A motion platform positioning method based on image recognition

Abstract

A method for positioning a motion platform based on image recognition includes the following steps: setting an array of unit patterns on a process chip; photographing the process chip through an imaging system to obtain a first image; comparing the first image with a reference image to calculate a first deflection angle, and driving the motion platform to rotate the first deflection angle; photographing the process chip through an imaging system to obtain a second image; comparing the second image with the reference image to calculate a first offset, and driving the motion platform to translate the first offset. Since a smaller unit pattern is set on the process chip, a photograph is taken through an imaging system with a magnification, and then the photographed unit pattern is compared with the reference image to calculate the angular deviation and translational deviation of the process chip, and finally the motion platform and the process chip are driven to rotate and translate together to reach a specified position to complete visual positioning. This process chip has high recognition accuracy and higher positioning accuracy through visual imaging comparison with magnification.

Description

Technical Field

[0001] The present invention relates to the technical field of automated precision machining, and in particular to a motion platform positioning method based on image recognition. Background Art

[0002] In the field of automated precision machining technology, the main positioning methods for workpiece positioning include mechanical limit positioning and electronic positioning. Mechanical limit positioning sets a mechanical mechanism at a specified position to block the movement of the motion platform to achieve the purpose of positioning, and electronic positioning positions the motion platform through sensor devices such as photoelectric switches and pressure sensors.

[0003] However, mechanical limit positioning is prone to deformation of the mechanical structure during the positioning process, which affects the positioning accuracy. The positioning method of the motion platform solely relying on electronic devices is also subject to the limitations of the sensor's response speed and accuracy, making it difficult to achieve high positioning accuracy. Summary of the invention

[0004] The main technical problem solved by the present invention is to improve the positioning accuracy of the workpiece.

[0005] In one embodiment, a motion platform positioning method based on image recognition is provided, comprising the following steps:

[0006] An array of unit patterns is arranged on the process chip, and only one complete unit pattern can be presented in a field of view of an imaging system with a magnification;

[0007] The process chip is fixed on the motion platform, and then the process chip is photographed by the imaging system to obtain a first image; the first image is compared with the reference image to calculate a first deflection angle, and the motion platform is driven to rotate the first deflection angle, and the reference image is the enlarged unit pattern;

[0008] The process chip is photographed by an imaging system to obtain a second image; the second image is compared with the reference image to calculate a first offset, and the motion platform is driven to translate the first offset to complete positioning.

[0009] Furthermore, the unit pattern is a square image, and the unit pattern includes nine sub-patterns, and the nine sub-patterns are arranged in a nine-square grid. The four sub-patterns located at the four corners of the unit pattern are non-rectangular and different patterns from each other, and the other five patterns are the same rectangular patterns.

[0010] Furthermore, the four non-rectangular sub-patterns are respectively a circle, a regular triangle, a rhombus and a regular hexagon.

[0011] Furthermore, during the calculation process of comparing the first image with the reference image, a complete first sub-pattern is extracted from the first image, and a first reference sub-pattern corresponding to the first sub-pattern is extracted from the reference image. The center of the first sub-pattern is then placed to coincide with the center of the first reference sub-pattern, and the first sub-pattern is rotated along the center and compared with the first reference sub-pattern to obtain the first deflection angle.

[0012] Furthermore, during the rotation comparison process, a window is opened for one side of the first reference sub-pattern to identify the deflection angle when the window has the most pixels of the first sub-pattern during the rotation of the first sub-pattern, and the deflection angle is calculated as the first deflection angle.

[0013] Furthermore, the window is a long rectangular frame covering the first reference sub-pattern.

[0014] Furthermore, in the process of comparing the second image with the reference image, a complete second sub-pattern is extracted from the second image, and a second reference sub-pattern corresponding to the second sub-pattern is extracted from the reference image, and the first offset is calculated according to the following formula:

[0015]

[0016] In the above formula, (Δx, Δy) is the first offset, (x0, y0) is the center coordinate of the second reference sub-pattern, (x, y) is the center coordinate of the second sub-pattern, and ρ is the magnification of the imaging system.

[0017] Furthermore, in the process of comparing and calculating the second image with the reference image, if there is only one complete non-rectangular sub-pattern in the second image, the complete non-rectangular sub-pattern is set as the second sub-pattern; if there are multiple complete non-rectangular sub-images in the second image, the distance between the center of each complete non-rectangular sub-image and the center of the corresponding reference sub-pattern is calculated, and the sub-image with the shortest distance to the center of the corresponding reference sub-pattern is set as the second sub-pattern.

