阅读说明：本技术 用于四象限光电探测器位置测量标定的自动分段拟合方法 (Automatic segmentation approximating method for the measurement calibration of four-quadrant photo detector position ) 是由 段发阶 张聪 傅骁 苏宇浩 刘文正 鲍瑞伽 于 2019-08-29 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标定的自动分段拟合方法,包括以下步骤：步骤一、自动确定分段拟合的分段点；四象限光电探测器(QPD)能够探测两个方向的光斑位置,仅以其中一个方向为例进行说明,另一个方向操作步骤相同；步骤二、对分段后每一段进行低次拟合,并求得光斑质心位置估计值。本方法针对QPD位置测量进行标定的典型案例,对QPD位置测量进行分段三次多项式拟合,提供与三次多项式拟合、七次多项式拟合的对比结果,验证本发明所提供方法的可行性、适用性、优越性。(The present invention discloses a kind of automatic segmentation approximating method for the measurement calibration of four-quadrant photo detector position, comprising the following steps: Step 1: automatically determining the waypoint of piecewise fitting；Four-quadrant photo detector (QPD) can detect the facula position of both direction, only be illustrated by taking one of direction as an example, another direction operation step is identical；Step 2: to each section of progress low order fitting after segmentation, and acquire facula mass center position estimation value.This method is directed to the typical case that the measurement of the position QPD is demarcated, the position QPD is measured and carries out segmental cubic polynomials fitting, comparing result with cubic polynomial fitting, the fitting of seven order polynomials is provided, the feasibility, applicability, superiority of method provided by the present invention are verified.)

1. the automatic segmentation approximating method for the measurement calibration of four-quadrant photo detector position, which is characterized in that including following Step:

Step 1: automatically determining the waypoint of piecewise fitting；Four-quadrant photo detector (QPD) can detect the light of both direction Spot position is only illustrated by taking one of direction as an example, another direction operation step is identical, specifically includes the following steps:

(101) to QPD facula position resolving value X=[x₁,x₂,...,x_n] and facula mass center position Y=[y₁,y₂,...,y_n] do Once fitting acquires first order a₁, constant term a₀, obtain fitting function (1)；

Y=a₁x+a₀ (1)

(102) by X=[x₁,x₂,...,x_n] as independent variable substitution (1), obtain facula mass center position estimation value Y '=[y '₁, y′₂,...,y′_n]；

(103) the residual error R=[r after fitting is sought according to formula (2)₁,r₂,...,r_n]；

R=Y-Y'(2)

(104) seven order polynomial fittings are carried out to X and R, acquires seven term coefficient b₇, six term coefficient b₆, five term coefficient b₅、 Four term coefficient b₄, term coefficient b three times₃, two-term coefficient b₂, Monomial coefficient b₁, constant term b₀, obtain fitting function (3)；

R=b₇x⁷+b₆x⁶+b₅x⁵+b₄x⁴+b₃x³+b₂x²+b₁x+b₀ (3)

(105) it asks single order to lead formula (3), obtains formula (4)；

R '=7b₇x⁶+6b₆x⁵+5b₅x⁴+4b₄x³+3b₃x²+2b₂x+b₁ (4)

(106) it asks second order to lead formula (3), obtains formula (5)；

R "=42b₇x⁵+30b₆x⁴+20b₅x³+12b₄x²+6b₃x+2b₂ (5)

(107) it asks three ranks to lead formula (3), obtains formula (6)；

R " '=210b₇x⁴+120b₆x³+60b₅x²+24b₄x+6b₃ (6)

(108) formula (4), (5) is enabled to be equal to 0, formula (6) is not equal to 0, acquires extreme point all within the scope of real number, inflection point, is equipped with p It is a, it sorts from small to large, is denoted as x_r1,x_r2,...,x_rp；

(109) extreme point outside rejecting X range, inflection point, select the waypoint of extreme point within the scope of X, inflection point as piecewise fitting, Equipped with m point, take less than waypoint or equal to waypoint QPD facula position resolving value as each section of right margin point, most Latter section of right margin point is x_n, all right margin points sort from small to large postscript be x_t1,x_t2,...,x_tm,x_n, take to be greater than and divide For the QPD facula position resolving value of section point as each section of left margin point, the left margin point of first segment is x₁, all left margin Sequence postscript is x to point from small to large₁,x_t1+1,x_t2+1,...,x_tm+1, entire section is divided into m+1 sections by waypoint, wherein hot spot position It sets resolving value and is divided into X₁、X₂…X_m+1, facula mass center corresponding with facula position resolving value position is divided into Y₁、Y₂…Y_m+1, such as Formula (7), (8)；

Step 2: to each section of progress low order fitting after segmentation, and acquire facula mass center position estimation value.

