Hardware and software combined diffraction pattern projection center correction method and system

Abstract

The invention provides a software and hardware combined diffraction pattern projection center correction method and system, and the method comprises a scanning step: moving a detector along a fixed axis, and scanning to obtain a plurality of groups of associated experiment diffraction patterns; and a calibration step: selecting a registration criterion of a crystal orientation angle and a PC coordinate according to the geometrical relationship of the multiple groups of associated experimental diffraction patterns, optimizing an objective function by using a Gaussian-Newton iterative algorithm so as to register the simulated diffraction patterns, and calibrating a PC value. The system error and accidental error of the calculation result are obviously superior to those of pure software and pure hardware correction methods, the flexibility is good, the pattern center potential deviation caused by equipment error or sample drifting and other factors can be corrected, it is ensured that the obtained diffraction image can accurately reflect the crystallography information of the sample, and the accuracy of the method is improved. And the accuracy and reliability of diffraction technology analysis are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of crystal material characterization and particle diffraction, and in particular to a method and system for correcting the projection center of a diffraction pattern combining software and hardware. Background Art

[0002] With the continuous advancement of materials science and engineering, the demand for research on the microstructure and properties of materials is increasing. Particle diffraction technology is an important non-destructive material characterization method, including X-ray diffraction, electron backscatter diffraction, electron transmission diffraction, and neutron diffraction. By analyzing information such as grain orientation, grain boundary distribution, dislocation density, stress and strain in materials at different scales, particle diffraction technology can help researchers gain a deeper understanding of the elastic-plastic properties and service performance of materials, providing important reference for materials design and engineering optimization.

[0003] The calibration accuracy of the particle diffraction technology system is a key factor that affects and limits the accuracy of experimental data analysis. The PC value of the projection center in the particle diffraction pattern is used to describe the position of the detected point of the sample relative to the detector. Accurate calibration of the PC value has always been a key issue, and careful calibration and adjustment are required to ensure that the crystallographic information in the electron backscattering pattern can be accurately mapped to the microstructure of the sample surface. If the PC calibration is inaccurate or deviates from the actual position, it may lead to misinterpretation of the crystal orientation and the generation of "phantom stress", thereby affecting the understanding and study of the microstructure and properties of the material. Traditional PC correction methods can be divided into two categories, hardware methods and software methods.

[0004] The hardware method involves specific hardware equipment and requirements, such as using samples with known crystal orientation angles for PC calibration, the projection method in which an object of known shape is fixed in front of the probe, and the screen-shifting method in which the probe can be moved along one axis to collect multiple images.

[0005] The software method does not involve special hardware. It simply aligns the simulated diffraction pattern with the experimental pattern and obtains the PC value from the conditions that generated the simulated pattern.

[0006] Both methods have their advantages and disadvantages. Hardware methods are expensive, complex and time-consuming to perform, and have high accidental errors, but their principles are clear and their systematic errors are low. Software methods generally have low accidental errors, but they rely heavily on simulation patterns. If the optical distortion, electron energy distribution, and band brightness asymmetry do not match the experimental images, the accuracy of the correction will be significantly affected. Combining hardware and software correction methods will combine the advantages of both methods and improve the correction effect. Summary of the Invention

[0007] In view of the defects in the prior art, the purpose of the present invention is to provide a method and system for correcting the projection center of a diffraction pattern that combines software and hardware.

[0008] According to the present invention, a method for correcting the projection center of a diffraction pattern, which combines software and hardware, comprises:

[0009] Scanning step: moving the detector along a fixed axis to scan and acquire multiple sets of related experimental diffraction patterns;

[0010] Calibration step: According to the geometric relationship of the multiple sets of associated experimental diffraction patterns, the alignment criteria of the crystal orientation angle and PC coordinates are selected, and the objective function is optimized using the Gauss-Newton iterative algorithm to align the simulated diffraction patterns and calibrate the PC value.

[0011] Preferably, the scanning step includes:

[0012] The detector moves to multiple positions along its straight line, scanning a fixed area on the sample surface multiple times and recording a series of scaled particle diffraction patterns.

[0013] Preferably, the detector corresponds to the same crystal orientation angle when moving, and each group of PC values ​​changes linearly.

[0014] Preferably, the calibration step comprises:

[0015] Multiple relatively scaled diffraction patterns are simultaneously registered with the simulated pattern, and the reduction of the residual difference between the experimental diffraction pattern gradient and the simulated diffraction pattern gradient is used as the objective function.

