A method for measuring and correcting goniometer tilt in a transmission electron microscope

Abstract

The application provides a method for measuring and correcting the deviation of a goniometer table of a transmission electron microscope, comprising the following steps: S1, collecting a Ronchigram image and extracting the accurate coordinates of the center of the image; S2, collecting a plurality of data points based on a polycrystalline FIB sample, wherein the data comprises the corresponding alpha and beta tilt angle data of a plurality of sample grains when the sample grains are tilted to the normal axis, so as to ensure the reliability and repeatability of the data statistics in the calibration process; S3, calculating the corresponding x and y coordinates of the grains on the image, namely Pixelx and Pixely, when the grains are tilted to the normal axis; S4, constructing a mathematical model for describing the geometric relationship between the actual tilting system of the transmission electron microscope and the image acquisition system; S5, performing fitting processing and solving parameters on the two groups of data of the corresponding Pixelx and Pixely data in relation to the actually collected alpha and beta tilt angle data; and S6, calculating the tilt angle of the electron microscope rotation shaft operation based on the calculation result of step S5; the application has the advantages of high precision, good stability and strong repeatability.

Description

Technical Field

[0001] This invention relates to the field of electron microscope equipment technology, and in particular to a method for measuring and correcting the deviation of the goniometer stage of a transmission electron microscope. Background Technology

[0002] Currently, transmission electron microscope (TEM) tilt stages generally employ a dual-tilt-axis structure, comprising an α-axis and a β-axis, which together form a tilt coordinate system (αOβ coordinate system). Theoretically, this coordinate system allows for the precise positioning of any target point in reciprocal space to the diffraction center through tilting operations. However, in actual imaging and data processing, an observation coordinate system (XOY coordinate system) is typically used for image acquisition and display. Ideally, the tilt coordinate system and the observation coordinate system should be strictly aligned to ensure accurate sample positioning during tilting. However, actual testing shows that due to factors such as manufacturing tolerances, assembly errors, and instrument relocation and reassembly, a certain deviation angle exists between the two coordinate systems; furthermore, the α-axis and β-axis may not be strictly orthogonal. Specifically, there is a deviation angle (denoted as γ) between the α-axis and the x-axis in the observation coordinate system, and the angle between the α-axis and β-axis may deviate from the ideal orthogonality (i.e., 90°) (denoted as θ). In practical applications and method design, it is usually assumed that there is no deviation between the tilt coordinate system and the observation coordinate system. However, experiments have shown that this deviation may cause an error of 2 to 3° when analyzing the tilt results.

[0003] To address the aforementioned issues, this invention proposes a method for correcting tilt axis deviation in transmission electron microscopes. Its main purpose is to verify and correct the deviation angle between the tilt coordinate system (αOβ) and the image observation coordinate system (XOY), thereby controlling the final tilt angle error within 0.5°. Summary of the Invention

[0004] This invention proposes a method for measuring and correcting the deviation of the goniometer stage of a transmission electron microscope, which can realize dynamic real-time correction of the tilt axis deviation of the transmission electron microscope and has the advantages of high precision, good stability and strong repeatability.

[0005] The present invention adopts the following technical solution.

[0006] A method for measuring and correcting the deviation of a transmission electron microscope goniometer stage includes the following steps;

[0007] Step S1: Acquire a Ronchigram image and extract the precise coordinates of the image center;

[0008] Step S2: Collect multiple data points based on the polycrystalline FIB sample. The data includes the α and β tilt angle data corresponding to the tilt of multiple sample grains when they are tilted to the positive axis, so as to ensure the reliability and repeatability of the data statistics in the calibration process.

[0009] Step S3: Calculate the x and y coordinates of the grain on the image when it tilts to the positive axis, i.e., Pixelx and Pixely;

[0010] Step S4: Construct a mathematical model to describe the geometric relationship between the actual tilting system and the image acquisition system of the transmission electron microscope;

[0011] Step S5: For the actual collected α and β tilt angle data, the corresponding Pixelx and Pixely data are fitted and the parameters are solved.

