CN114624006A - Method for measuring residual aberration of electron microscope by using emergent wave function of lower surface of sample - Google Patents
Method for measuring residual aberration of electron microscope by using emergent wave function of lower surface of sample Download PDFInfo
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Abstract
The invention discloses a method capable of directly utilizing a crystal to correct residual aberration in wave function reconstruction. The method adopts a 'segmented dimension reduction' algorithm for aberration coefficients based on 'amplitude contrast minimum standard'. On the premise of ensuring the calculation precision, the calculation amount is greatly reduced. Currently, acquiring atomic images in TEM is an indispensable research means in the field of material science. In principle, the phase image obtained by the wave function reconstruction can reflect the projected potential field in the sample, but this is often difficult to achieve due to the influence of residual aberrations. The present invention solves the problem of correcting residual aberrations in the crystal. Compared with an amorphous method, the method can be directly used in a crystal area, and the fact that the image contains amorphous is not required to be guaranteed when data are collected, so that great convenience is brought to experimental work. This method is capable of correcting higher order and numerically larger aberrations than previous crystallographic methods. The invention has wider application prospect in the field of material science.
Description
Technical Field
The invention discloses a method for measuring residual aberration of an electron microscope by utilizing an emergent wave function of the lower surface of a sample, belonging to the field of transmission electron microscope application technology and image processing.
Background
Wave function reconstruction is a way to acquire atomic images in Transmission Electron Microscopy (TEM) imaging mode, however, one cannot directly acquire atomic images due to the presence of residual aberrations. Currently, measuring the residual aberration of an electron microscope can be realized by amorphous or crystalline. In the amorphous method, a high-order aberration is converted into a low-order aberration by recording an amorphous tilting series image and a corresponding amorphous ring, so that the purpose of measuring the aberration is achieved. Residual aberrations can also be measured using standard deviation minimization theory in amorphous. However, the amorphous method requires that the image must contain amorphous, but the region of interest is usually a crystalline region, and if the sample region is moved, the aberration parameters are unstable, so the amorphous method brings difficulty to the actual aberration measurement process. There is also a small amount of work currently done to measure residual aberrations through the crystal. In recent years, an iterative algorithm based on "atoms exhibit point symmetry in the absence of aberrations" has been proposed, but this method can only correct high-order astigmatism. And the initial reconstruction wave function which we usually obtain also contains a certain residual under-focus amount. In addition, the method has very high requirements on the initial reconstructed wave function, so that the method is difficult to be effective on general experimental data. The idea of "when the sample satisfies the phase object approximation, if the aberration is completely corrected, the contrast of the corresponding amplitude image should be the lowest" is proposed. Thus, parameters representing image contrast, such as standard deviation and image entropy, are used to measure residual aberrations. When the standard deviation of the amplitude (entropy of the image) reaches a minimum value (maximum value), it means that there is no residual aberration in the wave function. However, when the residual aberration is corrected using the standard deviation, a plurality of minima of the amplitude standard deviation occur, and the global minimum of the standard deviation does not correspond to the correct residual aberration value. In practice, this problem is probably caused by factors such as low resolution of the electron microscope.
The calculation of the standard deviation is not complicated, so that it has the potential to be a simple way of measuring the residual aberration. However, currently only the "amplitude contrast minimum standard" is used to measure residual under-focus and third-order spherical aberration. However, as the requirements for image resolution become higher, higher order aberrations must also be incorporated into the measurement. If a plurality of aberration coefficients need to be measured, we will face the trouble of high-dimensional data optimization. If the high-order aberration is too large, the problem of "error accumulation" is also caused to the measurement process, resulting in an error measurement result. Therefore, it is necessary to develop a method for measuring residual aberration in both amorphous and crystalline states, and the method can reduce the computation of high-dimensional data and avoid the problem caused by "error accumulation" so as to achieve the purpose of measuring residual aberration of each order.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a method for measuring the residual aberration of an electron microscope by using an emergent wave function of the lower surface of a sample on the basis of 'amplitude image contrast minimum standard' and standard deviation as a characteristic parameter for representing image contrast.
