CN102128599B

CN102128599B - Contact aspheric surface shape test device

Info

Publication number: CN102128599B
Application number: CN2010106073421A
Authority: CN
Inventors: 王孝坤; 郑立功; 张学军
Original assignee: Changchun Institute of Optics Fine Mechanics and Physics of CAS
Current assignee: Changchun Institute of Optics Fine Mechanics and Physics of CAS
Priority date: 2010-12-27
Filing date: 2010-12-27
Publication date: 2012-06-13
Anticipated expiration: 2030-12-27
Also published as: CN102128599A

Abstract

The invention relates to a contact aspheric surface shape test device. The device comprises a computer and a laser tracker, wherein the computer integrates a physical coordinate system of an aspheric surface to be measured at the moment with a coordinate system of a computer-aided design (CAD) model into an integrated coordinate system by performing coordinate conversion on the position coordinate of a characteristic point on the aspheric surface to be measured, which is measured by the laser tracker, and the position coordinate of a corresponding characteristic point on the CAD model; the computer performs interpolation calculation to obtain the position coordinate of each point on the aspheric surface to be measured by using the position coordinates of a plurality of points on the aspheric surface in the integrated coordinate system, which are measured by the laser tracker; and the computer obtains the deviation between the coordinate value of each point on the aspheric surface to be measured in the integrated coordinate system and the coordinate value of each point on the CAD data model through analysis and solution, and fits deviation data to obtain the surface shape distribution of the aspheric surface to be measured. Data processing and data operation are simple, the experiment is easy to operate, detection cost is low, test time is short, and the device is suitable for the surface shape detection in the whole processing procedure of the aspheric surface.

Description

Contact Aspheric Surface Shape Inspection Device

技术领域 technical field

本发明涉及一种接触式光学非球面面形检验装置。The invention relates to a contact optical aspheric surface shape inspection device.

背景技术 Background technique

当前，检验非球面元件的方法有很多种，主要分为接触式测量和非接触式测量。接触式测量主要借助轮廓仪或者三坐标测量仪通过对光学元件进行多个离散点的测量，然后经过数据处理，拟合得到面形误差。非接触式测量主要有阴影法、激光扫描法、干涉法等。阴影法主要分为刀口法和哈特曼法(光阑法)，该方法主要观察阴影分布的图形和阴影图的明暗对比。这种方法设备简单，对于某些二次曲面测量方便，适于现场检验。但存在主观、定量困难、灵敏度欠高等缺点。激光扫描法可分平移法、旋转法，以及平移旋转法，这是一种利用光的直线性进行面形检测的方法，通过用激光束对被测面进行逐点测量可计算出非球面的面形参数。它通用性强，可以测量各种非球面，而且是对被测面进行绝对测量，精度高，缺点是相应的数据处理比较复杂。干涉法是一种短时间检测非球面的方法，由于它具有高分辨、高精度、高灵敏度、重复性好等优点，但是利用该技术测量非球面面形时，要求非球面表面有很好的光洁度和很高的反射能力。因此，干涉法一般适用于非球面精抛光和最终阶段的检测。At present, there are many methods for inspecting aspheric components, which are mainly divided into contact measurement and non-contact measurement. Contact measurement mainly uses a profiler or a three-coordinate measuring instrument to measure multiple discrete points on the optical element, and then after data processing, the surface shape error is obtained by fitting. Non-contact measurement mainly includes shadow method, laser scanning method, interferometry and so on. The shadow method is mainly divided into the knife-edge method and the Hartmann method (aperture method). This method mainly observes the shadow distribution graph and the light-dark contrast of the shadow map. This method has simple equipment, is convenient for measuring some quadratic surfaces, and is suitable for on-site inspection. However, there are disadvantages such as subjectivity, quantitative difficulty, and low sensitivity. The laser scanning method can be divided into translation method, rotation method, and translation and rotation method. This is a method of surface shape detection using the linearity of light. The aspheric surface can be calculated by point-by-point measurement of the measured surface with a laser beam. Surface parameters. It has strong versatility and can measure various aspheric surfaces, and it is an absolute measurement of the measured surface with high precision. The disadvantage is that the corresponding data processing is relatively complicated. Interferometry is a method for detecting aspheric surfaces in a short time. It has the advantages of high resolution, high precision, high sensitivity, and good repeatability. However, when using this technology to measure the aspheric surface shape, it is required to have a good smooth and highly reflective. Therefore, interferometry is generally suitable for aspheric surface finishing and final stage detection.

