阅读说明：本技术 一种用于四象限光电探测器位置测量的快速标定方法 (Rapid calibration method for position measurement of four-quadrant photoelectric detector ) 是由 段发阶 张聪 傅骁 刘文正 苏宇浩 余珍鑫 许昊宇 于 2019-10-15 设计创作，主要内容包括：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。(The invention discloses a quick calibration method for measuring the position of a four-quadrant photoelectric detector, which establishes a position measurement model of the four-quadrant photoelectric detector, 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; in addition, the invention also provides a method for rapidly obtaining the laser section radius under different measuring distances, the laser section radius under different measuring distances is obtained by calibration, the laser beam waist radius and the beam waist position are obtained by using a Levenberg-Marquardt method, the laser section radius at any position can be further obtained, and the position measurement under different distances is realized by using a four-quadrant photoelectric detector measuring model.)

1. A quick calibration method for measuring the position of a four-quadrant photoelectric detector is characterized in that the four-quadrant photoelectric detector can measure the positions of light spots in x and y directions, laser irradiates the photosensitive surface of the four-quadrant photoelectric detector, and the centroid position of the light spots 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 specifically comprises the following steps:

(1) obtaining relative position sigma of light spot in x and y directions by using photocurrent of four quadrants_x、σ_y；

(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 spot_x、σ_yAnd 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;

(3) inverse function erf of error function in equation (2)^-1(σ_x)、erf^-1(σ_y) 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

(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 device_iAnd the relative position σ of the four-quadrant photodetector_xiMoving 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 passed_xiThe calculated centroid position of the light spot is x_i(ω,σ_xi) (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);

(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.

2. The method for fast calibration of position measurement of four-quadrant photodetector as claimed in claim 1, wherein in step (5) in a uniform transparent medium, the laser is 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:

therefore, the specific steps for rapidly solving the laser section radius under different measuring distances are as follows:

(501) at different measuring distances z_iCalibrating the four-quadrant photoelectric detector to obtain different z values_iCorresponding laser section radius omega_iAcquiring 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、f_i(u)＝ω_i-ω(z_i) Represents the laser cross-sectional radius ω_iAnd the laser section radius ω (z) obtained by the formula (6)_i) F (u) ═ f₁(u),f₂(u)...f_M(u)]^TRepresenting f at different measuring distances_i(u)；

(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.

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 of Investigation of position calculation and calculation for evaluating the linear mean range for a source-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, the spot measurement precision depends on the degree of the polynomial, the higher degree of the polynomial, the higher the measurement precision is, but the larger the calculation amount is, and when calibrating, enough points need to be measured 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) 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 specifically comprises the following steps:

(1) obtaining relative position sigma of light spot in x and y directions by using photocurrent of four quadrants_x、σ_y；

(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 spot_x、σ_yAnd 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;

(3) inverse function erf of error function in equation (2)^-1(σ_x)、erf^-1(σ_y) 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

Using g (sigma)_y) To represent

(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 device_iAnd the relative position σ of the four-quadrant photodetector_xiMoving 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 passed_xiThe calculated centroid position of the light spot is x_i(ω,σ_xi) (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);

(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:

therefore, the specific steps for rapidly solving the laser section radius under different measuring distances are as follows:

(501) at different measuring distances z_iCalibrating the four-quadrant photoelectric detector to obtain different z values_iCorresponding laser section radius omega_iAcquiring 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、f_i(u)＝ω_i-ω(z_i) Represents the laser cross-sectional radius ω_iAnd the laser section radius ω (z) obtained by the formula (6)_i) F (u) ═ f₁(u),f₂(u)...f_M(u)]^TRepresenting f at different measuring distances_i(u)；

(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 quadrants_x、σ_y；

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 spot_x、σ_yAnd 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;

and 3, step 3: inverse function erf of error function in equation (2)^-1(σ_x)、erf^-1(σ_y) Expanding the Taylor series, and keeping the first four orders as a position measurement model of the four-quadrant photoelectric detector;

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 device_iAnd the relative position σ of the four-quadrant photodetector_xiMoving 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 passed_xiThe calculated centroid position of the light spot is x_i(ω,σ_xi) (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);

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 is transmitted along the z-axis direction, and the radius of the cross section of the laser when the measuring distance is z is as follows;

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 z_iCalibrating the four-quadrant photoelectric detector to obtain different z values_iCorresponding laser section radius omega_iAcquiring 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、f_i(u)＝ω_i-ω(z_i)、f(u)＝[f₁(u),f₂(u)...f_M(u)]^T；

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；

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.