[0016] Preferably, if the detector movement trajectory is parallel to its normal vector, the same group (x * ,y * ) coordinates give different experimental diffraction patterns; if the detector movement trajectory is not parallel to its normal vector, or the sample drifts during the experiment, each experimental diffraction pattern corresponds to a different (x * ,y * )coordinate.

[0017] According to the present invention, a diffraction pattern projection center correction system combining software and hardware is provided, comprising:

[0018] Scanning module: moves the detector along a fixed axis to scan and acquire multiple sets of related experimental diffraction patterns;

[0019] Calibration module: According to the geometric relationship of the multiple sets of associated experimental diffraction patterns, the alignment criteria of the crystal orientation angle and PC coordinates are selected, and the objective function is optimized using the Gauss-Newton iterative algorithm to align the simulated diffraction patterns and calibrate the PC values.

[0020] Preferably, the scanning module includes:

[0021] The detector moves to multiple positions along its straight line, scanning a fixed area on the sample surface multiple times and recording a series of scaled particle diffraction patterns.

[0022] Preferably, the detector corresponds to the same crystal orientation angle when moving, and each group of PC values ​​changes linearly.

[0023] Preferably, the calibration module includes:

[0024] Multiple relatively scaled diffraction patterns are simultaneously registered with the simulated pattern, and the reduction of the residual difference between the experimental diffraction pattern gradient and the simulated diffraction pattern gradient is used as the objective function.

[0025] Preferably, if the detector movement trajectory is parallel to its normal vector, the same group (x * ,y * ) coordinates give different experimental diffraction patterns; if the detector movement trajectory is not parallel to its normal vector, or the sample drifts during the experiment, each experimental diffraction pattern corresponds to a different (x * ,y * )coordinate.

[0026] Compared with the prior art, the present invention has the following beneficial effects:

[0027] 1. This invention moves the probe along a fixed axis, varying the distance from the probe to the sample, thereby capturing multiple diffraction patterns at different projection magnifications at the same point on the sample. This geometric relationship is exploited to select an appropriate registration criterion, and a multi-image registration method is employed to correlate a simulated diffraction pattern with multiple experimental patterns to calibrate the PC value. By applying multiple methods to the same set of experimental data, the proposed method significantly outperforms both software-only and hardware-only correction methods in terms of both systematic and random errors, achieving relative accuracy improvements of 21.8% and 74.0%, respectively.

[0028] 2. The correction method provided by the present invention is highly flexible and can correct potential deviations in the pattern center caused by factors such as equipment errors or sample drift, thereby ensuring that the acquired diffraction image can accurately reflect the crystallographic information of the sample, thereby improving the accuracy and reliability of diffraction technology analysis.

[0029] 3. This invention validates the accuracy of five PC calibration methods: software, hardware, and a combination of software and hardware. The combined software and hardware method effectively combines the advantages of both software and hardware calibration methods: the low random error of the software method and the clear principle and low systematic error of the hardware method. The difference between the three methods is within 0.5%, verifying the accuracy of each method.

[0030] 4. This method's experimental operation draws on the shifting screen method, requiring multiple scans of the same sample area, which is time-consuming. Because this method validates the accuracy and precision of software-based correction, pure software-based correction based on pattern gradient registration is feasible for most particle diffraction experiments, achieving a good compromise between analytical accuracy and speed. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Other features, objects and advantages of the present invention will become more apparent upon reading the detailed description of non-limiting embodiments with reference to the following drawings:

[0032] Figure 1 It is a schematic diagram of the screen-shifting method model in the comparative example of the present invention.

[0033] Figure 2 Schematic diagram of relative displacement in a comparative example of the present invention.

[0034] Figure 3 This is a relationship diagram for calculating z* using the traditional screen shifting method in the comparative example of the present invention.

[0035] Figure 4 In the embodiment of the present invention, the same (x * ,y * ) and different z * Simulated Kikuchi pattern calculated from standard diffraction pattern under different conditions.

[0036] Figure 5 Schematic diagram of the relationship between different calibration methods in the present invention.

[0037] Figure 6 EBSD scanning crystal orientation diagrams and diffraction patterns at different probe distances in an embodiment of the present invention.

[0038] Figure 7 Schematic diagram of PC calibration results of DD22 in an embodiment of the present invention.

[0039] Figure 8 Schematic diagram of the changes in x*(a) and y*(b) values ​​corrected by different methods as the detector distance increases in an embodiment of the present invention.

[0040] Figure 9 This is a diagram of relative PC fluctuations in three dimensions under DD18-DD22 conditions in an embodiment of the present invention.

[0041] Figure 10 This is a diagram of relative PC fluctuations in three dimensions under DD18-DD26 conditions in an embodiment of the present invention.

