WO2017107547A1 - 精密转台摆角测量方法和装置 - Google Patents

精密转台摆角测量方法和装置 Download PDF

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WO2017107547A1
WO2017107547A1 PCT/CN2016/097583 CN2016097583W WO2017107547A1 WO 2017107547 A1 WO2017107547 A1 WO 2017107547A1 CN 2016097583 W CN2016097583 W CN 2016097583W WO 2017107547 A1 WO2017107547 A1 WO 2017107547A1
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flat crystal
coefficient
standard flat
interferometer
turntable
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PCT/CN2016/097583
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English (en)
French (fr)
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苗二龙
武东城
苏东奇
高松涛
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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Publication of WO2017107547A1 publication Critical patent/WO2017107547A1/zh

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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B11/00—Measuring arrangements characterised by the use of optical techniques
    • G01B11/26—Measuring arrangements characterised by the use of optical techniques for measuring angles or tapers; for testing the alignment of axes
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B11/00—Measuring arrangements characterised by the use of optical techniques
    • G01B11/24—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B11/00—Measuring arrangements characterised by the use of optical techniques
    • G01B11/24—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures
    • G01B11/2441—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures using interferometry

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  • the invention belongs to the field of optical detection, and in particular relates to a method for measuring a swing angle of a precision turntable and a measuring device.
  • the precision turntable has a wide range of applications in instrumentation and manufacturing, and the shafting accuracy of the turntable is the key to measuring the precision of the turntable and one of the main indicators of the precision of the turntable.
  • the ideal turntable has only one degree of freedom of rotation about the Z axis.
  • Other linear motions along the X, Y, and Z directions and five degrees of freedom about the X and Y axes can be referred to as the axis error of the turntable.
  • the shafting error is that the other five degrees of freedom are generally converted into axial runout in the Z-axis direction, radial runout in the vertical direction of the Z-axis, and around the X, Y-axis when the turntable rotates. The swing.
  • Axial runout and radial runout can usually be placed in the center of the turntable using a standard ball.
  • the color difference sensor is used to measure the runout of the standard ball relative to the color difference sensor when the turntable is rotated.
  • the trigonometric function is used to fit the axial and radial runout of the turntable. .
  • the swinging of the turntable generally has two measurement methods. One is to use the standard cylinder to be placed in the center of the turntable, and to measure the jump of the upper and lower positions of the cylinder as the turntable rotates, and the measured jump and the length between the two positions can be calculated. The swing of the turntable.
  • Another method is to use a standard flat crystal, and use a collimator to measure the reflected angle of the reflected light during the rotation of the turret to obtain the turret angle.
  • These two methods rely heavily on the quality of the standard parts. For example, the roundness of the cylinder and the surface shape error of the standard flat crystal directly affect the measurement of the final swing angle. High-quality standard components are often difficult to manufacture and require regular calibration.
  • the present invention is intended to overcome at least one of the deficiencies in the prior art.
  • a precision turntable swing angle measuring method including the following steps:
  • Step 1 Fix the precision turntable on an interferometer five-dimensional adjustment table, and put the standard flat crystal Placed on a precision turntable, the reference surface is located directly below the interferometer, and a planar interference cavity is formed between the reference surface and the standard flat crystal;
  • Step 2 adjusting the position of the standard flat crystal by the five-dimensional adjustment stage of the interferometer, so that the collimated beam emitted by the interferometer forms a zero-strip interference between the reference surface and the standard flat crystal;
  • Step 3 Rotating the precision turntable, measuring 360°/n, measuring the interference fringes of the interference cavity formed by the standard flat crystal and the reference plane, and obtaining n sets of standard flat crystal faces, where n is a natural number greater than or equal to 2;
  • Step 4 Using the Zernike polynomial to fit the n sets of standard flat crystal shapes, respectively extract the second coefficient and the third coefficient of the n sets of Zernike polynomials;
  • Step 5 Synthesize and count the second coefficient and the third coefficient of the Zernike polynomial. After synthesis, the tilt angle of the flat crystal relative to the reference plane is obtained, and the tilt angle is calculated. The maximum value of the tilt angle is subtracted from the minimum value. Angular error.
