Line diameter measuring method based on optical diffraction

Through the optical diffraction-based linear diameter measurement method, the problems of cumbersome measurement of tungsten wire diameter and poor statistical reliability in the prior art are solved, and high-precision, fast and stable linear diameter measurement is achieved, which is suitable for multiple times in the production process Measure demand.

CN119468948APending Publication Date: 2025-02-18XIAMEN WEISHKEN TESTING TECHNOLOGY CO LTD
View PDF 0 Cites 0 Cited by

Patent Information

Application Number
CN202411635808.7
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-11-15
Publication Date
2025-02-18

AI Technical Summary

Technical Problem

The existing tungsten wire diameter measurement methods are cumbersome to operate, have poor statistical reliability, and cannot be measured multiple times during the production process, which affects production efficiency and product quality.

Method used

Using a linear diameter measurement method based on optical diffraction, the optical diffraction image of the thin filament is obtained, analog-to-digital conversion sampling is performed, the effective band is extracted, the noise is denoised, and the trough spacing is found, and the trough spacing is calculated based on the relationship between the trough spacing and the filament line diameter is calculated.

Benefits of technology

High-precision, high speed and high stability line diameter measurement is achieved, which significantly improves the reliability and accuracy of measurement, and can perform multiple measurements quickly and accurately during the production process.

✦ Generated by Eureka AI based on patent content.

Smart Images

  • Figure CN119468948A_ABST
    Figure CN119468948A_ABST
Patent Text Reader

Abstract

The invention discloses a wire diameter measuring method based on optical diffraction. The wire diameter measuring method comprises the following steps: acquiring an optical diffraction image of a filament to be measured; performing analog-to-digital conversion sampling on the optical diffraction image to generate a first waveform signal; extracting an effective wave band from the first waveform signal to generate a second waveform signal; performing denoising processing on the second waveform signal to generate a third waveform signal; searching the position of each wave trough in the third waveform signal, and calculating the distance between adjacent wave troughs to obtain a plurality of wave trough distances corresponding to dark fringe distances; and determining the wire diameter of the filament according to the relationship between the trough spacing and the wire diameter of the filament. The measuring method can be used for measuring the diameter of the filament.
Need to check novelty before this filing date? Find Prior Art

Description

Technical Field

[0001] The invention relates to the technical field of wire diameter measurement, and in particular to a wire diameter measurement method based on optical diffraction. Background Art

[0002] At present, there are two main methods for measuring the wire diameter of tungsten wire:

[0003] One is the weighing method, which requires cutting a section of tungsten wire and weighing it, and then substituting the length and mass of the tungsten wire into the formula to calculate the average wire diameter of the section of tungsten wire. This method is cumbersome to operate, and in order to reduce production costs, there is no way to sample a large number of samples, and the sample should not be too long. Therefore, for tungsten wires that are thousands or tens of thousands of meters long, the statistical reliability of this measurement method is too poor.

[0004] The other is the geometric measurement method, which uses mechanical tools such as vernier calipers and micrometers, or precision optical instruments such as reading microscopes, tool microscopes, and Abbe length meters to directly measure the diameter of the tungsten wire. This measurement method has improved measurement accuracy compared to the weighing method, but this measurement method also cannot be performed during the production process and requires suspending the production machine. Therefore, multiple measurements cannot be performed in daily production, and the reliability of the statistical results is not high.

[0005] Therefore, a reliable method for measuring the diameter of a filament is urgently needed to solve the problems existing in the existing wire diameter measurement methods. Summary of the invention

[0006] The purpose of the present invention is to overcome the above-mentioned defects or problems existing in the background technology and to provide a wire diameter measurement method based on optical diffraction, which can measure the wire diameter of a filament.

[0007] To achieve the above object, the present invention adopts the following technical solution:

[0008] Technical solution 1: A wire diameter measurement method based on optical diffraction, which includes: obtaining an optical diffraction image of the filament to be measured; sampling the optical diffraction image through analog-to-digital conversion to generate a first waveform signal; extracting an effective band from the first waveform signal to generate a second waveform signal; denoising the second waveform signal to generate a third waveform signal; finding the position of each trough in the third waveform signal, and calculating the spacing between adjacent troughs to obtain multiple trough spacings corresponding to the dark line spacings; determining the filament diameter based on the relationship between the trough spacing and the filament diameter.

