A method for predicting the thickness of a depletion layer of a quartz crucible based on single-point detection

Abstract

The application discloses a quartz crucible air bubble layer thickness area prediction method based on single-point detection, and the air bubble layer detection model is constructed by improving the YOLO11 network, the quartz crucible profile samples with different thicknesses and different bubble distributions are trained, and the two-dimensional position, size, quantity and key frame confidence of bubbles are output frame by frame; the starting frame, the ending frame and the end frame of the super-transparency layer are accurately positioned through confidence constraint and statistical prior compensation; based on the key frame number, the axial position calibrated by the pulse signal is combined to calculate the total thickness of the super-transparency layer, the spreading domain and the transparent layer; the three-dimensional construction is completed by combining the two-dimensional position of the bubbles with the axial position frame by frame. The to-be-measured area is divided into a plurality of grid areas according to a preset grid, and is adaptively classified into three categories of a mouth edge, a straight wall and an R corner, a discrete thickness field is constructed through differential interpolation, and the continuous transparent layer thickness distribution of the to-be-measured area is predicted and reconstructed through a deep network, thereby providing data support for the quality evaluation of the crucible.

Description

Technical Field

[0001] This invention belongs to the technical field of quartz crucible manufacturing and service performance evaluation, specifically relating to a method for predicting the thickness of the void layer in a quartz crucible based on single-point detection. Background Technology

[0002] The double-layer composite quartz crucible is the core melting vessel in the single-crystal silicon pulling process, and its structural stability and internal surface quality directly determine the growth quality of the single-crystal silicon. This crucible consists of a bubble-depleted layer and a bubble composite layer. The bubble-depleted layer, as the functional layer in direct contact with the molten silicon, is further divided into an ultra-transparent layer and a propagation domain. The ultra-transparent layer is located on the inner side of the crucible, has high purity and few bubbles, while the propagation domain, as a transition region, has more bubbles. The thickness and boundary definition of these two layers directly affect the service life of the crucible and the stability of single-crystal silicon production.

[0003] In the large-scale production of monocrystalline silicon, the thickness of the bubble depletion layer is a critical quality control step before the crucible leaves the factory. If the depletion layer thickness is insufficient or the boundary definition is inaccurate, bubbles in the bubble composite layer will diffuse into the depletion layer and rupture during high-temperature service, causing oxygen to escape into the silicon melt and disrupting crystal growth. Therefore, accurately detecting the thickness of the bubble depletion layer and the characteristics of the bubbles within it is crucial for ensuring the quality of monocrystalline silicon production.

[0004] Current methods for detecting bubble void layers have significant drawbacks: traditional methods such as spectral analysis and microscopic observation rely on specialized equipment and environments, resulting in complex processes, low efficiency, and an inability to meet the needs of batch testing in production settings; even the video-based detection solution proposed by our team in the past relies on simple rules for void layer boundary frame identification, without combining the image features of the start and end frames of the bubble void layer, which can easily lead to inaccurate thickness detection due to incorrect boundary frame positioning, and can only achieve single-point thickness measurement, failing to reflect the thickness distribution differences in different areas such as the crucible rim, straight wall, and R-angle, making it difficult to truly characterize the overall quality of the crucible.

[0005] In summary, existing technologies suffer from inaccurate layer boundary frame positioning and insufficient thickness detection accuracy. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to provide a method for predicting the thickness of the void layer in a quartz crucible based on single-point detection, which addresses the shortcomings of the prior art. The method is novel and reasonable in design, convenient to operate, accurate in detection, and easy to promote and use.

[0007] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0008] A method for predicting the thickness of the depletion layer in a quartz crucible based on single-point detection includes the following steps:

[0009] S1. Acquire single-point profile images;

[0010] The handheld measuring instrument is attached to the detection point on the inner wall of the crucible. A red ring light source illuminates the local area where the detection point is located. The servo motor drives the camera to move at a constant speed along the thickness direction of the crucible to acquire continuous cross-sectional images of the local area. At the same time, the servo motor pulse signal is collected to calibrate the axial position of each frame.

[0011] S2. Keyframe detection of depletion layer in single-point profile image;

[0012] The continuous profile images obtained in step S1 are input into the trained bubble void layer detection model. This model is built based on an improved YOLO11 network and trained using sample images of bubble void layer profiles from quartz crucibles with different thicknesses and bubble distributions. The two-dimensional position, size, number, and keyframe confidence of the bubbles are output frame by frame. Based on the confidence constraints and statistical prior compensation, the start and end frames of the void layer in this region are determined. The total two-dimensional area of ​​the bubbles in each frame within the two-frame interval is calculated, and the frame corresponding to the maximum value is taken as the end frame of the super-transparent layer.

[0013] S3, Single-point thickness calculation;

[0014] Based on the key frame number determined in step S2, and combined with the pulse signal in step S1, determine the axial position of each frame, and calculate the ultra-transparent layer thickness, the spread domain thickness, and the total transparent layer thickness at the detection point.

[0015] S4, 3D bubble construction;

[0016] Based on the two-dimensional positions of the bubbles output frame by frame in step S2, the three-dimensional size, number, and spatial distribution of the bubbles are determined in combination with the axial positions of each frame.

[0017] S5, Prediction of regional transparent layer thickness;

[0018] Repeat steps S1 to S4 to divide the area to be tested into several grid regions according to a preset grid, obtain the thickness data of the corresponding detection points in each grid region, adaptively divide each grid region into three categories: crucible rim, straight wall, and R-angle, and perform differential interpolation on the thickness data of each category to construct a discrete thickness field; then predict, reconstruct, and output the continuous transparent layer thickness distribution of the area to be tested through a deep network.

