CN114648611B - Method and device for three-dimensional reconstruction of local orbit function - Google Patents

The application discloses a three-dimensional reconstruction method and device of a local orbit function, wherein the method comprises the following steps: collecting image data of samples under a plurality of inclination angles, scattering points at equal intervals in a real space, and utilizing linear accumulation to obtain a calculated image under each inclination angle of the plurality of inclination angles, further obtaining gradients of a loss function relative to parameters to be optimized, optimizing the parameters to be optimized according to the gradients, screening out atoms meeting preset conditions, recalculating a new loss function until meeting convergence conditions, reconstructing three-dimensional space coordinates of the center of a local orbit function in the real space and the shape of the local orbit function, and obtaining a three-dimensional reconstruction result. Therefore, the technical problems that in the related art, only three-dimensional coordinates of atoms can be obtained from the reconstructed three-dimensional density matrix, errors cannot be corrected, the reconstruction process has high requirements on hardware, and the accuracy of the reconstructed three-dimensional coordinates is poor are solved.

局域轨道函数的三维重构方法及装置Method and device for three-dimensional reconstruction of local orbital function

技术领域technical field

本申请涉及三维成像技术领域，特别涉及一种局域轨道函数的三维重构方法及装置。The present application relates to the technical field of three-dimensional imaging, in particular to a method and device for three-dimensional reconstruction of local orbital functions.

背景技术Background technique

通常情况下样品的电子显微镜照片中蕴含着样品丰富的、难以直观获取的信息，应用三维重构算法从样品一系列电子显微镜投影照片中获取样品的三维结构信息对在根本的层面上理解材料成分和性能的关系有很大帮助。Under normal circumstances, the electron microscope photos of the sample contain rich information that is difficult to obtain intuitively. Applying the three-dimensional reconstruction algorithm to obtain the three-dimensional structure information of the sample from a series of electron microscope projection photos of the sample is essential for understanding the material composition at a fundamental level. It helps a lot in relation to performance.

近年来，随着数据采集方法、迭代三维重建算法和后处理方法的发展，AET(AtomicElectrical Tomography，原子尺度电子层析成像)已成为三维和四维原子尺度结构表征的有力工具，它提供了在原子水平上关联材料结构和性质的能力，相关技术中的AET能够以亚埃精度确定三维原子坐标和元素种类，并揭示其在动态过程中的原子尺度时间演化。In recent years, with the development of data acquisition methods, iterative 3D reconstruction algorithms and post-processing methods, AET (Atomic Electrical Tomography, atomic scale electron tomography) has become a powerful tool for 3D and 4D atomic scale structure characterization. The ability to correlate the structure and properties of materials horizontally, AET in related technologies can determine three-dimensional atomic coordinates and element types with sub-angstrom precision, and reveal their atomic-scale time evolution during dynamic processes.

然而，相关技术中，AET算法从重构出的三维密度矩阵中通过寻峰来获取原子的三维坐标，对硬件的需求较高，且在寻峰过程中，需要进行繁琐的人为干预，难以避免因人为干预造成的误差，同时，在直接对原子的三维坐标进行重构的同时，无法对采集图像时存在的样品漂移、样品台的机械倾转误差进行矫正，准确度较差，有待改善。However, in related technologies, the AET algorithm obtains the three-dimensional coordinates of atoms through peak-finding from the reconstructed three-dimensional density matrix, which requires high hardware requirements, and in the process of peak-finding, cumbersome human intervention is required, which is unavoidable Errors caused by human intervention. At the same time, while directly reconstructing the three-dimensional coordinates of atoms, it is impossible to correct the sample drift and the mechanical tilt error of the sample stage when collecting images. The accuracy is poor and needs to be improved.

发明内容Contents of the invention

本申请提供一种局域轨道函数的三维重构方法及装置，以解决相关技术中只能从重构出的三维密度矩阵中获取原子的三维坐标，且无法对误差进行校正，导致重构的过程对硬件需求较高，且重构的三维坐标精度较差的技术问题。The present application provides a method and device for three-dimensional reconstruction of local orbital functions to solve the problem of reconstruction in which the three-dimensional coordinates of atoms can only be obtained from the reconstructed three-dimensional density matrix, and errors cannot be corrected. The process has high hardware requirements and the technical problem of the reconstructed three-dimensional coordinates is poor.

本申请第一方面实施例提供一种局域轨道函数的三维重构方法，包括以下步骤：采集多个倾转角度下的样品的图像数据；基于所述图像数据，在实空间等间隔进行撒点并利用线性累加，得到所述多个倾转角度的每个倾转角度下的计算图像；以及根据每个倾转角度下的计算图像计算损失函数，并获取所述损失函数关于待优化参数的梯度，且根据所述梯度优化所述待优化参数，筛选出满足预设条件的原子，重新计算新的损失函数，直至满足收敛条件，在所述实空间重构局域轨道函数的中心的三维空间坐标和局域轨道函数的形状，得到三维重构结果。The embodiment of the first aspect of the present application provides a three-dimensional reconstruction method of a local orbital function, including the following steps: collecting image data of samples under multiple tilt angles; Point and use linear accumulation to obtain the calculation image under each tilt angle of the plurality of tilt angles; and calculate the loss function according to the calculation image under each tilt angle, and obtain the loss function about the parameter to be optimized , and optimize the parameters to be optimized according to the gradient, screen out the atoms that meet the preset conditions, recalculate the new loss function until the convergence condition is met, and reconstruct the center of the local orbital function in the real space The three-dimensional spatial coordinates and the shape of the local orbital function are used to obtain the three-dimensional reconstruction result.

可选地，在本申请的一个实施例中，采集所述多个倾转角度下的样品的图像数据，包括：获取所述多个倾转角度下的样品的初始图像数据；对所述初始图像数据进行对中合轴和降噪处理，并由处理后的图像归一化，得到所述图像数据。Optionally, in an embodiment of the present application, collecting the image data of the sample under the multiple tilt angles includes: acquiring initial image data of the sample under the multiple tilt angles; The image data is subjected to center axis and noise reduction processing, and the processed image is normalized to obtain the image data.

可选地，在本申请的一个实施例中，所述损失函数的计算公式为：Optionally, in one embodiment of the present application, the calculation formula of the loss function is:

其中，W代表损失函数，M代表倾转角度的总数，j代表倾转角度的序号，i代表局域轨道函数序号，P代表图像的边长，u代表图像中每个像素的横坐标，v代表图像中每个像素的纵坐标，f_j(u,v)代表第j个角度下计算得到的图像，b_j(u,v)代表第j个角度下实验所得的图像。Among them, W represents the loss function, M represents the total number of tilt angles, j represents the sequence number of the tilt angle, i represents the sequence number of the local orbit function, P represents the side length of the image, u represents the abscissa of each pixel in the image, v Represents the ordinate of each pixel in the image, f _j (u, v) represents the calculated image at the jth angle, and b _j (u, v) represents the experimental image at the jth angle.

可选地，在本申请的一个实施例中，所述筛选出满足预设条件的原子，包括：在每一步迭代更新完参数后，检测所有局域轨道函数的参数在检测到任一局域轨道函数的参数小于由所述所有局域轨道函数参数得到的阈值时，删除所述任一局域轨道函数的同时，通过建立二叉树得到局域轨道函数中心距离小于预设像素的局域轨道函数对索引，删除局域轨道函数对中的任意一个局域轨道函数；每一步迭代更新完参数并删除完所述局域轨道函数后，将每个局域轨道函数的参数均以预设概率减小为预设倍数，且设置保护时间，使得在所述保护时间内，不允许执行筛选操作和删除操作。Optionally, in one embodiment of the present application, the screening out the atoms satisfying the preset conditions includes: after updating the parameters in each step of iteration, detecting the parameters of all local orbital functions when any local orbital function is detected When the parameters of the orbital functions are less than the threshold obtained from the parameters of all the local orbital functions, while deleting any of the local orbital functions, a local orbital function whose center distance of the local orbital functions is less than a preset pixel is obtained by building a binary tree For the index, delete any local orbit function in the pair of local orbit functions; after each step iteratively updates the parameters and deletes the local orbit function, the parameters of each local orbit function are reduced by the preset probability Small is a preset multiple, and the protection time is set so that the screening operation and the deletion operation are not allowed to be performed within the protection time.

