述的旋转对称未知非球面面形误差的测量方法。该处理装置可以是计算机等任何具有信息处理能力的设备。The measuring device may further comprise processing means for acquiring a spatial position of the target probe to calculate an array of aspherical space coordinates to be measured and a measuring method for performing the rotationally symmetric unknown aspherical surface shape error. The processing device may be any device having information processing capabilities such as a computer.
所述干涉仪致动装置可以是任何能在X、Z、T三个方向上致动的设备,例如垂直设置的二维运动台和固定在二维运动台上的T向旋转台。所述二维运动台其能够在X方向和Z方向上作平移,T向旋转台上再固定所述干涉仪。The interferometer actuation device can be any device that can be actuated in three directions, X, Z, T, such as a vertically arranged two-dimensional motion table and a T-direction rotary table that is fixed to the two-dimensional motion table. The two-dimensional motion stage is capable of translating in the X direction and the Z direction, and the T is fixed to the rotating table.
所述干涉仪空间位置检测装置可以是任何能够获取干涉仪的目标测头空间位置的设备,例如,若干涉仪可以包括X向参考测头X、Z、T三个方向的参考测头,并另在固定位置设置X向参考测头反射镜、Z向参考测头反射镜和T向圆弧形反射镜,由此,可以直接由X、Z、T三个方向的参考测头获得干涉仪目标测头的空间位置。The interferometer spatial position detecting device may be any device capable of acquiring the spatial position of the target probe of the interferometer, for example, if the interferometer can include reference probes in three directions of the X-direction reference probes X, Z, and T, and In addition, an X-direction reference probe, a Z-direction reference probe, and a T-direction circular mirror are disposed at a fixed position, thereby obtaining an interferometer directly from the reference probes in the X, Z, and T directions. The spatial position of the target probe.
此外,装置还可包括转台,其旋转面为水平面,其上用于放置具有未知非球面的待测物体。转台可以是气浮转台,并可被控制以进行转动。转台上还可以具有调平调心工作台。 Further, the apparatus may further include a turntable whose rotating surface is a horizontal plane on which the object to be tested having an unknown aspherical surface is placed. The turntable can be an air float turret and can be controlled for rotation. There is also a leveling and aligning workbench on the turntable.
为了安装干涉仪及其他部件,测量装置还可包括安装平台,所述转台、二维运动台、X向参考测头、Z向参考测头均可安装在安装平台上。安In order to install the interferometer and other components, the measuring device may further comprise a mounting platform, the turntable, the two-dimensional motion table, the X-direction reference probe, and the Z-direct reference probe may be mounted on the mounting platform. Ann
下面以一个具体的实施例对本案进行进一步的详细说明,但是并不用于限制本案的保护范围。The present invention will be further described in detail below with reference to a specific embodiment, but is not intended to limit the scope of the present invention.
图1为旋转对称未知非球面面形误差的测量装置的结构示意图。该装置包括基座1,在基座1的上方跨设有龙门吊2,该龙门吊2包括横梁21和设置于横梁21下方的支架22,在基座1的上表面还设置有气浮转台3,该气浮转台3恰好位于龙门吊2的下方,在气浮转台3的上方固定安装有用来安装待非球面的调平调心工作台4,该调平调心工作台4可对待测非球面进行倾斜和偏心的调整,同时调平调心工作台4在气浮转台3的带动下可以进行旋转,且其转轴恰好与测量坐标系的Z轴重合,气浮转台3的上表面即为测量坐标系的XOY平面,气浮转台3的径向端跳及轴向端跳均小于0.1μm,在基座1上还固定安装有二维运动台5,为二维运动台5与气浮转台3上表面垂直,该二维运动台5可沿着测量坐标系的X轴方向和Z轴方向进行平移,在二维运动台5上垂直连接有T向旋转台6,该T向旋转台6可绕着与Y轴进行旋转,在龙门吊2的一侧支架22上固定设置有X向参考测头反射镜7,在龙门吊2的横梁21上固定设置有Z向参考测头反射镜8,且Z向参考测头反射镜8与X向参考测头反射镜7垂直。参见图3,二维运动台5通过第一悬臂梁12固定连接有T向圆弧形反射镜9,在二维运动台5和T向旋转台6上还连接有多波长干涉仪10,与气浮转台3、二维运动台5、T向旋转台6和多波长干涉仪10电连接有主控计算机11,该主控计算机11可控制气浮转台3、二维运动台5和T向旋转台6的运动,并接收多波长干涉仪10发送来的测量数据,依据所述测量数据进行计算和分析, 与主控计算机11连接有电源14。FIG. 1 is a schematic structural view of a measuring device for rotationally symmetric unknown aspherical surface shape error. The device includes a pedestal 1 , and a gantry crane 2 is disposed above the pedestal 1 . The gantry crane 2 includes a beam 21 and a bracket 22 disposed under the beam 21 . The air turret 3 is further disposed on the upper surface of the pedestal 1 . The air floating table 3 is located just below the gantry crane 2, and a leveling and aligning table 4 for mounting an aspherical surface is fixedly mounted above the air floating turret 3, and the leveling and aligning table 4 can be used for measuring the aspheric surface. The tilting and eccentric adjustment, while the leveling table 4 can be rotated by the air floating table 3, and its rotating shaft coincides with the Z axis of the measuring coordinate system, and the upper surface of the air floating table 3 is the measuring coordinate. The XOY plane of the system, the radial end jump and the axial end jump of the air floating turntable 3 are all less than 0.1 μm, and the two-dimensional motion stage 5 is fixedly mounted on the base 1, which is a two-dimensional motion stage 5 and an air floating turntable 3 The upper surface is vertical, the two-dimensional moving table 5 can be translated along the X-axis direction and the Z-axis direction of the measurement coordinate system, and the T-direction rotating table 6 is vertically connected to the two-dimensional moving table 5, and the T-direction rotating table 6 can be Rotating with the Y axis, X-direction ginseng is fixed on one side bracket 22 of the gantry crane 2 Probe mirror 7, on a fixed gantry 21 of the cross member 2 is provided with a Z reference mirror 8 to the probe, and the probe perpendicular to the Z direction reference mirror 7 to the reference mirror 8 and the probe X. Referring to FIG. 3, the two-dimensional moving table 5 is fixedly connected with a T-shaped circular mirror 9 through a first cantilever beam 12, and a multi-wavelength interferometer 10 is further connected to the two-dimensional moving table 5 and the T-direction rotating table 6, and The air floating turntable 3, the two-dimensional moving table 5, the T-direction rotating table 6 and the multi-wavelength interferometer 10 are electrically connected with a main control computer 11 which can control the air floating turntable 3, the two-dimensional moving table 5 and the T direction. Rotating the movement of the stage 6, and receiving the measurement data sent by the multi-wavelength interferometer 10, performing calculation and analysis according to the measurement data, A power source 14 is connected to the host computer 11.
