A small ball crown characteristic parameter extraction method for precision instrument lenses

Abstract

The application provides a small spherical crown characteristic parameter extraction method for precision instrument lenses, comprising: obtaining small spherical crown three-dimensional space data through laser wave number scanning and shift axis Fizeau interference measurement, considering the distortion of actual data, linearizing the spherical crown mathematical model and mapping it into a matrix form through the characteristic mathematical formula of a space sphere, finally using multiple linear regression to fit the small spherical crown curvature and the spherical crown center, and checking the goodness of fit. Since uncontrollable deformation is generated when the actual small spherical crown is collected through a special camera system, the axial distortion error model is considered, and a scalar least square formula is established. In order to facilitate subsequent fitting and calculation, the scalar least square formula needs to be separated through known quantities and unknown quantities, and the matrix form of the specific linear equation is constructed. Multiple linear regression is performed for fitting, and the accurate spherical center position, distortion coefficient and spherical crown curvature of the small spherical crown are obtained.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of visual sensor lens detection, in particular to a small spherical cap feature parameter extraction method for precision instrument lenses. BACKGROUND

[0002] With the rapid development of unmanned technology, the demand for its safety indicators is getting higher and higher, and its control algorithm cannot be separated from the image signal input obtained by the visual sensor, so the standard detection requirements for high-precision visual sensors based on unmanned vehicles are becoming more and more stringent.

[0003] The key part of the high-precision visual sensor of the unmanned vehicle-lens is composed of high-precision complex surfaces. It is required to efficiently and non-destructively measure and extract all geometric parameters. This has caused the urgent scientific problem of high-precision measurement in the depth (z) direction; the data acquisition area is extremely small (xoy); the high-resolution fitting is difficult, and the three-dimensional dynamic range is large, which is very demanding for data acquisition accuracy and data detection. In order to realize the accurate manufacturing of the visual sensor, the detection technology of the camera lens is urgently needed.

[0004] Based on the dimensional limitations of the prior art, the detection accuracy is low, the accuracy of the initial point set is greatly affected, and the corresponding robustness is poor, which leads to poor detection effect of the parameter indicators corresponding to the small spherical cap. Paper: TANG Dandan; YUAN Hui; YU Xiaoliu et al. Study of Precision Measurement for Small Spherical Cap Surface Parameter Based on Monocular Laser [J]. 2013. The corresponding data points are detected by the detection device, and the spherical surface point coordinates obtained are fitted by the least squares method. In the fitting process, the objective function is changed, and the fitting calculation is converted into solving the generalized eigenvalue.

[0005] This method is limited to the measurement of large spherical surfaces. Due to the existence of the denominator of the corresponding least squares formula, for a spherical cap with a large radius, that is, a small curvature, a small change in the actual data will have a great impact on the calculation result, and it is greatly affected by disturbance; for small spherical cap data with a small amount, the accuracy requirement is difficult to meet, and the detection of high-precision instrument lenses has a certain distance, and the recognition accuracy is not enough. SUMMARY

[0006] Therefore, the present application aims to provide a small spherical cap detection method, system, medium and equipment based on precision instrument lenses, to improve the detection accuracy of camera lenses. In the detection of small spherical cap lenses, the curvature and the center of the sphere are effectively detected under the consideration of height error.

[0007] In the present application, firstly, a wave number domain interference spectrum algorithm is established by using a random Fourier transform algorithm, a shift axis Fizeau interference measurement system is proposed to complete camera calibration and Z-axis calibration, so as to obtain small spherical crown three-dimensional space data, and the data obtained by the method is more accurate. Secondly, the present application considers the distortion of actual data, the spherical crown mathematical model is linearized and mapped into a matrix form through the characteristic mathematical formula of the space sphere, and finally the small spherical crown is fitted by using multiple linear regression, so that the curvature of the spherical crown and the center of the spherical crown can be effectively obtained. At the same time, since the present application considers the distortion of the data, the distortion parameters can be obtained at the same time when the spherical crown parameters are fitted, thereby providing help for the correction of the lens. The specific implementation scheme is as follows:

[0008] A small spherical crown three-dimensional data point detection method, comprising:

[0009] Random Fourier transform algorithm is adopted, and a wave number domain interference spectrum algorithm is established in the interference phase extraction process;

[0010] A shift axis Fizeau interference measurement system is proposed to improve the signal-to-noise ratio;

[0011] Camera calibration and Z-axis calibration of the interference measurement system are completed, so as to obtain small spherical crown three-dimensional space data;

[0012] The original data is preprocessed: blank point data is deleted, and repeated points are removed;

[0013] The compression error k of the elevation axis is considered, and the equation satisfied by the small spherical crown data points is listed (x-x0) 2 +(y-y0) 2 +(k·z-z0) 2 =r 2 ;

[0014] According to the above formula, the error model is obtained as follows:

[0015]

[0016] Wherein n is the number of data points, x0, y0, z0 is the center point to be fitted, x i , y i , z i is the known small spherical crown i data point set, and r is the radius of the small spherical crown to be fitted;

