A 3-D moire based ultra-precision out-of-plane rotation measurement method

Abstract

The application provides a kind of ultra-precision plane out of rotation measurement method based on 3-D Moiré, the method is based on 3-D Moiré technology, the measurement system it adopts includes camera for observation and label for selecting the plane of the object to be measured;The label contains two periodic masks etched on the opposite sides of glass wafer;The periodic mask is series mask;The camera adopts the camera model that image plane is sensitive to out of plane rotation height;When measuring, first, the label is pasted on the plane of the object to be measured, the moire fringe generated is projected to the image plane of the observation camera, and the principal point of the camera is at the label, then the principal point phase is acquired by using the camera to shoot the label, and the measurement is carried out based on the calibration system 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 moire fringe phase at the principal point of the image;The application can derive the measurement model of 3-D Moiré, and better measurement accuracy can be obtained.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of precision measurement, and particularly to a super-precision out-of-plane rotation measurement method based on 3-D Moiré. BACKGROUND

[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 images provided by an 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 with respect 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 the PNP algorithm or the correlation algorithm, which determines 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 not satisfactory. A more effective solution for out-of-plane rotation measurement involves developing an imaging process that is sensitive to rotation. A more effective solution for out-of-plane rotation measurement involves developing an imaging process that is sensitive to rotation. There are studies that have designed a metasurface consisting of a set of blocks with unique reflective properties. Under illumination, this metasurface has a flickering grayscale change that is sensitive to out-of-plane rotation. Although the reported accuracy is impressive, some drawbacks 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 methods take advantage of the sampling Moiré effect, which occurs when a camera captures a target with a periodic pattern very close to the frequency of the camera color filter array. The image of the sampling Moiré pattern is sensitive to the pose of the target, bringing the potential for super-precision measurement. However, the reported accuracy does not show an advantage compared to traditional solutions, which can be attributed to the inherently low-quality imaging associated with the sampling Moiré pattern. In addition, the working range is limited because the frequency of the target pattern and the frequency of the camera color filter array must remain closely matched.

[0003] However, the out-of-plane rotation measurement method based on 3-D Moire achieves a good balance among cost-effectiveness, easy deployment and high precision. Unlike 2-D Moire generated by two overlapping masks and sensitive to their relative displacement, 3-D Moire pattern is generated by non-coplanar masks and sensitive to the viewpoint motion. It has been proved that the measurement accuracy of 3-D Moire is superior to other vision methods. However, the measurement model of 3-D Moire is not derived explicitly. SUMMARY

[0004] The application provides an out-of-plane rotation measurement method based on 3-D Moire, which can derive the measurement model of 3-D Moire explicitly and achieve more excellent measurement accuracy.

[0005] The application adopts the following technical solutions.

[0006] The application provides an out-of-plane rotation measurement method based on 3-D Moire, which is based on 3-D Moire technology and adopts a measurement system including a camera for observation and a label for selecting the plane of an object to be measured; the label comprises two periodic masks etched on opposite sides of a glass wafer; the periodic masks are series masks; the camera adopts a camera model highly sensitive to out-of-plane rotation of an image plane; when measuring, the label is first attached to the plane of the object to be measured, so that the generated Moire fringes are projected to the image plane of the observation camera and the principal point of the camera is at the label, and then the camera is used to capture the label to obtain the principal point phase, and the measurement is performed based on the system parameter calibration 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 depend on the Moire fringe phase at the principal point.

[0007] The label is a self-identifying marker for selecting a region of interest of the plane of the object to be measured; the measurement method further comprises a calibration system and a deblurring method.

[0008] When the label is used to bind with the object to be measured, the measurement method detects the intersection points on the four corners of the label bound object, and takes the range containing the points as the Moire pattern range of the region of interest.

[0009] When the calibration system is used, the coordinates of the principal point are first obtained by calibrating the camera parameter with a matlab calibration toolbox; then a random row is selected in the region of interest, and extreme points are detected; the extreme points detected are taken as the center, and the range where the wave crest or wave trough is located is selected for quadratic surface fitting, so that the extreme points of the fitted surface and the characteristic direction are found, so as to obtain a ridge line of the wave crest or a valley line of the wave trough, and the position of the principal point in a period is calculated to obtain the phase at this moment.