多波长干涉仪10中目标测头1004出射的光垂直入射待测非球面15的上表面,通过合理控制二维运动台5的X向、Z向运动以及T向旋转台6的运动,使目标测头1004始终垂直于待测非球面15表面,且目标测头1004到被测非球面15上表面的距离恒定。固定于调平调心工作4上的被测非球面15在气浮转台3的带动下绕转轴匀速转动,在目标测头1004的平动及转动的共同作用下,实现整个被测非球面15的面形扫描。调平调心工作台4的功能是通过倾斜及偏心的调节使待测非球面15的光轴与转轴重合。由铟钢制作而成的龙门吊2的横梁21以及左侧支架22上分别固定了一块高精度长条Z向参考测头反射镜8和X向参考测头反射镜7,将多波长干涉仪10中Z向参考测头1002和X向参考测头1001的垂直入射光反射回去,实时反馈目标测头1004的X向和Z向位移量。基座1支撑起整个测量装置,基座1由大理石隔振台101以及用于大理石隔振台101支撑的气浮隔振腿102组成,其中气浮隔振腿102有效降低了周围环境振动对测量的影响。电源14与主控计算机11连接在一起,主控计算机11还与气浮转台3、二维运动台5、T向旋转台6和多波长干涉仪10连接,对气浮转台3、二维运动台5和T向旋转台6发送运动指令,同时实时读取多波干涉仪10中各测头的测量数据,然后进行分析和计算。The light emitted from the target probe 1004 in the multi-wavelength interferometer 10 is perpendicularly incident on the upper surface of the aspheric surface 15 to be measured, and the target is controlled by the X-direction and Z-direction movement of the two-dimensional motion table 5 and the movement of the T-direction rotary table 6 The probe 1004 is always perpendicular to the surface of the aspheric surface 15 to be measured, and the distance from the target probe 1004 to the upper surface of the aspheric surface 15 to be measured is constant. The measured aspheric surface 15 fixed on the leveling and aligning work 4 is rotated at a constant speed around the rotating shaft under the driving of the air floating turret 3, and the entire measured aspheric surface 15 is realized under the joint action of the target probe 1004. Face scan. The function of the leveling table 4 is to adjust the optical axis of the aspheric surface 15 to be measured to coincide with the axis of rotation by tilting and eccentricity adjustment. A high-precision long Z-direction reference probe 8 and an X-direction reference probe 7 are fixed to the beam 21 and the left bracket 22 of the gantry crane 2 made of indium steel, respectively, and the multi-wavelength interferometer 10 is used. The mid-Z direction reference probe 1002 and the X are reflected back to the normal incident light of the reference probe 1001, and the X-direction and Z-direction displacement amounts of the target probe 1004 are fed back in real time. The base 1 supports the entire measuring device. The base 1 is composed of a marble vibration isolation table 101 and an air floating vibration isolation leg 102 supported by the marble vibration isolation table 101. The air floating vibration isolation leg 102 effectively reduces the vibration of the surrounding environment. The impact of the measurement. The power source 14 is connected to the main control computer 11, and the main control computer 11 is also connected to the air floating turntable 3, the two-dimensional moving table 5, the T rotating table 6 and the multi-wavelength interferometer 10, to the air floating turntable 3, two-dimensional motion The stages 5 and T send motion commands to the rotary table 6, while reading the measurement data of each probe in the multi-wave interferometer 10 in real time, and then performing analysis and calculation.
其中,气浮转台3、调平调心工作台4、二维运动台5和T向旋转台6均为市购的成品。Among them, the air floating turntable 3, the leveling and aligning work table 4, the two-dimensional moving table 5 and the T-direction rotating table 6 are all commercially available finished products.
参见图2和图3,多波长干涉仪10包括X向参考测头1001、Z向参考测头1002、T向参考测头1003、目标测头1004,其中,参见图2,X向参考测头1001和Z向参考测头1002分别固定连接于T向圆弧形反射镜9的第一侧壁901和第二侧壁902上,且X向参考测头1001与X向 参考测头反射镜7相对,Z向参考测头1002与Z向参考测头反射镜8相对,参见图3,T向参考测头1003和目标测头1004背向连接,且通过第二悬臂梁13与T向旋转台6固定连接,参见图2,T向参考测头1003与T向圆弧形反射镜9的内弧面相对。2 and 3, the multi-wavelength interferometer 10 includes an X-directed reference probe 1001, a Z-directed reference probe 1002, a T-directed reference probe 1003, and a target probe 1004. Referring to FIG. 2, an X-directed reference probe The 1001 and Z-direction reference probes 1002 are fixedly coupled to the first side wall 901 and the second side wall 902 of the circular arc-shaped mirror 9 respectively, and the X-direction reference probes 1001 and X-directions Referring to the probe mirror 7, the Z-direction reference probe 1002 is opposed to the Z-reference probe mirror 8, see FIG. 3, the T-reference probe 1003 and the target probe 1004 are connected back, and through the second cantilever beam 13 is fixedly connected to the T to the rotary table 6, see Fig. 2, and the T-direction reference probe 1003 is opposed to the inner arc surface of the circular arc mirror 9.