[0012] Step S6: Calculate the tilt angle for the electron microscope rotation axis operation based on the calculation results of step S5.

[0013] The method is used for a transmission electron microscope tilt stage with a dual tilt axis structure, including an α-axis and a β-axis, which together form the αOβ tilt coordinate system. It is used to verify and correct the deviation angle between the tilt coordinate system αOβ and the image observation coordinate system XOY.

[0014] Step S1 specifically involves acquiring a Ronchigram image, processing the image using MATLAB, and extracting the precise coordinates of the current Ronchigram center; this is used to provide a reference benchmark for subsequent coordinate system calibration.

[0015] The method in step S1 is performed while the transmission electron microscope is in a vacuum state.

[0016] Step S2 is used to ensure that the Kiku Line can be clearly observed and tracked during the operation. A polycrystalline FIB sample with obvious Kiku Line characteristics is selected. This sample contains multiple grains, and the Kiku Line can be clearly displayed on each grain, which makes it easy to select multiple data points in different areas for collection.

[0017] In step S2, a polycrystalline FIB sample with mature preparation process, high stability, and the ability to meet the requirements of data repeatability and statistical reliability is used. The selected sample and the data points collected at the sample can form an accurate mapping between image coordinates and tilt angle.

[0018] In step S3, MATLAB is used to process the collected data and calculate the x and y coordinates of the grain on the image when it tilts to the positive axis, so as to realize the correspondence between the tilt angle and the image coordinates and provide a data basis for establishing a mathematical model.

[0019] In step S4, when establishing the model, it is assumed that: there is a deviation angle γ between the α-axis and the x-axis of the observation coordinate system; the angle θ between the β-axis and the α-axis may deviate from orthogonality; and the pixel size of the image is also considered. The established mathematical model is used to describe the geometric relationship between the actual tilting system and the image acquisition system of the transmission electron microscope, expressed by the formula:

[0020]

[0021] Step S5 specifically involves using MATLAB software to fit two sets of data: one set is the actual acquired tilt angle data of α and β, and the other set is the corresponding Pixelx and Pixely data; through mathematical fitting methods, the values ​​of deviation angle γ and θ and image pixel size PixelSize are accurately calculated and solved, thereby realizing quantitative correction of the tilt axis deviation and pixel calibration of the transmission electron microscope.

[0022] The results showed that the average error after correction was 0.28°, which was significantly lower than the empirical value of 2–3° before correction.

[0023] Step S6 specifically involves calculating the tilt angle of any point in the reciprocal space of the region related to the electron microscope rotation operation after obtaining the precise values ​​of γ, θ, and PixelSize. That is, based on the position of the point in the image, calculating the α and β values ​​corresponding to the point that needs to be tilted to the center position, in order to improve the efficiency and accuracy of the electron microscope rotation operation.

[0024] After step S6, all collected and processed data are archived for subsequent analysis, equipment maintenance, and parameter optimization. Based on long-term usage, periodic recalibration is performed to maintain long-term system stability and high-precision operation.

[0025] The technical advantages of this invention are:

[0026] 1. This invention provides an innovative calibration method to calibrate the goniometer stage and the observation coordinate system, specifically addressing the common deflection angle error in traditional transmission electron microscopes. In traditional systems, deviations often occur between the goniometer stage and the observation coordinate system due to manufacturing tolerances, assembly errors, and relocation / reassembly, directly affecting the reliability of data analysis. This invention precisely measures the deflection angle between the two coordinate systems and uses image processing and mathematical fitting algorithms to automatically correct this deviation angle, thereby ensuring strict alignment between the goniometer stage and the observation coordinate system.

[0027] 2. A center extraction method based on Ronchigram images was implemented. Specifically, Ronchigram images were acquired under vacuum conditions and processed using MATLAB to accurately extract the center coordinates of the images, providing a stable and reliable reference point for subsequent calibration.

