Electron beam focusing parameter self-adaptive calibration method based on regional recursive splitting and analytic field guidance

Abstract

The invention discloses an electron beam focusing parameter adaptive calibration method based on regional recursive splitting and analytic field guidance, and belongs to the technical field of electron beam equipment precision control. In order to solve the problems of low full-field uniform sampling efficiency and poor sparse sampling precision in large-view-field electron beam processing, the invention provides a dual-drive adaptive sampling strategy. According to the method, a theoretical curvature distribution diagram is constructed by using an electron optical analytical field to serve as prior guidance, and a distortion sensitive area in a view field is identified according to a multi-dimensional feature fusion criterion of physical prior, differential field nonlinearity and an actual measurement form; a recursive regional geometric subdivision structure is adopted to perform recursive splitting and encrypted sampling on the sensitive region, and narrow window rapid search is realized in combination with a parameter inheritance strategy; and finally, reconstructing a full-field high-precision model based on a scattered data interpolation algorithm. According to the method, sparse sampling can be automatically carried out in the smooth field curvature change region, encryption sampling can be carried out in the severe distortion region, and the calibration efficiency is remarkably improved on the premise of ensuring high focusing precision.

Description

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[0001] The application belongs to the technical field of precise control of electron beam equipment, and particularly relates to a focusing parameter self-adaptive calibration and field curvature model reconstruction method for large field of view electron beam processing. BACKGROUND

[0002] High-energy electron beam technology has been widely used in high-end manufacturing fields such as electron beam welding, electron beam melting and electron beam selective melting due to its extremely high energy density, beam spot resolution and excellent controllability. In these application scenarios, the electron beam usually needs to be deflected at a high speed in a large scanning field of view, and at the same time, the uniformity of the focused beam spot size must be maintained to ensure the processing precision or imaging quality. However, the electron optical system is generally subject to the field curvature effect. When the electron beam is guided to a position deviating from the central optical axis by the magnetic deflection coil, the geometric optical path of the electron beam to the workpiece surface will increase with the increase of the deflection angle, resulting in that the actual focusing point of the electron beam falls on a curved surface above the workpiece surface. If the control system cannot adjust the focusing current in real time to compensate for this optical path difference, the beam spot on the workpiece surface will be severely out of focus, especially in the edge region of the large field of view scanning, the out-of-focus phenomenon often shows a severe nonlinear deterioration, which seriously limits the effective working range and process performance of high-end equipment.

[0003] In order to compensate for the above-mentioned field curvature effect, the existing control system usually adopts dynamic focusing technology, that is, the exciting current of the focusing coil is adjusted in real time according to the scanning coordinates. At present, the method for obtaining the focusing parameter model mainly depends on pure physical model calculation or discrete point sampling calibration. Among them, the pure physical model calculation method derives the compensation value based on the electron optical formula, but due to the inevitable existence of pole shoe machining tolerance, coil assembly tilt and nonlinear magnetic hysteresis effect of soft magnetic material in the actual equipment, the pure theoretical calculation cannot cover these complex engineering errors, resulting in large residual aberration of open-loop control, which often cannot meet the high-precision processing demand. On the other hand, the calibration method based on actual measurement usually adopts uniform grid sampling in the whole field, that is, the field of view is divided into dense uniform grids and automatic focusing measurement is carried out point by point. Although this method can obtain high precision, in order to capture the nonlinear region of the field of view with severe distortion, it is necessary to maintain a very high sampling density in the whole field, resulting in a very time-consuming calibration process, which seriously reduces the production efficiency of the equipment and is not suitable for rapid calibration and maintenance in industrial field. If the sampling density is simply reduced to adopt sparse sampling, although the efficiency is improved, the underfitting phenomenon is easy to occur in the edge region of the field of view with high order aberration, and a high-precision full-field compensation model cannot be established.

