Remote plasma source quartz cavity bubble detection method and device

Abstract

The invention belongs to the technical field of remote plasma sources, and provides a remote plasma source reaction cavity bubble detection method and device. The method comprises the following steps: acquiring a quartz bubble image; identifying the edge contour of the bubble in the image; traversing the edge contour point set of all the bubbles based on Hough transform to obtain a circular image associated with the bubbles; updating the circular image to enable the circular image to be a minimum covering circle corresponding to the bubbles, and determining the number of the bubbles and the maximum diameter of the bubbles based on the circular image; and if the maximum diameter of the bubble is greater than a diameter threshold value, marking the bubble by using the circular image. According to the method, firstly, the circular image associated with the bubble is obtained based on Hough transform for the bubble edge contour, and then the circular image is updated to be the minimum coverage circle of the bubble, so that the number and the maximum diameter of bubble groups in a unit area can be efficiently and accurately identified online, and thus the process quality and reliability can be promoted to be improved; and the high-precision requirement of the remote plasma source quartz cavity is met.

Description

Technical Field

[0001] The present invention relates to the technical field of remote plasma sources, and in particular to a method and device for detecting bubbles in a quartz cavity of a remote plasma source. Background Art

[0002] A remote plasma source (RPS) is a device used to generate plasma and is widely used in the semiconductor, photovoltaic, and chemical industries. As a key device in semiconductor manufacturing, optical coatings, and specialty materials processing, the RPS's core component, a quartz chamber, is responsible for plasma generation and transmission. It is primarily used to dissociate gases like oxygen for etching processes like photoresist removal.

[0003] Quartz is widely used in RPS cavity manufacturing due to its high purity, high-temperature resistance, corrosion resistance, and excellent light transmittance. However, during the melt-molding process of quartz cavities, bubble defects (such as micron-sized pores or interlayer bubbles) are unavoidable. Under the high-temperature, high-frequency plasma load, these bubbles can cause structural failure, reduce process stability, and lead to the formation of particulate matter, reducing the lifespan and production efficiency of the RPS.

[0004] Due to the atomic arrangement and address factors in silicon ore, impurities such as iron and aluminum and bubble inclusions exist inside it. Under the action of high temperature and high pressure, impurities such as iron and aluminum will promote the crystallization of quartz sand. The quartz cavity manufactured by the process will have dense microbubbles with diameters of several to tens of μm at 1-2 mm on the inner surface. These microbubbles will continue to grow under high temperature conditions, which will directly affect the service life and mechanical strength of the RPS cavity. Therefore, how to effectively remove impurities and gas-liquid inclusions in quartz sand is crucial to the processing technology of RPS quartz cavity.

[0005] During the quartz cavity forming process, due to the extremely high temperatures, liquid inclusions on the quartz surface absorb and expand, causing bubbles and cracks on the cavity surface, affecting the cavity quality. Therefore, isomorphous metallic impurities and gas-liquid inclusions are generally considered the most important technical specifications for high-purity quartz sand used in quartz cavities. Therefore, to maintain the stability of quartz cavity quality, it is necessary to control the gas-liquid inclusions in the high-purity quartz sand used as the raw material for the quartz crucible to a low level.

[0006] In recent years, as semiconductor processes evolve toward higher precision and reliability, non-contact, high-resolution, in-line inspection technologies have become a research hotspot. Inspection solutions based on optical coherence tomography (OCT), laser-induced breakdown spectroscopy (LIBS), and machine vision have been gradually explored, but their stability in strong electromagnetic interference environments and adaptive imaging capabilities for complex curved surfaces remain challenging. Against this backdrop, developing a real-time, high-precision quartz cavity bubble detection system suitable for remote plasma source operation is crucial for improving equipment life and ensuring process consistency. It represents a technical challenge urgently needed to be overcome in the fields of intelligent manufacturing and advanced materials processing.

[0007] Current bubble detection technology for remote plasma source quartz cavities still faces the following key bottlenecks, hindering improvements in process quality and equipment reliability: 1) Inadequate offline detection and real-time performance. Mainstream detection methods (such as industrial CT scanning and ultrasonic testing) require disassembly of the cavity and offline operation, making in-situ real-time monitoring impossible during plasma process operation. 2) Limited sensitivity in micro-defect detection. For example, optical microscopy relies on surface transmittance, resulting in insufficient resolution for subsurface or deep-seated bubbles and susceptible to interference from optical path distortion caused by the cavity's curved surface structure. X-ray imaging: Although it can penetrate quartz, the density difference between micron-sized bubbles and the substrate is small, resulting in a low signal-to-noise ratio and the need for a high-power radiation source, raising safety and equipment cost issues. 3) Poor adaptability to complex working conditions. In the presence of electromagnetic interference, the high-frequency electromagnetic field generated by plasma excitation can easily interfere with traditional electronic sensors (such as capacitive probes), causing signal drift or misinterpretation. In high-temperature environments, the operating temperature of quartz cavities often exceeds 800°C. Conventional contact sensors (such as piezoelectric ultrasonic probes) cannot operate stably for a long time due to temperature limitations. Summary of the Invention

[0008] In view of the defects in the prior art, the present invention provides a method and device for detecting bubbles in a remote plasma source quartz cavity, so as to improve the reliability of bubble detection in the current remote plasma source reaction cavity.

[0009] In a first aspect, the present invention provides a method for detecting bubbles in a remote plasma source quartz cavity, comprising: Collect quartz bubble images; Identify the edge contours of bubbles in the image; Traverse the edge contour point set of all bubbles based on Hough transform to obtain the circular image associated with the bubble; updating the circular image so that the circular image is a minimum covering circle corresponding to the bubbles, and determining the number of bubbles and the maximum diameter of the bubbles based on the circular image; If the maximum bubble diameter is greater than the diameter threshold , the bubbles are marked with the circular image.

[0010] It can be seen from the above technical solution that the present invention provides a remote plasma source quartz cavity bubble detection method, which first obtains a circular image associated with the bubble based on the Hough transform for the bubble edge contour, and then updates the circular image to make it the minimum covering circle of the bubble. It can efficiently and accurately identify the number and maximum diameter of bubble groups per unit area online, thereby promoting the improvement of process quality and reliability and meeting the high-precision requirements of the remote plasma source quartz cavity.

[0011] Optionally, before identifying the edge contour of the bubble in the image, the method further includes performing Gaussian filtering and histogram equalization processing on the quartz bubble image.

