CN110120068B - Improved under-focus series iterative wave function reconstruction method - Google Patents
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Abstract
The invention discloses an improved iterative wave function reconstruction method for recovering a surface wave function under a sample by utilizing an under-focus series high-resolution image. The method is based on the traditional iterative wave function reconstruction method and the method of electron wave propagation in vacuum. The invention can obtain the reconstructed high-resolution image at the plane by transmitting the initial wave function reconstructed by the two images to the next under-focus plane. By comparing the reconstructed image with the experimentally recorded image, the method can effectively eliminate the difference of image contrast introduced due to the difference of the under-focus amount, so that the relative drift between the two images and the image after registration can be solved. By continuously iterating the above method, the accurately registered image can be solved, and the final wave function can be solved. The method solves the problem that the under-focus series images can not be accurately registered for a long time, and establishes a foundation for the quantitative analysis of high-resolution images.
Description
Technical Field
The invention discloses an improved iterative wave function reconstruction method for recovering a surface wave function under a sample by using an under-focus series image, belonging to the field of transmission electron microscope application technology and image processing.
Background
With the progress of material research, techniques such as transmission electron microscopy and the like for characterizing the microstructure inside the material have been developed rapidly. The phase contrast imaging mechanism is the most common imaging method for high resolution transmission electron microscopy. However, due to the limitation of various aberrations on the objective lens of the transmission electron microscope, the high resolution image is difficult to interpret. The under-focus series image wave function reconstruction technology is an important image post-processing method, and the method can remove the influence of various aberrations of a transmission electron microscope on an image and recover the phase of an electronic wave function on the lower surface of a sample. According to the interaction mechanism of electrons and the sample, the phase of the electronic wave function on the lower surface of the sample is related to the projection potential field of the atomic column in the sample once when the sample is thin. Therefore, the wave function reconstruction technology of the under-focus series has important significance for the interpretation of high-resolution images. Currently, commonly used wave function reconstruction algorithms include a paraboloid method (PAM), a maximum likelihood Method (MAL), a Wiener filter Method (MAL), and an iterative wave function reconstruction method (IWFR). Besides the IWFR method, other methods all require more images to be reconstructed to ensure the quality of reconstruction, and IWFR has the advantages of less required images, fast convergence of reconstruction errors, good suppression of noise and the like, so that the IWFR method is an excellent reconstruction method. However, generally, before the wave function reconstruction is performed, image registration is performed on the recorded series of images, so that each image is an image of the same sample region under different under-focus amounts. The IWFR method still adopts the conventional under-focus series image wave function reconstruction method, namely, Cross Correlation Function (CCF), Phase Correlation Function (PCF), rigid body registration (rigid body registration), and the like. These methods have a large error when the step size of the amount of focus loss of two adjacent images in the series is large. Therefore, a method with better image registration effect and faster calculation speed is urgently needed.
Disclosure of Invention
Technical problem to be solved
The technical problem to be solved by the invention is as follows: the wave function reconstruction method still has stable and reliable image registration effect when the under-focus step length is large and the under-focus series high-resolution images are few is provided.
(II) technical scheme
To solve the above problem, the present invention provides a method for image registration using an iterative wave function reconstruction method (IWFR, as shown in fig. 1c) and a vacuum propagation method of electron waves, which is called an improved iterative wave function reconstruction algorithm (mIWFR).
The method takes the under-focus series pictures as processing objects, and eliminates errors introduced by under-focus difference in image drift prediction by utilizing a traditional iterative wave function reconstruction method and an electronic wave propagation method in vacuum; obtaining a wave function of the under-focus series of images; the under-focus series pictures are pictures of the same sample obtained by the same electron microscope under the conditions of different under-focus step lengths or the same under-focus step length.
The invention increases the quantity of images for reconstruction in each iteration process, and improves the success rate and the signal-to-noise ratio of the reconstructed wave function.
