A method for detecting dislocations in gallium nitride crystals

Abstract

This invention relates to the field of semiconductor crystal detection technology, specifically a method for detecting dislocations in gallium nitride (GaN) crystals. The method includes: acquiring a set of original contrast images containing crystal orientation contrast distribution information using an electronic channel contrast imaging device; extracting local phase information of pixels using Hilbert transform and constructing a three-dimensional phase field; calculating the phase gradient to form a topological gradient field; identifying various dislocation feature points and constructing a dislocation line connection network; and filtering key dislocation feature points based on dual thresholds. The feature points are then input into a generative adversarial network (GAN) constrained by topological difference and phase continuity constraints, outputting an enhanced dislocation phase field. An enhanced dislocation image is generated through complex fusion, nonlinear dynamic iterative evolution, and wavelet reconstruction. This method can deeply mine hidden phase features in contrast images, accurately distinguish various dislocation structures in the crystal, and completely preserve subtle dislocation morphological details, achieving refined detection and characterization of dislocations in gallium nitride crystals.

Description

Technical Field

[0001] This invention relates to the field of semiconductor crystal detection technology, and in particular to a method for detecting dislocations based on gallium nitride crystals. Background Technology

[0002] Currently, gallium nitride (GaN) crystal dislocation detection generally relies on electron channel contrast imaging to acquire surface images. Dislocation structure identification is achieved by combining intuitive grayscale features with conventional pixel analysis methods. The overall detection process remains at the superficial level of interpreting two-dimensional contrast grayscale information. Conventional detection methods cannot uncover the local phase features inherent in image pixels, cannot analyze the deep distribution patterns of crystal orientation contrast from a spatial perspective, and cannot achieve fine differentiation of dislocation outcrops, dislocation termination points, and dislocation bends. Furthermore, the constructed dislocation line connection network deviates from the actual dislocation distribution in the crystal.

[0003] Traditional image enhancement methods fail to consider the correlation of dislocation topology and the coherence of phase distribution. The phase field output by the network model is prone to structural distortion. Conventional wavelet decomposition and reconstruction simply separate and integrate high- and low-frequency components of the image, which cannot adapt to the topological distribution characteristics of gallium nitride crystal dislocations. The processed image easily loses subtle dislocation morphological details, making it difficult to present a complete and realistic crystal dislocation distribution. Therefore, it is necessary to rely on phase field reconstruction and topological gradient analysis to uncover hidden defect information in contrast images. Simultaneously, combining a network model with specific constraints with a multi-dimensional image fusion evolution approach can improve the insufficient recognition accuracy and lack of imaging detail of traditional detection methods. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the existing technology and propose a method for detecting dislocations based on gallium nitride crystals.

[0005] To achieve the above objectives, the present invention employs the following technical solution: a method for detecting dislocations based on gallium nitride crystals, comprising: The raw contrast image set of gallium nitride crystal surface was acquired using an electronic channel contrast imaging device; The original contrast image set contains crystal orientation contrast distribution information; Perform a Hilbert transform on the original contrast image set to extract the local phase information of each pixel and construct a three-dimensional phase field; The phase gradient is calculated in the spatial dimension of the three-dimensional phase field to form a topological gradient field. The dislocation outcrop, dislocation termination point and dislocation bending point are identified from the topological gradient field through critical point analysis, and a dislocation line connection network is constructed. Dislocation outcrops that satisfy both a contrast concentration exceeding a set threshold and a dislocation extension length exceeding a set threshold are selected from the dislocation line connection network as key dislocation feature points. The key dislocation feature points are input into a generative adversarial network, and the generator outputs an enhanced dislocation phase field. Topological difference constraints and phase continuity constraints are introduced into the loss function of generative adversarial networks; The enhanced dislocation phase field and the low-frequency contrast components obtained by wavelet decomposition of the original contrast image set are complexly fused to construct a composite contrast field, and the composite contrast field is subjected to nonlinear dynamic iterative evolution. An optimized phase field is separated from the composite contrast field that has undergone iterative evolution, and the optimized phase field is reconstructed with the original high-frequency contrast detail components using wavelet reconstruction to generate a dislocation enhancement image.

[0006] As a further aspect of the present invention, the specific steps for acquiring the original contrast image set of the gallium nitride crystal surface using an electronic channel contrast imaging device are as follows: The gallium nitride crystal sample was fixed on the sample stage of the electronic channel contrast imaging device; Adjust the incident angle of the electron beam in the electron channel contrast imaging device so that the electron beam and the crystal plane of the gallium nitride crystal satisfy the Bragg diffraction condition. Backscattered electron images of the gallium nitride crystal surface were acquired at multiple different sample tilt angles. The backscattered electron images acquired at each sample tilt angle were recorded as a single original contrast image. All original contrast images of all samples at all tilt angles are organized into the original contrast image set according to the tilt angle sequence; A background subtraction operation is performed on each original contrast image in the original contrast image set to eliminate amorphous scattering background; Perform pixel value normalization on the original contrast image set after background subtraction to unify the grayscale range of all images.

[0007] As a further aspect of the present invention, the specific steps for performing Hilbert transform on the original contrast image set to extract the local phase information of each pixel and construct a three-dimensional phase field are as follows: Extract the two-dimensional grayscale distribution matrix of each original contrast image from the set of original contrast images; Perform a two-dimensional Hilbert transform on each two-dimensional gray-level distribution matrix to construct the complex analytic signal matrix of the original contrast image; The arctangent of the ratio of the imaginary part to the real part is extracted from each complex analytic signal matrix and used as the local phase angle of each pixel. The three-dimensional phase field is formed by organizing all local phase angles according to the sample tilt angle index as the first dimension, the pixel row index as the second dimension, and the pixel column index as the third dimension. Each element value in the three-dimensional phase field represents the local phase angle value at the corresponding pixel position under the corresponding tilt angle.

[0008] As a further aspect of the present invention, the specific steps for calculating the phase gradient in the spatial dimension of the three-dimensional phase field to form a topological gradient field, and identifying dislocation outburst points, dislocation termination points and dislocation bending points from the topological gradient field through critical point analysis are as follows: The three-dimensional phase field is divided into a two-dimensional phase distribution sub-map according to the tilt angle of each sample. For each two-dimensional phase distribution subgraph, calculate the spatial derivative of the phase in the horizontal direction and the spatial derivative of the phase in the vertical direction. The spatial derivatives of the phase in the horizontal direction and the spatial derivatives of the phase in the vertical direction are combined into a two-dimensional phase gradient vector field as the topological gradient field; Search for local minima of the gradient vector magnitude in the topological gradient field as candidate critical points; For each candidate critical point, calculate the divergence value of the phase gradient vector in its neighborhood; Candidate critical points are classified into dislocation outcrop points, dislocation termination points, or dislocation bending points based on the sign and magnitude of the divergence value. Candidate critical points with positive divergence values ​​and absolute values ​​exceeding a positive threshold are marked as dislocation outcrops. Candidate critical points with negative divergence values ​​and absolute values ​​exceeding a negative threshold are marked as dislocation termination points; Candidate critical points whose absolute divergence values ​​are below the intermediate threshold are marked as dislocation bending points.

[0009] As a further aspect of the present invention, the specific steps for constructing the dislocation line connection network are as follows: A forward streamline tracing is performed from each candidate critical point marked as a dislocation outcrop along the descent direction of the phase gradient of the topological gradient field; Starting from each candidate critical point marked as a dislocation termination point, perform reverse streamline tracing along the rising direction of the phase gradient of the topological gradient field; Connect the streamline segments obtained from forward and reverse streamline tracing in space to form a continuous streamline trajectory; All dislocation outcrops, dislocation bends, and dislocation terminations connected by streamline trajectories are classified as the same dislocation line. Record the sequence of pixel positions traversed by each dislocation line and the critical point type corresponding to each pixel position; The connection relationships of all dislocation lines are organized into a graph structure according to spatial adjacency, which is the dislocation line connection network.

[0010] As a further aspect of the present invention, the specific steps for selecting dislocation outcrops from the dislocation line connection network that satisfy the contrast concentration exceeding a set threshold and the dislocation extension length exceeding a set threshold as key dislocation feature points are as follows: For each dislocation outcrop in the dislocation line connection network, extract the contrast value sequence corresponding to the dislocation outcrop in the original contrast image set; The Gaussian weighted sum of the contrast value sequence of each dislocation outcrop point in the spatial neighborhood is calculated as the contrast concentration of the dislocation outcrop point; Dislocation outcrops with a contrast concentration exceeding a preset contrast threshold are marked as candidate feature points; For each candidate feature point, the total extended pixel length of the dislocation line where the candidate feature point is located is taken as the dislocation extension length. Candidate feature points whose dislocation extension length exceeds a preset length threshold are marked as key dislocation feature points.

[0011] As a further aspect of the present invention, the specific steps for inputting the key dislocation feature points into the generative adversarial network and having the generator output an enhanced dislocation phase field are as follows: The pixel coordinates and tilt angle indices corresponding to the key dislocation feature points are organized into a sparse feature tensor. The sparse feature tensor is input into the generator of the generative adversarial network; The generator of the generative adversarial network performs a deconvolution upsampling operation on the sparse feature tensor to generate a dense phase tensor with the same size as the three-dimensional phase field; Median filtering is performed on the dense phase tensor to eliminate isolated noise points generated by deconvolution; The dense phase tensor after median filtering is used as the output of the enhanced dislocation phase field.