[0012] Optionally, the edge contour of the bubble is obtained by identifying based on fusion morphology, including: Open operation eliminates small noise; Convert the input quartz bubble image from a grayscale image to a binary image to determine the hole area; Extract the boundary pixels of each hole and obtain the pixel average value of the boundary pixels; Fill the holes inside the bubble using the average pixel value; The filled image and the original grayscale image are subjected to difference processing to obtain the edge contour of the bubble.

[0013] Optionally, traversing the edge contour point sets of all bubbles based on the Hough transform to obtain a circular image associated with the bubbles includes: Traverse the edge point set of the edge contour to obtain the diameter of the bubble contour and the center coordinates The circular image is is the center of the circle, is a circular area with a diameter of .

[0014] Optionally, updating the circular image so that the circular image is the minimum covering circle of any bubble includes: Update the center coordinates of circular images based on simulated annealing particle swarm optimization and radius weight ; The standard equation of the obtained circular image in Cartesian space is , the constraint condition is that the circular image is the minimum covering circle of the quartz bubble outline.

[0015] Optionally, the bubble image is updated based on the simulated annealing particle swarm algorithm to obtain the optimal radius step weight of the circle center. ,include: According to the initial parameters of each circular image And the initial population parameters of the simulated annealing particle swarm algorithm, calculate the fitness of each particle; When the particle fitness satisfies the constraint conditions, determining whether the particle fitness is less than the optimal fitness; When the particle fitness is less than the current optimal fitness, the particle fitness is updated; Compare the individual optimal fitness of each particle with the optimal fitness of the group in turn to obtain the optimal fitness of the group under the current number of iterations; Update the position information of each particle and repeat the above steps until the number of iterations reaches , get the center coordinates and radius weight.

[0016] Optionally, if the particle fitness is not less than the current optimal fitness, the method further includes: According to the probability S and The size relationship between the two determines whether to update the current non-optimal solution to the optimal fitness of the particle individual; the probability , is the fitness of particle j, is the optimal fitness of particle j, To set the maximum number of iterations for optimization, T is the current number of iterations; When S is greater than When , the non-optimal solution is updated to the optimal solution, otherwise the individual optimal fitness remains unchanged; is any random constant in the interval [0,1].

[0017] Optionally, it also includes triggering an alarm according to a preset threshold, If the maximum diameter of the bubble exceeds the preset mark threshold, an alarm for the maximum diameter of the bubble is triggered; If the number of bubbles exceeds the preset bubble number threshold, an excessive bubble number alarm is triggered.

[0018] In a second aspect, the present invention provides a remote plasma source reaction chamber bubble detection device, comprising: An acquisition module, used for acquiring quartz bubble images; A recognition module, used to recognize the edge contours of bubbles in the image; An edge point traversal module is used to traverse the edge contour point sets of all bubbles based on Hough transform to obtain a circular image associated with the bubble; an updating module, configured to update the circular image so that the circular image becomes a minimum covering circle corresponding to the bubbles, and determine the number of bubbles and the maximum diameter of the bubbles based on the circular image; The marking module is configured to mark the bubble with the circular image if the maximum diameter of the bubble is greater than a diameter threshold.

[0019] By adopting the above technical solution, this application has the following beneficial effects: The present invention first obtains a circular image associated with the bubble based on the Hough transform for the bubble edge contour, and then updates the circular image to make it the minimum covering circle of the bubble. It can efficiently and accurately identify the number and maximum diameter of bubble groups per unit area online, thereby promoting the improvement of the quality and reliability of the cavity preparation process and meeting the high-precision requirements of the remote plasma source quartz cavity. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following briefly describes the drawings required for the specific embodiments or the description of the prior art. Similar elements or parts are generally identified by similar reference numerals throughout the drawings. Elements or parts in the drawings are not necessarily drawn to scale.

[0021] Figure 1 A flow chart showing a method for preparing a remote plasma source quartz cavity provided by an embodiment of the present invention is shown; Figure 2 A flow chart showing waste liquid recycling provided by an embodiment of the present invention is shown; Figure 3 A flow chart of a method for detecting bubbles in a quartz cavity of a remote plasma source provided by an embodiment of the present invention is shown; Figure 4 The flowchart of the simulated annealing particle swarm algorithm provided by the embodiment of the present invention is shown; Figure 5 A circular image schematic diagram showing a method for detecting bubbles in a quartz cavity of a remote plasma source provided by an embodiment of the present invention is shown; Figure 6 A schematic diagram showing the detection effect of a remote plasma source quartz cavity bubble detection method provided by an embodiment of the present invention is shown; Figure 6 (a) is a schematic diagram of a group of collected circular bubbles. Figure 6 (b) Figure 6 (a) is a partial enlarged view. Figure 6 (c) Figure 6 (b) Schematic diagram of the maximum bubble diameter and scanning position; Figure 7 A flow chart of a remote plasma source quartz cavity bubble elimination control method provided by an embodiment of the present invention is shown; Figure 8 A flowchart showing the importance of predicting the number of gas groups and the maximum diameter using random forest regression provided by an embodiment of the present invention is shown; Figure 9 A flowchart of decision tree construction provided by an embodiment of the present invention is shown; Figure 10 A schematic diagram showing the importance of process parameters to bubble data provided by an embodiment of the present invention is shown; Figure 11 A schematic diagram of coupling importance provided by an embodiment of the present invention is shown; Figure 12 A flowchart of a method for optimizing and updating membership weights provided by an embodiment of the present invention is shown; Figure 13 A diagram showing the recognition effect of bubbles using the Hough transform provided by an embodiment of the present invention; Figure 13 (a) is a comparison chart of the predicted and actual values ​​of the number of bubbles in a unit area. Figure 13 (b) Comparison of the predicted and actual values ​​of the maximum bubble diameter; Figure 14 A comparison diagram of quartz cavities prepared by practical dynamic process optimization provided by an embodiment of the present invention is shown; Figure 14 (a) is the actual detection effect diagram of the quartz cavity obtained before process optimization. Figure 14 (b) is the actual detection effect diagram of the quartz cavity obtained after process optimization. DETAILED DESCRIPTION

[0022] The following embodiments of the technical solution of the present invention will be described in detail with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention and are therefore only examples and are not intended to limit the scope of protection of the present invention. It should be noted that, unless otherwise specified, the technical or scientific terms used in this application should have the common meanings understood by those skilled in the art to which the present invention belongs.