[0004] In summary, existing electron beam focusing parameter calibration techniques suffer from a dilemma where sampling efficiency and modeling accuracy are difficult to balance. The root cause lies in the lack of adaptability in current sampling strategies, which cannot automatically adjust the sampling density based on the drastic changes in the physical field. Therefore, there is an urgent need for an intelligent calibration method that combines prior knowledge of electron-optical physics with real-time measurement feedback. This method would automatically perform sparse sampling in the central region where field curvature changes are gentle, and automatically perform dense sampling in the edge regions with complex distortions. This would minimize the number of sampling points while ensuring overall focusing accuracy, thus solving the technical challenges of low calibration efficiency and uneven accuracy in large field-of-view electron beam equipment. Summary of the Invention

[0005] This invention aims to address the challenge of balancing sampling efficiency and modeling accuracy in existing large field-of-view electron beam focusing parameter calibration techniques. To overcome the drawbacks of time-consuming full-field uniform sampling methods and insufficient accuracy in distortion regions with fixed sparse sampling methods, this invention proposes an adaptive calibration method. This method automatically adjusts the sampling grid distribution density based on the intrinsic curvature characteristics of the electron optical physical field and the real-time measurement difference characteristics. This significantly reduces the total number of sampling points and improves calibration efficiency while maintaining full field-of-view focusing consistency.

[0006] To achieve the above objectives, this invention provides an adaptive calibration method for electron beam focusing parameters based on regional recursive splitting and analytical field guidance. This method includes the following steps:

[0007] The first step involves constructing an analytical field prior model and a theoretical curvature distribution map. This method first establishes an ideal focusing current distribution model using electron optics physics, aiming to provide global trend guidance for subsequent adaptive sampling. Specifically, based on the actual geometric parameters of the electron beam equipment, including the object distance S from the electron gun emitting surface to the center of the focusing coil, the working distance H from the center of the focusing coil to the workpiece surface, and the accelerating voltage U of the electron beam, an analytical function of the ideal focusing current as a function of the deflection radius r is derived using electron optics imaging principles. Although this theoretical model does not include assembly errors in actual equipment or the nonlinear hysteresis effect of soft magnetic materials, it accurately describes the inherent topological structure of the electron beam field curvature effect. Based on this, the second derivative modulus of the theoretical model across the entire field of view is calculated using numerical differentiation, generating a theoretical curvature distribution map. This distribution map serves to prevent the omission of theoretically drastically changing regions, such as the center of the field of view, due to insufficient sampling points in the initial sparse sampling stage, thus acting as a safeguard against undersampling.

[0008] The second step is to initialize the sparse sampling grid. The system divides the maximum scanning field of view of the electron beam into an initial, low-density rectangular grid structure (e.g., or (A uniform mesh). This step aims to quickly establish the basic skeleton of the field-of-view focusing characteristics with a minimum number of sampling points, extracting the coordinates of all vertices of this initial mesh as the first list of sampling points to be tested. This sparse initialization strategy avoids the blind full-field high-density scanning of traditional methods in the initial stage, thus providing an efficient starting state for subsequent iterative splitting.

[0009] The third step involves performing automatic focusing measurements. The control system drives the electron beam deflection coils to sequentially deflect the electron beam to the coordinate positions listed in the sampling point list. For each sampling point, an automatic focusing search algorithm is run, adjusting the focusing coil current stepwise within a preset current range, and backscattered electron images are acquired in real time for sharpness evaluation. By finding the maximum value of the sharpness evaluation function, the actual optimal focusing current value corresponding to each sampling point is obtained. This process acquires real physical measurement data, including information on equipment assembly errors and distortion.

