Adaptive atomic force microscope (AFM) imaging method based on block compressed sensing

Abstract

The application provides an adaptive atomic force microscope (AFM) imaging method based on block compressed sensing, and comprises the following steps: step S1: a plurality of sub-blocks with the same size are divided on the surface of an AFM sample by using an overlapping block mode; step S2: each sub-block is pre-scanned, a row direction is taken as a fast scanning direction, a lower left corner is taken as a starting point of pre-scanning, and a pre-scanning sampling rate is calculated; step S3: a BP neural network is used to train a sample database, a relationship between a characteristic parameter and a required minimum sampling rate is obtained, and a suitable total sampling rate of each sub-block is adaptively obtained; step S4: a required number of sampling points are randomly selected on the surface of a current sub-block, and adaptive scanning is performed by using a continuous random scanning mode; and step S5: after all sampling points of a sub-block are collected, TVAL3 reconstruction algorithm is combined to perform reconstruction, and finally, all reconstructed sub-blocks are combined together; and the block effect is eliminated by using the overlapping block mode, so that each sample can obtain high and uniform imaging quality.

Description

Technical Field

[0001] The present invention relates to the technical field of atomic force microscopy, and in particular to an adaptive atomic force microscopy (AFM) imaging method based on block-based compressed sensing. Background Art

[0002] Nanotechnology studies the design, composition, and properties of materials and devices at scales below 100 nanometers. The atomic force microscope (AFM) is one of the most important tools helping researchers explore the nanoscale world. AFMs can observe and image conductors, semiconductors, and insulating materials at the nanoscale in a variety of environments and are also used for nanofabrication and manufacturing. Furthermore, compared to scanning tunneling microscopes, AFMs offer several unique advantages: they do not require testing the sample's conductivity or a rigorous scanning environment. These advantages have made AFMs indispensable instruments in many scientific and technological fields in recent years, achieving image resolution far exceeding that achieved by optical microscopes. Traditional raster scanning methods involve the AFM tip scanning the sample surface at a constant speed, ensuring the same scanning time for each sampling point. While increasing scanning speed, this also reduces the control time for each point, impacting control accuracy and, in turn, image quality. Methods for improving AFM imaging speed can be broadly divided into two categories: hardware optimization and the application of advanced control algorithms. The former involves improving the dynamic characteristics of AFM components to meet the requirements of high-speed imaging, including the use of shorter cantilevers and the design of new scanners. The latter involves employing control algorithms and novel scanning strategies to shorten AFM imaging times. While these methods have achieved success in acquiring high-speed AFM images, conventional high-speed AFM techniques rely on Nyquist-Shannon sampling to obtain sample morphology information, requiring the probe to perform point-by-point scans of the sample. However, natural images are compressible signals that exhibit sparse properties after discrete cosine transform (DCT) or multilevel wavelet transform. Therefore, it can be argued that the imaging process includes some unnecessary scans, conveying little valid information about the sample's morphology.

[0003] Because AFM probes use a contact-based, line-by-line, point-by-point scanning measurement principle, their imaging speed is generally slow. The characteristics and size of the probe tip also affect measurement accuracy. Most AFM systems still require a long time, ranging from tens of seconds to several minutes, to acquire a single sample image. This falls far short of the rapid imaging requirements of research, and image quality cannot be guaranteed. Therefore, it is crucial to effectively increase imaging speed and reduce tip wear while maintaining image quality. Summary of the Invention

[0004] The present invention proposes an adaptive atomic force microscope (AFM) imaging method based on block compressed sensing. By combining compressed sensing with undersampling scanning mode, the AFM imaging speed is greatly improved without affecting the quality. At the same time, an adaptive strategy is added on this basis to realize adaptive AFM imaging and further improve the imaging speed and quality.

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

[0006] An adaptive atomic force microscope (AFM) imaging method based on block compressed sensing includes the following steps:

[0007] Step S1: Divide the AFM sample surface into multiple sub-blocks of the same size using an overlapping block pattern;

[0008] Step S2: Pre-scan each sub-block, using the row direction as the fast scanning direction and the lower left corner as the starting point of the pre-scan, and calculate the sampling rate of the pre-scan;

[0009] Step S3: Use BP neural network to train the sample database, obtain the relationship between the characteristic parameters and the required minimum sampling rate, and adaptively obtain the appropriate total sampling rate for each sub-block;

[0010] Step S4: randomly selecting a required number of sampling points on the surface of the current sub-block and performing adaptive scanning using a continuous random scanning mode;

[0011] Step S5: After collecting all sampling points of a sub-block, reconstruct it using the TVAL3 reconstruction algorithm, and finally combine all the reconstructed sub-blocks together.