[0023] like Figure 1 As shown, a method for preparing a remote plasma source quartz cavity is provided, which includes ore dressing, followed by calcination, cleaning, grinding, dehydration, secondary calcination, microwave, acid washing, water washing, flotation, dehydration, dissolution, finishing and coating steps; The mineral processing steps are as follows: first, manually sorting the quartz sand raw material, selecting quartz sand with SiO2 content ≥ 99% as the raw material, controlling the particle size range to 0.1-0.2 mm, removing the quartz sand with visible impurities and foreign matter, washing and crushing it, washing it until there is no obvious impurity, and then drying it; The calcining step comprises: first, evacuating a quartz sand calcining furnace and preheating it to 600°C, and introducing a Cl2 and HCl mixed gas into the quartz sand calcining furnace at a flow rate of 50-60 ml / min, then placing the silicon ore into the quartz sand calcining furnace, continuing to heat the calcining furnace to 900°C, calcining at 900-1000°C for 0.5 hours, further raising the temperature in the furnace to 1200°C and maintaining the temperature for 60 minutes, then removing the calcined quartz sand from the furnace and cooling it to room temperature; under the high temperature condition, the quartz sand causes Cl2 to react with impurity ions, and the produced gaseous salts are removed from the microcracks of the quartz crystal, thereby achieving a purification effect; The cleaning step comprises: washing the quartz sand calcined in the previous step with deionized water (calibrated to 7.0 by a pH meter), wherein the conductivity of the pure water is not greater than 10 μs / cm, and the washing time is controlled within 2 minutes, after removing impurities visible to the naked eye; The grinding step comprises: placing the cleaned silicon ore material in the wet grinding mill and grinding it to 140-200 mesh; subjecting the ground quartz sand to magnetic separation in a magnetic separator with a magnetic field strength of 100-5000 GS to remove magnetic impurities; The dehydration step comprises: sending the quartz sand collected in the previous step into a centrifuge for dehydration, and drying it at 100-200° C. for 1 hour to reduce the water content of the quartz sand to less than 0.1%; The second calcination step comprises: mixing 400-450 ml of potassium bifluoride or sodium bifluoride and 100-120 ml of sodium chloride into each kilogram of quartz sand at a liquid-to-solid ratio of 5:1; and after uniform mixing, calcining the mixture under a vacuum environment at a pressure of 1.6 MPa and a reaction temperature of 200-220° C. for 3-4 hours; washing the quartz sand with deionized water and drying it at 200-300° C. for 2-3 hours to reduce the water content of the quartz sand to no more than 0.1%. The pressurized high-temperature leaching method can reduce the consumption of the salt solution, and the obtained quartz sand has a smaller particle size. The extremely high pressure causes the quartz sand to break, making it easier to remove impurities and gas-liquid inclusions in the quartz sand. The microwave step comprises: heating the quartz sand with microwaves to 500° C. under the action of microwaves, setting the power to 800W, the frequency to 50-70 kHz, and the duration to 30 minutes; performing microwave-assisted leaching, utilizing the selective heating characteristics of microwaves to enable the slurry to better absorb the microwave energy and heat rapidly, and utilizing the difference in dielectric constants between different materials to rapidly heat and vaporize the gas-liquid inclusions in the quartz sand, thereby achieving removal of the gas-liquid inclusions; The pickling step comprises: adding microwave-treated quartz sand to a pickling reactor, introducing an acid solution prepared by mixing 78% concentrated hydrofluoric acid solution, 60% concentrated hydrogen chloride solution, 98% concentrated nitric acid solution, 35% concentrated hydrochloric acid solution, and deionized water in a volume ratio of 2:1:1:8:15 at room temperature using a magnetic stirrer at a stirring speed of 1000 r / min, and maintaining stirring for 3 to 4 hours, filtering and separating the quartz sand to remove metal oxides; and converting the concentrated hydrofluoric acid, hydrogen chloride, or other volatile acid directly added to the pickling solution into a salt that can generate the corresponding acid during the calcination process. The high temperature condition can cause the salt to decompose or react with each other to generate acidic gas, and the gas molecules can enter the pores of the quartz sand. By effectively controlling the calcination temperature and time, the acidic gas is fully diffused into the cracks or pores on the surface of the quartz sand.

[0024] The water washing step comprises: after the pickling is completed, draining the acid solution in the pickling reactor, adding deionized water to wash 4 to 6 times until the pH of the material in the pickling reactor is neutral after adding deionized water, and releasing the quartz sand from the reactor; The flotation process is as follows: adding washed quartz sand into a flotation machine, then adding deionized water with a conductivity of no more than 10 μs / cm to adjust the pulp concentration in the flotation machine to 40% to 50%, and then starting flotation according to the following steps: ① Use hydrochloric acid or sulfuric acid to adjust the pH of the pulp to 2.0-3.0, add 180g / L dodecylamine hydrochloride solution and 120g / L xanthate as anionic and cationic collector and stir for 5 minutes, add 200g / L sodium hexametaphosphate as quartz inhibitor and stir for 5 minutes, then float for 20 minutes. After flotation, wash the quartz sand in the flotation machine with deionized water. ② Use sulfuric acid, hydrofluoric acid and hydrochloric acid in a mass ratio of 1:1:5 to adjust the pH of the pulp to 2.0-3.0, add mixed flotation agents: 130-150g / L ammonia water, 130-150g / L ammonium fluoride, 25-50g / L oleic acid, 15-20g / L cresol acid, 20-30g / L isobutanol, 15-30g / L sodium dodecylbenzene sulfonate, stir for 5 minutes, then add 60g / L octadecylamine hydrochloride solution as collector and adjust the pulp for flotation for 20 minutes; Repeat the flotation process of ① to ② above 2 to 3 times, then wash the flotated quartz sand with deionized water until the pH value is neutral before discharging; In view of the difference in floatability of different minerals, different capture agents are used for secondary flotation. The optimized secondary flotation can further reduce the content of heavy metal impurities in quartz sand and remove associated minerals such as feldspar and mica. The dehydration step comprises: sending the quartz sand collected in the previous step into a centrifuge for dehydration, and drying it at 100-200° C. for 1 hour to reduce the water content of the quartz sand to less than 0.1%; The dissolving step is as follows: adding the cleaned and dried quartz sand into a high-temperature furnace for melting, and carrying out the melting in the high-temperature furnace at 1400-1600°C for 30 minutes; The finished product steps are as follows: the melted liquid quartz sand is sprayed into the mold through a sprayer, and then compressed and compacted by a compacting machine; the compacted quartz sand needs to be naturally or artificially cooled and annealed at room temperature to stabilize it at room temperature; the cooled quartz cavity needs to be cut and polished to meet the requirements of the finished product.

