Cylindrical grating scribed line error detection method and system

Abstract

The invention belongs to the technical field of photoelectric displacement precision measurement, and particularly provides a cylindrical grating scribed line error detection method and system. The method comprises the following steps: firstly, calibrating a cylindrical grating positioning error through two angles, then collecting gray scale data of the cylindrical grating at different measurement angles according to a point light source and a linear array image sensor to calculate a non-coaxial error, and finally removing the non-coaxial error from the positioning error to realize the detection of the scribing error. According to the invention, interference of non-coaxial errors in a scribed line error detection process can be effectively suppressed, the inherent precision of cylindrical grating displacement measurement is effectively improved, and the method is suitable for industrial, aerospace and other scenes with high precision requirements.

Description

Technical Field

[0001] This invention belongs to the field of photoelectric displacement precision measurement technology, specifically providing a method and system for detecting errors in cylindrical grating engraving lines. Background Technology

[0002] Grating angular displacement measurement technology uses a high-precision circular grating to convert angular position information into corresponding binary code, achieving high-precision angular displacement measurement. This technology exhibits excellent measurement performance due to its advantages such as high measurement accuracy, wide measurement range, small size, and ease of maintenance. Grating angular displacement measurement has been widely applied in various fields such as photoelectric theodolites, robotic arms, CNC machine tools, and coordinate vector machines, playing a crucial role in industrial automation.

[0003] Existing grating displacement measurement technology is based on the "moiré fringe" method: moiré fringe signals are generated by the cooperation of an indicator grating and a calibration grating, which are then converted into electrical signals by a photoelectric conversion element, input to a microprocessor by a digital-to-analog converter, and finally obtained through "phase detection operation" to obtain the angular displacement information of the current position. However, this technology has certain limitations: (1) when using the "moiré fringe" measurement method alone, absolute position information cannot be obtained; (2) when using multiple code channels to achieve absolute position measurement, the time phase sequence of multiple signals must be aligned; (3) to further improve the measurement performance, the grating line density needs to be increased; (4) grating angular displacement measurement is extremely sensitive to code disk stains, which will reduce the measurement accuracy and even lead to code errors.

[0004] In contrast, cylindrical gratings are made by engraving absolute single-track codes on the cylindrical surface of the grating, so that each corner position corresponds to a unique optically encoded image. This eliminates the need for complex multi-track coordination, which simplifies installation requirements and indirectly enhances the fault tolerance and robustness of the system, making it a research hotspot in optoelectronic precision measurement. This technology has shown significant advantages in solving the above problems: (1) It is easy to achieve miniaturization design, which can greatly reduce the volume of the measurement system and is suitable for space-constrained application scenarios; (2) Due to its larger cross-sectional thickness, it can effectively suppress the tilt error of the grating in the longitudinal direction and improve measurement stability; (3) Its unique central hole structure is especially suitable for large hollow shaft equipment. However, the preparation of cylindrical gratings requires the use of a high-repetition-frequency laser scribing instrument to scribing the encoded grating lines on the cylindrical grating body with high precision. The slight offset of the laser scribing grating line position will cause scribing error, which will significantly reduce the inherent positioning accuracy of angular displacement. Summary of the Invention

[0005] In view of this, the present invention aims to provide a method and system for detecting scribing errors in cylindrical gratings; a spherical wave exposure device composed of a point light source and a linear array image sensor is used to collect grayscale data of cylindrical gratings at different measurement angles, calculate and extract the amplitude and phase information of errors on different axes; and then remove errors on different axes from the positioning errors obtained by calibration to realize the detection of scribing errors.