[0018] Furthermore, in the process of comparing the first image and the second image with the reference image respectively, the contour information of all reference sub-patterns in the reference image is first extracted, and then the contour information of the complete sub-pattern in the first image or the second image is extracted. By comparing the contour information of the sub-pattern with the contour information of the reference sub-pattern, the reference sub-pattern corresponding to the sub-pattern in the first image or the second image is obtained, and the center position of the sub-pattern in the first image or the second image and the center position of the reference sub-pattern are calculated through the contour information.

[0019] Furthermore, after the motion platform translates the first offset, a compensation positioning step is also included, and the compensation positioning step includes:

[0020] photographing the process chip through an imaging system to obtain a third image;

[0021] Extract all complete third sub-patterns from the third image, extract third reference sub-patterns corresponding to all complete third sub-patterns from the reference image, extract coordinates of centers of the complete third sub-patterns and coordinates of centers of the third reference sub-patterns, and then calculate the second deflection angle and the second offset according to the following formula;

[0022]

[0023]

[0024] In the above two equations, (x′ i , y′ i ) is the center coordinate of the ith complete third sub-pattern in the third image, (x i ,y i ) is the center coordinate of the third reference sub-pattern corresponding to the i-th reference image. x , T y ] is the translation offset of the third image relative to the reference image, θ is the rotation angle between the third image and the reference image, ρ is the magnification of the imaging system, θ is the second deflection angle, and (Δx, Δy) is the second offset;

[0025] The motion platform is driven to translate a second offset and rotate a second deflection angle.

[0026] According to the motion platform positioning method based on image recognition in the above embodiment, since a small-sized unit pattern is set on the process chip, a photo is taken by an imaging system with a magnification, and then the photographed unit pattern is compared with the reference image to calculate the angle deviation and translation deviation of the process chip, and finally the motion platform and the process chip are driven to rotate and translate together to reach the specified position to complete the visual positioning. The process chip has high recognition accuracy and higher positioning accuracy through visual imaging comparison with magnification. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 A flowchart of the steps of a method for positioning a motion platform in an embodiment;

[0028] Figure 2 is a schematic diagram of a unit pattern in an embodiment;

[0029] Figure 3 is a schematic diagram of a unit pattern array in an embodiment;

[0030] Figure 4 is a schematic diagram of a unit pattern being magnified into a reference image in an embodiment;

[0031] Figure 5 is a schematic diagram of a reference image profile in an embodiment;

[0032] Figure 6 is a schematic diagram of placing a first reference sub-pattern in a reference image in an embodiment in an image processing window W1;

[0033] Figure 7 is a schematic diagram of placing a first sub-pattern in a first image in an embodiment in an image processing window W2;

[0034] Figure 8 is a schematic diagram of comparing a reference image with a second image in an embodiment;

[0035] Fig. 9 is a schematic diagram of comparing a reference image with a second image in an embodiment;

[0036] Fig.10 The figure is a flow chart of the actual operation of the method for positioning a moving platform in one embodiment. DETAILED DESCRIPTION

[0037] The present invention is further described in detail below by specific embodiments in conjunction with the accompanying drawings. Wherein similar elements in different embodiments adopt associated similar element numbers. In the following embodiments, many detailed descriptions are for making the present application better understood. However, those skilled in the art can easily recognize that some features can be omitted in different situations, or can be replaced by other elements, materials, methods. In some cases, some operations related to the present application are not shown or described in the specification, this is to avoid the core part of the present application being overwhelmed by too much description, and for those skilled in the art, it is not necessary to describe these related operations in detail, and they can fully understand the related operations according to the description in the specification and the general technical knowledge in the art.

[0038] In addition, the features, operations or characteristics described in the specification can be combined in any appropriate manner to form various implementations. At the same time, the steps or actions in the method description can also be interchanged or adjusted in a manner that is obvious to those skilled in the art. Therefore, the various sequences in the specification and the drawings are only for the purpose of clearly describing a certain embodiment and are not meant to be a required sequence, unless otherwise specified that a certain sequence must be followed.