[0010] The measurement model derives the relationship between the angle change and the principal point phase by deducing the geometric relationship of the mask and the Moire 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 an optimization equation to obtain the intrinsic parameters of the calibration system.

[0012] The deblurring method deblurs by EPNP, and selects the measurement result close to the EPNP measurement result as the deblurred measurement angle result.

[0013] The measurement system includes a camera and a marker called RMoM; the RMoM is a thin glass wafer with a size of and a thickness of

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

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

[0016] The Z axes of the above two coordinate systems are along the observation direction of the camera;

[0017] Four intersection point features are etched on each corner of the front surface of the thin glass wafer, which are used to solve the periodic ambiguity problem;

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

[0019] In the measurement method, a complete rotation measurement includes an axis and an angle θ; by excluding the Y axis, the measurement calculation is limited to one-dimensional space, in which case the Y axis of O m is the rotation axis, and the Y axes of O m and O c are parallel. T i is designed as a vertical stripe; it can be considered as the derivation of a one-dimensional cosine function, that is:

[0020]

[0021] where w is the circular frequency, is the initial phase; the two masks share the same w to form the same frequency and stripe direction in the manufacturing and assembly process,

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

[0023] The method of deriving the geometric model between θ and S is specifically:

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

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

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

[0027] The distance between the camera and the two masks is defined as z i = |O c P i |; the gap between A i and P i is denoted as g i ; based on the similarity between triangles ΔO c XP and ΔO c X i A i , and triangle ΔX i A i P i , we have:

[0028]

[0029] X and X i must be positive, with x i on the same side, and z i - g i must be positive, with x i - p i and unsigned x to replace |X i P i | and |XP|;

[0030] The general mask point to corresponding image point mapping is given by the following equation:

[0031]

[0032] Combining this equation with T i (x) gives the projected transmission map T i p (x) as:

[0033]

[0034] The composite transmission map T is:

[0035]

[0036] The Moire pattern S is effectively the low frequency part of T, i.e. the left hand side of the last equation above;

[0037] There is:

[0038] The untwisted phase of the Moire pattern S is a function of the image point x, the rotation angle θ and the distance z i i.e.:

[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 primary point, i.e. x = 0, then: This leads to the measurement model:

[0041]

[0042] where and B = ws are internal parameters of the system;

[0043] The rotation angle required by the measurement model is simply related to the untwisted Moire phase at the image primary point and some internal parameters of the system; The main phase is called unwrapped.

[0044] The measurement method comprises the following steps:

[0045] Step S1, image de-distortion: calibrate the internal parameters of the camera using the MATLAB calibration tool, the internal parameters including the lens distortion coefficient, and then remove the lens distortion from the input image;

[0046] Step S2, main region segmentation of the region of interest: set the Moire pattern S in the main region, and mark the four corners of the main region with intersection points. Then, use the intersection point detection algorithm based on the gradient balance prior, and then crop the main region;

[0047] Step S3, projection correction: if there is a projection distortion in the observed S and the distortion will damage the sub-pixel accuracy of the subsequent steps, the image needs to be corrected, specifically: make the viewing angle face the RMoM, and realize the transformation by applying a homography transformation, which maps the four intersection points to the four image corner points; in this step, the main point will also be offset;

[0048] Step S4, wave trough recovery: the wave of S needs to be recovered; if the observed number of periods is small, the Fourier-based technique will encounter a serious leakage problem, therefore, a spatial-based technique is adopted, specifically: first, extract an arbitrary row of the corrected image to obtain a one-dimensional wave; use a Gaussian filter to smooth the wave to eliminate high-frequency components; identify the pixels with local minimum gray value as the wave trough points; second, fit a quadratic surface to the local area of each wave trough point; combine the surface center and the feature vector to recover the wave trough; at least two recovered wave troughs are obtained;

[0049] Step S5, main phase estimation: the phase of the main point is estimated based on the horizontal distance to the two wave troughs by linear interpolation in the range of ([0, 2π); then, the unwrapped main phase with period ambiguity is where k∈Z is unknown;

[0050] Step S6, rotation angle estimation: based on the known internal parameters A and B, use the unwrapped main phase to estimate the required rotation angle θ; if the period ambiguity is retained so that θ has multiple discrete solutions, in order to solve 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 the internal parameters A and B is specifically as follows:

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

[0053] Similar to θ, we get k n =k0+Δk n Where k0 is an unknown quantity, Δk n It 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] The optimal C and B can be found using the MATLAB Optimization Toolbox, and the difference term 2k0π can be... The inherent periodic ambiguity is absorbed, and this periodic ambiguity is eliminated by E-PnP.