[0006] To achieve the above objectives, the technical solution of the present invention is implemented as follows: A method for detecting errors in cylindrical grating scribing includes the following: Step 1, Cylindrical Grating Positioning Error Calibration: ,in To measure the angle, specifically the rotation angle of the cylindrical grating is read through the reading head. The rotation angle of the cylindrical grating is output as an angular reference that is coaxially connected to it. Step two, calculation of the misalignment error of the cylindrical grating, specifically includes the following: S1: Calculate the shortest transmission distance of the spherical wave emitted from the point light source, reflected by the cylindrical grating, to the pixel with the highest grayscale value on the linear image sensor. The calculation steps are as follows: S11: Establish the spherical wave emitted by the point light source, which is reflected by the cylindrical grating to any pixel on the linear image sensor. spherical wave transmission distance The expression: ; in, = 0 represents the center pixel. This represents the distance between the center pixel and the pixel with the highest grayscale value on a linear image sensor. S12: Establish spherical wave transmission distance and the grayscale value of the corresponding pixel Expressions between: ; in This represents the exposure coefficient of the linear image sensor. This represents the pixel physical size constant of a linear image sensor; grayscale values Perform the following processing to obtain information about The quadratic function expression: ; in , where is the maximum grayscale value, and the constant term, first-order polynomial coefficients, and second-order polynomial coefficients of the quadratic function expression are respectively , and ; S13: Based on the grayscale values ​​of all pixels on the linear array image sensor, the least squares method is used to fit the data and obtain the coefficients. , and The value; Based on coefficient , and The value was calculated. ; S2: Calculation ,in This represents the distance between the point light source and the pixel with the highest grayscale value on the linear image sensor. This represents the shortest distance from the point light source to the outer cylindrical surface of the cylindrical grating. This represents the shortest distance from the pixel with the highest grayscale value on the linear image sensor to the outer cylindrical surface of the cylindrical grating. express and The amount of distance change that will occur in all of them; S3: Calculate at multiple measurement angles Below ,by Fitting to the baseline yields... The amplitude of the curve. For the phase of the curve, This represents the DC component of the curve. S4: Calculation radius is The cylindrical grating at the measurement angle is Different axis errors under different conditions : ; in For different axis offset distances, ; Step 3: Obtain the engraving error of the cylindrical grating by subtracting the positioning error from the errors of different axes. .

[0007] A cylindrical grating engraving error detection system includes: Cylindrical grating; Reading head: Used to read the rotation angle of the cylindrical grating, denoted as the measurement angle; Angle reference: Under the drive of the motor, the angle reference rotates synchronously with the cylindrical grating and outputs its own rotation angle; Positioning error calibration module: used to calculate the difference between the measured angle and the rotation angle to obtain the positioning error; Spherical wave exposure detection equipment: includes a point light source and a linear array image sensor. The spherical wave emitted by the point light source illuminates the cylindrical grating. After being reflected by the cylindrical grating, it is received by the linear array image sensor, which generates pixel grayscale data. Different axis error calculation module: Calculates different axis errors based on the spherical wave characteristics of the point light source and the grayscale values ​​of the pixels on the linear array image sensor; Grating error detection module: It detects grading errors by eliminating errors of different axes from the positioning errors.

[0008] Preferably, the angle reference is an absolute encoder or an incremental encoder, and the angle reference is coaxially connected to the cylindrical grating and rotates synchronously.

[0009] Preferably, the cylindrical grating is an absolute single-track grating.

[0010] Preferably, the pixel arrangement of the linear image sensor is 1×N.

[0011] Compared with the prior art, the present invention can achieve the following beneficial effects: This invention, based on existing cylindrical grating angular displacement measurement technology, designs a module for calculating errors along different axes and a module for detecting engraving errors. It detects the shortest transmission distance of a point-source spherical wave reflected from a cylindrical grating to a linear image sensor in a spherical wave exposure device from multiple angles. Then, based on spatial geometry, the shortest transmission distance is converted into a vertical distance change, which is used to accurately calculate the amplitude and phase information of errors along different axes. Subsequently, the difference between the positioning error and the errors along different axes is used to separate and detect engraving errors. This effectively suppresses interference from errors along different axes during engraving error detection, significantly improving the inherent accuracy of cylindrical grating displacement measurement. It is suitable for high-precision applications such as industrial and aerospace applications. Attached Figure Description