[0039] The serial numbers of the components in this document, such as "first", "second", etc., are only used to distinguish the objects described and do not have any order or technical meaning. The "connection" and "coupling" mentioned in this application, unless otherwise specified, include direct and indirect connections (couplings).

[0040] The present application provides a method for positioning a motion platform based on image recognition. By means of image recognition, the collected process chip image is compared with a reference image to obtain the rotational deviation and translational deviation of the current position of the motion platform, and finally provide them to the motion platform as a basis for correcting the position.

[0041] The positioning method in this application uses a process chip that carries specific image information, and uses an image recognition method to calibrate a precise motion platform that includes a translation axis and a rotation axis to achieve the positioning of the process chip. The main basis for measuring and calculating the positioning accuracy of the motion platform in this positioning method is the image formed by the special process chip, and its accuracy can reach the pixel level. The specific conversion to the accuracy index of the motion platform needs to be combined with the magnification of the imaging system, the resolution of the imaging camera, and the manufacturing quality of the process chip.

[0042] like Figure 1 As shown, the motion platform positioning method based on image recognition of the present application mainly includes the following steps:

[0043] S01: Preparation process chip;

[0044] First, divide the front side of the process chip evenly into multiple blocks of equal area. Each block is a square of a×a, and its unit is μm. 2 , where a = b / ρ, b is the number of pixels of the side length of the square imaging field of view of the imaging system with magnification, that is, the image captured by the imaging system is an image of b×b pixels, and ρ is the magnification of the imaging system, in pixels / um.

[0045] The image recognition process of this method requires the use of image specified position windowing technology and contour moment information collection and processing technology of different types of patterns. Image specified position windowing technology is used to calculate the rotation angle of the image, and contour moment collection and processing is used to distinguish different patterns, to determine whether the current pattern is a reference pattern, and to calculate the image translation.

[0046] Contour moments, or Hu moments, are a set of features composed of seven invariant moments, which are invariant to rotation, scaling, and translation. The advantage of using contour moments to identify images is that the speed is very fast, but the disadvantage is that the recognition rate is relatively low. Therefore, it is necessary to identify larger objects in the image, especially to better recognize the shape of the image. Therefore, 5 different patterns are designed in the process chip to calculate the offset of the image.

[0047] like Figure 2As shown, specifically, a complete unit pattern can be presented in one field of view of the imaging system, and the unit pattern is a square of a×a, each unit pattern includes 9 sub-patterns, and the 9 sub-patterns are arranged in the form of a nine-square grid in the square, and the four sub-patterns at the four corners are non-rectangular and different sub-patterns, for example, the four patterns at the four corners are circles, regular triangles, rhombuses, and regular hexagons, respectively, and the four patterns at the four corners can also be regular triangles, rhombuses, regular pentagons, and regular hexagons, respectively. The five sub-patterns of the unit pattern other than the four corners are the same rectangle, so that each unit pattern includes five different patterns, and the rotation angle and offset can be calculated by identifying five different patterns.

[0048] like Figure 3 As shown, in order to ensure accuracy, the mutual spacing between the unit patterns is the same, and the directions between the unit patterns are consistent, that is, the unit patterns on the process chip are arranged in a four-square continuous array.

[0049] like Figure 4 As shown, after a unit pattern is set on the process chip, the unit pattern is enlarged and converted into the pixel size and pattern distribution of a specific image according to the unit pattern and the formula a=b / ρ, and the obtained image is a reference image under an ideal state. Figure 5 As shown, the contour data of the 9 reference sub-patterns in the reference image are collected respectively in advance, and the center coordinates of the 9 reference sub-patterns and the contour moments of the 9 reference sub-patterns are calculated using the contour data.

[0050] S02: Calculate the deflection angle and deflection;

[0051] The process chip prepared with the unit pattern is mounted on a motion platform, which has the functions of rotation and translation.

[0052] The process chip is photographed by an imaging system to obtain a first image, and a first sub-pattern B with a complete image outline is extracted from the photographed first image, and the outline moment of the first sub-pattern B is calculated. The first sub-pattern B is compared with the five reference sub-patterns in the reference image, and the first reference sub-pattern A in the reference image corresponding to the first sub-pattern B is identified. In order to improve the comparison efficiency and accuracy, non-rectangular and non-circular and complete sub-patterns are selected as the first sub-pattern B in the first image. If only the circular pattern and part of the rectangular pattern are complete patterns in the first image, the rectangular pattern located in the middle is selected as the first sub-pattern B.