[0010] The fourth step is grid cell evaluation and multidimensional splitting criterion calculation. The system traverses all current grid cells and calculates the comprehensive splitting weight J of each cell according to a preset multidimensional feature fusion strategy. This strategy includes the following three evaluation metrics:

[0011] 1. Physical prior indicators: Based on the theoretical curvature distribution map generated in the first step, the theoretical curvature features within the grid are extracted to prevent the omission of theoretically drastic regions due to initial sparse sampling;

[0012] 2. Differential Nonlinearity Index: Calculates the difference field between the measured focusing current and the theoretical value, and evaluates the spatial distortion and second-order rate of change of this difference field within the grid. This index eliminates the large theoretical field curvature background and is specifically designed to capture non-physical distortions caused by equipment assembly errors or hysteresis effects;

[0013] 3. Measured morphological indicators: Based on the currently acquired sampling points, a fitting model is constructed, and the measured geometric curvature at the grid position is calculated to approximate the real physical field morphology in the later stages of iteration.

[0014] Finally, the system integrates the above indicators using a dynamic weighting formula. If J exceeds a preset threshold, the region is determined to be a distortion-sensitive area, triggering recursive splitting.

[0015] The fifth step involves quadtree recursive splitting and parameter inheritance. For mesh cells determined to require splitting, a quadtree decomposition operation is performed, dividing their geometric space into four equal-sized sub-mesh areas. The vertices of the newly generated sub-mesh areas are then added to the sampling queue. When performing automatic focusing measurements on these newly generated child nodes, this invention innovatively employs a parameter inheritance and model-guided strategy: the system no longer blindly searches from zero, but instead comprehensively utilizes parent node inheritance, neighborhood interpolation, or predictions from the currently fitted model to calculate the predicted focusing current for that child node, using this as the initial value for the automatic focusing search. This strategy significantly narrows the search range, resulting in a substantial improvement in the convergence speed of new point measurements.

[0016] Step 6: Iteration and Termination. The system repeats the measurement, evaluation, and splitting processes described above, forming a closed-loop iteration. As the iteration progresses, the sampling mesh automatically becomes denser in regions with large curvature changes and severe distortion, while remaining sparse in flat regions. When the splitting weights of all mesh cells are below a preset threshold, or when the mesh size has reached the preset minimum resolution limit, the system determines that the calibration process has converged and stops the sampling loop.

[0017] Step 7: Non-uniform data reconstruction and output. Using the final non-uniform discrete sampling point set containing coordinates (x, y) and the corresponding optimal current I, a scrambled data interpolation algorithm with smooth and continuous characteristics is employed to reconstruct a continuous, high-precision focusing compensation current surface model covering the entire field of view. Finally, according to the requirements of the hardware controller, this continuous model is discretized into a regular high-density lookup table for real-time dynamic focusing control in subsequent electron beam processing.

[0018] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0019] This invention provides an adaptive calibration method for electron beam focusing parameters that integrates prior physical knowledge and data-driven feedback. By introducing dual criteria of analytical field guidance and differential feedback, it effectively solves the contradiction between the low efficiency of traditional full-field uniform sampling and the insufficient accuracy of fixed sparse sampling at the edge of the field of view. While ensuring high accuracy of the full-field focusing model, it significantly improves calibration efficiency compared to traditional calibration methods.

[0020] 1. An adaptive sampling grid distribution based on dual criteria breaks away from the rigid mode of traditional uniform sampling. It can automatically densify sampling in areas with large theoretical curvature guided by the analytical field, and automatically subdivide the grid in areas with severe measured distortion based on differential nonlinearity. This on-demand allocation strategy ensures the capture of all higher-order aberration features while significantly reducing invalid and redundant data in flat areas, reducing the total calibration time by an order of magnitude.

[0021] 2. A priori guidance mechanism based on the electro-optical analytical field is introduced, which utilizes the physical mechanisms of electro-optics to construct a theoretical curvature distribution map as a baseline constraint for initial sampling. This effectively avoids the undersampling dilemma that pure data-driven methods are prone to in the early stages of sparse sampling, prevents the omission of key physical features such as the field of view center due to the randomness of the initial sampling point positions, and significantly improves the robustness of the algorithm under extremely sparse data.