[0012] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1 This is a schematic diagram of the cylindrical grating engraving error detection system according to an embodiment of the present invention; Figure 2 This is a schematic diagram of spherical wave transmission in the spherical wave exposure detection device described in an embodiment of the present invention; Figure 3 This is a schematic diagram illustrating the change in vertical distance caused by different axes, as described in an embodiment of the present invention. Figure 4 This is a schematic diagram illustrating the geometric relationship between the vertical distance variation and the shortest transmission distance of spherical waves as described in an embodiment of the present invention. Figure 5 This is a schematic diagram illustrating the principle of different axis error generation as described in an embodiment of the present invention.

[0013] The reference numerals in the figures include: 1. Reading head; 2. Cylindrical grating; 3. Spherical wave exposure detection equipment; 31. Point light source; 32. Linear array image sensor; 4. Angle reference; 5. Motor; 6. Spindle; 7. Positioning error calibration module; 8. Different axis error calculation module; 9. Grating error detection module. Detailed Implementation

[0014] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not constitute a limitation thereof.

[0015] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0016] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicating orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on this invention. Furthermore, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, features defined with "first," "second," etc., may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0017] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0018] The invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0019] Example 1 In one embodiment of the present invention, a method for detecting errors in cylindrical grating scribing includes the following: Step 1: Calibrate the positioning error of cylindrical grating 2; Reading head 1 can acquire the rotation angle of the detection position on cylindrical grating 2, denoted as the measurement angle. The angle of synchronous rotation of the angle reference 4, which is coaxially connected to the cylindrical grating 2, is denoted as . Then the positioning error of cylindrical grating 2 for: ; Step 2, Calculation of different axis errors of cylindrical grating 2 (this part is the calculation method of different axis errors based on the spherical light exposure amplitude inversion method). The spherical wave emitted by the point light source 31 illuminates the cylindrical grating 2, and is then reflected by the cylindrical grating 2 to the linear image sensor 32. The cross-axis error is calculated based on the pixel grayscale data on the linear image sensor 32. Specifically, it includes the following: S1: Based on the pixel grayscale data on the linear image sensor 32, calculate the shortest transmission distance of the spherical wave emitted by the point light source 31 that illuminates the cylindrical grating 2 and is then reflected by the cylindrical grating 2 to the pixel with the largest grayscale value on the linear image sensor 32. (According to the definition of pixel grayscale value, when the grayscale value is the maximum, the light emitted by the point light source 31, reflected by a point on the cylindrical grating 2, travels the shortest distance to the pixel with the maximum grayscale value.) The calculation steps are as follows: S11: For any pixel on the linear image sensor 32 The spherical wave emitted by the point light source 31 is reflected by the cylindrical grating 2 to any pixel on the linear image sensor 32. spherical wave transmission distance The expression: ; The linear image sensor 32 has 1×N pixels. With the center pixel as the reading reference (origin) and the pixel arrangement direction as the X-axis, the position of any pixel on the linear image sensor 32 can be uniquely determined by one-dimensional coordinates. In the formula... These are the coordinates of any pixel; that is, the coordinates of a pixel represent the corresponding pixel. =0 represents the center pixel. This represents the distance on the X-axis between the center pixel and the pixel with the highest grayscale value on the linear image sensor 32, i.e., the distance between these two pixels; the pixel includes all pixels to the left and right of the center pixel.

