Ultra-precise out-of-plane rotation measurement method based on 3-D Moire

Abstract

The invention provides an ultra-precise out-of-plane rotation measurement method based on 3-D Moire, the method is based on a 3-D Moire technology, and a measurement system adopted by the method comprises a camera for observation and a label for selecting a plane of an object to be measured; the label comprises two periodic masks etched on two opposite sides of the glass wafer; the periodic masks are series masks; the camera adopts a camera model that an image plane is highly sensitive to out-of-plane rotation; during measurement, the label is pasted on the plane of an object to be measured, generated moire fringes are projected to the image plane of the observation camera, the main point of the camera is located at the label, then the camera is used for shooting the label to obtain the phase of the main point, and measurement is carried out based on the internal reference of the calibration system of the measurement model of the measurement system; in the measurement model, the rotation angle data of the plane of the object to be measured depends on the moire fringe phase at the main point of the image; according to the method, a 3-D Moire measurement model can be clearly derived, and more excellent measurement precision can be obtained.

Description

Technical Field

[0001] The invention relates to the field of precision measurement technology, in particular to an ultra-precision out-of-plane rotation measurement method based on 3-D Moiré. Background Art

[0002] Vision-based displacement measurement can be further divided into linear displacement measurement and angular displacement measurement. The goal of linear displacement measurement is to estimate the 2-D or 3-D translation of a moving target based on the image provided by the observation camera. It includes feature-based methods, Fourier-based methods, and correlation-based methods. The goal of angular displacement measurement is to estimate the angle of a rotating target relative to a specified rotation axis. When the axis is parallel or perpendicular to the camera optical axis, respectively, the rotation is called in-plane rotation or out-of-plane rotation, see Figure 2 . In-plane rotation measurement mainly includes feature-based methods and deep learning-based methods. Out-of-plane rotation measurement is more challenging than in-plane rotation measurement because the image difference of the target before and after rotation is significantly smaller. This problem has become a significant obstacle for many applications. The traditional solution is to use PNP algorithms or correlation algorithms, which determine the angle based on known visual features attached to the target. However, these features hardly move in the image because they mainly change in depth during out-of-plane rotation, see Figure 2 , so the accuracy is unsatisfactory. A more effective solution for out-of-plane rotation measurement involves the development of an imaging process that is sensitive to rotation. A more effective solution for out-of-plane rotation measurement involves the development of an imaging process that is sensitive to rotation. A metasurface consisting of a set of blocks with unique reflective properties was designed. Under illumination, the metasurface has a flickering grayscale change that is sensitive to out-of-plane rotation. Although the reported accuracy is impressive, several disadvantages hinder its practical application. First, the metasurface is difficult to manufacture. Second, its deployment is complex due to the need for a controlled light source, specific measurement conditions, and a complex calibration process. Other approaches exploit the sampling moiré effect, which occurs when a camera captures a target with a periodic pattern that is very close to the frequency of the camera's color filter array. The image of the sampled moiré pattern is sensitive to the pose of the target, bringing the potential for ultra-precision measurement. However, the reported accuracy does not show an advantage over conventional solutions, which may be attributed to the inherently low-quality imaging associated with the sampled moiré pattern. In addition, the working range is limited because the frequency of the target pattern and the frequency of the camera's color filter array must be kept closely matched.

[0003] However, the out-of-plane rotation measurement method based on 3-D Moiré achieves a good balance between cost-effectiveness, easy deployment and high accuracy. Unlike 2-DMoiré, which is generated by two overlapping masks and is sensitive to their relative displacement, the 3-DMoiré pattern is generated by non-coplanar masks and is sensitive to viewpoint motion. Studies have shown that the measurement accuracy of 3-D Moiré is superior to other visual methods. However, there is no clear derived measurement model. Summary of the invention

[0004] The present invention proposes an ultra-precision out-of-plane rotation measurement method based on 3-D Moiré, which can clearly derive a measurement model of 3-D Moiré and obtain more excellent measurement accuracy.

[0005] The present invention adopts the following technical solutions.