As a preferred scheme, the improved under-focus series iterative wave function reconstruction method utilizes the advantages of few images, fast reconstruction error convergence, good noise suppression and the like required by an iterative wave function reconstruction algorithm to reconstruct an initial wave function on the lower surface of a sample from two experimental images, then transmits an under-focus step length which is the same as that of the experimental image to the initial wave function, calculates the strength of the transmitted wave function, compares the strength with the experimental image recorded under the under-focus amount, calculates the cross correlation coefficient of the two, and determines the relative drift size of the image by utilizing a peak value to obtain three registered images. And then, reconstructing the three registered images by using an iterative wave function reconstruction algorithm to obtain a second initial wave function, spreading the second initial wave function by an under-focus step length, and calculating the relative drift size of a fourth image. The above steps are cycled through until the drift sizes of all images are calculated. And finally, performing wave function reconstruction on all the images by using an iterative wave function reconstruction algorithm to obtain an electronic wave function containing residual aberration. And (4) carrying out numerical correction on the aberration to obtain a wave function of the lower surface of the sample, which is not influenced by the aberration of the transmission electron microscope.
The method eliminates the error introduced by the under-focus difference in the image drift prediction by using the traditional iterative wave function reconstruction method and the electron wave propagation method in vacuum, not only keeps the characteristics of few images, fast convergence, high noise tolerance and the like required by the traditional iterative wave function reconstruction method, but also eliminates the error introduced by the under-focus difference during the image registration of the traditional under-focus series.
As a further preferred solution, the invention provides an improved under-focus series iterative wave function reconstruction method, which includes the following steps:
step one
Putting a sample into an electron microscope, centering the electron microscope, making an electron beam incident along the crystal band axis direction of the sample (for example, after the electron beam is incident along the [001] direction of an aluminum alloy sample), amplifying the image of the sample to more than 50 ten thousand times, and making a transmission electron microscope record a high-resolution crystal lattice image of the sample; recording a set of N under-focus series high resolution images with equal under-focus step length under the condition that the under-focus amount is A; numbering the pictures from 1, 2, 3, … … to N in sequence; the N is an integer of 3 or more, preferably any one of 6 to 30.
Step two
Calculating the maximum coefficient of a cross-correlation function (CCF) of two adjacent images in the under-focus series image by using a cross-correlation algorithm; finding out two images with the maximum cross-correlation coefficient, supposing that the two images are the ith and i +1 th images, and finding out the same area in the two images according to the position of the maximum coefficient to carry out image registration to obtain 2 images after registration; i is greater than or equal to 1 and less than N;
when i is 1, defining the two images after registration as a 1 st registration image and a 2 nd registration image respectively;
when i is N-1, defining the two images after registration as the N-1 registration image and the Nth registration image respectively;
when i is not 1 and is not N-1; defining the two images after registration as the ith registration image and the (i +1) th registration image respectively;
step three
Judging whether i is 1 or N-1;
if i is 1 or N-1, reconstructing the two images after registration by directly using an iterative wave function reconstruction method (figure 1c) to obtain an initial wave function;
if i is not 1 or N-1, splitting the under-focused series image into two parts, wherein the first part is from the 1 st image to the (i +1) th image, the second part is from the i th image to the N th image, and in the two series images, the i th and the (i +1) th reconstructed wave functions are respectively utilized to obtain an initial wave function;
step four
When i is 1; defining the initial wave function obtained in the step three as an initial wave function 1; transmitting the initial wave function 1 to a recording image plane of the 3 rd image in the step one, squaring the amplitude of the obtained wave function, obtaining an intensity graph of the initial wave function 1 in the transmission process, and recording the intensity graph as an intensity graph 3, then comparing the 3 rd image in the step one with the obtained intensity graph 3, and obtaining a relative offset value of the intensity graph 3 and the 3 rd image in the step one by using a cross-correlation method; obtaining a 3 rd registered image according to the obtained image deviation value; reconstructing a new wave function by using the 1 st registration image, the 2 nd registration image and the 3 rd registration image by adopting an iterative wave function reconstruction method; obtaining a wave function 3, replacing the initial wave function 1 with the obtained wave function 3, transmitting the wave function 3 to a recording image plane of the 4 th image in the step one, and solving an intensity graph of the wave function 3 in the transmission process, wherein the intensity graph is an intensity graph 4; then comparing the 4 