[0019] Furthermore, the improved YOLO11 network includes a backbone network, a neck network, and a head detection head;

[0020] The backbone network replaces the original convolutional downsampling module with the ADown downsampling module;

[0021] The neck network is a MSENeck multi-scale enhanced feature fusion structure, including a WFU wavelet upsampling module and a C3k2 module. The neck network adopts a skip connection structure to deeply fuse the WFU upsampling output with the feature maps of different levels extracted by the C3k2 module.

[0022] The detection head is used to simultaneously output the critical boundary frames of the depletion layer and the bubble detection results.

[0023] Furthermore, the ADown downsampling module first performs 2×2 average pooling, and then inputs the complete feature map in parallel into two branches: the first branch is processed by max pooling and convolution in sequence, and the second branch is processed by direct convolution; the output features of the two branches are then concatenated along the channel dimension.

[0024] Furthermore, the WFU wavelet upsampling module performs wavelet transform on the input features, decomposing them into low-frequency approximate components and three high-frequency components, and processes them in parallel between the high-frequency branch and the low-frequency branch:

[0025] The high-frequency branch adds the three high-frequency components and then performs feature enhancement through convolution and residual modules;

[0026] The low-frequency branch concatenates and convolves the low-frequency approximation component with the next-scale feature map after convolution processing to achieve feature fusion and channel adjustment.

[0027] The two outputs are spliced ​​together by channel and then reconstructed into a high-resolution feature map through inverse wavelet transform.

[0028] Furthermore, the bounding box regression branch IoU calculation layer of the detection head embeds parallel calculation modules of InnerIoU and MPDIoU in a weighted manner to replace the original IoU loss;

[0029] The expression for the parallel computing module is:

[0030]

[0031]

[0032]

[0033] in, The minimum point distance intersection-union ratio metric. IMPDIoU is the internal intersection-union ratio metric. and The composite crossover ratio loss metric For the prediction box, For the true frame, This is a bounding box scaling operator that, based on the center point of the detection box, performs synchronous and proportional scaling operations on the width and height of the predicted box and the ground truth box. For scaling hyperparameters, These are the minimum bounding box width and height of the predicted bounding box and the ground truth bounding box, respectively. The distance between the top-left corners of the predicted bounding box and the ground truth bounding box is the Euclidean distance. The distance between the bottom right corners of the predicted bounding box and the ground truth bounding box is the Euclidean distance. This is an area calculation function used to calculate the pixel area of ​​the region within the brackets.

[0034] Furthermore, in step S2, the process of determining the start and end frames of the depletion layer is as follows:

[0035] Based on the keyframe confidence of each frame of the bubble depletion layer output by the bubble depletion layer detection model, the frame with the highest confidence of the depletion layer start frame is taken as the candidate frame of the depletion layer start frame, and the frame with the highest confidence of the depletion layer end frame is taken as the candidate frame of the depletion layer end frame.

[0036] If the confidence level of a candidate frame is greater than or equal to the set confidence threshold, it is directly output as a key frame; if the confidence level of a candidate frame is less than the set confidence threshold, statistical prior is introduced for compensation.

[0037] The compensation rule is as follows: for the starting frame of the depletion layer, the position of the starting frame of the depletion layer is inferred by superimposing the historical average offset based on the first frame with bubbles in the continuous profile image of the detection point; for the ending frame of the depletion layer, the position of the ending frame of the depletion layer is inferred by superimposing the corresponding historical average span based on the determined starting frame of the depletion layer.

[0038] Further, in step S2, the two-dimensional total area sequence of the bubbles is smoothed using a moving average. The expression for the moving average smoothing is:

[0039]

[0040] in, For the smoothed first The first scan sequence The total two-dimensional area of ​​the bubble in the frame. Half the width of the window , The total two-dimensional area of ​​the bubble before smoothing. This is the frame offset index within the window.

[0041] Furthermore, in step S3, the formula for calculating the thickness of the ultra-transparent layer is:

[0042]

[0043] in, For the first The thickness of the ultra-transparent layer corresponding to each scan sequence. For the first End frame of the super-transparent layer in the scan sequence, For the first The starting frame of the super-transparent layer in the scan sequence, The axial propulsion speed of the motor. For camera acquisition rate, This is the refractive index correction factor;

[0044] The formula for calculating the thickness of the spread domain is:

[0045]

[0046] in, No. The thickness of the spread region corresponding to each scan sequence. For the first End frame of the spread domain in the scan sequence;

[0047] The formula for calculating the total thickness of the transparent layer is:

[0048]

[0049] in, For the first The total thickness of the transparent layer corresponding to each scan sequence, the starting frame of the supertransparent layer is the starting frame of the depletion layer, and the ending frame of the spread domain is the ending frame of the depletion layer.

[0050] Furthermore, in step S4, the process of constructing the three-dimensional bubble is as follows:

[0051] The axial depth of each frame is determined based on the axial position determined by the pulse signal. The two-dimensional image coordinates of the bubble and the axial depth are combined into three-dimensional spatial coordinates. After DBSCAN clustering and fusion of repeated detection of adjacent frames, the three-dimensional distribution of the bubble is constructed, and the three-dimensional size, number and spatial position information of the bubble are output.