[0006] An ultra-precision out-of-plane rotation measurement method based on 3-D Moiré is disclosed. The method is based on 3-D Moiré technology. The measurement system adopted by the method includes a camera for observation and a label for selecting the plane of the object to be measured; the label includes two periodic masks etched on opposite sides of a glass wafer; the periodic mask is a tandem mask; the camera adopts a camera model in which the image plane is highly sensitive to out-of-plane rotation; when measuring, the label is first attached to the plane of the object to be measured, so that the generated Moiré fringes are projected onto the image plane of the observation camera, and the camera principal point is at the label, and then the camera is used to shoot the label to obtain the principal point phase, and the measurement is performed based on the calibration system internal parameters of the measurement model of the measurement system; in the measurement model, the rotation angle data of the plane of the object to be measured depends on the Moiré fringes phase at the image principal point.

[0007] The tag is a self-identifying marker used to select an area of ​​interest on the plane of the object to be measured; the measurement method also includes a calibration system and a deambiguation method.

[0008] When the tag is used to bind to the object to be measured, the measuring method detects the intersection points on the four corners of the object to which the tag is bound, and takes the range contained in these points as the moiré pattern range of the region of interest.

[0009] When the calibration system is used, the camera internal parameters are calibrated with the MATLAB calibration toolbox to obtain the coordinates of the principal point; then a random row is selected from the region of interest to detect its extreme point, and the range where the peak or trough is located is selected with the detected extreme point as the initial point as the center to perform quadratic surface fitting, and the extreme point of the fitted surface and its characteristic direction are found to obtain a ridge line of a peak or a valley line of a trough, and the position of the principal point within a period is calculated to be the phase at this moment.

[0010] The measurement model derives the relationship between the angle change and the phase of the principal point by deriving the geometric relationship between the mask and the moiré pattern.

[0011] The measurement model obtains a set of principal point phase data according to the equally spaced rotation angles of the region of interest, and then performs nonlinear optimization according to the optimization equation to obtain the internal parameters of the calibration system;

[0012] The deambiguation method performs deambiguation through EPNP, and selects a measurement result close to the EPNP measurement result as a deambiguated measurement angle result.

[0013] The measurement system consists of a camera and a marker called RMoM; the RMoM is a thin glass wafer with a size of 100 mm and a thickness of 200 mm.

[0014] W=100mm, H=70mm, s=1mm;

[0015] Calibrate coordinate system O m Defined at the upper left corner of the front side of the thin glass wafer, the X and Y axes are aligned with the horizontal and vertical edges respectively; the camera coordinate system O c Defined at the optical center, the X and Y axes are parallel to the edge of the sensor;

[0016] The Z axis of the above two coordinate systems is along the viewing direction of the camera;

[0017] Etched at each corner of the front side of the thin glass wafer are four cross-point features that are used to resolve period ambiguity;

[0018] Two periodic masks are etched on opposite sides of the main area of ​​the region of interest, and their transmission map is denoted as T i , where i=1, 2 represent the front and back masks respectively.

[0019] In the measurement method, a complete rotation measurement includes one axis and one angle θ; by excluding the Y axis, the measurement calculation is limited to one-dimensional space. In this case, O m The Y axis is the rotation axis, and O m and O c The Y axis is parallel to T i The design is vertical stripes; it can be seen as a derivation of the one-dimensional cosine function, namely:

[0020]

[0021] where w is the circular frequency, is the initial phase; the two masks share the same w to facilitate the formation of the same frequency and fringe direction during manufacturing and assembly,

[0022] The two masks have different In the measurement, the RMoM is first attached to the target of interest, and then the camera is fixed in an appropriate position so that its Z axis intersects the main area of ​​the RMoM. After deployment, the camera observes a moiré pattern S in the main area, and the measurement system continuously estimates the rotation axis and angle θ based on S;

[0023] The method for deriving the geometric model between θ and S is as follows:

[0024] An example of a camera observing an RMoM with a rotation angle θ is Figure 3 As shown in;

[0025] O c The intersection points of the Z axis with the image plane and the two masks are denoted as P and P i , where i = 1, 2 represent the front and back masks respectively;

[0026] The general image point and its corresponding point on the two masks are denoted as X and X respectively. i ; P and X in O c The coordinates in are denoted as P c =(0,f) T and X c =(x, 0) T , where f is the focal length (|O c P|); P i and X i In O m The coordinates in are denoted as P i =(p i ,0) T and X i m =(x i ,0) T ; in O c The Z axis is connected to the X axis. i Define two auxiliary points A at the intersection of the horizontal lines i ;