可选地，在本申请的一个实施例中，所述待优化参数包括每个局域轨道函数中心的三维空间坐标、描述其形状的参数、每个转角对应的三个欧拉角、每个角度下样品的漂移、样品台的机械倾转偏差中的至少一项。Optionally, in an embodiment of the present application, the parameters to be optimized include the three-dimensional space coordinates of the center of each local orbital function, parameters describing its shape, three Euler angles corresponding to each corner, and each At least one of the drift of the sample under the angle and the mechanical tilt deviation of the sample stage.

本申请第二方面实施例提供一种局域轨道函数的三维重构装置，包括：采集模块，用于采集多个倾转角度下的样品的图像数据；累加模块，用于基于所述图像数据，在实空间等间隔进行撒点并利用线性累加，得到所述多个倾转角度的每个倾转角度下的计算图像；以及重构模块，用于根据每个倾转角度下的计算图像计算损失函数，并获取所述损失函数关于待优化参数的梯度，且根据所述梯度优化所述待优化参数，筛选出满足预设条件的原子，重新计算新的损失函数，直至满足收敛条件，在所述实空间重构局域轨道函数的中心的三维空间坐标和局域轨道函数的形状，得到三维重构结果。The embodiment of the second aspect of the present application provides a three-dimensional reconstruction device of a local orbital function, including: an acquisition module, used to collect image data of samples under multiple tilt angles; an accumulation module, used to collect image data based on the image data , sprinkle points at equal intervals in real space and use linear accumulation to obtain the calculated image at each tilt angle of the plurality of tilt angles; and the reconstruction module is used to calculate the image at each tilt angle calculating the loss function, and obtaining the gradient of the loss function with respect to the parameter to be optimized, and optimizing the parameter to be optimized according to the gradient, selecting atoms satisfying preset conditions, and recalculating a new loss function until the convergence condition is satisfied, The three-dimensional coordinates of the center of the local orbit function and the shape of the local orbit function are reconstructed in the real space to obtain a three-dimensional reconstruction result.

可选地，在本申请的一个实施例中，所述采集模块包括：获取单元，用于获取所述多个倾转角度下的样品的初始图像数据；降噪单元，用于对所述初始图像数据进行对中合轴和降噪处理，并由处理后的图像归一化，得到所述图像数据。Optionally, in an embodiment of the present application, the acquisition module includes: an acquisition unit, configured to acquire initial image data of the sample under the multiple tilt angles; a noise reduction unit, configured to The image data is subjected to center axis and noise reduction processing, and the processed image is normalized to obtain the image data.

可选地，在本申请的一个实施例中，所述损失函数的计算公式为：Optionally, in one embodiment of the present application, the calculation formula of the loss function is:

其中，W代表损失函数，M代表倾转角度的总数，j代表倾转角度的序号，i代表局域轨道函数序号，P代表图像的边长，u代表图像中每个像素的横坐标，v代表图像中每个像素的纵坐标，f_j(u,v)代表第j个角度下计算得到的图像，b_j(u,v)代表第j个角度下实验所得的图像。Among them, W represents the loss function, M represents the total number of tilt angles, j represents the sequence number of the tilt angle, i represents the sequence number of the local orbit function, P represents the side length of the image, u represents the abscissa of each pixel in the image, v Represents the ordinate of each pixel in the image, f _j (u, v) represents the calculated image at the jth angle, and b _j (u, v) represents the experimental image at the jth angle.

可选地，在本申请的一个实施例中，所述重构模块包括：检测单元，用于在每一步迭代更新完参数后，检测所有局域轨道函数的参数删除单元，用于在检测到任一局域轨道函数的参数小于由所述所有局域轨道函数参数得到的阈值时，删除所述任一局域轨道函数的同时，通过建立二叉树得到局域轨道函数中心距离小于预设像素的局域轨道函数对索引，删除局域轨道函数对中的任意一个局域轨道函数；保护单元，用于在每一步迭代更新完参数并删除完所述局域轨道函数后，将每个局域轨道函数的参数均以预设概率减小为预设倍数，且设置保护时间，使得在所述保护时间内，不允许执行筛选操作和删除操作。Optionally, in an embodiment of the present application, the reconstruction module includes: a detection unit, configured to detect the parameter deletion unit of all local orbital functions after each step of iteratively updating the parameters, configured to detect When the parameter of any local orbit function is less than the threshold value obtained by all the local orbit function parameters, delete any local orbit function and obtain the center distance of the local orbit function less than the preset pixel by establishing a binary tree Local orbital function pair index, deleting any local orbital function in the local orbital function pair; protection unit, used to update the parameters and delete the local orbital function in each step, and delete each local orbital function The parameters of the track function are all reduced to a preset multiple with a preset probability, and a guard time is set so that within the guard time, the screening operation and the deletion operation are not allowed to be performed.

可选地，在本申请的一个实施例中，所述待优化参数包括每个局域轨道函数中心的三维空间坐标、描述其形状的参数、每个转角对应的三个欧拉角、每个角度下样品的漂移、样品台的机械倾转偏差中的至少一项。Optionally, in an embodiment of the present application, the parameters to be optimized include the three-dimensional space coordinates of the center of each local orbital function, parameters describing its shape, three Euler angles corresponding to each corner, and each At least one of the drift of the sample under the angle and the mechanical tilt deviation of the sample stage.

本申请第三方面实施例提供一种电子设备，包括：存储器、处理器及存储在所述存储器上并可在所述处理器上运行的计算机程序，所述处理器执行所述程序，以实现如上述实施例所述的局域轨道函数的三维重构方法。The embodiment of the third aspect of the present application provides an electronic device, including: a memory, a processor, and a computer program stored on the memory and operable on the processor, and the processor executes the program to realize The three-dimensional reconstruction method of the local orbital function as described in the above-mentioned embodiments.

本申请第四方面实施例提供一种计算机可读存储介质，所述计算机可读存储介质存储计算机指令，所述计算机指令用于使所述计算机执行如上述实施例所述的局域轨道函数的三维重构方法。The embodiment of the fourth aspect of the present application provides a computer-readable storage medium, the computer-readable storage medium stores computer instructions, and the computer instructions are used to make the computer execute the local orbit function as described in the above-mentioned embodiments 3D reconstruction method.

本申请实施例基于采集的多个倾转角度下的样品的图像数据，获得多个倾转角度下的计算图像，进而计算出计算图像的损失函数，求取优化参数的梯度，从而获得优化参数，在经过反复筛选和计算后，直至损失函数满足收敛条件，进而获得三维重构结果，可以精简三维坐标的重构过程，不仅降低了对硬件的要求，还能减少繁琐的人为干预，节约劳动力成本，同时在迭代过程中，还可以矫正样品漂移和样品台的机械倾转误差，进而提高三维坐标重构的准确性。由此，解决了相关技术中只能从重构出的三维密度矩阵中获取原子的三维坐标，且无法对误差进行校正，导致重构的过程对硬件需求较高，且重构的三维坐标精度较差的技术问题。In the embodiment of the present application, based on the collected image data of samples under multiple tilt angles, the calculation images under multiple tilt angles are obtained, and then the loss function of the calculation images is calculated, and the gradient of the optimization parameters is obtained, thereby obtaining the optimization parameters , after repeated screening and calculation, until the loss function meets the convergence conditions, and then obtain the 3D reconstruction result, which can simplify the reconstruction process of 3D coordinates, not only reduce the requirements for hardware, but also reduce tedious human intervention and save labor At the same time, in the iterative process, the sample drift and the mechanical tilt error of the sample stage can be corrected, thereby improving the accuracy of the three-dimensional coordinate reconstruction. Therefore, it solves the problem that in related technologies, the three-dimensional coordinates of atoms can only be obtained from the reconstructed three-dimensional density matrix, and the error cannot be corrected, resulting in high requirements for hardware in the reconstruction process, and the accuracy of the reconstructed three-dimensional coordinates Poor technical issues.

本申请附加的方面和优点将在下面的描述中部分给出，部分将从下面的描述中变得明显，或通过本申请的实践了解到。Additional aspects and advantages of the application will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the application.

