WO2016173382A1 - 一种用法布里-珀罗标准具测量焦距和转角的方法 - Google Patents

一种用法布里-珀罗标准具测量焦距和转角的方法 Download PDF

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WO2016173382A1
WO2016173382A1 PCT/CN2016/078164 CN2016078164W WO2016173382A1 WO 2016173382 A1 WO2016173382 A1 WO 2016173382A1 CN 2016078164 W CN2016078164 W CN 2016078164W WO 2016173382 A1 WO2016173382 A1 WO 2016173382A1
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pixel
mirror
cone
focal length
angle
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朱鹤年
肖志刚
郭旭波
陈强
常缨
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Tsinghua University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M11/00—Testing of optical apparatus; Testing structures by optical methods not otherwise provided for
    • G01M11/02—Testing optical properties
    • G01M11/0221—Testing optical properties by determining the optical axis or position of lenses
    • 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
    • G01D—MEASURING NOT SPECIALLY ADAPTED FOR A SPECIFIC VARIABLE; ARRANGEMENTS FOR MEASURING TWO OR MORE VARIABLES NOT COVERED IN A SINGLE OTHER SUBCLASS; TARIFF METERING APPARATUS; MEASURING OR TESTING NOT OTHERWISE PROVIDED FOR
    • G01D5/00—Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable
    • G01D5/26—Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable characterised by optical transfer means, i.e. using infrared, visible, or ultraviolet light
    • G01D5/266—Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable characterised by optical transfer means, i.e. using infrared, visible, or ultraviolet light by interferometric means
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M11/00—Testing of optical apparatus; Testing structures by optical methods not otherwise provided for
    • G01M11/02—Testing optical properties
    • G01M11/0242—Testing optical properties by measuring geometrical properties or aberrations
    • G01M11/0271—Testing optical properties by measuring geometrical properties or aberrations by using interferometric methods

Definitions

  • the present invention relates to the field of optical field and geometric quantity measurement, and more particularly to a method for measuring focal length and rotation angle using a Brib-Perot etalon.
  • the self-collimator is used to determine the calibration curve by using a small angle generator designed by the tangent relationship of length and length, although it can be used under certain conditions and under certain conditions. It is less than 0.25% or even less than 1 ⁇ 10 -3 , but the variability error of the influence amount such as the stability during the verification period and the temperature during measurement restricts the actual measurement range and the use condition of the angle ⁇ .
  • the effective resolution and the Class A uncertainty associated with the repeatability standard deviation are limited by the pixel error of the line array (or area array) optoelectronic device.
  • the extended uncertainty of ⁇ measured by a self-collimator is 0.05′′ (additive component), and the beam distribution pattern with better control is used, and about 40 consecutive pixel signals are used to make the pixel coordinate of the center position of the beam focus.
  • the temperature of a line array (or area array) optoelectronic device pixel spacing W accuracy is high, but the deviation error of the equivalent geometric center of a single pixel and the photoelectric conversion rate error is often significant, such as some lines,
  • the pixel photoelectric conversion rate of the area array optoelectronic device has an error limit of ⁇ 5%.
  • the relative expansion uncertainty U f /f is generally only about 0.25%.
  • a primary object of the present invention is to provide a method for measuring focal length and rotation angle using a Brill-Perot etalon to solve the technical problems of the prior art which are less accurate.
  • the present invention provides a method for measuring a focal length using a Buri-Perot etalon, comprising the steps of: first step: transmitting a monochromatic light through a Fabry-Perot etalon to produce a a standard cone beam with a regular cone angle ⁇ i , the cone beam being reflected by the transflective mirror to the mirror, reflected by the mirror, transmitted through the semi-transparent mirror, and then passed through the objective lens at the objective lens
  • the surface of the planar array optoelectronic device forms a set of concentric rings;
  • the second step selecting a plurality of dot fields on each ring to subdivide the one-dimensional cells in each dot field;
  • the second step specifically includes: first finding an approximate center point of the concentric ring Then, at least three horizontal lines and at least three vertical lines are respectively formed near the approximate center point, so that the horizontal line and the vertical line intersect each ring to form two line segments, and the photoelectric signal extreme value points are obtained on each line segment.
  • the coordinate value of the fractional W which is divided by the average distance W of the pixels.
  • the second step specifically includes: first finding an approximate center point of the concentric ring Then, at least three horizontal lines and at least three vertical lines are respectively formed near the approximate center point, so that the horizontal line and the vertical line intersect each ring to form two line segments, and the photoelectric signal extreme value points are obtained in each line segment.
  • the coordinate value of the fractional W which is divided by the average distance W of the pixels.
  • Advantageous effects of the present invention in comparison with the prior art include: the usage of the Brie-Perot etalon of the present invention, which produces a set of standard cone beams with a regular cone angle as a reference beam, forming a series of concentric rings on the focal plane of the objective lens.
  • the Brie-Perot etalon of the present invention which produces a set of standard cone beams with a regular cone angle as a reference beam, forming a series of concentric rings on the focal plane of the objective lens.
  • the pixel subdivision technique of the area array optoelectronic device multiple rings are acquired, and each circle takes a plurality of dot fields, and each dot field contains information of a plurality of pixels.
  • Figure 1 is a structural view of an optical device used in the present invention
  • FIG. 2 is a flow chart of the use of the Buri-Perot etalon of the present invention to measure focal length and corner.