[0027] The distance between the camera and the two masks is defined as z i =|O c P i |;A i and P i The gap between them is represented by g i ; Based on triangle ΔO c XP and ΔO c X i A i The similarity between i A i P i ,have to:

[0028]

[0029] X and X i must be relative to P and P respectively i are on the same side, and z i -g i Must be positive, use x i -p i and an unsigned x to replace |X i P i | and |XP|;

[0030] The general mapping of mask points to corresponding image points is shown in the following formula:

[0031]

[0032] Combine this formula with T i (x) combined to obtain the projection transmission map T on the sensor i p (x) That is:

[0033]

[0034] The composite transmission diagram T is:

[0035]

[0036] The moiré pattern S is considered to be the low-frequency part of T, which is the left side of the last equation above;

[0037] have:

[0038] The undistorted phase of the moiré pattern S is the image point x, the rotation angle θ and the distance z i The function is:

[0039]

[0040] Where Δz=z1-z2, Δg=g1-g2, And Δp=p1-p2=-stan(θ); when the image point of interest happens to be the principal point, that is, x=0, then: This leads to the measurement model:

[0041]

[0042] in And B = ws is the internal parameter of the system;

[0043] The rotation angle required to measure the model is only the undistorted moiré phase at the image principal point It is simply related to some internal parameters; It is called the unwrapping main phase.

[0044] The measuring method comprises the following steps:

[0045] Step S1, image dedistortion: Use MATLAB calibration tools to calibrate the camera's intrinsic parameters, i.e., internal parameters, including lens distortion coefficients, and then remove lens distortion from the input image;

[0046] Step S2, main region segmentation of the region of interest: Assume that the moiré pattern S is located in the main region, and its four corners are marked by intersections. Use the intersection detection algorithm based on gradient balance prior, and then crop the main region;

[0047] Step S3, Projection Correction: If there is projective distortion in the observed S and this distortion will compromise the sub-pixel accuracy of subsequent steps, the image needs to be corrected, specifically: the view is oriented towards the RMoM, which is achieved by applying a homography that maps the four intersection points to the four image corners; the principal point is also offset in this step;

[0048] Step S4, trough recovery: The waveform of S needs to be restored; if the number of observed cycles is small, the Fourier-based technique will encounter serious leakage problems, so a space-based technique is used, specifically: first, extract any row of the corrected image to obtain a one-dimensional waveform; use a Gaussian filter to smooth the waveform to eliminate high-frequency components; identify pixels with local minimum grayscale values ​​as trough points; second, fit the local area of ​​each trough point through a quadratic surface; combine the surface center and the eigenvector to restore the trough; there will be at least two restored troughs;

[0049] Step S5: Main phase estimation: Phase at the main point In the range ([0, 2π), it is estimated by linear interpolation based on its horizontal distance to the two troughs; then, the undistorted main phase with periodic ambiguity is where k∈Z is unknown;

[0050] Step S6, rotation angle estimation: Based on the known internal parameters A and B, use the undistorted main phase Estimate the required rotation angle θ based on the measurement model; if the periodic ambiguity is retained so that θ has multiple discrete solutions, in order to resolve this ambiguity, use E-PnP based on the four intersection points to provide a low-precision but unique solution; select the discrete solution closest to the E-PnP solution as the output.

[0051] The calibration process of internal parameters A and B is as follows:

[0052] In order to calibrate the internal parameters A and B, the RMoM is fixed on an electric rotating stage with an accuracy of (0.001°). When the relative posture between the RMoM and the rotating stage is unknown, it is not easy to obtain the real θ, but it is easy to obtain the angle increment. Starting from an unknown rotation angle θ0, the rotating stage is gradually rotated by Δθ. For the nth angle θ n =θ0+nΔθ, the RMoM with periodic ambiguity and unwrapped main phase, i.e.

[0053] Similar to θ, we get k n =k0+Δk n , where k0 is the unknown quantity, Δk n is a known quantity;

[0054] Given N samples, we have:

[0055]

[0056] Where C = A-2k0π; there are only three unknowns here, including θ0, C and B, which can be solved when N≥3; the energy function is:

[0057]

[0058] Using the MATLAB Optimization Toolbox to solve the optimal C and B, the difference term 2k0π can be The inherent cycle ambiguity is absorbed and all the cycle ambiguity will be eliminated by E-PnP.

