An Artifact-Free Electronic Stack Reconstruction Method

Abstract

A method for artifact-free electron stack reconstruction includes: (1) four-dimensional scanning transmission electron microscope (4D-STEM) data acquisition; (2) reconstructing a sample image using a single-sideband electron stack reconstruction algorithm on the acquired data; (3) modulating the contrast transfer of the sample phase information during the implementation of the electron stack reconstruction algorithm; (4) generating a phase contrast image of the sample. The implementation of the above technical steps can eliminate the imaging contrast artifacts of the original single-sideband electron stack reconstruction algorithm, and realize the revelation of the intrinsic structure of the sample. The present invention eliminates the imaging contrast artifacts of the single-sideband electron stack reconstruction technology and improves the quality and credibility of the electron stack reconstruction image.

Description

Technical Field

[0001] The present invention provides an artifact-free electronic stack reconstruction method, which specifically involves modulating the contrast transfer of sample phase information during the execution of a single-sideband electronic stack reconstruction algorithm, and finally obtaining a sample phase contrast image without contrast artifacts, and belongs to the field of electron microscopy. Background Art

[0002] In recent years, the improvement of computer computing and storage capabilities and the development of direct electron detection cameras have further promoted the development of electron stacking reconstruction technology (Ptychography). As a computational imaging technology, electron stacking reconstruction technology has greatly enhanced the characterization capabilities of modern scanning transmission electron microscopes, especially the improvement of imaging resolution. Due to the reconstruction mechanism of the single-sideband electron stacking reconstruction algorithm, the reconstructed sample phase contrast image is seriously interfered by contrast artifacts, which greatly harms the imaging quality and reduces the credibility of the electron stacking reconstruction image.

[0003] The existing single-sideband electronic stack reconstruction algorithm execution process is mainly divided into the following steps:

[0004] (1) Obtain a set of 4D scanning transmission electron microscopy data: In the actual experimental process, a vacuum area without samples is usually selected to strictly align the center of the transmission beam spot with the center of the direct electron detection camera. That is, first select a suitable camera constant and turn on the electron beam, then a circular beam spot can be observed on the detector, and then the electron beam spot is moved to the center of the direct electron detector, and then the 4D scanning transmission electron microscopy data of the area of ​​interest can be collected; if simulation software is used to simulate the data, the experimental parameters under the corresponding experimental conditions can be used for simulation.

[0005] (2) When performing single sideband electron stack reconstruction on the collected (simulated) four-dimensional scanning transmission electron microscope data, Fourier transform is performed on the four-dimensional scanning transmission electron microscope data relative to the electron probe scanning position to obtain a new four-dimensional data set G. The specific mathematical formula is as follows:

[0006]

[0007] k is the position vector of the diffraction plane (detector plane), Q p is the image spatial frequency, r p is the probe position vector on the sample plane, ψ(k,r p ) is the electron wave function located in the diffraction plane.

[0008] (3) According to the single sideband electronic stacking reconstruction algorithm, the four-dimensional data set G can be regarded as a collection of image spatial frequencies Q p Separation of aperture function and image spatial frequency Qp The aperture function is defined as the convolution of the interference between the separated scattered beams:

[0009]

[0010] r0 is the aperture radius, and x and y are the two-dimensional position coordinates.

[0011] Therefore, there are only valid values ​​in the double overlapping area of ​​the aperture function in the four-dimensional data set G. Integrating the values ​​in the double overlapping area of ​​the aperture function can obtain a complex value I0. Performing an inverse Fourier transform on I0 can obtain the complex transmission function of the real space sample.

[0012] (4) Finally, the components of the complex transmission function of the sample at each probe position in the STEM scan are plotted to generate a phase contrast image of the sample.

[0013] However, the above-mentioned existing single-sideband electronic stack reconstruction algorithm process will cause contrast artifacts in the reconstructed image. Summary of the invention

[0014] The present invention aims to overcome the above-mentioned deficiencies of the prior art and provides an artifact-free electronic stack reconstruction method for eliminating contrast artifacts of single-sideband electronic stack reconstruction images and restoring the true structure of the sample.

[0015] An artifact-free electronic stack reconstruction method of the present invention comprises the following steps:

[0016] (1) Obtaining a set of four-dimensional scanning transmission electron microscopy data: In the actual experimental process, a vacuum area without a sample is selected to align the center of the transmission beam spot with the center of the direct electron detection camera. Specifically, the following steps are performed: first, a suitable camera constant is selected and the electron beam is turned on. A circular beam spot is observed on the detector. Then, the electron beam spot is moved to the exact center of the direct electron detector. Then, the four-dimensional scanning transmission electron microscopy data of the area of ​​interest can be collected. If simulation software is used to simulate the data, the experimental parameters under the corresponding experimental conditions are used for simulation.