  • a precision turret swing angle measuring apparatus including: an interferometer five-dimensional adjusting platform configured to fix a precision turret to be measured thereon for adjusting the precision turret to implement five Dimensional movement; standard flat crystal, configured to be placed on the precision turret; interferometer, including a reference plane directly below it, the reference plane above the standard flat, reference plane and the standard flat Forming a plane interference cavity, the interferometer is used to measure the interference fringes of the standard flat crystal in the plane interference cavity every 360°/n of the precision turntable, and obtain n sets of standard flat crystal faces, where n is greater than a natural number equal to 2; a processor for receiving a standard flat crystal shape measured by the interferometer, and fitting a planar shape of the n sets of standard flat and reference planes by using a Zernike polynomial, and counting a second term of the Zernike polynomial The coefficient and the third coefficient are then converted to the
  • the processor includes: a data acquiring unit: configured to receive a standard flat crystal shape measured by the interferometer; and a simulation unit: configured to fit n sets of standard flat crystal shapes by using a Zernike polynomial, respectively Extracting the second coefficient and the third coefficient of the n-group Zernike polynomial; statistical unit: synthesizing the second coefficient and the third coefficient of the Zernike polynomial and counting the resultant, and obtaining the tilt angle of the flat crystal relative to the reference plane after synthesis, and the statistical tilt angle , the maximum value of the tilt angle minus the minimum value is the tilt angle error of the turntable; output or display unit: output or display The swing angle error of the precision turntable.
  • a data acquiring unit configured to receive a standard flat crystal shape measured by the interferometer
  • a simulation unit configured to fit n sets of standard flat crystal shapes by using a Zernike polynomial, respectively Extracting the second coefficient and the third coefficient of the n-group Zernike polynomi
  • the interference cavity composed of the interferometer and the standard flat crystal is firstly subjected to the surface shape measurement, and the measured surface shape is fitted by the Zernike polynomial to obtain the tilt term, and the tilt change under different rotation angles can be counted. Get the swing angle error of the turntable.
  • the utility model has the advantages that the measurement accuracy of the interference surface shape is high, the angle measurement is converted into the surface shape measurement, and then the inclination of the flat crystal is obtained by fitting, which is not affected by the surface shape and the adjustment precision of the flat crystal and the reference surface.
  • the measurement accuracy greatly improves the detection accuracy due to the use of high-precision interference surface measurement, and the operation is simple, and does not depend on the measurement method of the accuracy of the standard parts.
  • FIG. 1 is a schematic diagram showing a measurement principle of a precision turret swing angle measuring method according to an exemplary embodiment of the present invention
  • FIG. 2 is a flow chart of a method for measuring a precision turret angle according to an exemplary embodiment of the present invention
  • FIG. 3 is a schematic diagram of a precision turret swing angle measuring device according to an exemplary embodiment of the present invention.
  • FIG. 4 is a block diagram of the processor of FIG.
  • the standard flat crystal is adjusted by the interferometer five-dimensional adjustment stage such that the reference surface forms a zero stripe parallel to the standard flat crystal, and the interferogram of the plane interference cavity in this state is measured to obtain a standard flat crystal plane shape.
  • the angle of the rotating air-floating table is 360°/n, and the standard flat surface shape is measured again.
  • n is a natural number greater than or equal to 2; the flat surface measured by Zernike polynomial fitting measurement Shape, extract the second and third items (X, Y).
  • the inclination term) coefficient is obtained by synthesizing and calculating the inclination angle of the flat crystal relative to the reference surface, and the statistically obtained inclination angle is obtained by subtracting the minimum value from the maximum value.