[0059] This invention can clearly derive the measurement model of 3-D Moiré and obtain better measurement accuracy. Attached Figure Description

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

[0061] Appendix Figure 1 This is a schematic diagram illustrating in-plane and out-of-plane rotation during measurement in this invention;

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

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

[0064] Appendix Figure 4 This is a schematic diagram of the angle measurement process of the present invention. Detailed Implementation

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

[0066] The label is a self-identifying marker for selecting a region of interest of the plane of the object to be measured; the measurement method further includes a calibration system and a deblurring method.

[0067] When the label is used to bind with the object to be measured, the measurement method detects the intersection points on the four corners of the label bound object, and takes the range containing the points as the Moiré pattern range of the region of interest.

[0068] When the calibration system is used, the coordinates of the principal point are first calibrated by using a matlab calibration toolbox to obtain the coordinates of the principal point; then a random row is selected in the region of interest, and extreme points are detected, and the range where a wave crest or a wave trough is located is selected as the center of the detected extreme points for quadratic surface fitting, and the extreme points of the fitted surface and the characteristic direction thereof are found to obtain a ridge line of a wave crest or a valley line of a wave trough, and the position of the principal point in a period is calculated to obtain the phase at this moment.

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

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

[0071] The deblurring method performs deblurring by EPNP, and selects a measurement result close to the EPNP measurement result as the deblurred measurement angle result.

[0072] The measurement system includes a camera and a label called RMoM; the RMoM is a thin glass wafer with a size of and a thickness of

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

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

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

[0076] Four cross-point features are etched at each corner of the front side of the thin glass wafer, which are used to solve the periodic ambiguity problem;

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

[0078] In the measurement method, a complete rotation measurement includes an axis and an angle θ; by excluding the Y axis, the measurement calculation is limited to one-dimensional space, in which case, the Y axis of O m is the rotation axis, and the Y axes of O m and O c are parallel. T i is designed as a vertical stripe; it can be considered as a derivation of one-dimensional cosine function, that is:

[0079]

[0080] where w is the circular frequency, is the initial phase; the two masks share the same w to form the same frequency and stripe direction in the manufacturing and assembly process,

[0081] The two masks have different In the measurement, first, the RMoM is attached to the target of interest, and then the camera is fixed in place so that its Z axis intersects the main region of the RMoM, after deployment, the camera observes the Moire pattern S in the main region, and the measurement system continuously estimates the rotation axis and the angle θ based on S;

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

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

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

[0085] A general image point and its corresponding point on the two masks are represented as X and Xi ; P and X in O c are represented 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 are represented as P i = (p i , 0) T and X i m = (x i , 0) T ; two auxiliary points A c are defined at the intersection of the Z axis of O i and the horizontal line through X i ;

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

[0087]

[0088] X and X i must be on the same side with respect to P and P i respectively, and z i -g i must be positive, replace |X i P i | and |XP| with x i -p i and unsigned x;

[0089] The general mask point to the corresponding image point mapping is as follows:

[0090]

[0091] Combine this formula with T i (x) to get the projection transmission map T ip (x) i.e.

[0092]

[0093] The composite transmission map T is:

[0094]

[0095] The Moire pattern S is considered as the low frequency part of T, i.e. the left hand side of the last equation above;

[0096] There is:

[0097] The untwisted phase of the Moire pattern S is a function of the image point x, the rotation angle θ and the distance z i i.e.