[0020] S12: Establish spherical wave transmission distance and its corresponding pixel grayscale value Expressions between: ; in This represents the sum of the shortest distance from the point light source 31 (approximately a point) to the outer cylindrical surface of the cylindrical grating 2 and the shortest distance from the pixel with the highest grayscale value on the linear image sensor 32 to the outer cylindrical surface of the cylindrical grating 2. This represents the exposure coefficient of the linear image sensor 32 (the exposure coefficient is the product of the exposure time and the system reference gain, and is determined by the performance of the linear image sensor 32 itself). This represents the pixel physical size constant of the linear image sensor 32; grayscale value of a pixel Perform the following processing to obtain information about any pixel. The quadratic function expression: ; in , representing the maximum grayscale value, and the constant term, first-order polynomial coefficients, and second-order polynomial coefficients of the quadratic function expression are respectively... , and ; S13: The grayscale values ​​of all pixels are read using the linear image sensor 32. Combining the grayscale value expression and normalization process from S12, the least squares method is used to fit the quadratic function expression obtained in step S12 to obtain the coefficients. , and The value (due to) and All of these can be read out by the linear image sensor 32. Therefore, the quadratic function expression can be fitted using the least squares method based on the pixel grayscale values ​​actually read out by the linear image sensor 32. Based on coefficient , and The numerical values ​​were used to calculate the shortest transmission distance for the spherical wave emitted by the point light source 31 to reach the pixel with the highest grayscale value on the linear image sensor 32 after reflection by the cylindrical grating 2. ; S2: Calculation ,in , This represents the distance between the point light source 31 and the pixel with the largest grayscale value on the linear image sensor 32, i.e., the vertical distance between the point light source 31 and the linear image sensor 32. This represents the shortest distance from point light source 31 to the outer cylindrical surface of cylindrical grating 2, i.e., the constant perpendicular distance between point light source 31 and cylindrical grating 2. This represents the shortest distance from the pixel with the highest grayscale value on the linear image sensor 32 to the outer cylindrical surface of the cylindrical grating 2, i.e., the constant perpendicular distance between the linear image sensor 32 and the cylindrical grating 2. This indicates that the rotation of the cylindrical grating 2 and the angle reference 4 is affected by their different axes (meaning that the theoretical axes of rotation of the cylindrical grating 2 and the angle reference 4 are different). and Both will produce changes in distance; that is to say, the axes of rotation of the cylindrical grating 2 and the angular reference 4 are different when they rotate, therefore and This will produce the same amount of distance change; S3: Calculate at multiple measurement angles The corresponding Among them, the measuring angle is Calculated in time Recorded as ,by Fitting to the baseline yields... The amplitude of the curve. The phase of the curve (i.e., phases on different axes). Let be the DC component of the curve, where , ; This represents the offset distance along different axes, specifically the distance between point O and point O1. The position aligned with the center of the field of view of the reading head 1 on the outer cylindrical surface of the cylindrical grating 2 on one side of the reading head 1 is defined as a theoretical reference point, denoted as point P. A cross section perpendicular to the rotation axis of the cylindrical grating 2 is made through point P. This cross section intersects with the cylindrical grating 2 to obtain a circular cross section. The center of this circular cross section is set as point O. An orthographic projection is made from the bottom of the angle reference 4 onto the circular cross section, and a circle is formed by the orthographic projection. The center of this circle is set as point O1. S4: Calculation radius is The cylindrical grating 2 is measured at an angle of The offset distance between different axes is and different axis phase Different axis errors under different conditions : ; Step 3, by correcting the positioning error With different axis errors By subtracting, the engraving error of cylindrical grating 2 can be obtained. . A cylindrical grating engraving error detection system, such as Figure 1 As shown, it includes: Reading head 1: Used to read the measurement angle of the detection position of cylindrical grating 2. Its angle positioning error includes different axis error and scale line error. Angle reference 4: Driven by motor 5, angle reference 4 rotates synchronously with cylindrical grating 2 and can output the rotation angle of its own axis. Positioning error calibration module 7: Used to calculate the difference between the measured angle and the rotation angle to obtain the positioning error; Spherical wave exposure detection device 3: includes a point light source 31 and a linear array image sensor 32, wherein the spherical wave emitted by the point light source 31 illuminates the cylindrical grating 2, and after being reflected by the cylindrical grating 2, it is received by the linear array image sensor 32, and the linear array image sensor 32 generates pixel grayscale data. Different axis error calculation module 8: Based on the spherical wave characteristics of the point light source 31 and the grayscale values ​​of the pixels on the linear image sensor 32, calculate the different axis error according to the method described in step two; Grating error detection module 9: It detects grading errors by eliminating errors of different axes from the positioning errors.