In order to solve the problems, the invention provides a method for measuring the residual aberration of an electron microscope by using an emergent wave function on the lower surface of a sample based on the 'amplitude contrast minimum standard'.
The invention relates to a method capable of directly utilizing crystal to correct residual aberration in wave function reconstruction, which is based on amplitude contrast minimum standard, takes standard deviation as a characteristic parameter for representing image contrast, and adopts a 'segmented dimension reduction' algorithm for aberration coefficients, so that accurate residual aberration coefficients are found in a plurality of aberration coefficients, and further a final atomic image is obtained.
The invention greatly reduces the calculation amount on the premise of ensuring the calculation accuracy. Compared with an amorphous method, the method can be directly used in a crystal area, and an experimenter does not need to ensure that the image contains amorphous during data acquisition, so that great convenience is brought to experimental work. This method corrects higher order and numerical aberrations compared to previous crystallographic methods.
As a preferred scheme, the invention relates to a method for measuring the residual aberration of an electron microscope by using an emergent wave function of the lower surface of a sample, which achieves the purpose of reducing the data dimension by processing high-dimensional data in a segmented manner. And the influence caused by error accumulation is avoided by introducing the candidate coefficients, so that an accurate residual aberration coefficient is found from a plurality of aberration coefficients, and a user is helped to obtain a residual aberration value and an atomic image.
The operation scheme comprises the following steps:
step one
Acquiring an initial reconstruction wave function of a sample image to be researched; selecting the range of residual aberration to be corrected; the residual aberration to be corrected comprises at least one of under focus, second-order astigmatism, third-order astigmatism and coma;
step two
Selecting a region in the initial reconstructed wave function amplitude image as an object for subsequent standard deviation calculation;
the size of the selected region is above 128 x 128 pixels;
selecting a portion of the region for subsequent standard deviation calculation; then, within the set range of the low-order aberration, the aberration value is changed in a certain step length, and the standard deviation corresponding to the amplitude image under each low-order aberration is calculated through a formula (1); obtaining a data set; the data set comprises a data set consisting of an under-focus amount, a second-order astigmatism angle and a second-order astigmatism amplitude; the low order aberration comprises an under focus amount and a second order astigmatism;
wherein STD is standard deviation, N is total pixel number of amplitude image, i is pixel number, and μ is pixel average value; step three
Making a three-dimensional graph in the obtained amplitude image standard deviation data set; wherein the amount of under-focus is the z-axis; each under-focus amount corresponds to a plane which can represent the change of the standard deviation of the amplitude along with the amplitude and the angle of the second-order astigmatism under a certain under-focus amount; extracting a corresponding plane under each under-focus amount, namely segmenting the amplitude image standard difference data set by a plane vertical to the z axis, wherein the four-dimensional data is converted into a plurality of three-dimensional data;
taking the low-order aberration coefficient corresponding to the minimum value of the amplitude standard deviation on each plane as a 'candidate coefficient' to participate in subsequent measurement;
step four
Expanding data points of the candidate coefficients into a range; forming a final low-order aberration candidate coefficient pool; step five
Combining the obtained low-order aberration candidate coefficient pool with a preset third-order astigmatism amplitude value and angle, and calculating a standard deviation of an amplitude image; at this time, since the lower order aberration has been reduced; and the influence of the high-order aberration on the image contrast is relatively small, so that the aberration coefficient corresponding to the minimum value of the standard deviation of the amplitude can be used as the final measurement result of the low-order aberration and the third-order astigmatism; that is, the influence of "error accumulation" can be avoided through the processing of the first four steps, and the residual aberration can be actually measured by using the "minimum amplitude contrast standard"; the higher order aberration is selected from coma and third order astigmatism.
Step six
And changing high-order aberration such as coma aberration, calculating the standard deviation of the amplitude image, and taking a high-order aberration coefficient corresponding to the minimum standard deviation as a final high-order aberration value. And correcting the residual aberration by the obtained aberration value to obtain a final phase atomic image.