Technical field

The invention belongs to technology of instrument and meter field, especially a kind of automatic point for four-quadrant photo detector calibration Section approximating method.

Background technique

Four-quadrant photo detector (Quadrant Photoelectric Detectors, QPD) is that four performances are complete Exactly the same photodiode requires photoelectric detector made of arrangement according to rectangular co-ordinate, has detectivity height, letter Number processing is simply and the advantages that strong antijamming capability, be usually used in laser guidance in laser alignment measurement.Three axis numerically controlled machine has 21 geometric errors are the quadrature error between the corresponding six degree of freedom error of each axis and every two axis respectively, and six degree of freedom Error includes position error, two-dimentional straightness error, pitch angle, deflection angle and roll angle, therefore straightness error is missed always Important proportion is occupied in difference.Laser alignment measurement system is usually used in lathe straight line degree measurement, the facula position measurement accuracy of QPD Determine the measurement accuracy of lathe straightness error.

When laser irradiation is to the surface QPD, four photodiodes are exported according to the size for being irradiated to its surface hot spot power Four tunnels correspond to the photo-signal of size, facula position resolving are carried out according to four tunnel photo-signals, since QPD is two-dimentional device Part, the facula position resolving value of available two orthogonal directions, facula position resolving value are not linear with facula mass center position Relationship, currently, method there are many kinds of the calibration measured about QPD facula position.When positional accuracy measurement is of less demanding, measurement model Hour is enclosed, document " the high-precision laser facula position detection technique research based on 4 quadrant detector " (Wu Jiabin, doctor is commonly used Academic dissertation, university, the Chinese Academy of Sciences, 2016) in the center approximation method mentioned solve, but as measurement range becomes larger, QPD Non-linear enhancing, nonlinearity erron become larger.Document " airborne photoelectric platform vibration characteristics Research on measuring technique " (Gao Zijun, doctor Academic dissertation, the Maritime Affairs University Of Dalian, 2014) data base query method the mentioned four road photoelectric currents that export QPD are arranged by ratio After column, database is demarcated and established with the centroid position of hot spot, will not be had in database by the method for linear interpolation Position is calculated, and this method needs to record a large amount of data, and calibration process is cumbersome, and mistake is brought in interpolation calculation Difference.Document " Investigation of positioning algorithm and method for increasing the linear measurement range for four-quadrant detector”(M.Chen,Y.Yang,X.Jia,et Al.Optik, 2013,124:6806-6809) polynomial fitting method mentioned is song according to resolving value and facula mass center position Line relationship acquires multinomial coefficient using least square method, for indicating resolving value and facula mass center positional relationship, facula measurement Precision depends on polynomial number, and number is higher, and measurement accuracy is higher, but calculation amount is also bigger.

When QPD is used for lathe straightness real-time measurement, it is desirable that calculating speed is fast, precision is high.Currently, center approximation method exists Low precision when measurement range is big, data base querying method data manipulation amount is big, is difficult to demarcate, and polynomial fitting method is requiring high-precision When fitting number it is high, computationally intensive, be unable to get application in lathe straightness real-time measurement.

Summary of the invention

Purpose of the invention is to overcome the shortcomings in the prior art, provides a kind of for four-quadrant photo detector position Set the automatic segmentation approximating method of measurement calibration.

The purpose of the present invention is what is be achieved through the following technical solutions: for the measurement calibration of four-quadrant photo detector position Automatic segmentation approximating method, comprising the following steps:

Step 1: automatically determining the waypoint of piecewise fitting；Four-quadrant photo detector (QPD) can detect both direction Facula position, be only illustrated by taking one of direction as an example, another direction operation step is identical, specifically includes following step It is rapid:

(101) to QPD facula position resolving value X=[x₁,x₂,...,x_n] and facula mass center position Y=[y₁,y₂,..., y_n] once fitting is done, acquire first order a₁, constant term a₀, obtain fitting function (1)；

Y=a₁x+a₀ (1)

(102) by X=[x₁,x₂,...,x_n] as independent variable substitute into (1), obtain facula mass center position estimation value Y '= [y′₁,y′₂,...,y′_n]；

(103) the residual error R=[r after fitting is sought according to formula (2)₁,r₂,...,r_n]；

R=Y-Y'(2)

(104) seven order polynomial fittings are carried out to X and R, acquires seven term coefficient b₇, six term coefficient b₆, five term coefficients b₅, four term coefficient b₄, term coefficient b three times₃, two-term coefficient b₂, Monomial coefficient b₁, constant term b₀, obtain fitting function (3)；

R=b₇x⁷+b₆x⁶+b₅x⁵+b₄x⁴+b₃x³+b₂x²+b₁x+b₀ (3)

(105) it asks single order to lead formula (3), obtains formula (4)；

R '=7b₇x⁶+6b₆x⁵+5b₅x⁴+4b₄x³+3b₃x²+2b₂x+b₁ (4)

