Transparent elastic ring parallelism detection method, device, medium and equipment

Abstract

This invention discloses a method, apparatus, medium, and device for detecting the parallelism of a transparent elastic ring. The method includes: acquiring multiple frames of color images containing a transparent elastic ring; dividing the transparent elastic ring into multiple sectors based on structural features; calculating the hue standard deviation of the hue channel of each sector as an interference feature quantity; fitting a fitting curve of the interference feature quantity as a function of the Z-axis, and extracting the peak position of the fitting curve as the interference peak position of the sector; and performing cosine function fitting to obtain a cosine fitting model to calculate the tilt direction and tilt angle. This invention directly outputs the low-side direction and tilt angle by sampling the entire circumference sector of the ring and performing cosine fitting; it eliminates the need for multi-sensor geometric calibration, extracts interference temporal features using hue standard deviation and circumferential statistics, eliminates the need to establish an absolute mapping between color and optical path difference, and is robust to overall brightness changes; the color interference distribution provides a visual indication of the low side in a single frame, facilitating visual coarse adjustment or algorithmic fine-tuning of the closed loop.

Description

Technical Field

[0001] This invention relates to the field of precision measurement technology, and in particular to a method, apparatus, medium, and equipment for detecting the parallelism of a transparent elastic ring. Background Technology

[0002] In precision assembly and machining scenarios, transparent elastic rings are used as interference elements, such as PDMS (polydimethylsiloxane) materials. The parallelism of these rings is measured using the effective diameter of the transparent elastic ring. Using the circular ring as a baseline, the local relative tilt of the two planes is measured within the ring-covered area. Therefore, the rapid and accurate adjustment of the parallelism of the two planes is crucial.

[0003] Existing methods for detecting the planar parallelism of transparent elastic rings have the following shortcomings: 1. Although traditional interferometers have high precision, they rely on complex optical paths, vibration isolation and high-quality reference surfaces, resulting in high cost and size, making them difficult to integrate as miniaturized or online detection modules; 2. Capacitive / laser displacement and other methods require multiple points to be arranged and relative positions to be calibrated. The installation and calibration process is complex and prone to errors. Some optical ranging methods (such as laser triangulation) are sensitive to surface reflection characteristics and have limited applicability to transparent / semi-transparent materials. 3. Existing solutions often output discrete values ​​or interference fringes that require professional interpretation, making it difficult for operators to directly determine the tilt direction from the image, which increases the difficulty of leveling operations and reduces efficiency.

[0004] Therefore, there is an urgent need for a low-cost, easily integrated method for detecting plane parallelism that can simultaneously provide the tilt direction and tilt angle, and offer intuitive visual leveling feedback. Summary of the Invention

[0005] In view of the above problems, the present invention is proposed to provide a method, apparatus, medium and device for detecting the parallelism of a transparent elastic ring that overcomes or at least partially solves the above problems.

[0006] Other features and advantages of the invention will become apparent from the following detailed description, or may be learned in part by practice of the invention.

[0007] According to a first aspect of the present invention, a method for detecting the parallelism of a transparent elastic ring is provided, comprising the following steps: S1. Adjust the gap height between the transparent elastic ring and the plane to be measured in the Z-axis direction, and simultaneously acquire multiple frames of color images containing the transparent elastic ring, and record the Z-axis coordinates corresponding to each frame of the image; S2. Detect the structural features of the transparent elastic ring from the acquired image, including the center position, inner radius and outer radius, and divide the transparent elastic ring into multiple sectors based on the structural features, and determine the central angle of each sector; S3. For each frame of the acquired image, extract the corresponding pixels in each sector of the transparent elastic ring in the image, convert them to the HSV color space, and calculate the hue standard deviation of the hue channel of each sector as the interference feature quantity of the sector under the corresponding Z-axis coordinate. S4. Based on the interference feature quantity and Z-axis coordinate corresponding to each sector in each frame image, fit a fitting curve of the interference feature quantity changing with the Z-axis, and extract the peak position of the fitting curve as the interference peak position of the sector. S5. Based on the corresponding interference peak positions and central angles of all sectors, a cosine function is fitted to obtain a cosine fitting model. The tilt direction and tilt angle of the plane to be measured relative to the plane where the transparent elastic ring is located are calculated according to the cosine fitting model.

[0008] In some embodiments of the present invention, step S2, dividing the transparent elastic ring into multiple sectors based on the structural features, includes: The transparent elastic ring is divided into N sectors, and the sector width is defined. and step length ,and ; Each interval along the circumference Divided into one sector, the first Sector coverage Its central angle is The number of sampling points is ; Among them, At that time, adjacent sectors overlap with each other. At that time, adjacent sectors are aligned with each other.

[0009] In some embodiments of the present invention, in step S3, the hue standard deviation of each sector hue channel is calculated using the following formula. : ; ; ; In the formula, This represents the number of valid pixels within a sector. For the first The hue radian value of each pixel, and The hue angles of the hue channels are respectively The corresponding sine arithmetic mean and cosine arithmetic mean, The length of the synthesized vector ( ).

[0010] In some embodiments of the present invention, step S4, which involves fitting a curve of the interference feature quantity as a function of the Z-axis based on the interference feature quantity and Z-axis coordinate of each sector in each frame image, includes: Constructing by skewness parameter By controlling the asymmetric peak shape of the kernel function and normalizing its peak value to 1, the kernel function used for fitting is obtained. The fitted function is obtained by translating and scaling the kernel function and adding a baseline bias. The interference feature quantity and Z-axis coordinate of each sector in each frame image are fitted based on a symmetric Gaussian fitting model to obtain the Gaussian fitting result. The Gaussian fitting result is used as the initial value of the fitting function, and the skewness parameter is set. The skewed normal fit is performed on the preset initial values ​​to obtain the fitting function with optimal parameters. for: ; In the formula, Peak amplitude, For position parameters, For scale parameters, This is the skewness parameter. Used as the baseline.

[0011] In some embodiments of the present invention, step S4, extracting the peak position of the fitted curve as the interference peak position of the sector, includes: The peak position of the fitted curve is determined by numerical search through traversing the fitted curve, and the peak position is used as the interference peak position of the sector. Based on the position parameters The standard error of the fitting curve is taken as the standard error of the fitted curve. If the skewed fitting of the fitted curve does not converge or the parameters exceed the limits, then the peak position and standard error in the Gaussian fitting result of the symmetric Gaussian fitting model shall be used as the interference peak position and standard error of the sector.