附图说明Description of drawings

本申请上述的和/或附加的方面和优点从下面结合附图对实施例的描述中将变得明显和容易理解，其中：The above and/or additional aspects and advantages of the present application will become apparent and easy to understand from the following description of the embodiments in conjunction with the accompanying drawings, wherein:

图1为根据本申请实施例提供的一种局域轨道函数的三维重构方法的流程图；Fig. 1 is a flow chart of a three-dimensional reconstruction method of a local orbital function provided according to an embodiment of the present application;

图2为根据本申请一个实施例的局域轨道函数的三维重构方法的流程图；FIG. 2 is a flow chart of a method for three-dimensional reconstruction of a local orbital function according to an embodiment of the present application;

图3为根据本申请一个实施例的待重构的10000个原子构成的小颗粒在25°、0°和-25°的模拟示意图；Fig. 3 is a schematic diagram of simulations at 25°, 0° and -25° of a small particle composed of 10,000 atoms to be reconstructed according to an embodiment of the present application;

图4为根据本申请一个实施例的局域轨道函数的三维重构方法的初始输入的原子坐标构成的散点示意图；FIG. 4 is a schematic diagram of scatter points formed by the initial input atomic coordinates of the three-dimensional reconstruction method of the local orbital function according to an embodiment of the present application;

图5为根据本申请一个实施例的局域轨道函数的三维重构方法的初始输入的局域轨道函数在倾转角度分别为25°、0°和-25°的计算示意图；Fig. 5 is a schematic diagram of calculating the initial input local orbit function at tilt angles of 25°, 0° and -25° according to the three-dimensional reconstruction method of the local orbit function according to an embodiment of the present application;

图6为根据本申请一个实施例的局域轨道函数的三维重构方法的迭代过程中损失函数的值的折线示意图；Fig. 6 is a broken line schematic diagram of the value of the loss function during the iterative process of the three-dimensional reconstruction method of the local orbit function according to an embodiment of the present application;

图7为根据本申请一个实施例的局域轨道函数的三维重构方法的收敛后获得的原子模型示意图；FIG. 7 is a schematic diagram of an atomic model obtained after convergence of a three-dimensional reconstruction method of a local orbital function according to an embodiment of the present application;

图8为根据本申请一个实施例的局域轨道函数的三维重构方法的收敛时计算图像与实验图像的差值；Fig. 8 is the difference between the calculated image and the experimental image during the convergence of the three-dimensional reconstruction method of the local orbit function according to an embodiment of the present application;

图9为根据本申请一个实施例的局域轨道函数的三维重构方法的收敛计算所得原子坐标与真实坐标之间的距离直方图；9 is a histogram of the distance between the atomic coordinates and the real coordinates obtained through the convergence calculation of the three-dimensional reconstruction method of the local orbital function according to an embodiment of the present application;

图10为根据本申请实施例提供的一种局域轨道函数的三维重构装置的结构示意图；FIG. 10 is a schematic structural diagram of a three-dimensional reconstruction device for a local orbital function according to an embodiment of the present application;

图11为根据本申请实施例提供的电子设备的结构示意图。FIG. 11 is a schematic structural diagram of an electronic device provided according to an embodiment of the present application.

具体实施方式Detailed ways

下面详细描述本申请的实施例，所述实施例的示例在附图中示出，其中自始至终相同或类似的标号表示相同或类似的元件或具有相同或类似功能的元件。下面通过参考附图描述的实施例是示例性的，旨在用于解释本申请，而不能理解为对本申请的限制。Embodiments of the present application are described in detail below, examples of which are shown in the drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below by referring to the figures are exemplary, and are intended to explain the present application, and should not be construed as limiting the present application.

下面参考附图描述本申请实施例的局域轨道函数的三维重构方法及装置。针对上述背景技术中心提到的相关技术只能从重构出的三维密度矩阵中获取原子的三维坐标，且无法对误差进行校正，导致重构的过程对硬件需求较高，且重构的三维坐标精度较差的技术问题，本申请提供了一种局域轨道函数的三维重构方法，在该方法中，基于采集的多个倾转角度下的样品的图像数据，获得多个倾转角度下的计算图像，进而计算出计算图像的损失函数，求取优化参数的梯度，从而获得优化参数，在经过反复筛选和计算后，直至损失函数满足收敛条件，进而获得三维重构结果，可以精简三维坐标的重构过程，不仅降低了对硬件的要求，还能减少繁琐的人为干预，节约劳动力成本，同时在迭代过程中，还可以矫正样品漂移和样品台的机械倾转误差，进而提高三维坐标重构的准确性。由此，解决了相关技术中只能从重构出的三维密度矩阵中获取原子的三维坐标，且无法对误差进行校正，导致重构的过程对硬件需求较高，且重构的三维坐标精度较差的技术问题。The method and device for three-dimensional reconstruction of a local orbital function according to the embodiments of the present application are described below with reference to the accompanying drawings. In view of the related technologies mentioned in the background technology center mentioned above, the three-dimensional coordinates of atoms can only be obtained from the reconstructed three-dimensional density matrix, and the errors cannot be corrected, resulting in high hardware requirements for the reconstruction process, and the reconstructed three-dimensional Due to the technical problem of poor coordinate accuracy, this application provides a three-dimensional reconstruction method of local orbital functions. In this method, multiple tilt angles are obtained based on the collected image data of samples under multiple tilt angles. Then calculate the loss function of the calculation image, obtain the gradient of the optimized parameter, and obtain the optimized parameter. After repeated screening and calculation, until the loss function meets the convergence condition, the 3D reconstruction result can be obtained, which can be simplified The reconstruction process of the three-dimensional coordinates not only reduces the requirements for hardware, but also reduces tedious human intervention and saves labor costs. At the same time, in the iterative process, it can also correct the sample drift and the mechanical tilt error of the sample stage, thereby improving the three-dimensional Accuracy of coordinate reconstruction. Therefore, it solves the problem that in related technologies, the three-dimensional coordinates of atoms can only be obtained from the reconstructed three-dimensional density matrix, and the error cannot be corrected, resulting in high requirements for hardware in the reconstruction process, and the accuracy of the reconstructed three-dimensional coordinates Poor technical issues.

具体而言，图1为本申请实施例所提供的一种局域轨道函数的三维重构方法的流程示意图。Specifically, FIG. 1 is a schematic flowchart of a method for three-dimensional reconstruction of a local orbital function provided by an embodiment of the present application.

如图1所示，该局域轨道函数的三维重构方法包括以下步骤：As shown in Figure 1, the three-dimensional reconstruction method of the local orbital function includes the following steps:

在步骤S101中，采集多个倾转角度下的样品的图像数据。In step S101, image data of samples under multiple tilt angles are collected.

在实际执行过程中，本申请实施例可以拍摄样品在一系列不同转角下的HAADF(High-Angle Annular Dark-Field imaging，高角环形暗场像)图像，进而获得样品多个倾转角度下的样品的图像数据，便于后续对图像数据进行处理，并进行三维坐标重构。In the actual implementation process, the embodiment of the present application can take HAADF (High-Angle Annular Dark-Field imaging) images of the sample under a series of different rotation angles, and then obtain samples under multiple tilt angles The image data is convenient for subsequent processing of the image data and reconstruction of three-dimensional coordinates.

可选地，在本申请的一个实施例中，采集多个倾转角度下的样品的图像数据，包括：获取多个倾转角度下的样品的初始图像数据；对初始图像数据进行对中合轴和降噪处理，并由处理后的图像归一化，得到图像数据。Optionally, in one embodiment of the present application, collecting image data of the sample under multiple tilt angles includes: acquiring initial image data of the sample under multiple tilt angles; performing centering and combining on the initial image data Axis and noise reduction processing, and normalized by the processed image to obtain image data.