[0059] The present invention can clearly derive a 3-D Moiré measurement model and can obtain better measurement accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments:

[0061] Attached Figure 1 It is a schematic diagram of in-plane rotation and out-of-plane rotation during measurement of the present invention;

[0062] Attached Figure 2 is a schematic diagram of a measurement model of the present invention;

[0063] Attached Figure 3 It is a schematic diagram of the principal point phase estimation process of the present invention;

[0064] Attached Figure 4 It is a schematic diagram of the angle measurement process of the present invention. DETAILED DESCRIPTION

[0065] As shown in the figure, an ultra-precision out-of-plane rotation measurement method based on 3-D Moiré is provided. The method is based on 3-DMoiré technology, and the measurement system adopted by the method includes a camera for observation and a label for selecting the plane of the object to be measured; the label includes two periodic masks etched on opposite sides of a glass wafer; the periodic mask is a tandem mask; the camera adopts a camera model in which the image plane is highly sensitive to out-of-plane rotation; when measuring, the label is first attached to the plane of the object to be measured, so that the generated Moiré fringes are projected onto the image plane of the observation camera, and the camera principal point is made at the label, and then the camera is used to shoot the label to obtain the principal point phase, and the measurement is performed based on the calibration system internal parameters of the measurement model of the measurement system; in the measurement model, the rotation angle data of the plane of the object to be measured depends on the Moiré fringes phase at the image principal point.

[0066] The tag is a self-identifying marker used to select an area of ​​interest on the plane of the object to be measured; the measurement method also includes a calibration system and a deambiguation method.

[0067] When the tag is used to bind to the object to be measured, the measuring method detects the intersection points on the four corners of the object to which the tag is bound, and takes the range contained in these points as the moiré pattern range of the region of interest.

[0068] When the calibration system is used, the camera internal parameters are calibrated with the MATLAB calibration toolbox to obtain the coordinates of the principal point; then a random row is selected from the region of interest to detect its extreme point, and the range where the peak or trough is located is selected with the detected extreme point as the initial point as the center to perform quadratic surface fitting, and the extreme point of the fitted surface and its characteristic direction are found to obtain a ridge line of a peak or a valley line of a trough, and the position of the principal point within a period is calculated to be the phase at this moment.

[0069] The measurement model derives the relationship between the angle change and the phase of the principal point by deriving the geometric relationship between the mask and the moiré pattern.

[0070] The measurement model obtains a set of principal point phase data according to the equally spaced rotation angles of the region of interest, and then performs nonlinear optimization according to the optimization equation to obtain the internal parameters of the calibration system;

[0071] The deambiguation method performs deambiguation through EPNP, and selects a measurement result close to the EPNP measurement result as a deambiguated measurement angle result.

[0072] The measurement system consists of a camera and a marker called RMoM; the RMoM is a thin glass wafer with a size of 100 mm and a thickness of 200 mm.

[0073] W=100mm, H=70mm, s=1mm;

[0074] Calibrate coordinate system Om Defined at the upper left corner of the front side of the thin glass wafer, the X and Y axes are aligned with the horizontal and vertical edges respectively; the camera coordinate system O c Defined at the optical center, the X and Y axes are parallel to the edge of the sensor;

[0075] The Z axis of the above two coordinate systems is along the viewing direction of the camera;

[0076] Etched at each corner of the front side of the thin glass wafer are four cross-point features that are used to resolve period ambiguity;

[0077] Two periodic masks are etched on opposite sides of the main area of ​​the region of interest, and their transmission map is denoted as T i , where i=1, 2 represent the front and back masks respectively.