[0012] In some embodiments of the present invention, in step S5, the cosine fitting model is obtained by performing cosine function fitting based on the corresponding interference peak positions and central angles of all sectors, and the tilt direction and tilt angle of the plane under test relative to the plane where the transparent elastic ring is located are calculated according to the cosine fitting model, including: A cosine fitting model is obtained by fitting a cosine function based on the corresponding interference peak positions and central angles of all sectors. The new peak positions of each sector are obtained by performing weighted least squares processing based on the standard error of the fitted curve. Based on the new peak position, the cosine fitting model is introduced to calculate the tilt direction and tilt angle of the plane under test relative to the plane where the transparent elastic ring is located.

[0013] In some embodiments of the present invention, the transparent elastic ring is a raised ring structure formed on a rigid substrate, and the transparent elastic ring is made of polydimethylsiloxane.

[0014] According to a second aspect of the present invention, a device for detecting the parallelism of a transparent elastic ring is provided, the device comprising: The image acquisition module is used to adjust the gap height between the transparent elastic ring and the plane to be measured in the Z-axis direction, and simultaneously acquire multiple frames of color images containing the transparent elastic ring, and record the Z-axis coordinates corresponding to each frame of the image. The annular region segmentation module is used to detect the structural features of the transparent elastic annular ring from the acquired image, including the center position, inner radius and outer radius, and to divide the transparent elastic annular ring into multiple sectors based on the structural features, and to determine the central angle of each sector; The sector interference feature extraction module is used to extract the corresponding pixels in each sector of the transparent elastic ring in each frame of the acquired image, convert them to the HSV color space, and calculate the hue standard deviation of the hue channel of each sector as the interference feature quantity of the sector in the corresponding Z-axis coordinate. The interference peak position extraction module is used to fit a fitting curve of the interference feature quantity as a function of the Z-axis based on the interference feature quantity and Z-axis coordinate of each sector in each frame image, and extract the peak position of the fitting curve as the interference peak position of the sector. The tilt parameter calculation module is used to obtain a cosine fitting model by performing cosine function fitting based on the corresponding interference peak positions and central angles of all sectors, and to calculate the tilt direction and tilt angle of the plane under test relative to the plane where the transparent elastic ring is located based on the cosine fitting model.

[0015] According to a third aspect of the present invention, a computer-readable storage medium is provided, wherein computer program instructions are stored therein, the computer program instructions being loaded and executed by a processor to perform the operations performed by the method described in any of the preceding claims.

[0016] According to a fourth aspect of the present invention, an electronic device is provided, including a processor and a memory, the memory storing computer program instructions executable by the processor, wherein when the processor executes the computer program instructions, it implements the instructions of any of the methods described above.

[0017] The technical solutions provided in the embodiments of the present invention have at least the following technical effects or advantages: This invention provides a method, apparatus, medium, and device for detecting the parallelism of a transparent elastic ring. The method directly outputs the low-side direction and tilt angle by sampling the entire circumference sector of the ring and performing cosine fitting. It does not require multi-sensor geometric calibration, and the directional resolution is guaranteed by the number of sectors. It extracts the interference time sequence features using HSV hue standard deviation (Hue Std) and circumferential statistics, without the need to establish an absolute mapping between color and optical path difference, and is robust to overall brightness changes. The color interference distribution provides a visual indication of the low side in a single frame, facilitating visual coarse adjustment or algorithmic fine-tuning of the closed loop.

[0018] The above description is merely an overview of the technical solution of the present invention. In order to better understand the technical means of the present invention and to implement it in accordance with the contents of the specification, and in order to make the above and other objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention are described below. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 This is a flowchart illustrating a method for detecting the parallelism of a transparent elastic ring according to an embodiment of the present invention. Figure 2 The reference images are for the rising, peak, and falling segments of the Hue Std(z) curve. Figure 3 A reference diagram illustrating the inner and outer circles, the center of the circle, the sector boundary, and the positions of the low and high side sectors; Figure 4 This is a comparative diagram of sector segmentation strategies; Figure 5 For comparison of Gaussian fitting results, please refer to the schematic diagram. Figure 6 This is a schematic diagram for reference of skewed normal fitting results; Figure 7 This is a reference figure for comparing cosine fitting; Figure 8A comparison chart of Hue Std(z) for two samples and one sector; Figure 9 A comparison graph of two-sample cosine fitting / polar coordinates; Figure 10 This is a schematic diagram of dual-frame data processing; Figure 11 This is a schematic diagram of the principle structure of a transparent elastic ring parallelism detection device provided in an embodiment of the present invention. Detailed Implementation

[0021] Exemplary embodiments of this application will now be described in more detail with reference to the accompanying drawings.

[0022] The accompanying drawings illustrate various structural schematics according to embodiments of this application. These drawings are not to scale, and some details have been enlarged for clarity, and some details may have been omitted. The shapes of the various regions and layers shown in the drawings, as well as their relative sizes and positional relationships, are merely exemplary and may deviate from reality due to manufacturing tolerances or technical limitations. Furthermore, those skilled in the art can design regions / layers with different shapes, sizes, and relative positions as needed.

[0023] It should be noted that the terms "first," "second," etc., used in this application can be used to describe various elements, but these elements are not limited by these terms. These terms are only used to distinguish the first element from the second element. The terms "comprising" and "having," and any variations thereof, used in this application, are intended to cover non-exclusive inclusion. The term "multiple" used in this application refers to two or more. In the context of this application, similar or identical parts may be represented by the same or similar reference numerals.

[0024] To better understand the above technical solutions, the following will describe the above technical solutions in detail with reference to specific implementation methods. It should be understood that the embodiments of this application and the specific features in the embodiments are detailed descriptions of the technical solutions of the present invention, rather than limitations on the technical solutions of the present invention. In the absence of conflict, the embodiments of the present invention and the technical features in the embodiments can be combined with each other.