[0028] 3. A multi-data-point calibration strategy was implemented, namely: using polycrystalline FIB samples to collect α and β data when multiple grains are tilted to the positive axis, and calculating the corresponding pixel coordinates on the image, thus realizing system calibration from multiple angles and multiple data points, which greatly improves the statistical reliability of the data.

[0029] 4. An innovative mathematical model was constructed, namely: the deviation angle γ between the α axis and the x-axis of the observation coordinate system, the deviation angle θ between the α axis and the β axis, and the pixel size parameter of the image were introduced into the model to construct a geometric model that comprehensively reflects the influence of various factors in the actual working environment, providing a theoretical basis for accurate correction.

[0030] 5. It can achieve precise calculation of tilting from any point to the center. That is, after calibration, the obtained parameters can be used to quickly calculate the α and β values ​​required for tilting any point on the image to the center, thereby greatly improving the efficiency and data accuracy of electron microscope axis rotation operation.

[0031] 6. It can realize automated and high-precision correction technology, that is, it provides a brand-new automated correction scheme, which combines image processing and mathematical model fitting to realize dynamic real-time correction of the tilt axis deviation of the transmission electron microscope, and has the advantages of high precision, good stability and strong repeatability.

[0032] The advantages of this invention also include:

[0033] 1. High-precision calibration:

[0034] By acquiring Ronchigram images and using MATLAB to accurately extract the image center, precise correction of the deviation angles (γ and θ) between the α and β axes and the image pixel size is achieved, effectively reducing the errors in traditional methods.

[0035] 2. Automated operation and real-time calibration:

[0036] Built-in data processing and model fitting algorithms can automatically calculate and update correction parameters, enabling real-time correction, reducing human intervention, and improving operational efficiency and data repeatability.

[0037] 3. Multi-data-point correction strategy:

[0038] Statistical calibration is performed using a large amount of grain data to ensure the stability and reliability of the calibration results, adapting to measurement needs in complex samples and variable environments.

[0039] 4. Precisely map pixels and tilt angles:

[0040] Precise calibration of the tilt angle (unit: mrad) corresponding to each pixel provides a reliable conversion relationship for subsequent image processing and quantitative analysis, improving the accuracy of the data.

[0041] 5. Improve operational efficiency:

[0042] After calibration, the α and β values ​​required for any image point to tilt to the center can be quickly calculated, greatly simplifying the electron microscope operation process, saving calibration time, and improving the overall efficiency of the equipment.

[0043] 6. Strong adaptability and good stability:

[0044] The design of the present invention takes into account factors such as changes in ambient temperature and mechanical wear, ensuring that it maintains high precision and high stability during long-term use, and is suitable for various high-end transmission electron microscope systems.

[0045] The method described in this invention can be implemented for the following purposes:

[0046] 1. Electron microscope calibration

[0047] Used for correcting tilt axis deviation in transmission electron microscopy, ensuring precise positioning of samples during multi-angle imaging, and improving the accuracy of image geometric correction and data reconstruction.

[0048] 2. Quantitative analysis of high-resolution images

[0049] It provides precise image coordinate and tilt angle conversion support for fields such as materials science, nanotechnology, and semiconductor detection, promoting quantitative analysis and structural resolution.

[0050] 3. Scientific research and industrial testing

[0051] Suitable for various scientific research laboratories and industrial testing scenarios, it improves the reliability and repeatability of transmission electron microscopy data acquisition through automatic calibration and parameter fitting.

[0052] 4. Sample positioning and tracking

[0053] It supports calculating the required axis adjustment for tilting to the center from any point on the image, enabling fast and accurate sample positioning and tracking, and adapting to the operational needs under dynamic experimental conditions.

[0054] 5. Equipment maintenance and performance optimization

[0055] By regularly calibrating and providing data feedback, the system monitors equipment status and shaft deviation, assisting in equipment maintenance and performance optimization, extending instrument lifespan, and reducing maintenance costs. Attached Figure Description

[0056] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0057] Appendix Figure 1 This is a schematic diagram illustrating the deviation between the αOβ and XOY coordinate systems;

[0058] Appendix Figure 2 This is a schematic diagram of step S1, which involves extracting the center coordinates of the Ronchigram.

