A method for self-positioning workpiece using monocular deflectometry

Abstract

The present invention belongs to the field of precision measurement technology, and specifically is a method for self-positioning a workpiece in monocular deflectometry. The steps of the present invention are: after completing the geometric calibration of the deflectometry system, a training sample for workpiece positioning is generated by simulating ray tracing based on the nominal surface shape of the workpiece, and a mapping relationship between the workpiece posture and the corresponding pixel distribution on the screen is established based on Gaussian process regression, and the workpiece positioning can be completed without additional instruments. The present invention can make the workpiece positioning in deflectometry get rid of the need for third-party instruments, and can still maintain micron-level positioning accuracy when there is a certain deviation between the workpiece surface shape and the nominal surface shape, which can effectively reduce the cost of deflectometry.

Description

Technical Field

[0001] The invention belongs to the technical field of precision measurement, and in particular relates to a workpiece self-positioning method for monocular deflection measurement. Background Art

[0002] With the development of optical precision manufacturing technology, optical components are widely used in precision instruments and high-end equipment in many fields. The surface quality of optical surfaces is one of the core indicators that determine the performance of the system in which they are located. Nowadays, the surface accuracy requirements for optical surfaces in many applications have reached the sub-micron level, which poses new challenges to optical surface measurement technology.

[0003] Monocular deflectometry based on a configurable optical detection system is an optical surface measurement technology that has developed rapidly in recent years. Its measurement system consists of only a camera, a screen, and the workpiece to be measured. Several groups of coded sinusoidal fringes are displayed on the screen, and the camera collects the distortion pattern after the workpiece is reflected. The gradient field of the surface to be measured is calculated based on the system geometry, and the three-dimensional surface shape can be reconstructed by gradient integration. Monocular deflectometry has attracted widespread attention from researchers due to its simple system configuration, high measurement efficiency, large dynamic range, strong anti-interference ability, and high sensitivity to relative surface deformation [L. Huang, M. Idir, C. Zuo, and A. Asundi, "Review of phase measuring deflectometry," Optics and Lasers in Engineering 2018; 107: 247-257.].

[0004] Since the gradient field of the surface to be measured is calculated based on the geometric relationship, the accuracy of the relative position of each component in the deflectometry system is one of the core factors that determine the measurement accuracy. In monocular deflectometry, the height-gradient uncertainty problem is suppressed by the nominal surface shape of the workpiece, and the workpiece positioning is equivalent to solving the accurate position of the nominal surface shape in the measurement world coordinate system. However, although in precision engineering, the actual surface shape and the nominal surface shape of the workpiece to be measured are inevitably subject to micron-level deviations, which leads to the dilemma of unstable convergence accuracy in the bundle adjustment method combined with numerical optimization. Therefore, the use of third-party instruments to assist workpiece positioning is still the mainstream at present, which undoubtedly increases the cost of deflectometry [T.Chen, YN Chen, XC Zhang, W. Wang, and M. Xu, "Workpiece positioning and error decoupling in the single-point diamond turning of freeform mirrors based on the monoscopic deflectometry," Precision Engineering 2022; 77: 16-23.].

[0005] For this purpose, the present invention is specially proposed, which aims at the situation that the deviation between the actual surface shape and the nominal surface shape of the workpiece in precision engineering is at the micron level or below, so that the workpiece positioning in the deflection measurement is freed from the need for third-party instruments, thereby reducing the cost of the deflection measurement while ensuring the positioning accuracy. Summary of the invention

[0006] The object of the present invention is to provide a workpiece self-positioning method for monocular deflection measurement which does not require additional instruments, does not affect the measurement accuracy and can effectively reduce the deflection measurement cost.

[0007] The present invention provides a method for self-positioning a workpiece by monocular deflectometry, comprising: generating a plurality of training samples by simulated ray tracing based on the nominal surface shape of the workpiece, parameterizing the samples by a set of basis functions to suppress the influence of high-frequency defects on the surface of the workpiece on positioning, establishing a mapping relationship between the workpiece posture and the workpiece corresponding to the distribution of screen pixels by Gaussian process regression to improve the robustness to the deviation between the nominal surface shape and the actual surface shape, thereby completing the positioning of the workpiece without introducing additional instruments, that is, relying only on the camera and screen in the monocular deflectometry system; the specific steps are as follows.

[0008] (1) For the deflectometry system that has completed geometric calibration, a multi-step phase shift method is used to make the screen display fringe patterns with different phases in two orthogonal directions. The phase is solved to obtain the screen pixel set {u sa ,v sa}.

[0009] (2) The pose when the workpiece coordinate system coincides with the world coordinate system obtained by geometric calibration of the deflectometry system is used as the reference pose, and a number of random workpiece poses that obey a uniform distribution are generated within a preset range.

[0010] (3) The nominal surface shape of the workpiece is taken as the reference surface shape, and the surface shape deviation is loaded. The deviation is represented by 1 to 36 Zernike polynomials, and each coefficient obeys Gaussian distribution. Several workpiece surface shapes that deviate from the nominal surface shape are obtained and used in the training set to approximate the common situation that the actual surface shape of the workpiece is not completely consistent with the nominal surface shape.