发明内容 Contents of the invention

本发明要解决的技术问题是提供一种适用于非球面加工整个过程的接触式非球面面形检验装置，该装置能够直接实现对非球面的测量，数据处理和数学运算简单，实验操作简单易行，测量时间短、测试成本低。The technical problem to be solved by the present invention is to provide a contact-type aspheric surface shape inspection device suitable for the entire process of aspheric surface processing. The device can directly realize the measurement of aspheric surfaces, and the data processing and mathematical operations are simple, and the experimental operation is simple and easy. OK, short measurement time and low cost of testing.

为了解决上述技术问题，本发明的接触式非球面面形检验装置包括计算机和激光跟踪仪；所述计算机包括存储待测非球面CAD模型的装置、坐标变换装置、求解位置坐标的装置和求解待测非球面面形分布的装置；激光跟踪仪首先测量待测非球面上特征点的位置坐标并将其传输给坐标变换装置，由坐标变换装置利用测量的待测非球面上特征点的位置坐标及CAD模型上对应的特征点的位置坐标，通过坐标变换求解得到待测非球面、CAD模型两个坐标系之间的平移量和旋转量，将待测非球面此时的物理坐标系与CAD模型的坐标系统一到同一坐标系；激光跟踪仪测量在统一坐标系下待测非球面上多点的位置坐标并将其传输给求解位置坐标的装置，由求解位置坐标的装置利用测得的统一坐标系下待测非球面上多点的位置坐标进行插值计算得到待测非球面上各点的位置坐标；求解待测非球面面形分布的装置分析求解得到统一坐标系下待测非球面上各点的坐标值与CAD数模上对应的各点坐标值之间的偏差，并对偏差数据进行拟合，得到待测非球面面形分布。In order to solve the above-mentioned technical problems, the contact type aspheric surface shape inspection device of the present invention includes a computer and a laser tracker; A device for measuring the distribution of an aspheric surface; the laser tracker first measures the position coordinates of the feature points on the aspheric surface to be measured and transmits it to the coordinate transformation device, and the coordinate transformation device uses the measured position coordinates of the feature points on the aspheric surface to be measured and the position coordinates of the corresponding feature points on the CAD model, the translation and rotation between the two coordinate systems of the aspheric surface to be measured and the CAD model are obtained by solving the coordinate transformation, and the physical coordinate system of the aspheric surface to be measured at this time is compared with the CAD The coordinate system of the model is one to the same coordinate system; the laser tracker measures the position coordinates of multiple points on the aspheric surface to be measured under the unified coordinate system and transmits them to the device for solving the position coordinates, and the device for solving the position coordinates uses the measured The position coordinates of multiple points on the aspheric surface to be measured are interpolated in the unified coordinate system to obtain the position coordinates of each point on the aspheric surface to be measured; the device analysis and solution for solving the surface shape distribution of the aspheric surface to be measured is obtained to obtain the aspheric surface to be measured in the unified coordinate system The deviation between the coordinate values of each point on the map and the corresponding coordinate values of each point on the CAD digital model, and the deviation data are fitted to obtain the aspherical surface shape distribution to be measured.

所述特征点为在待测非球面上设定的三个点，如侧面或者背部的轻量化圆孔、锥孔的圆心或者三角形孔的中心等。The feature points are three points set on the aspheric surface to be tested, such as the lightweight circular hole on the side or back, the center of the cone hole or the center of the triangular hole, etc.

本发明通过扩充激光跟踪仪的现有功能，利用激光跟踪仪的靶标球对非球面表面进行多点接触测量，并将测量的结果与数据模型进行分析对比、处理和运算，获得非球面的面形分布信息，无需其它辅助光学元件就能够准确的实现对大口径非球面面形的检测。本发明数据处理和数学运算简单，实验操作简单易行，检测成本很低，测试时间短，适用于非球面加工整个过程的面形检测。The present invention expands the existing functions of the laser tracker, uses the target ball of the laser tracker to perform multi-point contact measurement on the aspheric surface, and analyzes, compares, processes and calculates the measurement results with the data model to obtain the aspheric surface The shape distribution information can accurately realize the detection of the large-aperture aspheric surface shape without other auxiliary optical elements. The invention has simple data processing and mathematical operation, simple and easy experimental operation, low detection cost and short test time, and is suitable for surface shape detection in the whole process of aspheric surface processing.

附图说明 Description of drawings

下面结合附图和具体实施方式对本发明作进一步详细说明。The present invention will be described in further detail below in conjunction with the accompanying drawings and specific embodiments.