[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, i.e. x = 0, then we have: which leads to the measurement model:

[0100]

[0101] where and B = ws are internal parameters of the system;

[0102] The rotation angle required by the measurement model is simply related to the untwisted Moire phase at the principal point of the image and some internal parameters; which is called the unwrapped principal phase.

[0103] The measurement method comprises the following steps:

[0104] Step S1, image de-distortion: calibrate the internal parameters of the camera using the MATLAB calibration tool, the internal parameters being internal parameters including the lens distortion coefficient, and then remove the lens distortion from the input image;

[0105] Step S2, main region segmentation of the region of interest: set the Moire pattern S to be in the main region, the four corners of which are marked by intersection points. Use an intersection point detection algorithm based on gradient balance prior, and then crop the main region;

[0106] Step S3, projection correction: if there is a projection distortion in the observed S and this distortion will impair the sub-pixel accuracy of the subsequent steps, the image needs to be corrected, specifically: make the viewing angle face the RMoM, and achieve this by applying a homography transformation that maps the four intersection points to the four image corner points; in this step, the principal point will also be offset;

[0107] Step S4, wave trough recovery: the wave of S needs to be recovered; if the number of observed periods is small, Fourier-based techniques will encounter serious leakage problems, so spatial-based techniques are used, specifically: first, extract any row of the corrected image to obtain a one-dimensional wave; use a Gaussian filter to smooth the wave to eliminate high-frequency components; identify the pixels with local minimum gray value as wave trough points; second, fit a quadratic surface to the local area of each wave trough point; combine the surface center and the feature vector to recover the wave trough; at least two recovered wave troughs are obtained;

[0108] Step S5, principal phase estimation: the phase at the principal point is estimated based on its horizontal distance to the two wave troughs by linear interpolation in the range of ([0, 2π); then, the untwisted principal phase with period ambiguity is where k∈Z is unknown;

[0109] Step S6, rotation angle estimation: based on the known internal parameters A and B, use the untwisted principal phase to estimate the required rotation angle θ; if the period ambiguity is retained so that θ has multiple discrete solutions, in order to solve 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 a motorized rotary table with an accuracy of (0.001°); when the relative pose between the RMoM and the rotary table is unknown, it is not easy to obtain the true θ, but it is easy to obtain the angle increment, starting from an unknown rotation angle θ0, then rotating the rotary table step by step by Δθ; for the RMoM at the nth angle θ n = θ0+ nΔθ, the untwisted principal phase with period ambiguity is

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

[0113] Given N samples, we have:

[0114]

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

[0116]

[0117] Solve the optimal C and B using MATLAB optimization toolbox, the difference term 2k0π can be absorbed by Intrinsic periodic ambiguity, which will be eliminated by E-PnP.

[0118] In this example, after solving the optimal C and B using MATLAB optimization toolbox, it is possible to solve the real A from C, but it is not necessary, because the difference term 2k0π can be absorbed by Intrinsic periodic ambiguity, which will be eliminated by E-PnP in any case.

[0119] In this example, as shown in Figure 2 , frontmask and backmask are front and back masks respectively, imageplane is the image plane, and the coordinate system is established as shown in the figure. The point of the mask corresponding to a point X of the image plane is X1 X2, and the perpendiculars of the optical axis are drawn through X1 X2, and the intersection points are A1 A2, forming triangle X2A2O c and triangle X1A1O c and triangle XPO c constitute similar triangles. According to the derivation, the relationship between X1X2 and X can be obtained.

[0120] In this example, the moire fringe is the moire fringe, and the moire pattern is the moire pattern.

[0121] In this example, the measurement geometry model derivation process is shown in Figure 2 , as shown in Figure 2 , the camera imaging process is simulated, and in machine vision, the image plane is usually drawn in front of the optical center. The letters are defined as above, and the coordinate system is constructed as above. The relationship between a point on the mask plate and its corresponding point on the image can be obtained by using the similarity of triangles, i.e. the function of mask projection can be obtained. However, the function of the moire pattern is the product of two projection functions, and at the principal point, x=0, then the rotation angle and its phase relationship in the moire pattern can be derived, and the similarity of triangles is Figure Two three triangles with two equal angles and proportional sides constitute similar triangles.