th image in the step one with the obtained intensity graph 4, and calculating the relative offset value of the intensity graph 4 and the 4 th image in the step one by using a cross-correlation method; obtaining a 4 th registered image according to the obtained image deviation value; reconstructing a new wave function by using a 1 st registration image, a 2 nd registration image, a 3 rd registration image and a 4 th registration image through an iterative wave function reconstruction method to obtain a wave function 4, repeating the operation, replacing the wave function p-1 with the wave function p, transmitting the wave function p to a recording image plane of the p +1 th image in the step I, solving an intensity map of the wave function p in the transmission process, and calculating the intensity map as the intensity map p + 1; then comparing the p +1 th image in the first step with the obtained intensity map p +1, and calculating the relative offset value of the intensity map p +1 and the p +1 th image in the first step by using a cross-correlation method; obtaining a p +1 registration image according to the obtained image deviation value; reconstructing a new wave function by using the 1 st registration image, the 2 nd registration image, the 3 rd registration image and the 4 th registration image … … till the p +1 th registration image by adopting an iterative wave function reconstruction method; obtaining a wave function p +1, wherein p is more than or equal to 4 and less than or equal to N-1; when p +1 is equal to N, the obtained wave function is counted as a wave function N;
when i is N-1; defining the initial wave function obtained in the step three as an initial wave function N-1; transmitting the initial wave function N-1 to a recording image plane of the N-2 images in the step one, solving an intensity graph of the initial wave function N-1 in the transmission process, and calculating the intensity graph as an intensity graph N-2, then comparing the N-2 images in the step one with the obtained intensity graph N-2, and calculating a relative offset value of the intensity graph N-2 and the N-2 images in the step one by using a cross-correlation method; obtaining the N-2 registered images according to the solved image deviation value; reconstructing a new wave function by using the Nth registration image, the Nth registration image-1 registration image and the Nth registration image-2 registration image by using an iterative wave function reconstruction method; obtaining a wave function N-2, replacing the initial wave function N-1 with the obtained wave function N-2, transmitting the wave function N-2 to the recording image plane of the (N-3) th image in the first step, and solving an intensity graph of the wave function N-2 in the transmission process, wherein the intensity graph is counted as an intensity graph N-3; then comparing the N-3 images in the step one with the obtained intensity image N-3, and calculating the relative offset value of the intensity image N-3 and the N-3 images in the step one by using a cross-correlation method; obtaining an N-3 registered images according to the obtained image deviation value; reconstructing a new wave function by using the Nth registration image, the Nth-1 registration image, the Nth-2 registration image and the Nth-3 registration image by adopting an iterative wave function reconstruction method; obtaining a wave function N-3, repeating the operation, replacing the wave function N- (q-1) with the wave function N-q, transmitting the wave function N-q to the recording image plane of the (N- (q +1) th image in the step one, and obtaining an intensity map of the wave function N-q in the transmission process, wherein the intensity map is calculated as an intensity map N- (q + 1); then comparing the N- (q +1) th image in the first step with the obtained intensity map N- (q +1), and calculating the relative offset value of the intensity map N- (q +1) and the N- (q +1) th image in the first step by using a cross-correlation method; obtaining the N- (q +1) th registered image according to the obtained image deviation value; reconstructing a new wave function by using the Nth registration image, the (N-1) th registration image, the (N-2) th registration image, the (N-3) th registration image … … till the (N- (q +1) th registration image by adopting an iterative wave function reconstruction method; obtaining a wave function N- (q +1), wherein q is more than or equal to 3 and less than or equal to N-2;
when i is not 1 and is also not N-1; defining the initial wave function obtained in the step three as an initial wave function i; the under-focus series image obtained in the first step is split into two parts in the third step, wherein the first part is from the 1 st image to the (i +1) th image, and the second part is from the ith image to the Nth image;
for the first partial image, the initial wave function i is propagated to a recording image plane of the i-1 th image in the first step, an intensity graph of the initial wave function i in the propagation process is obtained and is counted as an intensity graph i-1, then the i-1 th image in the first step is compared with the obtained intensity graph i-1, and a relative offset value of the intensity graph i-1 and the i-1 th image in the first step is obtained by a cross-correlation method; obtaining the i-1 registered image according to the solved image deviation value; reconstructing a new wave function by using the i-1 th registration image, the i-1 th registration image and the i +1 th registration image by adopting an iterative wave function reconstruction method; obtaining a wave function i-1; replacing the initial wave function i with the obtained wave function i-1, transmitting the wave function i-1 to a recording image plane of the i-2 images