[0017] (2) When performing single-sideband electron stack reconstruction on the collected or simulated four-dimensional scanning transmission electron microscope data, Fourier transform is performed on the four-dimensional scanning transmission electron microscope data relative to the electron probe scanning position to obtain a new four-dimensional data set G. The specific mathematical formula is as follows:

[0018]

[0019] k is the position vector of the diffraction plane (detector plane), Q p is the image spatial frequency, r p is the probe position vector on the sample plane, ψ(k,rp ) is the electron wave function located in the diffraction plane.

[0020] (3) Modulate the contrast transfer of the sample phase information: According to the single-sideband electronic stacking reconstruction algorithm, the four-dimensional data set G can be regarded as a combination of the image spatial frequency Q p The aperture function separated from the image spatial frequency Q p The aperture function is defined as the convolution of the interference between the separated scattered beams:

[0021]

[0022] r0 is the aperture radius, and x and y are the two-dimensional position coordinates.

[0023] Therefore, only valid values ​​exist in the double overlap region of the aperture function in the four-dimensional data set G. By integrating the values ​​in the double overlap region of the aperture function, a complex value I0 can be obtained. At the same time, the number of pixels N contained in the double overlap region of the aperture function can be obtained. The complex value I0 is divided by the number of pixels N to obtain the unit pixel complex value I. The present invention applies this process to all data in the G set by analogy, thereby obtaining a series of corresponding pixel numbers N and complex values ​​I. In addition, the present invention modulates the contrast transfer of the sample phase information by generating a series of new N values ​​as a function of the spatial frequency. The specific function form is as follows:

[0024]

[0025] Where Q is the spatial frequency, δ and ε are adjustable parameters, and n is the function order. The present invention obtains a series of new N values ​​by adjusting various parameters, namely, N new . The modulated N new The value is multiplied by the corresponding unit pixel complex value I to obtain a new complex value I new , to I new The complex transmission function of the real-space sample can be obtained by performing an inverse Fourier transform. Therefore, by adjusting the value N of this function new The contrast transfer of sample phase information can be modulated.

[0026] (4) Finally, the components of the complex transmission function of the sample at each probe position in the STEM scan are plotted to generate a phase contrast image of the sample.

[0027] The present invention is characterized in that:

[0028] (1) Using a direct electron detection camera to simultaneously collect two-dimensional sample plane information and two-dimensional diffraction plane information to form a four-dimensional data set;

[0029] (2) Modulate the contrast transfer of sample phase information during the implementation of the electronic stack reconstruction algorithm.

[0030] The invention is beneficial in that it eliminates the imaging contrast artifacts of the single-sideband electronic stack reconstruction technology and improves the quality and credibility of the electronic stack reconstruction image. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 It is a work flow chart of the method of the present invention;

[0032] Figure 2 is a data slice schematic diagram of the data set G of the present invention;

[0033] Figure 3 It is the phase contrast image of the simulated molecular sieve reconstructed using the original single sideband electronic stacking reconstruction algorithm;

[0034] Figure 4 It is a phase contrast image of a simulated molecular sieve reconstructed using the improved single sideband electronic stacking reconstruction algorithm of the present invention. DETAILED DESCRIPTION

[0035] The present invention is described in detail below with reference to the accompanying drawings and examples. The present invention improves the single-sideband electron stack reconstruction algorithm to achieve artifact-free electron stack reconstruction phase contrast image. In order to verify the feasibility and reliability of the present invention, this example uses simulated data assuming that the sample is a molecular sieve to execute the original single-sideband electron stack reconstruction algorithm and the improved single-sideband electron stack reconstruction algorithm of the present invention and compare the reconstruction imaging effects. The main reason for using simulated data is that simulated data can eliminate interference from external uncertain factors, such as noise, etc., thereby proving the effectiveness of the present invention in improving the original single-sideband electron stack reconstruction algorithm.

[0036] The present invention provides an artifact-free electronic stack reconstruction method, and the specific implementation method is as follows:

[0037] (1) First, a four-dimensional scanning transmission electron microscopy data set of a molecular sieve sample is simulated, with a data size of 150×150×128×128 pixels. The data simulation conditions are: acceleration voltage 300 kV, convergence half angle 12 mrad, and sampling meets the Nyquist sampling frequency.

[0038] (2) When performing single sideband electron stack reconstruction on the simulated four-dimensional scanning transmission electron microscope data, Fourier transform is performed on the four-dimensional scanning transmission electron microscope data relative to the electron probe scanning position to obtain a new four-dimensional data set G. The specific mathematical formula is as follows:

[0039]

[0040] k is the position vector of the diffraction plane (detector plane), Q pis the image spatial frequency, r p is the probe position vector on the sample plane, ψ(k,r p ) is the electron wave function located in the diffraction plane. Figure 2 Visualization of a data slice of dataset G.