[0059] Appendix Figure 3 This is a schematic diagram of the data acquisition process in step S2;

[0060] Appendix Figure 4 This is a schematic diagram of obtaining the PixelX and PixelY coordinates in step S3;

[0061] Appendix Figure 5 This is a schematic diagram of the fitting results and error calculation in step S5. Detailed Implementation

[0062] As shown in the figure, a method for measuring and correcting the deviation of a transmission electron microscope goniometer stage includes the following steps;

[0063] Step S1: Acquire a Ronchigram image and extract the precise coordinates of the image center;

[0064] Step S2: Collect multiple data points based on the polycrystalline FIB sample. The data includes the α and β tilt angle data corresponding to the tilt of multiple sample grains when they are tilted to the positive axis, so as to ensure the reliability and repeatability of the data statistics in the calibration process.

[0065] Step S3: Calculate the x and y coordinates of the grain on the image when it tilts to the positive axis, i.e., Pixelx and Pixely;

[0066] Step S4: Construct a mathematical model to describe the geometric relationship between the actual tilting system and the image acquisition system of the transmission electron microscope;

[0067] Step S5: For the actual collected α and β tilt angle data, the corresponding Pixelx and Pixely data are fitted and the parameters are solved.

[0068] Step S6: Calculate the tilt angle for the electron microscope rotation axis operation based on the calculation results of step S5.

[0069] The method is used for a transmission electron microscope tilt stage with a dual tilt axis structure, including an α-axis and a β-axis, which together form the αOβ tilt coordinate system. It is used to verify and correct the deviation angle between the tilt coordinate system αOβ and the image observation coordinate system XOY.

[0070] Step S1 specifically involves acquiring a Ronchigram image, processing the image using MATLAB, and extracting the precise coordinates of the current Ronchigram center; this is used to provide a reference benchmark for subsequent coordinate system calibration.

[0071] The method in step S1 is performed while the transmission electron microscope is in a vacuum state.

[0072] Step S2 is used to ensure that the Kiku Line can be clearly observed and tracked during the operation. A polycrystalline FIB sample with obvious Kiku Line characteristics is selected. This sample contains multiple grains, and the Kiku Line can be clearly displayed on each grain, which makes it easy to select multiple data points in different areas for collection.

[0073] In step S2, a polycrystalline FIB sample with mature preparation process, high stability, and the ability to meet the requirements of data repeatability and statistical reliability is used. The selected sample and the data points collected at the sample can form an accurate mapping between image coordinates and tilt angle.

[0074] In step S3, MATLAB is used to process the collected data and calculate the x and y coordinates of the grain on the image when it tilts to the positive axis, so as to realize the correspondence between the tilt angle and the image coordinates and provide a data basis for establishing a mathematical model.

[0075] In step S4, when establishing the model, it is assumed that: there is a deviation angle γ between the α-axis and the x-axis of the observation coordinate system; the angle θ between the β-axis and the α-axis may deviate from orthogonality; and the pixel size of the image is also considered. The established mathematical model is used to describe the geometric relationship between the actual tilting system and the image acquisition system of the transmission electron microscope, expressed by the formula:

[0076]

[0077] Step S5 specifically involves using MATLAB software to fit two sets of data: one set is the actual acquired tilt angle data of α and β, and the other set is the corresponding Pixelx and Pixely data; through mathematical fitting methods, the values ​​of deviation angle γ and θ and image pixel size PixelSize are accurately calculated and solved, thereby realizing quantitative correction of the tilt axis deviation and pixel calibration of the transmission electron microscope.

[0078] The results showed that the average error after correction was 0.28°, which was significantly lower than the empirical value of 2–3° before correction.

[0079] Step S6 specifically involves calculating the tilt angle of any point in the reciprocal space of the region related to the electron microscope rotation operation after obtaining the precise values ​​of γ, θ, and PixelSize. That is, based on the position of the point in the image, calculating the α and β values ​​corresponding to the point that needs to be tilted to the center position, in order to improve the efficiency and accuracy of the electron microscope rotation operation.