具体地，本申请实施例通过拍摄获得多个倾转角度下的样品的初始图像数据后，为保证后续三维坐标重构的准确性，可以对初始图像数据进行对中和轴和降噪处理，在便于后续计算的同时，避免噪点对三维坐标重构的影响，再通过线性归一化，得到可用于后续计算的图像数据。Specifically, in the embodiment of the present application, after obtaining the initial image data of the sample under multiple tilt angles by shooting, in order to ensure the accuracy of the subsequent three-dimensional coordinate reconstruction, the initial image data can be centered and axis-aligned and denoised. While facilitating subsequent calculations, it avoids the influence of noise on the three-dimensional coordinate reconstruction, and then obtains image data that can be used for subsequent calculations through linear normalization.

其中，线性归一化的具体过程如下：Among them, the specific process of linear normalization is as follows:

其中，M代表倾转角度的总数，j代表倾转角度的序号，u代表图像中每个像素的横坐标，v代表图像中每个像素的纵坐标，b_j(u,v)代表第j个角度下实验得到的图像。Among them, M represents the total number of tilt angles, j represents the serial number of the tilt angle, u represents the abscissa of each pixel in the image, v represents the ordinate of each pixel in the image, b _j (u, v) represents the jth Images obtained from experiments at different angles.

在步骤S102中，基于图像数据，在实空间等间隔进行撒点并利用线性累加，得到多个倾转角度的每个倾转角度下的计算图像。In step S102, based on the image data, sprinkle points at equal intervals in the real space and use linear accumulation to obtain a calculated image at each of the multiple tilt angles.

作为一种可能实现的方式，本申请实施例首先可以基于上述步骤获得的图像数据，在实空间以一定规律设置离散化、有限数目的局域轨道函数作为迭代过程的初始输入，其中，每个局域轨道函数的强度H可以设置为1e^-5，宽度可以设置为1.4，各角度下的样品漂移量(u_j,v_j)和欧拉转角的偏移量皆可以设置为0。As a possible implementation, in the embodiment of the present application, based on the image data obtained in the above steps, a discretization and a limited number of local orbital functions can be set in real space with a certain rule as the initial input of the iterative process, wherein each The intensity H of the local orbital function can be set to 1e ^-5 , the width can be set to 1.4, the sample drift (u _j , v _j ) and the offset of the Euler rotation angle at each angle Both can be set to 0.

具体地，本申请实施例可以将不同角度下的局域轨道函数中心的三维坐标表示为：Specifically, in the embodiment of the present application, the three-dimensional coordinates of the center of the local orbital function at different angles can be expressed as:

其中，ψ_j、θ_j、为第j个角度对应的分布绕x轴、y轴、z轴的欧拉角，(x_i,y_i,z_i)为第i个局域轨道函数在未旋转(三个欧拉角皆为0)时的中心三维位置坐标，(u_ij,v_ij,w_ij)为第i个局域轨道函数在第j个角度下的中心三维位置坐标。Among them, ψ _j , θ _j , is the Euler angle corresponding to the distribution of the j-th angle around the x-axis, y-axis, and z-axis, and ( _xi , y _i , z _i ) is the i-th local orbit function without rotation (the three Euler angles are all 0), (u _ij , v _ij , w _ij ) is the center three-dimensional position coordinates of the i-th local orbit function at the j-th angle.

进一步地，本申请实施例可以计算各角度下局域轨道中心的坐标：Further, the embodiment of the present application can calculate the coordinates of the center of the local orbit at each angle:

进而，本申请实施例可以根据上述坐标，将局域轨道函数表示为三维高斯函数，计算每个局域轨道函数在各个角度下的值：Furthermore, the embodiment of the present application can express the local orbit function as a three-dimensional Gaussian function according to the above coordinates, and calculate the value of each local orbit function at each angle:

其中，D_ij表示第i个局域轨道函数在第j个角度下在实空间(u,v,w)位置处的值，H_i和B_i为待优化参数，分别代表第i个局域轨道函数的强度与宽度，(u,v,w)为实空间三维位置坐标，(u_ij,v_ij,w_ij)为第i个局域轨道函数在第j个角度下的中心三维位置坐标，(u_j,v_j,w_j)为第j个角度下局域轨道函数中心相对于真实位置(u_ij,v_ij,w_ij)的三维方向漂移。Among them, D _ij represents the value of the i-th local orbital function at the j-th angle in the real space (u, v, w) position, H _i and _Bi are the parameters to be optimized, representing the i-th local orbit function The strength and width of the orbital function, (u, v, w) are the three-dimensional position coordinates in real space, (u _ij , v _ij , w _ij ) are the center three-dimensional position coordinates of the i-th local orbital function at the j-th angle , (u _j ,v _j ,w _j ) is the three-dimensional drift of the center of the local orbital function relative to the true position (u _ij ,v _ij ,w _ij ) at the jth angle.

再通过线性累加，本申请实施例可以得到计算图像：Then through linear accumulation, the embodiment of this application can obtain the calculation image:

其中，N代表局域轨道函数总个数，D_ij表示第i个局域轨道函数在第j个角度下在实空间(u,v,w)位置处的值。Among them, N represents the total number of local orbital functions, and D _ij represents the value of the i-th local orbital function at the position (u, v, w) in the real space at the j-th angle.

在步骤S103中，根据每个倾转角度下的计算图像计算损失函数，并获取损失函数关于待优化参数的梯度，且根据梯度优化待优化参数，筛选出满足预设条件的原子，重新计算新的损失函数，直至满足收敛条件，在实空间重构局域轨道函数的中心的三维空间坐标和局域轨道函数的形状，得到三维重构结果。In step S103, the loss function is calculated according to the calculation image at each tilt angle, and the gradient of the loss function with respect to the parameters to be optimized is obtained, and the parameters to be optimized are optimized according to the gradient, and the atoms satisfying the preset conditions are screened out, and the new Loss function until the convergence condition is satisfied, the 3D space coordinates of the center of the local orbital function and the shape of the local orbital function are reconstructed in the real space, and the 3D reconstruction result is obtained.

在实际执行过程中，本申请实施例可以利用梯度的优化算法求解参数，并通过多次计算和筛选，在实空间重构局域轨道函数的中心的三维空间坐标和局域轨道函数的形状，得到三维重构结果。In the actual execution process, the embodiment of the present application can use the gradient optimization algorithm to solve the parameters, and through multiple calculations and screening, reconstruct the three-dimensional space coordinates of the center of the local orbit function and the shape of the local orbit function in the real space, Get the 3D reconstruction result.

具体地，本申请实施例可以利用上述步骤中计算获得的计算图像，计算损失函数，进而获取损失函数关于待优化参数的梯度，利用梯度的优化算法，优化待优化参数，进而筛选出满足预设条件的原子，并重复计算损失函数，直至满足收敛条件，从而在实空间重构局域轨道函数的中心的三维空间坐标和局域轨道函数的形状，得到三维重构结果。Specifically, the embodiment of the present application can use the calculation images obtained in the above steps to calculate the loss function, and then obtain the gradient of the loss function with respect to the parameters to be optimized, use the optimization algorithm of the gradient to optimize the parameters to be optimized, and then screen out the parameters that meet the preset requirements. Conditional atoms, and repeatedly calculate the loss function until the convergence condition is satisfied, so that the three-dimensional space coordinates of the center of the local orbital function and the shape of the local orbital function are reconstructed in the real space, and the three-dimensional reconstruction result is obtained.

本申请实施例可以直接获得样品原子的三维坐标，跳过了先得到三维密度矩阵再寻峰得到三维坐标的过程，不仅降低了对硬件的要求，还去除了寻峰过程中的繁琐人为干预，节约了劳动成本，同时在迭代过程中，还可以矫正样品漂移和样品台的机械倾转误差，进而提高三维坐标重构的准确性。The embodiment of the present application can directly obtain the three-dimensional coordinates of the sample atoms, skipping the process of first obtaining the three-dimensional density matrix and then finding the peak to obtain the three-dimensional coordinates, which not only reduces the requirements for hardware, but also removes the tedious human intervention in the process of peak finding. Labor costs are saved, and at the same time, sample drift and mechanical tilt errors of the sample stage can be corrected during the iterative process, thereby improving the accuracy of three-dimensional coordinate reconstruction.

需要注意的是，预设条件可以由本领域技术人员根据实际情况进行设置，在此不做具体限制。It should be noted that the preset conditions can be set by those skilled in the art according to actual conditions, and no specific limitation is set here.