[0025] Figure 1 This is a flowchart illustrating a method for detecting the parallelism of a transparent elastic ring according to an embodiment of the present invention. Figure 1 As shown, the method for detecting the parallelism of a transparent elastic ring includes the following steps: S1. Adjust the gap height between the transparent elastic ring and the plane to be measured in the Z-axis direction, and simultaneously acquire multiple frames of color images containing the transparent elastic ring, and record the Z-axis coordinates corresponding to each frame of the image; In this embodiment of the invention, the transparent elastic ring is a raised ring structure formed on a rigid substrate, and the material of the transparent elastic ring is polydimethylsiloxane. The output of the parallelism detection of the transparent elastic ring includes a tilt angle. That is, the angle between the two planes within the baseline range, and the direction of inclination. That is, the polar angle (or the center angle of the sector) corresponding to the side with the smaller gap, and finally based on the tilt angle. and the direction of tilt The tilt attitude of the plane under test is adjusted by a yaw adjustment mechanism, which may be, for example, a differential screw adjustment table.

[0026] In other embodiments of the present invention, the transparent elastic ring can also be a discrete boss array, an arc segment or a semi-ring structure, or a rigid transparent ring. For example, when the ring is a discrete boss array, the center needs to be estimated by fitting discrete points, which easily introduces geometric errors; the number of sectors is limited by the number of bosses, and the cosine fitting constraint is less; for example, when the ring is an arc segment or a semi-ring structure, it only covers part of the polar angle range, making processing simpler; however, the cosine fitting lacks symmetry constraints, and the direction extraction accuracy decreases; for example, when the ring is a rigid transparent ring such as glass, there is no elastic contact behavior, making gap control more difficult, but the interference signal is clearer. Since the rigid transparent ring lacks elastic deformation, the curve shape of Hue Std with z is different from that of the transparent elastic ring, and the peak extraction model and SNR threshold can be recalibrated according to the rigid transparent ring.

[0027] In this embodiment of the invention, the gap height between the transparent elastic ring and the plane to be measured in the Z-axis direction is adjusted by the Z-axis driving / measuring mechanism. That is, the Z-axis of the transparent elastic ring is controlled to gradually approach the plane to be measured. A color microscopic image is acquired at each Z-axis position by the microscopic imaging and broadband illumination unit and the corresponding Z-axis coordinates are recorded.

[0028] The scanning range of the microscopic imaging and broadband illumination unit covers the entire process from no obvious interference color to the contact between the ring and the plane. The Z-axis step size is recommended to be on the order of white light wavelength, for example, several hundred nanometers, to ensure that the discrete data points of the hue standard deviation (Hue Std) of each sector, varying with the Z-axis position, are sufficiently sampled near the peak. Finally, an image sequence and corresponding Z-axis coordinate list are obtained, arranged in ascending order of Z-axis coordinates. The scanning of the microscopic imaging and broadband illumination unit terminates based on the contact state: when equipped with a force sensor, the stopping condition is when the contact force reaches a threshold; when without a force sensor, the stopping condition is when the transparent elastic ring undergoes significant elastic deformation; after contact, the interference color tends to fade uniformly, and the hue standard deviation (Hue Std) continues to decrease, indicating that effective interference information has been acquired.

[0029] S2. Detect the structural features of the transparent elastic ring from the acquired image, including the center position, inner radius and outer radius, and divide the transparent elastic ring into multiple sectors based on the structural features, and determine the central angle of each sector; This invention employs ring detection to detect the structural features of the transparent elastic ring from the acquired image, including the center position. , inner radius and outer radius All values ​​are in pixels. The effective diameter of the transparent elastic ring is defined as... ,in These are pixel size calibration values, in μm / pixel. The unit is μm. The structural features of the transparent elastic ring can be detected using conventional methods such as edge extraction and circle fitting, and Hough circle transform; this invention does not limit the algorithm. Robustness can be improved by uniformly sampling multiple frames and taking the median.

[0030] Optionally, geometric calibration and distortion correction (radial / tangential) of the camera-microscope system can be performed before ring detection. When the field of view is small, the ring is located near the optical axis, and the effect of distortion on the estimation of the center and radius is negligible, this step can be skipped and ring detection can be performed directly on the original image.

[0031] In step S2, the present invention, based on the structural features, divides the transparent elastic ring into multiple sectors, including: The transparent elastic ring is divided into N sectors (typically 30–60, adjustable as needed within the range of 12–120), and the sector width is defined. and step length ,and ; Each interval along the circumference Divided into one sector, the first Sector coverage Its central angle is The central angle of the sector is the polar angle, and the number of sampling points is... ; Among them, When adjacent sectors overlap, the overlap can increase the angle sampling density of cosine fitting and smooth the boundary. exist At this time, adjacent sectors are aligned with each other, that is, the transparent elastic ring is divided into N sectors at equal intervals. , No. The central angle of each sector is The corresponding polar angle range is .

[0032] In this embodiment of the invention, a binary mask (or a uniformly generated integer label map) is pre-calculated for each sector, which is used for subsequent rapid extraction of pixels within the sector.

[0033] S3. For each frame of the acquired image, extract the corresponding pixels in each sector of the transparent elastic ring in the image, convert them to the HSV (Hue, Saturation, Value) color space, and calculate the hue standard deviation of the hue channel of each sector as the interference feature quantity of the sector in the corresponding Z-axis coordinate. In this embodiment of the invention, for each sector of each frame of image, the sector pixels are extracted and the image is converted to the HSV color space to extract the hue channel. (0°–360°), the standard deviation of hue is calculated using circumferential statistics. Before calculation, the hue angle is... Convert from degrees to radians, then participate and Operations, specifically: In step S3, the hue standard deviation of each sector hue channel is calculated using the following formula in this embodiment of the invention. : ; ; ; In the formula, This represents the number of valid pixels within a sector. For the first The hue radian value of each pixel, and The hue angles of the hue channels are respectively The corresponding sine arithmetic mean and cosine arithmetic mean, The length of the synthesized vector ( ).

[0034] The length of the synthesized vector needs to be truncated to... Open interval to ensure Meaningful. When the number of effective pixels in any sector is insufficient (e.g. When the hue standard deviation (Hue Std) is reached, the sector is marked as invalid and excluded from subsequent peak fitting. The final result is the Hue Std matrix. Each row of the matrix corresponds to a Z-position frame, and each column corresponds to a sector.