[0080] After step S6, all collected and processed data are archived for subsequent analysis, equipment maintenance, and parameter optimization. Based on long-term usage, periodic recalibration is performed to maintain long-term system stability and high-precision operation.

[0081] Example:

[0082] The usage process in this example is as follows:

[0083] 1. Ronchigram image acquisition and center localization

[0084] Ronchigram images were acquired using a transmission electron microscope in a vacuum environment. The acquired Ronchigram images were then processed using the accompanying MATLAB program to automatically extract the precise coordinates of the image center, which served as the reference point for subsequent correction.

[0085] 2. Data Collection and Recording

[0086] Using polycrystalline FIB samples as the experimental object, the operator tilted multiple grains to the positive axis position and recorded the α and β tilt angle data corresponding to each grain.

[0087] Sample selection criteria:

[0088] To ensure clear observation and tracking of the Kiku Line as a marker during the experiment, this invention selected a polycrystalline FIB sample with distinct Kiku Line characteristics. This sample contains multiple grains, each clearly displaying the Kiku Line, facilitating the selection of multiple data points in different regions for acquisition. Furthermore, the polycrystalline FIB sample has a mature and highly stable preparation process, meeting the requirements for data repeatability and statistical reliability, thus making it an ideal experimental subject.

[0089] Data point selection criteria:

[0090] To accurately determine the x and y coordinates corresponding to the α and β tilt axes in subsequent steps, this invention selects the Kikuchi pole as a key reference point. Specifically, the α and β tilt angles of the Kikuchi pole when it tilts to the positive axis are recorded, and the corresponding x and y coordinates in the image are calculated based on these. The selected data points must be obvious and easily identifiable feature points to ensure data accuracy and provide reliable foundational data for subsequent mathematical fitting.

[0091] Selection criteria and their relevance to the solution in this example:

[0092] The selection of samples and the determination of data points are directly related to the accurate mapping between image coordinates and tilt angles in the calibration scheme. Using polycrystalline FIB samples with clear Kikuchi line markings not only facilitates the identification of multiple representative feature points in each grain but also ensures comprehensive data acquisition during tilting. Furthermore, the strategy of using Kikuchi lines as reference points helps to accurately calculate the correspondence between α and β tilt angles and image coordinates, thus providing a solid data foundation for mathematical fitting and subsequent correction. Overall, these selection criteria ensure the statistical reliability and repeatability of the data during calibration and form an organic unity with the calibration scheme of this invention, thereby achieving high-precision quantitative correction of tilt axis deviation and pixel calibration in transmission electron microscopes.

[0093] 3. Image data processing and conversion

[0094] The acquired image data was processed using MATLAB to calculate the precise position of the grain in the observation coordinate system (XOY). The acquired tilt angle data was matched with the corresponding pixel coordinates to provide data support for the subsequent construction of mathematical models.

[0095] 4. Mathematical Model Construction and Parameter Fitting

[0096] A mathematical model is constructed, assuming an angle γ between the α-axis and x-axis, and an angle θ between the α-axis and β-axis, while also introducing the pixel size parameter of the image. MATLAB is used for data fitting, substituting the actual collected α and β tilt angles and their corresponding pixel x and pixel ly data into the model to solve for the accurate values ​​of γ, θ, and Pixel Size.

[0097] 5. Calculation and correction of tilt value at any point

[0098] Using the fitted γ, θ, and PixelSize parameters, the α and β values ​​required for any point on the image to tilt to the center position are calculated. Based on the calculation results, the rotation axis of the transmission electron microscope is adjusted for automatic correction to ensure accurate sample positioning.

[0099] 6. Data archiving and subsequent optimization

[0100] All collected and processed data are archived to facilitate subsequent analysis, equipment maintenance, and parameter optimization. Based on long-term usage, the system is periodically recalibrated to maintain long-term stability and high-precision operation.