[0011] (4) Generate training samples based on simulated ray tracing:

[0012] Based on the combination of the above random workpiece pose and the workpiece surface shape that deviates from the nominal surface shape, as well as the system geometric calibration results, simulated ray tracing is performed to obtain the tracing screen pixels corresponding to each random workpiece pose in the training sample, and the tracing screen pixels obtained at the reference pose without adding surface shape deviation are set as the reference screen pixels {u sr ,v sr}.

[0013] (5) Parameterized screen pixel distribution:

[0014] Taking the reference screen pixel coordinates as the horizontal coordinates, for any set of tracking screen pixel coordinates {u st ,v st}, and take the difference between it and the reference screen pixel coordinate as the ordinate, and we get the following two sets of point clouds:

[0015]

[0016] Among them, g represents the number of screen pixels corresponding to the workpiece surface; when the workpiece posture changes, the change of the back-propagating wavefront in the deflectometry system will mainly occur in the low-frequency component. The above two groups of point clouds are obtained by intercepting and subtracting the back-propagating wavefronts under two different workpiece postures by the plane where the screen is located, and obviously have smooth characteristics; a variety of basis functions can fit such point clouds well. Taking Zernike polynomials as an example, the distribution of screen pixels corresponding to the workpiece surface can be parameterized as follows:

[0017]

[0018] Where W(ρ,β) is the point cloud to be fitted normalized to the unit circle polar coordinate system, J is the number of basis functions used, and C j , Z jare the jth Zernike coefficient and basis function respectively, ρ and β represent the radius and azimuth coordinates in polar coordinates respectively; based on this method, the screen pixel distribution corresponding to each posture will be parameterized into 2J Zernike coefficients as the training input of the positioning model.

[0019] (6) Build positioning model:

[0020] Based on Gaussian process regression, the mapping relationship between parameterized screen pixel distribution and workpiece posture is established, and the kernel function based on Mahalanobis distance and automatic relevance determination (ARD) technology is used. Taking the Gaussian kernel function combined with ARD technology as an example, the covariance of two inputs x and x' can be expressed as:

[0021]

[0022] Where D is the dimension of the input, σ f and l d is a hyperparameter; the application of ARD technology allows features of different dimensions in the input to be given different weights during the positioning process. In addition, the mean function of the Gaussian process is set to 0, and all inputs and outputs are standardized to obey the Gaussian distribution; the training of the positioning model is achieved by maximizing the logarithmic marginal likelihood through a gradient-based numerical optimization method:

[0023]

[0024] Among them, y is the preset workpiece pose, that is, the training output of the positioning model, σ ε 2 It represents the variance of the noise level in the mapping relationship, I is the identity matrix, K is the covariance matrix, X contains the inputs in all training samples, and n is the number of samples.

[0025] (7) Positioning of actual workpiece:

[0026] For the screen pixel {u sa ,v sa}, the test input X of the positioning model is obtained by the same parameterization method * After calling the positioning model, the probability distribution of the six degrees of freedom of the workpiece posture in the world coordinate system is calculated by joint Gaussian distribution:

[0027]

[0028] Prediction distribution f * The mean and variance of are as follows, where the mean is the positioning result and the six degrees of freedom of the workpiece have the same prediction variance:

[0029]

[0030] By adopting the above technical solution, the same operation steps as general deflectometry can be adopted to achieve workpiece positioning without the need for third-party instruments. The positioning accuracy of the present invention can still meet the requirements of deflectometry when there is a micron-level deviation between the actual surface shape of the workpiece and the nominal surface shape, and can effectively reduce the cost of deflectometry without affecting the measurement accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 Flowchart for parameterizing screen pixel distribution.

[0032] Figure 2 It is the curved surface fitted according to the deviation between the actual screen pixels and the reference screen pixels in Example 1.

[0033] Figure 3 The figure is a flowchart of the method of the present invention. DETAILED DESCRIPTION

[0034] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. It should be noted that the description of these embodiments is used to help understand the present invention, but does not constitute a limitation of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0035] Example 1: First, a deflectometry system was built. The camera used was JAI SP-20000C-PMCL, with a resolution of 5120×3840 pixels, a frame rate of 16fps, a lens focal length of 50mm, and a screen used was iPad mini 2, with a resolution of 2048×1536 pixels and a single pixel size of 0.0784mm. The workpiece to be measured was an off-axis parabolic mirror, with a parent focal length of 45mm, a reference height of 0mm, an off-axis amount of 51.96mm, and an aperture of 30mm. The root mean square value and peak-to-valley value of the deviation between the actual surface shape and the nominal surface shape were 3.819μm and 18.961μm, respectively.