[0052] Further, in step S5, the adaptive partitioning process is as follows: based on the servo motor's propulsion distance and the spatial three-dimensional coordinates obtained by the camera's field of view, the geometric curvature of the crucible's inner surface is calculated, thereby classifying each grid region into the rim region, straight wall region, and R-corner region and assigning region labels;

[0053] The differential interpolation process employs a hybrid interpolation model formed by inverse distance weighting and Kriging joint interpolation, the expression of which is:

[0054]

[0055] in, For testing points The thickness estimate at that location, For the thickness of the grid region, The distance between grid cells. For Kriging weights, For balance coefficient, For region labels, The inverse distance-weighted power controls the distance decay rate. The total number of grid regions participating in the interpolation; the semi-variogram model is dynamically matched according to the region label, the isotropic spherical model is used for the straight wall region, the anisotropic Gaussian model is used for the R-corner region, and the exponential model is used for the edge region;

[0056] The process of deep network prediction and reconstruction is as follows: the discrete thickness field obtained by hybrid interpolation is processed by PointKAN to extract the region-aware features, and then input into the U-Net adaptive deep network integrating Transformer; combined with the category of each grid region and gradient constraints, the continuous transparent layer thickness distribution of the region to be tested is output.

[0057] Compared with the prior art, the present invention has the following advantages:

[0058] This invention constructs a bubble void layer detection model by setting an improved YOLO11 network and trains it using cross-sectional images of quartz crucibles with different thicknesses and bubble distributions. It abandons the original suggestion identification method that only relies on the appearance and disappearance of bubbles, and uses the model to accurately identify the image features of key frames of void layers. Combined with key frame confidence constraints and statistical prior compensation mechanisms, it achieves accurate positioning of the void layer start frame, end frame, and super-transparent layer end frame, thus avoiding misjudgment of layer boundary frames from the root.

[0059] Based on the key frame number determined by the model and the axial position of each frame calibrated by the servo motor pulse signal, the total thickness of the ultra-transparent layer, the spread domain, and the transparent layer is calculated. By coordinating the pulse signal and motion parameters for correction, motion errors and optical refraction errors are offset to ensure the accuracy of single-point thickness calculation.

[0060] By detecting the two-dimensional position, size, and number of bubbles frame by frame, and combining the axial position of each frame to complete the three-dimensional construction of the bubbles, the accurate acquisition of the two-dimensional features and three-dimensional spatial distribution of the bubbles is achieved. At the same time, the total two-dimensional area of ​​the bubbles is used as one of the criteria for determining the end frame of the ultra-transparent layer, providing more comprehensive data support for crucible quality assessment.

[0061] By dividing the test area into several grid regions according to a preset grid, adaptively classifying them into three categories: edge, straight wall, and rounded corner, and differentially interpolating the thickness data for each category, the problem of insufficient detection points is compensated for. Then, a deep network is used to predict and reconstruct the continuous transparent layer thickness distribution of the test area, accurately characterizing the spatial non-uniformity of the depletion layer thickness, providing a scientific basis for the overall quality assessment of the crucible, and adapting to the quality control needs of large-scale production in the monocrystalline silicon industry. The technical solution of this invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0062] Figure 1 This is a flowchart illustrating an embodiment of the present invention.

[0063] Figure 2 This is a schematic diagram of the ADown downsampling module structure according to an embodiment of the present invention.

[0064] Figure 3 This is a schematic diagram of the WFU upsampling module structure according to an embodiment of the present invention.

[0065] Figure 4 This is a schematic diagram of an improved YOLO11 network structure according to an embodiment of the present invention.

[0066] Figure 5 This is a flowchart illustrating the thickness detection process according to an embodiment of the present invention.

[0067] Figure 6 This is a schematic diagram of the crucible depletion layer structure according to an embodiment of the present invention.

[0068] Figure 7 This is a schematic diagram of the depletion layer start frame according to an embodiment of the present invention.

[0069] Figure 8 This is a schematic diagram of the end frame of the ultra-transparent layer in an embodiment of the present invention.

[0070] Figure 9 This is a schematic diagram of the end frame of the spread domain according to an embodiment of the present invention.

[0071] Figure 10 This is a schematic diagram of the depletion layer start frame features according to an embodiment of the present invention.

[0072] Figure 11 This is a schematic diagram of the depletion layer end frame features according to an embodiment of the present invention.

[0073] Figure 12 This is a schematic diagram of the handheld measuring instrument according to an embodiment of the present invention.

[0074] Explanation of reference numerals in the attached figures:

[0075] 1. Rubber base; 2. Ring light source; 3. Telecentric lens; 4. Camera; 5. Cooling fan; 6. Servo motor; 7. Stop button; 8. Hand grip; 9. Start button. Detailed Implementation

[0076] Example of a region prediction method for quartz crucible depletion layer thickness based on single-point detection:

[0077] like Figures 1-12 As shown, the method for predicting the thickness of the vacancy layer in a quartz crucible based on single-point detection includes the following steps:

[0078] S1. Acquire single-point profile images;

[0079] The staff member grasps the handheld handle 8 and places the handheld measuring instrument against the inner wall of the crucible for detection. The red ring light source 2 illuminates the area, and the servo motor 6 drives the camera 4 to move at a constant speed along the thickness direction of the crucible to acquire continuous cross-sectional images of the local area. At the same time, the pulse signal data emitted by the servo motor 6 in real time is collected to calibrate the axial position of each frame.