[0017] The target least square formula is expanded and separated to refine the known data, so as to solve the subsequent equation deformation;

[0018]

[0019] By observing the characteristics of the target equation, specific variable coefficients are constructed to achieve a chain reaction solution effect, and the following definitions are made:

[0020] A = k 2 , B = -2x0, C = -2y0, D = -2kz0,

[0021] Transform the internal formula of the above least square formula:

[0022] Construct a linear equation, where the target coefficients A, B, C, D, E are unknown, and the rest of the variables are known data point parameters;

[0023]

[0024] Through the obtained spherical cap space model data, consider all data points, bring into the matrix form of the linear equation, and replace the three matrices with P, X, F respectively, get;

[0025] PX = F

[0026] Where

[0027]

[0028] Express the least square equation in algebraic form:

[0029] argmin L(x0, y0, z0, k, R) = |PX-F| 2

[0030] Get the objective function |PX-Y| 2 , find the minimum target value;

[0031] Expand and simplify |PX-Y| 2 to facilitate derivation:

[0032] |PX-F| 2 = X T P T PX-2XP T F+F T F

[0033] Derive X in the above formula and let it be 0:

[0034]

[0035] Simplify the matrix equation to get X = [A B C D E] T The numerical value of the parameter X = (P T P) -1 P T F;

[0036] Calculate the parameters by X, A = k​2 From B = -2x0, we can get:

[0037] From C = -2y0, we can get:

[0038] From D = -2kz0, we can get:

[0039] From D = -2kz0, we can get:

[0040] From D = -2kz0, we can get:

[0041] Calculate the goodness of fit R 2 , R 2 The maximum value is 1. R 2 The value is closer to 1, the better the fitting degree of the regression curve to the observed value; on the contrary, the smaller the value of R 2 , the worse the fitting degree of the regression curve to the observed value.

[0042]

[0043] Where F i represents the i-th element of matrix F, P i represents the i-th row of matrix P, F represents the average value of the elements in matrix F;

[0044] Observe the goodness of fit R 2 , if the goodness of fit meets the requirements, the fitted spherical cap equation can be obtained as:

[0045]

[0046] The parameters of the small spherical cap can be obtained: the center of the sphere is The radius is The distortion parameter corresponding to the z-axis is

[0047] ​In the application, a high-precision small ball crown fitting method based on multiple linear regression includes: using random Fourier transform algorithm, and establishing wave number domain interference spectrum algorithm in interference phase extraction process, proposing a shift axis Fizeau interferometer measurement system to improve signal-to-noise ratio, completing camera calibration and Z-axis calibration, and obtaining small ball crown three-dimensional space data. Since uncontrollable deformation is generated when the actual small ball crown is collected by a special camera system, the axial distortion error model is considered, and the scalar least square formula is established. In order to facilitate subsequent fitting and calculation, the scalar least square formula needs to be separated by known quantities and unknown quantities, and the matrix form of the specific linear equation is constructed. Multiple linear regression is performed for fitting, and the accurate small ball crown center position, distortion coefficient and ball crown curvature are obtained. BRIEF DESCRIPTION OF DRAWINGS

[0048] In order to more clearly illustrate the technical solutions of the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or the prior art description. Obviously, the drawings in the following description are only a part of the embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor on the basis of the provided drawings.

[0049] Figure 1 A small ball crown parameter extraction method for precision instrument lenses is disclosed in the embodiment one of the present application.

[0050] Figure 2 A small ball crown parameter extraction method for precision instrument lenses is disclosed in the embodiment two of the present application. DETAILED DESCRIPTION

[0051] In order to make the purpose, technical scheme and advantages of the embodiments of the present application more clear, the technical scheme in the embodiments of the present application will be described clearly and completely in the following with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are a part of the embodiments of the present application, not all. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0052] The actual standard sphere R=43.31mm, the camera calibration and Z-axis calibration are completed by using the shift axis Fizeau interferometer measurement system, and the small ball crown three-dimensional space data is obtained, and there are 30000 data points;

[0053] Suppose the ball center point of the small ball crown is (x0, y0, z0), the radius is r, (x i , y i , z i ) is the generated simulation data point, and k is the height error.

[0054] Write the scalar least squares error equation:

[0055]

[0056] Unfold the internal and build the specific variable coefficient by observing the characteristics of the target equation, write the linear equation, where the target coefficients A, B, C, D, E are unknown, and the rest of the variables are known data point parameters;

[0057]

[0058] Through the obtained spherical cap space model data, consider all the data points, and bring them into the matrix form of the linear equation:

[0059]

[0060] Replace P, X, F with three matrices respectively to get PX=F. Where X=[A B C D E] T

[0061] Express the least squares equation in algebraic form:

[0062] argmin L(x0, y0, z0, k, R)=|PX-F| 2

[0063] Get the objective function |PX-Y| 2 , find the minimum objective value

[0064] Expand and simplify |PX-Y| 2 , and take the derivative of X, and let it be 0, X=[A B C D E] T The parameter value X=(P T P) -1 P T F=[1.0879-20.2404-25.0000-42.2335-1119.5404] T ;

[0065] Through the calculation, we know:

[0066] Calculate the goodness of fit:

[0067]

[0068] It can be seen that the fitting effect is accurate enough.