图1是本发明的接触式非球面面形检验装置结构示意图。Fig. 1 is a schematic structural view of a contact-type aspheric surface shape testing device of the present invention.

图2是计算机测量软件功能模块示意图。Figure 2 is a schematic diagram of the functional modules of the computer measurement software.

图3是待测非球面结构示意图。Fig. 3 is a schematic diagram of the structure of the aspheric surface to be tested.

图4是利用本发明对非球面面形进行检验的流程图。Fig. 4 is a flow chart of checking the aspheric surface shape by using the present invention.

具体实施方式 Detailed ways

如图1所示，本发明的接触式非球面面形检验装置包括计算机1和激光跟踪仪2；所述激光跟踪仪2与计算机1通过数据线进行连接。As shown in FIG. 1 , the contact-type aspheric surface shape inspection device of the present invention includes a computer 1 and a laser tracker 2; the laser tracker 2 is connected to the computer 1 through a data line.

激光跟踪仪2是一种高精度、大容量的便携式三位坐标测量设备，该激光跟踪仪使用两个旋转角编码器和一个激光距离测量系统，以跟踪和测量靶标球3的位置。靶标球3是由空心的直角反射镜组成，此反射镜精确固定在加工球体内。球体外表面到中心的距离已知(即球体半径)，激光跟踪仪测量软件利用球体半径进行测量偏移或补偿测量。激光跟踪仪发射并接收从靶标球返回的红色氦氖激光，激光跟踪仪机械轴的方向会根据其内部的位置感应探测器接收的两个旋转角编码器及距离测量系统反馈的信息不断进行调整。激光跟踪仪通过测量两个角度和一个距离来确定目标的坐标。这些角度由安装在顶点角轴和方位角轴上的编码器来测量。径向距离是由条纹计数干涉仪或一种相位偏移绝对距离测量系统(XtremeADM)来测量。激光跟踪仪一般用来测量物体之间的相对位置关系，并可以直接检验平面和球面物体的面形，但是对于非球面元件的面形却不能实现直接检验。The laser tracker 2 is a high-precision, large-capacity portable three-position coordinate measuring device, which uses two rotary angle encoders and a laser distance measurement system to track and measure the position of the target ball 3. The target ball 3 is made up of a hollow right-angle reflector, which is precisely fixed in the processing sphere. The distance from the outer surface of the sphere to the center is known (that is, the radius of the sphere), and the laser tracker measurement software uses the radius of the sphere for measurement offset or compensation measurement. The laser tracker emits and receives the red helium-neon laser returned from the target ball, and the direction of the mechanical axis of the laser tracker will be continuously adjusted according to the information fed back by the two rotary angle encoders and the distance measurement system received by its internal position sensing detector. . Laser trackers determine the coordinates of a target by measuring two angles and a distance. These angles are measured by encoders mounted on the apex and azimuth axes. The radial distance is measured by a fringe counting interferometer or a phase-shifted absolute distance measurement system (XtremeADM). Laser trackers are generally used to measure the relative positional relationship between objects, and can directly inspect the surface shape of plane and spherical objects, but the surface shape of aspheric components cannot be directly inspected.

如图2所示，所述计算机1的测量软件包括存储待测非球面CAD模型的装置11、坐标变换装置12、求解位置坐标的装置13和求解待测非球面面形分布的装置14。As shown in Figure 2, the measurement software of the computer 1 includes a device 11 for storing the CAD model of the aspheric surface to be measured, a coordinate transformation device 12, a device 13 for solving position coordinates, and a device 14 for solving the distribution of the aspheric surface to be measured.