[0012] As a further aspect of the present invention, the specific steps for introducing topological difference constraints and phase continuity constraints into the loss function of the generative adversarial network are as follows: In each round of training, the enhanced dislocation phase field output by the generator and the corresponding real dislocation phase field are simultaneously input into the discriminator; The difference norm between the topological gradient field of the enhanced dislocation phase field and the topological gradient field of the true dislocation phase field is calculated as a topological difference constraint term. The square integral of the Laplace operator modulus of the enhanced dislocation phase field is used as a phase continuity constraint term; The topological difference constraint term multiplied by the topological constraint weight and the phase continuity constraint term multiplied by the continuity constraint weight are simultaneously superimposed onto the original adversarial loss function of the discriminator. The discriminator loss function, which incorporates topological difference constraints and phase continuity constraints, is used to backpropagate and update the network parameters of the discriminator and generator.

[0013] As a further aspect of the present invention, the specific steps for complex-number fusion of the enhanced dislocation phase field and the low-frequency contrast component obtained by wavelet decomposition of the original contrast image set to construct a composite contrast field, and the nonlinear dynamic iterative evolution of the composite contrast field are as follows: Two-dimensional discrete wavelet transform is performed on each original contrast image in the original contrast image set to separate the low-frequency contrast approximation component and the high-frequency contrast detail component. All low-frequency contrast approximation components are organized into a low-frequency contrast component tensor according to the tilt angle index. The enhanced dislocation phase field is used as the imaginary part of the complex number, and the low-frequency contrast component tensor is used as the real part of the complex number to construct the initial complex contrast field. A nonlinear partial differential equation model containing a contrast diffusion term and a phase amplitude coupling term is established for the initial complex contrast field; The diffusion coefficient and coupling strength of the nonlinear partial differential equation model are set. The spatial boundary conditions of the nonlinear partial differential equation model are set as Neumann boundary conditions. The nonlinear partial differential equation model is subjected to time-progressive iterative calculations using an alternating direction implicit scheme. After each round of iterative calculation, it is determined whether the rate of change of the complex modulus over the entire spatial domain is lower than the preset convergence threshold. When the rate of change of the complex modulus is lower than the preset convergence threshold, the iteration stops and the current complex contrast field is taken as the composite contrast field that has completed the iterative evolution.

[0014] As a further aspect of the present invention, the specific steps for separating the optimized phase field from the composite contrast field that has completed iterative evolution and performing wavelet reconstruction of the optimized phase field with the original high-frequency contrast detail components to generate a dislocation enhancement image are as follows: The imaginary part numerical matrix is ​​extracted from the composite contrast field that has undergone iterative evolution as the optimized phase field; Spatial domain interpolation resampling is performed on the optimized phase field to make its spatial resolution consistent with the spatial resolution of the original high-frequency contrast detail components; The optimized phase field after resampling and the original high-frequency contrast detail components are synthesized layer by layer according to the same frequency band order in the two-dimensional discrete wavelet decomposition. A two-dimensional discrete wavelet inverse transform is performed on the result of layer-by-layer complex number synthesis to generate a spatial dislocation enhancement image; The final contrast value of each pixel is extracted from the spatial dislocation enhancement image and used as the grayscale value for dislocation display. Pixels whose grayscale values ​​exceed the display threshold are output as dislocation location markers.

[0015] Compared with the prior art, the advantages and positive effects of the present invention are as follows: Hilbert transform is used to extract local phase information pixel-by-pixel from the original contrast image set. A three-dimensional phase field is constructed based on this phase information, and a topological gradient field is generated by solving the phase gradient in the spatial dimension. Critical point analysis is used to distinguish different types of dislocation feature points and a dislocation line connection network is constructed. Key dislocation feature points are selected according to the contrast concentration and dislocation extension length thresholds. This approach breaks through the limitations of solely relying on image grayscale for dislocation identification, deeply explores the phase distribution information implicit in crystal orientation contrast, expands the analytical dimensions of dislocation features, refines the granularity of distinguishing different dislocation nodes, and ensures that the topological arrangement of the dislocation line connection network closely matches the actual extension morphology of internal crystal defects.

[0016] Topological difference constraints and phase continuity constraints are incorporated into the loss function of the generative adversarial network. The enhanced dislocation phase field output by the network is complexly fused with the low-frequency contrast components after wavelet decomposition of the original image. After constructing the composite contrast field, nonlinear dynamic iterative evolution is performed to extract and optimize the phase field, which is then reconstructed with the original high-frequency contrast detail components using wavelet reconstruction. The constraints maintain the overall topological structure of the dislocation without deformation, and the phase distribution trend remains natural and consistent. Complex fusion integrates phase features with basic low-frequency contrast information, nonlinear iterative evolution optimizes the internal distribution of the contrast field, and wavelet reconstruction fully preserves the high-frequency texture information of the original image, restoring more hidden micro-dislocation morphological features. Attached Figure Description

[0017] Figure 1 This is a flowchart of a method for detecting dislocations based on gallium nitride crystals according to the present invention; Figure 2 A flowchart for acquiring raw contrast image sets for electronic channel contrast imaging equipment; Figure 3 A flowchart for extracting local phase information from the Hilbert transform and constructing a three-dimensional phase field. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0019] In the description of this invention, it should be understood that the terms "length," "width," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicating orientation or positional relationships, are based on the orientation or positional relationships shown in the accompanying drawings and are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. Furthermore, in the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0020] See Figure 1 This invention provides a method for detecting dislocations in gallium nitride (GaN) crystals. The method includes: acquiring a raw contrast image set of the GaN crystal surface using an electronic channel contrast imaging device, the raw contrast image set containing crystal orientation contrast distribution information; performing a Hilbert transform on the raw contrast image set to extract local phase information for each pixel and constructing a three-dimensional phase field; calculating the phase gradient in the spatial dimension of the three-dimensional phase field to form a topological gradient field; identifying dislocation outcrops, dislocation termination points, and dislocation bends from the topological gradient field through critical point analysis and constructing a dislocation line connection network; selecting dislocation outcrops from the dislocation line connection network that satisfy both a contrast concentration exceeding a set threshold and a dislocation extension length exceeding a set threshold as key dislocation feature points; inputting the key dislocation feature points into a generative adversarial network (GAN), and having the generator output an enhanced dislocation phase field; and introducing topological difference constraints and phase continuity constraints into the loss function of the GAN. The enhanced dislocation phase field is complexly fused with the low-frequency contrast components obtained from wavelet decomposition of the original contrast image set to construct a composite contrast field, which is then subjected to nonlinear dynamic iterative evolution. An optimized phase field is extracted from the iteratively evolved composite contrast field, and this optimized phase field is reconstructed with the original high-frequency contrast detail components using wavelet recombination to generate the dislocation enhancement image.

[0021] In one embodiment of the present invention, see [reference] Figure 2The gallium nitride (GaN) crystal sample was fixed on the sample stage of the electron channel contrast imaging (ECI) device. The stage was secured using mechanical clamping or conductive adhesive to ensure the sample remained stable during subsequent adjustments. The electron beam incident angle of the ECI device was adjusted to ensure that the electron beam and the GaN crystal planes met the Bragg diffraction conditions. Specifically, the Bragg diffraction peak position was determined by observing the backscattered electron signal intensity as a function of the incident angle. Backscattered electron images of the GaN crystal surface were acquired at multiple different sample tilt angles. The step interval for each tilt angle was set to a fixed value between 0.5 and 2 degrees, and the coverage of the tilt angles was determined based on the crystal plane orientation distribution of the GaN crystal. Each backscattered electron image acquired at each sample tilt angle was recorded as a raw contrast image, with each raw contrast image having a pixel depth of 8 or 16 bits of grayscale. All raw contrast images at all sample tilt angles were organized into a raw contrast image set according to the tilt angle sequence, arranged in ascending order of tilt angle. Background subtraction is performed on each original contrast image in the original contrast image set to eliminate amorphous scattering background. The background subtraction operation uses morphological opening to estimate the background component and then subtracts this background component from the original image. Pixel value normalization is then performed on the original contrast image set after background subtraction to unify the grayscale range of all images. The normalization operation maps the minimum grayscale value of each image to 0 and the maximum grayscale value to 255 or 65535.

[0022] In the specific implementation, the gallium nitride crystal sample is fixed on the sample stage of the electronic channel contrast imaging device. The gallium nitride crystal sample is a gallium nitride epitaxial wafer with a diameter of two inches. The substrate layer of the gallium nitride epitaxial wafer is sapphire, and the surface orientation of the gallium nitride epitaxial wafer is (0001) crystal plane. The fixing method is to use conductive adhesive to attach the back of the gallium nitride crystal sample to the central area of ​​the sample stage. After attachment, a mechanical pressing plate is used to press the edge of the gallium nitride crystal sample from above to prevent the sample from shifting during subsequent angle adjustment. The sample stage itself is installed on the triaxial goniometer stage of the electronic channel contrast imaging device. The triaxial goniometer stage can realize rotation around the horizontal axis and vertical axis as well as translation along the three-dimensional direction.