[0012] The step S1 specifically includes the following steps:

[0013] Step S11: Divide the sample surface into 25 sub-blocks of the same size using an overlapping block pattern, and set the total sampling rate of some sub-blocks, with an overlapping ratio k=0.25.

[0014] The step S2 uses the pre-scanning mode of the under-sampled raster to pre-scan each sub-block, specifically comprising the following steps:

[0015] Step S21: After obtaining the sample, the sample row direction is used as the fast scanning direction, and the lower left corner is the starting point of the pre-scan;

[0016] Step S22: During the scanning process, the step length S in the row direction is set to 4 pixels; the row spacing is S / 2, and adjacent rows are staggered by S / 2 in the column direction; the side length of the sub-block is B=2 u (u∈N, U>2), calculate the pre-scan sampling rate δ pre is 0.125; the pre-scan time of each sub-block is approximately calculated as:

[0017]

[0018] Where T sam and T non-sam are the average time it takes for the tip of the scanning device to measure a sampling point and skip a non-sampling point in the horizontal direction, respectively.

[0019] The step S3 uses a BP neural network to train the sample database, obtains the relationship between the characteristic parameters and the required minimum sampling rate, and adaptively obtains the appropriate total sampling rate for each sub-block; specifically, it includes the following steps:

[0020] Step S31: Divide the 17 samples with a resolution of 512×512 into 25 sub-blocks using an overlapping block mode with an overlap rate of k=0.25, resulting in 425 images with a resolution of 128×128. Pre-scan and downsample these 425 images to obtain GTV, L, SD, and the image sampling rate sr, where GTV is the sum of the discrete gradient moduli of all undersampled points, Lu represents the range of the undersampled points, and SD is the standard deviation of the discrete gradient moduli of all undersampled points.

[0021] Step S32: construct a loop and slowly increase the sampling rate through iterative steps to make the PSNR of the image exceed 37dB;

[0022] Step S33: Then, a new loop is constructed to halve the step size through bisection to find a suitable sampling rate so that the image PSNR just reaches 37 dB. The sampling rate of each sub-block of 37 dB is obtained through this iterative method.

[0023] Step S34: Load the above data into the BP neural network, train the PSNR, and input the weights between GTV, Lu, SD and output sr when it reaches 37dB; after the training process is completed, input the values ​​of the feature parameters GTV, Lu and SD obtained by pre-scanning into the trained BP neural network model to adaptively obtain the appropriate sampling rate for each sub-block.

[0024] The step S4 specifically includes the following steps:

[0025] Step S41: For a sample block whose required sampling rate is greater than 0.125, a continuous random scanning mode is used to implement adaptive scanning.

[0026] Step S42: searching for the shortest broken line distance by continuous random scanning, and connecting all random sampling points in one direction;

[0027] Step S43: Calculate the nearest broken line using the simulated annealing algorithm.

[0028] The step S5 specifically includes the following steps:

[0029] Step S51: Construct a measurement matrix of the compressed sensing method. Its mathematical form is as follows:

[0030]

[0031] Step S52: Combine the sampled low-resolution image and the measurement matrix Φ m×m Substitute the following compressed sensing formula and use the TVAL3 algorithm to obtain the reconstructed high-resolution image X*;

[0032] Y=ΦX

[0033] Where Y is the sampled image;

[0034] Step S53: reconstruct the 25 reconstructed sub-blocks according to the overlapping block mode during the block division to obtain a high-quality AFM image.

[0035] In step S22 , the tip of the scanning device is a probe.

[0036] When training PSNR in step S34, the input layer is set to three neurons, the hidden layer is set to four neurons, and the output layer is set to one neuron.

[0037] When training PSNR in step S34, the maximum number of iterations is set to 50,000, the learning rate is set to 0.00093, and the noise with an intensity of 0.01 is generated using a normal distribution to prevent overfitting.

[0038] In step S34, if the obtained appropriate sampling rate is greater than 0.125, the sub-block must be additionally scanned, and sufficient sampling points must be added through the adaptive scanning mode of step S41.

[0039] This method uses overlapping blocks to eliminate blocking artifacts. Topographical parameters are used to predict the local morphological characteristics of the sample. A BP neural network is employed to determine the appropriate sampling rate for each sub-block. Through pre-scanning and adaptive supplementary scanning, combined with the TVAL3 reconstruction algorithm, each sample can achieve a low sampling time and high imaging quality.