[0022] 3. Decoupling Strategy Based on Differential Domain Detection and Global Reconstruction. This invention innovatively decouples the distortion detection and model reconstruction stages. In the mesh subdivision stage, the nonlinear characteristics of the differential field are constructed as a high-sensitivity criterion to eliminate the theoretical field curvature background and accurately locate non-physical distortions. In the final modeling stage, a scattered data reconstruction algorithm with high fidelity is switched to. This strategy effectively avoids the defect in traditional methods where small distortions are smoothly masked by directly using the residuals of the fitted model, achieving efficient capture and accurate reconstruction of complex distortion regions.

[0023] 4. Parameter Inheritance and Narrow Window Search Strategy in Quadtree Fission Process. Taking full advantage of the spatial continuity of the physical field, when generating new sampling points through mesh splitting, the initial search values ​​for child nodes are established by comprehensively utilizing parent node inheritance, neighborhood interpolation, or model fitting prediction. This strategy compresses the search interval of the autofocus algorithm from the entire domain to a local narrow window range near the initial value. This improvement significantly reduces the time complexity of single-point search from linear to linear, avoiding the inefficient process of blindly searching the entire domain for each point in traditional methods, and greatly shortening the convergence time of single-point measurements. Attached Figure Description

[0024] Figure 1 This is the main flowchart of the adaptive calibration method for electron beam focusing parameters based on regional recursive splitting and analytical field guidance of the present invention;

[0025] Figure 2 This is a schematic diagram of the physical model geometry of the electron beam focusing system in this invention (in the figure: 1-electron beam source, 2-focusing coil, 3-electron beam trajectory, 4-workpiece surface).

[0026] Figure 3 This is a flowchart illustrating the calculation and determination logic of the comprehensive splitting weight in this invention;

[0027] Figure 4 This is a schematic diagram of the recursive splitting of the quadtree region and the generation of sampling points in this invention;

[0028] Figure 5 This is a schematic diagram comparing the narrow-window search strategy based on parameter inheritance in this invention with the traditional global search strategy. Detailed Implementation

[0029] To enable those skilled in the art to better understand the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0030] This invention provides an adaptive calibration method for electron beam focusing parameters based on regional recursive splitting and analytical field guidance. The core idea of ​​this method is to break through the limitations of traditional uniform sampling, utilize the prior knowledge of the electron optical physical model to guide the initial sampling, and use the differential nonlinear characteristics of the measured data to drive the subsequent grid refinement. Thus, while ensuring the focusing accuracy at the edge of a large field of view, the number of sampling points is significantly reduced, and the calibration efficiency is improved.

[0031] like Figure 1 As shown, the method in this embodiment specifically includes the following steps:

[0032] Step 1: Constructing the analytical field prior model. First, establish the geometrical-optical model of the electron beam focusing system. For example... Figure 2 As shown (where: 1 - electron beam source, 2 - focusing coil, 3 - electron beam trajectory, 4 - working surface), let the object distance from the electron gun filament to the center of the focusing coil be... The working distance from the center of the focusing coil to the workpiece surface is H, the electron beam accelerating voltage is U, the number of coil turns is N, and the lens shape factor is k. When the electron beam deflects to coordinates (x, y) on the field of view plane, according to geometric relationships, the actual flight path length L of the electron beam is:

[0033]

[0034] Based on the principles of electron optical imaging, a theoretical model of the focusing current under ideal conditions is derived. :

[0035]

[0036] Based on this analytical expression, the system calculates the second derivative modulus of the function with respect to position coordinates across the entire field of view, generating a theoretical curvature distribution map. This distribution map quantitatively characterizes the inherent topological structure of the physical field, serving as a priori guide for subsequent mesh splitting and preventing feature omissions due to excessively sparse initial sampling.