[0023] In some embodiments, the electron beam incident angle of the electron channel contrast imaging device is adjusted so that the electron beam and the crystal plane of the gallium nitride crystal satisfy the Bragg diffraction condition. The accelerating voltage of the electron channel contrast imaging device is set to 30 kV, the electron beam spot size is set to 10 nm, and the electron beam current intensity is set to 10 nanoamps. The specific adjustment process is to control the triaxial goniometer stage to change the tilt angle of the sample stage relative to the fixed electron gun, and at the same time observe the signal intensity of the backscattered electrons on the fluorescent screen of the electron channel contrast imaging device. When the backscattered electron signal intensity reaches the maximum value, it is determined that the Bragg diffraction condition is satisfied. The Bragg angle of the electron beam incident angle relative to the (0001) crystal plane of the gallium nitride crystal at this time is recorded as the reference angle. The value of the reference angle is obtained by reading the goniometer of the electron channel contrast imaging device. Optionally, backscattered electron images of the gallium nitride crystal surface are acquired at multiple different sample tilt angles. The range of sample tilt angles extends 5 degrees to both sides of the reference angle, and the step interval of the tilt angle is set to 1 degree, thus forming a sampling sequence containing 11 different tilt angles. At each tilt angle position, a 30-second pause is made to allow the gallium nitride crystal sample and the sample stage to reach a mechanically stable state. Subsequently, a backscattered electron image is acquired by the backscattered electron detector of the electron channel contrast imaging device. The acquisition time of the backscattered electron detector is set to 5 seconds, and the resolution of each backscattered electron image is set to 1024 pixels multiplied by 768 pixels, with each pixel having a grayscale quantization level of 16 bits.

[0024] In specific implementations, the backscattered electron image acquired at each sample tilt angle is recorded as a raw contrast image. During the recording process, each raw contrast image is associated with an angle label in the format "tilt angle_value", where the value is accurate to one decimal place. All raw contrast images are stored on the computer hard drive in an uncompressed labeled image file format. In some embodiments, all raw contrast images at all sample tilt angles are organized into a raw contrast image set according to the tilt angle sequence. The tilt angle sequence is arranged in ascending order of angle value. The storage structure of the raw contrast image set is an array containing 11 elements. The i-th element in the array corresponds to the raw contrast image at the i-th tilt angle. The mapping relationship between the array index and the tilt angle value is recorded in a separate metadata file. It is understandable that a background subtraction operation is performed on each original contrast image in the original contrast image set to eliminate the amorphous scattering background. The specific steps of the background subtraction operation are as follows: First, a morphological opening operation is performed on each original contrast image. The morphological opening operation uses a circular structuring element with a radius of 15 pixels. The result of the morphological opening operation is used as the amorphous scattering background estimation image. Then, the gray value of each pixel in the original contrast image is subtracted from the gray value of the corresponding pixel in the background estimation image to obtain the original contrast image after background subtraction. For pixel positions with negative gray value difference, the gray value is forcibly set to zero.

[0025] Optionally, pixel value normalization is performed on the original contrast image set after background subtraction to unify the grayscale range of all images. The normalization operation first calculates the global minimum and global maximum grayscale values ​​of all images in the original contrast image set after background subtraction, and then transforms the grayscale value of each pixel in each image according to the formula: in: Indicates the pixel row index Pixel column index Inclination angle Normalized gray values ​​below This represents the grayscale value after background subtraction at the same coordinates and tilt angle. This represents the global minimum gray value in the original contrast image set after background subtraction. This represents the global maximum grayscale value in the original contrast image set after background subtraction. The normalized grayscale value is rounded to the nearest integer and stored as an 8-bit unsigned integer. It can be understood that each image in the original contrast image set after pixel value normalization has a uniform grayscale range of 0 to 255. The normalized original contrast image set serves as the input data for subsequent Hilbert transform processing.

[0026] In one embodiment of the present invention, see [reference] Figure 3A two-dimensional grayscale distribution matrix is ​​extracted from each original contrast image set. The number of rows and columns of each two-dimensional grayscale distribution matrix corresponds to the height and width pixel values ​​of the original contrast image, respectively. A two-dimensional Hilbert transform is performed on each two-dimensional grayscale distribution matrix to construct a complex analytic signal matrix of the original contrast image. The two-dimensional Hilbert transform is performed in the frequency domain by multiplying by a sign function. The arctangent value of the ratio of the imaginary part to the real part is extracted from each complex analytic signal matrix as the local phase angle of each pixel. The arctangent value is calculated using the four-quadrant arctangent function to obtain the phase angle value located in the negative to positive interval. All local phase angles are organized into a three-dimensional phase field according to the sample tilt angle index as the first dimension, the pixel row index as the second dimension, and the pixel column index as the third dimension. The data structure of this three-dimensional phase field is a three-dimensional array. The three-dimensional phase field is divided into a two-dimensional phase distribution sub-map according to each sample tilt angle. Each two-dimensional phase distribution sub-map corresponds to the phase angle distribution at a specific tilt angle. For each two-dimensional phase distribution sub-image, the spatial derivatives of the phase in the horizontal and vertical directions are calculated separately. A central difference scheme is used to improve the accuracy of the spatial derivatives. The spatial derivatives in the horizontal and vertical directions are combined into a two-dimensional phase gradient vector field as a topological gradient field, where each pixel location contains a two-dimensional vector. Local minima of the gradient vector magnitude are searched within the topological gradient field as candidate critical points. The search for local minima uses a neighborhood comparison method, determining whether the center point is the minimum magnitude within a 3x3 neighborhood window. For each candidate critical point, the divergence value of the phase gradient vector within its neighborhood is calculated. The divergence value is calculated using a difference approximation method within the four- or eight-neighborhood of the candidate critical point. Candidate critical points are classified into dislocation outcrops, dislocation termination points, or dislocation bending points based on the sign and magnitude of the divergence value. Candidate critical points with positive divergence values ​​and absolute values ​​exceeding the positive threshold are marked as dislocation outcrops, candidate critical points with negative divergence values ​​and absolute values ​​exceeding the negative threshold are marked as dislocation termination points, and candidate critical points with absolute divergence values ​​below the intermediate threshold are marked as dislocation bending points.

[0027] In the specific implementation, a two-dimensional grayscale distribution matrix of each original contrast image is extracted from the original contrast image set. The original contrast image set contains 11 original contrast images acquired at different tilt angles. The resolution of each original contrast image is 1024 pixels multiplied by 768 pixels. The grayscale value of each pixel is an 8-bit unsigned integer after normalization. For each original contrast image, the pixel grayscale values ​​are read into a two-dimensional floating-point array according to their row and column positions. The number of rows in the two-dimensional floating-point array is equal to the height of the original contrast image (768), and the number of columns in the two-dimensional floating-point array is equal to the width of the original contrast image (1024). The two-dimensional grayscale distribution matrices corresponding to all 11 original contrast images are stored together in a three-dimensional array. The first dimension of the three-dimensional array is 11, corresponding to the tilt angle index; the second dimension is 768, corresponding to the pixel row index; and the third dimension is 1024, corresponding to the pixel column index.

[0028] In some embodiments, a two-dimensional Hilbert transform is performed on each two-dimensional gray-level distribution matrix to construct the complex analytic signal matrix of the original contrast image. The two-dimensional Hilbert transform is performed in the frequency domain. First, a two-dimensional fast Fourier transform is performed on each two-dimensional gray-level distribution matrix to obtain a frequency domain matrix. The size of the frequency domain matrix is ​​the same as that of the two-dimensional gray-level distribution matrix, which is 768 rows by 1024 columns. Then, a two-dimensional sign function matrix is ​​constructed. The value of the two-dimensional sign function matrix in the first quadrant of the frequency plane is negative imaginary unit, the value in the second quadrant is positive imaginary unit, and the value in the third quadrant is positive imaginary unit. The values ​​in the first quadrant are positive imaginary units, those in the fourth quadrant are negative imaginary units, and those on the frequency axis are zero. The frequency domain matrix is ​​multiplied element-wise by the two-dimensional sign function matrix and then added to the frequency domain matrix itself. The result is subjected to a two-dimensional inverse fast Fourier transform. The real part of the two-dimensional inverse fast Fourier transform is the original two-dimensional gray-level distribution matrix, and the imaginary part is the result of the two-dimensional Hilbert transform. The real and imaginary parts are combined to form a complex analytic signal matrix. Each element in the complex analytic signal matrix is ​​a complex number, with the real part being the original gray-level value and the imaginary part being the value after the Hilbert transform.

[0029] Optionally, the arctangent value of the ratio of the imaginary part to the real part is extracted from each complex analytic signal matrix as the local phase angle of each pixel. For the complex element located in the i-th row and j-th column of the complex analytic signal matrix, it is assumed that the real part of the complex element is labeled as the real part value and the imaginary part of the complex element is labeled as the imaginary part value. The local phase angle is calculated by calling the four-quadrant arctangent function and using the imaginary part value as the first parameter and the real part value as the second parameter. The angle value returned by the four-quadrant arctangent function is located in the interval from negative to positive. When the real part value is zero and the imaginary part value is positive, it returns a positive half; when the real part value is zero and the imaginary part value is negative, it returns a negative half; when the real part value is zero and the imaginary part value is zero, it returns zero. The local phase angles of all pixels constitute a two-dimensional phase angle matrix with the same size as the original contrast image. It is understandable that all local phase angles are organized into a three-dimensional phase field according to the sample tilt angle index as the first dimension, the pixel row index as the second dimension, and the pixel column index as the third dimension. The sample tilt angle index ranges from 1 to 11, and each index value corresponds to a specific tilt angle value. The total data volume of the three-dimensional phase field is 11 times 768 times 1024 floating-point numbers. Each element value in the three-dimensional phase field represents the local phase angle value at the corresponding pixel position under the corresponding tilt angle. The unit of the local phase angle value is radians, and the value range is between negative and positive.

[0030] In the specific implementation, the three-dimensional phase field is divided into a two-dimensional phase distribution sub-map according to the tilt angle of each sample. The division operation traverses the first dimension of the three-dimensional phase field, namely the tilt angle index. For each tilt angle index value, the corresponding two-dimensional array of 768 rows multiplied by 1024 columns is extracted as a two-dimensional phase distribution sub-map, resulting in a total of 11 two-dimensional phase distribution sub-maps.