可选地，在本申请的一个实施例中，损失函数的计算公式为：Optionally, in one embodiment of the present application, the calculation formula of the loss function is:

其中，W代表损失函数，M代表倾转角度的总数，j代表倾转角度的序号，i代表局域轨道函数序号，P代表图像的边长，u代表图像中每个像素的横坐标，v代表图像中每个像素的纵坐标，f_j(u,v)代表第j个角度下计算得到的图像，b_j(u,v)代表第j个角度下实验所得的图像。Among them, W represents the loss function, M represents the total number of tilt angles, j represents the sequence number of the tilt angle, i represents the sequence number of the local orbit function, P represents the side length of the image, u represents the abscissa of each pixel in the image, v Represents the ordinate of each pixel in the image, f _j (u, v) represents the calculated image at the jth angle, and b _j (u, v) represents the experimental image at the jth angle.

具体地，本申请实施例可以通过上述步骤中的计算图像计算损失函数，并将损失函数写为关于计算图像和实验图像的函数：Specifically, the embodiment of the present application can calculate the loss function through the calculation image in the above steps, and write the loss function as a function about the calculation image and the experimental image:

其中，W代表损失函数，M代表倾转角度的总数，j代表倾转角度的序号，i代表局域轨道函数序号，P代表图像的边长，u代表图像中每个像素的横坐标，v代表图像中每个像素的纵坐标，f_j(u,v)代表第j个角度下计算得到的图像，b_j(u,v)代表第j个角度下实验所得的图像，m_j(u,v)为第j个角度下计算图像与实验图像之差。Among them, W represents the loss function, M represents the total number of tilt angles, j represents the sequence number of the tilt angle, i represents the sequence number of the local orbit function, P represents the side length of the image, u represents the abscissa of each pixel in the image, v Represents the ordinate of each pixel in the image, f _j (u,v) represents the image calculated at the jth angle, b _j (u,v) represents the experimental image at the jth angle, m _j (u ,v) is the difference between the calculated image and the experimental image at the jth angle.

可选地，在本申请的一个实施例中，待优化参数包括每个局域轨道函数中心的三维空间坐标、描述其形状的参数，每个转角对应的三个欧拉角，每个角度下样品的漂移、样品台的机械倾转偏差中的至少一项。Optionally, in one embodiment of the present application, the parameters to be optimized include the three-dimensional space coordinates of the center of each local orbital function, parameters describing its shape, three Euler angles corresponding to each corner, and each angle At least one of sample drift and mechanical tilt deviation of the sample stage.

在获取损失函数后，本申请实施例可以求出损失函数关于局域轨道函数中心三维坐标(x_i,y_i,z_i)、强度H_i、宽度B_i、每个角度下样品漂移量(u_j,u_j)、样品台角度偏差量ψ_j、θ_j、等参数的梯度。After obtaining the loss function, the embodiment of the present application can calculate the loss function with respect to the three-dimensional coordinates (xi _, y _i , z _i ) of the center of the local orbital function, the intensity H _i , the width B _i , and the amount of sample drift at each angle ( u _j ,u _j ), sample stage angle deviation ψ _j , θ _j , Gradients of equal parameters.

进一步地，本申请实施例可以利用计算获得的梯度对目标参数进行更新：Further, in this embodiment of the present application, the calculated gradient can be used to update the target parameters:

其中，和/>是各个参数的学习率。in, and /> is the learning rate of each parameter.

需要注意的是，梯度的求取可以利用具有自动求导功能的软件库实现，也可以通过解析表达式实现。It should be noted that the calculation of the gradient can be realized by using a software library with an automatic derivation function, or by an analytical expression.

可选地，在本申请的一个实施例中，筛选出满足预设条件的原子，包括：在每一步迭代更新完参数后，检测所有局域轨道函数的参数在检测到任一局域轨道函数的参数小于由所有局域轨道函数参数得到的阈值时，删除任一局域轨道函数的同时，通过建立二叉树得到局域轨道函数中心距离小于预设像素的局域轨道函数对索引，删除局域轨道函数对中的任意一个局域轨道函数；每一步迭代更新完参数并删除完局域轨道函数后，将每个局域轨道函数的参数均以预设概率减小为预设倍数，且设置保护时间，使得在保护时间内，不允许执行筛选操作和删除操作。Optionally, in one embodiment of the present application, the screening of atoms satisfying the preset conditions includes: after updating the parameters in each step of iteration, detecting the parameters of all local orbital functions and detecting any local orbital function When the parameter of is less than the threshold obtained by all local orbital function parameters, any local orbital function is deleted, and the local orbital function pair index whose center distance of the local orbital function is less than the preset pixel is obtained by building a binary tree, and the local orbital function is deleted. Any local orbital function in the pair of orbital functions; after updating the parameters and deleting the local orbital function in each step, reduce the parameters of each local orbital function to a preset multiple with a preset probability, and set Guard time, such that filter operations and delete operations are not allowed to be performed during the guard time.

可以理解的是，筛选出满足预设条件的原子包括删除冗余局域轨道函数和筛选局域轨道函数。It can be understood that the screening out atoms satisfying the preset conditions includes deleting redundant local orbital functions and screening local orbital functions.

其中，删除冗余局域轨道函数的方法为：在每一步迭代更新完参数后，检查所有局域轨道函数的参数H，若某局域轨道函数的参数H小于小于由所有局域轨道函数参数得到的阈值时，则删除该局域轨道函数，同时通过建立二叉树的方法，得到局域轨道函数中心距离预设像素的局域轨道函数对索引，删除局域轨道函数对中的任意一个局域轨道函数。Among them, the method to delete the redundant local orbit function is: after each step iteratively updates the parameters, check the parameter H of all local orbit functions, if the parameter H of a certain local orbit function is less than the parameter H set by all local orbit functions When the threshold value is obtained, the local orbit function is deleted, and at the same time, by establishing a binary tree method, the index of the local orbit function pair from the center of the local orbit function to the preset pixel is obtained, and any local orbit function in the local orbit function pair is deleted. track function.

需要注意的是，阈值可以由本领域技术人员根据实际情况进行设置，也可以设置为参考值，如所有局域轨道函数参数H最大值的0.01倍；预设像素可以由本领域技术人员根据实际情况进行设置，也可以设置为参考值，如2像素。It should be noted that the threshold can be set by those skilled in the art according to the actual situation, or it can be set as a reference value, such as 0.01 times the maximum value of all local orbital function parameters H; the preset pixel can be set by those skilled in the art according to the actual situation It can also be set as a reference value, such as 2 pixels.

筛选局域轨道函数的方法为：在每一步迭代更新完参数并删除完局域轨道函数后，每个局域轨道函数的参数H预设概率减小为预设倍数，且设置保护时间，在保护时间内局域轨道函数不可被筛选和删除。The method of screening the local orbit function is as follows: After updating the parameters and deleting the local orbit function in each step, the preset probability of the parameter H of each local orbit function is reduced to a preset multiple, and the protection time is set. Local orbital functions within guard time cannot be filtered and deleted.

需要注意的是，预设概率和预设倍数可以由本领域技术人员根据实际情况进行设置，也可以设置为参考值，如每个局域轨道函数的参数H皆以0.02的概率减小为0.1倍；保护事件可以由本领域技术人员根据实际情况进行设置，也可以设置为参考值，如设置保护时间T＝50。It should be noted that the preset probability and preset multiple can be set by those skilled in the art according to the actual situation, or can be set as a reference value, such as the parameter H of each local orbital function is reduced to 0.1 times with a probability of 0.02 ; The protection event can be set by those skilled in the art according to the actual situation, or can be set as a reference value, such as setting the protection time T=50.

下面结合图2至图9所示，以一个具体实施例对本申请实施例的局域轨道函数的三维重构方法的工作原理进行详细阐述。The working principle of the three-dimensional reconstruction method of the local orbital function in the embodiment of the present application will be described in detail below with reference to FIG. 2 to FIG. 9 .