  • the light source 1 emits a monochromatic light having a known vacuum wavelength of ⁇ 0 through a Fabry-Perot etalon having a pitch of d, a spacer of quartz glass material, and a refractive index of n. 3.
  • ⁇ i is the angle between the conical beam and the conical axis (referred to as the conical axis) perpendicular to the exit surface of the etalon.
  • the series of cone beams are reflected by the transflective mirror 4 toward the plane rotating mirror 5, and the object mirror 6 is reflected by the rotating mirror 5 and paralleled by the optical axis and the conical axis, on the focal plane of the objective lens 6 having the focal length f
  • the surface of the array optoelectronic device 7 produces a series of concentric rings 8 of diameter D i .
  • a combined element 2 comprising a filter and a diffusing sheet can also be arranged between the light source 1 and the Fabry-Perot etalon 3.
  • D i 2 is approximated as an order of difference.
  • the approximate simplified linear equation with -i as the dependent variable and D i 2 as the independent variable is
  • the above formula 5 reflects the law of diameter and cone angle distribution when the cone axis is parallel to the optical axis of the objective lens.
  • Set the concentric axis parallel to the optical axis when the center of the concentric ring is
  • the angle between the parallel beam of light and the optical axis of the objective lens is ⁇ l
  • the element parallel beams converge at the center of the spot (x l , y l ) of the focal plane to the center point
  • Radius R l is only related to the angle ⁇ l
  • the z-axis is perpendicular to the focal plane.
  • Plane Cartesian coordinates are The analytic geometry algorithm can be used to find the intersection of the ray and the focal plane parallel to the principal point of the object mirror and parallel to the cone axis.
  • the circular equation regression can be used to obtain the diameter D i of each circle. And degrees of freedom v i .
  • the bounds of the center of the circle should be used to find the average of the coordinates of the center of the circle. And its standard deviation
  • U fad in the above equation is an estimate of the extended uncertainty of focusing. Determining U fad is usually derived from the decision error limit of the minimum value of the focus point. t in the above formula is the t distribution factor.
  • the standard deviation of the coordinate after subdivision can be less than 0.1 W in the subdivision of the dot-domain coordinates, the half-width half-width HWHM of the annular stripe distribution line type can also be obtained at the same time, and the effective resolution can generally be less than 0.04. W. Since the objective lens aperture is usually larger than 30mm, W ⁇ 5 ⁇ m, it is not difficult to make the objective lens focal length f ⁇ 50mm.
  • v eff is the effective degree of freedom calculated according to the case method in the Measurement Uncertainty Assessment Guide.
  • the sum of the total corners U( ⁇ ) is The magnification component coefficient c 1 is the same as (13).
  • the invention will be further illustrated by a specific example.
  • the following table lists the nine consecutive concentric annular parameters measured when the conical axis is parallel to the optical axis of the objective lens. Each circle is rounded with 20 points. The focal length and center-weighted average obtained from the last 8 sets of data are also listed in the table.
  • the error of the substrate temperature estimation of the area array imaging device can reach ⁇ 5 °C, and the maximum allowable error of the pixel average spacing W measured at the reference temperature is estimated to be ⁇ 3 ⁇ 10 -5 , and the relative uncertainty of W is estimated.
  • the focus uncertainty is generally not greater than U fad /f ⁇ 1.7 ⁇ 10 -4
  • Additive component It decreases as the focal length increases. It is not difficult to infer: when the embodiment When increased to 500 mm, the sum component c 0 will be reduced to below 0.05" and the effective resolution will be below 0.01".
  • the monochromatic light is transmitted through the Fabry-Perot etalon, producing a set of standard cone beams of interference order of integer K i , cone angle ⁇ i .
  • the beam is reflected by the transflective mirror to the plane mirror, reflected by the plane mirror, and then passed through the objective lens with focal length f to produce a set of concentric rings on the surface of the array optoelectronic device located at its focal plane.
  • the displacement amount calculates the rotation angle ⁇ of the mirror.
  • the condition of the magnification component coefficient c 1 ⁇ 2 ⁇ 10 -4 in c 0 + c 1 ⁇ creates a condition.
  • the magnitude of the two components in 0 + c 1 ⁇ creates conditions.
  • the specific method is: to find the approximate center point of the concentric ring signal collected by the array photoelectric device. Then make 3 to 5 or more horizontal lines near the approximate center of the circle, for example ⁇ 0.6B, ⁇ B, and then make 3 to 5 or more vertical lines, for example ⁇ 0.6B, ⁇ B.
  • the subdivision method is divided into three steps for the calculation of a certain dimension of the pixel in each point domain (on the line segment).
  • the peak value of the pixel signal is I M , leaving both sides of the peak pixel 8 to 18 consecutive pixels; function of these pixel signals I i
  • the integer pixel coordinate x j and the subdivided coordinate y j * are determined in a similar manner.
  • the same ring is not less than 24 Coordinate values of points (x j * , y j ), (x j , y j * ), and the regression of a circular equation with concentric constraints, and find the diameter D i of each concentric ring and its standard deviation Simultaneously find the average of the center coordinates And its standard deviation
  • the signal processing method in the dot field (on line segment) of ⁇ 45 degrees is similar to the above, and can be regarded as new parallel data in the axial direction after the coordinates are rotated by 45 degrees.