[0078] In the measurement method, a complete rotation measurement includes one axis and one angle θ; by excluding the Y axis, the measurement calculation is limited to one-dimensional space. In this case, O m The Y axis is the rotation axis, and O m and O c The Y axis is parallel to T i The design is vertical stripes; it can be seen as a derivation of the one-dimensional cosine function, namely:

[0079]

[0080] where w is the circular frequency, is the initial phase; the two masks share the same w to facilitate the formation of the same frequency and fringe direction during manufacturing and assembly,

[0081] The two masks have different In the measurement, the RMoM is first attached to the target of interest, and then the camera is fixed in an appropriate position so that its Z axis intersects the main area of ​​the RMoM. After deployment, the camera observes a moiré pattern S in the main area, and the measurement system continuously estimates the rotation axis and angle θ based on S;

[0082] The method for deriving the geometric model between θ and S is as follows:

[0083] An example of a camera observing an RMoM with a rotation angle θ is Figure 3 As shown in;

[0084] O c The intersection points of the Z axis with the image plane and the two masks are denoted as P and P i , where i = 1, 2 represent the front and back masks respectively;

[0085] The general image point and its corresponding point on the two masks are denoted as X and X respectively.i ; P and X in O c The coordinates in are denoted as P c =(0,f) T and X c =(x, 0) T , where f is the focal length (|O c P|); P i and X i In O m The coordinates in are denoted as P i =(p i ,0) T and X i m =(x i ,0) T ; in O c The Z axis is connected to the X axis. i Define two auxiliary points A at the intersection of the horizontal lines i ;

[0086] The distance between the camera and the two masks is defined as z i =|O c P i |;A i and P i The gap between them is represented by g i ; Based on triangle ΔO c XP and ΔO c X i A i The similarity between i A i P i ,have to:

[0087]

[0088] X and X i must be relative to P and P respectively i are on the same side, and z i -g i Must be positive, use x i -p i and an unsigned x to replace |X i P i | and |XP|;

[0089] The general mapping of mask points to corresponding image points is shown in the following formula:

[0090]

[0091] Combine this formula with T i (x) combined to obtain the projection transmission map T on the sensor ip (x) That is:

[0092]

[0093] The composite transmission diagram T is:

[0094]

[0095] The moiré pattern S is considered to be the low-frequency part of T, which is the left side of the last equation above;

[0096] have:

[0097] The undistorted phase of the moiré pattern S is the image point x, the rotation angle θ and the distance z i The function is:

[0098]

[0099] Where Δz=z1-z2, Δg=g1-g2, And Δp=p1-p2=-stan(θ); when the image point of interest happens to be the principal point, that is, x=0, then: This leads to the measurement model:

[0100]

[0101] in And B = ws is the internal parameter of the system;

[0102] The rotation angle required to measure the model is only the undistorted moiré phase at the image principal point It is simply related to some internal parameters; It is called the unwrapping main phase.

[0103] The measuring method comprises the following steps:

[0104] Step S1, image dedistortion: Use MATLAB calibration tools to calibrate the camera's intrinsic parameters, i.e., internal parameters, including lens distortion coefficients, and then remove lens distortion from the input image;

[0105] Step S2, main region segmentation of the region of interest: Assume that the moiré pattern S is located in the main region, and its four corners are marked by intersections. Use the intersection detection algorithm based on gradient balance prior, and then crop the main region;

[0106] Step S3, Projection Correction: If there is projective distortion in the observed S and this distortion will compromise the sub-pixel accuracy of subsequent steps, the image needs to be corrected, specifically: the view is oriented towards the RMoM, which is achieved by applying a homography that maps the four intersection points to the four image corners; the principal point is also offset in this step;

[0107] Step S4, trough recovery: The waveform of S needs to be restored; if the number of observed cycles is small, the Fourier-based technique will encounter serious leakage problems, so a space-based technique is used, specifically: first, extract any row of the corrected image to obtain a one-dimensional waveform; use a Gaussian filter to smooth the waveform to eliminate high-frequency components; identify pixels with local minimum grayscale values ​​as trough points; second, fit the local area of ​​each trough point through a quadratic surface; combine the surface center and the eigenvector to restore the trough; there will be at least two restored troughs;

[0108] Step S5: Main phase estimation: Phase at the main point In the range ([0, 2π), it is estimated by linear interpolation based on its horizontal distance to the two troughs; then, the undistorted main phase with periodic ambiguity is where k∈Z is unknown;

[0109] Step S6, rotation angle estimation: Based on the known internal parameters A and B, use the undistorted main phase Estimate the required rotation angle θ based on the measurement model; if the periodic ambiguity is retained so that θ has multiple discrete solutions, in order to resolve this ambiguity, use E-PnP based on the four intersection points to provide a low-precision but unique solution; select the discrete solution closest to the E-PnP solution as the output.