  • the method uses an interferometer to convert the angle measurement into a surface measurement, and extracts the tilt angle by the surface Zernike polynomial, and the detection precision is not affected by the accuracy and adjustment precision of the standard part, and the detection precision is high.
  • a precision turret swing angle measuring method includes the following steps:
  • the precision turntable 4 is fixed on an interferometer five-dimensional adjustment table 5, and the standard flat crystal 3 is placed on the precision turntable 4, the reference surface 2 is located directly below the interferometer 1, and between the reference surface 2 and the standard flat crystal 3 Forming a planar interference cavity;
  • step S1 the precision turntable 4 is fixed to an interferometer five-dimensional adjustment table 5 for achieving five-dimensional motion of the precision turntable 4 thereon by the interferometer five-dimensional adjustment table 5, the five-dimensional motion including along X,
  • the linear motion in the Y and Z directions and the five dimensions of the rotation around the X and Y axes can also be converted into axial runout in the Z-axis direction, radial runout in the vertical direction of the Z-axis, and around the X in the rotation of the turntable. , the swing of the Y axis. Therefore, the five-dimensional adjustment can be used to adjust the position of the standard flat crystal 3 on the precision turntable 4 to form a zero-strip interference in the interference cavity in the subsequent measurement step, that is, the standard flat crystal 3 and the reference surface 2 are in parallel positions.
  • the standard flat crystal 3 and the reference surface 2 should be disposed opposite each other.
  • Ben The invention is arranged in such a way that the standard flat crystal 3 is placed on the precision turntable 4, the reference surface 2 is located directly below the interferometer 1, and a planar interference cavity is formed between the reference surface 2 and the standard flat crystal 3.
  • the collimated beam emitted by the interferometer 1 passes through the reference plane 2, a part of it is reflected back to the interferometer by the reference plane 2, continues to propagate through the reference plane 2, and is reflected back by the standard flat crystal 3, and is reflected by the light reflected by the reference plane 2. Interference, forming interference fringes.
  • the reference surface 2 can select flat crystal, there is no special requirement for the error of the flat shape and the roundness of the flat crystal. After the measurement step, the final statistical result can eliminate the corresponding error, therefore, various flat crystals can be used.
  • the invention of the application can select flat crystal, there is no special requirement for the error of the flat shape and the roundness of the flat crystal.
  • step S2 by adjusting the interferometer five-dimensional adjustment stage 5, the position between the standard flat crystal 3 and the reference surface 2 is indirectly adjusted to form a zero stripe, and interference is generated. At this time, the interference pattern of the plane interference cavity in the state is measured. Thereby, a face shape of the standard flat crystal 3 is obtained.
  • step S3 a plurality of measurements of the standard flat crystal 3 surface shape are performed by rotating the precision turntable 4.
  • the interference fringes of the standard flat crystal 3 in the plane interference cavity can be measured every 360°/n, and the surface shape of the n sets of standard flat crystals 3 can be obtained, and n is a natural number greater than or equal to 2.
  • n the larger the value of n, the more statistical samples, the more accurate the result.
  • a preferred value of n can be 24, 72 or 100.
  • step S4 the surface shape of the standard flat crystal 3 is fitted using a Zernike polynomial.
  • a face shape is obtained for each measurement, and the tilt term can be extracted from the Zernike polynomial to obtain the tilt of the standard flat crystal with respect to the reference plane 2.
  • the change in the size of the tilt during the rotation is the turret angle error.
  • the power series expansion is usually used to describe the aberrations of the optical system. Since the Zernike polynomial and the form of the aberration polynomial observed in optical detection are consistent, it is often used to describe the wavefront characteristics.
  • optical expression surface function F( ⁇ , ⁇ ) of the standard flat crystal 3 in this embodiment can be fitted to the equation (1) by the Zernike polynomial:
  • a k is the fitting coefficient of the polynomial
  • k is an integer from 0 to ⁇
  • ⁇ and ⁇ are polar coordinate parameters
  • Z k ( ⁇ , ⁇ ) is a Zernike polynomial function, which can be expressed as equation (2):
  • R( ⁇ ) is a radial function (Radial Function), which is a k-th order polynomial of ⁇ ; and G k ( ⁇ ) is a continuous function with a period of 2 ⁇ radians.