  • the distance between adjacent pixels where the diagonal line and the line segment coincide is If an equivalent pixel of a half-integer number is inserted, the photoelectric signal takes the average of the signal angles of the two symmetric pixels on both sides of the line segment that coincide with the pixel corner, which will make the equivalent image on the line of ⁇ 45 degrees.
  • the number of elements is doubled, and the spacing of adjacent equivalent pixels is reduced to
  • the coordinates of the subdivided peaks on the degree line segment are calculated by the plane geometry, converted into values in the Cartesian coordinate system, and then participate in the circle regression calculation.
  • the number of original pixels participating in the coordinate subdivision calculation is calculated by using multiple circles and each circle using multiple points for regression calculation. More than 1.5 ⁇ 10 3 , and these pixels are scattered in a large range of area array optoelectronic devices, the geometric error and photoelectric conversion error of a single pixel can be fully randomized, so that the standard deviation of the center coordinates after statistical calculation Reduced to below 0.02W, also makes the standard deviation of the circle diameter D 2 Reduce to less than 1/3 of the subdivision.
  • the Buri-Perot etalon of the present invention produces a set of conical beams of a cone angle standard as a reference beam, forming a series of concentric rings on the focal plane of the objective lens.
  • the pixel subdivision technique of the area array optoelectronic device is used to subdivide the extreme value point coordinates of the photoelectric signal, and multiple rings are collected, and each circle takes a plurality of dot fields, and each dot field contains information of a plurality of pixels.
  • Statistical calculations are performed on such a large number of large-scale pixel signals, so that the error effects of a single pixel are sufficiently randomized, and the accuracy and precision of the circular radius measurement and the concentric ring associated with the azimuth of the conical axis can be improved.
  • the accuracy and precision of the center coordinates that is, the accuracy and precision of the focal length and angle measurement.
  • the angular magnitude in the present invention is traced back to the spectral lamp monochromatic light wavelength ⁇ 0 and the etalon interval d, known It can be conveniently measured and controlled by fractional weight to make U d /d ⁇ 5 ⁇ 10 -6 , so that the small angle measuring instrument adopting the method of the invention has the advantages of traceability and convenience for calibration or verification.
  • the uncertainty of the traceable focal length measurement is reduced to less than 40% than the uncertainty U f /f ⁇ 2.5 ⁇ 10 -3 of the typical method.
  • the photoelectric signal extreme value point pixel coordinate subdivision technology also creates conditions for reducing the focus error limit and focusing automation.