[0110] The calibration process of internal parameters A and B is as follows:

[0111] In order to calibrate the internal parameters A and B, the RMoM is fixed on an electric rotating stage with an accuracy of (0.001°). When the relative posture between the RMoM and the rotating stage is unknown, it is not easy to obtain the real θ, but it is easy to obtain the angle increment. Starting from an unknown rotation angle θ0, the rotating stage is gradually rotated by Δθ. For the nth angle θ n =θ0+nΔθ, the RMoM with periodic ambiguity and unwrapped main phase, i.e.

[0112] Similar to θ, we get k n =k0+Δk n , where k0 is the unknown quantity, Δk n is a known quantity;

[0113] Given N samples, we have:

[0114]

[0115] Where C = A-2k0π; there are only three unknowns here, including θ0, C and B, which can be solved when N≥3; the energy function is:

[0116]

[0117] Using the MATLAB Optimization Toolbox to solve the optimal C and B, the difference term 2k0π can be The inherent cycle ambiguity is absorbed and all the cycle ambiguity will be eliminated by E-PnP.

[0118] In this example, after solving for the optimal C and B using the MATLAB Optimization Toolbox, it is possible to solve for the true A from C, but it is not necessary because the difference term 2k0π can be The inherent cycle ambiguity is absorbed, which would otherwise be eliminated by E-PnP.

[0119] In this example, if Figure 2 As shown, frontmask and backmask are the front and back masks respectively, imageplane is the image plane, and the coordinate system is established as shown in the figure. The point X on the image plane corresponds to the point X1 X2. Draw perpendicular lines through X1 X2 to the optical axis, and the intersection point is A1 A2, forming a triangle X2A2O c and triangle X1A1O c and triangle XPO c The triangles are similar. Based on the deduction, the relationship between X1X2 and X can be found.

[0120] In this case, moire fringes are moire fringes and moire patterns are moire patterns.

[0121] In this example, the schematic diagram of the measurement geometry model derivation process is as follows Figure 2 As shown, Figure 2 In the simulated camera imaging process, the image plane is usually drawn in front of the optical center in machine vision. The above letter definitions and coordinate system construction are as described above. The relationship between a certain point on the mask and its corresponding point on the image can be obtained by using triangle similarity, and the function of the mask projection can be calculated. However, the function of the moiré pattern is the product of the two projection functions. At the principal point, x=0, so the rotation angle and its phase relationship in the moiré pattern can be derived. The triangle similarity is expressed as Figure 2 Three triangles with two identical angles and proportional sides form similar triangles.

[0122] This example is based on the 3D moiré effect, which has the ability to amplify displacement. When a single mask is placed, it is equivalent to an ordinary marker. As the distance increases, its measurement effect becomes worse. However, using the moiré pattern, even if the angle changes slightly, the 3D moiré effect can also amplify the change. According to the above-mentioned set of deductions, its components are independent of the object distance, which means that the measurement accuracy is independent of the object distance. Even slight angle changes can still be predicted by the method described in this example.

[0123] Embodiment 1:

[0124] An ultra-precision out-of-plane rotation measurement method based on 3-D Moiré, as shown in the attached Figure 4 As shown, the following steps are included:

[0125] Attach the label to the object to be tested;

[0126] Get N groups of labeled images;

[0127] Get the principal point phase of each image;

[0128] Calibrate the internal parameters by optimizing the equation;

[0129] Bring the internal parameters back to the measurement model and combine them with the angle calculated by E-PNP to eliminate periodic ambiguity. We only need to match the angle closest to the E-PNP result to obtain the angle we measure.

Claims

1. An ultra-precision out-of-plane rotation measurement method based on 3-D Moiré, characterized in that: The method is based on 3-DMoiré technology, and the measurement system adopted by the method includes a camera for observation and a label for selecting the plane of the object to be measured; the label includes two periodic masks etched on opposite sides of a glass wafer; the periodic masks are tandem masks; the camera adopts a camera model in which the image plane is highly sensitive to out-of-plane rotation; when measuring, the label is first attached to the plane of the object to be measured, so that the generated moiré fringes are projected onto the image plane of the observation camera, and the camera principal point is at the label, and then the camera is used to shoot the label to obtain the principal point phase, and the measurement is performed based on the calibration system internal parameters of the measurement model of the measurement system; in the measurement model, the rotation angle data of the plane of the object to be measured depends on the moiré fringes phase at the image principal point.