[0031] In some embodiments, the phase spatial derivatives in the horizontal and vertical directions of each two-dimensional phase distribution sub-image are calculated. The phase spatial derivative in the horizontal direction adopts the central difference format. For a pixel located in the i-th row and j-th column, the horizontal derivative value is equal to the local phase angle value at the i-th row and j-th column minus the local phase angle value at the i-th row and j-th column minus twice the pixel spacing. The phase spatial derivative in the vertical direction adopts the central difference format. The vertical derivative value is equal to the local phase angle value at the i-th row and j-th column minus the local phase angle value at the i-th row and j-th column minus twice the pixel spacing. For pixels at the image boundary, the derivative is calculated using the forward difference or backward difference format. The pixel spacing is set to 1 pixel unit. Optionally, the spatial derivatives of the phase in the horizontal direction and the spatial derivatives of the phase in the vertical direction are combined into a two-dimensional phase gradient vector field as a topological gradient field. The vector component located in the i-th row and j-th column of the two-dimensional phase gradient vector field is a two-dimensional column vector. The first component of the two-dimensional column vector is the value of the horizontal derivative, and the second component is the value of the vertical derivative. The size of the entire two-dimensional phase gradient vector field is the same as that of the two-dimensional phase distribution subgraph, which is 768 rows by 1024 columns. A corresponding topological gradient field is generated for each tilt angle index, so a total of 11 topological gradient fields are generated.

[0032] In practice, local minima of the gradient vector magnitude are searched in the topological gradient field as candidate critical points. The gradient vector magnitude is calculated by taking the square root of the sum of the squares of the two components of each vector in the two-dimensional phase gradient vector field to obtain a scalar field of the same size as the two-dimensional phase distribution submap. A 3x3 pixel neighborhood window is used in this scalar field to search for local minima. For each pixel in the scalar field located at the center of the window, the gradient vector magnitude of the center point is compared with the gradient vector magnitudes of the eight neighboring pixels in the window one by one. If the gradient vector magnitude of the center point is less than the gradient vector magnitudes of all eight neighboring pixels, the center point is marked as a local minimum point. All local minimum points constitute the candidate critical point set. It can be understood that the divergence value of the phase gradient vector in the neighborhood of each candidate critical point is calculated. The divergence value is calculated using a difference approximation method. For a candidate critical point located in the i-th row and j-th column, the horizontal derivative value at that point is first obtained as the first component of the divergence calculation, and the vertical derivative value at that point is obtained as the second component of the divergence calculation. The divergence value is equal to the rate of change of the horizontal derivative in the horizontal direction plus the rate of change of the vertical derivative in the vertical direction. Specifically, a five-point difference scheme is used for calculation. The rate of change in the horizontal direction is approximately the horizontal derivative value at the i-th row and j-one-column minus the horizontal derivative value at the i-th row and j-one-column, divided by twice the pixel spacing. The rate of change in the vertical direction is approximately the vertical derivative value at the i-th row and j-th column minus the vertical derivative value at the i-th row and j-th column, divided by twice the pixel spacing. The two are added together to obtain the divergence value.

[0033] In some embodiments, candidate critical points are classified into dislocation outcrops, dislocation termination points, or dislocation bends based on the sign and magnitude of the divergence values. A positive threshold parameter with a value of 0.5 is set, a negative threshold parameter with a value of -0.5 is set, and an intermediate threshold parameter with a value of 0.1 is set. For candidate critical points with positive divergence values ​​and absolute divergence values ​​exceeding the positive threshold (i.e., divergence values ​​greater than 0.5), they are marked as dislocation outcrops. For candidate critical points with negative divergence values ​​and absolute divergence values ​​exceeding the negative threshold (i.e., divergence values ​​less than -0.5), they are marked as dislocation termination points. For candidate critical points with absolute divergence values ​​below the intermediate threshold (i.e., divergence values ​​greater than -0.1 and less than 0.1), they are marked as dislocation bends. For candidate critical points with absolute divergence values ​​between 0.1 and 0.5, no marking is performed, and they are excluded from subsequent processing. The marked dislocation outcrops, dislocation termination points, and dislocation bends are output as the results of critical point analysis and used for subsequent construction of dislocation line connection networks.

[0034] In one embodiment of the invention, forward streamline tracing is performed from each candidate critical point marked as a dislocation outcrop along the descent direction of the phase gradient of the topological gradient field. The forward streamline tracing uses a fourth-order Runge-Kutta integral method to calculate the coordinates of the streamline trajectory points. Reverse streamline tracing is performed from each candidate critical point marked as a dislocation termination point along the ascending direction of the phase gradient of the topological gradient field. The reverse streamline tracing also uses a fourth-order Runge-Kutta integral method, but with the gradient direction reversed. The streamline segments obtained from the forward and reverse streamline tracing are connected in space to form a continuous streamline trajectory. The connection operation is performed when the spatial distance between the endpoints of the streamline segments is less than one pixel. All dislocation outcrops, dislocation bends, and dislocation termination points connected by streamline trajectories are classified as the same dislocation line. All critical points on the same streamline trajectory constitute the node sequence of that dislocation line. The sequence of pixel positions traversed by each dislocation line and the type of critical point corresponding to each pixel position are recorded. The pixel position sequence is stored sequentially according to the streamline forward direction. All dislocation lines are organized into a graph structure based on spatial adjacency to form a dislocation line connection network. The nodes of this graph structure represent the pixel positions on the dislocation lines, and the edges represent the connections between adjacent pixels. For each dislocation outcrop in the dislocation line connection network, a contrast value sequence corresponding to that dislocation outcrop in the original contrast image set is extracted. This contrast value sequence consists of the grayscale values ​​of that dislocation outcrop in the original contrast images at different tilt angles. The Gaussian weighted sum of the contrast value sequence of each dislocation outcrop is calculated as the contrast concentration of that dislocation outcrop. The size of the spatial neighborhood is set to a 5x5 pixel window centered on the dislocation outcrop, and the standard deviation of the Gaussian weights matches the window size. Dislocation outcrops with a contrast concentration exceeding a preset contrast threshold are marked as candidate feature points. The preset contrast threshold is determined statistically based on the overall contrast distribution of the original contrast image set. For each candidate feature point, the total extended pixel length of the dislocation line containing that candidate feature point is taken as the dislocation extension length. The total extended pixel length is obtained by accumulating the Euclidean distance between adjacent pixels on the dislocation line. Candidate feature points whose dislocation extension length exceeds a preset length threshold are marked as key dislocation feature points. The value of the preset length threshold is determined based on the statistical length distribution of typical dislocation lines in gallium nitride crystals.

[0035] In practice, forward streamline tracing is performed from each candidate critical point marked as a dislocation outcrop along the descent direction of the phase gradient of the topological gradient field. A total of 156 dislocation outcrops are marked on the surface of the gallium nitride crystal sample. Each dislocation outcrop serves as the starting point for forward streamline tracing. The forward streamline tracing adopts the fourth-order Runge-Kutta integration method, with an integration step size of 0.5 pixels and a maximum integration step size of 500 steps. The integration termination condition is that the streamline reaches the boundary of the topological gradient field, or the streamline enters a marked dislocation termination point, or the streamline enters a marked dislocation bend point, or the position change in three consecutive integration steps is less than 0.01 pixels. The fourth-order Runge-Kutta integration method calculates the intermediate vectors in the four gradient directions in each integration step, and updates the current streamline position by weighted averaging of the four intermediate vectors.

[0036] In some embodiments, reverse streamline tracing is performed from each candidate critical point marked as a dislocation termination point along the rising direction of the phase gradient of the topological gradient field. A total of 89 dislocation termination points are marked on the surface of the gallium nitride crystal sample. Each dislocation termination point serves as the starting point for reverse streamline tracing. The reverse streamline tracing also adopts the fourth-order Runge-Kutta integration method and reverses the direction of the phase gradient vector as the tracing direction. The integration step size is set to 0.5 pixels, the maximum number of integration steps is set to 500 steps, and the integration termination condition is that the streamline reaches the boundary of the topological gradient field, or the streamline enters a marked dislocation outcrop, or the streamline enters a marked dislocation bend, or the position change of three consecutive integration steps is less than 0.01 pixels.

[0037] Optionally, the streamline segments obtained from forward and reverse streamline tracing are connected in space to form a continuous streamline trajectory. Forward streamline tracing generates forward streamline segments, and reverse streamline tracing generates reverse streamline segments. For the same combination of dislocation head point and dislocation termination point, if the Euclidean distance between the spatial position of the endpoint of the forward streamline segment and the spatial position of the endpoint of the reverse streamline segment is less than 1 pixel, then the forward streamline segment and the reverse streamline segment are spliced ​​into a complete streamline trajectory. If there is a dislocation bend point between the endpoint of the forward streamline segment and the endpoint of the reverse streamline segment, then the forward streamline segment, the dislocation bend point, and the reverse streamline segment are connected sequentially through the dislocation bend point to form a continuous streamline trajectory. It is understandable that all dislocation outcrops, dislocation bends, and dislocation terminations connected by streamline trajectories are classified as the same dislocation line. A total of 73 dislocation lines were identified in the gallium nitride crystal sample, including 42 through dislocation lines where dislocation outcrops and dislocation terminations appear in pairs, 19 surface-terminated dislocation lines that contain dislocation outcrops and dislocation bends but do not contain dislocation terminations, and 12 internal-terminated dislocation lines that contain dislocation terminations and dislocation bends but do not contain dislocation outcrops.