[0037] Step 2: Initialize the sparse sampling grid. Divide the maximum scanning field of view of the electron beam into an initial rectangular sparse grid (preferably N=5 in this embodiment). Extract the coordinates of all vertices of this grid to generate the first set of sampling points to be tested. This step aims to build the entire field's skeletal model with minimal time investment.

[0038] Step 3: Perform automatic focusing measurement. Control the electron beam to sequentially jump to the sampling point set. The coordinate positions of each point are determined. To ensure the accuracy of autofocus, in this embodiment, the calibration process is performed on a dedicated calibration plate placed on the workpiece table. The surface of the calibration plate is etched with a high-contrast grid array or dot array feature. If a calibration plate cannot be placed on the actual machining site, the natural texture of the metal powder bed surface can be used directly as a high-frequency feature source. For each sampling point, the coordinates calculated in the first step are used... Using the value as the center, a relatively narrow search interval is set, and a variable step-size extremum search algorithm is run. By acquiring and calculating the backscattered electron image sharpness evaluation function of the calibration plate features or powder bed texture in real time, the optimal measured value of the focusing current at that point is found and recorded. .

[0039] Step 4: Calculate the comprehensive splitting weight of the grid cells. This is the core criterion of this invention, and its calculation and judgment logic is as follows: Figure 3 As shown. The system traverses all current mesh cells and calculates the comprehensive splitting weight for each cell k. This quantitatively determines whether the area needs further encryption. In this preferred embodiment, the following linear weighted fusion formula is used for calculation:

[0040]

[0041] The physical meaning and calculation method of each variable in the formula are detailed below:

[0042] The first term is a physical prior. Among them, This represents a local eigenvalue of the theoretical curvature within the grid cell, preferably the maximum value of the second derivative modulus. The denominator is... This is the maximum theoretical curvature value of the entire field of view calculated in step S1. Its purpose is to normalize the physical prior indices, ensuring that the fundamental splitting weights approach α in the region where theoretical changes are most drastic.

[0043] The second term is a difference nonlinear term. Among them, Let be the nonlinear eigenvalue of the differential field for this grid cell k. The specific calculation steps are as follows: First, calculate the difference between the measured focusing current and the theoretical focusing current at the four vertices of the grid cell, and construct the local differential field. Subsequently, using the formula Calculate the topological characteristics of this difference field. Where, The distortion factor characterizes the degree of saddle-shaped distortion in the difference field; The curvature factor characterizes the degree of nonlinear arching or oscillation in the difference field. (Denominator) It represents the maximum differential nonlinear eigenvalue among all measured mesh cells in the full field of view in the current iteration step.

[0044] The third item is the measured morphology item. Among them, Let be the measured geometric curvature characteristic value of grid cell k. To fully utilize the spatial distribution information of all historical measurement data to obtain the most robust full-field morphology prediction capability, this term is preferably calculated using a global fitting strategy. That is, using all measured sampling points obtained in the current iteration step, a global thin-plate spline interpolation model is constructed, and the second derivative modulus of this TPS model at the current grid cell location is analytically calculated. (Denominator) This represents the maximum curvature value of the current fitted model across the entire field of view.

[0045] Regarding the weight coefficients α, β, and γ, they satisfy α + β + γ = 1. In practical engineering calculations, to enhance the numerical stability of the algorithm and prevent the denominator from approaching zero, this embodiment introduces a very small positive number ϵ as a protection value in the denominator term of the above formula. Furthermore, this embodiment employs a piecewise linear adjustment strategy to dynamically update the weights: in the initial stage, a larger α is set to highly trust the physical prior; in the transition stage, α decreases linearly with the increase in the number of sampling points; in the fine stage, a smaller α is locked while β and γ are increased, so that the system mainly relies on the differential nonlinear characteristics and the measured morphological curvature to accurately approximate the real physical distortion field.