2. The ultra-precision out-of-plane rotation measurement method based on 3-D Moiré according to claim 1, characterized in that: The tag is a self-identifying marker used to select a region of interest on the plane of the object to be measured; The measurement method also includes a calibration system and a deambiguation method.

3. The ultra-precision out-of-plane rotation measurement method based on 3-D Moiré according to claim 2, characterized in that: When the tag is used to bind to the object to be measured, the measuring method detects the intersection points on the four corners of the object to which the tag is bound, and takes the range contained in these points as the moiré pattern range of the region of interest.

4. The ultra-precision out-of-plane rotation measurement method based on 3-D Moiré according to claim 3, characterized in that: When the calibration system is used, the camera internal parameters are calibrated with the MATLAB calibration toolbox to obtain the coordinates of the principal point; then a random row is selected from the region of interest to detect its extreme point, and the range where the peak or trough is located is selected with the detected extreme point as the initial point as the center to perform quadratic surface fitting, and the extreme point of the fitted surface and its characteristic direction are found to obtain a ridge line of a peak or a valley line of a trough, and the position of the principal point within a period is calculated to be the phase at this moment.

5. The ultra-precision out-of-plane rotation measurement method based on 3-D Moiré according to claim 3, characterized in that: The measurement model derives the relationship between the angle change and the phase of the principal point by deriving the geometric relationship between the mask and the moiré pattern.

6. The ultra-precision out-of-plane rotation measurement method based on 3-D Moiré according to claim 5, characterized in that: The measurement model obtains a set of principal point phase data according to the equally spaced rotation angles of the region of interest, and then performs nonlinear optimization according to the optimization equation to obtain the internal parameters of the calibration system; the defuzzification method performs defuzzification through EPNP, and selects the measurement result close to the EPNP measurement result as the defuzzified measurement angle result.

7. The ultra-precision out-of-plane rotation measurement method based on 3-DMoiré according to claim 6, characterized in that: The measurement system consists of a camera and a marker RMoM; the RMoM is a thin glass wafer with dimensions W × H and thickness s; Calibrate coordinate system O m Defined at the upper left corner of the front side of the thin glass wafer, the X and Y axes are aligned with the horizontal and vertical edges respectively; the camera coordinate system O c Defined at the optical center, the X and Y axes are parallel to the edge of the sensor; The Z axis of the above two coordinate systems is along the viewing direction of the camera; Etched at each corner of the front side of the thin glass wafer are four cross-point features that are used to resolve period ambiguity; Two periodic masks are etched on opposite sides of the main area of ​​the region of interest, and their transmission map is denoted as T i , where i=1, 2 represent the front and back masks respectively.

8. The ultra-precision out-of-plane rotation measurement method based on 3-D Moiré according to claim 7, characterized in that: In the measurement method, a complete rotation measurement includes one axis and one angle θ; by excluding the Y axis, the measurement calculation is limited to one-dimensional space. In this case, O m The Y axis is the rotation axis, and O m and O c The Y axis is parallel to T i The design is vertical stripes; it can be seen as a derivation of the one-dimensional cosine function, namely: where w is the circular frequency, is the initial phase; the two masks share the same w to facilitate the formation of the same frequency and fringe direction during manufacturing and assembly, The two masks have different In the measurement, the RMoM is first attached to the target of interest, and then the camera is fixed in an appropriate position so that its Z axis intersects the main area of ​​the RMoM. After deployment, the camera observes a moiré pattern S in the main area, and the measurement system continuously estimates the rotation axis and angle θ based on S; The method for deriving the geometric model between θ and S is as follows: When a camera observes RMoM with a rotation angle θ; O c The intersection points of the Z axis with the image plane and the two masks are denoted as P and P i , where i = 1, 2 represent the front and back masks respectively; The general image point and its corresponding point on the two masks are denoted as X and X respectively. i ; P and X in O c The coordinates in are denoted as P c =(0,f) T and X c =(x, 0) T , where f is the focal length (|O c P|); P i and X i In O m The coordinates in are denoted as P i =(p i ,0) T and X i m =(x i ,0) T ; in O c The Z axis is connected to the X axis. i Define two auxiliary points A at the intersection of the horizontal lines i ; The distance between the camera and the two masks is defined as z i =|O c P i |;A i and P i The gap between them is represented by g i ; Based on triangle ΔO c XP and ΔO c X i A i The similarity between i A i P i ,have to: X and X i must be relative to P and P respectively i are on the same side, and z i -g i Must be positive, use x i -p i and an unsigned x to replace |X i P i | and |XP|; The general mapping of mask points to corresponding image points is shown in the following formula: Combine this formula with T i (x) Combined with the projection transmission map on the sensor, Right now: The composite transmission diagram T is: The moiré pattern S is considered to be the low-frequency part of T, that is, the left side of the last equation above; The undistorted phase of the moiré pattern S is the image point x, the rotation angle θ and the distance z i The function is: in And Δp=p1-p2=-stan(θ); When the image point of interest happens to be the principal point, that is, x = 0, then: This leads to the measurement model: in And B = ws is the internal parameter of the system; The rotation angle required to measure the model is only the undistorted moiré phase at the image principal point It is simply related to some internal parameters; It is called the unwrapping main phase.