  • Table 1 lists the top five items of the Zernike polynomial in the polar coordinate system:
  • the first term in Table 1 is a constant or a piston term, the coefficient of this term also represents the average optical path difference; and the second and third terms are the tilt terms in the X and Y directions, respectively ( Tilt terms), the fourth item represents focus. Therefore, extracting the second and third coefficient is the extraction of the oblique term in the X and Y directions.
  • step S5 a plurality of sets of tilt term errors in the X and Y directions are calculated.
  • the maximum value minus the minimum value is the rotational swing error of the precision turntable 4.
  • the embodiment of the present invention further provides a corresponding precision turret swing angle measuring device.
  • the measuring device may include:
  • the interferometer five-dimensional adjustment table 5 is configured to fix the precision turntable 4 to be measured thereon for adjusting the precision turntable 4 to realize five-dimensional direction motion; the five-dimensional direction includes linear motion along the X, Y, and Z directions And 5 dimensions that rotate around the X, Y axis.
  • the interferometer 1 comprises a reference surface 2 directly below it, said reference surface 2 being above said standard flat crystal 3, forming a planar interference cavity between the reference surface 2 and said standard flat crystal 3, said interferometer 1 For each rotation of the precision turntable 4, 360°/n, the interference fringes of the standard flat crystal 3 in the plane interference cavity are measured, and the surface shape of the n sets of standard flat crystals 3 is obtained, where n is a natural number greater than or equal to 2;
  • a processor 6 for receiving a surface shape of the standard flat crystal 3 measured by the interferometer 1, and fitting a set of standard flat crystal faces by a Zernike polynomial, and synthesizing a second coefficient and a third term of the Zernike polynomial The coefficient is then subtracted from the maximum value of the combined angle to the minimum value output as the rotational angle error of the precision turntable.
  • the processor 6 includes:
  • a data acquiring unit 601 configured to receive a surface shape of the standard flat crystal (3) measured by the interferometer 1;
  • the simulation unit 602 is configured to fit the n sets of standard flat crystal shapes by using a Zernike polynomial, and respectively extract the second coefficient and the third coefficient of the n sets of Zernike polynomials;
  • the statistic unit 603 synthesizes the second coefficient and the third coefficient of the Zernike polynomial, and statistically combines the angles of the n into the coefficients, and subtracts the minimum value from the maximum value into the rotational angle error of the precision turntable;
  • Output or display unit 604 outputs or displays a rotational swing error of the precision turntable.