[0069] The radius r=43.3114mm is very close to the actual 43.31mm, which proves that the fitting accuracy meets the requirements.

[0070] In this embodiment, firstly, the camera calibration and Z-axis calibration are completed by using the moving axis Fizeau interferometer measurement system, so as to obtain the three-dimensional space data of the small ball crown. Considering the axial error, the least square equation is established, the known quantity and the unknown quantity are separated, and the matrix form of the linear equation is constructed. The multivariate linear regression is carried out for fitting, and the radius of the small ball crown obtained by fitting is 43.3114 mm, which is very close to the actual standard ball 43.31 mm, and it is proved that the fitting accuracy meets the requirements.

Claims

1. A method for extracting small-pole crown characteristic parameters of a precision instrument lens, characterized in that, Comprise: Step S1: the wave number domain interference spectrum algorithm is established, the shift axis Fizeau interference measurement system is proposed to complete the camera calibration and Z axis calibration, so as to obtain the three-dimensional space data of the small spherical crown; Step S2: considering the elevation axis error model, the three-dimensional original data is used to establish the scalar least square form; Step S3: through variable conversion, observing the characteristics of the target equation, constructing specific separation variable coefficients, the least square form is constructed into the matrix form of linear equation; S31: Through observing the target equation characteristic to construct the specific variable coefficient, the chain reaction solving effect is achieved, and the internal formula of the least square formula in step S2 is Deformation: The following definitions are made Wherein n is the number of data points, x0, y0, z0 are the center points of the fitting sphere, x, y, z are the equation variables, k is the compression error of the elevation axis, and r is the radius of the fitting small spherical crown; Az 2 +Bx+Cy+Dz+E=-(x 2 +y 2 ) S32: the linear equation is constructed, wherein in addition to the target coefficient constructed by S31, the rest of the variables are known variables: S33: through the obtained spherical crown space model data, considering all the data points, the matrix form of the linear equation is obtained: Step S4: using multiple linear regression to fit the curvature, axial distortion and spherical crown center of the small spherical crown, and checking the goodness of fit. The process of S1 comprises:

2. The method of claim 1, wherein, Step S11: the random Fourier transform algorithm is adopted in principle, and the wave number domain interference spectrum algorithm is established in the interference phase extraction process; Step S12: the shift axis Fizeau interference measurement system is proposed to improve the signal-to-noise ratio; Step S13: the camera calibration and Z axis calibration of the interference measurement system are completed, so as to obtain the three-dimensional space data of the small spherical crown. The process of step S2 comprises:

3. The method of claim 1, wherein, Step S21: the original data is preprocessed, and the blank point data is deleted; Step S22: considering the compression error k of the elevation axis, the equation of the small spherical crown is: Therefore, the least square form of the error model is obtained as follows: (x - x0) 2 (y - y0) 2 (k - k0) 2 = r 2 Step S23: the target least square form is expanded and separated to obtain known data for subsequent equation deformation solution: where n is the number of data points, x0, y0, z0are the center of the sphere to be fitted, x i , y i , z i are the known data points of the small sphere crown, and r is the radius of the small sphere crown to be fitted. The process of step S4 comprises:

4. The method of claim 1, wherein, Step S41: the S33 formula is expressed by algebra, and the following equation is obtained: Then the least square form is written as: Step S42: the square of the matrix is expanded and simplified: argminL(x0,y0,z0,k,r) = |PX-F| 2 The objective function |PX-F| is obtained 2 , whose minimum objective value is sought Step S43: the derivative of X is taken for the above formula, and it is set to 0: | PX-F | 2 = X T P T PX-2 XP T F+F T F Step S44: the equation is simplified to obtain Step S47: if the goodness of fit meets the requirements, the fitted spherical crown equation is obtained as follows: X = (P T P) -1 P T F Step S45: Calculate the parameters by X = [A B C D E] T Carry out the calculation of parameters: By A = k 2 B = -2x0, C = -2y0, D = -2kz0, It is calculated that: Step S46: Calculate the goodness of fit R 2 R 2 The maximum value is 1; R 2 The closer the R value is to 1, the better the regression curve fits the observed values; conversely, the closer the R value is to 1, the better the regression curve fits the observed values. 2 The smaller the value, the worse the regression curve fits the observed values; where F i denotes the i-th element of the matrix F, P i represents the i-th row of the matrix P, denotes the average value of the elements in the matrix F; The computer readable storage medium stores a computer program, and the computer program is executed by the processor to realize the steps of the small spherical crown characteristic parameter extraction method for precision instrument lenses in any one of claims 1 to 4.

5. A computer readable storage medium, characterized in that, ​

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