[0041] (3) According to the single-sideband electronic stacking reconstruction algorithm, in the G data set, only the following Figure 2 There are valid values ​​in the double overlapping area of ​​the circular ring shown. By integrating the values ​​in the double overlapping area of ​​the circular ring, a complex value I0 can be obtained. At the same time, the number of pixels N contained in the double overlapping area of ​​the circular ring can be obtained. The complex value I0 is divided by the number of pixels N to obtain the unit pixel complex value I. The present invention applies this process to all data in the G set, thereby obtaining a series of corresponding pixel numbers N and complex values ​​I. In addition, the present invention modulates the contrast transfer of the sample phase information by generating a series of new N values ​​as a function of the spatial frequency. The specific function form is as follows:

[0042]

[0043] Where Q is the spatial frequency, δ and ε are adjustable parameters, and n is the function order. The present invention obtains a series of new N values ​​by adjusting various parameters, namely, N new In this example, in order to obtain the best imaging effect, n is set to 2, ε is set to 1, and δ is set to 7. new The value is multiplied by the corresponding unit pixel complex value I to obtain a new complex value I new , to I new Performing an inverse Fourier transform yields the complex transmission function of the real-space sample. Therefore, by adjusting the value of this function N new The contrast transfer of sample phase information can be modulated.

[0044] (4) Finally, the components of the complex transmission function of the sample at each probe position in the STEM scan are plotted to generate a phase contrast image of the sample.

[0045] Figure 3 The phase contrast image of the molecular sieve obtained by executing the original electron stacking reconstruction algorithm shows obvious contrast artifacts inside the molecular sieve pores.

[0046] Figure 4 In the molecular sieve phase contrast image obtained by executing the improved single-sideband electron stacking reconstruction algorithm of the present invention, it can be seen that the contrast artifacts inside the pores disappear and the intrinsic structure of the sample is clearly revealed.

[0047] The contents described in the embodiments of this specification are merely an enumeration of the implementation forms of the inventive concept. The protection scope of the present invention should not be regarded as limited to the specific forms described in the embodiments. The protection scope of the present invention also extends to equivalent technical means that can be conceived by those skilled in the art based on the inventive concept.

Claims

1. A method for artifact-free electronic stack reconstruction, comprising the following steps: (1) Obtaining a set of four-dimensional scanning transmission electron microscope data: In the actual experimental process, a vacuum area without a sample is selected to align the center of the transmission beam spot with the center of the direct electron detection camera, specifically including: first selecting a suitable camera constant and turning on the electron beam, observing a circular beam spot on the detector, then moving the electron beam spot to the center of the direct electron detector, and then collecting four-dimensional scanning transmission electron microscope data of the area of ​​interest; if simulation software is used to simulate the data, the experimental parameters under the corresponding experimental conditions are used for simulation; (2) When performing single-sideband electron stack reconstruction on the collected or simulated four-dimensional scanning transmission electron microscope data, Fourier transform is performed on the four-dimensional scanning transmission electron microscope data relative to the electron probe scanning position to obtain a new four-dimensional data set G. The specific mathematical formula is as follows: k is the position vector of the diffraction plane, i.e., the detector plane, Q p is the image spatial frequency, r p is the probe position vector on the sample plane, ψ(k,r p ) is the electron wave function in the diffraction plane; (3) Modulation of the contrast transfer of the sample phase information: According to the single-sideband electronic stacking reconstruction algorithm, the four-dimensional data set G is regarded as a combination of image spatial frequency Q p The aperture function separated from the image spatial frequency Q p The aperture function is defined as the convolution of the interference between the separated scattered beams: r0 is the aperture radius, x and y are the two-dimensional position coordinates; Therefore, only valid values ​​exist in the double overlap region of the aperture function in the four-dimensional data set G. Integrating the values ​​in the double overlap region of the aperture function gives a complex value I0, and at the same time, the number of pixels N contained in the double overlap region of the aperture function is obtained. The complex value I0 is divided by the number of pixels N to obtain the complex value I per unit pixel. This process is extended to all the data in the G set to obtain a series of corresponding pixel numbers N and complex values ​​I. In addition, a series of new N values ​​are generated as a function of the spatial frequency to modulate the contrast transfer of the sample phase information. The specific function form is as follows: Where Q is the spatial frequency, δ and ε are adjustable parameters, and n is the function order. By adjusting each parameter, a series of new N values ​​can be obtained, that is, N new ; The modulated N new The value is multiplied by the corresponding unit pixel complex value I to obtain a new complex value I new , to I new Performing an inverse Fourier transform yields the complex transmission function of the real-space sample; therefore, by adjusting the value of this function N new Modulating the contrast transfer of sample phase information; (4) Finally, the components of the complex transmission function of the sample at each probe position in the STEM scan are plotted to generate a phase contrast image of the sample.

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