[0053] like Figure 6As shown, the first reference sub-pattern A is placed in an image processing window W1, and the center of the first reference sub-pattern A coincides with the center of the image processing window W1. A window S1 is then opened on one side of the first reference sub-pattern A. The window S1 is a long rectangle, the long side of which is parallel to the side of the first reference sub-pattern A, and the rectangle is as long as possible so that the rectangle covers the side of the first reference sub-pattern A as much as possible. However, the short side of the window S1 is as short as possible so that the window S1 can cover most of the pixels on one side of the first reference sub-pattern A and does not cover the pixels on other sides.

[0054] The extracted first sub-pattern B is placed in an image processing window W2 having the same size as the window W1, and the center of the first sub-pattern B coincides with the center of the image processing window W2.

[0055] like Figure 7 As shown, a window S2 is opened in window W2 with the same position, size and shape as the window S1 in window W1. With the center of window W2 as the rotation center and the current position as the initial position, within the range of 45° in the clockwise and counterclockwise directions, with the minimum rotation deviation α required to be achieved when calibrating the motion platform as the step length, the first sub-pattern B is rotated 90° / α times in total. The number of pixels falling in window S2 is calculated and recorded accordingly for each rotation. Finally, it is compared to determine which of the 90° / α rotations has the largest number of contour pixels falling in window S2. At this time, the corresponding rotation angle θ of the first sub-pattern B is the first deflection angle of the motion platform.

[0056] The motion platform rotates at a first deflection angle, and the process chip and the motion platform rotate at the first deflection angle together, so that the process chip is positioned in an angle direction.

[0057] S03: Calculate the offset and displacement;

[0058] After the motion platform rotates the first deflection angle, the imaging system is used to photograph the process chip to obtain a second image. The second image is identified, the contour information of the complete sub-pattern is collected, and the contour of the complete sub-pattern is compared with the contour moments of the five reference sub-patterns in the reference image to identify several complete non-rectangular pattern contours in the second image.

[0059] like Figure 8 As shown, if there is only one complete non-rectangular sub-pattern in the second image, the complete non-rectangular sub-pattern is extracted as the second sub-pattern P1;

[0060] If there are multiple complete non-rectangular sub-patterns in the second image, the contour moments of several non-rectangular sub-patterns are first identified respectively, and compared one by one with the contour moments of the 5 reference sub-patterns in the reference image, to find the reference sub-patterns that correspond to the multiple non-rectangular sub-patterns one by one, and calculate the distances between the centers of the multiple non-rectangular sub-patterns and the corresponding reference sub-patterns respectively, compare and obtain the distance data, and select the non-rectangular sub-pattern with the shortest distance as the second sub-pattern P1.

[0061] like Fig. 9 As shown, there are two complete non-rectangular sub-patterns P1 and N1 in the second image, and two reference sub-patterns P0 and N0 corresponding to the non-rectangular sub-patterns P1 and N1 are found in the reference image. It can be calculated that the distance between the center of P1 and the center of P0 is smaller than the distance between the center of N1 and the center of N0, so that the non-rectangular sub-pattern P1 is used as the second sub-pattern P1.

[0062] After extracting the second sub-pattern P1 from the second image, find the second reference sub-pattern P0 corresponding to the second sub-pattern P1 in the reference image, collect the center coordinates (x, y) of the second sub-pattern P1, and collect the center coordinates (x0, y0) of the second reference sub-pattern P0. Calculate the first offset (Δx, Δy) between the second sub-pattern P1 and the second reference sub-pattern P0 using the following formula.

[0063]

[0064] Where ρ is the magnification of the imaging system.

[0065] The first offset between the second sub-pattern P1 and the second reference sub-pattern P0 is the first offset required by the motion platform.

[0066] The motion platform translates a first offset, and the process chip and the motion platform translate the first offset together, so that the process chip is positioned in the plane displacement direction.

[0067] In this embodiment, the positioning adjustment of the rotation deviation and translation deviation of the motion platform is a coarse adjustment. Since the amount of data collected and used for calculation is small, one positioning adjustment cannot achieve the desired accuracy, so the motion platform needs to be fine-tuned. The positioning method of this embodiment performs compensation positioning after deflection and offset positioning. The compensation positioning steps are as follows:

[0068] S04: compensation positioning;

[0069] The process chip is photographed by an imaging system to obtain a third image P3. At this time, the third image is substantially the same as the reference image because it has undergone one positioning adjustment.