所述坐标变换装置12查找待测非球面的CAD模型，提取与激光跟踪仪2测量的特征点p₁(x₁，y₁，z₁)，p₂(x₂，y₂，z₂)和p₃(x₃，y₃，z₃)相对应的CAD模型上的特征点的位置坐标P₁(X₁，Y₁，Z₁)，P₂(X₂，Y₂，Z₂)和P₃(X₃，Y₃，Z₃)，如图3所示；通过迭代法求解公式(1)和公式(5)联立的非线性方程组，得到待测非球面的物理坐标系相对CAD模型的坐标系在x方向、y方向、z方向上的平移量d_x、d_y和d_z以及待测非球面的物理坐标系相对CAD模型的坐标系绕x轴、y轴、z轴的转动角度量α、β和γ，进而将两个坐标系统一到同一坐标系；The coordinate transformation device 12 searches the CAD model of the aspheric surface to be measured, and extracts the characteristic points p ₁ (x ₁ , y ₁ , z ₁ ), p ₂ (x ₂ , y ₂ , z ₂ ) measured by the laser tracker 2 The position coordinates P ₁ (X ₁ , Y ₁ , Z ₁ ), P ₂ (X ₂ , Y ₂ , Z ₂ ) of the feature points on the CAD model corresponding to p ₃ (x ₃ , y ₃ , z ₃ ) and P ₃ (X ₃ , Y ₃ , Z ₃ ), as shown in Figure 3; through the iterative method to solve the simultaneous nonlinear equations of formula (1) and formula (5), the physical coordinate system of the aspheric surface to be measured is obtained Relative to the coordinate system of the CAD model in the x-direction, y-direction, and z-direction translation d _x , d _y and d _z and the physical coordinate system of the aspheric surface to be measured are relative to the coordinate system of the CAD model around the x-axis, y-axis, z The rotation angles α, β, and γ of the axis are used to convert the two coordinate systems to the same coordinate system;

$\{\begin{matrix} (({x x}_{11},, {y the y}_{11},, {z z}_{11},, 11)) = = (({X x}_{11},, {Y Y}_{11},, {Z Z}_{11},, 11)) \cdot &Center Dot; V V \\ (({x x}_{22},, {y the y}_{22} {,, z z}_{22},, 11)) = = (({X x}_{22},, {Y Y}_{22},, {Z Z}_{22},, 11)) \cdot &Center Dot; V V \\ (({x x}_{33},, {y the y}_{33},, {z z}_{33},, 11)) = = (({X x}_{33},, {Y Y}_{33},, {Z Z}_{33},, 11)) \cdot &Center Dot; V V \end{matrix} - - - - - - ((11))$

$V V = = [\begin{matrix} cos cos β β cos cos γ γ & cos cos β β sin sin γ γ & - - sin sin β β & 00 \\ sin sin α α sin sin β β cos cos γ γ - - cos cos α α sin sin γ γ & sin sin α α sin sin β β sin sin γ γ + + cos cos α α cos cos γ γ & sin sin α α cos cos β β & 00 \\ cos cos α α sin sin β β cos cos γ γ + + sin sin α α sin sin γ γ & cos cos α α sin sin β β sin sin γ γ - - sin sin α α cos cos γ γ & cos cos α α cos cos β β & 00 \\ {d d}_{x x} & {d d}_{y the y} & {d d}_{z z} & 11 \end{matrix}] - - - - - - ((55))$

其中(x₁，y₁，z₁，1)为p₁(x₁，y₁，z₁)点在待测非球面的物理坐标系中的坐标行矩阵，(X₁，Y₁，Z₁，1)为与p₁(x₁，y₁，z₁)点相对应的P₁(X₁，Y₁，Z₁)点在CAD模型坐标系中的坐标行矩阵；(x₂，y₂，z₂，1)为p₂(x₂，y₂，z₂)点在待测非球面的物理坐标系中的坐标行矩阵，(X₂，Y₂，Z₂，1)为与p₂(x₂，y₂，z₂)点相对应的P₂(X₂，Y₂，Z₂)点在CAD模型坐标系中的坐标行矩阵；(x₃，y₃，z₃，1)为p₃(x₃，y₃，z₃)点在待测非球面的物理坐标系中的坐标行矩阵，(X₃，Y₃，Z₃，1)为与p₃(x₃，y₃，z₃)点相对应的P₃(X₃，Y₃，Z₃)点在CAD模型坐标系中的坐标行矩阵；d_x、d_y和d_z分别为待测非球面的物理坐标系相对CAD模型坐标系在x方向、y方向、z方向上的平移量，α、β和γ分别为待测非球面的物理坐标系相对CAD模型坐标系绕x轴、y轴、z轴的转动角度量。Where (x ₁ , y ₁ , z ₁ , 1) is the coordinate row matrix of point p ₁ (x ₁ , y ₁ , z ₁ ) in the physical coordinate system of the aspherical surface to be measured, (X ₁ , Y ₁ , Z ₁ , 1) is the coordinate row matrix of point P ₁ (X ₁ , Y ₁ , Z ₁ ) corresponding to point p ₁ (x ₁ , y ₁ , z ₁ ) in the CAD model coordinate system; (x ₂ , y ₂ , z ₂ , 1) is the coordinate row matrix of point p ₂ (x ₂ , y ₂ , z ₂ ) in the physical coordinate system of the aspheric surface to be measured, and (X ₂ , Y ₂ , Z ₂ , 1) is The coordinate row matrix of point P ₂ (X ₂ , Y ₂ , Z ₂ ) corresponding to point p ₂ (x ₂ , y ₂ , z ₂ ) in the coordinate system of the CAD model; (x ₃ , y ₃ , z ₃ , 1) is the coordinate row matrix of point p ₃ (x ₃ , y ₃ , z ₃ ) in the physical coordinate system of the aspheric surface to be measured, (X ₃ , Y ₃ , Z ₃ , 1) is the coordinate matrix of point p ₃ (x 3 , Z 3 , 1) ₃ , y ₃ , z ₃ ) point P ₃ (X ₃ , Y ₃ , Z ₃ ) corresponding to the coordinate row matrix in the CAD model coordinate system; d _x , d _y and d _z are respectively the aspheric surface to be measured The translation of the physical coordinate system relative to the CAD model coordinate system in the x direction, y direction, and z direction, α, β, and γ are respectively the physical coordinate system of the aspheric surface to be measured relative to the CAD model coordinate system around the x axis, y axis, The amount of rotation on the z-axis.