[0025] The coating process comprises the following steps: the cooled quartz cavity is washed and dried, then placed in a coating reactor, heated to 900-1000°C, and kept warm. After evacuating the coating reactor, a high-purity inert gas is introduced for 20 minutes to remove any residual air. At a temperature of 900-1000°C and under vacuum conditions, methane or acetylene gas is introduced into the coating reactor for 2-3 hours. After coating, the cavity is evacuated again, and after cooling to room temperature, air is introduced to atmospheric pressure, and the carbon-coated quartz cavity is removed. By directly coating the quartz cavity with a carbon film using methane or acetylene gas as a carbon source under vacuum conditions, a uniform, smooth, and dense carbon film layer can be formed on the entire inner and outer walls of the quartz cavity.

[0026] like Figure 2 As shown, the volatilized gases from the second calcination are collected and recycled by recrystallization of the fluorine-containing sodium salt; the filtrate from the pickling is centrally treated and recycled in the pickling step; the flotation step removes associated minerals such as feldspar and mica from the quartz sand, and the filtered wastewater is recycled three times. This not only avoids corrosion to the flotation equipment and the introduction of corrosive impurities, but also facilitates the recycling of the fluorine-containing wastewater after flotation treatment, reducing wastewater treatment pressure. In semiconductor or photovoltaic processes, bubbles within the quartz chamber of a remote plasma source can affect its mechanical strength, thermal stability, and optical properties.

[0027] The secondary calcination method is adopted in the preparation process, and the pressurized high-temperature leaching can reduce the consumption of salt solution. The obtained quartz sand has a smaller particle size. The extremely high pressure causes the quartz sand to break, making it easier to remove impurities and inclusions in the quartz sand. The process of the present invention can more completely remove impurities such as iron and aluminum, and the impurity removal is more thorough.

[0028] The volatilized gases from the second calcination are collected and recycled through recrystallization of the fluorine-containing sodium salt. The filtrate from the pickling process is centrally treated and recycled back to the pickling step. The flotation step removes associated minerals such as feldspar and mica from the quartz sand, and the filtered wastewater is recycled three times. This not only avoids corrosion to the flotation equipment and the introduction of corrosive impurities, but also facilitates the recycling of the fluorine-containing wastewater after flotation treatment, reducing the burden on wastewater treatment.

[0029] The above preparation method can effectively remove the gas-liquid inclusions in the quartz cavity and improve the quality of the quartz cavity; but how to determine the degree of bubble defects in the quartz cavity, on this basis, Figure 3 As shown, a remote plasma source quartz cavity bubble detection method is provided, comprising: S110. Capture an image of the quartz bubble. Use a high-resolution industrial camera (e.g., a 20-megapixel CCD) with a magnification of 20-200x. Set the lighting conditions to backlight or coaxial illumination to enhance the contrast between the bubble edge outline and the background pixels.

[0030] Before executing step S120 , the method further includes performing Gaussian filtering and histogram equalization processing on the quartz bubble image.

[0031] First, filtering is performed based on the Gaussian function. The core idea is to perform weighted averaging on the image through the Gaussian function, effectively suppressing noise while retaining edge information. The expression is as follows: (1) Where (x, y) is the offset of the pixel coordinate relative to the center of the filter kernel; is the standard deviation that controls the smoothing strength of the filter kernel, The larger it is, the blurrier the image will be. Histogram equalization is then used to increase contrast. The fundamental idea behind histogram equalization is to adjust the pixel distribution of the original image, resulting in a higher dynamic range for the equalized image. Assume the grayscale values ​​of the original image are f(x,y)=s, and after histogram enhancement, they become g(x,y)=t. Histogram enhancement can then be transformed into finding a transformation function that satisfies t=T(s). This requires two conditions: T(s) is monotonically increasing within the range 0 ≤ s ≤ L-1, and when 0 ≤ s ≤ L-1, 0 ≤ T(s) ≤ L-1.

[0032] The cumulative distribution function of the grayscale s of the original image can convert the distribution of s into a uniform distribution of t, which is expressed as: (2) After bubble image preprocessing, edge-enhanced images are obtained.

[0033] S120. Identify the edge contour of the bubble in the image.

[0034] Bubble edge detection and identification are performed using fused morphological processing. This fused morphological processing eliminates small noise points through an opening operation followed by an erosion followed by an expansion operation. It then fills the holes inside the bubbles using a closing operation. The holes are then compared with the surrounding pixels and filled using an algorithm based on the similarity of the surrounding holes. Assuming A is the original image and B is the selected structural element, the expansion operation of the structural element on the original image can be defined as (3) represents the reflection set of the structural element B, Represents the empty set.

[0035] Correspondingly, the erosion operation of the original image by the structural element can be defined as (4) Opening and closing operations are generated by combining the basic operations erosion and dilation; The opening operation is to first select the structural element to corrode the original image, and then perform an expansion operation on the result after corrosion, which is defined as: (5) The closing operation fills the holes inside the bubble and can be defined as: (6) Step S120 specifically includes: S121. Open operation to eliminate small noise points; S122. Convert the input quartz bubble image from a grayscale image to a binary image to determine the hole area; that is, pixels greater than the pixel threshold are set to 1, pixels less than or equal to the pixel threshold are set to 0, and the area with a pixel value of 1 and surrounded by pixel values ​​of 0 is the location of the hole.

[0036] S123. Extract each hole boundary pixel point, determine whether the pixel values ​​of multiple hole boundaries are similar, that is, the error is less than the pixel similarity threshold, and obtain the pixel average value of the boundary pixel points.

[0037] By selecting the structural element B in formula (6) for the target hole area, the combined operation of morphological processing can extract the approximate boundary of the quartz cavity bubble image.

[0038] S124. Fill the holes inside the bubble using the pixel average value.

[0039] S125. Perform differential processing on the filled image and the original grayscale image to obtain the edge contour of the bubble. If the pixel value of the area surrounding the quartz bubble is lower than that of the center of the bubble, it is identified as background. Perform differential comparison processing on the filled image and the original grayscale image to accurately obtain the edge contour of the bubble.

