CN110793435B - Rapid calibration method for position measurement of four-quadrant photoelectric detector - Google Patents

Rapid calibration method for position measurement of four-quadrant photoelectric detector Download PDF

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CN110793435B
CN110793435B CN201910978033.6A CN201910978033A CN110793435B CN 110793435 B CN110793435 B CN 110793435B CN 201910978033 A CN201910978033 A CN 201910978033A CN 110793435 B CN110793435 B CN 110793435B
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段发阶
张聪
傅骁
刘文正
苏宇浩
余珍鑫
许昊宇
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Tianjin University
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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
    • G01B11/002—Measuring arrangements characterised by the use of optical techniques for measuring two or more coordinates
    • 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
    • G01B11/27—Measuring arrangements characterised by the use of optical techniques for measuring angles or tapers; for testing the alignment of axes for testing the alignment of axes
    • G01B11/272—Measuring arrangements characterised by the use of optical techniques for measuring angles or tapers; for testing the alignment of axes for testing the alignment of axes using photoelectric detection means

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Abstract

本发明公开一种用于四象限光电探测器位置测量的快速标定方法，本发明方法建立了四象限光电探测器位置测量模型，使用位移测量标准装置对四象限光电探测器进行标定，通过最小二乘法求出该测量距离下的激光截面半径，代入位置测量模型实现该测量距离下的位置测量；此外本发明还提供快速求得不同测量距离下激光截面半径的方法，通过标定得到几处不同测量距离下的激光截面半径，使用Levenberg‑Marquardt法得到激光束腰半径与束腰位置，进而可得到任意位置的激光截面半径，利用四象限光电探测器测量模型，实现不同距离下的位置测量。

Figure 201910978033

The invention discloses a fast calibration method for four-quadrant photoelectric detector position measurement. The method of the invention establishes a four-quadrant photoelectric detector position measurement model, and uses a displacement measurement standard device to calibrate the four-quadrant photoelectric detector. The laser cross-section radius under the measurement distance is obtained by multiplication, and the position measurement model is substituted into the position measurement model to realize the position measurement under the measurement distance; in addition, the present invention also provides a method for quickly obtaining the laser cross-section radius under different measurement distances, and several different measurements are obtained through calibration. For the laser cross-section radius at the distance, use the Levenberg-Marquardt method to obtain the laser beam waist radius and beam waist position, and then obtain the laser cross-section radius at any position, and use the four-quadrant photodetector measurement model to achieve position measurement at different distances.