[0080] like Figure 12 As shown, the handheld measuring instrument includes: a handheld main body shell for housing various functional modules and easy for operators to hold with one or two hands; a rubber base 1 for non-destructive contact with the inner wall of the crucible; a ring light source 2 using longer wavelength red light for better penetration of the crucible's transparent layer; a telecentric lens 3 for increasing optical magnification while preventing image distortion; a high-speed industrial camera 4 for quickly and stably acquiring continuous images along the crucible's thickness direction; a stepper motor for driving the camera 4 and telecentric lens 3 at a constant speed while continuously emitting pulses for high-precision calculation of the advancing distance; a cooling fan 5 for reducing the temperature of the handheld device; a start button 9 for starting the light source, motor, and camera 4; and a stop button 7 for pausing the light source, motor, and camera 4.

[0081] S2. Keyframe detection of depletion layer in single-point profile image;

[0082] like Figure 5 As shown, the continuous profile images obtained in step S1 are input into the trained bubble void layer detection model. This model is built based on an improved YOLO11 network and trained using sample images of bubble void layer profiles from quartz crucibles with different thicknesses and bubble distributions. The model outputs the two-dimensional position, size, number, and keyframe confidence of the bubbles frame by frame. Based on the aforementioned confidence constraints and statistical prior compensation, the starting and ending frames of the void layer in this region are determined. The total two-dimensional area of ​​the bubbles in each frame within the two-frame interval is calculated, and the frame corresponding to the maximum value is taken as the ending frame of the super-transparent layer. The starting frame of the bubble void layer is shown below. Figure 10 As shown, it often exhibits characteristics such as white spots, scratches, black spots, bumps, bubbles, crystal powder, and water stains; the bubble-deficient layer ends as shown in the following frame. Figure 11 As shown, a distinct sponge-like structure exists.

[0083] like Figure 4 As shown, the improved YOLO11 network includes a backbone network, a neck network, and a head detection head. It should be noted that... Figure 4The green conv represents a 3×3 convolution operation. ADown is the downsampling module added in this invention. C3k2 is the original feature extraction module in YOLOv11. The light blue C3k2 in the main trunk represents the inactive hyperparameter state, and the orange C3k2 in the neck represents the activated hyperparameter state. SPPF is the original feature pyramid, C2PSA is the original deep feature extraction module, the yellow conv represents a 1×1 convolution operation, WFU is the wavelet upsampling module added in this invention, concat represents the tensor concatenation operation, Detect represents the original detection head, and the green arrow represents the ADown downsampling module, while the black arrow represents the copy operation.

[0084] Specifically, the backbone network replaces the original convolutional downsampling module with an ADown downsampling module; as follows: Figure 2 As shown, the ADown downsampling module first performs 2×2 average pooling to retain more spatial details; then the complete feature map is input into two branches in parallel: the first branch is processed by max pooling and convolution in sequence to enhance subtle features; the second branch is processed by direct convolution; the output features of the two branches are concatenated along the channel dimension to provide richer context and detail information. Figure 2 In this context, AvgPool2d represents two-dimensional average pooling, Chunk represents tensor splitting, conv represents 3×3 convolution, MaxPool2d represents two-dimensional max pooling, and concat represents tensor concatenation.

[0085] like Figure 3 As shown, the neck network is a multi-scale enhanced feature fusion structure (MSENeck), comprising a WFU wavelet upsampling module and a C3k2 module. The neck network employs a skip connection structure to deeply fuse the WFU upsampling output with feature maps from different levels extracted by the C3k2 module. The skip connection structure is inspired by the skip connection structures of MAF-YOLO and U-Net.

[0086] Among them, such as Figure 3 As shown, the WFU (Wavelet-FeatureUpsampler) wavelet upsampling module processes the input features. Perform WT wavelet transform to decompose into low-frequency approximate components. With three high-frequency components The process is divided into high-frequency and low-frequency branches for parallel processing. The high-frequency branch adds the three high-frequency components and performs feature enhancement through convolution and residual modules to enhance edge and texture features. The low-frequency branch combines the low-frequency approximate components with the next-scale feature map after convolution. The two outputs are concatenated and convolved to achieve feature fusion and channel adjustment, thereby supplementing low-frequency context information and adjusting the number of channels to match the needs of subsequent concatenation. The two outputs are then concatenated by channel and reconstructed into a high-resolution feature map by inverse wavelet transform. . Figure 3 middle There are three high-frequency components, representing details in the diagonal, vertical, and horizontal directions respectively. Residual Block represents the residual operation, IWT represents the inverse wavelet transform operation, High-frequency indicates the path used to process high-frequency components, Enhanced indicates enhancement, and Low-frequency indicates the path used to process low-frequency components.

[0087] The neck network first upsamples high-level features using the WFU module to restore spatial resolution, and then fuses them with feature maps extracted from different levels by C3k2 to achieve deep interaction of multi-scale and multi-semantic features. This design preserves high-frequency details while also taking into account multi-scale semantics, enabling the fused features to provide more expressive and robust representations for both large and small targets.

[0088] The detection head is used to synchronously output the key layer boundary frames of the depletion layer and the bubble detection results. The bounding box regression branch IoU calculation layer of the head embeds parallel calculation modules of InnerIoU (Inner Intersection over Union) and MPDIoU (Minimum Point Distance Intersection over Union) in a weighted form to replace the original IoU loss.