in the step I, and solving an intensity map of the wave function i-1 in the transmission process, wherein the intensity map is calculated as an intensity map i-2; then comparing the i-2 th image in the first step with the obtained intensity map i-2, and calculating the relative offset value of the intensity map i-2 and the i-2 th image in the first step by using a cross-correlation method; obtaining an i-2 registered image according to the obtained image deviation value; reconstructing a new wave function by using the i-2 registration images, the i-1 registration images, the i registration images and the i +1 registration images by adopting an iterative wave function reconstruction method; obtaining a wave function i-2, repeating the operation, replacing the wave function i- (t-11) with the wave function i-t, transmitting the wave function i-t to the recording image plane of the i- (t +1) th image in the step I, and obtaining an intensity map of the wave function i-t in the transmission process, wherein the intensity map is recorded as an intensity map i- (t + 1); then comparing the i- (t +1) th image in the first step with the obtained intensity map i- (t +1), and calculating the relative offset value of the intensity map i- (t +1) and the i- (t +1) th image in the first step by using a cross-correlation method; obtaining an i- (t +1) th registered image according to the obtained image offset value; reconstructing a new wave function by using the i +1 th registration image, the i-2 nd registration image … … until the i- (t +1) th registration image by using an iterative wave function reconstruction method; obtaining a wave function i- (t +1), wherein t is more than or equal to 2 and less than or equal to i-2;
for the second partial image, the initial wave function i is transmitted to a recording image plane of the (i + 2) th image in the first step, an intensity graph of the initial wave function i in the transmission process is calculated and is designated as an intensity graph i +2, then the (i + 2) th image in the first step is compared with the obtained intensity graph i +2, and a relative offset value of the intensity graph i +2 and the (i + 2) th image in the first step is calculated by using a cross-correlation method; obtaining an i +2 th registered image according to the obtained image deviation value; reconstructing a new wave function by using the ith, the (i +1) th and the (i + 2) th registration images by adopting an iterative wave function reconstruction method; obtaining a wave function i + 2; replacing the initial wave function i with the obtained wave function i +2, transmitting the wave function i +2 to the recording image plane of the (i + 3) th image in the step I, and solving an intensity map of the wave function i +2 in the transmission process, wherein the intensity map is an intensity map i + 3; then comparing the (i + 3) th image in the first step with the obtained intensity map i +3, and calculating the relative offset value of the intensity map i +3 and the (i + 3) th image in the first step by using a cross-correlation method; obtaining an i +3 registered images according to the solved image deviation value; reconstructing a new wave function by using the ith registration image, the (i +1) th registration image, the (i + 2) th registration image and the (i + 3) th registration image by using an iterative wave function reconstruction method to obtain a wave function i + 3; repeating the operation, replacing the wave function i + s-1 with the wave function i + s, transmitting the wave function i + s to the recording image plane of the i + s +1 th image in the step I, and solving an intensity map of the wave function i + s in the transmission process to obtain an intensity map i + s + 1; then comparing the i + s +1 th image in the first step with the obtained intensity map i + s +1, and calculating the relative offset value of the intensity map i + s +1 and the i + s +1 th image in the first step by using a cross-correlation method; obtaining an i + s +1 th registered image according to the obtained image deviation value; reconstructing a new wave function by using an iterative wave function reconstruction method from the ith registration image, the (i +1) th registration image, the (i + 2) th registration image, the (i + 3) th registration image … … to the (i + s +1) th registration image; obtaining a wave function i + s +1, wherein s is more than or equal to 3; and i + s +1 is less than or equal to N;
step five
Combining the N registered series of images, and reconstructing a wave function by using an iterative wave function reconstruction method; obtaining a wave function without eliminating the residual coefficient;
step six
And adjusting the residual aberration coefficient in the wave function without eliminating the residual coefficient to obtain the wave function of the lower surface of the sample.
The invention relates to an improved under-focus series iterative wave function reconstruction method, wherein in N under-focus series high-resolution images with equal under-focus step length, the magnification of any image relative to an observation point is more than or equal to 60 ten thousand times.
The invention relates to an improved under-focus series iterative wave function reconstruction method, wherein the under-focus step length is less than 10nm, and preferably 1nm-10 nm.
The invention discloses an improved under-focus series iterative wave function reconstruction method. For adjusting the Residual aberration in the wave function, see the document S.Uhlemann, M.Haider, reactive wave interferences in the first spectral interference corrected transmission electron microscope, Ultramicroscopy,72(1998) 109-.
The invention relates to an improved under-focus series iterative wave function reconstruction method.