Figure 201910978033

Description

Rapid calibration method for position measurement of four-quadrant photoelectric detector
Technical Field
The invention belongs to the technical field of instruments and meters, and particularly relates to a quick calibration method for measuring the position of a four-quadrant photoelectric detector.
Background
The four-quadrant photoelectric detector is a photoelectric detector formed by arranging four photodiodes with completely same performance according to the rectangular coordinate requirement, has the advantages of high detection sensitivity, simple signal processing, strong anti-interference capability and the like, and is commonly used in laser guidance and laser collimation measurement. The three-axis numerical control machine tool has 21 geometric errors which are respectively a six-degree-of-freedom error corresponding to each axis and an orthogonal error between every two axes, and the six-degree-of-freedom errors comprise a positioning error, a two-dimensional straightness error, a pitch angle, a yaw angle and a roll angle, so that the straightness errors occupy an important proportion in the total errors. A laser collimation measuring system with a four-quadrant photoelectric detector as a position detector is commonly used for measuring the straightness of a machine tool, and the measurement precision of the spot position on the four-quadrant photoelectric detector determines the measurement precision of the straightness error of the machine tool.
When laser irradiates the surface of a four-quadrant photoelectric detector, four photodiodes output four paths of photocurrent signals with corresponding sizes according to the intensity of power of light spots irradiated on the surface, spot position calculation is carried out according to the four paths of photocurrent signals, because the four-quadrant photoelectric detector is a two-dimensional device, spot position calculation values in two orthogonal directions can be obtained, the spot position calculation values and the spot centroid positions are not in a linear relation, a polynomial fitting method mentioned in the literature 'Investigation of position calculation and method for evaluating the linear measurement range for a source-square detector' (M.Chen, Y.Yang, X.Jia, et al. Optik,2013,124:6806-6809) is used for calculating a polynomial coefficient by using a least square method according to the curve relation of the calculation values and the spot centroid positions to express the relation of the calculation values and the spot centroid positions, and the spot measurement accuracy depends on the times of the polynomial, the higher the number of times, the higher the measurement accuracy, but the larger the calculation amount, and the calibration needs to measure enough points for fitting, which takes a lot of time.
When the measurement distance is increased, the light intensity distribution of the laser cross section irradiated on the four-quadrant photoelectric detector is changed, namely the radius of the Gaussian beam cross section is changed, and when the error caused by the change of the laser cross section radius is unacceptable, the four-quadrant photoelectric detector needs to be calibrated under the measurement distance. Therefore, when long-distance measurement is performed, the four-quadrant photodetector needs to be calibrated at different measurement distances, a lot of time is spent, and at this time, it is very important to find a method for quickly calibrating the four-quadrant photodetector.
Disclosure of Invention
The invention aims to overcome the defects in the prior art and provides a quick calibration method for measuring the position of a four-quadrant photoelectric detector.
The purpose of the invention is realized by the following technical scheme:
a quick calibration method for measuring the position of four-quadrant photoelectric detector features that the four-quadrant photoelectric detector can measure the light spots in x and y directions, the laser irradiates the photosensitive surface of four-quadrant photoelectric detector, and the center of mass of light spot is (x)0,y0) Four-quadrant photoelectric detectorThe photocurrent generated by the first quadrant of the photosurface is I1The photocurrent generated in the second quadrant is I2The photocurrent generated in the third quadrant is I3The photocurrent generated in the fourth quadrant is I4The quick calibration method specifically comprises the following steps:
(1) obtaining relative position sigma of light spot in x and y directions by using photocurrent of four quadrantsx、σy；
Figure BDA0002234287440000021
(2) The light spot energy is concentrated in the photosensitive surface of the four-quadrant photoelectric detector, the light spot energy distribution follows Gaussian distribution, and the relative position sigma of the light spotx、σyAnd the spot centroid position x0、y0The relationship is that omega is the radius of the light spot on the photosensitive surface of the four-quadrant photoelectric detector;