[0040] S130. Traverse the edge contour point sets of all bubbles based on Hough transform to obtain a circular image associated with the bubbles.

[0041] Traverse the edge point set of the edge contour to obtain the diameter of the bubble contour and the center coordinates ; The circular image is is the center of the circle, is a circular area with a diameter of .

[0042] The Hough transform is an image processing technique used to detect features of any shape in an image. The main idea is to transform from image space to parameter space and then find statistical peaks in the parameter space to detect features.

[0043] The standard equation of the circular bubble image in Cartesian space can be expressed as: (7) Where (x0, y0) is the coordinate of the center of the circle; (x, y) is the coordinate of any point on the circle; r is the initial radius of the circular image, is the maximum diameter of the final bubble contour, where In circular image detection, the three-dimensional Hough space (x0, y0, r) is first established. In order to convert the pixel points (x, y) on the circumference of the image into the parameter space (x0, y0, r), Equation (7) can be rewritten as: (8) in, It is the angle between the straight line from the pixel point (x, y) on the circumference to the center of the circle (x0, y0) and the horizontal axis.

[0044] like Figure 13 As shown in (a) and (b), the determination of the number of bubbles and the maximum diameter of bubbles based on Hough transform is verified. Figure 13 The linear fitting slope between the predicted value and the actual value of the number of bubbles in the unit area in (a) is 0.89, and the overall prediction accuracy of the surface model is high, with a root mean square error (RMSE) of 0.8. Figure 13 The linear fitting slope between the predicted value and the actual value of the maximum bubble diameter in (b) is 0.91, and the root mean square error (RMSE) is 11.2 μm, which proves that the Hough transform can meet the prediction accuracy requirements in complex actual working conditions.

[0045] Before performing the Hough transform, a continuous image of the quartz bubble is obtained by image acquisition in step S110 , and a discretized image of the continuous image is obtained after preprocessing by Gaussian filtering and histogram equalization, and an array set of image edges is obtained.

[0046] S140. Update the circular image so that the circular image is the minimum covering circle of the corresponding bubble, and determine the number of bubbles and the maximum diameter of the bubbles based on the circular image.

[0047] In order to improve the algorithm to solve the optimal radius step size of each circular image To ensure accuracy and rapid convergence, a simulated annealing mechanism is introduced as a condition for the particle swarm algorithm to determine whether to update the individual and group optimal solutions. This mechanism allows the particle swarm algorithm to iterate with a certain probability of escaping the local optimal solution, thereby improving the reliability of the algorithm in finding the global optimal solution during iteration and reducing the number of iterations.

[0048] The radius weight is updated using a method based on simulated annealing particle swarm optimization. , so that the radius step size The circular image formed by the circle center (x0, y0) can just cover the quartz bubble, where the center of the circle is located at the center point of the maximum diameter.

[0049] Update the center coordinates of circular images based on simulated annealing particle swarm optimization and radius weight ; The standard equation of the obtained circular image in Cartesian space is , the constraint condition is that the circular image is the minimum covering circle of the quartz bubble outline.

[0050] like Figure 4 As shown, step S140 includes: S141. Based on the initial parameters of each circular image And the initial population parameters of the simulated annealing particle swarm algorithm, calculate the fitness of each particle; S142. When the particle fitness satisfies the constraint condition, determine whether the particle fitness is less than the optimal fitness.

[0051] The position information corresponding to each particle in the particle swarm algorithm represents a solution to the objective function. The fitness of each particle is the objective function value under the position information of the particle. Each particle iterates through the speed and position transformation strategy, constantly approaches the optimal position, and obtains the optimal solution. The particle swarm algorithm updates the position and speed information of each particle. The update formula is: (9) (10) Where j is the particle number; is the position information of particle j; is the optimal position of particle j up to the Ith generation; is the optimal position of all particles up to the Ith generation; in, is the individual learning factor; is the global learning factor, which reflects the information exchange between particle swarms; for A random constant between is the inertia weight, used to adjust Exploration optimization capability, related to the number of iterations, inertia weight The calculation formula is: (11) in, 、 are the maximum and minimum values ​​of the inertia weight respectively; To set the maximum number of iterations for optimization.

[0052] S143. When the particle fitness is less than the current optimal fitness, update the particle fitness; When the particle fitness is greater than the current optimal fitness, a simulated annealing mechanism is introduced, and the Metropolis sampling criterion is used to determine whether the particle fitness should be updated to the optimal fitness. That is, the Metropolis sampling criterion is used to calculate the probability S and Compare the random constants between and determine whether the current non-optimal solution should enter the next step, so as to ensure that it will not fall into the local optimum. The algorithm is described as (12) is the fitness of particle j, is the optimal fitness of particle j.

[0053] When S is greater than one When S is a random constant between , the non-optimal solution is updated to the optimal solution; when S is less than the random constant, the original optimal solution remains unchanged.

[0054] S144. Compare the individual optimal fitness of each particle with the optimal fitness of the group in turn, and obtain the optimal fitness of the group under the current number of iterations; S145. Update the position information of each particle and repeat S141-S144 until the number of iterations is , get the center coordinates and radius weight.

[0055] S150. If the maximum diameter of the bubble is greater than the diameter threshold , mark the bubbles with circular images.

[0056] Also included: S160. triggering an alarm according to a preset threshold; If the maximum diameter of the bubble exceeds the preset mark threshold, an alarm for the maximum diameter of the bubble is triggered; If the number of bubbles exceeds the preset bubble number threshold, an excessive bubble number alarm is triggered.

[0057] See also Figure 5 The circular image formed by the optimal diameter step 2λr updated in step S140 can just cover a group of bubble group images, indicating that the diameter step 2λr is the maximum diameter of the bubble group. ; Identify the center of a circular image The number of bubble groups per unit area can be calculated, that is, the center set of circular images within the unit area The number n represents n bubble groups per unit area. Figure 6, a set of circular bubble group feature points were obtained under the 200x field of view per unit area, and the maximum diameter of the observation area was 111.8μm. The bubble detection algorithm can meet the requirements of online collection of the number and maximum diameter of bubble groups under engineering conditions.