为了降低环境对于该装置测量的影响,在本实施方案中,参见图1,将基座1设计为包括:大理石隔振台101以及用于所述大理石隔振台101支撑的气浮隔振腿102。In order to reduce the influence of the environment on the measurement of the device, in the present embodiment, referring to FIG. 1, the base 1 is designed to include: a marble vibration isolation table 101 and an air floating vibration isolation leg for supporting the marble vibration isolation table 101. 102.
在本实施方案中,T向圆弧形反射镜9为圆心角为120°的弧形镜,且弧形镜的圆度<1μm,反射率>95%。In the present embodiment, the T-direction circular mirror 9 is an arc mirror having a central angle of 120°, and the circular mirror has a roundness of <1 μm and a reflectance of >95%.
如图2所示,1002为Z向参考测头,焦距200mm,从Z向参考测头1002出射的多波长光束垂直入射在长条Z向参考测头反射镜8上并被反射回来形成干涉,产生载频信号,通过移相算法得到Z向的位移量并发送到主控计算机11中。同理,1001为X向参考测头,焦距250mm,从X向参考测头1001出射的多波长光束被长条X向参考测头反射镜7反射回来形成干涉,产生载频信号,通过移相算法得到X向的位移量并发送到主控计算机11中。1003为T向参考测头,焦距10mm,从T向参考测头1003出射的多波长光束垂直入射在T向圆弧形反射镜9上并被反射回来形成干涉,产生载频信号,通过移相算法得到T向参考测头1003到弧形反射镜的径向位移量并发送到主控计算机11中。1004为目标测头,焦距约2.7mm,从目标测头1004出射的多波长光束垂直入射待测面并被反射回去产生干涉,产生载频信号,通过移相算法得到目标测头到待测面的距离并发送到主控计算机中。As shown in FIG. 2, 1002 is a Z-direction reference probe with a focal length of 200 mm, and a multi-wavelength beam emitted from the Z-to-reference probe 1002 is vertically incident on the long Z-directed reference probe 8 and reflected back to form an interference. The carrier frequency signal is generated, and the displacement amount in the Z direction is obtained by the phase shift algorithm and sent to the host computer 11. Similarly, 1001 is an X-direction reference probe with a focal length of 250 mm. The multi-wavelength beam emitted from the X to the reference probe 1001 is reflected by the strip X to the reference probe mirror 7 to form an interference, and a carrier frequency signal is generated. The algorithm obtains the amount of displacement in the X direction and sends it to the host computer 11. 1003 is a T-direction reference probe with a focal length of 10 mm. The multi-wavelength beam emitted from T to the reference probe 1003 is perpendicularly incident on the T-direction circular mirror 9 and reflected back to form an interference, generating a carrier frequency signal, by phase shifting. The algorithm obtains the radial displacement of the T-direct reference probe 1003 to the curved mirror and sends it to the host computer 11. 1004 is the target probe with a focal length of about 2.7 mm. The multi-wavelength beam emitted from the target probe 1004 is perpendicularly incident on the surface to be measured and reflected back to generate interference, and a carrier frequency signal is generated, and the target probe is obtained by the phase shift algorithm to the surface to be tested. The distance is sent to the master computer.
如图3所示,Z向参考测头1002及T向圆弧形反射镜9通过第一悬臂梁12固定在二维运动台5上,T向参考测头1003及目标测头1004则通过第二悬臂梁13固定在T向旋转台6上,而T向旋转台6又被固 定在二维运动台5上。因此,当二维运动台5发生平移运动时,所有的测头都随之发生平移运动,与此同时,T向旋转台6还可以使目标测头1004及T向参考测头1003产生旋转运动,从而使目标测头1004到待测面的距离维持恒定。这种平移与旋转的同步进行是实现目标测头到待测面距离不变,光强不变的基本保证,也是实现未知非球面表面矢高的高精度扫描的前提。As shown in FIG. 3, the Z-direction reference probe 1002 and the T-direction circular mirror 9 are fixed to the two-dimensional motion stage 5 through the first cantilever beam 12, and the T-direction reference probe 1003 and the target probe 1004 pass the first The two cantilever beams 13 are fixed on the T-direction rotating table 6, and the T-direction rotating table 6 is solidified again. It is set on the two-dimensional exercise table 5. Therefore, when the two-dimensional motion table 5 undergoes a translational motion, all of the probes undergo a translational motion, and at the same time, the T-direction rotary table 6 can also cause the target probes 1004 and T to generate a rotational motion to the reference probe 1003. Thus, the distance of the target probe 1004 to the surface to be measured is maintained constant. The synchronization of the translation and the rotation is the basic guarantee for the constant distance between the target probe and the surface to be measured, and the light intensity is constant, and is also a prerequisite for realizing high-precision scanning of the unknown aspheric surface.
如图4所示,在对待测非球面面形进行扫描测试时,目标测头1004始终垂直于被测表面。测头的运动是沿着非球面矢高面给出的矢高切线方向进行的,目标测头距离待测面表面的距离稍大于焦距。这是因为焦点处光斑直径为4μm,容易受灰尘颗粒及表面瑕疵的干扰,因此,测量点偏离焦点位置,增大了测量光斑的直径,提高了测头抗环境干扰的能力。设定好径向及圆周向的采样间隔,目标测头沿着X,Z及T向运动时,气浮转台3同步发生旋转运动,最终扫描完待测面的整个通光口径区域。As shown in FIG. 4, when the aspherical surface to be tested is subjected to a scanning test, the target probe 1004 is always perpendicular to the surface to be measured. The motion of the probe is performed along the tangential direction of the azimuth of the aspherical plane, and the distance of the target probe from the surface of the surface to be measured is slightly larger than the focal length. This is because the spot diameter at the focus is 4 μm, which is easily disturbed by dust particles and surface flaws. Therefore, the measurement point deviates from the focus position, which increases the diameter of the measurement spot and improves the ability of the probe to resist environmental interference. The radial and circumferential sampling interval is set. When the target probe moves along the X, Z and T directions, the air floating turntable 3 synchronously rotates, and finally scans the entire clear aperture area of the surface to be tested.