The invention relates to an improved under-focus series iterative wave function reconstruction method, wherein the under-focus amount is A; the A should make the image taken be a high resolution lattice image of the sample.
The invention relates to an improved under-focus series iterative wave function reconstruction method, which is carried out by using a cross-correlation algorithm introduced in R.R.Meyer, A.I.Kirkland, W.O.Saxton, A new method for the determination of the wave interference function for high resolution TEM 1.Measurement of the systematic interference, ultra microscopy,92(2002)89-109 when calculating the maximum coefficient of the cross-correlation function (CCF) of two adjacent images in an under-focus series image. Of course, other cross-correlation algorithms may be used with the present invention.
The invention relates to an improved under-focus series iterative wave function reconstruction method.
The invention relates to an improved under-focus series iterative wave function reconstruction method, wherein in N under-focus series high-resolution images with equal under-focus step length, the magnification of any image relative to an observation point is more than or equal to 60 ten thousand times.
In the invention, the characteristics of the propagation method of the electronic wave in vacuum are skillfully utilized when the wave function is propagated to the next picture.
The invention provides a method for comparing an experimental image by using repeated propagation of a reconstructed wave function so as to improve the image drift calibration precision and the reconstructed wave function precision.
Advantageous effects
The method adopts the traditional iterative wave function reconstruction method to carry out image registration and reconstruction on the under-focus series high-resolution images in combination with the wave function vacuum propagation method, has the advantages of high registration precision, good reconstruction effect, high calculation speed and the like, and solves the problem of difficult registration of the wave function reconstruction series images at present. The method has great significance for quantitative and accurate analysis of high-resolution images and quantitative measurement of microstructures in materials.
Drawings
Fig. 1 is an algorithm flow chart of an improved iterative wave function reconstruction algorithm.
FIG. 2 is a high resolution image of 20 under-focus series of aluminum matrix and S-phase.
Figure 3 is a registered under-focus series of images.
Fig. 4 shows the relative offset in the x and y directions of the under-focus series of images.
Fig. 5 is a diagram of the effect of mIWFR reconstruction.
The algorithm principle of the iterative wave function reconstruction algorithm and the work flow thereof can be seen from fig. 1.
From fig. 2, it can be seen that the aluminum matrix and S-phase 20-piece under-focus series high resolution images were taken in the laboratory. The electron beam is incident along the [001] direction of the Al substrate. The arrows in the figure show the positional shift of the precipitated phases in the figure.
From fig. 3, it can be seen that the images of the under-focus series are registered by the present invention for the images shown in fig. 2. The electron beam is incident along the [001] direction of the Al substrate.
The magnitude of the relative offset of the under-focused series of images in the x and y directions can be seen in fig. 4.
The reconstruction effect of the mIWFR method of the present invention can be seen in fig. 5. (a) A phase map of the reconstructed wave function; (b) error convergence curve of mIWFR; (c) an enlarged view of the yellow frame region in FIG. (a).
Detailed Description
The invention will be further explained 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 transmission sample used in this example was a 2000 series aluminum alloy, the transmission electron microscope used was FEI Tecnai F20, and the incident direction of the electron beam was [001]]Al。
S1: in a conventional centering operation of an electron microscope, and an electron beam is made to be incident along the [001] direction of an aluminum substrate of a sample, the magnification is about 590000 times, a set of (N, N is 20) under-focus series high resolution images with equal under-focus step size are recorded under the condition of-229.3 nm under-focus, the number of pixels of the images is 1024 x 1024, and the under-focus step size is-4.77 nm, as shown in FIG. 2.
S2: and calculating the maximum coefficient of the cross-correlation function (CCF) of two adjacent images in the under-focus series of images by using a cross-correlation algorithm. And (3) finding two images with the maximum cross correlation coefficient, namely 7 th image and 8 th image, and carrying out image registration according to the position (510,509) of the maximum coefficient to obtain the registered images, wherein the size of the registered images is 1022 × 1020.
S3: the under-focused series of images is split into two parts, the first part is from the 1 st image to the 8 th image, and the second part is from the 7 th image to the 20 th image, as shown in fig. 1 a. In these two series of images, the reconstructed wave functions of the 7 th and 8 th images were used, respectively.
S4: in the two series of images, the reconstructed initial wave function is propagated to the image plane of the next recorded image, the intensity map of the propagated function is obtained and compared with the image recorded by experiment, and the relative offset value of the two images is obtained by the CCF method. Obtaining N from the obtained image offset value0(N03,4 …) are registered, and a new wave function is reconstructed using these images with an iterative wave function reconstruction method.