所述特征点p₁(x₁，y₁，z₁)，p₂(x₂，y₂，z₂)和p₃(x₃，y₃，z₃)为待测非球面侧面或者背部的轻量化圆孔、锥孔的圆心或者三角形孔的中心。可通过先测量圆孔或锥孔边缘上任意三个点的坐标，然后再计算得到其圆心坐标；三角形孔中心的坐标可利用三角形三个顶点的坐标通过计算得到。The feature points p ₁ (x ₁ , y ₁ , z ₁ ), p ₂ (x ₂ , y ₂ , z ₂ ) and p ₃ (x ₃ , y ₃ , z ₃ ) are the side or back of the aspheric surface to be measured The lightweight round hole, the center of a tapered hole or the center of a triangular hole. The coordinates of any three points on the edge of the circular hole or tapered hole can be measured first, and then the coordinates of the center of the circle can be obtained by calculation; the coordinates of the center of the triangular hole can be obtained by calculation using the coordinates of the three vertices of the triangle.

所述求解位置坐标的装置13利用测量得到的非球面上多点的位置坐标，通过三次样条插值或牛顿插值方法计算求解得到非球面上各点的位置坐标。The device 13 for calculating position coordinates uses the measured position coordinates of multiple points on the aspheric surface to calculate and solve the position coordinates of each point on the aspheric surface through cubic spline interpolation or Newton interpolation method.

如图4所示，利用本发明对非球面面形进行检验的步骤如下：As shown in Figure 4, the steps of utilizing the present invention to check the aspherical surface shape are as follows:

1)首先，建立待测非球面的CAD模型，并将该CAD模型导入计算机1的测量软件中；1) First, set up the CAD model of the aspheric surface to be measured, and import the CAD model into the measurement software of computer 1;

2)利用激光跟踪仪2测量待测非球面侧面或者背部的三个特征点p₁，p₂和p₃的位置坐标p₁(x₁，y₁，z₁)，p₂(x₂，y₂，z₂)和p₃(x₃，y₃，z₃)；2) Use the laser tracker 2 to measure _{the position coordinates p 1 (x 1 , y 1 , z 1} ₎ _, _p ₂ ₍ _x ₂ _, y ₂ , z ₂ ) and p ₃ (x ₃ , y ₃ , z ₃ );

3)查找非球面的CAD模型，提取与测量的特征点p₁(x₁，y₁，z₁)，p₂(x₂，y₂，z₂)和p₃(x₃，y₃，z₃)相对应的CAD数模上的特征点的位置坐标P₁(X₁，Y₁，Z₁)，P₂(X₂，Y₂，Z₂)和P₃(X₃，Y₃，Z₃)；3) Find the CAD model of the aspheric surface, extract and measure the feature points p ₁ (x ₁ , y ₁ , z ₁ ), p ₂ (x ₂ , y ₂ , z ₂ ) and p ₃ (x ₃ , y ₃ , z ₃ ) corresponding to the position coordinates P ₁ (X ₁ , Y ₁ , Z ₁ ), P ₂ (X ₂ , Y ₂ , Z ₂ ) and P ₃ (X ₃ , Y ₃ ) of the feature points on the CAD digital model , Z ₃ );

4)通过坐标变换，可以求解得到两个坐标系之间的平移量和旋转量，从而使得待测非球面此时的物理坐标系与CAD模型的坐标系一致；4) Through coordinate transformation, the translation and rotation between the two coordinate systems can be solved, so that the physical coordinate system of the aspheric surface to be measured at this time is consistent with the coordinate system of the CAD model;