[0046] It should be noted that the above formula is only a preferred embodiment of the present invention. In practical applications, the comprehensive subdivision weights... The calculation can also employ nonlinear weighting, fuzzy logic reasoning, or machine learning-based decision models. As long as the decision input features include physical priors and differential nonlinear features, they should fall within the protection scope of this invention.

[0047] Step 5: Recursive splitting of the quadtree and parameter inheritance. Combine all the splitting weights... Exceeding the preset threshold The mesh cells are marked as distortion-sensitive regions. For example... Figure 4 As shown, a quadtree decomposition operation is performed on these units, dividing them into four sub-grids and generating new sampling points to be measured. When performing automatic focusing measurements on the newly generated child nodes, this embodiment employs a strategy combining parameter inheritance and model guidance: as follows... Figure 5 As shown, the automatic focusing search for child nodes no longer starts from zero. Instead, it comprehensively utilizes methods such as direct inheritance from the parent node, neighborhood distance weighted interpolation, or fitted model prediction to calculate the estimated focusing current of the child node, using this estimated current as the starting center of the search, and limiting the search range to a relatively narrow window near the estimated value. To prevent the optimal focusing point from falling outside this narrow window due to excessively large abrupt changes in local distortion, the system has a backoff mechanism: if the sharpness evaluation function curve calculated within the narrow window does not show a maximum peak, or if the peak is located at the boundary of the narrow window, the system will automatically trigger a global search mode or gradually expand the search window to ensure the reliability of the measurement results.

[0048] Step 6: Iteration and Termination. Repeat steps 3 through 5, continuously updating the sample point set and re-evaluating the grid state. Stop iterating when any of the following conditions are met:

[0049] 1. The combined splitting weights of all current grid cells. All values ​​are below the preset threshold (indicating that the model is accurate enough);

[0050] 2. The grid size has reached the minimum resolution allowed by the system (e.g., 0.5mm, to prevent infinite subdivision).

[0051] Step 7: Surface Reconstruction and Discretization. Utilizing the final obtained non-uniform sampling point set... A full-field continuous focusing model is established using a scattered data reconstruction algorithm. To ensure high-fidelity reproduction of the measured physical field and guarantee smooth continuity in the final model, this embodiment preferably uses a thin-plate spline model with high-fidelity characteristics. The TPS algorithm, by minimizing the bending energy function, can generate a physical surface that conforms to the continuous variation characteristics of the electron beam magnetic field while balancing data fidelity and surface smoothness. Of course, those skilled in the art can also choose other algorithms with smooth reconstruction capabilities, such as radial basis functions or kriging models, depending on actual computing resources and noise reduction requirements. Finally, according to the interface requirements of the hardware controller, the reconstructed full-field continuous model is resampled in a regularized manner to generate a high-density discrete lookup table, which is then output to a real-time control system such as an FPGA for dynamic focusing compensation during processing.

Claims

1. An electron beam focusing parameter self-adaptive calibration method based on area recursive splitting and analytical field guiding, characterized in that, The method comprises the following steps: Step S1: constructing a priori model of the analysis field. Based on the geometric structure parameters of the electron beam focusing system and the electron optical imaging principle, a focusing current distribution model in an ideal state is constructed, and a full field theoretical curvature distribution is calculated; Step S2: initializing a sparse sampling grid. The electron beam scanning field is divided into an initial sparse grid area, and the grid vertices are extracted as the first batch of to-be-measured sampling points; Step S3: performing automatic focusing measurement. The electron beam is deflected to the to-be-measured sampling point position, and an automatic focusing search algorithm is run to obtain the best measured value of the focusing current of each sampling point; Step S4: grid cell evaluation and subdivision determination. The comprehensive subdivision weight of each grid cell is calculated according to a preset multi-dimensional feature fusion strategy, which is based on three dimensions of features: the theoretical curvature feature of the priori model of the analysis field, the difference field nonlinearity feature formed by the measured focusing current and the theoretical value, and the morphological curvature feature of the measured focusing current itself; if the comprehensive subdivision weight of a certain grid cell exceeds a preset threshold, it is determined that the area is a distortion sensitive area; Step S5: recursive subdivision and parameter inheritance of the area. Recursive area geometric subdivision is performed on the grid cells determined as the distortion sensitive area to generate new sub-grids and to-be-measured sampling points; when measuring the new sampling points, the calibration results of the measured reference points are used to determine the search initial value; Step S6: iterative cycle and convergence termination. Steps S3 to S5 are repeatedly executed until the preset convergence condition is met; Step S7: surface reconstruction and data output. The non-uniform discrete sampling point set obtained after the iteration is used, the point set has a high density distribution characteristic in the distortion sensitive area, and a scattered data interpolation or approximation algorithm with smooth and continuous characteristics is used to reconstruct a full field continuous focusing compensation model.