如图5所示,当目标测头1004位于非球面顶点P0(x0,y0,t0)时,光强大小为I0,此处目标测头1004的光轴与气浮转台3的转轴重合,目标测头1004到待测面的距离为L,略大于测头焦距f0,沿X轴方向运动dxi的小量到达Pi点,此时的光强为Ii,保持当前X,Z位置不变,转动目标测头1004,找到光强最大值时对应的旋转角ti,认为此角度下测头垂直于待测面。然后通过合理控制目标测头1004在X向和Z向的步进量,使目标测头1004始终沿着ti倾斜角方向接近或远离待测面运动。根据光强值由大变小的趋势,找到光强值为I0时的位置,此时Pi点坐标为(xi,zi,ti)。依此法继续移动目标测头1004直至待测面的边缘,从而 得到一系列的采样点的坐标。将得到的采样点的坐标,通过最小二乘法拟合,即可计算得到非球面的顶点曲率半径,二次项系数及高次项系数等几何参数。As shown in FIG. 5, when the target probe 1004 is located at the aspherical vertex P 0 (x 0 , y 0 , t 0 ), the light intensity is I 0 , where the optical axis of the target probe 1004 and the air float table 3 The rotation axes coincide, the distance from the target probe 1004 to the surface to be measured is L, which is slightly larger than the focal length f 0 of the probe, and a small amount of motion dx i along the X-axis direction reaches the point P i , and the light intensity at this time is I i , The current X, Z position is unchanged, the target probe 1004 is rotated, and the corresponding rotation angle t i is found when the light intensity is maximum. It is considered that the probe is perpendicular to the surface to be tested at this angle. Then, by properly controlling the step amount of the target probe 1004 in the X direction and the Z direction, the target probe 1004 is always moved toward or away from the surface to be measured along the tilt angle of t i . According to the trend that the light intensity value changes from large to small, the position where the light intensity value is I 0 is found, and the coordinates of the point P i are (x i , z i , t i ). According to this method, the target probe 1004 is continuously moved to the edge of the surface to be tested, thereby obtaining coordinates of a series of sampling points. By calculating the coordinates of the obtained sampling points by the least squares method, the geometric parameters such as the radius of curvature of the aspherical surface, the quadratic coefficient and the high-order coefficient can be calculated.
上述各个方案中的旋转对称未知非球面面形误差的测量装置,适用于中心无孔的旋转对称抛光非球面或锥面的面形测量,其具体的测量过程为:The measuring device for the rotationally symmetric unknown aspherical surface shape error in each of the above solutions is suitable for the surface measurement of the non-spherical or non-spherical rotationally symmetric aspheric or tapered surface. The specific measurement process is as follows:
步骤i:将待测非球面安装在调平调心工作台4上,旋转待测非球面,通过目测将待测非球面光轴尽量与气浮转台3的转轴调一致,再次旋转气浮转台3,然后利用精度1μm的杠杆表,测量非球面的偏心量,利用垂直于非球面表面的多波长干涉仪10测量非球面的倾斜,通过多次调整气浮转台3的偏心和倾斜使非球面的光轴与转轴重合。Step i: mounting the aspheric surface to be tested on the leveling and aligning worktable 4, rotating the aspherical surface to be tested, and visually adjusting the aspherical optical axis to be measured to coincide with the rotating shaft of the air floating turret 3, and rotating the air floating turret again. 3. Then, using an L1 table with an accuracy of 1 μm, the amount of eccentricity of the aspherical surface is measured, and the inclination of the aspherical surface is measured by the multi-wavelength interferometer 10 perpendicular to the aspherical surface, and the aspherical surface is adjusted by adjusting the eccentricity and inclination of the air-floating turntable 3 a plurality of times. The optical axis coincides with the axis of rotation.
步骤ii:将多波长干涉仪10的目标测头1004置于非球面顶点位置且过光轴,从目标测头1004出射的光垂直入射非球面表面,目标测头1004到非球面的距离约2.7mm,记录此时目标测头距离非球面表面的精确距离以及光强值。移动目标测头1004至偏离顶点1/8口径处,调整目标测头1004的空间坐标(x,z,t),使目标测头1004到非球面的距离及光强值与顶点位置处一致,以此点为起始点,沿着接近顶点方向进行逐点扫描,直至扫描完通光口径范围,在整个扫描过程中保持目标测头1004到非球面表面的距离及光强值不变。Step ii: placing the target probe 1004 of the multi-wavelength interferometer 10 at the aspherical vertex position and passing the optical axis. The light emitted from the target probe 1004 is perpendicularly incident on the aspheric surface, and the distance from the target probe 1004 to the aspheric surface is about 2.7. Mm, record the precise distance and intensity value of the target probe from the aspheric surface at this time. Moving the target probe 1004 to the 1/8 diameter of the apex, adjusting the spatial coordinates (x, z, t) of the target probe 1004, so that the distance from the target probe 1004 to the aspheric surface and the light intensity value coincide with the apex position. Starting from this point, the point-by-point scanning is performed along the direction of the vertex until the range of the aperture is scanned, and the distance from the target probe 1004 to the aspheric surface and the intensity value are kept constant throughout the scanning process.