[0035] In other embodiments of the present invention, the interference feature quantity can also be selected from other parameters, such as RGB channel intensity and contrast, absolute hue value, or frequency domain features; the RGB channel intensity and contrast are more sensitive to lighting conditions and are suitable for scenarios where robustness requirements are not high; the absolute hue value requires precise calibration of the correspondence between hue and gap, and is suitable for scenarios where calibration workload is not critical; the frequency domain feature is, for example, a Fast Fourier Transform (FFT), which is suitable for scenarios where computational load is not limited and spatial resolution is critical.

[0036] S4. Based on the interference feature quantity and Z-axis coordinate corresponding to each sector in each frame image, fit a fitting curve of the interference feature quantity changing with the Z-axis, and extract the peak position of the fitting curve as the interference peak position of the sector. For each sector Interference peak positions are extracted from discrete data points based on the variation of hue standard deviation (Hue Std) with z. Within the Z-scan range of this embodiment, the data points typically exhibit single-peak or broad-peak characteristics, eliminating the need for primary / secondary peak differentiation; peak position parameters can be obtained by fitting discrete data points.

[0037] In implementing step S4, this embodiment of the invention can default to using the symmetric Gaussian fitting method as the extraction method for the interference peak positions. The fitting function at this time... for: ; In the formula, Peak amplitude, This is the peak position. For the peak width, Use the baseline. Fitting can simultaneously obtain the goodness of fit. and the standard error of the peak position .

[0038] Since the discrete data points of hue standard deviation (Hue Std) as a function of z are often asymmetrical due to factors such as elastic contact, a skewed normal distribution fitting method is needed to replace the symmetrical Gaussian fitting method to improve fitting accuracy. Taking the process of the torus gradually approaching the plane to be measured as the observation direction, the Hue Std(z) curve during the PDMS elastic contact process usually shows a slow increase, and a rapid decrease after contact or flattening. The skewed normal distribution fitting method introduces a skewness parameter on the basis of standard normality. The direction of asymmetry in the control curve, i.e.: exist Time: The steepness is different on both sides of the peak. The sign depends on the Z-coordinate orientation, and this invention only utilizes its asymmetric fitting ability to obtain a more stable peak position.

[0039] exist At that time: it degenerates into a symmetrical Gaussian distribution.

[0040] When fitting a skewed normal distribution, the peak position is taken as the mode of the distribution rather than the location parameter. (The two are generally not equal). Standard error of the fitted parameters Obtained through covariance matrix propagation.

[0041] The implementation process of fitting a skewed normal distribution in this embodiment of the invention is as follows: In step S4, fitting a curve of the interference feature quantity as a function of the Z-axis based on the interference feature quantity and Z-axis coordinate of each sector in each frame image includes: Constructing by skewness parameter By controlling the asymmetric peak shape of the kernel function and normalizing its peak value to 1, the kernel function used for fitting is obtained. The fitted function is obtained by translating and scaling the kernel function and adding a baseline bias. Let the standardized variables Define the skewed normal kernel function: ; in For standard normal PDFs, It is a standard normal CDF.

[0042] Normalizing the kernel function to a peak value of 1 yields: ; The interference feature quantity and Z-axis coordinate of each sector in each frame image are fitted based on a symmetric Gaussian fitting model to obtain the Gaussian fitting result. The Gaussian fitting result is used as the initial value of the fitting function, and the skewness parameter is set. The skewed normal fit is performed on the preset initial values ​​to obtain the fitting function with optimal parameters. for: ; In the formula, Peak amplitude, For position parameters, For scale parameters, This is the skewness parameter. This serves as the baseline. In this embodiment of the invention, peak value normalization is used to normalize the parameters. Directly indicates the deduction of baseline The peak amplitude afterwards.

[0043] The Gaussian fitting result obtained based on the symmetric Gaussian fitting model is: , and then with , , (This reflects the prior expectation of a slow rise and rapid fall in PDMS elastic contact. If the current Z-coordinate direction is opposite to the "gradual approach" process,) Using initial values, a skewed-normal fit is performed to obtain the fitted function with optimal parameters. .

[0044] In step S4, extracting the peak position of the fitted curve as the interference peak position of the sector includes: The peak position of the fitted curve is determined by numerical search through traversing the fitted curve, and the peak position is used as the interference peak position of the sector. Based on the position parameters The standard error of the fitting curve is taken as the standard error of the fitted curve. If the skewed fitting of the fitted curve does not converge or the parameters exceed the limits, then the peak position and standard error in the Gaussian fitting result of the symmetric Gaussian fitting model shall be used as the interference peak position and standard error of the sector.

[0045] To prevent the fitting from diverging, this embodiment of the invention first performs a symmetric Gaussian fitting to obtain initial values, and then uses these initial values ​​to perform a skewed normal fitting to obtain the fitting function with optimal parameters. In the case where the skewed fitting of the fitted curve does not converge or the parameters exceed the limits, it is possible to choose to revert to symmetric Gaussian fitting, and use the peak position and standard error in the Gaussian fitting result as the interference peak position and standard error of the sector.

[0046] In this embodiment of the invention, when performing skewed normal fitting, the peak position is... Pick The maximum value corresponding to Coordinates. For a given mode deviation The quantity is a fixed value and can be pre-calculated by looking up a table. Furthermore, the mode of a skewed distribution is generally not equal to the location parameter. .

[0047] In this embodiment of the invention, the symmetric Gaussian fitting is directly taken as... The fitting standard error is used as the standard error. When fitting a skewed normal distribution, the position parameters are used. The fitting standard error is used as the standard error. Approximation (due to mode and) The relationship (Lower local sensitivity).

[0048] In other embodiments of the present invention, the extraction method for the interference peak position can also be the direct peak method, the weighted centering method, or parabolic interpolation. The direct peak method takes the Z coordinate corresponding to the maximum value of the hue standard deviation (Hue Std). This method has no model assumptions and is suitable for scenarios with dense sampling and high signal-to-noise ratio. The weighted centering method first subtracts the baseline and calculates the weighted average position using the hue standard deviation (Hue Std) as the weight. This method is simple to calculate but sensitive to baseline estimation. The parabolic interpolation fits a quadratic parabola to the data points near the peak and finds the vertex position, which can achieve sub-sampling interval accuracy.