S5: in this two series of images, step S4 is repeated as shown in fig. 1 b. The images after registration are shown in fig. 3, and the amount of shift between each image is shown in fig. 4.
S6: and combining the two registered serial images obtained in the above step to obtain a final registered serial image with the size of 998 × 990, and reconstructing a wave function by using an iterative wave function reconstruction method, wherein the iteration time is 20.
S7: the residual aberration coefficient (three-level spherical aberration of 1.2mm, under-focus of-27 nm, under-focus spread of 8nm, divergence angle of 0.15mrad, information with filtering frequency higher than 0.14 nm) in the wave function was adjusted to obtain the wave function of the lower surface of the sample, as shown in fig. 5.
Claims (4)
1. An improved under-focus series iterative wave function reconstruction method is characterized in that: the method comprises the steps that an under-focus series image is taken as a processing object, an iterative wave function reconstruction method and an electronic wave propagation method in vacuum are utilized to eliminate errors introduced by under-focus difference in image drift prediction, and a wave function of the under-focus series image is obtained; the under-focus series images are images obtained by the same electron microscope on the same sample under the conditions of different under-focus step lengths or the same under-focus step length; the specific operation comprises the following steps:
step one
Putting a sample into an electron microscope, centering the electron microscope, making an electron beam incident along the direction of a crystal band axis of the sample, and amplifying the image of the sample to more than 50 ten thousand times so that the transmission electron microscope records a high-resolution crystal lattice image of the sample; recording a set of N under-focus series high resolution images with equal under-focus step length under the condition that the under-focus amount is A; numbering the pictures from 1, 2, 3, … … to N in sequence; n is an integer greater than or equal to 3;
step two
Calculating the maximum coefficient of the cross-correlation function of two adjacent images in the under-focus series of images by using a cross-correlation algorithm; finding out two images with the maximum cross-correlation coefficient, supposing that the two images are the ith and i +1 th images, and finding out the same area in the two images according to the position of the maximum coefficient to carry out image registration to obtain 2 images after registration; i is greater than or equal to 1 and less than N;
when i is 1, defining the two images after registration as a 1 st registration image and a 2 nd registration image respectively;
when i is N-1, defining the two images after registration as the N-1 registration image and the Nth registration image respectively;
when i is not 1 and is not N-1; defining the two images after registration as the ith registration image and the (i +1) th registration image respectively;
step three
Judging whether i is 1 or N-1;
if i is 1 or N-1, reconstructing the two registered images by directly using an iterative wave function reconstruction method to obtain an initial wave function;
if i is not 1 or N-1, splitting the under-focus series image into two parts, wherein the first part is from the 1 st image to the (i +1) th image, the second part is from the i th image to the N th image, and in the two series images, the i th and the (i +1) th reconstructed wave functions are respectively utilized to obtain an initial wave function;
step four
When i is 1, defining the initial wave function obtained in the step three as an initial wave function 1; transmitting the initial wave function 1 to a recording image plane of the 3 rd image in the step one, squaring the amplitude of the obtained wave function to obtain an intensity graph of the initial wave function 1 in the transmission process, recording the intensity graph as an intensity graph 3, comparing the 3 rd image in the step one with the obtained intensity graph 3, and obtaining a relative offset value of the intensity graph 3 and the 3 rd image in the step one by using a cross-correlation method; obtaining a 3 rd registered image according to the obtained relative deviation value of the image; reconstructing a new wave function by using the 1 st registration image, the 2 nd registration image and the 3 rd registration image by adopting an iterative wave function reconstruction method; obtaining a wave function 3, replacing the initial wave function 1 with the obtained wave function 3, transmitting the wave function 3 to a recording image plane of the 4 th image in the step I, and solving an intensity graph of the wave function 3 in the transmission process, and recording the intensity graph as an intensity graph 4; then comparing the 4 th image in the step one with the obtained intensity graph 4, and calculating the relative offset value of the intensity graph 4 and the 4 th image in the step one by using a cross-correlation method; obtaining a 4 th registered image according to the calculated relative deviation value of the images; reconstructing a new wave function by using a 1 st registration image, a 2 nd registration image, a 3 rd registration image and a 4 th registration image through an iterative wave function reconstruction method to obtain a wave function 4, repeating the operation, replacing the wave function p-1 with the wave function