如图2所示，以重构10000个原子组成的小颗粒为例，本申请实施例包括以下步骤：As shown in Figure 2, taking the reconstruction of a small particle composed of 10,000 atoms as an example, the embodiment of this application includes the following steps:

步骤S201：采集图像数据。如图3所示，本申请实施例需要重构10000个原子组成的小颗粒，通过在角度为±25°、±20°、±15°、±5°、0°时倾转，获得其模拟图像，图3中第1、2、3列分别对应25°、0°和-25°的图像。Step S201: collecting image data. As shown in Figure 3, the embodiment of the present application needs to reconstruct a small particle composed of 10,000 atoms, and obtain its simulation by tilting at an angle of ±25°, ±20°, ±15°, ±5°, and 0° Image, columns 1, 2, and 3 in Figure 3 correspond to images at 25°, 0°, and -25°, respectively.

步骤S202：计算图像。本申请实施例可以基于图像数据，在实空间等间隔进行撒点并利用线性累加，得到多个倾转角度的每个倾转角度下的计算图像。如图4所示，初始撒点集合为等间隔原子构成的圆柱形，并参考图5所示，利用公式得到迭代初始的各个角度下的计算图像，其中，第1、2、3列分别对应25°、0°和-25°的图像。Step S202: Calculate the image. In the embodiment of the present application, based on the image data, the points are sprinkled at equal intervals in the real space and linear accumulation is used to obtain a calculated image at each tilt angle of multiple tilt angles. As shown in Figure 4, the initial set of scattered points is a cylinder composed of equally spaced atoms, and referring to Figure 5, using the formula Obtain the calculated images at various angles at the beginning of the iteration, where the first, second, and third columns correspond to images of 25°, 0°, and -25°, respectively.

步骤S203：计算损失函数，并对目标参数进行迭代更新。本申请实施例可以计算损失函数及目标参数的梯度，并利用以下公式对目标参数进行迭代更新：Step S203: Calculate the loss function, and iteratively update the target parameters. The embodiment of this application can calculate the loss function and the gradient of the target parameter, and use the following formula to iteratively update the target parameter:

其中，和/>是各个参数的学习率。in, and /> is the learning rate of each parameter.

步骤S204：删除、筛选局域轨道函数。进一步地，本申请实施例可以删除强度H小于最强局域轨道函数强度Hmax*0.01的局域轨道函数，同时以0.02的概率重置该局域轨道函数，使局域轨道函数强度H减小为原来的0.1倍，设置保护周期T＝50。Step S204: Delete and filter local orbital functions. Further, the embodiment of the present application can delete the local orbital function whose strength H is less than the strongest local orbital function strength Hmax*0.01, and at the same time reset the local orbital function with a probability of 0.02, so that the local orbital function strength H decreases It is 0.1 times of the original value, and the protection period T=50 is set.

通过循环计算损失函数，并更新各目标参数，删除和筛选局域轨道函数的操作，直至局域轨道函数数目收敛，实现三维坐标重构。By cyclically calculating the loss function, updating each target parameter, deleting and filtering the operation of local orbital functions, until the number of local orbital functions converges, the three-dimensional coordinate reconstruction is realized.

其中，损失函数的值随迭代过程的折线图如图6所示；最终收敛时得到的原子模型的示意图如图7所示；计算图像与实验图像的差值参考图如图8所示，其中，第1列为计算图，第2列为实验图，第3列为二者差值，第1行为倾转角度为25°下的数据，第2行为倾转角度为20°下的数据；计算所得原子坐标与真实坐标距离直方图如图9所示。Among them, the line graph of the value of the loss function along with the iterative process is shown in Figure 6; the schematic diagram of the atomic model obtained at the final convergence is shown in Figure 7; the reference image of the difference between the calculated image and the experimental image is shown in Figure 8, where , the first column is the calculation graph, the second column is the experimental graph, the third column is the difference between the two, the first row is the data at a tilt angle of 25°, and the second row is the data at a tilt angle of 20°; The histogram of the distance between the calculated atomic coordinates and the real coordinates is shown in Figure 9.

根据本申请实施例提出的局域轨道函数的三维重构方法，基于采集的多个倾转角度下的样品的图像数据，获得多个倾转角度下的计算图像，进而计算出计算图像的损失函数，求取优化参数的梯度，从而获得优化参数，在经过反复筛选和计算后，直至损失函数满足收敛条件，进而获得三维重构结果，可以精简三维坐标的重构过程，不仅降低了对硬件的要求，还能减少繁琐的人为干预，节约劳动力成本，同时在迭代过程中，还可以矫正样品漂移和样品台的机械倾转误差，进而提高三维坐标重构的准确性。由此，解决了相关技术中只能从重构出的三维密度矩阵中获取原子的三维坐标，且无法对误差进行校正，导致重构的过程对硬件需求较高，且重构的三维坐标精度较差的技术问题。According to the three-dimensional reconstruction method of the local orbit function proposed in the embodiment of the present application, based on the collected image data of the sample under multiple tilt angles, the calculation images under multiple tilt angles are obtained, and then the loss of the calculation images is calculated function to obtain the gradient of the optimized parameters, so as to obtain the optimized parameters, after repeated screening and calculation, until the loss function meets the convergence conditions, and then obtain the 3D reconstruction result, which can simplify the reconstruction process of 3D coordinates, not only reducing the cost to the hardware It can also reduce cumbersome human intervention and save labor costs. At the same time, in the iterative process, it can also correct sample drift and mechanical tilt errors of the sample stage, thereby improving the accuracy of 3D coordinate reconstruction. Therefore, it solves the problem that in related technologies, the three-dimensional coordinates of atoms can only be obtained from the reconstructed three-dimensional density matrix, and the error cannot be corrected, resulting in high requirements for hardware in the reconstruction process, and the accuracy of the reconstructed three-dimensional coordinates Poor technical issues.

其次参照附图描述根据本申请实施例提出的局域轨道函数的三维重构装置。Next, a three-dimensional reconstruction device for a local orbital function proposed according to an embodiment of the present application will be described with reference to the accompanying drawings.

图10是本申请实施例的局域轨道函数的三维重构装置的方框示意图。Fig. 10 is a schematic block diagram of a device for three-dimensional reconstruction of a local orbital function according to an embodiment of the present application.

如图10所示，该局域轨道函数的三维重构装置10包括：采集模块100、累加模块200和重构模块300。As shown in FIG. 10 , the device 10 for three-dimensional reconstruction of the local orbit function includes: an acquisition module 100 , an accumulation module 200 and a reconstruction module 300 .

具体地，采集模块100，用于采集多个倾转角度下的样品的图像数据。Specifically, the collection module 100 is configured to collect image data of samples under multiple tilt angles.

累加模块200，用于基于图像数据，在实空间等间隔进行撒点并利用线性累加，得到多个倾转角度的每个倾转角度下的计算图像。The accumulating module 200 is configured to, based on the image data, sprinkle points at equal intervals in the real space and use linear accumulation to obtain a calculated image at each of the multiple inclination angles.

重构模块300，用于根据每个倾转角度下的计算图像计算损失函数，并获取损失函数关于待优化参数的梯度，且根据梯度优化待优化参数，筛选出满足预设条件的原子，重新计算新的损失函数，直至满足收敛条件，在实空间重构局域轨道函数的中心的三维空间坐标和局域轨道函数的形状，得到三维重构结果。The reconstruction module 300 is used to calculate the loss function according to the calculation image at each tilt angle, and obtain the gradient of the loss function with respect to the parameters to be optimized, and optimize the parameters to be optimized according to the gradient, select atoms satisfying the preset conditions, and re- Calculate the new loss function until the convergence condition is satisfied, reconstruct the 3D space coordinates of the center of the local orbital function and the shape of the local orbital function in the real space, and obtain the 3D reconstruction result.

可选地，在本申请的一个实施例中，采集模块100包括：获取单元和降噪单元。Optionally, in an embodiment of the present application, the collection module 100 includes: an acquisition unit and a noise reduction unit.

其中，获取单元，用于获取多个倾转角度下的样品的初始图像数据。Wherein, the acquiring unit is used to acquire initial image data of the sample under multiple tilting angles.

降噪单元，用于对初始图像数据进行对中合轴和降噪处理，并由处理后的图像归一化，得到图像数据。The noise reduction unit is used to perform alignment and noise reduction processing on the initial image data, and normalize the processed image to obtain image data.