步骤iii:根据非球面公式,利用最小二乘拟合法将测量得到的多点采样数据进行数据处理和求解,得到非球面的几何参数。将计算得到的非球面几何参数输入测量软件中,在软件的控制下,对整个非球面进行逐点扫描,再将扫描得到的数据与理想非球面比较,得到非球面面形误差,从而完成非球面面形测量。Step iii: According to the aspherical formula, the measured multi-point sampling data is processed and solved by the least squares fitting method to obtain geometric parameters of the aspheric surface. The calculated aspherical geometric parameters are input into the measurement software. Under the control of the software, the whole aspheric surface is scanned point by point, and the scanned data is compared with the ideal aspherical surface to obtain an aspherical surface shape error, thereby completing the non-spherical Spherical surface measurement.
具体测量步骤是: The specific measurement steps are:
首先,给测量装置上电,打开相应的测量软件,待系统稳定后,将待测非球面15置于调平调心工作台4上。将一杠杆表表针与非球面外缘相接触,转动气浮转台3,通过调节非球面的偏心,最后使非球面旋转一周,杠杆表的读数在微米量级变化。将目标测头1004置于待测非球面15上方,该位置距离中心位置约3/4口径处,通过二维运动台5及T向旋转台6的调整,使目标测头1004垂直于待测面。再次转动气浮转台3,通过调整待测非球面的倾斜,使待测非球面旋转一周,目标测头1004到被测非球面距离的变化量在微米量级。综合考虑杠杆表及目标测头的读数,反复调整非球面的偏心及倾斜,最后使非球面旋转一周,杠杆表及目标测头读数的变化均小于1μm。此时可以认为非球面光轴与转轴重合。First, the measuring device is powered on, and the corresponding measuring software is turned on. After the system is stabilized, the aspheric surface 15 to be tested is placed on the leveling and aligning table 4. The lever of the lever is brought into contact with the outer edge of the aspherical surface, the air float table 3 is rotated, the aspherical surface is rotated by adjusting the eccentricity of the aspheric surface, and the reading of the lever table is changed in the order of micrometers. The target probe 1004 is placed above the aspheric surface 15 to be tested, and the position is about 3/4 of the diameter from the center position. The adjustment of the two-dimensional motion table 5 and the T to the rotary table 6 makes the target probe 1004 perpendicular to the test. surface. Turning the air float table 3 again, by adjusting the tilt of the aspheric surface to be tested, the aspheric surface to be tested is rotated one revolution, and the amount of change of the target probe 1004 to the measured aspherical surface is on the order of micrometers. Considering the readings of the lever table and the target probe, the eccentricity and tilt of the aspheric surface are repeatedly adjusted. Finally, the aspheric surface is rotated for one week, and the change of the reading of the lever table and the target probe is less than 1 μm. At this time, it can be considered that the aspherical optical axis coincides with the rotating shaft.
然后将目标测头1004移至待测非球面1004顶点位置上方,并使目标测头1004的光轴与气浮转台3转轴重合,目标测头1004到待测非球面1004的距离略大于焦距f,记录此时目标测头1004的位置坐标P0(x0,z0,t0),及光强大小I0。其中x0的值由X向参考测头1001给出,z0的值由Z向参考测头1002给出,t0的值由T向参考测头1003给出,I0的值由目标测头1004给出。Then, the target probe 1004 is moved above the vertex position of the aspheric surface 1004 to be tested, and the optical axis of the target probe 1004 coincides with the axis of rotation of the air floating turntable 3. The distance of the target probe 1004 to the aspheric surface 1004 to be tested is slightly larger than the focal length f. The position coordinates P 0 (x 0 , z 0 , t 0 ) of the target probe 1004 at this time, and the light intensity I 0 are recorded. Wherein the value of x 0 is given by X to the reference probe 1001, the value of z 0 is given by the Z to the reference probe 1002, the value of t 0 is given by the reference probe 1003, and the value of I 0 is determined by the target. Head 1004 is given.
目标测头1004沿着X轴远离中心位置的方向运动一小段距离dx后到达P1点,此时目标测头接收到的光强值为I1。保持当前X,Z位置不变,转动目标测头,找到光强最大值时对应的旋转角t1,认为此角度下目标测头垂直于待测面。严格控制二维运动台X向和Z向的步进量,使测头始终沿着倾斜角t1方向接近或远离待测面。当光强值由大变小时,在这附近即可找到光强值为I0时的位置,记录此时测头的位置坐标 P1(x1,z1,t1)。依此法继续移动测头直至待测面的边缘,从而得到一系列的采样点的坐标
Figure PCTCN2016108999-appb-000003
其中N为总采样点数。
After the movement target probe 1004 short distance dx along an X-axis direction away from the center position P 1 reaches the point where the probe is received target light intensity value I 1. Keep the current X, Z position unchanged, turn the target probe, and find the corresponding rotation angle t 1 when the light intensity is maximum. It is considered that the target probe is perpendicular to the surface to be tested at this angle. Strict control of dimensional movement table and the X-direction stepping amount Z direction, so that the inclination angle of the probe always t 1 along a direction close to or away from the measurement surface. When the light intensity value changes from large to small, the position where the light intensity value is I 0 can be found in the vicinity, and the position coordinate P 1 (x 1 , z 1 , t 1 ) of the probe at this time is recorded. According to this method, the probe is continuously moved to the edge of the surface to be measured, thereby obtaining a series of coordinates of the sampling points.
Figure PCTCN2016108999-appb-000003
Where N is the total number of sampling points.