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Abstract

一种精密转台摆角测量方法,包括：将精密转台（4）固定于一干涉仪五维调整台（5）上，将标准平晶（3）放置在精密转台（4）上，参考面（2）与标准平晶（3）之间形成平面干涉腔；通过干涉仪五维调整台（5）调节标准平晶（3）的位置，使得干涉仪（1）发出的光束在参考面（2）与标准平晶（3）之间形成零条纹干涉；旋转所述精密转台（4），获得n组标准平晶（3）的面形；利用Zernike多项式拟合n组标准平晶（3）的面形，提取和统计n组Zernike多项式的第二项和第三项系数；将Zernike多项式的第二项系数和第三项系数合成并统计，计算精密转台的转动摆角误差。通过将角度的测量转化为面形测量，不受平晶自身面形的影响，提高了检测精度。还公开了一种精密转台摆角测量装置。

Description

精密转台摆角测量方法和装置 技术领域
本发明属于光学检测领域，尤其涉及一种精密转台摆角测量方法以及测量装置。
背景技术
精密转台在仪器设备和生产制造中有着广泛的应用，而转台的轴系精度是衡量转台精密程度的关键，也是转台精密度的主要指标之一。理想的转台只有一个绕着Z轴转动的自由度，其它沿着X，Y，Z方向的直线运动和绕X，Y轴转动的5个自由度都可称为转台的轴系误差。而在转台的实际应用中，轴系误差也就是其他5个自由度的运动一般转化为Z轴方向的轴向跳动、沿Z轴垂直方向的径向跳动和转台转动时绕着X，Y轴的摆动。轴向跳动和径向跳动通常可以使用标准球放在转台中心，利用色差传感器测量转台旋转时标准球相对于色差传感器的跳动，利用三角函数进行拟合后可以得到转台的轴向和径向跳动。而转台的摆动一般有两种测量方法，一种是利用标准圆柱放在转台中心，测量圆柱上下两个位置随转台转动时的跳动，通过测得的跳动和两个位置之间的长度可以计算出转台的摆动。另外一种方法是使用一块标准平晶，利用平行光管测量反射光在转台转动过程中反射光倾角变化而得到转台摆角。这两种方法严重依赖于标准件的质量，例如圆柱的圆度和标准平晶的面形误差都会直接影响最终摆角的测量结果。而高质量的标准元件制造往往比较困难，需要定期进行严格标定。
发明内容
旨在克服现有技术中的缺陷中的至少一个方面提出本发明。
根据本发明实施例的一方面，提供了一种精密转台摆角测量方法，包括如下步骤：
步骤一：将精密转台固定于一干涉仪五维调整台上，将标准平晶放 置在精密转台上，参考面位于干涉仪正下方，参考面与标准平晶之间形成平面干涉腔；
步骤二：通过所述干涉仪五维调整台调节标准平晶的位置，使得干涉仪发出的准直光束在参考面与标准平晶之间形成零条纹干涉；
步骤三：旋转所述精密转台，每旋转360°/n，测量一次标准平晶与参考平面形成的干涉腔的干涉条纹，获得n组标准平晶的面形，n为大于等于2的自然数；
步骤四：利用Zernike(泽尼克)多项式拟合n组标准平晶的面形，分别提取n组Zernike多项式的第二项系数和第三项系数；
步骤五：将Zernike多项式的第二项系数和第三项系数合成并统计，合成后得到平晶相对于参考面倾斜角度，统计倾斜角度，用倾斜角度最大值减去最小值即为转台转动摆角误差。
根据本发明实施例的一方面，提供了一种精密转台摆角测量装置，包括：干涉仪五维调整台，配置为在其上固定待测量的精密转台，用于调整所述精密转台实现五维方向运动；标准平晶，配置为放置于所述精密转台上；干涉仪，包括其正下方的参考面，所述参考面在所述标准平晶上方，参考面和所述标准平晶之间形成平面干涉腔，所述干涉仪用于在所述精密转台每旋转360°/n，测量一次标准平晶在平面干涉腔的干涉条纹，获得n组标准平晶的面形，n为大于等于2的自然数；处理器，用于接收所述干涉仪测量的标准平晶的面形，并且利用Zernike多项式拟合n组标准平晶与参考面的面形，以及统计Zernike多项式的第二项系数和第三项系数，然后将第二项系数与第三项系数合成后的最大值减去最小值输出为精密转台的转动摆角误差。