可选地，在本申请的一个实施例中，损失函数的计算公式为：Optionally, in one embodiment of the present application, the calculation formula of the loss function is:

其中，W代表损失函数，M代表倾转角度的总数，j代表倾转角度的序号，i代表局域轨道函数序号，P代表图像的边长，u代表图像中每个像素的横坐标，v代表图像中每个像素的纵坐标，f_j(u,v)代表第j个角度下计算得到的图像，b_j(u,v)代表第j个角度下实验所得的图像。Among them, W represents the loss function, M represents the total number of tilt angles, j represents the sequence number of the tilt angle, i represents the sequence number of the local orbit function, P represents the side length of the image, u represents the abscissa of each pixel in the image, v Represents the ordinate of each pixel in the image, f _j (u, v) represents the calculated image at the jth angle, and b _j (u, v) represents the experimental image at the jth angle.

可选地，在本申请的一个实施例中，重构模块300包括：检测单元和保护单元。Optionally, in an embodiment of the present application, the reconstruction module 300 includes: a detection unit and a protection unit.

其中，检测单元，用于在每一步迭代更新完参数后，检测所有局域轨道函数的参数删除单元，用于在检测到任一局域轨道函数的参数小于由所有局域轨道函数参数得到的阈值时，删除任一局域轨道函数的同时，通过建立二叉树得到局域轨道函数中心距离小于预设像素的局域轨道函数对索引，删除局域轨道函数对中的任意一个局域轨道函数。Among them, the detection unit is used to detect the parameter deletion unit of all local orbital functions after updating the parameters in each step of iteration, and is used to detect that the parameters of any local orbital function are smaller than those obtained by all local orbital function parameters When the threshold is reached, while deleting any local orbit function, the index of the local orbit function pair whose center distance of the local orbit function is smaller than the preset pixel is obtained by building a binary tree, and any local orbit function in the local orbit function pair is deleted.

保护单元，用于在每一步迭代更新完参数并删除完局域轨道函数后，将每个局域轨道函数的参数均以预设概率减小为预设倍数，且设置保护时间，使得在保护时间内，不允许执行筛选操作和删除操作。The protection unit is used to reduce the parameters of each local orbital function to a preset multiple with a preset probability after each step iteratively updates the parameters and deletes the local orbital function, and sets the protection time so that in the protection During the time, filter operations and delete operations are not allowed.

可选地，在本申请的一个实施例中，待优化参数包括每个局域轨道函数中心的三维空间坐标、描述其形状的参数，每个转角对应的三个欧拉角，每个角度下样品的漂移、样品台的机械倾转偏差中的至少一项。Optionally, in one embodiment of the present application, the parameters to be optimized include the three-dimensional space coordinates of the center of each local orbital function, parameters describing its shape, three Euler angles corresponding to each corner, and each angle At least one of sample drift and mechanical tilt deviation of the sample stage.

需要说明的是，前述对局域轨道函数的三维重构方法实施例的解释说明也适用于该实施例的局域轨道函数的三维重构装置，此处不再赘述。It should be noted that, the foregoing explanations on the embodiment of the method for three-dimensional reconstruction of the local orbital function are also applicable to the apparatus for three-dimensional reconstruction of the local orbital function in this embodiment, which will not be repeated here.

根据本申请实施例提出的局域轨道函数的三维重构装置，基于采集的多个倾转角度下的样品的图像数据，获得多个倾转角度下的计算图像，进而计算出计算图像的损失函数，求取优化参数的梯度，从而获得优化参数，在经过反复筛选和计算后，直至损失函数满足收敛条件，进而获得三维重构结果，可以精简三维坐标的重构过程，不仅降低了对硬件的要求，还能减少繁琐的人为干预，节约劳动力成本，同时在迭代过程中，还可以矫正样品漂移和样品台的机械倾转误差，进而提高三维坐标重构的准确性。由此，解决了相关技术中只能从重构出的三维密度矩阵中获取原子的三维坐标，且无法对误差进行校正，导致重构的过程对硬件需求较高，且重构的三维坐标精度较差的技术问题。According to the three-dimensional reconstruction device of the local orbital function proposed in the embodiment of the present application, based on the collected image data of the sample at multiple tilt angles, the calculation images at multiple tilt angles are obtained, and then the loss of the calculation images is calculated function to obtain the gradient of the optimized parameters, so as to obtain the optimized parameters, after repeated screening and calculation, until the loss function meets the convergence conditions, and then obtain the 3D reconstruction result, which can simplify the reconstruction process of 3D coordinates, not only reducing the cost to the hardware It can also reduce cumbersome human intervention and save labor costs. At the same time, in the iterative process, it can also correct sample drift and mechanical tilt errors of the sample stage, thereby improving the accuracy of 3D coordinate reconstruction. Therefore, it solves the problem that in related technologies, the three-dimensional coordinates of atoms can only be obtained from the reconstructed three-dimensional density matrix, and the error cannot be corrected, resulting in high requirements for hardware in the reconstruction process, and the accuracy of the reconstructed three-dimensional coordinates Poor technical issues.

图11为本申请实施例提供的电子设备的结构示意图。该电子设备可以包括：FIG. 11 is a schematic structural diagram of an electronic device provided by an embodiment of the present application. This electronic equipment can include:

存储器1101、处理器1102及存储在存储器1101上并可在处理器1102上运行的计算机程序。Memory 1101 , processor 1102 , and computer programs stored in memory 1101 and executable on processor 1102 .

处理器1102执行程序时实现上述实施例中提供的局域轨道函数的三维重构方法。When the processor 1102 executes the program, the method for three-dimensional reconstruction of the local orbit function provided in the above-mentioned embodiments is realized.

进一步地，电子设备还包括：Further, the electronic equipment also includes:

通信接口1103，用于存储器1101和处理器1102之间的通信。The communication interface 1103 is used for communication between the memory 1101 and the processor 1102 .

存储器1101，用于存放可在处理器1102上运行的计算机程序。The memory 1101 is used to store computer programs that can run on the processor 1102 .

存储器1101可能包含高速RAM存储器，也可能还包括非易失性存储器(non-volatile memory)，例如至少一个磁盘存储器。The memory 1101 may include a high-speed RAM memory, and may also include a non-volatile memory (non-volatile memory), such as at least one disk memory.

如果存储器1101、处理器1102和通信接口1103独立实现，则通信接口1103、存储器1101和处理器1102可以通过总线相互连接并完成相互间的通信。总线可以是工业标准体系结构(Industry Standard Architecture，简称为ISA)总线、外部设备互连(PeripheralComponent，简称为PCI)总线或扩展工业标准体系结构(Extended Industry StandardArchitecture，简称为EISA)总线等。总线可以分为地址总线、数据总线、控制总线等。为便于表示，图11中仅用一条粗线表示，但并不表示仅有一根总线或一种类型的总线。If the memory 1101, the processor 1102, and the communication interface 1103 are implemented independently, the communication interface 1103, the memory 1101, and the processor 1102 may be connected to each other through a bus to complete mutual communication. The bus may be an Industry Standard Architecture (Industry Standard Architecture, ISA for short) bus, a Peripheral Component Interconnect (PCI for short) bus, or an Extended Industry Standard Architecture (EISA for short) bus. The bus can be divided into address bus, data bus, control bus and so on. For ease of representation, only one thick line is used in FIG. 11 , but it does not mean that there is only one bus or one type of bus.

可选地，在具体实现上，如果存储器1101、处理器1102及通信接口1103，集成在一块芯片上实现，则存储器1101、处理器1102及通信接口1103可以通过内部接口完成相互间的通信。Optionally, in specific implementation, if the memory 1101, processor 1102, and communication interface 1103 are integrated on one chip, then the memory 1101, processor 1102, and communication interface 1103 may communicate with each other through the internal interface.

处理器1102可能是一个中央处理器(Central Processing Unit，简称为CPU)，或者是特定集成电路(Application Specific Integrated Circuit，简称为ASIC)，或者是被配置成实施本申请实施例的一个或多个集成电路。The processor 1102 may be a central processing unit (Central Processing Unit, referred to as CPU), or a specific integrated circuit (Application Specific Integrated Circuit, referred to as ASIC), or configured to implement one or more of the embodiments of the present application integrated circuit.