[0058] In one embodiment, a remote plasma source reaction chamber bubble detection device is provided, comprising: An acquisition module, used for acquiring quartz bubble images; A recognition module, used to recognize the edge contours of bubbles in the image; An edge point traversal module is used to traverse the edge contour point sets of all bubbles based on Hough transform to obtain a circular image associated with the bubble; an updating module, configured to update the circular image so that the circular image becomes a minimum covering circle corresponding to the bubbles, and determine the number of bubbles and the maximum diameter of the bubbles based on the circular image; The marking module is configured to mark the bubble with the circular image if the maximum diameter of the bubble is greater than a diameter threshold.

[0059] The remote plasma source reaction cavity bubble detection device provided in the embodiment of the present application adopts the same inventive concept as the above-mentioned remote plasma source reaction cavity bubble detection method and can achieve the same beneficial effects, which will not be described in detail here.

[0060] Based on the above bubble detection results, such as Figure 7 As shown, a remote plasma source quartz cavity bubble elimination control method is also provided, comprising: S210. Obtain bubble data of the quartz cavity, including the number of bubbles and the maximum diameter of the bubbles. Specific bubble data can be obtained using the above-mentioned bubble detection method. After data acquisition, it is also necessary to obtain initial process parameters, including calcination temperature T and duration t, vacuum pressure P, annealing cooling rate V l , stirring speed V p , raw material purity s and other process parameters as input features, the above remote plasma source quartz cavity bubble detection method is used to output the target in real time, that is, the number of bubble groups per unit area M and the maximum diameter of the bubble group D as the target variables; the continuous variables are normalized by Z-score: (13) S220. Based on the random forest algorithm, obtain the importance of different process parameters to each bubble data.

[0061] Based on the historical operating process parameter data obtained above, after data preprocessing, an array set of the number of bubble groups, the maximum diameter and the process parameters is constructed; The random forest algorithm, due to its dual randomness of random sampling and random feature selection—data sampling and feature selection—restrains overfitting. It performs well on datasets, is robust to noise, is less susceptible to overfitting, and is adaptable to high-dimensional data. It can also quantify the importance of input variables to target values, providing a theoretical basis for feature engineering. Variable importance E is calculated by analyzing the out-of-bag error (E(OOB)): (14) Among them, p is the number of Bootstrap sampling, Represents the feature The out-of-bag error after random permutation, is the original out-of-bag error. The larger the E value of a feature, the more important it is to the target variable. Random forest regression predicts the importance of the number of gas groups and the maximum diameter, such as Figure 8 As shown, the steps are as follows: S221.Bootstrap Sampling From the original data set D, T subsample sets {D1, D2, ..., DT} are extracted with replacement, and the sample size of each subset is N. The probability P(N) of each sample being selected in a single sampling is: (15) Then, the samples that are not selected constitute the out-of-bag dataset OOB, which is used for error estimation and feature importance analysis.

[0062] S222. Random selection of features Let the total number of features be M t , for each subset D t ,like Figure 9 As shown, construct a regression decision tree h t (x), randomly select m features (m≤M t ).

[0063] The goal of node splitting in regression tree is to minimize the mean square error (MSE). For feature j and splitting threshold and RR(j,s), select the optimal split pair (j * ,s * ): (16) Among them, RL and RR are the left and right child node sample sets after splitting, c L and c R are the predicted values ​​of the left and right child nodes respectively. That is, the target mean of the subset samples: (17) S223. Prediction result integration The prediction mean of all decision trees is used as the final output, and ensemble learning is used to reduce the uncertainty of single tree predictions. The final output is as follows: (18) in, is the average result; is the prediction result of a single decision tree; T is the number of decision trees.

[0064] S224. Model performance evaluation indicators The root mean square error (RMSE) indicator is used to quantify the accuracy of predicting the number of bubble groups and the maximum diameter per unit area: (19) Determine whether the root mean square error between the number of bubble groups per unit area and the maximum diameter meets the error accuracy requirement, that is, it is less than or equal to the bubble group number error threshold M R and the maximum diameter error threshold D of the bubble group R ; Otherwise, return to step P1 and continue iterating until the maximum number of iterations is reached; S225. Feature Importance Assessment Analysis Feature importance is measured by the change in out-of-bag (OOB) error after permuting the feature value. After randomly permuting feature Xj, its importance is measured by the change in out-of-bag error. If the error increases significantly after permutation, it indicates that the feature has a significant impact on the model prediction. Importance is calculated as follows: (20) Among them, MSE t is the OOB error of the t-th tree.

[0065] On this basis, the predicted mean of all decision trees is used as the final output to fit the number of bubbles per unit area M and the maximum bubble diameter D of quartz bubbles formed by the combination of process parameters, and the importance of each process parameter to the number of bubble groups and the maximum bubble diameter is ranked.

[0066] By collecting and inputting historical operating process parameter data and outputting the number and maximum diameter of bubble groups per unit area in step S210, it can be seen that the relationship between the importance of each process parameter to the number and maximum diameter of bubbles is expressed as follows: 1) The higher the vacuum degree, the easier it is to extract the gas dissolved in the fused quartz, and the diameter of the bubble group is significantly reduced. In other words, the number and diameter characteristics of the bubble group are negatively correlated with the vacuum degree; 2) The lower the purity of the raw material, the more gas will be released, which will significantly increase the number and diameter of the bubble groups. In other words, the number and diameter of the bubble groups are negatively correlated with the purity of the raw material; 3) Increasing the calcination temperature reduces the viscosity of the quartz melt, promotes gas diffusion and escape, and is beneficial to reducing the number of bubble groups. However, if the temperature continues to rise, local overheating is likely to occur, which in turn generates large bubbles and results in bubble groups with excessively large diameters. In other words, the number of bubble groups is negatively correlated with the calcination temperature, while the bubble group diameter is positively correlated with the calcination temperature. 4) If the calcination time is too short, the gas does not fully escape, and a large number of small bubbles remain, resulting in an excessive number of bubble groups. If the calcination time is too long, the quartz melt crystallizes, causing small bubbles to merge and an alarm indicating that the maximum bubble diameter is too large. In other words, the number of bubble groups is negatively correlated with the calcination time, while the bubble group diameter is positively correlated with the calcination temperature. 5) A faster cooling rate (such as quenching process) can inhibit the merging of bubbles to form larger bubbles, but will retain more small bubbles and increase the number of bubble groups; slow cooling (such as annealing process) allows bubbles to continue to escape and merge, reducing the number of bubbles but increasing the average diameter; that is, the number characteristics of bubble groups are positively correlated with the cooling rate, while the bubble group diameter characteristics are negatively correlated with the cooling rate; 6) Faster stirring speeds can break up bubbles and promote their upward flow. However, too fast a stirring speed can introduce shear forces, breaking large bubbles into small ones, reducing the diameter of the bubble groups. This, in turn, traps air in the quartz melt, increasing the number of small bubbles. This means that the number of bubble groups is positively correlated with the stirring speed, while the diameter of the bubble groups is negatively correlated with the stirring speed. Based on the importance of different process parameters to each bubble data point obtained in step S220, the process can be optimized for situations where the number of bubble groups is excessive and the maximum diameter is too large. In actual operating conditions, the raw material purity is relatively fixed. However, considering the economic and practical requirements of high vacuum, vacuum calcination technology is used to increase the pressure to raise the vacuum level to a fixed set value, forcing gas removal. Therefore, in the optimization process, this embodiment adjusts the calcination temperature, calcination time, stirring speed, and cooling rate to adjust the number of bubbles and the maximum diameter.