[0038] In practice, the sequence of pixel positions traversed by each dislocation line and the critical point type corresponding to each pixel position are recorded. The pixel position sequence is stored in the order from the dislocation protrusion point to the dislocation termination point. Each pixel position records its row index and column index. The critical point types include dislocation protrusion point type, dislocation bend point type, dislocation termination point type, and non-critical point type. For pixel positions on the streamline trajectory that do not belong to any critical point, the critical point type is marked as non-critical point.

[0039] In some embodiments, the connection relationships of all dislocation lines are organized into a graph structure according to spatial adjacency as a dislocation line connection network. The node set of the graph structure contains the pixel positions of all dislocation lines. Each node contains three attributes: row index, column index, and critical point type. The edge set of the graph structure connects the spatial adjacency relationships between two adjacent pixel positions on the same streamline trajectory. Each edge contains the starting node index and the ending node index. The graph structure uses an adjacency list storage method to support subsequent node traversal operations. The dislocation line connection network contains a total of 2847 nodes and 2846 edges. Optionally, for each dislocation outcrop in the dislocation line connection network, extract the contrast value sequence corresponding to the dislocation outcrop in the original contrast image set. The original contrast image set contains 11 original contrast images at different tilt angles. Each dislocation outcrop is located at a fixed pixel row index and pixel column index. Traverse the 11 tilt angle indices and read the normalized gray value at the pixel coordinate in the original contrast image at each tilt angle. Arrange the 11 read gray values ​​in ascending order of tilt angle to form a contrast value sequence of length 11.

[0040] It is understandable that the contrast concentration of each dislocation outcrop point is calculated as the Gaussian weighted cumulative value of the contrast value sequence in the spatial neighborhood. The spatial neighborhood is defined as a 5-pixel rectangular window centered on the pixel coordinates of the dislocation outcrop point. The Gaussian weights are generated by a two-dimensional Gaussian function with a standard deviation of 1.5 pixel units. For each pixel position within the window, the Gaussian weight value is calculated. The contrast value of the pixel position at all tilt angles in the original contrast image set is multiplied by the corresponding Gaussian weight and then accumulated. The accumulated result is divided by the sum of all Gaussian weights to obtain the contrast concentration. The calculated contrast concentration value of dislocation outcrop point A is shown in Table 1.

[0041] Table 1: Calculation Results of Contrast Concentration at Dislocation Outcrops In practice, dislocation outcrops with a contrast concentration exceeding a preset contrast threshold are marked as candidate feature points. The preset contrast threshold is set to 120.0. According to the data in the table above, the contrast concentration of dislocation outcrop D001 (187.3) exceeds 120.0, the contrast concentration of dislocation outcrop D002 (45.6) does not exceed 120.0, the contrast concentration of dislocation outcrop D003 (212.8) exceeds 120.0, the contrast concentration of dislocation outcrop D004 (98.2) does not exceed 120.0, and the contrast concentration of dislocation outcrop D005 (163.7) exceeds 120.0. Therefore, D001, D003, and D005 are marked as candidate feature points, while D002 and D004 are excluded.

[0042] In some embodiments, the total extended pixel length of the dislocation line tracing the candidate feature point is used as the dislocation extension length, where the dislocation line consists of a series of consecutive pixel positions, and the total extended pixel length is... : in: This indicates the total number of pixel positions on the dislocation line. Indicates the first on the dislocation line The row index value at the pixel position. Indicates the first on the dislocation line The column index value at each pixel position. Indicates the first The row index value at the pixel position. Indicates the first The column index values ​​at pixel positions, summed from... equal to 1 to Subtract 1.

[0043] Optionally, candidate feature points whose dislocation extension length exceeds a preset length threshold are marked as critical dislocation feature points. The preset length threshold is set to 50 pixel units. For the dislocation line where candidate feature point D001 is located, the number of pixel positions on the dislocation line is 137. According to the formula, the total extension pixel length is calculated to be 136.2 pixel units, which exceeds 50 pixel units. Therefore, D001 is marked as a critical dislocation feature point. For the dislocation line where candidate feature point D003 is located, the number of pixel positions on the dislocation line is... The number of dislocation outcrops is 28, and the calculated total extended pixel length is 27.5 pixels, which is less than 50 pixels. Therefore, D003 is not marked as a key dislocation feature point. For the dislocation line where candidate feature point D005 is located, the number of pixel positions on the dislocation line is 94, and the calculated total extended pixel length is 93.8 pixels, which is more than 50 pixels. Therefore, D005 is marked as a key dislocation feature point. Finally, 24 key dislocation feature points are selected from 156 original dislocation outcrops. It can be understood that all dislocation outcrops marked as key dislocation feature points and their corresponding dislocation line information are used as input data for the generative adversarial network. The pixel coordinates, tilt angle index, and correlation of the key dislocation feature points belonging to the same dislocation line are all recorded and saved in a comma-separated value format file.

[0044] In one embodiment of the invention, the pixel coordinates and tilt angle indices corresponding to key dislocation feature points are organized into a sparse feature tensor. The non-zero elements of this sparse feature tensor correspond to the spatial and angular coordinates of the key dislocation feature points, while the zero elements correspond to the positions of non-key feature points. This sparse feature tensor is input into the generator of a generative adversarial network (GAN), which employs a fully convolutional network structure with one input channel. The GAN generator performs deconvolution upsampling on the sparse feature tensor to generate a dense phase tensor with the same size as the three-dimensional phase field. The deconvolution upsampling operation uses a stacked transposed convolutional layer structure, with each transposed convolutional layer followed by a batch normalization layer and an activation function layer. Median filtering is performed on the dense phase tensor to eliminate isolated noise points generated by deconvolution. The median filtering window size is set to 3x3 pixels or 5x5 pixels. The median-filtered dense phase tensor is output as the enhanced dislocation phase field. In each training round, the enhanced dislocation phase field output by the generator and the corresponding true dislocation phase field are simultaneously input into the discriminator. The discriminator employs a convolutional neural network structure, and its output is a scalar discriminant value. The difference norm between the topological gradient fields of the enhanced dislocation phase field and the true dislocation phase field is calculated as a topological difference constraint term. The topological gradient field is calculated using the same gradient calculation method as described above, and the difference norm is either the Frobenius norm or the L2 norm. The square integral of the magnitude of the Laplacian operator of the enhanced dislocation phase field is calculated as a phase continuity constraint term. The Laplacian operator is obtained by convolving the discrete Laplacian template with the phase field. The topological difference constraint term multiplied by the topological constraint weight and the phase continuity constraint term multiplied by the continuity constraint weight are then simultaneously superimposed onto the discriminator's original adversarial loss function. The values ​​of the topological constraint weight and the continuity constraint weight both range from 0.1 to 10. Backpropagation updates the network parameters of the discriminator and generator using a discriminator loss function with superimposed topological difference constraints and phase continuity constraints. The backpropagation employs an adaptive moment estimation optimizer with a learning rate set to 0.0001.

[0045] In the specific implementation, the pixel coordinates and tilt angle indices corresponding to the key dislocation feature points are organized into a sparse feature tensor. The pixel row index, pixel column index, and tilt angle index of each key dislocation feature point are extracted from the 24 key dislocation feature points. The range of the pixel row index is 1 to 768, the range of the pixel column index is 1 to 1024, and the range of the tilt angle index is 1 to 11. The dimension of the sparse feature tensor is set to 11 times 768 times 1024. All elements in the sparse feature tensor are initialized to zero. For each key dislocation feature point, the element values ​​at the corresponding positions in the three dimensions of tilt angle index, pixel row index, and pixel column index of the sparse feature tensor are set to 1, and the other positions are kept to zero. The storage format of the sparse feature tensor adopts the compressed sparse row format to save storage space.

[0046] In some embodiments, the sparse feature tensor is input into the generator of a generative adversarial network (GAN). The GAN employs a deep convolutional GAN ​​architecture, and the generator consists of five stacked deconvolutional layers. The input layer of the generator receives the sparse feature tensor as input. The sparse feature tensor is first mapped to a 4x4x512 feature map size through a fully connected layer. The output of the fully connected layer is then fed into the first deconvolutional layer after passing through a batch normalization layer and a modified linear unit activation function layer. The first deconvolutional layer has a 4x4 kernel size, a stride of 2, and 256 output channels. The feature map size output by the first deconvolutional layer is 7x7. Multiply by 256, the kernel size of the second deconvolution layer is 4x4, the stride is 2, the number of output channels is 128, and the output feature map size is 14x14x128. The kernel size of the third deconvolution layer is 4x4, the stride is 2, the number of output channels is 64, and the output feature map size is 28x28x64. The kernel size of the fourth deconvolution layer is 4x4, the stride is 2, the number of output channels is 32, and the output feature map size is 56x56x32. The kernel size of the fifth deconvolution layer is 4x4, the stride is 2, the number of output channels is 1, and the output feature map size is 112x112x1.

[0047] Optionally, the generator of the generative adversarial network performs deconvolution upsampling on the sparse feature tensor to generate a dense phase tensor with the same size as the three-dimensional phase field, which is 11 x 768 x 1024. The size of the generator's output feature map is 112 x 112 x 1, requiring further upsampling. A bilinear upsampling layer is added after the generator's output feature map, with a target size of 768 x 1024, resulting in a two-dimensional feature map of size 768 x 1024 x 1. This two-dimensional feature map is then copied 11 times and concatenated along the first dimension to generate a dense phase tensor of size 11 x 768 x 1024. Each element in the dense phase tensor is a floating-point number with a value ranging from negative to positive. It is understandable that median filtering is performed on the dense phase tensor to eliminate isolated noise points generated by deconvolution. The median filtering uses a three-dimensional filtering window of 3 x 3 pixels x 3 pixels. The filtering window slides simultaneously in the three dimensions of the dense phase tensor. For the center position of each window, the density phase values ​​of all 27 pixels in the window are collected. These 27 density phase values ​​are sorted by numerical value and the median value is taken as the new value of the center position. The boundary region of the filtered dense phase tensor is processed by mirror filling to ensure that the boundary pixels can also participate in the filtering.