[0089] The expression for the parallel computing module is:

[0090]

[0091]

[0092]

[0093] in, The minimum point distance intersection-union ratio metric. IMPDIoU is the internal intersection-union ratio metric. and The composite crossover ratio loss metric For the prediction box, For the true frame, This is a bounding box scaling operator that, based on the center point of the detection box, performs synchronous and proportional scaling operations on the width and height of the predicted box and the ground truth box. These are scaling hyperparameters used to... The scaling factor is used to adjust the scaling ratio of the detection box's width and height. These are the minimum bounding box width and height of the predicted bounding box and the ground truth bounding box, respectively. The distance between the top-left corners of the predicted bounding box and the ground truth bounding box is the Euclidean distance. The distance between the bottom right corners of the predicted bounding box and the ground truth bounding box is the Euclidean distance. This is an area calculation function used to calculate the pixel area of ​​the region within the brackets.

[0094] The coordinates of the top-left and bottom-right corners of the predicted bounding box and the ground truth bounding box are respectively , and , The minimum point distance is calculated as shown in the formula below.

[0095]

[0096] Combining InnerloU and MPDIoU in the detection head can fully leverage their respective advantages: InnerloU enhances the sensitivity to the internal overlap relationship of small bubbles, ensuring that the gradient of small bubbles can still be effectively transmitted even if the large frame covers the small bubbles; MPDIoU provides constraints on the boundary position and shape, so that the regression results maintain geometric consistency on a global scale, thereby forming a composite regression metric suitable for nested bubbles in bubble void layers.

[0097] In step S2, the process of determining the start and end frames of the depletion layer is as follows:

[0098] Based on the keyframe confidence of each frame of the bubble depletion layer output by the bubble depletion layer detection model, the frame with the highest confidence of the depletion layer start frame is taken as the candidate frame of the depletion layer start frame, and the frame with the highest confidence of the depletion layer end frame is taken as the candidate frame of the depletion layer end frame.

[0099] If the confidence level of a candidate frame is greater than or equal to the set confidence threshold, it is directly output as a key frame; if the confidence level of a candidate frame is less than the set confidence threshold, statistical prior is introduced for compensation.

[0100] The compensation rules are as follows: For the starting frame of the depletion layer, the position of the starting frame is inferred by overlaying the historical average offset with the first frame containing bubbles in the continuous profile image of that detection point; for the ending frame of the depletion layer, the position of the ending frame is inferred by overlaying the corresponding historical average span with the determined starting frame of the depletion layer. The three keyframe images are shown below. Figure 7 , 8 As shown in Figures 9 and 9.

[0101] Specifically, let the first A total of axial scan sequences Frame, the detection network for the first The confidence scores of the super-transparent layer start frame and the spread domain end frame of the output frame are denoted as follows: and The positions of the two types of candidate frames are defined as follows:

[0102]

[0103]

[0104] This article sets the confidence threshold for keyframes. For the starting frame of the super-transparent layer, if the maximum confidence of the candidate frame is lower than the threshold, or the candidate frame number exceeds the preset upper bound... The upper and lower bounds are the frame numbers corresponding to the start and end frames of the depletion layer; if so, it is considered that the frame has not been reliably detected, that is,

[0105]

[0106] Record No. The first frame in the sequence to detect a bubble is:

[0107]

[0108] in For the first The number of bubbles detected in the frame.

[0109] Since the location of the first visible bubble is affected by the focal plane, the bubble size, and its distance from the inner surface, this paper does not use a fixed frame interval, but introduces the average offset of the starting frame relative to the first bubble frame. Compensation is then performed. Therefore, the final position of the super-transparent layer's starting frame is:

[0110]

[0111] When the starting frame is reliably detected, the actual offset is defined as:

[0112]

[0113] And an exponential moving average is used to update the prior:

[0114]

[0115] in, Update the coefficients for the offset prior. This update only occurs when... It will be carried out in a timely manner.

[0116] For the end frame of the propagation domain, i.e., the end frame of the depletion layer, its position is related to the measurement location. Since the transparent layer thickness varies significantly at the rim, straight wall, and R-corner, this paper maintains a priori average span for each location. Let the measurement location category be... Rim, straight walls, rounded corners The corresponding average span is denoted as If the maximum confidence of a candidate frame is lower than the threshold, or the candidate frame number is less than the preset lower bound. If the frame is not reliably detected, then it is considered that the frame was not reliably detected.

[0117]

[0118] Its final position is defined as:

[0119]

[0120] in, This indicates rounding to the nearest integer.

[0121] When both the start frame of the super-transparent layer and the end frame of the spread domain are reliably detected, the actual span is denoted as:

[0122]

[0123] And update the span prior for the corresponding part:

[0124]

[0125] in, The span prior update coefficients.

[0126] The end frame of the super-transparent layer is not directly detected as an independent visual target, but is determined based on the statistical characteristics of the bubbles. Let the first... The first frame The area of ​​each bubble detection frame is The total area of ​​the bubbles in this frame is defined as follows:

[0127]

[0128] Under forward illumination, the visibility of deep bubbles decreases after entering the bubble propagation domain; therefore, the area near the end frame of the supertransparency layer typically corresponds to the region with the highest concentration of detectable bubbles. Compared to the number of bubbles alone, the total bubble area can simultaneously characterize both quantity and size changes; therefore, this paper uses it as the primary criterion. Within the effective range, the end frame of the super-transparent layer is defined as the position where the total area of ​​the bubble reaches its maximum value, and its expression is:

[0129]

[0130] To reduce frame-by-frame fluctuations, a moving average smoothing is applied to the two-dimensional total area sequence of bubbles. The expression for the moving average smoothing is as follows:

[0131]

[0132] in, For the smoothed first The first scan sequence The total two-dimensional area of ​​the bubble in the frame. Half the width of the window , The total two-dimensional area of ​​the bubble before smoothing. This is the frame offset index within the window.