In the invention, the range of residual aberration (under focus, second order astigmatism, third order astigmatism and coma) needs to be corrected, and the selected range is specifically as follows:
search range of under-focus amount: 50nm to 50nm, step length of 1 nm;
search range of second order astigmatism amplitude: 1 nm-10 nm, step length 1 nm;
search range of second order astigmatism angle: 0.1 to 3.1rad, step size of 0.1rad,
search range of third-order astigmatism amplitude: 0 to 1000nm, step length of 50nm,
search range of third-order astigmatism angle: 1.1 to 3.1rad, step size of 0.1rad,
search range of coma amplitude: 0 to 1000nm, step length of 50nm,
search range of coma angle: -3.1 to 3.1rad, 0.1 rad.
In general, the aberration ranges as shown in table 1 are sufficient for correction of residual aberrations. It is worth mentioning that the operator must adjust the second order astigmatism to a relatively small range when recording the under-focused series, so that a range of 10nm is sufficient for the correction of the residual second order astigmatism. At this time, the initially reconstructed wave function phase does not faithfully reflect the atomic structure of the sample to be investigated due to the presence of residual aberrations.
In step two, the size of the selected region is guaranteed to be more than 128 × 128 pixels in order to make the calculation result of the standard deviation have statistical significance. It should be noted that the "multiple solution problem" of the crystal is inevitable. The simpler the crystal structure, the more pronounced the multi-solution problem, and therefore the selected region needs to contain less symmetric crystals such as amorphous or orthorhombic, triclinic, and monoclinic. In addition, in practical application, it is not necessary to use the whole graph for calculation, because the substrate in the graph and even the amorphous part with a large area are not the main study objects, and the main purpose of selecting a part of the region of interest for performing the subsequent standard deviation calculation is to reduce the image size and increase the operation speed. Then, the aberration value is changed by a certain step within a set range of the low order aberration (the under focus amount and the second order astigmatism), and the standard deviation corresponding to the amplitude image at each low order aberration is calculated by the formula (1). A data set as shown in fig. 2a is obtained.
Wherein STD is standard deviation, N is total pixel number of amplitude image, i is pixel number, and μ is pixel average value;
in the third step of the invention, after the amplitude image standard deviation data set is obtained, the accurate low-order aberration value cannot be obtained by using the 'amplitude contrast minimum standard'. The main reason is that the higher order aberrations are not corrected, and if the lower order aberrations are corrected directly using the "amplitude contrast minimization criteria", errors are introduced into the lower order aberrations. When higher order aberrations are subsequently measured, measurement errors in lower order aberrations can adversely affect the correction of higher order aberrations. This problem of "error accumulation" presents difficulties to our measurements. In the step, the concept of 'candidate coefficients' is introduced, so that the problem of 'error accumulation' is effectively avoided. In the amplitude image standard deviation data set shown in fig. 2a, each under-focus amount (z-axis) may correspond to a plane that represents the variation of the amplitude standard deviation with the magnitude and angle of the second-order astigmatism at a certain under-focus amount. We extract the corresponding plane at each under-focus amount, which is equivalent to segmenting the amplitude image standard deviation data set shown in fig. 2a (as shown in fig. 2b, the plane perpendicular to the z-axis segments the amplitude image standard deviation data set), and then the four-dimensional data is converted into a plurality of three-dimensional data. As mentioned in step 1, the second-order astigmatism has a relatively small range, so that the problem of multiple extrema does not occur in each segmented plane. That is, in each plane, the correct aberration coefficient of the lower order must exist among the aberration coefficients corresponding to the minimum of the standard deviation of the amplitude. Only the amplitude standard deviation global minimum at this time cannot correspond to the final correct low-order aberration coefficient. Therefore, the low-order aberration coefficient corresponding to the minimum value of the standard deviation of the amplitude on each plane can be used as a "candidate coefficient" to participate in the subsequent measurement. Fig. 3a shows the selected candidate coefficients.
In step four of the present invention, many data points in the candidate coefficient shown in fig. 3a are very close, which allows one to expand the data points into a range (as shown in the block in fig. 3 b), as follows: in the algorithm, a computer senses and finds data points with similar aberration coefficients, and then automatically searches the median of each cluster of data points (if the number of certain cluster of data is an even number, the median is selected to be smaller). And expanding a certain value to each aberration coefficient in two directions by taking the median as a center. The extension ranges are respectively the under focus amount +/-4 nm, the second-order astigmatism amplitude +/-3 nm and the second-order astigmatism angle +/-0.3 rad. We have simulated the contrast transfer function whose shape cannot be changed too much by the above extended value, thus determining the above extended range of low order aberrations. After the expansion is completed, a final low-order aberration candidate coefficient pool is formed.
