Workpiece surface reconstruction method based on adaptive monocular deflection of space-varying sphere model

Abstract

A method for reconstructing the surface shape of a workpiece to be measured based on an adaptive monocular deflectometry of a space-variable sphere model is proposed to solve the height-slope uncertainty problem caused by the unknown surface shape of the workpiece to be measured in monocular deflectometry. The method steps are as follows: First, an arbitrary point on the surface of the workpiece to be measured is taken as a marker point, and the height of the marker point is measured using a third-party tool. Then, the incident light and reflected light corresponding to the marker point are obtained according to the monocular deflectometry, and the normal vector of the marker point is obtained by combining the law of reflection. Then, the radius and center coordinates of the sphere are iteratively optimized using the reverse tracing method to obtain the optimal initial surface shape of the sphere model fitting. In order to improve the fitting accuracy of complex workpieces to be measured, the workpiece surface is divided into multiple areas, and the sphere model is used for fitting respectively, and finally the global optimal space-variable sphere model of the workpiece to be measured is obtained.

Description

Technical Field

[0001] The invention belongs to the technical field of optical engineering, and in particular is a workpiece surface shape reconstruction method based on space-variable sphere model adaptive monocular deflection, which is suitable for three-dimensional measurement of workpieces with unknown nominal surface shape equations. Background Art

[0002] Optical free-form surfaces have large degrees of freedom and asphericity, which can improve the optical performance of the system while simplifying the system structure. The demand for them in the fields of lithography, aerospace, and laser weapons is increasing, and the requirements for their surface shape detection accuracy are also increasing. Monocular deflectometry has received widespread attention due to its advantages such as large dynamic range, simple measurement system, strong anti-interference, and high measurement accuracy. The principle of monocular deflectometry is that the display screen generates coded stripes, and the camera obtains the deformed stripes reflected by the workpiece to be measured. Combined with the nominal surface shape of the workpiece to be measured, the surface gradient information of the workpiece is obtained through the law of reflection, and then the three-dimensional surface shape of the workpiece is obtained. Then in actual measurement, when the nominal surface shape of the workpiece to be measured is missing or deviates greatly from the actual surface shape, the deflectometry will cause the problem of height-slope uncertainty, which seriously affects the measurement accuracy and application scope. Summary of the invention

[0003] In order to solve the height-slope uncertainty problem caused by the unknown surface shape of the workpiece to be measured in the existing monocular deflectometry, so as to improve the measurement accuracy and application scope, the present invention provides a workpiece surface shape reconstruction method based on the space-variable sphere model adaptive monocular deflectometry, which solves the height-slope uncertainty problem caused by the unknown surface shape of the workpiece to be measured in the existing monocular deflectometry, and improves the measurement accuracy and application scope.

[0004] The technical solution of the present invention is as follows:

[0005] A method for workpiece surface reconstruction based on space-varying sphere model adaptive monocular deflection, characterized in that the method comprises the following steps:

[0006] ① Select any point on the surface of the workpiece to be measured as the mark point F, and use the measuring tool to measure the height h of the mark point F;

[0007] ② Build the detection optical path: Set the coordinates of the optical center of the camera (X0, Y0, Z0), measure the workpiece to be measured by monocular deflectometry, and obtain the screen coordinates of the mark point F on the surface of the workpiece to be measured (X S , Y S , Z S ) and the camera pixel coordinates (X ca , Y ca , Z ca );

[0008] ③According to the camera pixel coordinates (X ca , Y ca, Z ca ) and the camera optical center coordinates (X0, Y0, Z0), calculate the unit direction vector (a) of the reflected light of the marker point F m , b m , c m ), and obtain the reflected light equation of the landmark point F, the formula is as follows:

[0009]

[0010] ④Substitute the height h of the mark point F into the reflected light equation to obtain the workpiece coordinates of the mark point F (X m , Y m , Z m ):

[0011]

[0012]

[0013] Z m =h

[0014] ⑤ Calculate the normal vector of the reflected light at the landmark point F and the normal vector of the incident light ray at the landmark point F The formula is as follows:

[0015]

[0016]

[0017] Calculate the normal vector of the landmark point F The formula is as follows:

[0018]

[0019] ⑥ Ball model fitting: Use a spherical surface to fit the workpiece to be measured. The center of the ball is located on the straight line between the mark point F and the normal vector. By tracing the reverse ray of the mark point F, the optimal ball radius is iteratively obtained, as follows:

[0020] a) Given any spherical radius R, combined with the coordinates of the landmark point F and the normal vector (N x , N y , N z ) to get the coordinates of the center of the sphere (X c , Y c , Z c );

[0021]

[0022] b) From the coordinates of the sphere center (X c , Y c , Z c), the spherical radius R and the camera pixel coordinates of each measuring point to obtain the measuring point coordinates, the normal vector and the direction vector of the incident light;

[0023] c) performing reverse tracing according to the coordinates of each measuring point and the direction vector of the incident light, and calculating the screen coordinates of the tracing, comparing the screen coordinates of the measuring point with the initial screen coordinates, and obtaining the reverse tracing error;

[0024] d) judging whether the reverse tracking error satisfies the preset acceptable minimum error, if not, returning to step a); if satisfied, terminating the iteration process, outputting the optimal sphere center radius and the corresponding initial surface shape obtained by fitting;

[0025] ⑦ Obtain the global optimal spatial variation sphere model of the workpiece to be measured, and obtain the reconstructed surface shape of the component to be measured through monocular deflectometry. The specific process is as follows:

[0026] 7.1) Perform step ⑥ on the surface of the workpiece to be measured, optimize the ball model fitting, and substitute the deflectometry to obtain the reconstructed surface shape G n ;

[0027] 7.2) Set the loop parameter t, and set the initial t = 2;

[0028] 7.3) Divide the workpiece to be tested into t areas, and the areas partially overlap;

[0029] 7.4) Perform step ⑥ on region 1 to optimize the ball model fitting and obtain the fitting initial surface shape g1;

[0030] 7.5) Take any point in the common area of ​​area 1 and area 2 as the mark point F2 of area 2, and perform step ⑥ on area 2 to fit the initial surface shape g2. Similarly, perform the above operation on the tth area of ​​the workpiece to be measured to obtain g t Finally, the global reconstructed surface shape G of the workpiece to be measured is obtained t , G t =g1+g2+……g t ;

[0031] F) Determine the global reconstructed surface shape G t and G n Whether the error of meets the preset acceptable minimum value, if not, let G n =G t , t=t+1, return to step 7.3); if satisfied, terminate the iteration process, output the coordinates of all measurement points, and obtain the final reconstructed surface shape.

[0032] Compared with the prior art, the beneficial effects of the present invention are: it is applicable to a workpiece to be measured whose nominal surface shape equation is missing or deviates from the actual surface shape equation, and improves the measurement accuracy and range. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 It is a schematic diagram of solving the parameters of the spherical model;

[0034] Figure 2 It is a flowchart for solving the ball model;

[0035] Figure 3 It is the surface partition of the workpiece to be measured;

[0036] Figure 4 It is the flow chart of solving the space-changing ball model;

[0037] Figure 5 These are the surface images obtained by different detection methods. DETAILED DESCRIPTION

[0038] The present invention will be described in detail below with reference to the embodiments and drawings, but the protection scope of the present invention shall not be limited thereto.

[0039] Example 1: Build a monocular deflectometry measurement system, which mainly includes: a camera (JAI SP-20000C-USB, 5210×3840 pixels, USB3 interface), a screen (iPad mini 2, 2048×1536 pixels, single pixel size 0.0784mm), and an off-axis parabolic mirror to be measured (focal length 45mm, aperture 30mm, off-axis offset 51.96mm). The measurement results of the interferometer (Zygo GPI XP / D) are used as a reference. The mirror of the off-axis parabolic mirror to be measured is placed horizontally at any position on the measuring platform for deflectometry. Take a mark point in the middle area of ​​the surface to be measured, and use an altimeter with an accuracy of 10um to measure the height h of the mark point F. Combined with the camera pixel coordinates and system calibration parameters obtained by deflectometry, the corresponding reflected light is obtained. The height h of the mark point F is used as the height Z of the measured mark point. m Substitute into the above expression of the reflected light straight line to calculate the X of the measured mark point F m , Y m The coordinates of the actual marker point are combined with the screen coordinates to obtain the normal vector of the measured marker point. Given the coordinates and normal vector of the marker point, the reverse ray tracing is used to iteratively obtain the spherical model parameters. Finally, the measured mirror surface is fitted with a space-variant spherical model: the above spherical model parameters are estimated for the middle area where the marker point is located, and the spherical model is gradually estimated for the adjacent areas until the surface reconstruction error meets the requirements and the global space-variant spherical model is obtained.