(106) it asks second order to lead formula (3), obtains formula (5)；

R "=42b₇x⁵+30b₆x⁴+20b₅x³+12b₄x²+6b₃x+2b₂ (5)

(107) it asks three ranks to lead formula (3), obtains formula (6)；

R " '=210b₇x⁴+120b₆x³+60b₅x²+24b₄x+6b₃ (6)

(108) formula (4), (5) is enabled to be equal to 0, formula (6) is not equal to 0, extreme point all within the scope of real number, inflection point are acquired, if There is p point, sorts from small to large, be denoted as x_r1,x_r2,...,x_rp；

(109) extreme point outside rejecting X range, inflection point select point of extreme point within the scope of X, inflection point as piecewise fitting Duan Dian is equipped with m point, take less than waypoint or equal to waypoint QPD facula position resolving value as each section of right margin Point, the right margin point of final stage are x_n, all right margin points sort from small to large postscript be x_t1,x_t2,...,x_tm,x_n, take Greater than waypoint QPD facula position resolving value as each section of left margin point, the left margin point of first segment is x₁, all Left margin point sorts postscript from small to large as x₁,x_t1+1,x_t2+1,...,x_tm+1, entire section is divided into m+1 sections by waypoint, wherein Facula position resolving value is divided into X₁、X₂…X_m+1, facula mass center corresponding with facula position resolving value position is divided into Y₁、Y₂… Y_m+1, such as formula (7), (8)；

Step 2: to each section of progress low order fitting after segmentation, and acquire facula mass center position estimation value.

Compared with prior art, the beneficial effects brought by the technical solution of the present invention are as follows:

1. the method for the present invention can automatically determine waypoint according to facula position resolving value and facula mass center positional relationship, it is segmented Every section of progress polynomial of lower degree fitting afterwards, it is generally the case that the effect of high-order moment fitting can be obtained, and greatly reduce fortune Calculation amount.

2. the method for the present invention is directed to the typical case that the measurement of the position QPD is demarcated, segmentation three is carried out to the measurement of the position QPD Order polynomial fitting provides the comparing result with cubic polynomial fitting, the fitting of seven order polynomials, verifies side provided by the present invention Feasibility, applicability, the superiority of method.

3. the method for the present invention automatically determines the waypoint of piecewise fitting, it is not necessarily to artificial selection, is once intended according to initial data The feature of residual error after conjunction, can more accurately select waypoint；

4. the method for the present invention carries out polynomial of lower degree fitting after being segmented to initial data, this method substantially cuts down operand, The precision of high-order moment fitting is provided simultaneously.

Detailed description of the invention

Fig. 1 shows the calibration maps and residual plot for 1 data of table using cubic polynomial fitting.

Fig. 2 shows the calibration maps and residual plot for 1 data of table using the fitting of seven order polynomials.

Fig. 3 shows the calibration maps and residual plot that automatic segmentation fitting process is used for 1 data of table.

Specific embodiment

The present invention is described in further detail below in conjunction with the drawings and specific embodiments.It should be appreciated that described herein Specific embodiment be only used to explain the present invention, be not intended to limit the present invention.

The present invention protect it is a kind of for four-quadrant photo detector position measurement calibration automatic segmentation approximating method, by with Lower part is grouped as:

First part automatically determines the waypoint of piecewise fitting；

QPD can detect the facula position of both direction, only be illustrated by taking one of direction as an example here, another Direction operation step is identical, determines that waypoint comprises the steps of:

Step 1: to QPD facula position resolving value X=[x₁,x₂,...,x_n] and facula mass center position Y=[y₁,y₂,..., y_n] once fitting is done, acquire first order a₁, constant term a₀, obtain fitting function (1)；

Y=a₁x+a₀ (1)

Step 2: by X=[x₁,x₂,...,x_n] as independent variable substitute into (1), obtain facula mass center position estimation value Y '= [y′₁,y′₂,...,y′_n]；

Step 3: the residual error R=[r after fitting is asked according to formula (2)₁,r₂,...,r_n]；

R=Y-Y'(2)

Step 4: doing high order fitting to X and R, and number is higher, and the waypoint acquired is more accurate, carries out seven fittings here, Acquire seven term coefficient b₇, six term coefficient b₆, five term coefficient b₅, four term coefficient b₄, term coefficient b three times₃, two-term coefficient b₂, Monomial coefficient b₁, constant term b₀, obtain fitting function (3)；

R=b₇x⁷+b₆x⁶+b₅x⁵+b₄x⁴+b₃x³+b₂x²+b₁x+b₀ (3)

Step 5: asking single order to lead to (3), obtains formula (4)；

R '=7b₇x⁶+6b₆x⁵+5b₅x⁴+4b₄x³+3b₃x²+2b₂x+b₁ (4)