[0009] Technical solution two based on technical solution one: analyze the first waveform signal, determine the waveform peak positions corresponding to the two sides of the filament, and calculate two corresponding maximum values ​​based on the two waveform peaks, divide the first waveform signal by the maximum values ​​to obtain two valid bands, and select one of the valid bands as the second waveform signal.

[0010] Technical solution three based on technical solution one: adopt a smoothing filtering algorithm to denoise the second waveform signal to generate a third waveform signal.

[0011] Technical solution four based on technical solution three: The smoothing filtering algorithm includes the following steps: setting a window for data selection of the second waveform signal; calculating the average value of the data in the window, generating smoothed waveform data, and moving the window to the next position; repeating the average value calculation and window moving of the data in the window until the entire second waveform signal is processed.

[0012] Technical solution five based on technical solution one: adopt 3sigma filtering algorithm to denoise the second waveform signal to generate a third waveform signal.

[0013] Technical solution six based on technical solution five: The 3sigma filtering algorithm includes the following steps: setting a window for data selection of the second waveform signal; calculating the mean and standard deviation of the data in the window, and for each data point in the window, if its value exceeds the range of the mean plus or minus three times the standard deviation, replacing it with the mean; repeating the calculation of the mean and standard deviation of the data in the window and the replacement of data points until the entire second waveform signal is processed.

[0014] Technical solution seven based on technical solution one: adopt a sliding window algorithm to find the position of each trough in the third waveform signal, and calculate the spacing between adjacent troughs through a multiplication algorithm to obtain multiple trough spacings corresponding to the dark pattern spacings.

[0015] Technical solution eight based on technical solution seven: the trough spacing is obtained by the following steps: setting a window for data selection of the third waveform signal, and sliding the window on the third waveform signal to determine the local minimum value and index of the data in the window at different positions; forming a set of trough positions according to the indexes of all local minimum values; enlarging the window by logical recursion so that each window size is consistent, thereby obtaining the trough spacing.

[0016] Technical solution nine based on technical solution one: the filament diameter is calculated according to a predetermined binomial power fitting equation for representing the relationship between the trough spacing and the filament diameter.

[0017] Technical solution 10 based on technical solution 9: The binomial power fitting equation is determined by the following steps: obtaining optical diffraction images of multiple groups of filaments with known wire diameters, and obtaining multiple groups of trough spacings corresponding to filaments with different wire diameters based on the images; using the binomial power equation f(x)=a·x b +c for fitting, where x is the trough spacing, a, b, c are fitting coefficients, and f(x) is the filament diameter.

[0018] It can be seen from the above description of the present invention that, compared with the prior art, the present invention has the following beneficial effects:

[0019] The present invention provides a wire diameter measurement method based on optical diffraction. After acquiring the optical diffraction image of the filament to be measured, the measuring method first samples the optical diffraction image through analog-to-digital conversion to generate a first waveform signal, then extracts the effective band from the first waveform signal to generate a second waveform signal. The obtained second waveform signal has a lot of noise, so after the second waveform signal is denoised, a third waveform signal is generated, and then based on the third waveform signal, a plurality of trough spacings corresponding to the dark pattern spacings are obtained, and then the filament diameter is determined according to the relationship between the trough spacing and the filament diameter. The wire diameter measurement method provided by the present invention realizes high-precision, high-speed, and high-stability wire diameter measurement from acquiring the optical diffraction image to finally determining the filament diameter. In particular, through denoising and accurate calculation of the trough spacing, the reliability and accuracy of the measurement are significantly improved.

[0020] Among them, the denoising process makes the waveform smoother and the trough position clearer, thereby improving the accuracy of the trough spacing measurement. According to actual needs, different denoising algorithms can be selected, such as a smoothing filter algorithm or a 3sigma filter algorithm.

[0021] In addition, the sliding window algorithm finds the trough position by sliding a fixed-size window on the waveform signal, and the doubling algorithm continuously enlarges the window through recursive logic, making each window size close to the same, thereby quickly and accurately finding the trough spacing. This method significantly improves the speed of finding the trough position and shortens the measurement time.