  • the equations (8) to (9) avoid the difficulty with the comparative measurement method.
  • the coefficient of magnification component in the traceable corner uncertainty is reduced to less than 2/5 compared to conventional instruments. It is also one of the advantages of the present invention to achieve simultaneous measurement of two-dimensional corners with a single optical system and a single area array photo-receiving device.
  • the one-dimensional linear CCD device is used to measure the deflection angle of the one-dimensional mirror reflected beam, which can achieve nonlinear relative error. Quasi-static or dynamic measurement of high effective resolution limited to a beam deflection angle of less than 0.01%.

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Abstract

一种用法布里-珀罗标准具测量焦距和转角的方法，包括：用单色光经法布里-珀罗标准具（3）透射，产生一组圆锥角θ i规律准确的标准圆锥光束，所述圆锥光束经过半透半反平面镜（4）反射向转镜（5）；经转镜（5）反射后的光束透过半透半反平面镜（4），再经过物镜（6），在位于所述物镜（6）的焦平面的面阵光电器件（7）表面形成一组同心圆环（8）；在各圆环（8）上选取多个点域，对各个点域内的一维像元用光电信号极值点位像元坐标细分方法；用圆环（8）上的多个极值点位坐标作圆回归求出各圆的直径Di及其标准差SDi；由所述圆锥光束的同心圆环（8）直径Di及其标准差SDi，按圆锥角θi分布规律由Di＝2(fi/W)tanθi求出fi/W，fi/W是由单个圆直径Di算出的焦距fi与所述面阵光电器件（7）的平均像元间距W的比值，进而求出fi/W的加权平均值（I），以得出被测焦距f；转镜（5）转角为δθ时，入射向物镜的圆锥光束中心轴将转过2δθ角，使同心圆环（8）圆心平移（II），通过所述同心圆环（8）的圆心（x̅0，y̅0）的以W为相对单位的平移量计算出转镜转角δθ。该方法能提高焦距以及转角测量的准确度与精密度。

Description

一种用法布里-珀罗标准具测量焦距和转角的方法 技术领域
本发明涉及光学领域及几何量测量领域，特别是涉及一种用法布里-珀罗标准具测量焦距和转角的方法。
背景技术
目前测小转角的自准直仪的原理方案中，准确度指标受到两方面的制约：(1)多数自准直仪在测量小转角δθ时，用式Uδθ＝c0+c1δθ表示的扩展不确定度中倍率项系数c1受到焦距不确定度Uf/f的制约。运用由长度量正切关系设计的小角度发生器对自准直仪进行定度或给出检定曲线，虽能使一定周期、一定条件下的
Figure PCTCN2016078164-appb-000001
小于0.25％，甚至小于1×10-3，但其检定周期内的稳定性、测量时温度等影响量的变动性误差等制约了角度δθ的实际测量范围及使用条件。(2)有效分辨率及与重复性标准差相关联的A类不确定度受到线阵(或面阵)光电器件像元误差的限制。某型自准直仪测δθ的扩展不确定度达0.05″(加和分量)，采用控制较好的光束分布线型，用约40个连续像元信号做光束聚焦中心位置的像元坐标细分。温度一定时线阵(或面阵)光电器件像元的平均间距W准确度高，但是单个像元的等效几何中心的偏离误差与光电转换率的误差常常较显著，如一些线、面阵光电器件的像元光电转换率的误差限可达±5％。
目前测物镜焦距f的方法或仪器，相对扩展不确定度Uf/f一般仅约0.25％。虽有文献报道过Uf/f达10-4量级的实验，但因其测量结果可溯源性差而受到另一些专业文献的质疑。
以上背景技术内容的公开仅用于辅助理解本发明的发明构思及技术方案，其并不必然属于本专利申请的现有技术，在没有明确的证据表明上述内容在本专利申请的申请日已经公开的情况下，上述背景技术不应当用于评价本申请的新颖性和创造性。
发明内容
本发明主要目的在于提出一种用法布里-珀罗标准具测量焦距和转角的方法，以解决上述现有技术存在的准确度较低的技术问题。
为此，本发明提出一种用法布里-珀罗标准具测量焦距的方法，其特征在于：包括如下步骤：第一步：用单色光经法布里-珀罗标准具透射，产生一组圆锥角θi规律准确的标准圆锥光束，所述圆锥光束经半透半反平面镜反射射向转镜，经转镜反射后透过半透半反镜，再经过物镜，在位于所述物镜的焦平面的面阵光电器件表面形成一组同心圆环；第二步：在各圆环上选取多个点域，对各个点域内的一维像元作细分；第三步：由所述圆锥光束的同心圆环直径Di及其标准差
Figure PCTCN2016078164-appb-000002
，按圆锥角θi分布规律由Di＝2(fi/W)tanθi求出fi/W，fi/W是由单个圆直径Di算出的焦距fi与所述面阵光电器件的平均像元间距W的比值，进而求出fi/W的加权平均值
Figure PCTCN2016078164-appb-000003
以得出被测焦距f。
在一个实施例中，所述第二步具体包括：先找出所述同心圆环的近似圆心点
Figure PCTCN2016078164-appb-000004
再在近似圆心点附近分别作至少3条水平线、至少3条垂直线，使所述水平线和垂直线与每个圆环相交形成2个线段，在每条线段上求出光电信号极值点位的、细分后包含小数的、以像元平均间距W为单位的坐标值。
本发明还提出了一种用法布里-珀罗标准具测量转角的方法，包括如下步骤：第一步：用单色光经法布里-珀罗标准具透射，产生一组圆锥角θi规律准确的标准圆锥光束，所述圆锥光束经半透半反平面镜反射射向转镜，经转镜反射后透过半透半反镜，，再经过物镜，在位于所述物镜的焦平面的面阵光电器件表面形成一组同心圆环；第二步：在各圆环上选取多个点域，对各个点域内的一维像元作细分；第三步：由所述圆锥光束的同心圆环直径Di及其标准差
Figure PCTCN2016078164-appb-000005