[0122] This example is based on 3D moire effect, which has the ability to amplify displacement, which is reflected in the single mask placement as a common marker, as the distance increases, its measurement effect becomes worse, and even if the angle changes slightly, 3D moire effect can have an amplification change. According to the above conclusion, the composition is irrelevant to the object distance, that is, the measurement accuracy is irrelevant to the object distance, and even if the angle changes slightly, the method described in this example can still be predicted.

[0123] Embodiment 1:

[0124] A kind of ultra-precision plane out of rotation measurement method based on 3-D Moiré, as shown in Fig. 1, comprising the following steps: Figure 4

[0125] Paste the label on the object to be measured;

[0126] Get N groups of label images;

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

[0128] Calibrate the intrinsic parameter by optimizing equation;

[0129] Bring the intrinsic parameter back to the measurement model, combine the angle calculated by E-PNP to eliminate the periodic ambiguity, and only match the closest to the E-PNP result to get the measured angle.​

Claims

1. A 3-D Moire based ultra-precision out-of-plane rotation measurement method, characterized in that: The method is based on 3-D Moire technology, and a measurement system used in the method includes a camera for observation and a label for selecting a plane of an object to be measured; the label includes two periodic masks etched on opposite sides of a glass wafer; the periodic masks are serial masks; the camera uses an image plane-to-plane rotation highly sensitive camera model; when measuring, the label is first attached to the plane of the object to be measured, so that the generated Moire fringes are projected to the image plane of the observation camera, and the principal point of the camera is at the label, and then the label is photographed by the camera to obtain the principal point phase, and the measurement is performed based on the system parameters of the calibration system of the measurement model; 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 image principal point; In the measurement method, a complete rotation measurement includes one axis and one angle θ; by excluding the Y-axis, the measurement calculation is restricted to one-dimensional space, in which case O m The Y-axis is the axis of rotation, and O m and O c The Y-axis is parallel; T i The design features vertical stripes; it can be viewed as a derivation of a one-dimensional cosine function, namely: where w is the circular frequency, is the initial phase; both masks share the same w to ease the manufacturing and assembly process to form the same frequency and fringe direction, The two masks have different In the measurement, the RMoM is first attached to the target of interest, and then the camera is fixed at a proper position so that its Z axis intersects with the main area of the RMoM; after deployment, the camera observes the Moire pattern S in the main area, and the measurement system continuously estimates the rotation axis and the angle θ based on S; The method for deriving the geometric model between θ and S is as follows: When a camera observes the RMoM with a rotation angle θ; O c The intersection 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 points on the two masks are denoted as X and X i respectively c The coordinates of P and X in O c are denoted as P T = (0, f) c and X T = (x, 0) c , where f is the focal length (|O i P|) ; the coordinates of P i and X m in O i are denoted as P i = (p T , 0) i and X m = (x i , 0) T ; two auxiliary points A c are defined at the intersection of the Z axis of O i and the horizontal line passing through X 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 as g i ; based on triangle ΔO c XP and ΔO c X i A i Similarity between A i A i P i , we get: X and X i must be positive, with x i on the same side, and z i - g i must be positive, with x i - p i and the unsigned x replacing |X i P i | and |XP|; The general mask point-to-image point mapping is as follows: Combining this equation with T i (x) gives the projected transmission map T i p (x) i.e. The composite transmission graph T is: The Moire pattern S is equivalent to the low-frequency part of T, that is, the left part of the last equation; There are: The untwisted phase of the Moire pattern S is a function of the image point x, the rotation angle θ and the distance z, i.e.: i S = x + θ + z where Δz = z1- z2, Δg = g1- g2, and Δp = p1- p2= -stan(θ); when the image point of interest is exactly the principal point, i.e. x = 0, then we have: leading to the measurement model: wherein and B = ws is an internal parameter of the system; The rotation angle required for the measurement model is simply related to the unwrapped moire phase at the image principal point and some internal parameters; is called the unwrapped primary phase.