[0021] Preferably, the angle reference 4 is an absolute encoder or an incremental encoder, and the angle reference 4 is coaxially connected to the cylindrical grating 2 and rotates synchronously.

[0022] Preferably, the cylindrical grating 2 is an absolute single-track grating.

[0023] Preferably, the pixel arrangement of the linear image sensor 32 is 1×N.

[0024] Example 2 A cylindrical grating engraving error detection system includes a reading head 1, a cylindrical grating 2, a spherical wave exposure detection device 3, and an angle reference 4. The cylindrical grating 2 and the angle reference 4 are connected by a main shaft 6 and driven to rotate by a drive mechanism. The reading head 1 is positioned opposite the cylindrical grating 2 via a bracket and is used to read the rotation angle of the cylindrical grating 2. The angle reference 4 is an encoder in a high-precision servo motor of brand SEROTECH, model ADRS-200-MA-NS-AS.

[0025] The spherical wave exposure detection device 3 includes a point light source 31 and a linear image sensor 32. The point light source 31 emits a light beam towards the cylindrical grating 2. After being reflected by the cylindrical grating 2, the light beam enters the linear image sensor 32, which outputs the grayscale value data of each pixel. The spatial positions of the point light source 31 and the linear image sensor 32 are relatively fixed, and they are located on one side of the cylindrical grating 2.

[0026] The cylindrical grating 2 is an absolute single-track grating.

[0027] The reading head 1 is specifically a Renishaw RESOLUTE absolute circular grating BiSS communication reading head RA26BBA075B50A, which is set opposite to the cylindrical grating 2 and is used to read the rotation angle of a specific detection position on the cylindrical grating 2.

[0028] The light emitted by the point light source 31 is a spherical wave.

[0029] The cylindrical grating 2 and the angle reference 4 are sequentially fitted onto the outer periphery of the main shaft 6 along the axial direction. The driving mechanism is a motor 5, which is a disc motor.

[0030] The main shaft 6 passes through the angle reference 4, i.e. the encoder shaft, and then enters the cylindrical grating 2. The disc motor drives the cylindrical grating 2 and the angle reference 4 to rotate synchronously through the main shaft 6.

[0031] The main shaft 6 is fitted inside the rotor disc of the disc motor. The linear image sensor has a 32-pixel arrangement of 1×N.

[0032] The point light source 31 and the linear array image sensor 32 are fixed to one side of the motor 5 by a bracket, and the reading head 1 is fixed to the other side of the motor 5 by a bracket.