具体算法步骤如下：The specific algorithm steps are as follows:

设定p₁点在待测非球面的物理坐标系中的坐标表示为行矩阵(x₁，y₁，z₁，1)，与p₁相对应的P₁点在CAD模型坐标系中的坐标表示为行矩阵(X₁，Y₁，Z₁，1)；假定待测非球面的物理坐标系相对CAD模型的坐标系在x方向、y方向、z方向上的平移量分别为d_x、d_y和d_z，待测非球面的物理坐标系相对CAD模型的坐标系绕x轴、y轴、z轴的转动角度量分别为α、β和γ，则根据坐标变换理论，待测非球面的物理坐标系上的特征位置坐标与CAD模型上对应特征的位置坐标有如下关系：Set the coordinates of point p ₁ in the physical coordinate system of the aspheric surface to be measured as a row matrix (x ₁ , y ₁ , z ₁ , 1), and the coordinates of point P ₁ corresponding to p ₁ in the coordinate system of the CAD model The coordinates are expressed as a row matrix (X ₁ , Y ₁ , Z ₁ , 1); it is assumed that the translation of the physical coordinate system of the aspheric surface to be measured relative to the coordinate system of the CAD model in the x direction, y direction, and z direction is respectively d _x , d _y and d _z , the rotation angles of the physical coordinate system of the aspheric surface to be measured relative to the coordinate system of the CAD model around the x-axis, y-axis and z-axis are α, β and γ respectively, then according to the coordinate transformation theory, the measured The feature position coordinates on the physical coordinate system of the aspheric surface have the following relationship with the position coordinates of the corresponding features on the CAD model:

$\{\begin{matrix} (({x x}_{11},, {y the y}_{11},, {z z}_{11},, 11)) = = (({X x}_{11},, {Y Y}_{11},, {Z Z}_{11},, 11)) \cdot \cdot V V \\ (({x x}_{22},, {y the y}_{22} {,, z z}_{22},, 11)) = = (({X x}_{22},, {Y Y}_{22},, {Z Z}_{22},, 11)) \cdot \cdot V V \\ (({x x}_{33},, {y the y}_{33},, {z z}_{33},, 11)) = = (({X x}_{33},, {Y Y}_{33},, {Z Z}_{33},, 11)) \cdot &Center Dot; V V \end{matrix} - - - - - - ((11))$

其中V为两个坐标系之间的变换矩阵，它是平移变换矩阵T和旋转变换矩阵R之间的乘积，即：where V is the transformation matrix between two coordinate systems, which is the product between the translation transformation matrix T and the rotation transformation matrix R, namely:

V＝T·R (2)V＝T·R (2)

$T T = = {T T}_{x x} . . {T T}_{y the y} {. . T T}_{z z} = = [\begin{matrix} 11 & 00 & 00 & 00 \\ 00 & 11 & 00 & 00 \\ 00 & 00 & 11 & 00 \\ {d d}_{x x} & 00 & 00 & 11 \end{matrix}] [\begin{matrix} 11 & 00 & 00 & 00 \\ 00 & 11 & 00 & 00 \\ 00 & 00 & 11 & 00 \\ {d d}_{y the y} & 00 & 00 & 11 \end{matrix}] [\begin{matrix} 11 & 00 & 00 & 00 \\ 00 & 11 & 00 & 00 \\ 00 & 00 & 11 & 00 \\ {d d}_{z z} & 00 & 00 & 11 \end{matrix}] = = [\begin{matrix} 11 & 00 & 00 & 00 \\ 00 & 11 & 00 & 00 \\ 00 & 00 & 11 & 00 \\ {d d}_{x x} & {d d}_{y the y} & {d d}_{z z} & 11 \end{matrix}] - - - - - - ((33))$

其中T_x、T_y和T_z分别为两个行矩阵在x方向、y方向和z方向上的平移矩阵。T _x , T _y and T _z are the translation matrices of the two row matrices in the x direction, y direction and z direction respectively.