，按圆锥角θi分布规律由Di＝2(fi/W)tanθi求出fi/W，fi/W是由单个圆直径Di算出的焦距fi与所述面阵光电器件的平均像元间距W的比值，进而求出fi/W的加权平均值
Figure PCTCN2016078164-appb-000006
第四步：根据转镜产生转角δ0后，入射向物镜的圆锥光束中心轴将转过2δθ角，使同心圆环圆心平移
Figure PCTCN2016078164-appb-000007
通过所述同心圆环的圆心
Figure PCTCN2016078164-appb-000008
的平移量计算出转镜转角δθ。
在一个实施例中，所述第二步具体包括：先找出所述同心圆环的近似圆心点
Figure PCTCN2016078164-appb-000009
再在近似圆心点附近分别作至少3条水平线、至少3条垂直线，使所述水平线和垂直线与每个圆环相交形成2个线段，在每条线段内求出光电信号极值点位的、细分后包含小数的、以像元平均间距W为单位的坐标值。
本发明与现有技术对比的有益效果包括：本发明用法布里-珀罗标准具，产生一组圆锥角规律准确的标准圆锥光束作为参考光束，在物镜焦平面上形成系列同心圆环。采用面阵光电器件的像元细分技术，采集多个圆环、每个圆取多个点域，每个点域含多个像元的信息。对这样大数量、大范围内的像元信号作统计计算，使单个像元的误差影响被充分随机化，能提高圆半径测量的准确度与精密度以及与圆锥轴方位角关联的同心圆环圆心坐标的准确度与精密度，即提高焦距以及转角测量的准确度与精密度。
附图说明
图1是本发明所使用的光学器件的结构图；
图2是本发明的用法布里-珀罗标准具测量焦距和转角的流程图。
具体实施方式
下面结合具体实施方式并对照附图对本发明作进一步详细说明。应该强调的是，下述说明仅仅是示例性的，而不是为了限制本发明的范围及其应用。
参照以下附图，将描述非限制性和非排他性的实施例，其中相同的附图标记表示相同的部件，除非另外特别说明。
说明书中量的符号、名称及单位见下表
Figure PCTCN2016078164-appb-000010
下面对本发明再做进一步的详细说明。如图1、图2所示，光源1发出已知真空波长为λ0的单色光经过间距为d、隔圈为石英玻璃材料、间隔空气折射率为n的法布里-珀罗标准具3，产生干涉级次为整数Ki的一组圆锥光束(Ki＝k0-i，式中i＝0，1，2，...，imax)，圆锥光束的半圆锥角为θi。θi即圆锥面光束与垂直于标准具出射面的圆锥轴(简称圆锥轴)的夹角。这里k0是标准具出射光束角θi最小时(i＝0)所对应的整数干涉级次，即2dn/λ0＝k0+ε的整数部分，ε是级次的小数部分，0≤ε＜1。系列圆锥光束经过半透半反平面镜4反射射向平面转镜5，经转镜5反射、再经光轴与圆锥轴平行的被测物镜6，在焦距为f的物镜6的焦平面上的面阵光电器件7的表面产生一系列直径为Di的同心圆环8。在光源1和法布里-珀罗标准具3之间还可设置包含滤光片和漫射片的组合元件2。
当圆锥轴与物镜光轴平行时，由M.波恩与E.沃尔夫的著作《光学原理》(科学出版社，1978，P429-444)中的关系式可得
Figure PCTCN2016078164-appb-000011
Figure PCTCN2016078164-appb-000012
Di 2近似成等差级数。以-i为因变量、以Di 2为自变量的近似简化直线方程为
Figure PCTCN2016078164-appb-000013
对上式模型作直线拟合求出截距
Figure PCTCN2016078164-appb-000014
此即ε的近似值。将
Figure PCTCN2016078164-appb-000015
代入下式，以Di 2为因变量、以
Figure PCTCN2016078164-appb-000016
i为自变量作加权直线拟合，模型方程为
Figure PCTCN2016078164-appb-000017
(4)式的截距b0与斜率b1之比为
Figure PCTCN2016078164-appb-000018
进而可得小数ε的值。
Figure PCTCN2016078164-appb-000019
计算小数ε的标准差sε。
上述5式反映当圆锥轴与物镜光轴平行时直径与锥角分布的规律。设圆锥轴平行与光轴时同心圆环圆心为
Figure PCTCN2016078164-appb-000020
当元平行光束与物镜光轴的夹角为θl时，元平行光束汇聚于焦平面的光点中心(xl，yl)到圆心点
Figure PCTCN2016078164-appb-000021
的半径
Figure PCTCN2016078164-appb-000022
Rl只与夹角θl有关，
Figure PCTCN2016078164-appb-000023
在以焦平面为中心面的球坐标系中，z轴垂直于焦平面。当圆锥轴与光轴有夹角(φr，θr)时，焦平面上的同心圆环圆心将平移到以
Figure PCTCN2016078164-appb-000024
为极坐标原点、极坐标为(φr，Rr)的位置，Rr＝(f/W)tanθr。平面直角坐标为
Figure PCTCN2016078164-appb-000025
Figure PCTCN2016078164-appb-000026
可用解析几何算法求出通过物镜像方主点、并和圆锥轴平行的光线与焦平面的交点
Figure PCTCN2016078164-appb-000027
按照熊友伦的《精密测量的数学方法》(中国计量出版社，1989，P30)中的最小二乘求圆半径的方法作圆方程回归，能分别得出各个圆的直径Di、
Figure PCTCN2016078164-appb-000028
及自由度vi。在同心圆环回归时要用共圆心的约束条件，求出圆心坐标的平均值
Figure PCTCN2016078164-appb-000029
及其标准差
Figure PCTCN2016078164-appb-000030
由(1)式可得从单个圆直径Di求fi/W的单步算式
Figure PCTCN2016078164-appb-000031
由(1)式可得
Figure PCTCN2016078164-appb-000032
由式
Figure PCTCN2016078164-appb-000033
出发评定fi/W的不确定度。因
Figure PCTCN2016078164-appb-000034
忽略k0的不确定度影响，可得
Figure PCTCN2016078164-appb-000035
求各个fi/W的加权平均值
Figure PCTCN2016078164-appb-000036
及其标准差
Figure PCTCN2016078164-appb-000037
Figure PCTCN2016078164-appb-000038
焦距的最佳估值为
Figure PCTCN2016078164-appb-000039
f的相对扩展不确定度为
Figure PCTCN2016078164-appb-000040