[0040] Figure 5(a)-5(d) are the surface shapes obtained by using four different detection methods (interferometer, monocular deflectometry based on the space-varying sphere model, monocular deflectometry with a traditional known surface shape equation, and monocular deflectometry with a plane model), and the detection results are fitted with Zernike polynomials and the Z1-Z4 items are removed. Compared with the interferometer detection results, the surface shape detection error RMS values ​​of the monocular deflectometry method for measuring the workpiece to be measured based on the space-varying sphere model, the monocular deflectometry with a traditional known surface shape equation, and the monocular deflectometry with a plane model are 22.2nm, 31.76nm, and 54.39nm, respectively. Experiments show that compared with the existing plane model, the result error of the method of the present invention is reduced by about 2.5 times. Therefore, the measurement method of the workpiece to be measured based on the space-varying sphere model adaptive monocular deflectometry of the present invention can be applied to the workpiece to be measured whose nominal surface shape equation is missing or deviates from the actual surface shape equation, and its reconstruction accuracy is comparable to or even exceeds the traditional deflectometry with a known nominal surface shape.

[0041] The specific embodiments described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for workpiece surface reconstruction based on adaptive monocular deflection of a space-varying sphere model, characterized in that: The method comprises the following steps: ① Select any point on the surface of the workpiece to be measured as the mark point F, and use the measuring tool to measure the height h of the mark point F; ② Build the detection optical path: Set the coordinates of the optical center of the camera (X0, Y0, Z0), measure the workpiece to be measured by monocular deflectometry, and obtain the screen coordinates of the mark point F on the surface of the workpiece to be measured (X S , Y S , Z S ) and the camera pixel coordinates (X ca , Y ca , Z ca ); ③According to the camera pixel coordinates (X ca , Y ca , Z ca ) and the camera optical center coordinates (X0, Y0, Z0), calculate the unit direction vector (a) of the reflected light of the marker point F m , b m , c m ), and obtain the reflected light equation of the landmark point F, the formula is as follows: ④Substitute the height h of the mark point F into the reflected light equation to obtain the workpiece coordinates of the mark point F (X m , Y m , Z m ): Z m =h ⑤ Calculate the normal vector of the reflected light at the landmark point F and the normal vector of the incident light ray at the landmark point F The formula is as follows: Calculate the normal vector of the landmark point F The formula is as follows: ⑥ Ball model fitting: Use a spherical surface to fit the workpiece to be measured. The center of the ball is located on the straight line between the mark point F and the normal vector. By tracing the reverse ray of the mark point F, the optimal ball radius is iteratively obtained, as follows: a) Given any spherical radius R, combined with the coordinates of the landmark point F and the normal vector (N x , N y , N z ) to get the coordinates of the center of the sphere (X c , Y c , Z c ); b) From the coordinates of the sphere center (X c , Y c , Z c ), the spherical radius R and the camera pixel coordinates of each measuring point to obtain the measuring point coordinates, the normal vector and the direction vector of the incident light; c) performing reverse tracing according to the coordinates of each measuring point and the direction vector of the incident light, and calculating the screen coordinates of the tracing, comparing the screen coordinates of the measuring point with the initial screen coordinates, and obtaining the reverse tracing error; d) judging whether the reverse tracking error satisfies the preset acceptable minimum error, if not, returning to step a); if satisfied, terminating the iteration process, outputting the optimal sphere center radius and the corresponding initial surface shape obtained by fitting; ⑦ Obtain the global optimal spatial variation sphere model of the workpiece to be measured, and obtain the reconstructed surface shape of the component to be measured through monocular deflectometry. The specific process is as follows: 7.1) Perform step ⑥ on the surface of the workpiece to be measured, optimize the ball model fitting, and substitute the deflectometry to obtain the reconstructed surface shape G n ; 7.2) Set the loop parameter t, and set the initial t = 2; 7.3) Divide the workpiece to be tested into t areas, and the areas partially overlap; 7.4) Perform step ⑥ on region 1 to optimize the ball model fitting and obtain the fitting initial surface shape g1; 7.5) Take any point in the common area of ​​area 1 and area 2 as the mark point F2 of area 2, and perform step ⑥ on area 2 to fit the initial surface shape g2. Similarly, perform the above operation on the tth area of ​​the workpiece to be measured to obtain g t Finally, the global reconstructed surface shape G of the workpiece to be measured is obtained t , G t =g1+g2+……g t ; F) Determine the global reconstructed surface shape G t and G n Whether the error of meets the preset acceptable minimum value, if not, let G n =G t , t=t+1, return to step 7.3); if satisfied, terminate the iteration process, output the coordinates of all measurement points, and obtain the final reconstructed surface shape.

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