[0033] Reading head 1 outputs the measured angle Angle reference 4 outputs rotation angle The positioning error calibration module 7 will measure the angle. With rotation angle Difference is calculated to achieve positioning error. The calibration is calculated using the following formula: ; The spherical wave exposure detection device 3 includes a point light source 31 and a linear image sensor 32. The spatial positions of the point light source 31 and the linear image sensor 32 are fixed and are located on one side of the cylindrical grating 2. The pixel arrangement on the linear image sensor 32 is 1×N. The light emitted by the point light source 31 is a spherical wave. The spherical wave emitted by the point light source 31 illuminates the cylindrical grating 2, and after reflection by the cylindrical grating 2, it is received by the linear image sensor 32. The grayscale data on the linear image sensor 32 can be used to calculate the error of different axes. The specific steps are as follows: S1: First, it is necessary to determine the shortest transmission distance of the spherical wave emitted from the point light source 31, which illuminates the cylindrical grating 2 and then reaches the pixel with the highest gray value on the linear image sensor 32 after reflection. Therefore, a method for calculating the error of different axes based on the spherical light exposure amplitude inversion method is proposed, the steps of which are as follows: S11: As Figure 2As shown, the center pixel on the linear image sensor 32 is marked as point m, and the pixel with the largest gray value on the linear image sensor 32 is marked as point v. An X-axis is established with point m as the origin, so that all pixels on the linear image sensor 32 are located on the X-axis. The direction in which point v moves along the X-axis to point m is the positive direction, and the opposite is the negative direction. Point v is located in the negative direction of the X-axis. This represents the distance between point v and point m. The spherical wave emitted by point light source 31 illuminates the cylindrical grating 2, and is then reflected by the cylindrical grating 2 to any pixel on the linear image sensor 32. This represents the spherical wave transmission distance. Represented as: ; S12: Let the sum of the shortest distance from the point light source 31 to the outer cylindrical surface of the cylindrical grating 2 and the shortest distance from the pixel with the largest grayscale value on the linear image sensor 32 to the outer cylindrical surface of the cylindrical grating 2 be... The spherical wave emitted by the point light source 31 illuminates the cylindrical grating 2, and is then reflected by the cylindrical grating 2 to any pixel on the linear image sensor 32. The spherical wave transmission distance is The angle between the spherical wave beam directed at any pixel on the linear image sensor 32 and the beam directed at the center pixel is... It can be represented as: ; Since the light intensity of point light source 31 varies with angle The cosine attenuation follows Lambert's cosine law, and the pixel's photosensitive area varies with angle. The intensity of the spherical wave emitted by point light source 31 decreases as the light transmission distance increases; the intensity of the spherical wave decreases inversely with the square of the light transmission distance; by analyzing the relationship between the spherical wave transmission distance and the pixel gray value change, the spherical wave transmission distance from point light source 31 to linear image sensor 32 is established. and the grayscale value of its corresponding pixel Relationship equations: ; in This represents the exposure coefficient of the linear image sensor 32. This represents the pixel physical size constant of the linear image sensor 32.

[0034] grayscale value of a pixel Maximum grayscale value Normalization based on the baseline can yield results for any pixel. The quadratic function expression: ; The constant term, first-order polynomial coefficients, and second-order polynomial coefficients of the quadratic function expression are respectively... , and ; S13: The grayscale values ​​of all pixels are read by the linear image sensor 32, and the coefficients are obtained by fitting the quadratic function expression using the least squares method. , and .

[0035] Here, in order to obtain the grayscale value of the pixel... Relative to any pixel To analyze the variation pattern, the 640 pixels on the linear image sensor 32 were divided into 16 groups of 40 pixels each. The pixel with the highest grayscale value in each group was selected as the fitting pixel. The grayscale values ​​corresponding to the 16 fitting pixels were used as the final data. The quadratic function expression was then fitted using the least squares method with the final data and the maximum grayscale value. , and .

[0036] Based on coefficient , and The value was calculated. .

[0037] S2: To determine the shortest transmission distance of the cylindrical grating 2 for spherical waves under different rotational degrees. The influence can be transformed into analyzing the changes in the vertical distance between the point light source 31 and the linear image sensor 32 and the cylindrical grating 2, respectively. like Figure 3 As shown, for ease of description and calculation, the position aligned with the center of the field of view of the reading head 1 on the outer cylindrical surface of the cylindrical grating 2 on one side of the reading head 1 is defined as a theoretical reference point, denoted as point P (this point P represents the theoretical position of the center of the field of view of the reading head 1 on the surface of the cylindrical grating 2). A cross section perpendicular to the rotation axis of the cylindrical grating 2 is made through point P. This cross section intersects with the cylindrical grating 2 to obtain a circular cross section. The center of this circular cross section is set as point O. An orthographic projection is made from the bottom of the angle reference 4 onto the circular cross section. A circle is formed by the orthographic projection, and the center of this circle is set as point O1. Theoretically, points O and O1 should completely coincide, but in reality, there is a deviation between them. The theoretical perpendicular distance constant from point light source 31 to cylindrical grating 2 is: (i.e., the shortest distance from point light source 31 to the outer cylindrical surface of cylindrical grating 2), the theoretical vertical distance constant from the pixel with the highest grayscale value on linear image sensor 32 to cylindrical grating 2 is... (That is, the shortest distance from the pixel with the highest grayscale value on the linear image sensor 32 to the outer cylindrical surface of the cylindrical grating 2); because the cylindrical grating 2 and the angle reference 4 have micron-level misalignment during actual installation (their theoretical rotation axes are different), point O1 does not coincide with point O. and The angle will change with the direction of rotation of point O. It changes with the change (point O revolves around point O1, the radius of rotation is e, and the included angle is...). It is the angle between OO1 and the horizontal direction during the rotation. It is the offset distance between different axes, that is, the length of OO1. This indicates that the misalignment of the cylindrical grating 2 and the angular reference 4 during rotation leads to... and The change in distance that will occur is expressed as: ; like Figure 4 As shown, the shortest propagation distance of a spherical wave can be obtained through S1 based on spatial geometric relationships. To calculate , This represents the distance between the point light source 31 and the pixel with the highest grayscale value on the linear image sensor 32, i.e., the vertical distance between the point light source 31 and the linear image sensor 32. This represents the radius of cylindrical grating 2.