[0049] In an optional embodiment of the present invention, the sampling density is at least 7 sampling points (preferably ≥11) near the peak of the Hue Std(z) curve for each sector to support the stability of symmetrical Gaussian fitting or skewed normal fitting; the typical number of frames is, for example, 30–50 frames; the stopping condition is, for example, when ≥80% of the sector's Hue Std has crossed the peak and entered a continuous decline phase, the scanning can be terminated; the effective frame screening is, for example, determining that the global contrast is below a threshold as out of focus, and determining that the proportion of high grayscale pixels is too high as exposure saturation.

[0050] S5. Based on the corresponding interference peak positions and central angles of all sectors, a cosine function is fitted to obtain a cosine fitting model. The tilt direction and tilt angle of the plane to be measured relative to the plane where the transparent elastic ring is located are calculated according to the cosine fitting model.

[0051] In this embodiment of the invention, the tilt direction is represented by the low-side direction, which is the polar angle direction corresponding to the side with the smaller gap between the two planes (the plane to be measured and the plane containing the transparent elastic ring). In step S5, the cosine fitting model is obtained by performing cosine function fitting based on the corresponding interference peak positions and central angles of all sectors. The tilt direction and tilt angle of the plane to be measured relative to the plane containing the transparent elastic ring are calculated according to the cosine fitting model, including: A cosine fitting model is obtained by fitting a cosine function based on the corresponding interference peak positions and central angles of all sectors. The new peak positions of each sector are obtained by performing weighted least squares processing based on the standard error of the fitted curve. Based on the new peak position, the cosine fitting model is introduced to calculate the tilt direction and tilt angle of the plane under test relative to the plane where the transparent elastic ring is located.

[0052] When the plane is tilted, the lower side gap of the annulus is smaller and the higher side gap is larger, and the interference peak positions of each sector are... With polar angle It exhibits a cosine distribution relationship, among which For the first The central angle of each sector then has a cosine fitting model. for: ; In the formula, The cosine amplitude (Z-axis displacement count) represents the Z-coordinate offset from the average height to the lowest (or highest) side; the maximum height difference along the annular diameter is... ; The angle is the tilt direction (°), i.e., the polar angle in the low-side direction; This is the bias term, corresponding to the average height of the plane being measured.

[0053] To improve numerical stability, this embodiment of the invention employs an equivalent linear form for solving the problem, that is, transforming the nonlinear cosine fitting into a linear form to improve numerical stability and reproducibility consistency. Let: ; Fitting Afterwards, by , Restore the cosine amplitude and tilt direction.

[0054] For parameter normalization constraints, the tilt direction Normalization to If nonlinear fitting is used and the fitted result is... Then let and (Re-model 360°).

[0055] Weighted least squares objective function: ; That is, weights and Proportional to standard error Smaller sectors contribute more to the fit. (Regarding the standard error) Set a lower limit (e.g.) ), to prevent individual sectors from being affected by standard error The abnormally small value dominates the fitting result.

[0056] The tilt angle is then calculated using the cosine amplitude and the geometric dimensions of the ring. First, the cosine amplitude is converted into physical length: ; In the formula, Divide the physical length (nm / count) corresponding to the Z-axis displacement count by 1000 to convert the result to micrometers (μm). The maximum height difference (μm) in the diameter direction of the transparent elastic ring.

[0057] Then the tilt angle for: ; In the formula, The effective diameter (μm) of the transparent elastic ring can be given by the structural design value or obtained by conversion from imaging calibration; the tilt angle The output unit is degrees (°).

[0058] After calculating the tilt direction and tilt angle of the plane to be tested relative to the plane containing the transparent elastic ring, this embodiment of the invention further includes calculating the signal-to-noise ratio (SNR) of the cosine fit as the confidence level for the cosine fit evaluation, wherein the confidence level is used to evaluate the reliability of the fitting result: ; In the formula, The signal-to-noise ratio (SNR) represents the standard deviation of the cosine fit residuals and reflects the significance of the cosine fit amplitude relative to the residual noise, thus characterizing the reliability of the direction and angle output.

[0059] In this embodiment of the invention, the reference threshold range of the signal-to-noise ratio (SNR) is as follows: when the SNR < 1.5, the confidence level is low, indicating that the cosine signal is submerged in noise, and the direction and angle outputs are unreliable; when the SNR 1.5 ≤ SNR < 3, the confidence level is medium, indicating that the signal is identifiable but not sufficiently so, and the direction information is only for reference; when the SNR ≥ 3, the confidence level is high, indicating that the cosine signal has statistical significance, and the direction and angle outputs are reliable. The reference threshold range of the SNR can be adaptively adjusted according to the system noise characteristics in actual applications, thereby selecting other numerical ranges; in the closed-loop automated leveling scenario, the SNR can be used as a convergence criterion for the control loop. When it drops below the threshold, the adjustment stops to prevent oscillations based on unreliable outputs. When the two planes are nearly parallel, the cosine fitting amplitude approaches zero, and manufacturing errors (such as uneven ring height) become the dominant factor. At this time, the direction and angle of the fitted output are no longer reliable. The signal-to-noise ratio (SNR) can be used as a validity indicator for subsequent steps to determine whether to accept the current fitting result.

[0060] In other embodiments of the present invention, the calculation of the tilt direction can also employ a plane fitting method, a maximum-minimum method, or a Fourier analysis method. The plane fitting method treats the peak position of each sector as a normal vector of the three-dimensional point cloud fitting plane. The maximum-minimum method uses only the sectors with the maximum and minimum peak positions to determine the direction. The Fourier analysis method performs Fourier analysis on the peak position sequence to extract the fundamental frequency component. A reasonable calculation method can be selected according to the actual application scenario, and the embodiments of the present invention do not limit this.

[0061] Example 1: Visualization of the entire process of a single sample (Sample 02).

[0062] This embodiment uses a set of samples with obvious tilt (Sample 02) as the object. The dataset uses Sample 02 (47 frames) and a tilt of 0.13° was introduced by manual adjustment before acquisition.

[0063] The experimental conditions are as follows: Ring specifications: PDMS is spin-coated onto a glass substrate and patterned into a raised ring with an outer diameter of approximately 1000 μm, a ring width of approximately 50 μm, and a height of approximately 5 μm; the ring is at the bottom, and the objective lens focuses on the protrusion from the top. Imaging system: white LED, 10× microscope objective, CMOS camera, image size 2048×1080 pixels; Displacement and yaw control: The upper plane is driven to approach the ring by a piezoelectric ceramic Z-axis; the tilt attitude of the upper plane is adjusted by a differential screw adjustment table; Number of sectors: ; Z-axis step size: approximately 0.35 μm / step (approximately 0.28–0.39 μm range), with a total of 47 frames acquired.