[0133] S3, Single-point thickness calculation;

[0134] Based on the key frame number determined in step S2, and combined with the pulse signal in step S1, determine the axial position of each frame, and calculate the ultra-transparent layer thickness, the spread domain thickness, and the total transparent layer thickness at that detection point.

[0135] Specifically, in step S3, the formula for calculating the thickness of the ultra-transparent layer is:

[0136]

[0137] in, For the first The thickness of the ultra-transparent layer corresponding to each scan sequence. For the first End frame of the super-transparent layer in the scan sequence, For the first The starting frame of the super-transparent layer in the scan sequence, The axial propulsion speed of the motor. For camera acquisition rate, This is the refractive index correction factor; considering that the imaging process is affected by the material refraction effect, a refractive index correction factor is introduced.

[0138] The formula for calculating the thickness of the spread domain is:

[0139]

[0140] in, No. The thickness of the spread region corresponding to each scan sequence. For the first End frame of the spread domain of the scan sequence;

[0141] The formula for calculating the total thickness of the transparent layer is:

[0142]

[0143] in, For the first The total thickness of the transparent layer corresponding to each scan sequence; such as Figure 6 As shown, the starting frame of the super-transparent layer is the starting frame of the depletion layer, and the ending frame of the propagation domain is the ending frame of the depletion layer.

[0144] S4, 3D bubble construction;

[0145] Based on the two-dimensional positions of the bubbles output frame by frame in step S2, the three-dimensional size, number, and spatial distribution of the bubbles are determined by combining the axial positions of each frame. Specifically, the axial depth position corresponding to each frame image is determined based on the servo motor pulse signal, and the two-dimensional image coordinates of the bubbles are combined with the axial depth to form three-dimensional spatial coordinates. After DBSCAN clustering and fusion of repeated detection of adjacent frames, the three-dimensional distribution of the bubbles is constructed, and the three-dimensional size, number, and spatial position information of the bubbles are output.

[0146] S5, Prediction of regional transparent layer thickness;

[0147] Repeat steps S1 to S4, dividing the area to be tested into several grid regions according to a preset grid, acquiring the thickness data of the corresponding detection points in each grid region, adaptively classifying each grid region into three categories: crucible rim, straight wall, and R-corner, and differentially interpolating the thickness data for each category to construct a discrete thickness field; then, using a depth network to predict, reconstruct, and output the continuous transparent layer thickness distribution of the area to be tested. The adaptive classification process involves calculating the geometric curvature of the crucible's inner surface based on the servo motor's propulsion distance and the spatial three-dimensional coordinates obtained from the camera's field of view, thereby classifying each grid region into rim region, straight wall region, and R-corner region and assigning category labels.

[0148] Based on the servo motor's propulsion distance and the spatial three-dimensional coordinates (x, y, z) obtained from the camera's field of view, the geometric curvature of the crucible's inner surface is calculated. Based on the curvature characteristics, the detection area of ​​the crucible's transparent layer is automatically divided into three sub-regions with different thickness distribution characteristics: the crucible rim area, the straight-wall area, and the R-corner area. The system assigns a corresponding region label to each sparse thickness measurement point. This label serves as prior information and is used throughout the entire thickness reconstruction process.

[0149] The above differential interpolation process uses inverse distance weighting and Kriging joint interpolation to form a hybrid interpolation model, the expression of which is:

[0150]

[0151] in, For testing points The thickness estimate at that location, For the thickness of the grid region, The distance between grid cells. For Kriging weights, For balance coefficient, For region labels, The inverse distance-weighted power controls the distance decay rate. This represents the total number of grid regions participating in the interpolation. A semi-variogram model is dynamically matched based on the region labels: an isotropic spherical model is used for the straight-walled region, an anisotropic Gaussian model for the R-corner region, and an exponential model for the edge region.

[0152] Among them, Kriging weights The determination of the weights is jointly determined by the spatial distance between the detection point and the known points, and the spatial correlation structure between the known points. Specifically, the Kriging weights are dynamically calculated by solving the Kriging equations, and their core relies on the variogram. The dependent data are the spatial distances between each sampling point and their corresponding residual values. The determination process is as follows: first, the experimental variogram is calculated, i.e., the pairwise semivariogram values ​​between known residual points are calculated; then, a theoretical model is fitted, and the weights are solved. Once the theoretical model is fitted, the system will solve the following linear equations based on the spatial relationships between the detection point and the known points, and between known points themselves:

[0153]

[0154] in, Using Kriging weights, it ensures that the valuation is unbiased and that the valuation variance is minimized. For Lagrange multipliers; For the first The and the first The distance between known points; For the first The distance between a known point and a detection point; It is a semi-variogram. and The values ​​of the semivariogram are taken for the corresponding spatial distance.

[0155] Regarding the balance coefficient The determination process is as follows: with the goal of minimizing RMSE, leave-one-out cross-validation is used to jointly optimize the power of IDW (Inverse Distance Weighted Interpolation) and the Kriging mutation function to achieve the best combination of trend extraction and residual correction, thereby ensuring that the interpolated surface retains local features and has good generalization performance.