[0038] S3: In order to obtain the result during rotation Regarding the measurement angle The change curve is obtained by repeating the exposure and calculation process of S1 and S2 every 9° rotation to obtain the results at multiple measurement angles. Below ， Among them, the measurement angle is Calculated in time Recorded as ,by Curve fitting is performed using the baseline to obtain... The amplitude of the curve. The phase of the curve (i.e., phases on different axes). This represents the DC component of the curve. Compare the sum of the two distances in S2 and S3. The expression can be obtained as follows: , ; Compare the two groups in S2 and S3 The expression can be used to obtain the offset distances of the cylindrical grating 2 along different axes. offset angle . S4: As Figure 5 As shown, during the assembly and adjustment of the cylindrical grating 2, when point O1 and point O do not completely coincide, the measurement angle obtained by the reading head 1 is... There are different axis errors in the middle. The distance between point O1 and point O along different axes is... Different axis phase is (That is, the angle between OZ and OO1). Wherein, Figure 5 In the middle, OP is the horizontal direction. Point F represents the intersection of the extension line of OO1 extending towards point O1 and the outer wall of the cylindrical grating 2, that is, the intersection of the extension line of OO1 extending towards point O1 and the circumference of the circular cross-section where point O is located. Point Z represents a fixed reference point on the absolute zero position region of the cylindrical grating 2, and it is located on the circular cross-section of the cylindrical grating 2 made through point P, that is, on the circular cross-section where point O is located.

[0039] Let ∠OPO1 be ∠POO1 is ∠PO1F is Then the different axis errors of cylindrical grating 2 Depend on and The difference is: ; The radius OP of the cylindrical grating 2 is... ∠POZ represents the measured angle. Point O1 has an offset distance OO1 relative to point O. Phase ∠O1OZ on different axes = Construct OQ⊥PO1 (with the foot of the perpendicular at Q). OQ can be represented on △POQ and △OO1Q as follows: ; The calculation radius is The cylindrical grating 2 in the angle measurement Offset distance on different axes and different axis phases Different axis errors under different conditions The expression is: ; S5: The present invention provides a method and system for detecting errors in cylindrical grating engravings. The engraving error detection module 9 detects the positioning error obtained by the positioning error calibration module 7. Different axis errors obtained from different axis error calculation module 8 By subtraction, the engraving error can be obtained. . Finally, the detected engraving error will be... Substituting the cylindrical grating 2 into the angular displacement measurement system for measuring angle After performing scribing error compensation, the system finally outputs the calibration angle. It can be represented as: . The embodiments of the present invention not only effectively suppress the interference of different axis errors in the detection of engraving errors of the cylindrical grating 2, but also further improve the inherent measurement accuracy of the cylindrical grating 2 through the above method; at the same time, it also enhances the ability of the small-volume cylindrical grating 2 to achieve high-precision measurement, providing support for its reliable application in measurement scenarios of industrial precision equipment and aerospace core components with limited space and stringent accuracy requirements.