[0042] Figure 11 Schematic diagram of the mean square error of each PC component under DD18-DD22 conditions in an embodiment of the present invention.

[0043] Figure 12 z calibrated by different methods in the embodiments of the present invention * Comparison chart with nominal detector distance under DD18, DD22, DD26 and DD30 conditions.

[0044] Figure 13 The full-field KAM distribution map calculated based on the four nearest neighbor pixels in the DD18-DD22 dataset in the embodiment of the present invention is

[0045] Figure 14 Flow chart of the method of the present invention. DETAILED DESCRIPTION

[0046] The present invention will be described in detail below with reference to specific embodiments. The following examples will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those skilled in the art, several changes and improvements can be made without departing from the scope of the present invention. These all fall within the scope of protection of the present invention.

[0047] Reference Figure 14 As shown, the present invention proposes a new PC correction method that combines software and hardware, based on the traditional screen shifting method and simulation and experimental pattern registration methods, which provides an effective way to solve this problem.

[0048] By using a mobile probe to capture multiple sets of experimental diffraction patterns, and based on the internal geometric relationships of the particle diffraction system and the registration criterion of setting the same crystal orientation, a Gauss-Newton iterative algorithm is used to optimize the objective function, thereby registering the simulated diffraction patterns and calibrating the PC values. This method significantly improves the accuracy of PC correction, thereby enhancing the accuracy and reliability of particle diffraction data analysis.

[0049] This invention will help advance the application of particle diffraction technology in fields such as materials science, providing researchers with more reliable methods for material characterization and promoting the development of materials research and engineering practice. By improving the calibration method for PC values, a more comprehensive and accurate understanding of the microstructural characteristics of materials can be achieved, providing deeper insights and support for aspects such as material design, performance optimization, and failure analysis.

[0050] The present invention provides a method for calibrating the projection center of a diffraction pattern by combining a screen-shifting method with a simulation and experimental pattern registration method, and takes the electron backscatter diffraction (EBSD) technology in a scanning electron microscope as an example to introduce its advantages and application examples. By moving the probe in the axial direction of the detector, multiple sets of related experimental diffraction patterns are scanned and acquired. According to their geometric relationship, the registration criteria of the crystal orientation angle and the PC coordinate are selected, and an objective function is established to characterize the gap between the experimental pattern and the simulated pattern. The projection parameters P including the Euler angle and the pattern center coordinate are set, and the Gauss-Newton optimization algorithm is used to correct the parameters. The objective function is gradually reduced until convergence, and the corrected projection parameters P are obtained, thereby more accurately calibrating the PC value.

[0051] This method can improve the accuracy and precision of PC value calibration in various particle diffraction techniques and has broad application prospects in microstructure research and analysis.

[0052] Comparative Example 1

[0053] Reference Figure 1 and Figure 2 As shown, in the traditional screen shifting method, (x * ,y * ) is the coordinate of the center of the diffraction pattern relative to the reference frame, z * is the distance between the sample and the detector (detector distance, DD). When the detector moves along the normal direction of the Z axis, the experimental diffraction pattern can be obtained at different positions. Figure 1 It can be seen that the diffraction patterns are magnified from left to right at a certain ratio, and there may be partial image overlap between them. There is a proportional relationship with the distance of DD change, and when the experimental geometry is well set, the center of the diffraction pattern (x * ,y * ) does not change with the change of DD.

[0054] The screen shifting method can use the experimental diffraction pattern with the smallest DD as the reference group f0(x) and calculate the remaining groups as the experimental groups f i (x) is the relative displacement compared with the reference group. x is the two-dimensional space where the experimental diffraction pattern is located, specifically the surface space of the detector. Figure 2 In the relative displacement case, according to the characteristics of the projection center, when the relative displacement of a certain pixel point is zero, the position of this point should be (x * ,y * ).

[0055] like Figure 2 As shown, (ac) correspond to the diffraction patterns with increasing probe-sample distance, (a) is the reference group, and the relative displacement of (bc) is plotted in the form of arrows.

[0056] If the signal projection imaging is distortion-free, the magnification ratio of the diffraction pattern is DD. Therefore, the relative displacement between diffraction patterns with different DD is linearly related to the pixel coordinates. Therefore, the relative displacement between patterns in the x and y directions can be expressed by a first-order polynomial:

[0057] U x (x,D)=d(xx * )

[0058] U y (x,D)=d(yy * )

[0059] (U x ,U y ) is the relative displacement between two different DD modes in the x and y directions, D = (x * ,y * ,d) is the parameter of the screen shifting method, where d is the linear displacement coefficient. In the calculation of relative displacement, U x With y (and U y The linear relationship with x) is neglected because it represents the shearing effect between the diffraction patterns during the screen shifting process, which does not exist in the projection process of the diffraction image.