9. The ultra-precision out-of-plane rotation measurement method based on 3-DMoiré according to claim 8, characterized in that: The measuring method comprises the following steps: Step S1, image dedistortion: Use MATLAB calibration tools to calibrate the camera's intrinsic parameters, i.e., internal parameters, including lens distortion coefficients, and then remove lens distortion from the input image; Step S2, main region segmentation of the region of interest: Assume that the moiré pattern S is located in the main region, and its four corners are marked by intersections. Use the intersection detection algorithm based on gradient balance prior, and then crop the main region; Step S3, Projection Correction: If there is projective distortion in the observed S and this distortion will compromise the sub-pixel accuracy of subsequent steps, the image needs to be corrected, specifically: the view is oriented towards the RMoM, which is achieved by applying a homography that maps the four intersection points to the four image corners; the principal point is also offset in this step; Step S4, trough recovery: The waveform of S needs to be restored; if the number of observed cycles is small, the Fourier-based technique will encounter serious leakage problems, so a space-based technique is used, specifically: first, extract any row of the corrected image to obtain a one-dimensional waveform; use a Gaussian filter to smooth the waveform to eliminate high-frequency components; identify pixels with local minimum grayscale values ​​as trough points; second, fit the local area of ​​each trough point through a quadratic surface; combine the surface center and the eigenvector to restore the trough; there will be at least two restored troughs; Step S5: Main phase estimation: Phase at the main point In the range ([0, 2π), it is estimated by linear interpolation based on its horizontal distance to the two troughs; then, the undistorted main phase with periodic ambiguity is where k∈Z is unknown; Step S6, rotation angle estimation: Based on the known internal parameters A and B, use the undistorted main phase Estimate the required rotation angle θ based on the measurement model; if the periodic ambiguity is retained so that θ has multiple discrete solutions, in order to resolve this ambiguity, use E-PnP based on the four intersection points to provide a low-precision but unique solution; select the discrete solution closest to the E-PnP solution as the output.

10. The ultra-precision out-of-plane rotation measurement method based on 3-DMoiré according to claim 9, characterized in that: The calibration process of internal parameters A and B is as follows: In order to calibrate the internal parameters A and B, the RMoM is fixed on an electric rotating stage with an accuracy of (0.001°). When the relative posture between the RMoM and the rotating stage is unknown, it is not easy to obtain the real θ, but it is easy to obtain the angle increment. Starting from an unknown rotation angle θ0, the rotating stage is gradually rotated by Δθ. For the nth angle θ n =θ0+nΔθ, the RMoM with periodic ambiguity and unwrapped main phase, i.e. Similar to θ, we get k n =k0+Δk n , where k0 is the unknown quantity, Δk n is a known quantity; Given N samples, we have: Where C = A-2k0π; there are only three unknowns here, including θ0, C and B, which can be solved when N≥3; the energy function is: Using the MATLAB Optimization Toolbox to solve the optimal C and B, the difference term 2k0π can be The inherent cycle ambiguity is absorbed and all the cycle ambiguity will be eliminated by E-PnP.

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