[0040] Although embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention.

[0041] The specific embodiments of the present invention described above do not constitute a limitation on the scope of protection of the present invention. Any other corresponding changes and modifications made in accordance with the technical concept of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A method for detecting errors in cylindrical grating scribing, characterized in that, Includes the following: Step 1, Cylindrical Grating Positioning Error Calibration: ,in To measure the angle, specifically the rotation angle of the cylindrical grating is read through the reading head. The rotation angle of the cylindrical grating is output as an angular reference that is coaxially connected to it. Step two, calculation of the misalignment error of the cylindrical grating, specifically includes the following: S1: Calculate the shortest transmission distance of the spherical wave emitted from the point light source, reflected by the cylindrical grating, to the pixel with the highest grayscale value on the linear image sensor. The calculation steps are as follows: S11: Establish the spherical wave emitted by the point light source, which is reflected by the cylindrical grating to any pixel on the linear image sensor. spherical wave transmission distance The expression: ； in, = 0 represents the center pixel. This represents the distance between the center pixel and the pixel with the highest grayscale value on a linear image sensor. S12: Establish spherical wave transmission distance and the grayscale value of the corresponding pixel Expressions between: ； in This represents the exposure coefficient of the linear image sensor. This represents the pixel physical size constant of a linear image sensor; grayscale values Perform the following processing to obtain information about The quadratic function expression: ； in , where is the maximum grayscale value, and the constant term, first-order polynomial coefficients, and second-order polynomial coefficients of the quadratic function expression are respectively , and ; S13: Based on the grayscale values ​​of all pixels on the linear array image sensor, the least squares method is used to fit the data and obtain the coefficients. , and The value; Based on coefficient , and The value was calculated. ; S2: Calculation ,in This represents the distance between the point light source and the pixel with the highest grayscale value on the linear image sensor. This represents the shortest distance from the point light source to the outer cylindrical surface of the cylindrical grating. This represents the shortest distance from the pixel with the highest grayscale value on the linear image sensor to the outer cylindrical surface of the cylindrical grating. express and The amount of distance change that will occur in all of them; S3: Calculate at multiple measurement angles Below ,by Fitting to the baseline yields... The amplitude of the curve. For the phase of the curve, This represents the DC component of the curve. S4: Calculation radius is The cylindrical grating at the measurement angle is Different axis errors under different conditions : ； in For different axis offset distances, ; Step 3: Obtain the engraving error of the cylindrical grating by subtracting the positioning error from the errors of different axes. .

2. A cylindrical grating engraving error detection system, characterized in that, include: Cylindrical grating; Reading head: Used to read the rotation angle of the cylindrical grating, denoted as the measurement angle; Angle reference: Under the drive of the motor, the angle reference rotates synchronously with the cylindrical grating and outputs its own rotation angle; Positioning error calibration module: used to calculate the difference between the measured angle and the rotation angle to obtain the positioning error; Spherical wave exposure detection equipment: includes a point light source and a linear array image sensor. The spherical wave emitted by the point light source illuminates the cylindrical grating. After being reflected by the cylindrical grating, it is received by the linear array image sensor, which generates pixel grayscale data. Different axis error calculation module: Calculates different axis errors based on the spherical wave characteristics of the point light source and the grayscale values ​​of the pixels on the linear array image sensor; Grating error detection module: It detects grading errors by eliminating errors of different axes from the positioning errors.

3. The cylindrical grating engraving error detection system according to claim 2, characterized in that, The angle reference is an absolute encoder or an incremental encoder, and the angle reference is coaxially connected to the cylindrical grating and rotates synchronously.

4. The cylindrical grating engraving error detection system according to claim 2, characterized in that, The cylindrical grating is an absolute single-track grating.

5. The cylindrical grating engraving error detection system according to claim 2, characterized in that, The pixel arrangement of the linear image sensor is 1×N.

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