[0048] In practice, the dense phase tensor after median filtering is used as the output of the enhanced dislocation phase field. The size of the enhanced dislocation phase field is 11 x 768 x 1024, the data type is single-precision floating-point, and the unit is the same as the local phase angle in radians. In some embodiments, in each training round, the enhanced dislocation phase field output by the generator and the corresponding real dislocation phase field are simultaneously input into the discriminator. The real dislocation phase field is obtained by high-precision electron backscatter diffraction calibration of the gallium nitride crystal sample. The discriminator adopts a convolutional neural network structure, consisting of four convolutional layers and one fully connected layer. The kernel size of the four convolutional layers is 4x4, the stride is 2, and the number of output channels is 64, 128, 256, and 512, respectively. Each convolutional layer is followed by a leakage correction linear unit activation function layer with a negative slope of 0.2. The output of the last convolutional layer is flattened and fed into the fully connected layer. The fully connected layer outputs a scalar value, ranging from 0 to 1, representing the probability that the discriminator judges the input as the real phase field. Optionally, the difference norm between the topological gradient field of the enhanced dislocation phase field and the topological gradient field of the real dislocation phase field is calculated as a topological difference constraint term. The formula for calculating the topological difference constraint term is: in: This represents the numerical value of the topology difference constraint term. This represents the tilt angle index, with values ​​ranging from 1 to 11. This represents the pixel row index, with values ​​ranging from 1 to 768. This represents the pixel column index, with values ​​ranging from 1 to 1024. Indicates the index at the tilt angle , pixel row index Pixel column index The gradient vector of the enhanced dislocation phase field at that location, This represents the gradient vector of the true dislocation phase field at the same index position. This represents the square of the vector's second norm. It can be understood that the integral of the square of the modulus of the Laplace operator used to calculate the phase field of the enhanced dislocation is used as a phase continuity constraint term. The formula for calculating the phase continuity constraint term is: in: This represents the numerical value of the phase continuity constraint term. Indicates the index at the tilt angle , pixel row index Pixel column index The numerical value of the enhanced dislocation phase field at that location. This represents the second-order partial derivative of the enhanced dislocation phase field along the pixel row direction. This represents the second-order partial derivative of the enhanced dislocation phase field in the pixel column direction. The second-order partial derivative is calculated using a five-point difference scheme.

[0049] In practice, the topology difference constraint term multiplied by the topology constraint weight and the phase continuity constraint term multiplied by the continuity constraint weight are simultaneously superimposed on the original adversarial loss function of the discriminator. The original adversarial loss function adopts the form of cross-entropy loss function, the topology constraint weight is set to 0.5, and the continuity constraint weight is set to 0.1. The discriminator loss function after superposition is expressed as the original adversarial loss function plus the topology constraint weight multiplied by the topology difference constraint term plus the continuity constraint weight multiplied by the phase continuity constraint term. The discriminator loss function value is calculated at the beginning of each training round, see Table 2.

[0050] Table 2: Loss Function Values ​​During Generative Adversarial Network Training In some embodiments, the network parameters of the discriminator and generator are updated via backpropagation using a discriminator loss function that incorporates topological difference constraints and phase continuity constraints. The backpropagation employs an adaptive moment estimation optimizer (IME), with a first-order moment decay factor of 0.9, a second-order moment decay factor of 0.999, a learning rate of 0.0001, a batch size of 4, and a total training epoch of 1000. In each training epoch, the discriminator parameters are updated first, followed by the generator parameters. The generator parameters are kept fixed during discriminator parameter updates, and vice versa. The discriminator loss function, after taking the partial derivative with respect to the discriminator parameters, updates the parameter values ​​along the gradient descent direction. The generator loss function, also containing topological difference constraints and phase continuity constraints, updates the parameters along the gradient descent direction with the opposite direction of their respective terms in the discriminator loss function. Optionally, after 1000 rounds of training, the quality of the enhanced dislocation phase field output by the generator reaches a stable state. The trained generator is then saved as the final model to a disk file. This generator can accept new sparse feature tensor inputs and output the corresponding enhanced dislocation phase field for subsequent complex fusion processing. It can be understood that in each training round, the discriminator simultaneously receives the enhanced dislocation phase field and the true dislocation phase field as inputs. The true dislocation phase field is extracted from the electron backscatter diffraction calibration results of the same region of the gallium nitride crystal sample. The spatial resolution of the electron backscatter diffraction calibration is consistent with the spatial resolution of the original contrast image, both being 1024 pixels multiplied by 768 pixels. The tilt angle step of the electron backscatter diffraction calibration is the same as the acquisition step of the original contrast image set, both being 1 degree.

[0051] In one embodiment of the present invention, a two-dimensional discrete wavelet transform is performed on each original contrast image in the original contrast image set to separate low-frequency contrast approximation components and high-frequency contrast detail components. The two-dimensional discrete wavelet transform uses a Dobessie wavelet basis or a bioorthogonal wavelet basis, and the number of decomposition layers is set to 1 or 2. All low-frequency contrast approximation components are organized into a low-frequency contrast component tensor according to the tilt angle index. The dimension of the low-frequency contrast component tensor is consistent with the dimension of the three-dimensional phase field. An initial complex contrast field is constructed by using the enhanced dislocation phase field as the imaginary part of the complex number and the low-frequency contrast component tensor as the real part of the complex number. Each element of the initial complex contrast field is a complex number whose magnitude is the square root of the sum of the squares of the real and imaginary parts. A nonlinear partial differential equation (PDE) model is established for the initial complex contrast field, including a contrast diffusion term and a phase amplitude coupling term. This PDE model is expressed as the partial derivative of the complex modulus with respect to time equal to the diffusion coefficient multiplied by the Laplace operator acting on the complex modulus, plus the coupling strength multiplied by the square of the imaginary part of the modulus. The diffusion coefficient of the PDE model is set to be between 0.1 and 1.0, and the coupling strength is set to be between 0.01 and 0.1. The spatial boundary conditions of the PDE model are set to von Neumann boundary conditions, which require that the gradient component in the boundary normal direction be zero.

[0052] An alternating direction implicit scheme is employed for time-progressive iterative computation of the nonlinear partial differential equation model. This scheme decomposes the two-dimensional problem into alternating one-dimensional implicit solutions to reduce computational complexity. After each iteration, the rate of change of the complex modulus over the entire spatial domain is checked to ensure it is below a preset convergence threshold. The rate of change of the complex modulus is equal to the sum of the squares of the differences between the complex modulus of the current iteration step and the previous iteration step, divided by the sum of the squares of the complex modulus of the current iteration step. When the rate of change of the complex modulus falls below the preset convergence threshold, the iteration stops, and the current complex contrast field is taken as the composite contrast field after iterative evolution. The imaginary part numerical matrix is ​​extracted from the composite contrast field after iterative evolution as the optimized phase field. Spatial domain interpolation and resampling are performed on the optimized phase field to ensure its spatial resolution matches that of the original high-frequency contrast detail components. Bilinear interpolation is used to ensure the continuity of the phase field. The resampled optimized phase field and the original high-frequency contrast detail components are synthesized layer by layer using the same frequency band order as in the two-dimensional discrete wavelet decomposition. The complex synthesis operation combines the optimized phase field as the imaginary component with the high-frequency detail components as the real or imaginary components according to the transform specification. A two-dimensional discrete wavelet inverse transform is performed on the result of the layer-by-layer complex synthesis to generate a spatial domain dislocation enhancement image. The two-dimensional discrete wavelet inverse transform uses the same wavelet basis functions as the aforementioned two-dimensional discrete wavelet transform. The final contrast value of each pixel is extracted from the spatial domain dislocation enhancement image as the dislocation display grayscale value, which ranges from 0 to 255. Pixels with dislocation display grayscale values ​​exceeding a display threshold are output as dislocation location markers. The display threshold is set to the percentile of the dislocation display grayscale value distribution or a fixed grayscale value such as 128.

[0053] In the specific implementation, a two-dimensional discrete wavelet transform is performed on each original contrast image in the original contrast image set to separate the low-frequency contrast approximation component and the high-frequency contrast detail component. The original contrast image set contains 11 original contrast images, each with a resolution of 1024 pixels multiplied by 768 pixels. The db4 wavelet in the Dobessi wavelet basis is used as the wavelet basis function for the two-dimensional discrete wavelet transform, and the decomposition level is set to 1 level. For each original contrast image, the two-dimensional discrete wavelet transform generates four component sub-bands, namely the low-frequency contrast approximation component, the horizontal high-frequency contrast detail component, the vertical high-frequency contrast detail component, and the diagonal high-frequency contrast detail component. The size of the low-frequency contrast approximation component is 512 pixels multiplied by 384 pixels, and the size of the high-frequency contrast detail component is also 512 pixels multiplied by 384 pixels.