p, transmitting the wave function p to a recording image plane of the p +1 th image in the step I, and solving an intensity graph of the wave function p in the transmission process, wherein the intensity graph is recorded as the intensity graph p + 1; then comparing the p +1 th image in the first step with the obtained intensity map p +1, and calculating the relative offset value of the intensity map p +1 and the p +1 th image in the first step by using a cross-correlation method; obtaining a p +1 registered image according to the calculated relative deviation value of the image; reconstructing a new wave function by using the 1 st registration image, the 2 nd registration image, the 3 rd registration image and the 4 th registration image … … till the p +1 th registration image by adopting an iterative wave function reconstruction method; obtaining a wave function p +1, wherein p is more than or equal to 4 and less than or equal to N-1; when p +1 is equal to N, the obtained wave function is marked as a wave function N;
when i is N-1, defining the initial wave function obtained in the step three as an initial wave function N-1; transmitting the initial wave function N-1 to a recording image plane of the N-2 images in the step one, solving an intensity graph of the initial wave function N-1 in the transmission process, recording the intensity graph as an intensity graph N-2, then comparing the N-2 images in the step one with the obtained intensity graph N-2, and solving a relative offset value of the intensity graph N-2 and the N-2 images in the step one by using a cross-correlation method; obtaining the N-2 registered images according to the calculated relative deviation value of the images; reconstructing a new wave function by using the Nth registration image, the Nth registration image-1 registration image and the Nth registration image-2 registration image by using an iterative wave function reconstruction method; obtaining a wave function N-2, replacing the initial wave function N-1 with the obtained wave function N-2, transmitting the wave function N-2 to the recording image plane of the (N-3) th image in the first step, and solving an intensity graph of the wave function N-2 in the transmission process, wherein the intensity graph is recorded as an intensity graph N-3; then comparing the N-3 images in the step one with the obtained intensity image N-3, and calculating the relative offset value of the intensity image N-3 and the N-3 images in the step one by using a cross-correlation method; obtaining an N-3 registered images according to the calculated relative deviation value of the images; reconstructing a new wave function by using the Nth registration image, the Nth-1 registration image, the Nth-2 registration image and the Nth-3 registration image by adopting an iterative wave function reconstruction method; obtaining a wave function N-3, repeating the operation, replacing the wave function N- (q-1) with the wave function N-q, transmitting the wave function N-q to the recording image plane of the (N- (q +1) th image in the step one, and obtaining an intensity map of the wave function N-q in the transmission process, wherein the intensity map is recorded as the intensity map N- (q + 1); then comparing the N- (q +1) th image in the first step with the obtained intensity map N- (q +1), and calculating the relative offset value of the intensity map N- (q +1) and the N- (q +1) th image in the first step by using a cross-correlation method; obtaining an N- (q +1) th registered image according to the obtained relative image deviation value; reconstructing a new wave function by using the Nth registration image, the (N-1) th registration image, the (N-2) th registration image, the (N-3) th registration image … … till the (N- (q +1) th registration image by adopting an iterative wave function reconstruction method; obtaining a wave function N- (q +1), wherein q is more than or equal to 3 and less than or equal to N-2;
when i is not 1 and is not N-1, defining the initial wave function obtained in the step three as an initial wave function i; the under-focus series image obtained in the first step is split into two parts in the third step, wherein the first part is from the 1 st image to the (i +1) th image, and the second part is from the ith image to the Nth image;
for the first partial image, the initial wave function i is transmitted to a recording image plane of the i-1 th image in the first step, an intensity graph of the initial wave function i in the transmission process is obtained and recorded as an intensity graph i-1, then the i-1 th image in the first step is compared with the obtained intensity graph i-1, and a relative offset value of the intensity graph i-1 and the i-1 th image in the first step is obtained by a cross-correlation method; obtaining the i-1 registered image according to the calculated relative deviation value of the image; reconstructing a new wave function by using the i-1 th registration image, the i-1 th registration image and the i +1 th registration image by adopting an iterative wave function reconstruction method; obtaining a wave function i-1; replacing the initial wave function i with the obtained wave function i-1, transmitting the wave function i-1 to a recording image plane of the i-2 images in the step I, and solving an intensity map of the wave function i-1 in the transmission process, and recording the intensity map as an intensity map i-2; then comparing the i-2 th image in the first step with the obtained intensity map