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

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

4. The 3-D Moire based ultra-precision out-of-plane rotation measurement method according to claim 3, characterized in that: In use, the calibration system first calibrates the camera parameters by using the matlab calibration toolbox to obtain the coordinates of the principal point; then, a random row is selected in the region of interest, and extreme points are detected; taking the detected extreme points as the center, the range where the wave crest or wave trough is located is selected for quadratic surface fitting, and the extreme points and characteristic directions of the fitted surface are found to obtain a ridge line of the wave crest or a valley line of the wave trough; the position of the principal point in a period is calculated to obtain the phase at this moment.

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

6. The 3-D Moire based ultra-precision out-of-plane rotation measurement method according to claim 5, characterized in that: The measurement model obtains a group 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 system parameters of the calibration system; the deblurring method uses EPNP to deblur, and selects the measurement result close to the EPNP measurement result as the deblurred measurement angle result.

7. The 3-D Moire based ultra-precision out-of-plane rotation measurement method according to claim 6, characterized in that: The measurement system includes a camera and a labeled RMoM; the RMoM is a thin glass wafer with a size of WxH and a thickness of s; Calibration 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; Camera coordinate system O c Defined at the optical center, the X and Y axes are parallel to the edges of the sensor; The Z axes of the above two coordinate systems are along the observation direction of the camera; Four intersection point features are etched on each corner of the front surface of the thin glass wafer, which are used to solve the periodic ambiguity problem; Two periodic masks are etched on the opposite sides of the main region of the region of interest, whose transmission map is denoted as T i where i = 1, 2 represent the front and back masks, respectively.

8. The 3-D Moire based ultra-precision out-of-plane rotation measurement method according to claim 1, characterized in that: The measurement method includes the following steps: Step S1, image de-distortion: calibrate the intrinsic parameters of the camera using MATLAB calibration tool, which includes lens distortion coefficients, and then remove the lens distortion from the input image; Step S2, main region segmentation of the region of interest: set the Moire pattern S in the main region, whose four corners are marked by intersection points; use the intersection point detection algorithm based on gradient balance prior, and then crop the main region; Step S3, projection correction: if there is projection distortion in the observed S and such distortion will damage the sub-pixel accuracy of the subsequent steps, the image needs to be corrected, specifically: make the viewing angle face the RMoM, and realize it by applying a homography transformation, which maps the four intersection points to the four image corner points; in this step, the main point will also be offset; Step S4, wave trough recovery: it is necessary to recover the wave form of S; if the observed period is less, the Fourier-based technique will encounter serious leakage problems, so the spatial-based technique is adopted, specifically: first, extract any row of the corrected image to obtain a one-dimensional wave form; use a Gaussian filter to smooth the wave form to eliminate high-frequency components; identify the pixel with the local minimum gray value as the wave trough point; second, fit a quadratic surface to the local area of each wave trough point; combine the surface center and the feature vector to recover the wave trough; at least two recovered wave troughs are obtained; Step S5, main phase estimation: phase at main point In the range ([0, 2π), it is estimated by linear interpolation based on its horizontal distance to two wave troughs; then, the untwisted 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 unwrapped principal phase Estimate the required rotation angle θ from the measurement model; if the periodic ambiguity is preserved leaving multiple discrete solutions for θ, 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.

9. The 3-D Moire based ultra-precision out-of-plane rotation measurement method according to claim 8, characterized in that: The calibration process of the intrinsic parameters A and B is as follows: To calibrate the internal parameters A and B, the RMoM is fixed on a motorized rotation stage with an accuracy of (0.001°); when the relative pose between the RMoM and the rotation stage is unknown, it is not easy to obtain the true θ, but it is easy to obtain the angular increment, starting from an unknown rotation angle θ0, then rotating the rotation stage step by step by Δθ; for the RMoM at the n-th angle θ n = θ0+ nΔθ, the main phase of the disentanglement with periodic ambiguity is As with θ, we get k n = k0+ Δk n where k0is an unknown quantity and Δk n is a known quantity; Given N samples, we have: where C=A-2k0π; here there are only three unknowns, including θ0, C and B, which can be solved when N≥3; the energy function is: The optimal C and B are solved using MATLAB optimization toolbox, and the difference term 2k0π can be eliminated The inherent periodic ambiguities are absorbed, and all the periodic ambiguities are eliminated by E-PnP.

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