非球面方程表达式被写为:The aspheric equation expression is written as:
Figure PCTCN2016108999-appb-000004
Figure PCTCN2016108999-appb-000004
其中,z为非球面的矢高,c=1/R0为顶点曲率,R0为顶点曲率半径,K为二次曲面常数,ρ为球面的径向坐标,An为高次项系数,M为非球面系数的总阶数。将采样得到的位置坐标∑Pi(xi,zi,ti)的x,z向的值代入非球面方程中并取平方和得到下式:Where z is the azimuth of the aspherical surface, c=1/R 0 is the curvature of the vertex, R 0 is the radius of curvature of the vertex, K is the quadratic constant, ρ is the radial coordinate of the sphere, and A n is the coefficient of the high order term, M Is the total order of the aspheric coefficients. Substituting the values of the x, z directions of the sampled position coordinates ∑P i (x i , z i , t i ) into the aspheric equation and taking the sum of squares to obtain the following formula:
Figure PCTCN2016108999-appb-000005
Figure PCTCN2016108999-appb-000005
当上式的值最小时,计算得到非球面的顶点曲率半径,二次项系数及高次项系数等几何参数,该计算方法即为最小二乘法拟合法。When the value of the above formula is the smallest, the geometric parameters such as the radius of curvature of the aspherical surface, the quadratic coefficient and the high-order coefficient are calculated. The calculation method is the least squares fitting method.
最后,将计算得到的非球面几何参数逐一输入到测量软件中计算得到待测非球面的理想矢高面,主控计算机11发出指令使目标测头垂直非球面表面,并从偏离光轴1/8通光口径的距离处开始扫描,直至测头运动至非球面边缘。扫描过程中气浮转台3始终以一恒定速率转动,该速率由采样间隔决定,扫描完成后,将所测得的整个面的测量矢高面与理想矢高面比较,即可获得非球面面形误差,从而完成旋转对称未知非球面面形的测量。Finally, the calculated aspherical geometric parameters are input into the measurement software one by one to calculate the ideal vector height surface of the aspheric surface to be tested, and the main control computer 11 issues an instruction to make the target probe perpendicular to the aspherical surface, and deviates from the optical axis by 1/8. The distance from the aperture is scanned until the probe moves to the aspherical edge. During the scanning process, the air-floating turntable 3 is always rotated at a constant rate, which is determined by the sampling interval. After the scanning is completed, the measured sagittal plane of the entire surface is compared with the ideal vector height surface to obtain an aspherical surface error. , thereby completing the measurement of the rotationally symmetric unknown aspherical surface shape.
为了实现高精度测量,还需要完成以下工作:In order to achieve high-precision measurements, you also need to do the following:
二维运动台5中X向、Z向运动机构直线度误差标定,Z向参考测头与转轴夹角的标定,X向参考测头与转轴垂直度的标定。T向旋转台 与T向圆弧形反射镜的圆度误差,目标测头光轴相对转轴的偏心量标定等。In the two-dimensional motion table 5, the X-direction and Z-direction motion mechanism straightness error calibration, the Z-direction reference probe and the rotation axis angle are calibrated, and the X-direction reference probe and the rotation axis perpendicularity are calibrated. T-direction rotary table The roundness error with the T-direction circular mirror, the eccentricity of the target probe optical axis with respect to the rotation axis, and the like.
光学测量传感器容易受环境的温度、湿度、压强以及气流扰动的影响,温度、湿度、压强的变化使空气折射率发生变化,气流扰动引起空气折射率的分布不均匀。因此,除了对测量环境的温度、湿度、压强进行严格控制外,还增加了防护罩降低气流扰动的影响。The optical measuring sensor is easily affected by the temperature, humidity, pressure and airflow disturbance of the environment. The change of temperature, humidity and pressure changes the refractive index of the air, and the airflow disturbance causes the distribution of the refractive index of the air to be uneven. Therefore, in addition to strict control of the temperature, humidity, and pressure of the measurement environment, a protective cover is added to reduce the influence of airflow disturbance.
以上所述仅为本案的优选实施例而已,并不用于限制本案,对于本领域的技术人员来说,本案可以有各种更改和变化。凡在本案的精神和原则之内,所作的任何修改、等同替换、改进等,均应包含在本案的保护范围之内。 The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention, and various changes and modifications may be made by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of this case shall be included in the scope of protection of this case.

Claims (17)

  1. 一种旋转对称未知非球面面形误差的测量方法,包括以下步骤:A method for measuring a rotationally symmetric unknown aspherical surface shape error, comprising the following steps:
    使用干涉仪沿待测非球面表面一经线方向进行逐点扫描采样,获得一组关于待测非球面空间坐标的数组L(x,z,t),其中,所述数组L(x,z,t)中包含待测非球面的顶点空间坐标,x、z、t分别是X向、Z向和T向的坐标,X向一个水平方向、Z向为竖直方向,T向是绕XZ平面的法线的旋转方向;Using an interferometer to perform point-by-point scanning sampling along the aspherical surface of the aspherical surface to be tested, obtaining a set of arrays L(x, z, t) with respect to the aspherical space coordinates to be tested, wherein the array L(x, z, t) contains the vertex space coordinates of the aspheric surface to be tested, and x, z, and t are the coordinates of the X direction, the Z direction, and the T direction, respectively, X is a horizontal direction, the Z direction is a vertical direction, and the T direction is a XZ plane. The direction of rotation of the normal;
    依据所述数组L(x,z,t),利用最小二乘拟合法计算获得所述待测非球面的顶点曲率半径R0、二次项系数K和高次项系数AnCalculating, according to the array L(x, z, t), obtaining a vertex curvature radius R 0 , a quadratic coefficient K and a high-order coefficient A n of the aspheric surface to be tested by using a least squares fitting method;
    依据所述待测非球面的顶点曲率半径R0、二次项系数K和高次项系数An,计算获得所述待测非球面的理想矢高面;Obtaining an ideal sagittal plane of the aspheric surface to be tested according to a vertex curvature radius R 0 , a quadratic coefficient K, and a high-order coefficient A n of the aspheric surface to be tested;
    使用干涉仪对所述待测非球面整个表面进行逐点扫描采样,获得所述待测非球面的测量矢高面;Performing point-by-point scanning sampling on the entire surface of the aspheric surface to be tested using an interferometer to obtain a measured sagittal plane of the aspheric surface to be tested;
    将所述待测非球面的测量矢高面与所述待测非球面的理想矢高面进行比较,获得所述待测非球面的面形误差。Comparing the measured sagittal plane of the aspheric surface to be tested with the ideal sagittal plane of the aspheric surface to be tested, and obtaining a surface shape error of the aspheric surface to be tested.