Figure BDA0002234287440000022
(3) inverse function erf of error function in equation (2)-1(σx)、erf-1(σy) Expanding by Taylor series, and reserving the first four orders as a position measurement model of the four-quadrant photoelectric detector, wherein g (sigma)x) To represent
Figure BDA0002234287440000023
Using g (sigma)y) To represent
Figure BDA0002234287440000024
Figure BDA0002234287440000025
(4) Using a displacement measurement standard device to measure and calibrate the position of the four-quadrant photoelectric detector in the x direction, moving the four-quadrant photoelectric detector in the x direction, and recording the displacement measurement standard deviceMeasurement result X ofiAnd the relative position σ of the four-quadrant photodetectorxiMoving the four-quadrant photoelectric detector for N times, and recording N groups of data, wherein N is more than 5;
(5) solving using least squares, a position residual mathematical model I (ω) is first constructed, see equation (4), where the spot radius ω and relative position σ are passedxiThe calculated centroid position of the light spot is xi(ω,σxi) (ii) a Then, a first derivative is obtained from the formula (4) and is made to be zero, and the optimal laser section radius omega is obtained, see the formula (5);
Figure BDA0002234287440000031
Figure BDA0002234287440000032
(6) the formula (5) is substituted for the formula (3) to realize the position measurement of the four-quadrant photoelectric detector under the fixed measurement distance.
Further, in the step (5), in the uniform transparent medium, the laser is a gaussian beam, and the beam waist radius of the laser is ω0The position of the girdling is z0The laser wavelength is lambda, the laser propagates along the z-axis direction, and the laser section radius when the measurement distance is z is:
Figure BDA0002234287440000033
therefore, the specific steps for rapidly solving the laser section radius under different measuring distances are as follows:
(501) at different measuring distances ziCalibrating the four-quadrant photoelectric detector to obtain different z valuesiCorresponding laser section radius omegaiAcquiring M groups of data, wherein M is larger than 5;
(502) the function f (u) is constructed as follows, where the vector u ═ ω0,z0)TRepresenting the beam waist radius omega0And the girdling position z0、fi(u)＝ωi-ω(zi) Represents the laser cross-sectional radius ωiAnd the laser section radius ω (z) obtained by the formula (6)i) F (u) ═ f1(u),f2(u)...fM(u)]TRepresenting f at different measuring distancesi(u)；
Figure BDA0002234287440000034
(503) Solving laser beam waist omega when F (u) is minimum value by using Levenberg-Marquardt method in solving nonlinear least square problem0Waist position z0；
(504) Laser beam waist radius omega0And the position z of the girdling0And substituting the formula (6) to obtain the laser section radius under different measuring distances, and substituting the formula (3) with the laser section radius to realize position measurement under different measuring distances.
Compared with the prior art, the technical scheme of the invention has the following beneficial effects:
(1) the method establishes a four-quadrant photoelectric detector position measurement model according to the characteristics of laser spot light intensity Gaussian distribution, calibrates the four-quadrant photoelectric detector by using a displacement measurement standard device, calculates the laser section radius under the measurement distance by a least square method, and substitutes the laser section radius into the position measurement model to realize the position measurement under the measurement distance;
(2) the invention provides a method for rapidly obtaining laser section radiuses at different measuring distances, which comprises the steps of calibrating to obtain the laser section radiuses at different measuring distances, obtaining the laser beam waist radius and the laser beam waist position by using a Levenberg-Marquardt method, obtaining the laser section radius at any position by using Gaussian beam propagation characteristics, and realizing position measurement at different measuring distances by using a four-quadrant photoelectric detector measuring model.
Drawings
Fig. 1 is a diagram of four quadrant photodetector spot position measurement.
Fig. 2 is a diagram for measuring the position of a light spot under different measuring distances of a four-quadrant photoelectric detector.
Detailed Description
The invention is described in further detail below with reference to the figures and specific examples. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The invention provides a quick calibration method for measuring the position of a four-quadrant photoelectric detector, which mainly comprises the following two parts:
the first part is a rapid calibration method for measuring the position of a four-quadrant photoelectric detector under a fixed measuring distance;
the four-quadrant photodetector can measure the position of a light spot in the x direction and the y direction, as shown in fig. 1, laser irradiates the photosensitive surface of the four-quadrant photodetector, and the centroid position of the light spot is (x)0,y0) The photocurrent generated by the first quadrant of the photosensitive surface of the four-quadrant photoelectric detector is I1The photocurrent generated in the second quadrant is I2The photocurrent generated in the third quadrant is I3The photocurrent generated in the fourth quadrant is I4The quick calibration method for measuring the position of the four-quadrant photoelectric detector under the fixed measurement distance comprises the following steps of:
step 1: obtaining relative position sigma of light spot in x and y directions by using photocurrent of four quadrantsx、σy；
Figure BDA0002234287440000041
Step 2: the light spot energy is concentrated in the photosensitive surface of the four-quadrant photoelectric detector, the light spot energy distribution follows Gaussian distribution, and the relative position sigma of the light spotx、σyAnd the spot centroid position x0、y0The relationship is that omega is the radius of the light spot on the photosensitive surface of the four-quadrant photoelectric detector;
Figure BDA0002234287440000042
and 3, step 3: in the formula (2)Error function of (2)-1(σx)、erf-1(σy) Expanding the Taylor series, and keeping the first four orders as a position measurement model of the four-quadrant photoelectric detector;
Figure BDA0002234287440000051
and 4, step 4: using a displacement measurement standard device to measure and calibrate the position of the four-quadrant photoelectric detector in the X direction, moving the four-quadrant photoelectric detector in the X direction, and recording the measurement result X of the displacement measurement standard deviceiAnd the relative position σ of the four-quadrant photodetectorxiMoving the four-quadrant photoelectric detector for N times, and recording N groups of data, wherein N is more than 5;
and 5, step 5: solving using least squares, a position residual mathematical model I (ω) is first constructed, see equation (4), where the spot radius ω and relative position σ are passedxiThe calculated centroid position of the light spot is xi(ω,σxi) (ii) a Then, a first derivative is obtained from the formula (4) and is made to be zero, and the optimal laser section radius omega is obtained, see the formula (5);
Figure BDA0002234287440000052
Figure BDA0002234287440000053
and 6, step 6: the formula (5) is substituted into the formula (3) to realize the position measurement of the four-quadrant photoelectric detector at the fixed measurement distance;
the second part provides a method for rapidly obtaining the laser section radius under different measuring distances, so as to realize the rapid calibration of the four-quadrant photoelectric detector;
in a uniform transparent medium, the laser is a Gaussian beam, and the beam waist radius of the laser is omega0The position of the girdling is z0The laser wavelength is lambda, the laser propagates along the z-axis direction, and the laser measures the distance zThe section radius is as follows;
Figure BDA0002234287440000054
the method for rapidly solving the laser section radius under different measuring distances comprises the following steps:
step 1: as shown in fig. 2, at different measuring distances ziCalibrating the four-quadrant photoelectric detector to obtain different z valuesiCorresponding laser section radius omegaiAcquiring M groups of data, wherein M is larger than 5;
step 2: the function f (u) is constructed as follows, where the vector u ═ ω0,z0)T、fi(u)＝ωi-ω(zi)、f(u)＝[f1(u),f2(u)...fM(u)]T；
Figure BDA0002234287440000055
And 3, step 3: method for solving laser beam waist omega when F (u) is minimum value by utilizing Levenberg-Marquardt method commonly used in solving nonlinear least square problem0Waist position z0；
And 4, step 4: laser beam waist radius omega0And the position z of the girdling0And substituting the formula (6) to obtain the laser section radius under different measuring distances, and substituting the section radius into the formula (3) to realize position measurement under different measuring distances.
The present invention is not limited to the above-described embodiments. The foregoing description of the specific embodiments is intended to describe and illustrate the technical solutions of the present invention, and the above specific embodiments are merely illustrative and not restrictive. Those skilled in the art can make many changes and modifications to the invention without departing from the spirit and scope of the invention as defined in the appended claims.