Claims

1. A method for measuring and correcting the deviation of a transmission electron microscope goniometer stage, characterized in that: Includes the following steps; Step S1: Acquire a Ronchigram image and extract the precise coordinates of the image center; Step S2: Collect multiple data points based on the polycrystalline FIB sample. The data includes the α and β tilt angle data corresponding to the tilt of multiple sample grains when they are tilted to the positive axis, so as to ensure the reliability and repeatability of the data statistics in the calibration process. Step S3: Calculate the x and y coordinates of the grain on the image when it tilts to the positive axis, i.e., Pixelx and Pixely; Step S4: Construct a mathematical model to describe the geometric relationship between the actual tilting system and image acquisition system of the transmission electron microscope. When establishing the model, it is assumed that: there is a deviation angle γ between the α-axis and the x-axis of the observation coordinate system; the angle θ between the β-axis and the α-axis may deviate from orthogonality; and the pixel size of the image is also considered. The established mathematical model, used to describe the geometric relationship between the actual tilting system and image acquisition system of the transmission electron microscope, is expressed by the following formula: ； Step S5: Fit the α and β tilt angle data and the corresponding Pixelx and Pixely data to solve for the deviation angles γ and θ and the pixel size PixelSize of the image. Step S6: Calculate the tilt angle for the electron microscope rotation axis operation based on the calculation results of step S5. The method is used for a dual tilt axis structure, including an α-axis and a β-axis, with the two axes together forming an αOβ tilt coordinate system, and is used to verify and correct the deviation angle between the tilt coordinate system αOβ and the image observation coordinate system XOY. Step S2 is used to ensure that the Kikuchi line can be clearly observed and tracked as a marker during the operation. A polycrystalline FIB sample with obvious Kikuchi line characteristics is selected. This sample contains multiple grains, and the Kikuchi line can be clearly displayed on each grain, which makes it easy to select multiple data points in different areas for collection. The polycrystalline FIB sample used can meet the requirements of data repeatability and statistical reliability. The selected sample and the data points collected at the sample can form an accurate mapping between image coordinates and tilt angle. In step S3, MATLAB is used to process the collected data and calculate the x and y coordinates of the grain on the image when it tilts to the positive axis, so as to realize the correspondence between the tilt angle and the image coordinates and provide a data basis for establishing a mathematical model. To calculate the x and y coordinates corresponding to the α and β tilt axes on the image, the Kikuchi pole is selected as the key reference point. Specifically, the α and β tilt angle data of the Kikuchi pole when it tilts to the positive axis are recorded, and the corresponding x and y coordinates in the image are calculated accordingly.

2. The method for measuring and correcting the deviation of a transmission electron microscope goniometer stage according to claim 1, characterized in that: Step S1 specifically involves acquiring a Ronchigram image, processing the image using MATLAB, and extracting the precise coordinates of the current Ronchigram center to provide a reference benchmark for subsequent coordinate system calibration.

3. The method for measuring and correcting the deviation of a transmission electron microscope goniometer stage according to claim 2, characterized in that: The method in step S1 is performed while the transmission electron microscope is in a vacuum state.

4. The method for measuring and correcting the deviation of a transmission electron microscope goniometer stage according to claim 1, characterized in that: Step S5 specifically involves using MATLAB software to fit two sets of data: one set is the actual acquired tilt angle data of α and β, and the other set is the corresponding Pixelx and Pixely data; through mathematical fitting methods, the deviation angles γ and θ and the pixel size PixelSize of the image are accurately calculated and solved, thereby realizing the quantitative correction of the tilt axis deviation and pixel calibration of the transmission electron microscope.

5. The method for measuring and correcting the deviation of a transmission electron microscope goniometer stage according to claim 4, characterized in that: Step S6 specifically involves calculating the tilt angle of any point in the reciprocal space of the region related to the electron microscope rotation operation after obtaining the precise values ​​of γ, θ, and PixelSize. That is, based on the position of the point in the image, calculating the α and β values ​​corresponding to the point that needs to be tilted to the center position, in order to improve the efficiency and accuracy of the electron microscope rotation operation.

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