[0060] In this way, the experimental group f can be determined i (x) The main mode of relative displacement compared with the reference group, that is, the mode with the most significant effect. At the same time, applying the same set of relative displacement parameters to all experimental samples can improve the robustness and stability of the model.

[0061] The parameters D of the screen shifting method are obtained by global diffraction pattern registration. First, the residual parameter ρ(x, D) = [f i (d(xx * )+x * ,d(yy * )+y * )-f0(x,y)] to simplify the following expression. i (x+U(D)) is the result of the displacement of the experimental group plus the reference group. The sum of the mean square error of the experimental image and the reference group image of the same group is listed as the objective function Θ T :

[0062]

[0063] Since the relative displacement U(D) is composed of a regular function and is smooth, the gradient-based Gauss-Newton algorithm can be used to optimize D to minimize the objective function. The specific process is as follows:

[0064] Calculate the objective function ΘT The first-order derivative of each parameter of d,

[0065]

[0066] Or more specifically,

[0067]

[0068]

[0069]

[0070] In order to make the optimization algorithm find the optimal solution more accurately, judge the concavity and convexity of the curve and the optimization direction, and accelerate the convergence speed of the algorithm, calculate the objective function Θ T The second-order partial derivatives of each parameter of D,

[0071]

[0072] The collection of second-order derivatives forms the Hessian matrix [N], which is used to minimize Θ by forming a system of linear equations. T , and thus calculate the change in parameters in each iteration:

[0073] [N]{δD}={κ}

[0074] where {κ} is the second term, representing the negative gradient vector {δD} is the change in displacement parameter D during each iteration, and sets its stopping condition (e.g., ε d =10 -4 ), and optimize D. When it is lower than the stopping condition, the calculation is considered to be completed and the most suitable relative displacement parameters are found. Otherwise, the next iteration is performed.

[0075] {D (n)}={D (n-1)}+{δD (n)}

[0076] So far, we have obtained the projection center PC and the relative scaling parameter d. The subscript T indicates that the traditional screen shifting method mainly uses the geometric relationship of similar triangles for calculation.

[0077] For the z in the projection center PC * ,Depend on Figure 3 ,According to the relative displacement parameter d, which represents the ,displacement result in the x,y direction, it can be found that the ,screen displacement distances ΔDD and d of the reference group and ,the experimental group have a similar triangle relationship.

[0078] The specific calculation method is as follows:

[0079]

[0080] To calculate DD in mm and pixels To understand the proportional relationship between the two, the physical size l of the diffraction pattern pixel needs to be substituted, which is 17.84μm in the case used in this technical briefing.

[0081] It is worth noting that in calculating The difference of DD is used instead of directly transforming DD by the size factor l. This is because the difference of DD is a relative value (and therefore more reliable), while DD itself may deviate from the true value due to zero point error. The PC value of the traditional screen shifting method is recorded as Hereinafter referred to as "Method T".

[0082] Example 1

[0083] The core of this invention is a PC correction method that combines software and hardware. Based on experimental data obtained by the screen shifting method, it uses simulation and experimental image registration to accurately correct the PC value. The detailed steps are as follows:

[0084] The particle diffraction standard pattern is calculated using EMsoft and other software, and is recorded as Figure 4 G(u) in [1]. u is the two-dimensional space where the plane diffraction standard pattern is located, specifically the equatorial plane of the unit sphere, and G(u) is the projection of the southern half of the spherical diffraction standard pattern onto the equatorial plane when projected toward the North Pole. In the method proposed in this study, multiple electron diffraction patterns (EBSPs) can be simultaneously registered to the simulated pattern G(u). For the sake of simplicity, this paper does not consider further complications of the method, such as optical distortion, variations in backscattered electron energy, or the presence of residual stress, but incorporating these factors only requires a small effort.

[0085] Generally speaking, the projection parameters to be used when simultaneously registering n diffraction patterns should be In the formula is the crystal orientation angle corresponding to the i-th diffraction pattern, are the coordinates of its projection center (the three-dimensional coordinates of the sample micro-area that produces the pattern relative to the camera).

[0086] like Figure 1 Since the series of experimental diffraction patterns are obtained when the detector is moved, and the electron beam scans the same area, the series of experimental diffraction patterns have the same crystal orientation angle, that is, At the same time, PC coordinates (x * ,y * ) does not depend on the position of the detector. Therefore, when simultaneously registering multiple diffraction patterns obtained by the screen-shifting method, the projection parameter P can be expressed as: The degree of freedom of the parameters is reduced from 6n to (n+5), and this method is denoted as method M c , the subscript c means constrained.