[0067] Therefore Figure 10 As shown in the figure, the importance of different process parameters to each bubble data is as follows: The importance of different process parameters on the number of bubbles is as follows: when the raw material purity remains unchanged, the parameters of vacuum degree, calcination temperature and calcination time have the highest influencing factors; The importance of different process parameters to the maximum diameter of bubbles is as follows: when the raw material purity remains unchanged, the parameters of vacuum degree, stirring speed and cooling rate have the highest influencing factors.

[0068] When the bubble detection method is used, step S160 triggers an alarm indicating excessive bubble numbers, i.e., the number of bubble groups is large but the diameter is small, and since the calcination temperature and calcination time are the most influential factors, the optimization process is to increase the calcination temperature by 10% for the first and second calcinations, respectively, and extend the calcination time by 15%; Similarly, when an alarm is detected indicating that the bubble group diameter is too large, that is, the number of bubble groups is small but the diameter is large, the stirring speed and cooling rate are the most influencing factors. The process optimization is as follows: in the pickling step, the mechanical stirring rate and stirring time need to be increased by 20% to break up the bubbles and promote floating and discharge; the annealing process adopts gradient cooling annealing, and the high temperature is quickly cooled at 15°C / min to shorten the high temperature holding time and reduce the chance of bubble merging; the medium and low temperature are slowly cooled to reduce residual stress and assist in the escape of tiny bubbles.

[0069] If the alarms of excessive number of bubble groups and excessive diameter are detected at the same time, that is, the number of bubble groups is large and the diameter is large; the importance of the bubble data needs to be comprehensively considered and the process parameters should be adjusted according to the coupling importance.

[0070] S230. Integrate the importance of each bubble data to obtain the coupling importance.

[0071] Specifically, the coupling importance degree is obtained based on the center of gravity method.

[0072] Output Find the centroid value of each element and its corresponding membership degree in and get the output x.

[0073] Among them, A1 and A2 are the importance of vacuum degree corresponding to the number and diameter of bubble groups; B1 and B2 are the importance of calcination temperature corresponding to the number and diameter of bubble groups; C1 and C2 are the importance of stirring speed corresponding to the number and diameter of bubble groups; D1 and D2 are the importance of cooling rate corresponding to the number and diameter of bubble groups; E1 and E2 are the importance of calcination time corresponding to the number and diameter of bubble groups; F1 and F2 are the importance of raw material purity corresponding to the number and diameter of bubble groups; (twenty one) in, is the central value of the membership function interval corresponding to the output quantity, for The corresponding membership degree.

[0074] Furthermore, if Figure 11 As shown in the figure, the coupling importance is manifested as follows: when the vacuum level and raw material purity remain unchanged, the calcination temperature and stirring speed have the highest parameter influence factors. In other words, the calcination temperature is the key parameter affecting the number of bubble groups, and the stirring speed is the key parameter affecting the maximum diameter of the bubble groups.

[0075] S240. Establish an error objective function regarding the number of bubbles M and the maximum diameter D, and optimize and update the membership weights of the number of bubbles M and the maximum diameter D.

[0076] The number of bubbles detected M is respectively related to the maximum bubble diameter D and the bubble number threshold M s , maximum diameter threshold D s Make a difference, then the error objective function (twenty two) is the bubble number error threshold, is the maximum bubble diameter error threshold, 、 are the membership weights of the number of bubbles and the maximum diameter of bubbles, respectively.

[0077] like , it means that the number of bubbles exceeds the threshold and the membership weight of the bubble number M needs to be updated first. ,like , it means that the maximum diameter of the bubble exceeds the threshold and the membership weight of the maximum diameter of the bubble D needs to be updated first. .

[0078] Membership weight 、 The optimization update method of , specifically using genetic algorithm, such as Figure 12 Shown, including: 1) Population initialization Initialize the population parameters for the first time, that is, input the bubble number data set , bubble maximum diameter dataset and process parameter data sets, and initialize the membership weights 、 ; 2) Fitness calculation Based on the parameter population that arranges the process parameters, a fitness function suitable for population iteration that can measure the quality of solutions or individuals, i.e., the objective function, is established. The fitness value of the population function is evaluated and calculated step by step to obtain the most suitable individual for survival (i.e., the individual with the optimal weight). 3) Select operation Based on the basic idea of ​​"survival of the fittest," selection operators are applied to the population. The goal is to pass on the superior genes of individuals with higher fitness values ​​to the next generation through inheritance or crossover. In other words, individuals with higher fitness values ​​are retained, while those with lower fitness values ​​are eliminated to ensure survival.

[0079] 4) Crossover operation The crossover operator is applied to the population. After the "selection operation", two chromosomes are randomly selected from the new individual for recombination, combining the excellent feature information with each other and thus inheriting it to the new individual.

[0080] 5) Mutation operation The purpose of applying the mutation operator to the population is to reduce the probability of the algorithm falling into local optimality while ensuring the diversity of chromosome types. That is, some changes are made to the gene value of a certain locus of the individual strings in the population to produce a population with higher fitness value.

[0081] 6) Termination condition judgment In the evolutionary iterative process, the termination condition is judged to be the objective function value F, that is, formula (22) is less than or equal to the target threshold , when the individual with the maximum fitness value is obtained, the optimal solution is output and the operation can be terminated; the membership weight of the optimal solution is output.

[0082] S250. Compare the optimized membership weights with the corresponding initial values ​​to obtain the rate of change of each process parameter per unit time; S260. Based on the error rate relationship between the number of bubbles M and the maximum diameter D, the process is dynamically optimized according to the rate of change of the process parameters.