[0054] In some embodiments, all low-frequency contrast approximation components are organized into a low-frequency contrast component tensor according to the tilt angle index. The tilt angle index ranges from 1 to 11, and each tilt angle index corresponds to a low-frequency contrast approximation component. The 11 low-frequency contrast approximation components are stacked along the first dimension in ascending order of the index to form a three-dimensional low-frequency contrast component tensor with a size of 11 x 512 x 384. Each element in the low-frequency contrast component tensor is a floating-point number with a value range consistent with the grayscale range of the original contrast image, which is 0 to 255. Optionally, an initial complex contrast field is constructed by using the enhanced dislocation phase field as the imaginary part of the complex number and the low-frequency contrast component tensor as the real part of the complex number. The size of the enhanced dislocation phase field is 11 x 768 x 1024, while the size of the low-frequency contrast component tensor is 11 x 512 x 384. Since their spatial resolutions are inconsistent, a spatial downsampling operation is first performed on the enhanced dislocation phase field. The downsampling uses bilinear interpolation to reduce the size of the enhanced dislocation phase field from 768 x 1024. Scaling the image to 512 x 384, the downsampled enhanced dislocation phase field and the low-frequency contrast component tensor have the same spatial resolution. For each pixel position under each tilt angle index, the real value in the low-frequency contrast component tensor is used as the real part of a complex number, and the corresponding value in the downsampled enhanced dislocation phase field is used as the imaginary part of a complex number. A complex number is constructed, and the set of all complex numbers constitutes the initial complex contrast field, with a size of 11 x 512 x 384. It can be understood that a nonlinear partial differential equation model containing a contrast diffusion term and a phase amplitude coupling term is established for the initial complex contrast field. The nonlinear partial differential equation model is expressed as: in: Represents the horizontal coordinates in space Spatial vertical coordinates Inclination angle Number of iterations The value of the complex contrast field at that location, The value range is from 1 to 512. The value range is from 1 to 384. The values ​​correspond to tilt angle indices 1 to 11. This represents the number of iterations from the initial time step. This represents the first-order partial derivative of the complex contrast field with respect to the number of iterations. Indicates the contrast diffusion coefficient. The Laplace operator representing the complex contrast field acts on superior, Represents the phase-amplitude coupling coefficient. Indicates taking the complex number The imaginary part, It represents the square of the modulus.

[0055] In specific implementations, the dimensionless contrast diffusion coefficient of the nonlinear partial differential equation model is set to 0.5, and the dimensionless phase amplitude coupling coefficient is set to 0.05. Both coefficients are dimensionless constants. The value of the diffusion coefficient determines the diffusion rate of the contrast in space, and the coupling strength coefficient determines the degree of nonlinear influence of the imaginary part of the phase on the complex modulus. In some embodiments, the spatial boundary conditions of the nonlinear partial differential equation model are set to von Neumann boundary conditions. Von Neumann boundary conditions require that the partial derivatives of the complex contrast field along the boundary normal direction are zero at the boundary of the entire spatial domain. For the left boundary, i.e. The boundary condition for the position equal to 1 is expressed as follows: For the right boundary, i.e. The position equal to 512, also For the upper boundary, i.e. The boundary condition for the position equal to 1 is expressed as follows: For the lower boundary, i.e. The position equal to 384, also For the boundary of the tilt angle direction, i.e. equal to 1 and Neumann boundary conditions are also applied to the index position equal to 11, i.e. .

[0056] Optionally, an alternating direction implicit scheme is used to perform time-progressive iterative calculations on the nonlinear partial differential equation model. The dimensionless iteration step size is set to 0.1, and the total number of iterations is set to 1000. The alternating direction implicit scheme decomposes the original two-dimensional Laplace operator into two one-dimensional implicit operators in the horizontal and vertical directions. Within each dimensionless iteration step, the tridiagonal equation system is solved first along the horizontal direction to update the intermediate variables, and then the tridiagonal equation system is solved along the vertical direction to update the complex contrast field. The tridiagonal equation system is solved using a chasing method, and the computational complexity of the chasing method is O(n log n). ,in Given the number of grid points, the computational cost within each dimensionless iteration step is approximately 512 multiplied by 384 multiplied by 11 multiplied by two pursuit methods. It can be understood that after each iteration, it is determined whether the rate of change of the complex modulus over the entire spatial domain is lower than a preset convergence threshold. The formula for calculating the rate of change of the complex modulus is: in: Indicates the number of iterations Rate of change of the complex modulus at point, Indicates coordinates and number of iterations The modulus of the complex contrast field at that location. This indicates an iteration step size of 0.1. The numerator is the sum of squares of the differences between the complex moduli of the current iteration step and the previous iteration step, and the denominator is the sum of squares of the complex moduli of the current iteration step. The preset convergence threshold is set to... .

[0057] In practice, iteration stops when the rate of change of the complex modulus falls below a preset convergence threshold, and the current complex contrast field is used as the composite contrast field to complete the iterative evolution. In this example, after approximately 800 dimensionless iteration steps, the rate of change of the complex modulus decreases to... lower than The iteration stops, and the size of the composite contrast field after iterative evolution is 11 x 512 x 384, with each element being a complex number. In some embodiments, the imaginary part numerical matrix is ​​separated from the composite contrast field after iterative evolution as an optimized phase field. For each complex element in the composite contrast field, its imaginary part is extracted to form a pure real number matrix. The size of the imaginary part numerical matrix is ​​11 x 512 x 384, and each value in the matrix is ​​in radians, ranging from negative to positive. The imaginary part numerical matrix is ​​named the optimized phase field. Optionally, spatial domain interpolation resampling is performed on the optimized phase field to make its spatial resolution consistent with that of the original high-frequency contrast detail component. The spatial resolution of the original high-frequency contrast detail component is 512 pixels by 384 pixels, and the spatial resolution of the optimized phase field is also 512 pixels by 384 pixels. Since the spatial resolutions of the two are exactly the same, there is no need to perform interpolation resampling. However, the original high-frequency contrast detail component has three directions: horizontal, vertical and diagonal, each with a size of 512 pixels by 384 pixels. The optimized phase field is consistent with the high-frequency detail components in these three directions in terms of spatial resolution.

[0058] It is understandable that the resampled optimized phase field and the original high-frequency contrast detail components are synthesized layer by layer in the same frequency band order as in the two-dimensional discrete wavelet decomposition. Since there is only one decomposition layer, the frequency band order is low-frequency approximation component, horizontal high-frequency detail component, vertical high-frequency detail component, and diagonal high-frequency detail component. The optimized phase field and low-frequency approximation component have already been used to construct the composite contrast field. Here, the optimized phase field needs to be synthesized with the three high-frequency detail components. The synthesis operation uses the optimized phase field as the imaginary part and each high-frequency detail component as the real part to generate three complex matrices. The size of each complex matrix is ​​512 pixels by 384 pixels. These three complex matrices correspond to the horizontal high-frequency coefficient matrix, vertical high-frequency coefficient matrix, and diagonal high-frequency coefficient matrix required for the two-dimensional discrete wavelet inverse transform.

[0059] In practice, a two-dimensional discrete wavelet inverse transform is performed on the result after layer-by-layer complex synthesis to generate a spatial dislocation enhancement image. The two-dimensional discrete wavelet inverse transform uses the same wavelet basis function as the aforementioned two-dimensional discrete wavelet transform, namely the db4 wavelet. The input of the inverse transform includes four components: the low-frequency approximation component is set as a zero matrix because the low-frequency information has been processed by the real part of the composite contrast field; the horizontal high-frequency coefficient matrix is ​​set as the real part of the aforementioned horizontal complex synthesis matrix; the vertical high-frequency coefficient matrix is ​​set as the real part of the vertical complex synthesis matrix; and the diagonal high-frequency coefficient matrix is ​​set as the real part of the diagonal complex synthesis matrix. The two-dimensional discrete wavelet inverse transform outputs a spatial dislocation enhancement image with a size of 1024 pixels multiplied by 768 pixels. Each pixel of the spatial dislocation enhancement image is a floating-point number, and the value range is automatically determined according to the inverse transform result.

[0060] In some embodiments, the final contrast value of each pixel is extracted from the spatial domain dislocation enhancement image as the dislocation display grayscale value. The floating-point value range in the spatial domain dislocation enhancement image is linearly mapped to the integer grayscale range of 0 to 255. The linear mapping formula is to map the minimum value in the image to 0, the maximum value to 255, and the intermediate value to a linear ratio to obtain the dislocation display grayscale value matrix with a matrix size of 1024 multiplied by 768. Optionally, pixels whose grayscale values ​​exceed the display threshold are output as dislocation location markers. The display threshold is set to the 90th percentile of all pixel grayscale values ​​in the dislocation display grayscale value matrix. After calculating the histogram of the dislocation display grayscale value matrix, the grayscale value corresponding to the 90th percentile is determined to be 187. All 1024 multiplied by 768 pixels in the matrix are traversed, and the row and column indices of pixels with grayscale values ​​greater than 187 are recorded in the dislocation location marker set, for a total of 1247 dislocation location markers. Each marker contains two integer coordinate values: row index and column index. These markers are output in a comma-separated value file format. The first line of the file contains the column header row index and column index, and each subsequent line corresponds to the coordinates of a dislocation location marker.