Step 6: asking second order to lead to (3), obtains formula (5)；

R "=42b₇x⁵+30b₆x⁴+20b₅x³+12b₄x²+6b₃x+2b₂ (5)

Step 7: asking three ranks to lead to (3), obtains formula (6)；

R " '=210b₇x⁴+120b₆x³+60b₅x²+24b₄x+6b₃ (6)

Step 8: enabling formula (4), (5) be equal to 0, and formula (6) is not equal to 0, acquires extreme point all within the scope of real number, inflection point, Equipped with p point, sorts from small to large, be denoted as x_r1,x_r2,...,x_rp；

Step 9: extreme point, inflection point outside rejecting X range select point of extreme point within the scope of X, inflection point as piecewise fitting Duan Dian is equipped with m point, take less than waypoint or equal to waypoint QPD facula position resolving value as each section of right margin Point, the right margin point of final stage are x_n, all right margin points sort from small to large postscript be x_t1,x_t2,...,x_tm,x_n, take Greater than waypoint QPD facula position resolving value as each section of left margin point, the left margin point of first segment is x₁, all Left margin point sorts postscript from small to large as x₁,x_t1+1,x_t2+1,...,x_tm+1, entire section is divided into m+1 sections by waypoint, wherein Facula position resolving value is divided into X₁、X₂…X_m+1, facula mass center corresponding with facula position resolving value position is divided into Y₁、Y₂… Y_m+1, such as formula (7), (8)；

Second part: to each section of progress low order fitting after segmentation, and facula mass center position estimation value is acquired, here with three It is illustrated, comprises the steps of for secondary fitting:

Step 1: cubic fit is carried out respectively to each section after segmentation, acquires the term coefficient c three times of paragraph 1_1,3, quadratic term Coefficient c_1,2, Monomial coefficient c_1,1, constant term c_1,0, acquire the 2nd section of term coefficient c three times_2,3, two-term coefficient c_2,2, first order Coefficient c_2,1, constant term c_2,0, and so on, acquire m+1 sections of term coefficient c three times_M+1,3, two-term coefficient c_M+1,2, first order Coefficient c_M+1,1, constant term c_M+1,0；

Step 2: the intersection point of matched curve after segmentation is sought, sorts from small to large, is denoted as x_s1,x_s2...x_sm；

Step 3: facula mass center position estimation value Y is calculated according to piecewise fitting result_s=[y_s1,y_s2,...y_sn], such as formula (9)；

It is illustrated by taking the calibration of one group of QPD facula position resolving value and facula mass center position as an example, initial data is shown in Table 1, table 1 indicates one group of initial data of QPD facula position resolving value and facula mass center position in the present embodiment, shares 21 points Data；Once fitting is carried out to initial data, fitting coefficient is shown in Table 2；It calculates facula mass center position estimation value and seeks its residual error, tie Fruit is shown in Table 3；Seven order polynomial fittings are carried out to residual error after once fitting, fitting coefficient is obtained, is shown in Table 4；Seven order polynomial of residual error Extreme point, inflection point waypoint as piecewise fitting of the fitting function within the scope of X, is shown in Table 5；It the results are shown in Table 6 after segmentation；Segmentation The fitting coefficient of cubic polynomial fitting is shown in Table 7；For the effect for comparing segmental cubic polynomials fitting, 1 data of table are carried out Cubic polynomial is fitted and asks residual error, and calibration maps and residual error are shown in Fig. 1；Seven order polynomials are carried out to 1 data of table to be fitted and ask residual Difference, calibration maps and residual error are shown in Fig. 2；The calibration maps and residual error obtained using segmental cubic polynomials fitting process proposed by the present invention are shown in Fig. 3；Three kinds of method discoveries are compared, the residual error being fitted using segmental cubic polynomials is obviously smaller than cubic polynomial regression criterion, It is suitable with the residual error of seven order polynomials fitting, but substantially cut down operand.

Table 1

Table 2: it is directed to 1 data once fitting coefficient of table

Table 3: for the estimated value and residual error after 1 data once fitting of table

Table 4: the fitting coefficient for using seven order polynomials to be fitted for the residual error after 1 data once fitting of table.

Table 5: for the waypoint of 1 data automatic segmentation of table

Table 6: for the result of 1 data automatic segmentation of table

Table 7: the fitting coefficient of automatic segmentation fitting process is used for 1 data of table

The present invention is not limited to embodiments described above.Above the description of specific embodiment is intended to describe and say Bright technical solution of the present invention, the above mentioned embodiment is only schematical, is not restrictive.This is not being departed from In the case of invention objective and scope of the claimed protection, those skilled in the art may be used also under the inspiration of the present invention The specific transformation of many forms is made, within these are all belonged to the scope of protection of the present invention.