本实施例还提供一种计算机可读存储介质，其上存储有计算机程序，该程序被处理器执行时实现如上的局域轨道函数的三维重构方法。This embodiment also provides a computer-readable storage medium, on which a computer program is stored, and when the program is executed by a processor, the above three-dimensional reconstruction method of the local orbit function is realized.

在本说明书的描述中，参考术语“一个实施例”、“一些实施例”、“示例”、“具体示例”、或“一些示例”等的描述意指结合该实施例或示例描述的具体特征、结构、材料或者特点包含于本申请的至少一个实施例或示例中。在本说明书中，对上述术语的示意性表述不必须针对的是相同的实施例或示例。而且，描述的具体特征、结构、材料或者特点可以在任一个或N个实施例或示例中以合适的方式结合。此外，在不相互矛盾的情况下，本领域的技术人员可以将本说明书中描述的不同实施例或示例以及不同实施例或示例的特征进行结合和组合。In the description of this specification, descriptions referring to the terms "one embodiment", "some embodiments", "example", "specific examples", or "some examples" mean that specific features described in connection with the embodiment or example , structure, material or characteristic is included in at least one embodiment or example of the present application. In this specification, the schematic representations of the above terms are not necessarily directed to the same embodiment or example. Moreover, the described specific features, structures, materials or characteristics may be combined in any one or N embodiments or examples in an appropriate manner. In addition, those skilled in the art can combine and combine different embodiments or examples and features of different embodiments or examples described in this specification without conflicting with each other.

此外，术语“第一”、“第二”仅用于描述目的，而不能理解为指示或暗示相对重要性或者隐含指明所指示的技术特征的数量。由此，限定有“第一”、“第二”的特征可以明示或者隐含地包括至少一个该特征。在本申请的描述中，“N个”的含义是至少两个，例如两个，三个等，除非另有明确具体的限定。In addition, the terms "first" and "second" are used for descriptive purposes only, and cannot be interpreted as indicating or implying relative importance or implicitly specifying the quantity of indicated technical features. Thus, the features defined as "first" and "second" may explicitly or implicitly include at least one of these features. In the description of the present application, "N" means at least two, such as two, three, etc., unless otherwise specifically defined.

流程图中或在此以其他方式描述的任何过程或方法描述可以被理解为，表示包括一个或更N个用于实现定制逻辑功能或过程的步骤的可执行指令的代码的模块、片段或部分，并且本申请的优选实施方式的范围包括另外的实现，其中可以不按所示出或讨论的顺序，包括根据所涉及的功能按基本同时的方式或按相反的顺序，来执行功能，这应被本申请的实施例所属技术领域的技术人员所理解。Any process or method description in a flowchart or otherwise described herein may be understood to represent a module, segment or portion of code comprising one or more executable instructions for implementing a custom logical function or step of a process , and the scope of preferred embodiments of the present application includes additional implementations in which functions may be performed out of the order shown or discussed, including in substantially simultaneous fashion or in reverse order depending on the functions involved, which shall It should be understood by those skilled in the art to which the embodiments of the present application belong.

在流程图中表示或在此以其他方式描述的逻辑和/或步骤，例如，可以被认为是用于实现逻辑功能的可执行指令的定序列表，可以具体实现在任何计算机可读介质中，以供指令执行系统、装置或设备(如基于计算机的系统、包括处理器的系统或其他可以从指令执行系统、装置或设备取指令并执行指令的系统)使用，或结合这些指令执行系统、装置或设备而使用。就本说明书而言，"计算机可读介质"可以是任何可以包含、存储、通信、传播或传输程序以供指令执行系统、装置或设备或结合这些指令执行系统、装置或设备而使用的装置。计算机可读介质的更具体的示例(非穷尽性列表)包括以下：具有一个或N个布线的电连接部(电子装置)，便携式计算机盘盒(磁装置)，随机存取存储器(RAM)，只读存储器(ROM)，可擦除可编辑只读存储器(EPROM或闪速存储器)，光纤装置，以及便携式光盘只读存储器(CDROM)。另外，计算机可读介质甚至可以是可在其上打印所述程序的纸或其他合适的介质，因为可以例如通过对纸或其他介质进行光学扫描，接着进行编辑、解译或必要时以其他合适方式进行处理来以电子方式获得所述程序，然后将其存储在计算机存储器中。The logic and/or steps represented in the flowcharts or otherwise described herein, for example, can be considered as a sequenced listing of executable instructions for implementing logical functions, can be embodied in any computer-readable medium, For use with instruction execution systems, devices, or devices (such as computer-based systems, systems including processors, or other systems that can fetch instructions from instruction execution systems, devices, or devices and execute instructions), or in conjunction with these instruction execution systems, devices or equipment used. For the purposes of this specification, a "computer-readable medium" may be any device that can contain, store, communicate, propagate or transmit a program for use in or in conjunction with an instruction execution system, device or device. More specific examples (non-exhaustive list) of computer readable media include the following: electrical connection with one or N wires (electronic device), portable computer disk case (magnetic device), random access memory (RAM), Read Only Memory (ROM), Erasable and Editable Read Only Memory (EPROM or Flash Memory), Fiber Optic Devices, and Portable Compact Disc Read Only Memory (CDROM). In addition, the computer-readable medium may even be paper or other suitable medium on which the program can be printed, as it may be possible, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or other suitable processing if necessary. The program is processed electronically and stored in computer memory.

应当理解，本申请的各部分可以用硬件、软件、固件或它们的组合来实现。在上述实施方式中，N个步骤或方法可以用存储在存储器中且由合适的指令执行系统执行的软件或固件来实现。如，如果用硬件来实现和在另一实施方式中一样，可用本领域公知的下列技术中的任一项或他们的组合来实现：具有用于对数据信号实现逻辑功能的逻辑门电路的离散逻辑电路，具有合适的组合逻辑门电路的专用集成电路，可编程门阵列(PGA)，现场可编程门阵列(FPGA)等。It should be understood that each part of the present application may be realized by hardware, software, firmware or a combination thereof. In the above embodiments, the N steps or methods may be implemented by software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware as in another embodiment, it can be implemented by any one or a combination of the following techniques known in the art: a discrete Logic circuits, ASICs with suitable combinational logic gates, Programmable Gate Arrays (PGA), Field Programmable Gate Arrays (FPGA), etc.

本技术领域的普通技术人员可以理解实现上述实施例方法携带的全部或部分步骤是可以通过程序来指令相关的硬件完成，所述的程序可以存储于一种计算机可读存储介质中，该程序在执行时，包括方法实施例的步骤之一或其组合。Those of ordinary skill in the art can understand that all or part of the steps carried by the methods of the above embodiments can be completed by instructing related hardware through a program, and the program can be stored in a computer-readable storage medium. During execution, one or a combination of the steps of the method embodiments is included.

此外，在本申请各个实施例中的各功能单元可以集成在一个处理模块中，也可以是各个单元单独物理存在，也可以两个或两个以上单元集成在一个模块中。上述集成的模块既可以采用硬件的形式实现，也可以采用软件功能模块的形式实现。所述集成的模块如果以软件功能模块的形式实现并作为独立的产品销售或使用时，也可以存储在一个计算机可读取存储介质中。In addition, each functional unit in each embodiment of the present application may be integrated into one processing module, each unit may exist separately physically, or two or more units may be integrated into one module. The above-mentioned integrated modules can be implemented in the form of hardware or in the form of software function modules. If the integrated modules are implemented in the form of software function modules and sold or used as independent products, they can also be stored in a computer-readable storage medium.

上述提到的存储介质可以是只读存储器，磁盘或光盘等。尽管上面已经示出和描述了本申请的实施例，可以理解的是，上述实施例是示例性的，不能理解为对本申请的限制，本领域的普通技术人员在本申请的范围内可以对上述实施例进行变化、修改、替换和变型。The storage medium mentioned above may be a read-only memory, a magnetic disk or an optical disk, and the like. Although the embodiments of the present application have been shown and described above, it can be understood that the above embodiments are exemplary and should not be construed as limitations on the present application, and those skilled in the art can make the above-mentioned The embodiments are subject to changes, modifications, substitutions and variations.