$R R = = {R R}_{x x} {\cdot &Center Dot; R R}_{y the y} \cdot &Center Dot; {R R}_{z z} = = [\begin{matrix} 11 & 00 & 00 & 00 \\ 00 & cos cos α α & sin sin α α & 00 \\ 00 & - - sin sin α α & cos cos α α & 00 \\ 00 & 00 & 00 & 11 \end{matrix}] [\begin{matrix} cos cos β β & 00 & - - sin sin β β & 00 \\ 00 & 11 & 00 & 00 \\ sin sin β β & 00 & cos cos β β & 00 \\ 00 & 00 & 00 & 11 \end{matrix}] [\begin{matrix} cos cos γ γ & sin sin γ γ & 00 & 00 \\ - - sin sin γ γ & cos cos γ γ & 00 & 00 \\ 00 & 00 & 11 & 00 \\ 00 & 00 & 00 & 11 \end{matrix}] - - - - - - ((44))$

$= = [\begin{matrix} cos cos β β cos cos γ γ & cos cos β β sin sin γ γ & - - sin sin β β & 00 \\ sin sin α α sin sin β β cos cos γ γ - - cos cos α α sin sin γ γ & sin sin α α sin sin β β sin sin γ γ + + cos cos α α cos cos γ γ & sin sin α α cos cos β β & 00 \\ cos cos α α sin sin β β cos cos γ γ + + sin sin α α sin sin γ γ & cos cos α α sin sin β β sin sin γ γ - - sin sin α α cos cos γ γ & cos cos α α cos cos β β & 00 \\ 00 & 00 & 00 & 11 \end{matrix}]$

其中R_x、R_y和R_z分别为两个行矩阵在x方向、y方向和z方向上的旋转矩阵。Among them, R _x , R _y and R _z are the rotation matrices of the two row matrices in the x direction, y direction and z direction respectively.

则由(3)-(4)可推导得到两个坐标系之间的变换矩阵V为公式(5)，Then from (3)-(4), the transformation matrix V between the two coordinate systems can be derived as formula (5),

因为三个特征点分别在两个坐标系中的坐标值是已知的，通过迭代法求解公式(1)和公式(5)联立的非线性方程组，即可得到待测非球面的物理坐标系相对CAD模型的坐标系在x方向、y方向、z方向上的平移量d_x、d_y和d_z以及待测非球面的物理坐标系相对CAD模型的坐标系绕x轴、y轴、z轴的转动角度量α、β和γ，从而可以将两个坐标系统一起来；Because the coordinate values of the three feature points in the two coordinate systems are known, the physical properties of the aspheric surface to be measured can be obtained by solving the nonlinear equations of formula (1) and formula (5) by iterative method The translation of the coordinate system relative to the coordinate system of the CAD model in the x direction, y direction, and z direction d _x , d _y and d _z and the physical coordinate system of the aspheric surface to be measured are relative to the coordinate system of the CAD model around the x axis and the y axis , the rotation angles of the z axis α, β and γ, so that the two coordinate systems can be combined;

5)两个坐标系一致后，利用激光跟踪仪1测量在统一坐标系下待测非球面上多点的位置坐标；5) After the two coordinate systems are consistent, use the laser tracker 1 to measure the position coordinates of multiple points on the aspheric surface to be measured under the unified coordinate system;

6)利用测量得到的待测非球面上多点的位置坐标，通过三次样条插值计算求解得到待测非球面上各点的位置坐标；6) Using the measured position coordinates of multiple points on the aspheric surface to be measured, the position coordinates of each point on the aspheric surface to be measured are obtained through cubic spline interpolation calculation;

7)分析求解得到统一坐标系下待测非球面上各点的坐标值与对应CAD模型上各点坐标值的偏差，对偏差数据进行拟合，即为待测非球面的面形分布。7) Analyze and solve to obtain the deviation between the coordinate values of each point on the aspheric surface to be measured in the unified coordinate system and the coordinate values of each point on the corresponding CAD model, and fit the deviation data, which is the surface shape distribution of the aspheric surface to be measured.

Claims

1. a contact aspheric surface verifying attachment is characterized in that comprising computing machine (1) and laser tracker (2); Said computing machine (1) comprises device (11), the coordinate transformation device (12) of storing aspheric surface cad model to be measured, finds the solution the device (13) of position coordinates and finds the solution the device (14) that aspheric surface to be measured distributes; Laser tracker (2) is at first measured the position coordinates of unique point on the aspheric surface to be measured and it is transferred to coordinate transformation device (12); The position coordinates of characteristic of correspondence point on the position coordinates of unique point and the cad model on the aspheric surface of utilize measuring by coordinate transformation device (12) to be measured; Find the solution translational movement and the rotation amount that obtains between aspheric surface to be measured, two coordinate systems of cad model through coordinate transform, physical coordinates system at this moment is unified to the same coordinate system with the coordinate system of cad model with aspheric surface to be measured; Laser tracker (2) is measured under unified coordinate system on the aspheric surface to be measured the position coordinates of multiple spot and it is transferred to the device (13) of finding the solution position coordinates, under the unified coordinate system that records by the device of finding the solution position coordinates (13) utilization on the aspheric surface to be measured the position coordinates of multiple spot carry out the position coordinates that interpolation calculation obtains each point on the aspheric surface to be measured; Find the solution device (14) analysis and solution that aspheric surface to be measured distributes and obtain under the unified coordinate system on the aspheric surface to be measured deviation between the each point coordinate figure corresponding on the coordinate figure of each point and cad model; And deviation data carried out match, obtain aspheric surface to be measured and distribute.