[0040] In the case of a lack of sampling in certain areas of the AFM image with obvious details, the present invention uses an overlapping block method to eliminate the blocking effect, so that each sample can obtain high and uniform imaging quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments:

[0042] Attachment Figure 1 It is a schematic flow chart of the method of the present invention;

[0043] Attachment Figure 2Schematic diagram of the scanning order and overlapping block mode of sub-blocks in one embodiment of the present invention;

[0044] Attachment Figure 3 Schematic diagram of a pre-scan mode of under-sampling raster scanning in one embodiment of the present invention;

[0045] Attachment Figure 4 This is a flow chart for calculating the sampling rate required for 37dB reconstruction quality of a training model sub-block in one embodiment of the present invention;

[0046] Attachment Figure 5 Schematic diagram of a training model for adaptive sampling rate according to an embodiment of the present invention;

[0047] Attachment Figure 6 Schematic diagram of an adaptive supplementary scanning mode for continuous random scanning in one embodiment of the present invention;

[0048] Attachment Figure 7 The following is an evaluation of the quality of images reconstructed using different methods according to an embodiment of the present invention. DETAILED DESCRIPTION

[0049] like Figure 1 As shown, the adaptive atomic force microscope AFM imaging method (ABCS) based on block compressed sensing includes the following steps:

[0050] Step S1: Figure 2 As shown, the overlapping block pattern is used to divide the AFM sample surface into multiple sub-blocks of the same size;

[0051] Step S2: Pre-scan each sub-block, using the row direction as the fast scanning direction and the lower left corner as the starting point of the pre-scan, and calculate the sampling rate of the pre-scan;

[0052] Step S3: Use BP neural network to train the sample database, obtain the relationship between the characteristic parameters and the required minimum sampling rate, and adaptively obtain the appropriate total sampling rate for each sub-block;

[0053] Step S4: randomly selecting a required number of sampling points on the surface of the current sub-block and performing adaptive scanning using a continuous random scanning mode;

[0054] Step S5: After collecting all sampling points of a sub-block, reconstruct it using the TVAL3 reconstruction algorithm, and finally combine all the reconstructed sub-blocks together.

[0055] The step S1 specifically includes the following steps:

[0056] Step S11: Divide the sample surface into 25 sub-blocks of the same size using an overlapping block pattern, and set the total sampling rate of some sub-blocks, with an overlapping ratio k=0.25.

[0057] The step S2 uses the pre-scan mode of the under-sampled raster to pre-scan each sub-block. Figure 3 It is a pre-scan mode for undersampled raster scanning, which includes the following steps:

[0058] Step S21: After obtaining the sample, the sample row direction is used as the fast scanning direction, and the lower left corner is the starting point of the pre-scan;

[0059] Step S22: During the scanning process, the step length S in the row direction is set to 4 pixels; the row spacing is S / 2, and adjacent rows are staggered by S / 2 in the column direction; the side length of the sub-block is B=2 u (u∈N, U>2), calculate the pre-scan sampling rate δ pre is 0.125; the pre-scan time of each sub-block is approximately calculated as:

[0060]

[0061] Where T sam and T non-sam are the average time it takes for the tip of the scanning device to measure a sampling point and skip a non-sampling point in the horizontal direction, respectively.

[0062] Step S3 uses a BP neural network to train a sample database, obtains the relationship between the characteristic parameters and the required minimum sampling rate, and adaptively obtains a suitable total sampling rate for each sub-block; Figure 4 A flowchart showing the sampling rate required for training the model sub-block with 37dB reconstruction quality, including the following steps:

[0063] Step S31: Divide the 17 samples with a resolution of 512×512 into 25 sub-blocks using an overlapping block mode with an overlap rate of k=0.25, resulting in 425 images with a resolution of 128×128. Pre-scan and downsample these 425 images to obtain GTV, L, SD, and the image sampling rate sr, where GTV is the sum of the discrete gradient moduli of all undersampled points, Lu represents the range of the undersampled points, and SD is the standard deviation of the discrete gradient moduli of all undersampled points.

[0064] Step S32: construct a loop and slowly increase the sampling rate through iterative steps to make the PSNR of the image exceed 37dB;

[0065] Step S33: Then, a new loop is constructed to halve the step size through bisection to find a suitable sampling rate so that the image PSNR just reaches 37 dB. The sampling rate of each sub-block of 37 dB is obtained through this iterative method.

[0066] Step S34: Load the above data into the BP neural network and train the PSNR. When the PSNR reaches 37dB, the weights between input GTV, Lu, SD and output sr are calculated. Figure 5 To adaptively obtain the appropriate sampling rate model for each sub-block, we trained the weights between the input (GTV, Lu, SD) and the output sr for a PSNR of 37dB. After the training process is complete, the trained BP neural network model is fed with the pre-scanned feature parameters GTV, Lu, and SD to adaptively obtain the appropriate sampling rate for each sub-block.