Claims (2)

1.一种用于四象限光电探测器位置测量的快速标定方法，其特征在于，四象限光电探测器能够测量x、y两个方向的光斑位置，激光照射到四象限光电探测器光敏面上，光斑质心位置为(x0,y0)，四象限光电探测器光敏面第一象限产生的光电流为I1，第二象限产生的光电流为I2，第三象限产生的光电流为I3，第四象限产生的光电流为I4，快速标定方法具体包括以下步骤：1. a kind of fast calibration method for four-quadrant photodetector position measurement, it is characterized in that, four-quadrant photodetector can measure the spot position of two directions of x, y, and laser is irradiated on the photosensitive surface of four-quadrant photodetector , the spot centroid position is (x 0 , y 0 ), the photocurrent generated by the first quadrant of the photosensitive surface of the four-quadrant photodetector is I 1 , the photocurrent generated by the second quadrant is I 2 , and the photocurrent generated by the third quadrant is I 3 , the photocurrent generated in the fourth quadrant is I 4 , and the rapid calibration method specifically includes the following steps: (1)利用四个象限的光电流求得x、y两个方向的光斑相对位置σx、σy；(1) Use the photocurrents of the four quadrants to obtain the relative positions σ x and σ y of the light spots in the x and y directions;
Figure FDA0002629724060000011
Figure FDA0002629724060000011
 (2)认为光斑能量集中在四象限光电探测器光敏面内，且光斑能量分布遵循高斯分布，光斑相对位置σx、σy与光斑质心位置x0、y0有以下关系，其中ω为四象限光电探测器光敏面上的光斑半径；(2) It is considered that the spot energy is concentrated in the photosensitive surface of the four-quadrant photodetector, and the spot energy distribution follows a Gaussian distribution. The relative positions of the spot σ x , σ y and the spot centroid positions x 0 , y 0 have the following relationship, where ω is four The spot radius on the photosensitive surface of the quadrant photodetector;
Figure FDA0002629724060000012
Figure FDA0002629724060000012
 (3)将(2)式中的误差函数反函数erf-1(σx)、erf-1(σy)泰勒级数展开，保留前四阶作为四象限光电探测器位置测量模型，其中用g(σx)表示
Figure FDA0002629724060000013
用g(σy)表示
Figure FDA0002629724060000014
(3) Expand the error function inverse functions erf -1 (σ x ) and erf -1 (σ y ) Taylor series in equation (2), and retain the first four orders as the four-quadrant photodetector position measurement model, in which we use g(σ x ) means
Figure FDA0002629724060000013
represented by g(σ y )
Figure FDA0002629724060000014
Figure FDA0002629724060000015
Figure FDA0002629724060000015
 (4)使用位移测量标准装置对四象限光电探测器进行x方向位置测量标定，沿x方向移动四象限光电探测器，记录位移测量标准装置的测量结果Xi以及四象限光电探测器的相对位置σxi，移动四象限光电探测器N次，记录N组数据，其中N大于5；(4) Use the displacement measurement standard device to measure and calibrate the position of the four-quadrant photodetector in the x direction, move the four-quadrant photodetector along the x direction, and record the measurement result X i of the displacement measurement standard device and the relative position of the four-quadrant photodetector σ xi , move the four-quadrant photodetector N times to record N groups of data, where N is greater than 5; (5)使用最小二乘法进行求解，首先构建位置残差数学模型I(ω)，见式(4)，其中通过光斑半径ω和相对位置σxi算出来的光斑质心位置为xi(ω,σxi)；然后对式(4)求一阶导数并令一阶导数为零，求出最优的激光截面半径ω，见式(5)；(5) Use the least squares method to solve, first build the position residual mathematical model I(ω), see formula (4), where the spot centroid position calculated by the spot radius ω and the relative position σ xi is x i (ω, σ xi ); then obtain the first derivative of formula (4) and set the first derivative to zero to obtain the optimal laser cross-section radius ω, see formula (5);
Figure FDA0002629724060000021
Figure FDA0002629724060000021
Figure FDA0002629724060000022
Figure FDA0002629724060000022
 (6)将式(5)代入式(3)实现在固定测量距离下四象限光电探测器位置测量。(6) Substitute the formula (5) into the formula (3) to realize the position measurement of the four-quadrant photodetector under a fixed measurement distance. 2.根据权利要求1所述一种用于四象限光电探测器位置测量的快速标定方法，其特征在于，步骤(5)中在均匀的透明介质中，激光为高斯光束，激光的束腰半径为ω0，束腰位置为z0，激光波长为λ，激光沿z轴方向传播，测量距离为z时的激光截面半径为：2. a kind of fast calibration method for four-quadrant photodetector position measurement according to claim 1, is characterized in that, in step (5), in uniform transparent medium, laser is Gaussian beam, and the beam waist radius of laser is ω 0 , the beam waist position is z 0 , the laser wavelength is λ, the laser propagates along the z-axis direction, and the laser cross-section radius when the measurement distance is z is:
Figure FDA0002629724060000023
Figure FDA0002629724060000023
 因此快速求解不同测量距离下激光截面半径具体步骤如下：Therefore, the specific steps to quickly solve the laser cross-section radius under different measurement distances are as follows: (501)在不同的测量距离zi下进行四象限光电探测器标定，分别得到不同zi对应的激光截面半径ωi，获取M组数据，其中M大于5；(501) Four-quadrant photodetector calibration is performed under different measurement distances zi , respectively, to obtain the laser cross-section radius ω i corresponding to different zi , and obtain M sets of data, where M is greater than 5; (502)构建函数F(u)如下，其中向量u＝(ω0,z0)T表示束腰半径ω0和束腰位置z0、fi(u)＝ωi-ω(zi)表示激光截面半径ωi与通过式(6)求得的激光截面半径ω(zi)之差、f(u)＝[f1(u),f2(u)...fM(u)]T表示不同测量距离下的fi(u)；(502) The function F(u) is constructed as follows, where the vector u=(ω 0 , z 0 ) T represents the beam waist radius ω 0 and the beam waist position z 0 , f i (u)=ω i −ω(z i ) represents the difference between the laser cross-section radius ω i and the laser cross-section radius ω(z i ) obtained by equation (6), f(u)=[f 1 (u), f 2 (u)...f M (u )] T represents f i (u) under different measurement distances;
Figure FDA0002629724060000024
Figure FDA0002629724060000024
 (503)利用求解非线性最小二乘问题中的Levenberg-Marquardt法求解F(u)为极小值时的激光束腰半径ω0、束腰位置z0；(503) Use the Levenberg-Marquardt method in solving the nonlinear least squares problem to solve the laser beam waist radius ω 0 and the beam waist position z 0 when F(u) is a minimum value; (504)将激光束腰半径ω0与束腰位置z0代入式(6)，得到不同测量距离下的激光截面半径，将激光截面半径代入式(3)实现不同测量距离下的四象限光电探测器位置测量。(504) Substitute the laser beam waist radius ω 0 and the beam waist position z 0 into Equation (6) to obtain the laser cross-section radius under different measurement distances, and substitute the laser cross-section radius into Equation (3) to realize the four-quadrant optoelectronics under different measurement distances Detector position measurement.
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