  2. 按照权利要求1所述的旋转对称未知非球面面形误差的测量方法,依据所述数组L(x,z,t),利用最小二乘拟合法计算获得所述待测非球面的顶点曲率半径R0、二次项系数K和高次项系数An步骤,具体为:The method for measuring a rotationally symmetric unknown aspherical surface shape error according to claim 1, wherein the radius of curvature of the vertex of the aspheric surface to be tested is obtained by using a least squares fitting method according to the array L(x, z, t) The steps of R 0 , the quadratic coefficient K and the high-order coefficient A n are specifically:
    将所述数组L(x,z,t)中各采样点对应的x向和z向值代入到公式(a)中,当公式(a)的值最小时,计算得到待测非球面相应的顶点曲率半径R0、二次项系数K和高次项系数AnSubstituting the x-direction and z-direction values corresponding to each sampling point in the array L(x, z, t) into the formula (a), when the value of the formula (a) is the smallest, calculating the corresponding aspheric surface to be tested Vertex curvature radius R 0 , quadratic coefficient K and high order coefficient A n ;
    所述公式(a)具体为, The formula (a) is specifically
    Figure PCTCN2016108999-appb-100001
    Figure PCTCN2016108999-appb-100001
    其中,N为采样点个数,c=1/R0为顶点曲率,R0为顶点曲率半径,K为二次项系数,M为非球面系数的总阶数,An为高次项系数。Where N is the number of sampling points, c=1/R 0 is the curvature of the vertex, R 0 is the radius of curvature of the vertex, K is the coefficient of the quadratic term, M is the total order of the aspherical coefficients, and A n is the coefficient of the high order term .
  3. 按照权利要求1所述的旋转对称未知非球面面形误差的测量方法,依据所述待测非球面的顶点曲率半径R0、二次项系数K和高次项系数An,计算获得所述待测非球面的理想矢高面公式为:The method for measuring a rotationally symmetric unknown aspherical surface shape error according to claim 1, wherein the calculation is obtained according to a vertex curvature radius R 0 , a quadratic coefficient K, and a high-order coefficient A n of the aspheric surface to be measured The ideal sagittal plane formula for the aspheric surface to be tested is:
    Figure PCTCN2016108999-appb-100002
    Figure PCTCN2016108999-appb-100002
    其中,z为非球面的矢高,c=1/R0为顶点曲率,R0为顶点曲率半径,K为二次项系数,ρ为非球面的径向坐标,M为非球面系数的总阶数,An为高次项系数。Wherein, z non-spherical high vector, c = 1 / R 0 is the vertex curvature, R 0 is the vertex radius of curvature, K is the quadratic coefficient, ρ is non-spherical radial coordinate, M total non-order spherical coefficient Number, A n is the high order coefficient.
  4. 按照权利要求1所述的旋转对称未知非球面面形误差的测量方法,干涉仪进行扫描采样过程中,干涉仪的测量头始终保持与待测非球面垂直,且测量头到待测非球面的距离保持恒定。The method for measuring a rotationally symmetric unknown aspherical surface shape error according to claim 1, wherein during the scanning and sampling process of the interferometer, the measuring head of the interferometer is always perpendicular to the aspheric surface to be tested, and the measuring head is to the aspheric surface to be tested. The distance remains constant.
  5. 按照权利要求4所述的旋转对称未知非球面面形误差的测量方法,所述测量头到被测非球面的距离大于测量头的焦距。The method for measuring a rotationally symmetric unknown aspherical surface shape error according to claim 4, wherein the distance from the measuring head to the measured aspheric surface is greater than the focal length of the measuring head.
  6. 一种旋转对称未知非球面面形误差的测量装置,用于执行权利要求1至5中任一项所述的旋转对称未知非球面面形误差的测量方法。A measuring device for rotationally symmetric unknown aspherical surface shape error for performing a method for measuring a rotationally symmetric unknown aspherical surface shape error according to any one of claims 1 to 5.
  7. 根据权利要求6所述的旋转对称未知非球面面形误差的测量装置,包括干涉仪致动装置,用于使干涉仪的目标测头对待测物体的未知非球面进行扫描,并在扫描过程中使所述目标测头始终垂直于所述未知非球面且保持固定的距离。The apparatus for measuring a rotationally symmetric unknown aspherical surface shape error according to claim 6, comprising an interferometer actuating means for causing the target probe of the interferometer to scan an unknown aspheric surface of the object to be measured, and during the scanning process The target probe is always perpendicular to the unknown aspheric surface and maintained at a fixed distance.
  8. 根据权利要求7所述的旋转对称未知非球面面形误差的测量装 置,还包括干涉仪空间位置检测装置,用于在所述扫描过程中实时获得所述目标测头的空间位置。The measuring device for rotationally symmetric unknown aspherical surface shape error according to claim 7 The apparatus further includes an interferometer spatial position detecting device for obtaining a spatial position of the target probe in real time during the scanning process.
  9. 根据权利要求8所述的旋转对称未知非球面面形误差的测量装置,还包括处理装置,用于获取所述目标测头的空间位置以计算待测非球面空间坐标的数组及执行权利要求1至5中任一项所述的旋转对称未知非球面面形误差的测量方法。The apparatus for measuring rotationally symmetric unknown aspherical surface shape error according to claim 8, further comprising processing means for acquiring a spatial position of said target probe to calculate an array of aspherical space coordinates to be measured and performing claim 1 A method of measuring a rotationally symmetric unknown aspherical surface shape error as described in any one of 5.