[0087] Another possible situation is that the sample has drifted between the two diffraction pattern acquisitions, or the detector has moved in a trajectory that is not perpendicular to its own plane. In this case, (x * ,y * ) coordinates will be different in different scans, so the projection parameter P must be expanded to The degree of freedom of the parameter is (3n+3) to adapt to different modes. This method is also named method M. f , the subscript f means floating.

[0088] The calculation process is the same as the screen shifting method. The sum of the mean square errors of multiple experimental images and simulated projection images is listed as the objective function Θ M :

[0089]

[0090] Where n is the maximum number of the experimental pattern, i is the number of the picture, and f i is the diffraction pattern obtained experimentally, g i is the simulated diffraction pattern, projected from the standard diffraction pattern: g i (x) = G(u i (P,x)), such as Figure 4 As shown. i,x ,f i,y (and the corresponding g i,y ,g i,x ) is f i (g i ) in the x,y directions.

[0091] Here, the parameter P is adjusted to minimize the objective function. The present invention continues to use the gradient-based Gauss-Newton algorithm for optimization. The objective function Θ M For the three crystal orientation angle parameters (φ1, φ2, φ3), the projection center coordinate parameters The calculation method of the first-order derivative and second-order partial derivative is the same as the traditional screen-shifting method in the previous section, so it will not be repeated here.

[0092] It is worth noting that the two variants of the multi-image registration method M c , Method M f It can be considered as an extension of the single calibration method. The application examples involve the comparison of different calibration methods. Their main characteristics and classification are shown in Figure 5 .

[0093] To test the accuracy of the PC values ​​determined by the present invention, four scans were performed on the same area of ​​a polycrystalline Al-Mg alloy. The EBSD probe was moved to detection distances (DD) of 18, 22, 26, and 30 mm, respectively, to acquire a series of high-resolution (1140 × 1600 pix) Kikuchi images. The scanning electron microscope used was a Tescan MAIA2, and the EBSD probe was a Bruker e-FlashHD. The probe tilt angle was set to 0°, the electron beam current was 20 nA, the electron beam dwell time was 0.3 seconds, and the step size was 3.43 μm. The four EBSD data sets were designated DD18, DD22, DD26, and DD30, respectively.

[0094] Figure 6 The crystal orientation maps and experimental diffraction patterns scanned at DD18, DD22, DD26, and DD30 are shown. It can be seen that as the DD increases, the size of the diffraction pattern increases by a certain proportion, while the quality of the diffraction pattern also decreases.

[0095] The overlapping portion of these four experimental grains was selected for analysis. Since diffraction pattern quality decreases with increasing DD, particularly at DD30, where the solid angle decreases and the number of electrons captured by the phosphor screen decreases, this example uses DD18 as the reference group and DD22, DD26, and DD30 as experimental groups to test the correction effects of the traditional screen-shifting method and the new method.

[0096] Figure 7 The screen shifting method (method T), single image calibration method (method S, G), and multiple image registration method (method M) were compared. c ,M f ) The results of PC calibration of DD22. Among them, (ac) uses the screen shifting method; (df) uses the single calibration method; (gi) uses the gradient-based single calibration method; (jl) uses the multi-image registration method (M f ); (mo) using multiple registration method (M c ). Both the screen shifting method and the multi-image registration method are based on the datasets DD18 and DD22.

[0097] When multiple experimental diffraction patterns are used (Method T, M c ,M f ), use data sets DD18 and DD22 for calculation.

[0098] The following conclusions can be drawn:

[0099] 1. The PC calibration image of Method S shows very clear grain outlines, while this microstructure is less obvious in the other methods. This indicates that Method S's PC calibration contains systematic errors related to crystal orientation. This deviation is caused by the failure of the simulated pattern to account for the "excess-deficit effect," where the bands in the experimental diffraction pattern are generally brighter at the top and darker at the bottom. The use of gradient-based methods greatly reduces the impact of this effect, making Method G and the multi-image registration method virtually unaffected by this deviation. It is worth noting that even the screen-shifting method, which does not use simulated patterns, exhibits a similar slight deviation.

[0100] 2. PC results obtained by different methods The differences are very small. The difference between them is between 1-3 pixels, accounting for no more than 0.3% of the image size (1140×1600). and In comparison, the difference is 3-6 pixels (about 0.5%).

[0101] 3. In most cases, the gradient-based single-image calibration method provides a high-accuracy PC calibration. Although combining the screen-shifting method with the multi-image registration method can achieve a more uniform PC distribution, its high computational cost may limit its systematic use.