[0061] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments that can be applied to other fields. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A method for detecting dislocations based on gallium nitride crystals, characterized in that, include: The raw contrast image set of gallium nitride crystal surface was acquired using an electronic channel contrast imaging device; The original contrast image set contains crystal orientation contrast distribution information; Perform a Hilbert transform on the original contrast image set to extract the local phase information of each pixel and construct a three-dimensional phase field; The phase gradient is calculated in the spatial dimension of the three-dimensional phase field to form a topological gradient field. The dislocation outcrop, dislocation termination point and dislocation bending point are identified from the topological gradient field through critical point analysis, and a dislocation line connection network is constructed. Dislocation outcrops that satisfy both a contrast concentration exceeding a set threshold and a dislocation extension length exceeding a set threshold are selected from the dislocation line connection network as key dislocation feature points. The key dislocation feature points are input into a generative adversarial network, and the generator outputs an enhanced dislocation phase field. Topological difference constraints and phase continuity constraints are introduced into the loss function of generative adversarial networks; The enhanced dislocation phase field and the low-frequency contrast components obtained by wavelet decomposition of the original contrast image set are complexly fused to construct a composite contrast field, and the composite contrast field is subjected to nonlinear dynamic iterative evolution. An optimized phase field is separated from the composite contrast field that has completed iterative evolution, and the optimized phase field is reconstructed with the original high-frequency contrast detail components using wavelet reconstruction to generate a dislocation enhancement image. The specific steps for constructing a dislocation line connection network are as follows: Forward streamline tracing is performed from each candidate critical point marked as a dislocation outcrop along the descent direction of the phase gradient of the topological gradient field; Starting from each candidate critical point marked as a dislocation termination point, perform reverse streamline tracing along the rising direction of the phase gradient of the topological gradient field; Connect the streamline segments obtained from forward and reverse streamline tracing in space to form a continuous streamline trajectory; All dislocation outcrops, dislocation bends, and dislocation terminations connected by streamline trajectories are classified as the same dislocation line. Record the sequence of pixel positions traversed by each dislocation line and the critical point type corresponding to each pixel position; The connection relationships of all dislocation lines are organized into a graph structure according to spatial adjacency, which is the dislocation line connection network.

2. The method for detecting dislocations based on gallium nitride crystals according to claim 1, characterized in that, The specific steps for acquiring the original contrast image set of gallium nitride crystal surface using an electronic channel contrast imaging device are as follows: The gallium nitride crystal sample was fixed on the sample stage of the electronic channel contrast imaging device; Adjust the incident angle of the electron beam in the electron channel contrast imaging device so that the electron beam and the crystal plane of the gallium nitride crystal satisfy the Bragg diffraction condition. Backscattered electron images of the gallium nitride crystal surface were acquired at multiple different sample tilt angles. The backscattered electron images acquired at each sample tilt angle were recorded as a single original contrast image. All original contrast images of all samples at all tilt angles are organized into the original contrast image set according to the tilt angle sequence; A background subtraction operation is performed on each original contrast image in the original contrast image set to eliminate amorphous scattering background; Perform pixel value normalization on the original contrast image set after background subtraction to unify the grayscale range of all images.

3. The method for detecting dislocations based on gallium nitride crystals according to claim 1, characterized in that, The specific steps for performing a Hilbert transform on the original contrast image set to extract the local phase information of each pixel and construct a three-dimensional phase field are as follows: Extract the two-dimensional grayscale distribution matrix of each original contrast image from the set of original contrast images; Perform a two-dimensional Hilbert transform on each two-dimensional gray-level distribution matrix to construct the complex analytic signal matrix of the original contrast image; Extract the arctangent value of the ratio of the imaginary part to the real part from each complex analytic signal matrix as the local phase angle of each pixel; The three-dimensional phase field is formed by organizing all local phase angles according to the sample tilt angle index as the first dimension, the pixel row index as the second dimension, and the pixel column index as the third dimension. Each element value in the three-dimensional phase field represents the local phase angle value at the corresponding pixel position under the corresponding tilt angle.

4. The method for detecting dislocations based on gallium nitride crystals according to claim 3, characterized in that, The specific steps for calculating the phase gradient in the spatial dimension of the three-dimensional phase field to form a topological gradient field, and identifying dislocation outburst points, dislocation termination points, and dislocation bending points from the topological gradient field through critical point analysis are as follows: The three-dimensional phase field is divided into a two-dimensional phase distribution sub-map according to the tilt angle of each sample. For each two-dimensional phase distribution subgraph, calculate the spatial derivative of the phase in the horizontal direction and the spatial derivative of the phase in the vertical direction. The phase space derivatives in the horizontal direction and the phase space derivatives in the vertical direction are combined to form a two-dimensional phase gradient vector field as the topological gradient field; Search for local minima of the gradient vector magnitude in the topological gradient field as candidate critical points; For each candidate critical point, calculate the divergence value of the phase gradient vector in its neighborhood; Candidate critical points are classified into dislocation outcrop points, dislocation termination points, or dislocation bending points based on the sign and magnitude of the divergence value. Candidate critical points with positive divergence values ​​and absolute values ​​exceeding a positive threshold are marked as dislocation outcrops. Candidate critical points with negative divergence values ​​and absolute values ​​exceeding a negative threshold are marked as dislocation termination points; Candidate critical points whose absolute divergence values ​​are below the intermediate threshold are marked as dislocation bending points.

5. The method for detecting dislocations based on gallium nitride crystals according to claim 4, characterized in that, The specific steps for selecting dislocation outcrops that satisfy both a contrast concentration exceeding a set threshold and a dislocation extension length exceeding a set threshold as key dislocation feature points from the dislocation line connection network are as follows: For each dislocation outcrop in the dislocation line connection network, extract the contrast value sequence corresponding to the dislocation outcrop in the original contrast image set; The Gaussian weighted sum of the contrast value sequence of each dislocation outcrop point in the spatial neighborhood is calculated as the contrast concentration of the dislocation outcrop point; Dislocation outcrops with a contrast concentration exceeding a preset contrast threshold are marked as candidate feature points; For each candidate feature point, the total extended pixel length of the dislocation line where the candidate feature point is located is taken as the dislocation extension length. Candidate feature points whose dislocation extension length exceeds a preset length threshold are marked as key dislocation feature points.

6. The method for detecting dislocations based on gallium nitride crystals according to claim 5, characterized in that, The specific steps for inputting the key dislocation feature points into the generative adversarial network and having the generator output the enhanced dislocation phase field are as follows: The pixel coordinates and tilt angle indices corresponding to the key dislocation feature points are organized into a sparse feature tensor. The sparse feature tensor is input into the generator of the generative adversarial network; The generator of the generative adversarial network performs a deconvolution upsampling operation on the sparse feature tensor to generate a dense phase tensor with the same size as the three-dimensional phase field; Median filtering is performed on the dense phase tensor to eliminate isolated noise points generated by deconvolution; The dense phase tensor after median filtering is used as the output of the enhanced dislocation phase field.

7. The method for detecting dislocations based on gallium nitride crystal according to claim 6, characterized in that, The specific steps for introducing topological difference constraints and phase continuity constraints into the loss function of generative adversarial networks are as follows: In each round of training, the enhanced dislocation phase field output by the generator and the corresponding real dislocation phase field are simultaneously input into the discriminator; The difference norm between the topological gradient field of the enhanced dislocation phase field and the topological gradient field of the true dislocation phase field is calculated as a topological difference constraint term. The square integral of the Laplace operator modulus of the enhanced dislocation phase field is used as a phase continuity constraint term; The topological difference constraint term multiplied by the topological constraint weight and the phase continuity constraint term multiplied by the continuity constraint weight are then simultaneously superimposed onto the original adversarial loss function of the discriminator. The discriminator loss function, which incorporates topological difference constraints and phase continuity constraints, is used to backpropagate and update the network parameters of the discriminator and generator.

8. The method for detecting dislocations based on gallium nitride crystal according to claim 7, characterized in that, The specific steps for constructing a composite contrast field by complex-number fusion of the enhanced dislocation phase field and the low-frequency contrast components obtained by wavelet decomposition of the original contrast image set, and the nonlinear dynamic iterative evolution of the composite contrast field are as follows: Two-dimensional discrete wavelet transform is performed on each original contrast image in the original contrast image set to separate the low-frequency contrast approximation component and the high-frequency contrast detail component. All low-frequency contrast approximation components are organized into a low-frequency contrast component tensor according to the tilt angle index. The enhanced dislocation phase field is used as the imaginary part of the complex number, and the low-frequency contrast component tensor is used as the real part of the complex number to construct the initial complex contrast field. A nonlinear partial differential equation model containing a contrast diffusion term and a phase amplitude coupling term is established for the initial complex contrast field; The diffusion coefficient and coupling strength of the nonlinear partial differential equation model are set. The spatial boundary conditions of the nonlinear partial differential equation model are set as Neumann boundary conditions. The nonlinear partial differential equation model is subjected to time-progressive iterative calculations using an alternating direction implicit scheme. After each round of iterative calculation, it is determined whether the rate of change of the complex modulus over the entire spatial domain is lower than the preset convergence threshold. When the rate of change of the complex modulus is lower than the preset convergence threshold, the iteration stops and the current complex contrast field is taken as the composite contrast field that has completed the iterative evolution.

9. The method for detecting dislocations based on gallium nitride crystals according to claim 8, characterized in that, The specific steps for separating the optimized phase field from the composite contrast field that has completed iterative evolution and reconstructing the optimized phase field with the original high-frequency contrast detail components using wavelet reconstruction to generate a dislocation enhancement image are as follows: The imaginary part numerical matrix is ​​extracted from the composite contrast field that has undergone iterative evolution as the optimized phase field; Spatial domain interpolation resampling is performed on the optimized phase field to make its spatial resolution consistent with the spatial resolution of the original high-frequency contrast detail components; The optimized phase field after resampling and the original high-frequency contrast detail components are synthesized layer by layer according to the same frequency band order in the two-dimensional discrete wavelet decomposition. A two-dimensional discrete wavelet inverse transform is performed on the result of layer-by-layer complex number synthesis to generate a spatial dislocation enhancement image; The final contrast value of each pixel is extracted from the spatial dislocation enhancement image and used as the grayscale value for dislocation display. Pixels whose grayscale values ​​exceed the display threshold are output as dislocation location markers.

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