可选地，所述处理器包括：数据获取单元：用于接收所述干涉仪测量的标准平晶的面形；模拟单元：用于利用Zernike多项式拟合n组标准平晶的面形，分别提取n组Zernike多项式的第二项系数和第三项系数；统计单元：合成Zernike多项式的第二项系数和第三项系数并统计，合成后得到平晶相对于参考面倾斜角度，统计倾斜角度，利倾斜角度最大值减去最小值即为转台转动摆角误差；输出或显示单元：输出或显示 所述精密转台的摆角误差。
根据本发明的测量方法，利用干涉仪和标准平晶组成的干涉腔首先进行面形测量，利用Zernike多项式对测量得到的面形进行拟合得到倾斜项，统计不同转动角度下的倾斜变化就可以得到转台的摆角误差。其优点在于利用了干涉面形测量精度高的特点，将角度的测量转化为面形测量，然后通过拟合得到平晶的倾斜，不受平晶和参考面自身面形和调节精度的影响，而测量精度由于利用了高精度的干涉面形测量而大大提高了检测精度，操作简单，不依赖于标准件精度的测量方法。
附图说明
图1为根据本发明的示例性实施例的精密转台摆角测量方法的测量原理示意图；
图2为根据本发明的示例性实施例的精密转台摆角测量方法的流程图；
图3为根据本发明的示例性实施例的精密转台摆角测量装置的示意图；
图4为图3的处理器的方框图。
具体实施方式
虽然将参照含义本发明的较佳实施例的附图充分描述本发明，但在此描述之前应了解本领域的普通技术人员可修改本文中所描述的发明，同时获得本发明的技术效果。因此，须了解一下的描述对本领域的普通技术人员而言为一广泛的揭示，且其内容不在于限制本发明所描述的示例性实施例。
根据本发明的实施例，在测量时，通过干涉仪五维调整台调节标准平晶使得参考面与标准平晶平行形成零条纹，测量此状态下平面干涉腔干涉图，得到标准平晶面形，旋转气浮台角度为360°/n，再次测量此时标准平晶面形，重复上述步骤，共测量n次,n为大于等于2的自然数；利用Zernike多项式拟合测量得到的平晶面形，提取第二、三项(X,Y 倾斜项)系数，合成计算后得到平晶相对于参考面倾斜角度，统计得到的倾斜角度，用最大值减去最小值即为转台转动摆角误差。本方法利用干涉仪将角度测量转化为面形测量，通过面形Zernike多项式提取出倾斜角度，其检测精度不受标准件精度和调整精度的影响，检测精度高。
以下将具体说明根据本发明的示例性实施例的精密转台摆角测量方法。
参见图1和图2，根据本发明的示例性实施例的精密转台摆角测量方法包括以下步骤：
S1：将精密转台4固定于一干涉仪五维调整台5上，将标准平晶3放置在精密转台4上，参考面2位于干涉仪1正下方，参考面2与标准平晶3之间形成平面干涉腔；
S2：通过所述干涉仪五维调整台5调节标准平晶3的位置，使得干涉仪1发出的准直光束在参考面2与标准平晶3之间形成零条纹干涉；
S3：旋转所述精密转台4，每旋转360°/n，测量一次标准平晶3在平面干涉腔的干涉条纹，获得n组标准平晶的面形，n为大于等于2的自然数；
S4：利用Zernike多项式拟合n组标准平晶3的面形，分别提取n组Zernike多项式的第二项系数和第三项系数；
S5：将Zernike多项式的第二项系数和第三项系数合成并统计，合成后得到平晶相对于参考面倾斜角度，统计倾斜角度，用倾斜角度最大值减去最小值即为转台转动摆角误差。
步骤S1中，将精密转台4固定于一干涉仪五维调整台5上目的在于通过干涉仪五维调整台5实现其上的精密转台4的五维运动，该五维运动包括沿着X，Y，Z方向的直线运动以及绕X，Y轴转动的5个维度的运动方式，也可转化为Z轴方向的轴向跳动、沿Z轴垂直方向的径向跳动和转台转动时绕着X，Y轴的摆动。因此，通过该五维调节可以满足后续测量步骤中将精密转台4上标准平晶3的位置调节至在干涉腔内形成零条纹干涉，即标准平晶3与参考面2处于平行位置。