[0102] One difficulty in comparing the correction methods in this study is that the “ground truth” is unknown. Figure 7 The numerical dispersion shown provides a clue to an “evaluation metric” for the study. Figure 8 (a) and (b) show the x under different methods and different DD (detector distance) conditions. * and y * It should be noted that when the calibration method requires the use of two sets of EBSP, data DD18 is always used; and to compare the results of DD18, DD22 is used as an auxiliary EBSP. Therefore, for the screen shift method and the multi-image registration method (method M c ), the PC means and standard deviations are the same at DD18 and DD22. However, for method M f , DD18 and DD22 are also used, but the PC calculation results of DD18 and DD22 will be given separately, so the statistical results will be slightly different.

[0103] exist Figure 8 In (a) and 8(b), x obtained by all methods and different distances * and y *The values ​​are close to the same value, which is represented by the black horizontal line. This also reflects the core value of the screen shifting method in PC calibration. At the same time, it can be found that as expected, the larger the detector distance, the more noise the image has, and the uncertainty of PC calibration also increases. In addition, compared with other methods, the multiple registration method (method M c ) shows the smallest discreteness. Therefore, in the following analysis, for the two variants of the multiple registration method, method M will be preferred. c , instead of M f .

[0104] The surface of the EBSD experimental sample is smooth, so the calibrated PC can be fitted into a plane, and then the deviation of each point relative to the plane is calculated as an indicator to evaluate the correction accuracy of the PC. Specifically, a plane is fitted into a plane by linear regression. Fit to all estimated x * The position of , makes the L2 norm of the residual minimum:

[0105]

[0106] Figure 9 (corresponding to DD18-DD22) and Figure 10 (corresponding to D18-D26) shows the application of the screen shift method (T) and the multiple registration method (M c )Calculate δx * It can be found that when processing the same pair of diffraction patterns, method M c The resulting relative fluctuations are much smaller than those of method T. It should be noted that the two methods process exactly the same experimental data and are affected by the same basic noise and relative motion uncertainty, so this comparison is fair.

[0107] like Figure 9 As shown, under the conditions of DD18-DD22, the relative PC fluctuations in the three-dimensional direction (δx * ,δy * ,δz * )(pix). It can be observed that compared with the screen shifting method (T), the multi-image registration method (M c ) The local fluctuations on all PC components are significantly reduced, showing higher accuracy. The area marked by the ellipse has large fluctuations and will be further analyzed in the subsequent Figure 13 Further analysis.

[0108] like Figure 10 As shown, under the conditions of DD18-DD26, the relative PC fluctuations in the three-dimensional direction (δx * ,δy * ,δz *)(pix). The screen shifting method (T) shows significantly higher local fluctuations, while the multi-image registration method (M c ) provides a more stable PC component estimate. The area marked by the ellipse has large fluctuations and will be discussed in the subsequent Figure 13 Further analysis.

[0109] from Figure 9 and Figure 10 It can be seen that the multiple registration method (M c ) calibrated PC values ​​are more concentrated and less discrete than those of the screen shifting method (T). In order to quantitatively compare the PC calibration accuracy of different methods, the root mean square (RMS) value of the relative fluctuation of the PC field σ is used as the evaluation indicator:

[0110]

[0111] Here, “method” indicates the calibration method used.

[0112] Figure 11 The uncertainty level σ of each PC component under DD18-DD22 conditions using different calibration methods is shown. It can be clearly seen that the multiple registration method (M c ) provides better calibration accuracy than the screen-shifting method (T) and the gradient-based single-image calibration method (G). Taking the dataset DD18 as an example, method M c Compared with method T, the uncertainty reductions of 74%, 66%, and 86% were achieved on the three components of PC, respectively; compared with method G, the reductions were 24%, 13%, and 19%, respectively.

[0113] against Figure 11 , you can make the following comments:

[0114] Among the three PC components, the σ(δz * ) is the highest. For the gradient-based single-image calibration method (G) and the multi-image registration method (M c ),σ(δz * ) is significantly smaller than σ(δx * ) and σ(δy * ). * In terms of calibration, method G performs particularly well, while method T performs the worst in this component. This is mainly because when matching the experimental pattern with the simulation pattern, x * and y * There is a high correlation between the crystal orientation parameters.

[0115] In method T, the uncertainty of PC calibration is about 2.5‰-5.0‰ of the pattern width; while for methods G and M c, the value is reduced to about 1‰. This once again verifies the advantage of the software-based calibration method in terms of accuracy.