[0156] The deep network prediction and reconstruction process is as follows: the discrete thickness field obtained by hybrid interpolation is processed by PointKAN to extract region-aware features, and then input into a U-Net adaptive deep network integrating Transformer; combining the region categories of each grid and gradient constraints, the continuous transparency layer thickness distribution of the test region is output. Specifically, to achieve differentiated feature extraction, discrete region labels are... Mapped to continuous learnable region embedding vectors PointKAN outputs local structural features f and spatial coordinates. and The features are concatenated to form a multi-channel input feature map that includes regional physical priors:

[0157]

[0158] This design allows PointKAN's learnable edge activation function to adaptively adjust the complexity of the nonlinear mapping based on whether the current block belongs to a straight wall or an R-angle.

[0159] Adaptive deep networks employ U-Net architectures with integrated Transformer modules (such as the TransUNet architecture) to achieve coordinated local and global prediction. When the Laplacian operator is introduced to extract the second-order gradient as explicit physical guidance, an adaptive guidance weight allocation mechanism based on region attributes is constructed.

[0160]

[0161] in, The thickness distribution output by the network. For different categories of second-order gradient penalty coefficients, For adaptive deep network mapping functions, Input feature map; Second-order gradient features extracted for the Laplacian operator; These are learnable parameters for the network. The system assigns extremely high sensitivity to the R-corner region, which is prone to stress concentration and dramatic thickness variations. The value forces the network to pay close attention to the high-frequency curvature characteristics of the region; while the straight-wall region... The low value prompts the network to focus on the global smoothing trend. Ultimately, the dual branches of the CNN (Convolutional Neural Network) and MLP (Multilayer Perceptron) output a continuous thickness distribution.

[0162] The above description is merely a preferred embodiment of the present invention and does not constitute any limitation on the present invention. Any simple modifications, alterations, or equivalent structural changes made to the above embodiments based on the technical essence of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A method for predicting the thickness of the vacancy layer in a quartz crucible based on single-point detection, characterized in that: Includes the following steps: S1. Acquire single-point profile images; The handheld measuring instrument is attached to the detection point on the inner wall of the crucible. A red ring light source illuminates the local area where the detection point is located. The servo motor drives the camera to move at a constant speed along the thickness direction of the crucible to acquire continuous cross-sectional images of the local area. At the same time, the servo motor pulse signal is collected to calibrate the axial position of each frame. S2. Keyframe detection of depletion layer in single-point profile image; The continuous profile images obtained in step S1 are input into the trained bubble void layer detection model. This model is built based on an improved YOLO11 network and trained using sample images of bubble void layer profiles from quartz crucibles with different thicknesses and bubble distributions. The two-dimensional position, size, number, and keyframe confidence of the bubbles are output frame by frame. Based on the confidence constraints and statistical prior compensation, the start and end frames of the void layer in this region are determined. The total two-dimensional area of ​​the bubbles in each frame within the two-frame interval is calculated, and the frame corresponding to the maximum value is taken as the end frame of the super-transparent layer. S3, Single-point thickness calculation; Based on the key frame number determined in step S2, and combined with the pulse signal in step S1, determine the axial position of each frame, and calculate the ultra-transparent layer thickness, the spread domain thickness, and the total transparent layer thickness at the detection point. S4, 3D bubble construction; Based on the two-dimensional positions of the bubbles output frame by frame in step S2, the three-dimensional size, number, and spatial distribution of the bubbles are determined in combination with the axial positions of each frame. S5, Prediction of regional transparent layer thickness; Repeat steps S1 to S4 to divide the area to be tested into several grid areas, obtain the thickness data of the corresponding detection points in each grid area, adaptively divide each grid area into three categories: crucible edge, straight wall, and R-angle, and perform differential interpolation on the thickness data of each category to construct a discrete thickness field; then predict, reconstruct, and output the continuous transparent layer thickness distribution of the area to be tested through a deep network.

2. The method for predicting the thickness of the vacancy layer in a quartz crucible based on single-point detection according to claim 1, characterized in that: The improved YOLO11 network includes a backbone network, a neck network, and a head detection head; The backbone network replaces the original convolutional downsampling module with the ADown downsampling module; The neck network is a MSENeck multi-scale enhanced feature fusion structure, including a WFU wavelet upsampling module and a C3k2 module. The neck network adopts a skip connection structure to deeply fuse the WFU upsampling output with the feature maps of different levels extracted by the C3k2 module. The detection head is used to simultaneously output the critical boundary frames of the depletion layer and the bubble detection results.

3. The method for predicting the thickness of the vacancy layer in a quartz crucible based on single-point detection according to claim 2, characterized in that: The ADown downsampling module first performs 2×2 average pooling, then inputs the complete feature map in parallel into two branches: the first branch is processed by max pooling and convolution in sequence, and the second branch is processed by direct convolution; the output features of the two branches are then concatenated along the channel dimension.

4. A method for predicting the thickness of the vacancy layer in a quartz crucible based on single-point detection according to claim 2, characterized in that: The WFU wavelet upsampling module performs wavelet transform on the input features, decomposing them into low-frequency approximate components and three high-frequency components, and processes them in parallel between the high-frequency and low-frequency branches: The high-frequency branch adds the three high-frequency components and then performs feature enhancement through convolution and residual modules; The low-frequency branch concatenates and convolves the low-frequency approximation component with the next-scale feature map after convolution processing to achieve feature fusion and channel adjustment. The two outputs are spliced ​​together by channel and then reconstructed into a high-resolution feature map through inverse wavelet transform.