In the fifth step of the invention, the obtained low-order aberration candidate coefficient pool is combined with the previously preset third-order astigmatism amplitude and angle, and the standard deviation of the amplitude image is calculated. At this time, since the low order aberrations have been reduced to the boxes shown in FIG. 3b, each box has an under focus of + -4 nm, a second order astigmatism amplitude of + -3 nm, and a second order astigmatism of + -0.3 rad, which is already very small. And the influence of high-order aberration such as coma aberration on image contrast is relatively small, so that the aberration coefficient corresponding to the minimum value of the standard deviation of the amplitude can be used as the final measurement result of the low-order aberration and the third-order astigmatism. That is, after the first four steps, the effect of "error accumulation" can be avoided, and the residual aberration can be actually measured by using the "minimum amplitude contrast standard".
In the sixth step of the invention, high-order aberration such as coma aberration is changed, the standard deviation of the amplitude image is calculated, and the high-order aberration coefficient corresponding to the minimum standard deviation is taken as the final high-order aberration value. After correcting the residual aberration by the obtained aberration value, the resulting phase image is shown in fig. 4b, and the image quality is significantly improved compared to the uncorrected image (fig. 4 a). The S-phase atomic structure shown in fig. 4c can be clearly seen in fig. 4 b.
Advantageous effects
Based on the minimum standard of amplitude contrast, the invention provides a method for measuring the residual aberration of an electron microscope by using an emergent wave function of the lower surface of a sample. The method can be successfully applied to the area containing the amorphous crystal or the crystal with low symmetry, and heavy calculation amount brought by high-dimensional data can be greatly reduced on the premise of ensuring calculation accuracy. In the case of multi-parameter measurement, the problem of "error accumulation" always affects the correct measurement of the parameter. The method can effectively avoid the influence caused by error accumulation, and finally obtain the correct residual image difference value. In addition, the method has a good effect on data with large residual aberration. The problem that the residual aberration is difficult to directly measure through the crystal at present is solved. The method can improve the resolution to the resolution limit of an electron microscope, and has great significance for helping material scientists to recognize materials at the atomic scale.
Drawings
FIG. 1 is a flow chart of an algorithm for reconstructing residual aberrations using a crystal correction wave function.
FIG. 2 shows the process of using the crystal correction wave function to reconstruct the residual aberration algorithm to segment the low-order aberration.
Fig. 3 shows a process of obtaining a low-order aberration candidate parameter by using a crystal correction wave function reconstruction residual aberration algorithm.
Fig. 4 is a comparison graph of a phase image with aberration corrected and an aberration uncorrected phase image in simulation data by the algorithm.
Fig. 5 is an under-focus series image recorded experimentally. The boxes in the diagram a are the parts shown for the subsequent results.
Fig. 6 shows an amplitude and phase image of the initial wave function reconstructed from the experimental data.
Fig. 7 shows a phase image obtained by correcting the aberration with this algorithm in experimental data.
The principle of the algorithm for reconstructing residual aberrations using the crystal correction wave function and its workflow can be seen from fig. 1.
From fig. 2, it can be seen how the algorithm performs the piecewise dimensionality reduction on the data.
From fig. 3, it can be seen how the algorithm selects reliable candidate parameters and implements extended optimization of the parameters.
It can be seen from fig. 4 that in the simulation data, the algorithm was able to successfully correct the residual aberration, obtaining an atomic image.
As can be seen from FIG. 5, 20 out of 20 under-focus series TEM images of 2xxx aluminum alloy were obtained by using a transmission electron microscope ThermoFisher Chemis G2300 TEM, the scanning ranges are respectively 0nm to-38 nm, and the step size is-2 nm. Only a portion of the image is shown.