  10. 根据权利要求8所述的旋转对称未知非球面面形误差的测量装置,所述空间位置指X向、Z向和T向的坐标,所述X向一个水平方向、Z向为竖直方向,T向是绕XZ平面的法线的旋转方向。The apparatus for measuring a rotationally symmetric unknown aspherical surface shape error according to claim 8, wherein the spatial position is a coordinate of an X direction, a Z direction, and a T direction, the X direction being a horizontal direction and the Z direction being a vertical direction, The T direction is the direction of rotation about the normal to the XZ plane.
  11. 根据权利要求10所述的旋转对称未知非球面面形误差的测量装置,所述干涉仪致动装置包括二维运动台(5)和T向旋转台(6),A measuring apparatus for rotationally symmetric unknown aspherical surface shape error according to claim 10, said interferometer actuating means comprising a two-dimensional moving table (5) and a T-direction rotating table (6),
    所述二维运动台(5)其能够在X方向和Z方向上作平移;The two-dimensional motion stage (5) is capable of translation in the X direction and the Z direction;
    T向旋转台(6),固定于所述二维运动台(5)上,其上固定所述二涉仪。The T-direction rotating table (6) is fixed to the two-dimensional moving table (5) on which the two instruments are fixed.
  12. 根据权利要求11所述的旋转对称未知非球面面形误差的测量装置,所述干涉仪空间位置检测装置包括X向参考测头反射镜(7)、Z向参考测头反射镜(8)、T向圆弧形反射镜(9);The apparatus for measuring a rotationally symmetric unknown aspherical surface shape error according to claim 11, wherein said interferometer spatial position detecting means comprises an X-directed reference probe (7), a Z-directed reference probe (8), T-direction circular mirror (9);
    所述干涉仪(10)还包括X向参考测头(1001)、Z向参考测头(1002)、T向参考测头(1003);The interferometer (10) further includes an X-directed reference probe (1001), a Z-directed reference probe (1002), and a T-directed reference probe (1003);
    所述X向参考测头(1001)与所述X向参考测头反射镜(7)相对,所述Z向参考测头(1002)与所述Z向参考测头反射镜(8)相对,所述T向参考测头(1003)和目标测头(1004)背向连接,且各参考测头均与所述T向旋转台(6)固定连接,所述T向参考测头(1003)与所述T向圆弧形反射镜(9)的内弧面相对。The X-directed reference probe (1001) is opposite to the X-directed reference probe (7), and the Z-directed reference probe (1002) is opposite to the Z-directed reference probe (8). The T-direction reference probe (1003) and the target probe (1004) are connected in a back direction, and each reference probe is fixedly connected to the T-direction rotary table (6), and the T-direction reference probe (1003) Opposite the inner arc surface of the T-arc mirror (9).
  13. 根据权利要求12所述的旋转对称未知非球面面形误差的测量 装置,还包括转台(3),其旋转面为水平面,其上用于放置具有未知非球面的待测物体。Measurement of rotationally symmetric unknown aspherical surface shape error according to claim The apparatus further includes a turntable (3) whose rotating surface is a horizontal plane on which an object to be tested having an unknown aspherical surface is placed.
  14. 根据权利要求13所述的旋转对称未知非球面面形误差的测量装置,还包括安装平台,所述转台、二维运动台(5)、X向参考测头(1001)、Z向参考测头(1002)均安装在安装平台上。The apparatus for measuring rotationally symmetric unknown aspherical surface shape error according to claim 13, further comprising a mounting platform, the turntable, the two-dimensional motion stage (5), the X-direction reference probe (1001), and the Z-direction reference probe. (1002) are all installed on the installation platform.
  15. 根据权利要求14所述的旋转对称未知非球面面形误差的测量装置,所述安装平台包括基座(1)和跨设于所述基座(1)的上方的龙门吊(2),龙门吊(2)包括横梁(21)和设置于所述横梁(21)下方的支架(22);The apparatus for measuring a rotationally symmetric unknown aspherical surface error according to claim 14, wherein the mounting platform comprises a base (1) and a gantry crane (2) spanning above the base (1), the gantry crane ( 2) comprising a beam (21) and a bracket (22) disposed below the beam (21);
    所述转台(3)位于所述龙门吊(2)的下方,安装于所述基座(1)的上表面;The turntable (3) is located below the gantry crane (2) and is mounted on an upper surface of the base (1);
    所述X向参考测头反射镜(7)固定设置于所述龙门吊(2)的一侧支架(22)上;The X-direction reference probe mirror (7) is fixedly disposed on one side bracket (22) of the gantry crane (2);
    所述Z向参考测头反射镜(8)固定设置于所述龙门吊(2)的横梁(21)上,且与所述X向参考测头反射镜(7)垂直。The Z-directed reference probe (8) is fixedly disposed on the beam (21) of the gantry crane (2) and perpendicular to the X-direction reference probe (7).
  16. 根据权利要求15所述的旋转对称未知非球面面形误差的测量装置,还包括调平调心工作台(4),其固定安装于所述气浮转台(3)的上方。The apparatus for measuring a rotationally symmetric unknown aspherical surface error according to claim 15, further comprising a leveling and aligning table (4) fixedly mounted above said air floating turntable (3).
  17. 按照权利要求16所述旋转对称未知非球面面形误差的测量装置,所述基座(1)包括大理石隔振台(101)以及用于所述大理石隔振台(101)支撑的气浮隔振腿(102)。 A measuring apparatus for rotationally symmetric unknown aspherical surface shape error according to claim 16, said base (1) comprising a marble vibration isolating table (101) and an air floating partition for supporting the marble vibration isolating table (101) Vibrate the leg (102).
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