[0022] In addition, by collecting multiple sets of trough spacing data and performing mean processing, the influence of random errors is reduced; the binomial power equation is used for fitting, and a standard filament with a known diameter is used for calibration to ensure the accuracy of the fitting equation. This method makes the measurement results more stable and the repeatability higher. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0024] Figure 1 A schematic diagram of a process flow of a wire diameter measurement method based on optical diffraction provided in an embodiment of the present invention;

[0025] Figure 2 is a schematic diagram of a first waveform signal in an embodiment;

[0026] Figure 3 is a schematic diagram of a third waveform signal in the embodiment;

[0027] Figure 4 A schematic diagram of calculating the trough spacing in the embodiment;

[0028] Figure 5 Graph of the binomial power fitting equation in the embodiment. DETAILED DESCRIPTION

[0029] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are preferred embodiments of the present invention and should not be regarded as excluding other embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0030] In the claims, description and the above-mentioned drawings of the present invention, unless otherwise clearly defined, the use of terms such as "first", "second" or "third" etc. are for distinguishing different objects rather than for describing a specific order.

[0031] In the claims, specification and the above-mentioned drawings of the present invention, unless otherwise explicitly defined, directional words, such as the terms "center", "lateral", "longitudinal", "horizontal", "vertical", "top", "bottom", "inside", "outside", "up", "down", "front", "back", "left", "right", "clockwise", "counterclockwise", etc., indicating directions or positional relationships are based on the directions and positional relationships shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific direction or be constructed and operated in a specific direction, and therefore cannot be understood as limiting the specific protection scope of the present invention.

[0032] In the claims, specification and the above drawings of the present invention, unless otherwise clearly defined, if the term "fixed connection" or "fixed connection" is used, it should be understood in a broad sense, that is, any connection method without a displacement relationship and relative rotation relationship between the two, that is to say, including non-detachable fixed connection, detachable fixed connection, integrated connection and fixed connection through other devices or elements.

[0033] In the claims, description and drawings of the present invention, if the terms "include", "have" and their variations are used, they are intended to mean "including but not limited to".

[0034] Laser diffraction measurement of wire diameter is a method for measuring the size of small objects based on the diffraction phenomenon of light. It is widely used in optical sensing, optical communication, computational imaging, laser beam shaping, biomedicine and optical data storage. When light waves encounter obstacles (small holes, hair, slits, fine needles, etc.) during propagation, the light will interact with the object to produce diffraction phenomena, forming a series of diffraction images. Taking tungsten wire as an example, its diffraction image is dark and bright lines that alternate between light and dark. We can obtain the diffraction image through array optoelectronic devices and convert the image into an electrical signal. Finally, through the software process pre-entered in the microprocessor, the distance between the bright and dark lines in the diffraction image can be calculated in real time, thereby obtaining the size of the filament.

[0035] An embodiment of the present invention provides a wire diameter measurement method based on optical diffraction, which can determine the wire diameter of a filament through an optical diffraction image.

[0036] Specifically, refer to Figure 1 , the line diameter measurement method based on optical diffraction provided by the embodiment of the present invention includes:

[0037] S100: Acquire an optical diffraction image of the filament to be tested.

[0038] S200: Sampling the optical diffraction image through analog-to-digital conversion to generate a first waveform signal;

[0039] S300: extracting a valid band from the first waveform signal to generate a second waveform signal;

[0040] S400: performing denoising processing on the second waveform signal to generate a third waveform signal;

[0041] S500: Find the position of each trough in the third waveform signal, and calculate the distance between adjacent troughs to obtain

[0042] a plurality of trough spacings corresponding to dark fringe spacings;

[0043] S600: Determine the diameter of the filament according to the relationship between the trough spacing and the diameter of the filament.

[0044] The above steps are further described below.