It can be seen from fig. 6 that the phase image of the initial reconstructed wave function does not faithfully show the position of the atom due to the influence of the residual aberration.
It can be seen from fig. 7 that in the experimental data, the algorithm can successfully correct the residual aberration to obtain the atomic image.
Detailed Description
The invention will be further described in detail by means of a specific embodiment. The following examples are intended to illustrate the invention, but the specific embodiments of the invention are not limited to the following examples.
The sample used in this example was a 2000-series (Al-Cu-Mg) aluminum alloy, and the study object was the S phase of a precipitated phase commonly found in 2000-series aluminum alloys, and the transmission electron microscope used was FEI Tecnai F20. Fig. 5 is an under-focus series of images for wave function reconstruction. The aberrations we intend to correct in this data are under-focus, second order astigmatism, third order astigmatism, coma. For ease of illustration, only portions of the boxed area will be shown subsequently.
Step one
An initial reconstructed wave function of an image of a sample to be studied is obtained. And selecting the range of residual aberration (under focus, second order astigmatism, third order astigmatism and coma) to be corrected, wherein the selected range is shown in the following table. In general, the aberration ranges shown in the following table are sufficient for correction of residual aberration. It is worth mentioning that the operator must adjust the second order astigmatism to a relatively small range when recording the under-focused series, so that a range of 10nm is sufficient for the correction of the residual second order astigmatism. At this time, the initially reconstructed wave function phase does not faithfully reflect the atomic structure of the sample to be investigated due to the presence of residual aberrations. Fig. 6 shows an amplitude image and a phase image corresponding to the reconstructed initial wave function, and a region in the amplitude image is selected for calculating the standard deviation (the region within the box).
The under-focus amount and the second-order astigmatism are varied in a certain step within a certain range and the standard deviation of the selected area in S1 is calculated.
Search range and step length table for preset aberration coefficient
Step two
And selecting a block of area in the amplitude image of the initial reconstructed wave function as an object for subsequently calculating the standard deviation. In order to make the calculation of the standard deviation statistically significant, it is necessary to ensure that the size of the selected region is above 128 × 128 pixels. It should be noted that the "multiple solution problem" of the crystal is inevitable. The simpler the crystal structure, the more pronounced the multi-solution problem, and therefore the selected region needs to contain less symmetric crystals such as amorphous or orthorhombic, triclinic, and monoclinic. In addition, in practical application, it is not necessary to use the whole graph for calculation, because the substrate and even the large-area amorphous part in the graph are not the main study objects, and the selection of a part of the region of interest for the calculation of the subsequent standard deviation is mainly to reduce the image size and increase the operation speed. Then, the aberration value is changed by a certain step within a set range of the low order aberration (the under focus amount and the second order astigmatism), and the standard deviation corresponding to the amplitude image at each low order aberration is calculated by the formula (1). A data set as shown in fig. 2a is obtained.
Where STD is standard deviation, N is total number of amplitude pixels, i is number of pixels, and μ is average value of pixels
Step three
After obtaining the amplitude image standard deviation data set as shown in fig. 2a, we cannot use the "amplitude contrast minimum standard" to obtain an accurate low-order image difference value at this time. The main reason is that the higher order aberrations are not corrected, and if the lower order aberrations are corrected directly using the "amplitude contrast minimization criteria", errors are introduced into the lower order aberrations. When higher order aberrations are subsequently measured, measurement errors in lower order aberrations can adversely affect the correction of higher order aberrations. This problem of "error accumulation" presents difficulties to our measurements. In the step, the concept of 'candidate coefficients' is introduced, so that the problem of 'error accumulation' is effectively avoided. In the amplitude image standard deviation data set shown in fig. 2a, each under-focus amount (z-axis) may correspond to a plane that represents the variation of the amplitude standard deviation with the magnitude and angle of the second-order astigmatism at a certain under-focus amount. We extract the corresponding plane at each under-focus amount, which is equivalent to segmenting the amplitude image standard deviation data set shown in fig. 2a (as shown in fig. 2b, the plane perpendicular to the z-axis segments the amplitude image standard deviation data set), and then the four-dimensional data is converted into a plurality of three-dimensional data. As mentioned in step 1, the second-order astigmatism has a relatively small range, so that the problem of multiple extrema does not occur in each segmented plane. That is, in each plane, the correct aberration coefficient of the lower order must exist among the aberration coefficients corresponding to the minimum of the standard deviation of the amplitude. Only the global minimum of the amplitude standard deviation at this time does not correspond to the final correct low order aberration coefficients. Therefore, the low-order aberration coefficient corresponding to the minimum value of the standard deviation of the amplitude on each plane can be used as a "candidate coefficient" to participate in the subsequent measurement. Fig. 3a shows the selected candidate coefficients.