[0116] Method M c Calibration accuracy is improved by repeated measurements and full use of geometric constraints. Simultaneous correlation processing of high-quality patterns (i.e., patterns with shorter detector distances) can further improve accuracy.

[0117] After excluding method S with systematic error, the calibration accuracy of each method is ranked from high to low as follows: M, G, T. In order to select the best calibration method, this study finally selected method M. c , because its result dispersion is the smallest and the performance is the best.

[0118] Using a detector pixel size of 17.84 μm, this study calibrated the z * Compared with the nominal detection distance (DD), the results are as follows Figure 12 As shown, the data bars of the four methods are offset in the vertical direction (each method is vertically offset by multiples of 2 mm in the figure, but the regression line function obtained by fitting is not offset).

[0119] Although these methods have differences in uncertainty, the uncertainty of each method T, G, M f and M c The calculated z * The trend of the values ​​is consistent. In addition, the z * This is usually about 1.4 mm smaller than the nominal DD given by the scanning electron microscope (SEM), which may be due to inaccurate zero point positioning. Therefore, the nominal DD value should be used with caution. Figure 12 The offsets shown in the regression equation are 1.391, 1.405, 1.405, and 1.415 mm, corresponding to T, G, and M, respectively. f and M c Method z on 4 DD * Fitting results. It is worth noting that the z obtained by these four methods * The offset discreteness is very small, only 0.025 mm, further verifying the consistency between these EBSD correction methods.

[0120] In addition to the PC coordinates, software-based PC corrections can also provide crystal orientation. Comparison of Methods G and M cThe calibrated crystal orientation is also very meaningful. Specifically, KAM (Kernel Average Misorientation) can be used to assess the local crystal rotation and degree of plastic deformation of the sample. This is achieved by calculating the orientation difference between each pixel and its neighbors. In this study, the samples used were as-cast and had not undergone plastic deformation, so the KAM value should be very small. Therefore, the average KAM value can be used as an effective indicator of the quality of the orientation measurement.

[0121] Figure 13 The full-field KAM distribution map calculated based on the four nearest neighbor pixels in the DD18-DD22 dataset is shown. The ellipse marks the area with higher KAM values. For method G, the KAM value of DD22 is higher than that of DD18 because the larger detector distance means that the captured solid angle is smaller and the image quality is worse. For method M c , since a unified crystal orientation setting is used in the calculation, the KAM fields obtained under DD18 and DD22 conditions are consistent.

[0122] Multiple image registration method (M c ) improves the calibration accuracy of crystal orientation, thereby reducing the KAM value. Table 1 lists the average KAM values ​​of the entire scanning area under DD18 and DD22 conditions. Compared with the single-sheet calibration method (G), method M c The average KAM values ​​of the two groups decreased by 11.8% (DD18) and 26.1% (DD22), respectively.

[0123] Table 1 Average KAM values ​​of the whole experimental group of DD18 and DD22 (°)

[0124]

[0125]

[0126] It is worth noting that in methods T and M c Under these conditions, regions with higher KAM values ​​also tend to exhibit higher PC calibration uncertainties, e.g. Figure 9 、 Figure 10 and Figure 13 The reason for this phenomenon is that although the shifting screen method assumes that the two EBSD images cover the same sample area, this is not entirely true in practice. Due to the displacement of the sample during the scanning process and the relatively large step size (3.43μm in this experiment), the electron beam may illuminate slightly different areas. Therefore, the premise of imposing the same crystal orientation on the pattern pair is not completely accurate in the presence of sample drift, which may affect the calibration results. This effect is particularly pronounced in areas with higher crystal orientation inconsistency (i.e., areas with higher KAM).

[0127] The present invention also provides a software and hardware combined diffraction pattern projection center correction system. The software and hardware combined diffraction pattern projection center correction system can be implemented by executing the process steps of the software and hardware combined diffraction pattern projection center correction method, that is, those skilled in the art can understand the software and hardware combined diffraction pattern projection center correction method as a preferred implementation of the software and hardware combined diffraction pattern projection center correction system.

[0128] Specifically, a diffraction pattern projection center correction system combining software and hardware includes:

[0129] Scanning module: moves the detector along a fixed axis to scan and acquire multiple sets of related experimental diffraction patterns;

[0130] Calibration module: According to the geometric relationship of the multiple sets of associated experimental diffraction patterns, the alignment criteria of the crystal orientation angle and PC coordinates are selected, and the objective function is optimized using the Gauss-Newton iterative algorithm to align the simulated diffraction patterns and calibrate the PC values.

[0131] The scanning module includes:

[0132] The detector moves to multiple positions along its straight line, scanning a fixed area on the sample surface multiple times and recording a series of scaled particle diffraction patterns.