[0045] In step S100, when the tungsten wire production machine starts to operate, the laser emits a laser with a constant wavelength, and the light beam passes through the collimating lens and hits the moving tungsten wire. Since light has the characteristics of waves, when it encounters obstacles, it will interact with these objects, causing the wavefront to bend or diffuse, thereby forming an image with alternating light and dark stripes. This is the diffraction phenomenon, and thus a diffraction image appears. At the same time, when the light passes through an inhomogeneous medium, a part of the light will deviate from the original propagation direction and scatter, thereby forming a scattered image. Among them, the collimating lens refers to an instrument that can convert the light from each point in the aperture column into a parallel collimated light column. In this step, the received light signal can be converted into a continuous electrical signal by a photodetector.

[0046] In step S200, the analog-to-digital converter performs instantaneous sampling of the electrical signal in each sampling period to generate a series of sample values ​​at discrete time points; each sample value is then quantized to the closest discrete value, and the number of quantization bits determines the sampling accuracy; the quantized value is then converted into a binary codeword to generate a final digital waveform signal, which is the first waveform signal mentioned above. Figure 2 , which shows the first waveform signal. In this step, the appropriate sampling frequency and quantization bit number can ensure that the sampled digital signal can accurately reflect the changes in the original analog signal. Digital signal processing technology can effectively reduce the impact of noise and interference and improve the reliability of measurement. The digitized signal can be easily processed by subsequent digital signals, such as filtering, analysis and calculation. Through the above-mentioned analog-to-digital conversion sampling process, the present invention can obtain high-quality digital waveform signals from the optical diffraction image, providing a reliable basis for subsequent waveform analysis and filament diameter calculation.

[0047] In step S300, the process of extracting effective bands is to filter out the parts related to the measurement target from the complex waveform signal, thereby reducing noise and unnecessary information and improving the accuracy and efficiency of subsequent processing. The following is a specific process of extracting effective bands: analyzing the first waveform signal, determining the waveform peak positions corresponding to the two sides of the filament, and calculating two corresponding maximum values ​​according to the two waveform peaks, dividing the first waveform signal by the maximum value, obtaining two effective bands, and selecting one of the effective bands as the second waveform signal. Among them, it includes the following process: analyzing the waveform signal to find the maximum value position in the waveform. These positions usually appear at the waveform peaks on both sides of the obstruction (filament). According to the maximum value position found, determine the effective bands on both sides of the filament. Extract the selected effective band from the original waveform signal to generate a second waveform signal. Among them, the definition of local maximum value: let the array be data, the length be n, and the definition of local maximum value is: for a certain position i, if data[i]>data[i-1] and data[i]>data[i+1], then data[i] is a local maximum value. Index set of local maximum values: Let the index set of local maximum values ​​be E, then E = {i|1≤i≤n-2 and data[i]>data[i-1] and data[i]>data[i+1]}. Through step S300, the noise and irrelevant information in the waveform signal can be removed to improve the accuracy of subsequent processing. And only the bands related to the measurement target are processed, which reduces unnecessary calculations and improves the processing speed. At the same time, the selection of effective bands is based on the maximum position of the waveform, avoiding human intervention and improving the stability of the measurement results. Reference Figure 3 , which shows the second waveform signal.

[0048] In step S400, the selection of the effective band is based on the maximum position of the waveform, avoiding human intervention and improving the stability of the measurement result. The embodiment of the present invention provides two methods for denoising, namely a smoothing filter algorithm and a 3Sigma filter algorithm, which are described below.

[0049] The smoothing filtering algorithm includes the following steps: setting a window for data selection of the second waveform signal; calculating the average value of the data in the window to generate smoothed waveform data, and moving the window to the next position; repeating the average value calculation of the data in the window and moving the window until the entire second waveform signal is processed.

[0050] Specifically, let the array be data, the length be n, the window size be w, and the calculation formula for the i-th element of the smoothed data smoothedData be: Where i ranges from 0 to nw.

[0051] The 3sigma filtering algorithm includes the following steps: setting a window for data selection of the second waveform signal; calculating the mean and standard deviation of the data in the window, and for each data point in the window, if its value exceeds the range of the mean plus or minus three times the standard deviation, replacing it with the mean; repeating the calculation of the mean and standard deviation of the data in the window and the replacement of the data points until the entire second waveform signal is processed.

[0052] Specifically, let the array be data, the length be n, the window size be w, and the formula for calculating the mean within the window be: The formula for calculating the standard deviation within the window is: For each data point data[i], if data[i] is out of range, [μ i -3σ i ,μ i +3σ i ], then replace it with the mean μ i .