上式中的Ufad是调焦的扩展不确定度的估值。确定Ufad时通常由取聚焦点极小值的判定误差限来导出。上式中的t是t分布因子。本发明中，由于在点域坐标细分时能使细分后坐标标准差小于0.1W，也能同时求出圆环条纹分布线型的半峰值半宽度HWHM，其有效分辨率一般能小于0.04W。由于物镜孔径通常大于30mm，W＜5μm，当物镜焦距f≥50mm时不难做到使
Figure PCTCN2016078164-appb-000041
平面转镜转动角度(φr，δθ)时，将使入射向物镜的圆锥光束的圆锥轴在φr方向转过θr＝2δθ。通过物镜像方主点、并且和圆锥轴平行的光线与焦平面的相交点坐标为
Figure PCTCN2016078164-appb-000042
此即转镜转动后的准同心圆环圆心。设圆锥轴与物镜光轴平行时的同心圆环圆心为
Figure PCTCN2016078164-appb-000043
两维转角的大小与方向分别由同心圆环圆心的两维坐标平移量求出。转动前后焦平面上同心圆环圆心的位移量值为
Figure PCTCN2016078164-appb-000044
转角δθ为
Figure PCTCN2016078164-appb-000045
将(8)式结果的
Figure PCTCN2016078164-appb-000046
代入作计算，本质上是用比较测量法，焦距误差与调焦误差这两个因素的影响被减消了大部分。其中转镜的一维转角为
Figure PCTCN2016078164-appb-000047
一维转角δθX的标准不确定度评定时只需计算以下两个分量项：
Figure PCTCN2016078164-appb-000048
的 标准差及
Figure PCTCN2016078164-appb-000049
通常|δθX|＜0.05rad，
Figure PCTCN2016078164-appb-000050
的标准差近似为
Figure PCTCN2016078164-appb-000051
因为独立分量标准差合成时
Figure PCTCN2016078164-appb-000052
稍加放大后可将δθX的不确定度U(δθX)写成如下形式
Figure PCTCN2016078164-appb-000053
式中t是t分布因子，v是求
Figure PCTCN2016078164-appb-000054
时的自由度，veff是按照《测量不确定度评定指南》中案例方法计算的有效自由度。将0.2c0作为一维转角的有效分辨率Re(δθX)
Re(δθX)≈0.2c0         (14)
总转角U(δθ)的加和分量为
Figure PCTCN2016078164-appb-000055
倍率分量系数c1同(13)式。
下面通过一个具体例子对本发明做进一步说明。测量仪器与条件参量为：汞灯黄线波长λ01＝577.119 84×10-6mm，λ01/n＝576.959 81×10-6mm。标准具的间隔d＝2.032 056 2mm，物镜焦距
Figure PCTCN2016078164-appb-000056
W≈0.004 70mm，k0＝7044。
下表中列出了测量得到圆锥轴与物镜光轴平行时的9个连续的同心圆环参量，每圆环用20点作圆回归。用后8组数据求出的焦距、圆心加权平均值也列于表中。
Figure PCTCN2016078164-appb-000057
加温度测量部件后，对面阵成像器件基片温度估计的误差限可达±5℃，参考温度下像元平均间距W测量的最大允许误差估计为±3X10-5，W的相对不确定度估计约为UW/W≈5×10-5，调焦不确定度一般不大于Ufad/f≤1.7×10-4
由(10)式可得
Figure PCTCN2016078164-appb-000058
该例说明：所用焦距f≈70mm时，已经能使焦距的相对扩展不确定度小于3×10-4。
按(13)式计算一维转角测量不确定度U(δθX)的两个分量
U(δθX)的加和分量
Figure PCTCN2016078164-appb-000059
倍率分量系数
Figure PCTCN2016078164-appb-000060
有效分辨率Re(δθX)≈0.2c0≈0.04″。
加和分量
Figure PCTCN2016078164-appb-000061
随着焦距的增加而减小。不难推论：当实施例的
Figure PCTCN2016078164-appb-000062
增加到500mm时，加和分量c0将减小到0.05″以下，有效分辨率将达到0.01″以下。
用真空波长相对不确定度
Figure PCTCN2016078164-appb-000063
的单色光经法布里-珀罗标准具透射，产生一组干涉级次为整数Ki、圆锥角θi的标准圆锥光束。光束经半透半反平面镜反射射向平面转镜，经平面转镜反射，再经过焦距为f的物镜，在位于其焦平面的面阵光电器件表面产生一组同心圆环。由同心圆环圆心
Figure PCTCN2016078164-appb-000064
的位移量计算出转镜转角δθ。
石英间隔圈的法布里-珀罗标准具间隔d的稳定性和光束圆锥角规律的准确性，能保证测量转角δθ方法的可溯源性，同时为使转角测量的扩展不确定度Uδθ＝c0+c1δθ中的倍率分量系数c1≤2×10-4创造了条件。产生一系列倾斜角规律 准确度高、中心轴重复性高的已知标准光束，能减小焦距不确定度Uf/f对转角δθ的不确定度Uδθ的影响，为降低Uδθ＝c0+c1δθ中的两个分量的量值创造条件。
按一定规律选取各圆环上的多个点域，具体做法是：对面阵光电器件采集的同心环信号，先找出近似圆心点
Figure PCTCN2016078164-appb-000065
再在近似圆心附近分别作3～5条或更多的水平线，例如使
Figure PCTCN2016078164-appb-000066
±0.6B、±B，再作3～5条或更多的垂直线，例如使
Figure PCTCN2016078164-appb-000067
±0.6B、±B。这里W是平均像元间距。要求使B＜2％D10，D10是由内而外i＝10的第11个圆环直径。通常有D10＞1600W。例如取B＝30时，如果圆心位于坐标原点，圆环上点的未细分的某坐标值由30W改变至(30±0.5)W，内圆D2≈720W的圆半径的最大变化不超过±0.042W，这就是能用一维的光电信号极值点位像元坐标细分方法来高速地简化处理二维面阵信息的原因，因为锐角直角三角形斜边长度对短直角边长的变化不敏感。
对各个点域内(线段上)的某一维像元作细分计算，细分方法分三步。
(1)删除过小信号以降噪并使计算简化。对线段上的连续像元信号(或±45度线段两侧两个像元角点重合于线段上的对称像元的信号均值)，记像元信号峰值为IM，保留峰值像元两侧8～18个连续像元；以这些像元信号Ii的函数
Figure PCTCN2016078164-appb-000068
为因变量、以像元序号i(或对应值)及其平方i2为自变量作二次回归；基本模型式为Zi＝b0+b1i+b2i2.