[0070] Extract all complete sub-patterns from the third image, and find the reference sub-patterns that correspond to all the complete sub-patterns from the reference image. Then extract the coordinates of the centers of all the complete sub-patterns, and then extract the coordinates of the centers of the reference sub-patterns that correspond to the complete sub-patterns. Calculate the second deflection angle and the second offset of the third image and the reference image based on the two sets of center coordinate data. The specific calculation is as follows:

[0071] If there are n complete third sub-patterns in the third image, let (x′ i , y′ i ) is the center coordinate of the ith complete third sub-pattern in the third image, (x i ,y i ) is the center coordinate of the third reference sub-pattern corresponding to the i-th reference image. x , T y ] is the translation offset of the third image relative to the reference image, and θ is the second deflection angle between the third image and the reference image. According to the coordinate transformation relationship, the following formula is obtained:

[0072]

[0073] The second deflection angle θ of the motion platform is calculated by the above formula. The second offset [Δx, Δy] of the motion platform is as follows, where ρ is the magnification of the imaging system.

[0074]

[0075] According to the finally obtained θ, Δx, Δy, the rotational deviation and translational deviation of the motion platform are compensated, and finally the process chip and the motion platform are rotated and translated together to complete the positioning.

[0076] In the motion platform positioning method based on image recognition of this embodiment, a small-sized unit pattern is set on the process chip, and a photo is taken by an imaging system with a magnification, and then the photographed unit pattern is compared with the reference image to calculate the angle deviation and translation deviation of the process chip, and finally the motion platform and the process chip are driven to rotate and translate together to reach the specified position to complete the visual positioning. The process chip has high recognition accuracy through visual imaging comparison with magnification, and has higher positioning accuracy.

[0077] This embodiment also provides a practical operation example of a positioning method, which is as follows:

[0078] (1) Operating environment:

[0079] There should be a carrier platform on the motion platform for placing process chips. The carrier platform is required to be firmly installed on the motion platform and ensure that there is no relative movement between the carrier platform and the contact surface between the carrier platform and the motion platform.

[0080] The carrier platform should be equipped with a permanent or temporarily detachable reliable positioning structure to ensure the placement accuracy of the process chip each time it is loaded onto the carrier platform, and that the process chip will not move relative to the carrier platform during the movement of the motion platform.

[0081] (2) Fig.10 As shown, the operation steps are:

[0082] S101: placing the process chip on the loading platform of the motion platform and fixing it.

[0083] S102: Move the motion platform to a calibration point and take a photo to obtain a first image S1.

[0084] S103: Compare and process the first image S1 with the reference image S0 to calculate a first deflection angle θ of the motion platform.

[0085] S104: adjusting the rotation axis of the motion platform according to the calculated first deflection angle θ.

[0086] S105: Imaging the process chip on the calibrated motion platform to obtain a second image S2.

[0087] S106: Compare and process the second image S2 with the reference image S0, and calculate the offsets (Δx, Δy) of the motion platform on the X-axis and Y-axis.

[0088] S107: Coarsely adjust the offset of the motion platform according to the offset (Δx, Δy) and the magnification ρ of the imaging system.

[0089] S108: photographing the process chip on the coarsely adjusted motion platform to obtain a third image S3.

[0090] S109: Compare and process the third image S3 with the reference image S0 to obtain more accurate rotation deviation θ· and translation deviations Δx' and Δy' of the motion platform.

[0091] S110: fine-tune the motion platform according to the obtained fine-tuning amounts θ·, Δx' and Δy' to complete the overall calibration of the motion platform.

[0092] Through the above steps, the motion platform is roughly and finely adjusted by visual imaging, which can locate the high-precision process chip to the specified position and improve the accuracy of chip production.

[0093] The above specific examples are used to illustrate the present invention, which is only used to help understand the present invention and is not intended to limit the present invention. For those skilled in the art, according to the concept of the present invention, some simple deductions, modifications or substitutions can be made.