Step four
The close proximity of many data points in the candidate coefficients shown in FIG. 3a allows one to expand the data points into a range (as shown in the box in FIG. 3 b) as follows: in the algorithm, a computer senses and finds data points with similar aberration coefficients, and then automatically searches the median of each cluster of data points (if the number of certain cluster of data is an even number, the median is selected to be smaller). And expanding a certain numerical value to each aberration coefficient in two directions by taking the median as a center. The extension ranges are respectively the under focus amount +/-4 nm, the second-order astigmatism amplitude +/-3 nm and the second-order astigmatism angle +/-0.3 rad. We have simulated the contrast transfer function whose shape cannot change too much due to the above extended value, thus determining the above extended range of low order aberrations. After the expansion is completed, a final low-order aberration candidate coefficient pool is formed.
Step five
And combining the obtained low-order aberration candidate coefficient pool with the previously preset third-order astigmatism amplitude and angle, and calculating the standard deviation of the amplitude image. At this time, since the low order aberrations have been reduced to the boxes shown in FIG. 3b, each box has an under focus of + -4 nm, a second order astigmatism amplitude of + -3 nm, and a second order astigmatism of + -0.3 rad, which is already very small. And the influence of high-order aberration such as coma aberration on image contrast is relatively small, so that the aberration coefficient corresponding to the minimum value of the standard deviation of the amplitude can be used as the final measurement result of the low-order aberration and the third-order astigmatism. That is, through the first four steps, the effect of "error accumulation" can be avoided, and the residual aberration can be actually measured by using the "minimum standard of amplitude contrast".
Step six
And changing high-order aberration such as coma aberration, calculating standard deviation of the amplitude image, and taking a high-order aberration coefficient corresponding to the minimum standard deviation as a final high-order aberration value. After correcting the residual aberration by the obtained aberration value, the resulting phase image is shown in fig. 4b, and the image quality is significantly improved compared to the uncorrected image (fig. 4 a). The S-phase atomic structure shown in fig. 4c can be clearly seen in fig. 4 b. Fig. 7 is a phase image after final aberration correction, which can truly reflect the unit cell structure of S phase.
Claims (6)
1. A method for directly utilizing crystal to correct residual aberration in wave function reconstruction is characterized in that: based on the amplitude contrast minimum standard, the standard deviation is used as a characteristic parameter for representing the image contrast, and a segmented dimensionality reduction algorithm is adopted for the aberration coefficient, so that an accurate residual aberration coefficient is found from a plurality of aberration coefficients, and a final atomic image is obtained.
2. The method for measuring the residual aberration of the electron microscope by using the emergent wave function of the lower surface of the sample according to claim 1, wherein: the aim of reducing the dimensionality of the data is achieved by segmenting the high-dimensional data. And the influence caused by error accumulation is avoided by introducing the candidate coefficients, so that accurate residual aberration coefficients are found from a plurality of aberration coefficients, and further residual image difference values and atomic images are obtained.