[0064] Z-axis scanning and data acquisition: The Z-axis is gradually moved closer to the plane under test, and a color microscopic image is acquired at each Z position, combined with... Figure 2 The image shown is a reference image corresponding to the rising segment, peak segment, and falling segment of the Hue Std(z) curve. Figure 2 middle, Figure 2 (a) That is, the left image is in a distant state, with no obvious interference. The rising segment of the Hue Std(z) curve corresponding to the color standard deviation is shown. Figure 2 (b) That is, the frame with the strongest interference in the middle image, where the colors on the lower side are most concentrated, corresponding to the peak segment of the Hue Std(z) curve. Figure 2 (c) That is, the image on the right shows the color tending to be uniform or faded after contact, corresponding to the descending segment of the Hue Std(z) curve.

[0065] Ring detection and sector segmentation: Detecting the center of a circle in an image sequence and inner and outer radii , Press the ring... Equal angle segmentation, sector angle width .

[0066] set up and ,like Sector overlap can improve angular resolution.

[0067] See Figure 3The diagram shown illustrates the positions of the inner and outer circles, the center of the circle, the sector boundaries, and the lower and higher side sectors; see reference. Figure 4 The diagram shown is a comparison of sector segmentation strategies, with a magnified view of the 0°–36° area. Figure 4 a represents the non-overlapping region segmentation, comprising 6 sectors (S0–S5), each at 6°; Figure 4 b represents a sliding window overlap segmentation with a width of 9°, a step size of 6°, and an overlap of 33%.

[0068] Hue Standard Deviation (Hue Std) Feature Extraction and Peak Fitting: Calculate the hue standard deviation (Hue Std) for each sector, extract the peak position of the Hue Std(z) curve for each sector, and plot a scatter plot of Hue Std versus Z coordinate for one representative sector near the low side and one near the high side. Then, overlay the plots to obtain the final result. Figure 5 and Figure 6 See Figure 5-6 As shown, Figure 5 For comparison, please refer to the schematic diagram. Figure 6 This is a reference diagram showing the results of skewed normal fitting, compared to Gaussian fitting where the result is directly taken. It is suitable for nearly symmetric curves; skewness parameters are introduced for skewed normal curves. The peak value is taken as the mode to characterize the asymmetry caused by contact. In this example, the skewed fitting average... This indicates that the curve exhibits significant asymmetry.

[0069] Cosine fitting and tilt angle calculation: Peak position of each sector With polar angle For cosine fitting, please refer to [link / reference]. Figure 7 The cosine fitting comparison reference figure is shown below. Figure 7 'a' is a schematic diagram of the scatter-point fitted curve using equal-weighted cosine fitting. Figure 7 b is A schematic diagram of the inverse variance weighted fitting curve; color depth reflects weights, arranged according to... Inverse variance weighting gives higher weights to sectors with lower uncertainty. The implementation steps based on the aforementioned embodiment calculate the tilt angle and tilt direction from the cosine amplitude and the diameter of the ring.

[0070] Confidence assessment and output, the output of Sample 02 is shown in Table 1 below: Table 1 Confidence Assessment

[0071] Example 2: Two-sample comparison verification (Sample 01 vs Sample 02).

[0072] This embodiment, under the same equipment and algorithm parameters, compares two groups of samples with different tilt states to verify the ability of the method steps corresponding to the aforementioned embodiment to distinguish different degrees of tilt. The effectiveness of confidence assessment.

[0073] Datasets: Sample 01, 32 frames, nearly horizontal; Sample 02, 47 frames, approximately 0.13° tilted. Both datasets used the same PDMS ring, with the tilt changed only by manual adjustment.

[0074] The experimental conditions were the same as in Example 1, with Sample 01 stepping at approximately 0.53 μm / step (approximately 0.49–0.57 μm range), for a total of 32 frames.

[0075] Sectors at the same polar angle were selected, and the Hue Std(z) curves of the two samples were overlaid for comparison. Figure 8 As shown, Figure 8 This is a comparison chart of Hue Std(z) for two samples and one sector. Figure 8 The image shows two representative sectors with the same polar angles (low side / high side, approximately 357° and 177°). The Z-coordinate is then adjusted... After normalization, the Hue Std(z) scatter plots and fitted curves of Sample 01 (blue) and Sample 02 (orange) are superimposed. Figure 8 The curve shapes of the two samples differ in the low / high side sectors: Sample 01 generally has a higher peak amplitude, while Sample 02 has a slightly lower fit quality in the high side sector. The decrease reflects the stripe distortion and increased asymmetry caused by tilt.

[0076] Combination Figure 9 As shown, Figure 9 This is a comparison chart of two-sample cosine fitting and polar coordinates. Figure 9 a is the cosine fit of Sample 01 ( counts , , (The direction is unclear) Figure 9 b is the cosine fit of Sample 02 ( counts , , (The direction is clear) Figure 9 c represents polar coordinates: the radial direction represents the offset of the peak value Z relative to its respective average value. Sample 01 is nearly circular, while Sample 02 is an elliptical stretch.

[0077] The comparison results are shown in Table 2 below: Table 2 Comparison Results of Sample 01 vs Sample 02

[0078] Weighted Fitting Explanation: Cosine fitting uses the standard error based on the peak fitting value. Inverse variance weighted ( The reliable sector has a higher weight, avoiding high-side distortion from affecting the polarization amplitude estimation.

[0079] Results Analysis: The angle difference between the two groups was 0.169°, which is on the same order of magnitude as the nominal difference of 0.13° for manual adjustment; the deviation mainly comes from the adjustment reading, uneven ring height, and sampling step distance; the signal-to-noise ratio of Sample 02... For high confidence, the signal-to-noise ratio of Sample 01 It has a medium confidence level.

[0080] Example 3: Simplified implementation of manual leveling for dual frames.

[0081] The input consists of two image frames: frame 1 shows no obvious interference colors; frame 2 is within the interference-sensitive region (color fringes appear but are not in contact). The output is the tilt direction. With fit credibility It does not output the tilt angle.