[0133] The detector corresponds to the same crystal orientation angle when moving, and each group of PC values ​​changes linearly.

[0134] The calibration module includes:

[0135] Multiple relatively scaled diffraction patterns are simultaneously registered with the simulated pattern, and the reduction of the residual difference between the experimental diffraction pattern gradient and the simulated diffraction pattern gradient is used as the objective function.

[0136] If the detector movement trajectory is parallel to its normal vector, then the same group (x * ,y * ) coordinates give different experimental diffraction patterns; if the detector movement trajectory is not parallel to its normal vector, or the sample drifts during the experiment, each experimental diffraction pattern corresponds to a different (x * ,y * )coordinate.

[0137] Those skilled in the art will appreciate that, in addition to implementing the system and its various devices, modules, and units provided by the present invention in purely computer-readable program code, it is entirely possible to implement the same functions of the system and its various devices, modules, and units provided by the present invention in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. Therefore, the system and its various devices, modules, and units provided by the present invention can be considered a hardware component, and the devices, modules, and units included therein for implementing various functions can also be considered as structures within the hardware component; the devices, modules, and units for implementing various functions can also be considered as both software modules implementing the method and structures within the hardware component.

[0138] The above describes specific embodiments of the present invention. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art may make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. The embodiments of this application and the features in the embodiments may be combined with each other in any manner unless there is a conflict.

Claims

1. A software and hardware combined diffraction pattern projection center correction method, characterized in that: include: Scanning step: moving the detector along a fixed axis to scan and acquire multiple sets of related experimental diffraction patterns; Calibration step: According to the geometric relationship of the multiple sets of associated experimental diffraction patterns, the alignment criteria of the crystal orientation angle and PC coordinates are selected, and the objective function is optimized using the Gauss-Newton iterative algorithm to align the simulated diffraction patterns and calibrate the PC value.

2. The software-hardware combined diffraction pattern projection center correction method according to claim 1, characterized in that: The scanning step comprises: The detector moves to multiple positions along its straight line, scanning a fixed area on the sample surface multiple times and recording a series of scaled particle diffraction patterns.

3. The software-hardware combined diffraction pattern projection center correction method according to claim 2, characterized in that: The detector corresponds to the same crystal orientation angle when moving, and each group of PC values ​​changes linearly.

4. The software-hardware combined diffraction pattern projection center correction method according to claim 1, characterized in that: The calibration steps include: Multiple relatively scaled diffraction patterns are simultaneously registered with the simulated pattern, and the reduction of the residual difference between the experimental diffraction pattern gradient and the simulated diffraction pattern gradient is used as the objective function.

5. The software-hardware combined diffraction pattern projection center correction method according to claim 4, characterized in that: If the detector movement trajectory is parallel to its normal vector, then the same group (x * ,y * ) coordinates give different experimental diffraction patterns; If the detector movement trajectory is not parallel to its normal vector, or the sample drifts during the experiment, each experimental diffraction pattern will correspond to a different (x * ,y * )coordinate.

6. A software and hardware combined diffraction pattern projection center correction system, characterized in that: include: Scanning module: moves the detector along a fixed axis to scan and acquire multiple sets of related experimental diffraction patterns; Calibration module: According to the geometric relationship of the multiple sets of associated experimental diffraction patterns, the alignment criteria of the crystal orientation angle and PC coordinates are selected, and the objective function is optimized using the Gauss-Newton iterative algorithm to align the simulated diffraction patterns and calibrate the PC values.

7. The software-hardware combined diffraction pattern projection center correction system according to claim 6, characterized in that: The scanning module includes: The detector moves to multiple positions along its straight line, scanning a fixed area on the sample surface multiple times and recording a series of scaled particle diffraction patterns.

8. The software-hardware combined diffraction pattern projection center correction system according to claim 7, characterized in that: The detector corresponds to the same crystal orientation angle when moving, and each group of PC values ​​changes linearly.

9. The software-hardware combined diffraction pattern projection center correction system according to claim 6, characterized in that: The calibration module includes: Multiple relatively scaled diffraction patterns are simultaneously registered with the simulated pattern, and the reduction of the residual difference between the experimental diffraction pattern gradient and the simulated diffraction pattern gradient is used as the objective function.

10. The software-hardware combined diffraction pattern projection center correction system according to claim 9, characterized in that: If the detector movement trajectory is parallel to its normal vector, then the same group (x * ,y * ) coordinates give different experimental diffraction patterns; If the detector movement trajectory is not parallel to its normal vector, or the sample drifts during the experiment, each experimental diffraction pattern will correspond to a different (x * ,y * )coordinate.

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