3. The method for measuring the residual aberration of the electron microscope by using the emergent wave function of the lower surface of the sample as claimed in claim 1, wherein: comprises the following steps;
step one
Acquiring an initial reconstruction wave function of a sample image to be researched; selecting the range of residual aberration to be corrected; the residual aberration to be corrected comprises at least one of under focus, second-order astigmatism, third-order astigmatism and coma;
step two
Selecting a region in the initial reconstructed wave function amplitude image as an object for subsequent standard deviation calculation;
the size of the selected region is above 128 x 128 pixels;
selecting a portion of the region for subsequent standard deviation calculation; then, changing the aberration value in a certain step length within the set range of the low-order aberration, and calculating the standard deviation corresponding to the amplitude image under each low-order aberration through a formula (1); obtaining a data set; the data set comprises a data set consisting of an under-focus amount, a second-order astigmatism angle and a second-order astigmatism amplitude; the low order aberration comprises an under focus amount and a second order astigmatism;
wherein STD is standard deviation, N is total pixel number of amplitude image, i is pixel number, and μ is pixel average value;
step three
Making a three-dimensional graph in the obtained amplitude image standard deviation data set; wherein the amount of under-focus is the z-axis; each under-focus amount corresponds to a plane which can represent the change of the standard deviation of the amplitude along with the amplitude and the angle of the second-order astigmatism under a certain under-focus amount; extracting a corresponding plane under each under-focus amount, namely segmenting the amplitude image standard difference data set by a plane vertical to the z axis, wherein the four-dimensional data is converted into a plurality of three-dimensional data;
taking the low-order aberration coefficient corresponding to the minimum value of the amplitude standard deviation on each plane as a 'candidate coefficient' to participate in subsequent measurement;
step four
Expanding data points of the candidate coefficients into a range; forming a final low-order aberration candidate coefficient pool;
step five
Combining the obtained low-order aberration candidate coefficient pool with the previously preset third-order astigmatism amplitude and angle, and calculating the standard deviation of the amplitude image; at this time, since the low order aberration has been reduced; and the influence of the high-order aberration on the image contrast is relatively small, so that the aberration coefficient corresponding to the minimum value of the standard deviation of the amplitude can be used as the final measurement result of the low-order aberration and the third-order astigmatism; that is, the influence of "error accumulation" can be avoided through the processing of the first four steps, and the residual aberration can be actually measured by using the "minimum amplitude contrast standard"; the high-order aberration is selected from at least one of coma aberration and third-order astigmatism;
step six
And changing high-order aberration such as coma aberration, calculating standard deviation of the amplitude image, and taking a high-order aberration coefficient corresponding to the minimum standard deviation as a final high-order aberration value. And correcting the residual aberration through the obtained aberration value to obtain a final phase and an atomic image.
4. The method for measuring the residual aberration of the electron microscope by using the surface emergent wave function of the sample as claimed in claim 3, wherein: the residual aberration to be corrected is under-focus amount, second-order astigmatism, third-order astigmatism and coma aberration; wherein:
search range of under-focus amount: 50nm to 50nm, step length of 1 nm;
search range of second order astigmatism amplitude: 1 nm-10 nm, step length 1 nm;
search range of second order astigmatism angle: 0.1 to 3.1rad, step size of 0.1rad,
search range for third order astigmatism amplitude: 0 to 1000nm, step length of 50nm,
search range for third order astigmatism angle: 1.1 to 3.1rad, step size of 0.1rad,
search range of coma amplitude: 0 to 1000nm, step length of 50nm,
search range of coma angle: -3.1 to 3.1rad, 0.1 rad.
5. The method for measuring the residual aberration of the electron microscope by using the surface emergent wave function of the sample as claimed in claim 3, wherein:
the candidate coefficients are expanded to a range, specifically as follows: in the algorithm, a computer senses and finds data points with similar aberration coefficients, then automatically finds the median of each cluster of data points, if the number of a certain cluster of data is an even number, the median is selected to be smaller, and each pair of aberration coefficients is expanded by a certain numerical value in two directions by taking the median as a center; the extension ranges are respectively the under focus amount +/-4 nm, the second-order astigmatism amplitude +/-3 nm and the second-order astigmatism angle +/-0.3 rad.
6. The method for measuring the residual aberration of the electron microscope by using the surface emergent wave function of the sample as claimed in claim 3, wherein:
combining the obtained low-order aberration candidate coefficient pool with a preset third-order astigmatism amplitude value and angle, and calculating a standard deviation of an amplitude image; at this time, since the low order aberration has been reduced to the under focus variation of. + -.4 nm, the second order astigmatism amplitude variation of. + -.3 nm, and the second order astigmatism variation of. + -.0.3 rad.
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