[0053] Reference Figure 4 , which is the third waveform signal obtained after denoising by a smoothing filtering algorithm.

[0054] In step S500, a sliding window algorithm is used to find the position of each trough in the third waveform signal, and the spacing between adjacent troughs is calculated by a doubling algorithm to obtain a plurality of trough spacings corresponding to the dark pattern spacings. The trough spacings are obtained by the following steps: setting a window for data selection of the third waveform signal, sliding the window on the third waveform signal, determining the local minimum value and index of the data in the window at different positions; forming a set of trough positions according to the indexes of all local minimum values; enlarging the window by logical recursion to make each window of the same size, thereby obtaining the trough spacing.

[0055] Specifically, the sliding window algorithm is as follows: let the array be data, the length be n, and the window size be w.

[0056] (1) Definition of sliding window: For each position i, the sliding window range is defined as

[0057] (2) Definition of local minimum: Find the minimum value min(data[j]) in the sliding window, where the range of j is

[0058] (3) Index set of local minimum values: M = {i|min(data[j]) = data[i] and

[0059] The doubling algorithm is as follows:

[0060] (1) Using recursive logic to calculate smooth data and local minimum values;

[0061] (2) Calculate the distances between adjacent troughs: Let the array be data, with a length of m, distances[i] = data[i+1]-data[i]; the range of i is 0 to m-2.

[0062] Thus, the trough spacings in the third waveform signal can be obtained, and the trough spacings correspond to the dark fringe spacings in the optical diffraction image.

[0063] In step S600, the diameter of the filament is calculated according to a predetermined binomial power fitting equation for representing the relationship between the trough spacing and the filament diameter. The binomial power fitting equation is determined by the following steps: obtaining multiple sets of optical diffraction images of filaments with known diameters, and obtaining multiple sets of trough spacings corresponding to filaments with different diameters based on the images; using the binomial power equation f(x)=a·x b +c for fitting, where x is the trough spacing, a, b, c are fitting coefficients, and f(x) is the filament diameter.

[0064] Specifically, when calculating the diameter of the filament, it is necessary to establish a binomial power fitting equation. The binomial power fitting equation requires selecting multiple groups of standard filaments with known diameters for measurement, and using the above steps S100 to S500 to perform optical diffraction measurements on each group of standard filaments to generate trough spacing data. Then, according to the trough spacing data and the diameter of the filament, it is substituted into the binomial power equation, the fitting coefficient is determined, and the final binomial power fitting equation is obtained. Figure 5 , which is a graph of the binomial power fitting equation. Afterwards, the filament to be measured is measured, and the data of the trough spacing is obtained according to the optical diffraction image, and is brought into the above binomial power fitting equation to obtain the wire diameter of the filament.

[0065] The present invention provides a wire diameter measurement method based on optical diffraction. After obtaining an optical diffraction image of a filament to be measured, the optical diffraction image is first sampled by analog-to-digital conversion to generate a first waveform signal, and then an effective band is extracted from the first waveform signal to generate a second waveform signal. The obtained second waveform signal has more noise, so after the second waveform signal is denoised, a third waveform signal is generated, and then based on the third waveform signal, a plurality of trough spacings corresponding to the dark ripple spacings are obtained, and then the filament diameter is determined according to the relationship between the trough spacing and the filament diameter. The wire diameter measurement method provided by the present invention realizes high-precision, high-speed and high-stability wire diameter measurement from obtaining an optical diffraction image to finally determining the filament diameter. In particular, through denoising and accurate calculation of the trough spacing, the reliability and accuracy of the measurement are significantly improved. Among them, the denoising makes the waveform smoother and the trough position clearer, thereby improving the accuracy of the trough spacing measurement. According to actual needs, different denoising algorithms can be selected, such as a smoothing filter algorithm or a 3sigma filter algorithm. In addition, the sliding window algorithm finds the trough position by sliding a fixed-size window on the waveform signal, and the doubling algorithm continuously enlarges the window through recursive logic, so that each window size is close to the same, so as to quickly and accurately find the trough spacing. This method significantly improves the speed of finding the trough position and shortens the measurement time. In addition, by collecting multiple sets of trough spacing data and performing mean processing, the influence of random errors is reduced; the binomial power equation is used for fitting, and calibration is performed with a standard filament of known diameter to ensure the accuracy of the fitting equation. This method makes the measurement results more stable and has higher repeatability.