5. A method for predicting the thickness of the vacancy layer in a quartz crucible based on single-point detection according to claim 2, characterized in that: The bounding box regression branch IoU calculation layer of the detection head embeds parallel calculation modules of InnerIoU and MPDIoU in a weighted manner to replace the original IoU loss; The expression for the parallel computing module is: in, The minimum point distance intersection-union ratio metric. IMPDIoU is the internal intersection-union ratio metric. and The composite crossover ratio loss metric For the prediction box, For the true frame, This is a bounding box scaling operator that, based on the center point of the detection box, performs synchronous and proportional scaling operations on the width and height of the predicted box and the ground truth box. For scaling hyperparameters, These are the minimum bounding box width and height of the predicted bounding box and the ground truth bounding box, respectively. The distance between the top-left corners of the predicted bounding box and the ground truth bounding box is the Euclidean distance. The distance between the bottom right corners of the predicted bounding box and the ground truth bounding box is the Euclidean distance. This is an area calculation function used to calculate the pixel area of ​​the region within the brackets.

6. A method for predicting the thickness of the vacancy layer in a quartz crucible based on single-point detection according to claim 1, characterized in that: In step S2, the process of determining the start and end frames of the depletion layer is as follows: Based on the keyframe confidence of each frame of the bubble depletion layer output by the bubble depletion layer detection model, the frame with the highest confidence of the depletion layer start frame is taken as the candidate frame of the depletion layer start frame, and the frame with the highest confidence of the depletion layer end frame is taken as the candidate frame of the depletion layer end frame. If the confidence level of a candidate frame is greater than or equal to the set confidence threshold, it is directly output as a key frame; if the confidence level of a candidate frame is less than the set confidence threshold, statistical prior is introduced for compensation. The compensation rule is as follows: for the starting frame of the depletion layer, the position of the starting frame of the depletion layer is inferred by superimposing the historical average offset based on the first frame with bubbles in the continuous profile image of the detection point; for the ending frame of the depletion layer, the position of the ending frame of the depletion layer is inferred by superimposing the corresponding historical average span based on the determined starting frame of the depletion layer.

7. A method for predicting the thickness of the vacancy layer in a quartz crucible based on single-point detection according to claim 6, characterized in that: In step S2, the two-dimensional total area sequence of the bubbles is smoothed by moving average. The expression for the moving average smoothing is: in, For the smoothed first The first scan sequence The total two-dimensional area of ​​the bubble in the frame. Half the width of the window , The total two-dimensional area of ​​the bubble before smoothing. This is the frame offset index within the window.

8. A method for predicting the thickness of the vacancy layer in a quartz crucible based on single-point detection according to claim 1, characterized in that: In step S3, the formula for calculating the thickness of the ultra-transparent layer is: in, For the first The thickness of the ultra-transparent layer corresponding to each scan sequence, For the first End frame of the super-transparent layer in the scan sequence, For the first The starting frame of the super-transparent layer in the scan sequence, The axial propulsion speed of the motor, For camera acquisition rate, This is the refractive index correction factor; The formula for calculating the thickness of the spread domain is: in, No. The thickness of the spread region corresponding to each scan sequence. For the first End frame of the spread domain in the scan sequence; The formula for calculating the total thickness of the transparent layer is: in, For the first The total thickness of the transparent layer corresponding to each scan sequence, the starting frame of the supertransparent layer is the starting frame of the depletion layer, and the ending frame of the spread domain is the ending frame of the depletion layer.

9. A method for predicting the thickness of the vacancy layer in a quartz crucible based on single-point detection according to claim 1, characterized in that: In step S4, the process of constructing the three-dimensional bubble is as follows: The axial depth of each frame is determined based on the axial position determined by the pulse signal. The two-dimensional image coordinates of the bubble and the axial depth are combined into three-dimensional spatial coordinates. After DBSCAN clustering and fusion of repeated detection of adjacent frames, the three-dimensional distribution of the bubble is constructed, and the three-dimensional size, number and spatial position information of the bubble are output.

10. A method for predicting the thickness of the vacancy layer in a quartz crucible based on single-point detection according to claim 1, characterized in that: In step S5, the adaptive partitioning process is as follows: based on the servo motor's propulsion distance and the spatial three-dimensional coordinates obtained by the camera's field of view, the geometric curvature of the crucible's inner surface is calculated, thereby classifying each grid region into the rim region, straight wall region, and R-corner region and assigning region labels. The differential interpolation process employs a hybrid interpolation model formed by inverse distance weighting and Kriging joint interpolation, the expression of which is: in, For testing points The thickness estimate at that location, For the thickness of the grid region, The distance between grid cells. For Kriging weights, For balance coefficient, For region labels, The inverse distance-weighted power controls the distance decay rate. The total number of grid regions participating in the interpolation; the semi-variogram model is dynamically matched according to the region label, the isotropic spherical model is used for the straight wall region, the anisotropic Gaussian model is used for the R-corner region, and the exponential model is used for the edge region; The process of deep network prediction and reconstruction is as follows: the discrete thickness field obtained by hybrid interpolation is processed by PointKAN to extract the region-aware features, and then input into the U-Net adaptive deep network integrating Transformer; combined with the category of each grid region and gradient constraints, the continuous transparent layer thickness distribution of the region to be tested is output.

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