[0036] In this embodiment, the first 36 Zernike polynomials are selected to fit the point cloud S obtained by subtracting the screen pixels corresponding to different workpiece postures. u , S v , and use the Gaussian kernel function combined with ARD technology in Gaussian process regression. Figure 1 The screen pixel distribution corresponding to the surface of the workpiece to be tested in the process parameterization experiment shown in the figure, S u , S v The fitting results are as follows Figure 2As shown. The positioning model is trained using 1000 simulation samples. Compared with the reference pose, the range of the translation and rotation components in the random pose is [-10, 10] mm and [-5°, 5°] respectively. The standard deviation of the random surface deviation in each sample is 5 μm. Based on the positioning model, the workpiece positioning results are output. The translation component errors in the X, Y, and Z axis directions of the world coordinate system and the rotation component errors around the X, Y, and Z axes are: -4.507 μm, 3.959 μm, -1.831 μm, -3.532×10 -4 °, 10.181×10 -4 °, 1.563×10 -4 The 17×17 mm range of the workpiece center is measured, and three-dimensional reconstruction is performed based on the real pose of the workpiece and the pose output by the positioning model of the present invention. The root mean square value of the deviation between the two reconstructed surfaces is only 0.824 nm, which shows that the positioning accuracy meets the requirements of deflectometry.

Claims

1. A method for self-positioning a workpiece by monocular deflection measurement, characterized in that: include: Several training samples are generated by simulating ray tracing based on the nominal surface shape of the workpiece. The samples are parameterized by a set of basis functions to suppress the influence of high-frequency defects on the surface of the workpiece on positioning. The mapping relationship between the workpiece posture and the corresponding screen pixel distribution of the workpiece is established by Gaussian process regression to improve the robustness of the deviation between the nominal surface shape and the actual surface shape, thereby completing the positioning of the workpiece without introducing additional instruments. The specific steps are as follows: (1) For the deflectometry system that has completed geometric calibration, a multi-step phase shift method is used to make the screen display fringe patterns with different phases in two orthogonal directions. The phase is solved to obtain the screen pixel set {u sa ,v sa }; (2) Taking the pose when the workpiece coordinate system and the world coordinate system obtained by geometric calibration of the deflectometry system coincide with each other as the reference pose, a number of random workpiece poses that obey a uniform distribution are generated within a preset range; (3) Taking the nominal surface shape of the workpiece as the reference surface shape, loading the surface shape deviation, wherein the deviation is represented by 1 to 36 Zernike polynomials, and each coefficient obeys Gaussian distribution, and obtaining several workpiece surface shapes that have deviations from the nominal surface shape, which are used in the training set to approximate the situation where the actual surface shape of the workpiece is not completely consistent with the nominal surface shape; (4) Generate training samples based on simulated ray tracing: Based on the combination of the above-mentioned random workpiece posture and the workpiece surface shape that deviates from the nominal surface shape, as well as the system geometry calibration result, simulated ray tracing is performed to obtain the tracing screen pixels corresponding to each random workpiece posture in the training sample, and the tracing screen pixels obtained at the reference posture without adding the surface shape deviation are set as the reference screen pixels {u sr ,v sr }; (5) Parameterized screen pixel distribution: Taking the reference screen pixel coordinates as the horizontal coordinates, for any set of tracking screen pixel coordinates {u st ,v st }, and take the difference between it and the reference screen pixel coordinate as the ordinate, and we get the following two sets of point clouds: Among them, g represents the number of screen pixels corresponding to the workpiece surface; when the workpiece posture changes, the change of the back-propagating wavefront in the deflectometry system mainly occurs in the low-frequency component. The above two groups of point clouds are obtained by intercepting the back-propagating wavefronts under two different workpiece postures by the plane where the screen is located and making a difference, which has the characteristic of smoothness; a variety of basis functions can be used to fit such point clouds. Using Zernike polynomials, the distribution of screen pixels corresponding to the workpiece surface can be parameterized as follows: Where W(ρ,β) is the point cloud to be fitted normalized to the unit circle polar coordinate system, J is the number of basis functions used, and C j , Z j are the jth Zernike coefficient and basis function, ρ and β represent the radius and azimuth coordinates in polar coordinates, respectively; the screen pixel distribution corresponding to each posture is parameterized into 2J Zernike coefficients as the training input of the positioning model; (6) Build positioning model: Gaussian process regression is used to establish the mapping relationship between parameterized screen pixel distribution and workpiece posture, and the kernel function based on Mahalanobis distance and ARD technology is used. The covariance of the two inputs x and x' is expressed as: Where D is the dimension of the input, σ f and l d is a hyperparameter; the application of ARD technology enables the features of different dimensions in the input to be given different weights during the positioning process. In addition, the mean function of the Gaussian process is set to 0, and all inputs and outputs are standardized to obey the Gaussian distribution; The training of the localization model uses a gradient-based numerical optimization method to maximize the logarithmic marginal likelihood: Among them, y is the preset workpiece pose, that is, the training output of the positioning model, σ ε 2 Represents the variance of the noise level in the mapping relationship, I is the identity matrix, K is the covariance matrix, X contains the inputs in all training samples, and n is the number of samples; (7) Positioning of actual workpiece: For the screen pixel {u sa ,v sa }, the test input X of the positioning model is obtained by the same parameterization method * After calling the positioning model, the probability distribution of the six degrees of freedom of the workpiece posture in the world coordinate system is calculated by joint Gaussian distribution: Prediction distribution f * The mean and variance of are as follows, where the mean is the positioning result and the six degrees of freedom of the workpiece have the same prediction variance:

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