(2)调和加权回归。由于因变量Zi的标准差估值
Figure PCTCN2016078164-appb-000069
变动大，常规权因子为
Figure PCTCN2016078164-appb-000070
采用调和的加权二次回归，Zi的相对权因子取
Figure PCTCN2016078164-appb-000071
这里α取0.5～1.8的数，β取-1～0的数。标准具细度较小时(α，β)典型值为(1，0)，细度较大时典型值为(1，-1)，介于等权因子(0，0)与一般加权因子(2，-1)之间。回归方程为
Figure PCTCN2016078164-appb-000072
(3)由回归所得系数b1，b2求出细分后极值点位坐标为
Figure PCTCN2016078164-appb-000073
平行于Y轴的点域内按类似方法定出整数像元坐标xj及细分后坐标yj *.对 多个圆环(一般不少于8个)、同一圆环上用不少于24点的(xj *，yj)、(xj，yj *)等坐标值，作有同心约束的圆方程回归，求出各同心圆环的直径Di及其标准差
Figure PCTCN2016078164-appb-000074
同时求出圆心坐标平均值
Figure PCTCN2016078164-appb-000075
及其标准差
Figure PCTCN2016078164-appb-000076
±45度的点域内(线段上)信号处理方法也与上述类似，可以看作是坐标旋转45度后的新的平行于轴向的数据。对角线与线段重合的相邻像元间距为
Figure PCTCN2016078164-appb-000077
如果内插入半整数序号的等效像元，光电信号取线段两侧的、像元角点重合于线段上的两对称像元的信号平均值，就会使±45度线段上的等效像元数增加一倍，相邻等效像元的间距减小到
Figure PCTCN2016078164-appb-000078
度线段上的细分后峰位点的坐标要经过平面几何计算，转化成直角坐标系中的值，再参与圆回归计算。
由于有50％的点位坐标值经过用多个相邻像元量值的细分计算，用多个圆、每个圆用多个点作回归计算，参与坐标细分计算的原始像元数目大于1.5×103，并且这些像元散布在面阵光电器件的很大范围内，就能使单个像元的几何误差与光电转换误差被充分随机化，使统计计算后圆心坐标的标准差
Figure PCTCN2016078164-appb-000079
降低到0.02W以下，也使圆直径平方D2的标准差
Figure PCTCN2016078164-appb-000080
减小到细分前的1/3以下。
本发明用法布里-珀罗标准具，产生一组圆锥角标准的圆锥光束作为参考光束，在物镜焦平面上形成系列同心圆环。采用面阵光电器件的像元细分技术对光电信号极值点位坐标细分，采集多个圆环、每个圆取多个点域，每个点域含多个像元的信息。对这样大数量、大范围内的像元信号作统计计算，使单个像元的误差影响被充分随机化，能提高圆半径测量的准确度与精密度以及与圆锥轴方位角关联的同心圆环圆心坐标的准确度与精密度，即提高焦距以及转角测量的准确度与精密度。
本发明中的角度量值溯源到光谱灯单色光波长λ0及标准具间隔d，已知
Figure PCTCN2016078164-appb-000081
能较方便地用小数重合法测量并控制使Ud/d≤5×10-6，进而使采用本发明方法的小角度测量仪器具有可溯源性和便于定度或检定的优点。
可溯源的焦距测量不确定度比已有典型方法的不确定度Uf/f≈2.5×10-3减少到40％以下。光电信号极值点位像元坐标细分技术同时为减少调焦误差限及调焦 自动化创造了条件。
以往多数光电自准直仪的测量线性度和测角准确度受物镜焦距不确定度制约，本发明中的(8)式到(9)式，用比较测量方法避开了这一难点，能使可溯源的转角不确定度中的倍率分量系数比常规仪器减小到2/5以下。用单一光学系统及单一面阵光电接收器件实现二维转角的同时测量，也是本发明的优点之一。
用法布里-珀罗标准具与信号极值点位像元坐标细分技术准确测定焦距后，进而用一维的线阵CCD器件测量一维转镜反射光束偏转角，能实现非线性相对误差限小于0.01％的光束偏转角的高有效分辨率的准静态或动态测量。
本领域技术人员将认识到，对以上描述做出众多变通是可能的，所以实施例仅是用来描述一个或多个特定实施方式。
尽管已经描述和叙述了被看作本发明的示范实施例，本领域技术人员将会明白，可以对其作出各种改变和替换，而不会脱离本发明的精神。另外，可以做出许多修改以将特定情况适配到本发明的教义，而不会脱离在此描述的本发明中心概念。所以，本发明不受限于在此披露的特定实施例，但本发明可能还包括属于本发明范围的所有实施例及其等同物。

Claims (6)

  1. 一种用法布里-珀罗标准具测量焦距的方法，其特征在于：包括如下步骤：
    第一步：用单色光经法布里-珀罗标准具透射，产生一组圆锥角θi规律准确的标准圆锥光束，所述圆锥光束经半透半反平面镜反射到转镜，经转镜反射后透过半透半反镜，再经过物镜，在位于所述物镜的焦平面的面阵光电器件表面形成一组同心圆环；
    第二步：在各圆环上选取多个点域，对各个点域内的一维像元作细分；
    第三步：由所述圆锥光束的同心圆环直径Di及其标准差
    Figure PCTCN2016078164-appb-100001