2. contact aspheric surface verifying attachment according to claim 1 is characterized in that said coordinate transformation device (12) searches aspheric cad model to be measured, extracts the unique point p that measures with laser tracker (2) ₁(x ₁, y ₁, z ₁), p ₂(x ₂, y ₂, z ₂) and p ₃(x ₃, y ₃, z ₃) the position coordinates P of unique point on the corresponding cad model ₁(X ₁, Y ₁, Z ₁), P ₂(X ₂, Y ₂, Z ₂) and P ₃(X ₃, Y ₃, Z ₃); Through the Nonlinear System of Equations of solution by iterative method formula (1) and formula (5) simultaneous, the translational movement d of coordinate system on x direction, y direction, z direction that to obtain aspheric physical coordinates to be measured be relative cad model _x, d _yAnd d _zAnd the aspheric physical coordinates to be measured coordinate system that is relative cad model is around angle of rotation tolerance α, β and the γ of x axle, y axle, z axle, and then two coordinate systems are unified to the same coordinate system;

\{\begin{matrix} (x_{1}, y_{1}, z_{1}, 1) = (X_{1}, Y_{1}, Z_{1}, 1) \cdot V \\ (x_{2}, y_{2}, z_{2}, 1) = (X_{2}, Y_{2}, Z_{2}, 1) \cdot V \\ (x_{3}, y_{3}, z_{3}, 1) = (X_{3}, Y_{3}, Z_{3}, 1) \cdot V \end{matrix} - - - (1)

V = [\begin{matrix} \cos β \cos γ & \cos β \sin γ & - \sin β & 0 \\ \sin α \sin β \cos γ - \cos α \sin γ & \sin α \sin β \sin γ + \cos α \cos γ & \sin α \cos β & 0 \\ \cos α \sin β \cos γ + \sin α \sin γ & \cos α \sin β \sin γ - \sin α \cos γ & \cos α \cos β & 0 \\ d_{x} & d_{y} & d_{z} & 1 \end{matrix}] - - - (5)

(x wherein ₁, y ₁, z ₁, 1) and be p ₁(x ₁, y ₁, z ₁) the coordinate row matrix of point in aspheric physical coordinates to be measured is, (X ₁, Y ₁, Z ₁, 1) be and p ₁(x ₁, y ₁, z ₁) put corresponding P ₁(X ₁, Y ₁, Z ₁) the coordinate row matrix of point in the cad model coordinate system; (x ₂, y ₂, z ₂, 1) and be p ₂(x ₂, y ₂, z ₂) the coordinate row matrix of point in aspheric physical coordinates to be measured is, (X ₂, Y ₂, Z ₂, 1) be and p ₂(x ₂, y ₂, z ₂) put corresponding P ₂(X ₂, Y ₂, Z ₂) the coordinate row matrix of point in the cad model coordinate system; (x ₃, y ₃, z ₃, 1) and be p ₃(x ₃, y ₃, z ₃) the coordinate row matrix of point in aspheric physical coordinates to be measured is, (X ₃, Y ₃, Z ₃, 1) be and p ₃(x ₃, y ₃, z ₃) put corresponding P ₃(X ₃, Y ₃, Z ₃) the coordinate row matrix of point in the cad model coordinate system; d _x, d _yAnd d _zBeing respectively aspheric physical coordinates to be measured is the translational movement of relative cad model coordinate system on x direction, y direction, z direction, and it is the angle of rotation tolerance of relative cad model coordinate system around x axle, y axle, z axle that α, β and γ are respectively aspheric physical coordinates to be measured.

3. contact aspheric surface verifying attachment according to claim 1; The position coordinates that it is characterized in that multiple spot on the aspheric surface that the said device (13) of finding the solution position coordinates utilization measures calculates through cubic spline interpolation or Newton interpolation and to find the solution the position coordinates that obtains each point on the aspheric surface.