其中，为了形成干涉腔，标准平晶3和参考面2应当相对设置。本 发明的设置方式是将标准平晶3放置在精密转台4上，参考面2位于干涉仪1正下方，参考面2与标准平晶3之间形成平面干涉腔。当干涉仪1发出的准直光束经过参考面2时，一部分被参考面2反射回干涉仪，透过参考面2继续传播，并由标准平晶3反射回去，与参考面2反射的光进行干涉，形成干涉条纹。
其中，参考面2可以选择平晶，对于该平晶的面形和圆度等误差没有特别的要求，通过后的测量步骤，最终的统计结果可以排除相应误差，因此，各种平晶都可应用的本发明。
步骤S2中，通过调节干涉仪五维调整台5，间接调整标准平晶3和参考面2之间的位置，以形成零条纹，产生干涉，此时测量该状态下平面干涉腔的干涉图，从而得到标准平晶3的一个面形。
步骤S3中，通过旋转精密转台4进行标准平晶3面形的多次测量。可以采用每旋转360°/n，测量一次标准平晶3在平面干涉腔的干涉条纹，获得n组标准平晶3的面形，n为大于等于2的自然数。
对于n的选择，n取值越大，统计的样本更多，结果也就更精确。优选的n的取值可以为24、72或者100。
步骤S4中，利用Zernike多项式对标准平晶3的面形进行拟合。每次测量会得到一个面形，利用Zernike多项式可以从中提取出倾斜项，得到此时标准平晶相对于参考面2的倾斜。倾斜的大小在转动过程中发生变化即为转台摆角误差。
通常会使用幂级数展开式的形式来描述光学系统的像差，由于泽尼克多项式和光学检测中观测到的像差多项式的形式是一致的，因而它常常被用来描述波前特性。
本实施例中的标准平晶3的光学干涉面形数学表述函数F(ρ，θ)可以用Zernike多项式拟合为式(1)：
Figure PCTCN2016097583-appb-000001
其中，ak为多项式的拟合系数，k为0至∞的整数，ρ和θ为极坐标参数，Zk(ρ,θ)为泽尼克多项式函数，该函数可以表述为式(2)：
Zk(ρ,θ)＝Rk(ρ)Gk(θ)    (2)
式(2)中，R(ρ)为径向函数(Radial Function)，是ρ的k次多项式；Gk(θ)为以2π弧度为周期的连续函数。其中，表1列举出了极坐标系下的泽尼克多项式前五项：
表1
项数 多项式
一 1
二 ρcosθ
三 ρsinθ
四 -1-2ρ2
五 ρ2cos(2θ)
表1中的第一项是常数或者说是平移项(piston term)，这一项的系数也代表了平均光程差；而第二项和第三项分别是X和Y方向的倾斜项(tilt terms)，第四项代表了聚焦。因此，提取第二项和第三项系数就是提取了X和Y方向的倾斜项。
结合步骤S5，计算多组X和Y方向的倾斜项误差。通过合成Zernike多项式的第二项系数和第三项系数并统计合成后角度的最大值和最小值，将最大值减去最小值即为精密转台4的转动摆角误差。
基于同一发明构思，参照以上实施例提供的精密转台摆角测量方法，本发明实施例还提供了相应的精密转台摆角测量装置。参见图3所示，所述测量装置可以包括：
干涉仪五维调整台5，配置为在其上固定待测量的精密转台4，用于调整所述精密转台4实现五维方向运动；五维方向包括沿着X，Y，Z方向的直线运动以及绕X，Y轴转动的5个维度。
标准平晶3，配置为放置于所述精密转台4上；
干涉仪1，包括其正下方的参考面2，所述参考面2在所述标准平晶3上方，参考面2和所述标准平晶3之间形成平面干涉腔，所述干涉仪1用于在所述精密转台4每旋转360°/n，测量一次标准平晶3在平面干涉腔的干涉条纹，获得n组标准平晶3的面形，n为大于等于2的自然数；
处理器6，用于接收所述干涉仪1测量的标准平晶3的面形，并且利用Zernike多项式拟合n组标准平晶的面形，以及合成Zernike多项式的第二项系数和第三项系数，然后将合成后的角度最大值减去最小值输出为精密转台的转动摆角误差。