i-2, and calculating the relative offset value of the intensity map i-2 and the i-2 th image in the first step by using a cross-correlation method; obtaining the i-2 registered images according to the calculated relative deviation value of the images; reconstructing a new wave function by using the i-2 registration images, the i-1 registration images, the i registration images and the i +1 registration images by adopting an iterative wave function reconstruction method; obtaining a wave function i-2, repeating the operation, replacing the wave function i- (t-1) with the wave function i-t, transmitting the wave function i-t to the recording image plane of the i- (t +1) th image in the step I, and obtaining an intensity map of the wave function i-t in the transmission process, wherein the intensity map is recorded as the intensity map i- (t + 1); then comparing the i- (t +1) th image in the first step with the obtained intensity map i- (t +1), and calculating the relative offset value of the intensity map i- (t +1) and the i- (t +1) th image in the first step by using a cross-correlation method; obtaining an i- (t +1) th registered image according to the calculated relative image deviation value; reconstructing a new wave function by using the i +1 th registration image, the i-2 nd registration image … … until the i- (t +1) th registration image by using an iterative wave function reconstruction method; obtaining a wave function i- (t +1), wherein t is more than or equal to 2 and less than or equal to i-2;
for the second partial image, the initial wave function i is transmitted to the recording image plane of the (i + 2) th image in the first step, the intensity graph of the initial wave function i in the transmission process is obtained and recorded as an intensity graph i +2, then the (i + 2) th image in the first step is compared with the obtained intensity graph i +2, and the relative offset value of the intensity graph i +2 and the (i + 2) th image in the first step is obtained by using a cross-correlation method; obtaining an i +2 registered image according to the calculated relative deviation value of the image; reconstructing a new wave function by using the ith, the (i +1) th and the (i + 2) th registration images by adopting an iterative wave function reconstruction method; obtaining a wave function i + 2; replacing the initial wave function i with the obtained wave function i +2, transmitting the wave function i +2 to the recording image plane of the (i + 3) th image in the step I, and solving an intensity map of the wave function i +2 in the transmission process, wherein the intensity map is marked as an intensity map i + 3; then comparing the (i + 3) th image in the first step with the obtained intensity map i +3, and calculating the relative offset value of the intensity map i +3 and the (i + 3) th image in the first step by using a cross-correlation method; obtaining an i +3 registered images according to the calculated relative deviation value of the images; reconstructing a new wave function by using the ith registration image, the (i +1) th registration image, the (i + 2) th registration image and the (i + 3) th registration image by using an iterative wave function reconstruction method to obtain a wave function i + 3; repeating the operation, replacing the wave function i + s-1 with the wave function i + s, transmitting the wave function i + s to the recording image plane of the i + s +1 th image in the step I, and solving an intensity map of the wave function i + s in the transmission process, wherein the intensity map is recorded as the intensity map i + s + 1; then comparing the i + s +1 th image in the first step with the obtained intensity map i + s +1, and calculating the relative offset value of the intensity map i + s +1 and the i + s +1 th image in the first step by using a cross-correlation method; obtaining an i + s +1 th registered image according to the calculated relative offset value of the image; reconstructing a new wave function by using an iterative wave function reconstruction method from the ith registration image, the (i +1) th registration image, the (i + 2) th registration image, the (i + 3) th registration image … … to the (i + s +1) th registration image; obtaining a wave function i + s +1, wherein s is more than or equal to 3; and i + s +1 is less than or equal to N;
step five
Combining the N registered series images, and reconstructing a wave function by using an iterative wave function reconstruction method; obtaining a wave function without eliminating the residual coefficient;
step six
And adjusting the residual aberration coefficient in the wave function without eliminating the residual coefficient to obtain the wave function of the lower surface of the sample.
2. The improved under-focus series iterative wave function reconstruction method according to claim 1, characterized in that: in N under-focus series high-resolution images with equal under-focus step length, the magnification of any one image relative to an observation point is more than or equal to 60 ten thousand times.
3. The improved under-focus series iterative wave function reconstruction method according to claim 1, characterized in that: the step length of under-focus is less than 10 nm.
4. The improved under-focus series iterative wave function reconstruction method according to claim 1, characterized in that: in step six, the value of the residual aberration was measured by zemlin-tableau method.
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