[0083] when When the process is optimized, the rate of change per unit time of the first and second calcination temperatures is ; when When the process is optimized, the stirring speed increases and the rate of change per unit time is ; and It is obtained by calculating the rate of change of the optimized membership weight compared to the initial value.

[0084] Based on this, the calcination temperature is avoided from rising too quickly. Although it is beneficial to the diffusion and escape of gas and the reduction of the number of bubble groups, it is easy to cause local overheating, which in turn generates large bubbles and causes the bubble groups to have too large diameters. The faster the stirring speed, the larger bubbles are broken into small bubbles, making the bubble group diameter smaller, but it causes air to be trapped in the quartz melt, increasing the number of small bubbles.

[0085] The dynamic optimization effect of the process is verified as follows.

[0086] Figure 14 (a) and (b) are the actual detection effect diagrams of the quartz cavity obtained before and after process optimization. Figure 14In (a), three groups of circular bubble feature points are obtained under 200x field of view per unit area. The maximum diameters of the observation area are 137.02μm, 105.13μm, and 86.98μm, respectively. The density of circular feature points is about 3.8 particles / cm 2 ; Figure 14 In (b), a set of circular bubble feature points is obtained under 200x field of view per unit area. The maximum diameter of the observation area is 12.33μm, and the density of circular feature points is about 0.1 particles / cm 2 It can be seen that the number and diameter of bubbles in the quartz cavity are reduced, and the dynamic optimization of the process obviously meets the requirements of the preparation process.

[0087] Table 1

[0088] Furthermore, during the beneficiation stage of the preparation process, the same raw material was subjected to three separate preparation processes. The resulting quartz chambers were then fully analyzed for chemical elements using the JC / T2027-2010 "Determination of impurity content in high-purity quartz—Inductively coupled plasma atomic emission spectrometry." The main impurity elements found in the test results are shown in Table 1.

[0089] As can be seen from Table 1, the purity of the quartz cavity product obtained after three preparation and purification processes is very high. The total impurity content can be reduced to below 100 ppm, the partial Al content can be reduced to below 20 ppm, the Fe content can be reduced to below 0.5 ppm, and the SiO2 content can reach above 99.99%.

[0090] The above-described embodiments merely represent several implementation methods of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that a person skilled in the art could make various modifications and improvements without departing from the spirit of the present application, all of which fall within the scope of protection of the present application. Therefore, the scope of protection of the present patent application shall be determined by the appended claims.

Claims

1. A method for detecting bubbles in a remote plasma source reaction chamber, characterized in that: include: Collect quartz bubble images; Identify the edge contours of bubbles in the image; Traverse the edge contour point set of all bubbles based on Hough transform to obtain the circular image associated with the bubble; updating the circular image so that the circular image is a minimum covering circle corresponding to the bubbles, and determining the number of bubbles and the maximum diameter of the bubbles based on the circular image; If the maximum bubble diameter is greater than the diameter threshold , the bubbles are marked with the circular image.

2. The method according to claim 1, characterized in that Before identifying the edge contour of the bubble in the image, the method further includes performing Gaussian filtering and histogram equalization processing on the quartz bubble image.

3. The method according to claim 2, wherein the edge contour of the bubble is identified and obtained based on fusion morphology, comprising: Open operation eliminates small noise; Convert the input quartz bubble image from a grayscale image to a binary image to determine the hole area; Extract the boundary pixels of each hole and obtain the pixel average value of the boundary pixels; Fill the holes inside the bubble using the average pixel value; The filled image and the original grayscale image are subjected to difference processing to obtain the edge contour of the bubble.

4. The method according to claim 1, wherein The step of traversing the edge contour point sets of all bubbles based on the Hough transform to obtain a circular image associated with the bubbles includes: Traverse the edge point set of the edge contour to obtain the diameter of the bubble contour and the center coordinates The circular image is is the center of the circle, is a circular area with a diameter of .

5. The method according to claim 4, characterized in that The updating of the circular image so that the circular image is the minimum covering circle of any bubble includes: Update the center coordinates of circular images based on simulated annealing particle swarm optimization and radius weight ; The standard equation of the obtained circular image in Cartesian space is , the constraint condition is that the circular image is the minimum covering circle of the quartz bubble outline.

6. The method according to claim 5, characterized in that The optimal radius step weight of the bubble image is updated based on the simulated annealing particle swarm algorithm ,include: According to the initial parameters of each circular image And the initial population parameters of the simulated annealing particle swarm algorithm, calculate the fitness of each particle; When the particle fitness satisfies the constraint conditions, determining whether the particle fitness is less than the optimal fitness; When the particle fitness is less than the current optimal fitness, the particle fitness is updated; Compare the individual optimal fitness of each particle with the optimal fitness of the group in turn to obtain the optimal fitness of the group under the current number of iterations; Update the position information of each particle and repeat the above steps until the number of iterations reaches , get the center coordinates and radius weight.

7. The method according to claim 6, characterized in that If the particle fitness is not less than the current optimal fitness, the method further includes: According to the probability S and The size relationship between the two determines whether to update the current non-optimal solution to the optimal fitness of the particle individual; the probability , is the fitness of particle j in the current iteration, is the optimal fitness of particle j, To set the maximum number of iterations for optimization, T is the current number of iterations; When S is greater than When , the non-optimal solution is updated to the optimal solution, otherwise the individual optimal fitness remains unchanged; is any random constant in the interval [0,1].

8. The method according to claim 1, characterized in that It also includes triggering alarms based on preset thresholds, If the maximum diameter of the bubble exceeds the preset mark threshold, an alarm for the maximum diameter of the bubble is triggered; If the number of bubbles exceeds the preset bubble number threshold, an excessive bubble number alarm is triggered.

9. A remote plasma source reaction chamber bubble detection device, characterized in that: include: An acquisition module, used for acquiring quartz bubble images; A recognition module, used to recognize the edge contours of bubbles in the image; An edge point traversal module is used to traverse the edge contour point sets of all bubbles based on Hough transform to obtain a circular image associated with the bubble; an updating module, configured to update the circular image so that the circular image becomes a minimum covering circle corresponding to the bubbles, and determine the number of bubbles and the maximum diameter of the bubbles based on the circular image; The marking module is configured to mark the bubble with the circular image if the maximum diameter of the bubble is greater than a diameter threshold.

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