2. The method of claim 1, wherein, In step S4, the integrated subdivision weight The calculation of the integrated subdivision weight employs the following linearly weighted fusion formula: wherein k is the index of the current grid cell to be evaluated; is the local eigenvalue of the theoretical curvature within the grid cell k; is the maximum value of the theoretical curvature of the full field of view calculated in step S1, used for normalizing the physical prior term; is the differential field nonlinear eigenvalue of the grid cell k, which is calculated by constructing a local differential field based on the difference between the measured focusing current and the theoretical focusing current within the grid cell, and calculating the spatial twist and the second-order change rate of the differential field in the grid; is the maximum differential nonlinear eigenvalue of all measured grid cells in the full field of view in the current iteration step, used for normalizing the differential term; is the measured morphological curvature eigenvalue of the grid cell k, which is calculated by constructing a fitting model based on the measured sampling point set obtained in the current iteration step, and calculating the second-order derivative modulus or curvature eigenvalue of the fitting model at the current grid cell position; is the maximum curvature value of the current full field of view measured fitting surface, used for normalizing the measured morphological term; α, β, γ are the corresponding weight coefficients.

3. The method of claim 2, wherein, The weight coefficients a, b, g adopt a dynamic adjustment mechanism that evolves with the iteration calibration process: in the early stage of iteration or when the number of sampling points is small, a higher physical prior weight a is set to give priority to the analysis field model to prevent distortion of the full field fitting model caused by sparse sampling; as the number of iterations increases or the number of sampling points increases, the physical prior weight a is gradually reduced, and the difference field nonlinearity weight b and the measured morphological curvature weight g are simultaneously increased, so that the calibration process smoothly transitions from relying on the theoretical model to relying on the measured data for driving, to accurately approximate the real physical distortion field.

4. The method of claim 1, wherein, In step S5, the recursive area geometric subdivision specifically adopts a multi-scale space geometric splitting strategy; the strategy adopts a multi-branch tree decomposition structure; wherein, for a two-dimensional scanning field, the multi-branch tree decomposition structure is preferably a quadtree decomposition structure; for the grid cells determined as the distortion sensitive area, the geometric space is divided into four subspaces, and the vertices or centroids of the newly generated subspaces are added to the to-be-measured sampling queue.

5. The method of claim 1, wherein, In step S5, the initial value of the search is determined by using the calibration results of the measured reference points, and a strategy combining parameter inheritance and model guidance is adopted: the measured node data in the spatial neighborhood of the new sampling point is obtained, and the focused current prediction value of the new sampling point is calculated by using one or more of direct inheritance of parent nodes, neighborhood distance weighted interpolation, or fitting model prediction; the prediction value is set as the center initial value of the autofocus search algorithm, and the window width of the search interval is adaptively adjusted according to the local distortion degree of the current region.

6. The method of claim 1, wherein, In step S7, the surface reconstruction specifically adopts a scattered data reconstruction algorithm with smooth and continuous characteristics, including a thin plate spline interpolation algorithm, a radial basis function interpolation algorithm, or a Kriging interpolation algorithm.

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