[0082] use Sector (sector angle width 6°), select 6 representative sectors. For the sector center angle, ring detection, sector segmentation, and Hue Std calculation reuse sections 2.5.2–2.5.4. The difference is calculated for each sector. , Example values ​​are shown in Table 3 below for reference: Table 3 Example value

[0083] Perform cosine fitting: ; Cosine fitting yielded , , , The confidence level meets the threshold.

[0084] See Figure 10 The image shown is a schematic diagram of dual-frame data processing. Figure 10 a shows a schematic diagram of frame 1 / frame 2 and a diagram of sector segmentation. Figure 10 b is Scatter points and cosine fitting curve, Figure 10 c represents the polar coordinate scatter plot and the fitted graph. Figure 10Showing goodness of fit As a credibility indicator (empirical threshold) If frame 2 is too far or too close, The amplitude is insufficient and the directional output is unstable; it should be re-acquired.

[0085] This embodiment only outputs the direction and does not estimate the angle; it is sensitive to the timing of frame 2 acquisition and must be ensured to be within the interference-sensitive range. This embodiment, together with visual coarse adjustment and complete Z-scan (Embodiment 1), constitutes two leveling schemes: the former is manual visual coarse adjustment, and the latter is automatic fine adjustment; Embodiment 2 is only used for comparison and illustration.

[0086] The method for detecting the parallelism of a transparent elastic ring described in this invention has the following advantages compared to existing technologies: 1. By sampling the entire circumference sector of the circular ring and performing cosine fitting, the low-side direction and tilt angle are directly output; no multi-sensor geometric calibration is required, and the directional resolution is guaranteed by the number of sectors; 2. Interference time sequence features are extracted using HSV hue standard deviation (Hue Std) and circumferential statistics. There is no need to establish an absolute mapping between color and optical path difference, and it is robust to changes in overall brightness. The color interference distribution provides a visual indication of the low side of a single frame, which is convenient for visual coarse adjustment or algorithmic fine-tuning of the closed loop. 3. Using a transparent elastic continuous PDMS ring as the interference-sensitive structure, combined with ordinary white LED illumination, white light air thin film interference is formed. The interference generated by the structural component replaces the optical path of the complex interferometer, reducing the dependence on vibration isolation and reference surface. The detection head can be modularized, improving its applicability.

[0087] Based on the above embodiments, as a supplement to the above... Figure 1 The present invention provides an embodiment of a transparent elastic ring parallelism detection device, which is similar to the method shown. Figure 1 Corresponding to the method embodiments shown, this device can be specifically applied to various electronic devices, see reference. Figure 11 As shown, the transparent elastic ring parallelism detection device includes: The image acquisition module 100 is used to adjust the gap height between the transparent elastic ring and the plane to be measured in the Z-axis direction, and simultaneously acquire multiple frames of color images containing the transparent elastic ring, and record the Z-axis coordinates corresponding to each frame of the image. The annular region segmentation module 200 is used to detect the structural features of the transparent elastic annular ring from the acquired image, including the center position, inner radius and outer radius, and to divide the transparent elastic annular ring into multiple sectors based on the structural features, and to determine the central angle of each sector; The sector interference feature extraction module 300 is used to extract the corresponding pixels in each sector of the transparent elastic ring in each frame of the acquired image, convert them to the HSV color space, and calculate the hue standard deviation of the hue channel of each sector as the interference feature quantity of the sector in the corresponding Z-axis coordinate. The interference peak position extraction module 400 is used to fit a fitting curve of the interference feature quantity as a function of the Z-axis based on the interference feature quantity and Z-axis coordinate of each sector in each frame image, and extract the peak position of the fitting curve as the interference peak position of the sector. The tilt parameter calculation module 500 is used to obtain a cosine fitting model by performing cosine function fitting based on the corresponding interference peak positions and central angles of all sectors, and to calculate the tilt direction and tilt angle of the plane under test relative to the plane where the transparent elastic ring is located based on the cosine fitting model.

[0088] The transparent elastic ring parallelism detection device described in this embodiment of the invention can perform the transparent elastic ring parallelism detection method provided in the above embodiments. The transparent elastic ring parallelism detection device has the corresponding functional steps and beneficial effects of the transparent elastic ring parallelism detection method described in the above embodiments. For details, please refer to the embodiments of the transparent elastic ring parallelism detection method described above. The embodiments of the present invention will not be repeated here.

[0089] This invention also provides an electronic device, which may include a processor and a memory, wherein the processor and memory can be connected via a bus or other means. The processor may be a Central Processing Unit (CPU). The processor may also be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, or combinations thereof. The memory, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs, non-transitory computer-executable programs, and modules, such as the program instructions / modules corresponding to the transparent elastic ring parallelism detection method in this invention embodiment. The processor executes various functional applications and data processing by running the non-transitory software programs, instructions, and modules stored in the memory, thereby implementing the transparent elastic ring parallelism detection method in the above method embodiments.

[0090] The memory may include a program storage area and a data storage area. The program storage area may store the operating system and at least one application program required for a function; the data storage area may store data created by the processor, etc. Furthermore, the memory may include high-speed random access memory and non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. One or more modules are stored in the memory and, when executed by the processor, perform the transparent elastic ring parallelism detection method as described in the above method embodiments. Specific details of the above electronic device can be understood by referring to the corresponding descriptions and effects in the above method embodiments, and will not be repeated here. Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, it may include the processes of the embodiments of the above methods. The storage medium may be a read-only memory (ROM), a random access memory (RAM), a flash memory, a hard disk drive (HDD), or a solid-state drive (SSD), etc.; the storage medium may also include a combination of the above types of memory.

[0091] Numerous specific details are set forth in the specification provided herein. However, it will be understood that embodiments of the invention may be practiced without these specific details. In some instances, well-known methods, structures, and techniques have not been shown in detail so as not to obscure the understanding of this specification.

[0092] Similarly, it should be understood that, for the purpose of simplification and aiding understanding of one or more aspects of the invention, various features of the invention are sometimes grouped together in a single embodiment, figure, or description thereof in the description of exemplary embodiments of the invention above. Other embodiments of the invention will readily occur to those skilled in the art upon consideration of the specification and practice of the disclosure herein. This application is intended to cover any variations, uses, or adaptations of the invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein. The specification and embodiments are to be considered exemplary only, and it should be noted that the above embodiments are illustrative of the invention and not restrictive, and that alternative embodiments can be devised by those skilled in the art without departing from its scope.