Claims

1. A motion platform positioning method based on image recognition, characterized in that: The steps include: A plurality of unit patterns arranged in an array are arranged on the process chip. Only one complete unit pattern can be presented in a field of view of an imaging system with a magnification. The unit pattern is a square image, and the area unit of the unit pattern is um. 2 , the unit pattern includes nine sub-patterns, the nine sub-patterns are arranged in a nine-square grid, the four sub-patterns located at the four corners of the unit pattern are non-rectangular and different patterns, and the other five patterns are the same rectangular pattern; Fixing the process chip on a moving platform, and then photographing the process chip through an imaging system to obtain a first image; Compare the first image with a reference image to calculate a first deflection angle, and drive the motion platform to rotate the first deflection angle, wherein the reference image is an enlarged unit pattern; The process chip is photographed by an imaging system to obtain a second image; the second image is compared with the reference image to calculate a first offset, and the motion platform is driven to translate the first offset to complete positioning.

2. The motion platform positioning method based on image recognition according to claim 1, characterized in that: The four non-rectangular sub-patterns are circle, regular triangle, rhombus and regular hexagon.

3. The motion platform positioning method based on image recognition according to claim 1, characterized in that: During the calculation process of comparing the first image with the reference image, a complete first sub-pattern is extracted from the first image, and a first reference sub-pattern corresponding to the first sub-pattern is extracted from the reference image. Then, the center of the first sub-pattern is placed to coincide with the center of the first reference sub-pattern, and the first sub-pattern is rotated along the center and compared with the first reference sub-pattern to obtain the first deflection angle.

4. The motion platform positioning method based on image recognition as claimed in claim 3, characterized in that: During the rotation comparison process, a window is opened for recognition of one side of the first reference sub-pattern, and then the deflection angle of the first sub-pattern when the window has the most pixels of the first sub-pattern during the rotation process is calculated as the first deflection angle.

5. The motion platform positioning method based on image recognition as claimed in claim 4, characterized in that: The window is a long rectangular frame covering the first reference sub-pattern.

6. The method for positioning a motion platform based on image recognition according to claim 4, characterized in that: In the process of comparing and calculating the second image with the reference image, a complete second sub-pattern is extracted from the second image, and a second reference sub-pattern corresponding to the second sub-pattern is extracted from the reference image, and the first offset is calculated according to the following formula: In the above formula, (Δx, Δy) is the first offset, (x0, y0) is the center coordinate of the second reference sub-pattern, (x, y) is the center coordinate of the second sub-pattern, and ρ is the magnification of the imaging system.

7. The motion platform positioning method based on image recognition according to claim 6, characterized in that: During the comparison and calculation process between the second image and the reference image, if there is only one complete non-rectangular sub-pattern in the second image, the complete non-rectangular sub-pattern is set as the second sub-pattern; if there are multiple complete non-rectangular sub-images in the second image, the distance between the center of each complete non-rectangular sub-image and the center of the corresponding reference sub-pattern is calculated, and the sub-image with the shortest distance to the center of the corresponding reference sub-pattern is set as the second sub-pattern.

8. The method for positioning a motion platform based on image recognition according to claim 6, characterized in that: In the process of comparing the first image and the second image with the reference image respectively, the contour information of all reference sub-patterns in the reference image is first extracted, and then the contour information of the complete sub-pattern in the first image or the second image is extracted. The reference sub-pattern corresponding to the sub-pattern in the first image or the second image is obtained by comparing the contour information of the sub-pattern with the contour information of the reference sub-pattern, and the center position of the sub-pattern in the first image or the second image and the center position of the reference sub-pattern are calculated through the contour information.

9. The motion platform positioning method based on image recognition according to any one of claims 1 to 8, characterized in that: After the motion platform translates the first offset, a compensation positioning step is further included, and the compensation positioning step includes: photographing the process chip through an imaging system to obtain a third image; Extract all complete third sub-patterns from the third image, extract third reference sub-patterns corresponding to all complete third sub-patterns from the reference image, extract coordinates of centers of all complete third sub-patterns and coordinates of centers of third reference sub-patterns, and then calculate the second deflection angle and the second offset according to the following formula; In the above two formulas, is the center coordinate of the ith complete third sub-pattern in the third image, is the center coordinate of the third reference sub-pattern corresponding to the i-th reference image, [ ] is the translation offset of the third image relative to the reference image, is the rotation angle between the third image and the reference image, is the magnification of the imaging system, is the second deflection angle, ( ) is the second offset; The motion platform is driven to translate the second offset and rotate the second deflection angle to complete compensation positioning.

Images