[0066] The description of the above specification and embodiments is used to explain the protection scope of the present invention, but does not constitute a limitation on the protection scope of the present invention. Through the enlightenment of the present invention or the above embodiments, ordinary technicians in this field can obtain modifications, equivalent substitutions or other improvements to the embodiments of the present invention or part of the technical features thereof through logical analysis, reasoning or limited experiments, which should be included in the protection scope of the present invention.

Claims

1. A line diameter measurement method based on optical diffraction, characterized in that: include: Acquiring an optical diffraction image of the filament to be tested; The optical diffraction image is sampled by analog-to-digital conversion to generate a first waveform signal; Extracting a valid band from the first waveform signal to generate a second waveform signal; Performing denoising processing on the second waveform signal to generate a third waveform signal; Finding the position of each trough in the third waveform signal, and calculating the spacing between adjacent troughs to obtain a plurality of trough spacings corresponding to the dark pattern spacings; The diameter of the filament is determined according to the relationship between the trough spacing and the diameter of the filament.

2. A line diameter measurement method based on optical diffraction as claimed in claim 1, characterized in that: Analyze the first waveform signal to determine the waveform peak positions corresponding to the two sides of the filament, and calculate two corresponding maximum values ​​based on the two waveform peaks. Divide the first waveform signal by the maximum values ​​to obtain two effective bands, and select one of the effective bands as the second waveform signal.

3. The line diameter measurement method based on optical diffraction according to claim 1, characterized in that: A smoothing filtering algorithm is used to perform denoising processing on the second waveform signal to generate a third waveform signal.

4. A line diameter measurement method based on optical diffraction as claimed in claim 3, characterized in that: The smoothing filter algorithm comprises the following steps: Setting a window for data selection of the second waveform signal; The data in the window are averaged to generate smoothed waveform data, and the window is moved to the next position; the average value calculation and window movement of the data in the window are repeated until the entire second waveform signal is processed.

5. The line diameter measurement method based on optical diffraction according to claim 1, characterized in that: The 3sigma filtering algorithm is used to perform denoising on the second waveform signal to generate a third waveform signal.

6. A line diameter measurement method based on optical diffraction as claimed in claim 5, characterized in that: The 3sigma filtering algorithm includes the following steps: Setting a window for data selection of the second waveform signal; Calculate the mean and standard deviation of the data in the window. For each data point in the window, if its value is outside the range of the mean plus or minus three times the standard deviation, replace it with the mean. The calculation of the mean and standard deviation of the data in the window and the replacement of the data points are repeated until the entire second waveform signal is processed.

7. The line diameter measurement method based on optical diffraction according to claim 1, characterized in that: A sliding window algorithm is used to find the position of each trough in the third waveform signal, and the spacing between adjacent troughs is calculated by a multiplication algorithm to obtain a plurality of trough spacings corresponding to the dark pattern spacings.

8. The line diameter measurement method based on optical diffraction according to claim 7, characterized in that: The trough spacing is obtained by the following steps: setting a window for data selection of the third waveform signal, and sliding the window on the third waveform signal, Determine the local minimum values ​​and their indices of data in windows at different positions; According to the indices of all local minima, a set of trough positions is formed; The window is enlarged by logical recursion to make each window of the same size, thereby obtaining the trough spacing.

9. The line diameter measurement method based on optical diffraction according to claim 1, characterized in that: The filament diameter is calculated according to a predetermined binomial power fitting equation for representing the relationship between the trough spacing and the filament diameter.

10. A line diameter measurement method based on optical diffraction as claimed in claim 9, characterized in that: The binomial power fitting equation is determined by the following steps: Acquire multiple groups of optical diffraction images of filaments with known wire diameters, and obtain multiple groups of trough spacings corresponding to filaments with different wire diameters based on the images; Using the binomial power equation f(x) = a·x b +c for fitting, where x is the trough spacing, a, b, c are fitting coefficients, and f(x) is the filament diameter.