Claims

1. A method for detecting the parallelism of a transparent elastic ring, characterized in that, Includes the following steps: S1. Adjust the gap height between the transparent elastic ring and the plane to be measured in the Z-axis direction, and simultaneously acquire multiple frames of color images containing the transparent elastic ring, and record the Z-axis coordinates corresponding to each frame of the image; S2. Detect the structural features of the transparent elastic ring from the acquired image, including the center position, inner radius and outer radius, and divide the transparent elastic ring into multiple sectors based on the structural features, and determine the central angle of each sector; S3. For each frame of the acquired image, extract the corresponding pixels in each sector of the transparent elastic ring in the image, convert them to the HSV color space, and calculate the hue standard deviation of the hue channel of each sector as the interference feature quantity of the sector under the corresponding Z-axis coordinate. S4. Based on the interference feature quantity and Z-axis coordinate corresponding to each sector in each frame image, fit a fitting curve of the interference feature quantity changing with the Z-axis, and extract the peak position of the fitting curve as the interference peak position of the sector. S5. Based on the corresponding interference peak positions and central angles of all sectors, a cosine function is fitted to obtain a cosine fitting model. The tilt direction and tilt angle of the plane to be measured relative to the plane where the transparent elastic ring is located are calculated according to the cosine fitting model.

2. The method for detecting the parallelism of a transparent elastic ring according to claim 1, characterized in that, In step S2, dividing the transparent elastic ring into multiple sectors based on the structural features includes: The transparent elastic ring is divided into N sectors, and the sector width is defined. and step length ,and ; Each interval along the circumference Divided into one sector, the first Sector coverage Its central angle is The number of sampling points is ; Among them, At that time, adjacent sectors overlap with each other. At that time, adjacent sectors are aligned with each other.

3. The method for detecting the parallelism of a transparent elastic ring according to claim 1, characterized in that, In step S3, the hue standard deviation of each sector's hue channel is calculated using the following formula. : ； ； ； In the formula, This represents the number of valid pixels within a sector. For the first The hue radian value of each pixel, and The hue angles of the hue channels are respectively. The corresponding sine arithmetic mean and cosine arithmetic mean, The length of the synthesized vector ( ).

4. The method for detecting the parallelism of a transparent elastic ring according to claim 1, characterized in that, In step S4, fitting a curve of the interference feature quantity as a function of the Z-axis based on the interference feature quantity and Z-axis coordinate of each sector in each frame image includes: Constructing by skewness parameter By controlling the asymmetric peak shape of the kernel function and normalizing its peak value to 1, the kernel function used for fitting is obtained. The fitted function is obtained by translating and scaling the kernel function and adding a baseline bias. The interference feature quantity and Z-axis coordinate of each sector in each frame image are fitted based on a symmetric Gaussian fitting model to obtain the Gaussian fitting result. The Gaussian fitting result is used as the initial value of the fitting function, and the skewness parameter is set. The skewed normal fit is performed on the preset initial values ​​to obtain the fitting function with optimal parameters. for: ； In the formula, Peak amplitude, For position parameters, For scale parameters, This is the skewness parameter. Used as the baseline.

5. The method for detecting the parallelism of a transparent elastic ring according to claim 4, characterized in that, In step S4, extracting the peak position of the fitted curve as the interference peak position of the sector includes: The peak position of the fitted curve is determined by numerical search through traversing the fitted curve, and the peak position is used as the interference peak position of the sector. Based on the position parameters The standard error of the fitting curve is taken as the standard error of the fitted curve. If the skewed fitting of the fitted curve does not converge or the parameters exceed the limits, then the peak position and standard error in the Gaussian fitting result of the symmetric Gaussian fitting model shall be used as the interference peak position and standard error of the sector.

6. The method for detecting the parallelism of a transparent elastic ring according to claim 5, characterized in that, In step S5, the cosine fitting model is obtained by fitting a cosine function based on the corresponding interference peak positions and central angles of all sectors. The tilt direction and tilt angle of the plane under test relative to the plane containing the transparent elastic ring are calculated based on the cosine fitting model, including: A cosine fitting model is obtained by fitting a cosine function based on the corresponding interference peak positions and central angles of all sectors. The new peak positions of each sector are obtained by performing weighted least squares processing based on the standard error of the fitted curve. Based on the new peak position, the cosine fitting model is introduced to calculate the tilt direction and tilt angle of the plane under test relative to the plane where the transparent elastic ring is located.

7. The method for detecting the parallelism of a transparent elastic ring according to claim 1, characterized in that: The transparent elastic ring is a raised ring structure formed on a rigid substrate, and the transparent elastic ring is made of polydimethylsiloxane.

8. A transparent elastic ring parallelism detection device, applied to the method described in any one of claims 1-7, characterized in that, The device includes: The image acquisition module is used to adjust the gap height between the transparent elastic ring and the plane to be measured in the Z-axis direction, and simultaneously acquire multiple frames of color images containing the transparent elastic ring, and record the Z-axis coordinates corresponding to each frame of the image. The annular region segmentation module is used to detect the structural features of the transparent elastic annular ring from the acquired image, including the center position, inner radius and outer radius, and to divide the transparent elastic annular ring into multiple sectors based on the structural features, and to determine the central angle of each sector; The sector interference feature extraction module is used to extract the corresponding pixels in each sector of the transparent elastic ring in each frame of the acquired image, convert them to the HSV color space, and calculate the hue standard deviation of the hue channel of each sector as the interference feature quantity of the sector in the corresponding Z-axis coordinate. The interference peak position extraction module is used to fit a fitting curve of the interference feature quantity as a function of the Z-axis based on the interference feature quantity and Z-axis coordinate of each sector in each frame image, and extract the peak position of the fitting curve as the interference peak position of the sector. The tilt parameter calculation module is used to obtain a cosine fitting model by performing cosine function fitting based on the corresponding interference peak positions and central angles of all sectors, and to calculate the tilt direction and tilt angle of the plane under test relative to the plane where the transparent elastic ring is located based on the cosine fitting model.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer program instructions that are loaded and executed by a processor to perform the operations described in any one of claims 1-7.

10. An electronic device comprising a processor and a memory, characterized in that, The memory stores computer program instructions that can be executed by the processor, and when the processor executes the computer program instructions, it implements the instructions of the method as described in any one of claims 1-7.

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