    按圆锥角θi分布规律由Di＝2(fi/W)tanθi求出fi/W，fi/W是由单个圆直径Di算出的焦距fi与所述面阵光电器件的平均像元间距W的比值，进而求出fi/W的加权平均值
    Figure PCTCN2016078164-appb-100002
    以得出被测焦距f。
  2. 如权利要求1所述的测量焦距的方法，其特征在于：所述第二步具体包括：先找出所述同心圆环的近似圆心点
    Figure PCTCN2016078164-appb-100003
    再在近似圆心点附近分别作至少3条水平线、至少3条垂直线和方位角是±45度的至少各3条平行斜线，使所述每条水平线、垂直线或±45度线与每个圆环相交形成2个线段，在每条线段上运用光电信号极值点位像元坐标细分方法，求出包含小数的、以像元平均间距W或
    Figure PCTCN2016078164-appb-100004
    为单位的坐标值。
  3. 如权利要求2所述的测量焦距的方法，其特征在于：所述的光电信号极值点位像元坐标细分方法包括如下步骤：对线段上的连续像元信号，或±45度线段两侧两个像元角点重合于线段上的对称像元的信号均值，记像元信号峰值为IM，保留峰值像元两侧8～18个连续像元，含峰值；以这些像元信号Ii的函数
    Figure PCTCN2016078164-appb-100005
    为因变量、以像元序号i或对应值及其平方i2为自变量作二次回归；由于Zi的标准差估值
    Figure PCTCN2016078164-appb-100006
    变动大，采用调和的加权二次回归，Zi的相对权因子取
    Figure PCTCN2016078164-appb-100007
    这里α取0.5～1.8的数，β取-1～0的数。标准具细度较小时(α，β)典型值为(1，0)，细度较大时典型值为(1，-1)，介于等权因子(0，0)与一般加权因子(2，-1)之 间。回归方程为
    Figure PCTCN2016078164-appb-100008
    细分后极值点位坐标为
    Figure PCTCN2016078164-appb-100009
  4. 一种用法布里-珀罗标准具测量转角的方法，其特征在于：包括如下步骤：
    第一步：用单色光经法布里-珀罗标准具透射，产生一组圆锥角θi规律准确的标准圆锥光束，所述圆锥光束经半透半反平面镜反射到转镜，经转镜反射后透过半透半反镜，再经过物镜，在位于所述物镜的焦平面的面阵光电器件表面形成一组同心圆环；
    第二步：在各圆环上选取多个点域，对各个点域内的一维像元作细分；
    第三步：由所述圆锥光束的同心圆环直径Di及其标准差
    Figure PCTCN2016078164-appb-100010
    按圆锥角θi分布规律由Di＝2(fi/W)tanθi求出fi/W，fi/W是由单个圆直径Di算出的焦距fi与所述面阵光电器件的平均像元间距W的比值，进而求出fi/W的加权平均值
    Figure PCTCN2016078164-appb-100011
    第四步：根据转镜产生转角δ0后，入射向物镜的圆锥光束中心轴将转过2δ0角，使同心圆环圆心平移
    Figure PCTCN2016078164-appb-100012
    通过所述同心圆环的圆心
    Figure PCTCN2016078164-appb-100013
    的平移量计算出转镜转角δθ。
  5. 如权利要求4所述的测量转角的方法，其特征在于：所述第二步具体包括：先找出所述同心圆环的近似圆心点
    Figure PCTCN2016078164-appb-100014
    再在近似圆心点附近分别作至少3条水平线、至少3条垂直线和方位角是±45度的至少各3条平行斜线，使所述每条水平线、垂直线或±45度线与每个圆环相交形成2个线段，在每条线段上运用光电信号极值点位像元坐标细分方法，求出包含小数的、以像元平均间距W或
    Figure PCTCN2016078164-appb-100015
    为单位的坐标值。
  6. 如权利要求5所述的测量转角的方法，其特征在于：所述的光电信号极值点位像元坐标细分方法包括如下步骤：对线段上的连续像元信号，或±45度线段两侧两个像元角点重合于线段上的对称像元的信号均值，记像元信号峰值为IM，保留峰值像元两侧8～18个连续像元，含峰值；以这些像元信号Ii的函数
    Figure PCTCN2016078164-appb-100016
    为因变量、以像元序号i或对应值及其平方i2为自变量作二次回归；由于Zi的标 准差估值
    Figure PCTCN2016078164-appb-100017
    变动大，采用调和的加权二次回归，Zi的相对权因子取
    Figure PCTCN2016078164-appb-100018
    这里α取0.5～1.8的数，β取-1～0的数。标准具细度较小时(α，β)典型值为(1，0)，细度较大时典型值为(1，-1)，介于等权因子(0，0)与一般加权因子(2，-1)之间。回归方程为
    Figure PCTCN2016078164-appb-100019
    细分后极值点位坐标为
    Figure PCTCN2016078164-appb-100020
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