图4为图3的处理器的方框图。其中，处理器6包括：
数据获取单元601：用于接收所述干涉仪1测量的标准平晶(3)的面形；
模拟单元602：用于利用Zernike多项式拟合n组标准平晶的面形，分别提取n组Zernike多项式的第二项系数和第三项系数；
统计单元603：合成Zernike多项式的第二项系数和第三项系数，统计n组合成系数的角度，并将角度最大值减去最小值为精密转台的转动摆角误差；以及
输出或显示单元604：输出或显示所述精密转台的转动摆角误差。
以上所述，仅为本发明的具体实施方式，但本发明的保护范围并不局限于此，任何熟悉本技术领域的技术人员在本发明揭露的技术范围内，可轻易想到变化或替换，都应涵盖在本发明的保护范围之内。因此，本发明的保护范围应以所述权利要求的保护范围为准。

Claims (5)

  1. 一种精密转台摆角测量方法，包括如下步骤：
    步骤一：将精密转台(4)固定于一干涉仪五维调整台(5)上，将标准平晶(3)放置在精密转台(4)上，参考面(2)位于干涉仪(1)正下方，参考面(2)与标准平晶(3)之间形成平面干涉腔；
    步骤二：通过所述干涉仪五维调整台(5)调节标准平晶的位置，使得干涉仪发出的准直光束在参考面(2)与标准平晶(3)之间形成零条纹干涉；
    步骤三：旋转所述精密转台(4)，每旋转360°/n，测量一次标准平晶(3)在平面干涉腔的干涉条纹，获得n组标准平晶(3)的面形，n为大于等于2的自然数；
    步骤四：利用Zernike多项式拟合n组标准平晶的面形，分别提取n组Zernike多项式的第二项系数和第三项系数；
    步骤五：将Zernike多项式的第二项系数和第三项系数合成并统计，合成计算后得到平晶相对于参考面的倾斜角度，统计所述倾斜角度，用最大值减去最小值即为转台转动摆角误差。
  2. 根据权利要求1所述的精密转台摆角测量方法，其特征在于，所述的参考面(2)由一平晶所形成。
  3. 一种精密转台摆角测量装置，其特征在于包括：
    干涉仪五维调整台(5)，配置为在其上固定待测量的精密转台(4)，用于调整所述精密转台(4)实现五维方向运动；
    标准平晶(3)，配置为放置于所述精密转台(4)上；
    干涉仪(1)，包括其正下方的参考面(2)，所述参考面(2)在所述标准平晶(3)上方，参考面(2)和所述标准平晶(3)之间形成平面干涉腔，所述干涉仪(1)用于在所述精密转台(4)每旋转360°/n，测量一次标准平晶(3)在平面干涉腔的干涉条纹，获得n组标准平晶(3)的面形，n为大于等于2的自然数；
    处理器，用于接收所述干涉仪(1)测量的标准平晶(3)的面形， 并且利用Zernike多项式拟合n组标准平晶的面形，以及统计Zernike多项式的第二项系数和第三项系数，并且将Zernike多项式的第二项系数和第三项系数合成并统计，合成所得角度的最大值减去最小值为精密转台的转动摆角误差。
  4. 根据权利要求3所述的精密转台摆角测量装置，其特征在于，所述的参考面(2)由一平晶所形成。
  5. 根据权利要求3所述的精密转台摆角测量装置，其特征在于，所述处理器包括：
    数据获取单元：用于接收所述干涉仪(1)测量的标准平晶(3)的面形；
    模拟单元：用于利用Zernike多项式拟合n组标准平晶的面形，分别提取n组Zernike多项式的第二项系数和第三项系数；
    统计单元：将Zernike多项式的第二项系数和第三项系数合成并统计，合成系数所得角度的最大值减去最小值为精密转台的转动摆角误差；
    输出或显示单元：输出或显示所述精密转台的转动摆角误差。
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