[0067] The step S4 specifically includes the following steps:

[0068] Step S41: For a sample block whose required sampling rate is greater than 0.125, a continuous random scanning mode is used to implement adaptive scanning.

[0069] Step S42: searching for the shortest broken line distance by continuous random scanning, and connecting all random sampling points in one direction;

[0070] Step S43: Calculate the nearest broken line using the simulated annealing algorithm.

[0071] The step S5 specifically includes the following steps:

[0072] Step S51: Construct a measurement matrix of the compressed sensing method. Its mathematical form is as follows:

[0073]

[0074] Step S52: Combine the sampled low-resolution image and the measurement matrix Φ m×n Substitute the following compressed sensing formula and use the TVAL3 algorithm to obtain the reconstructed high-resolution image X*;

[0075] Y=ΦX

[0076] Where Y is the sampled image;

[0077] Step S53: reconstruct the 25 reconstructed sub-blocks according to the overlapping block mode during the block division to obtain a high-quality AFM image.

[0078] refer to Figure 7 The ABCS imaging scheme proposed in this example is compared with two non-adaptive imaging schemes (BCS and CS) through image evaluation indicators (PSNR, SSIM and reconstruction time). It can be seen that the ABCS-based imaging method in this example can not only improve the scanning speed of AFM, but also save the reconstruction time of AFM images.

[0079] In step S22 , the tip of the scanning device is a probe.

[0080] When training PSNR in step S34, the input layer is set to three neurons, the hidden layer is set to four neurons, and the output layer is set to one neuron.

[0081] In the step S34, the maximum number of iterations is set to 50,000 and the learning rate is set to 0.00093 when training the PSNR. Noise with an intensity of 0.01 is generated using a normal distribution to prevent overfitting.

[0082] In the step S34, if the obtained suitable sampling rate is greater than 0.125, the sub-block must be subjected to a supplementary scan, and sufficient sampling points are supplemented through the adaptive scan mode of the step S41, such as the adaptive supplementary scan mode shown in the following table. Figure 6

[0083] The above description is only the preferred embodiment of the present application, and any equivalent changes and modifications made within the scope of the present application should be included in the scope of the present application.​

Claims

1. An adaptive atomic force microscope (AFM) imaging method based on block-based compressed sensing, characterized by: The following steps are included: Step S1: Divide the AFM sample surface into multiple sub-blocks of the same size using an overlapping block pattern; Step S2: Pre-scan each sub-block, using the row direction as the fast scanning direction and the lower left corner as the starting point of the pre-scan, and calculate the sampling rate of the pre-scan; Step S3: Use BP neural network to train the sample database, obtain the relationship between the characteristic parameters and the required minimum sampling rate, and adaptively obtain the appropriate total sampling rate for each sub-block; Step S4: randomly selecting a required number of sampling points on the surface of the current sub-block and performing adaptive scanning using a continuous random scanning mode; Step S5: After collecting all sampling points of a sub-block, reconstruct it using the TVAL3 reconstruction algorithm, and finally combine all the reconstructed sub-blocks together; The step S2 uses the pre-scanning mode of the under-sampled raster to pre-scan each sub-block, specifically comprising the following steps: Step S21: After obtaining the sample, the sample row direction is used as the fast scanning direction, and the lower left corner is the starting point of the pre-scan; Step S22: During the scanning process, the step length S in the row direction is set to 4 pixels; the row spacing is S / 2, and adjacent rows are staggered by S / 2 in the column direction; the side length of the sub-block is B=2 u (u∈N,U>2), calculate the pre-scan sampling rate δ pre is 0.125; the pre-scan time of each sub-block is approximately calculated as: Where T sam and T non-sam are the average time for the tip of the scanning device to measure a sampling point and skip a non-sampling point in the horizontal direction, respectively; The step S3 uses a BP neural network to train the sample database, obtains the relationship between the characteristic parameters and the required minimum sampling rate, and adaptively obtains the appropriate total sampling rate for each sub-block; specifically, it includes the following steps: Step S31: Divide the 17 samples with a resolution of 512×512 into 25 sub-blocks using an overlapping block mode with an overlap rate of k=0.25, resulting in 425 images with a resolution of 128×128. Pre-scan and downsample these 425 images to obtain GTV, L, SD, and the image sampling rate sr, where GTV is the sum of the discrete gradient moduli of all undersampled points, Lu represents the range of the undersampled points, and SD is the standard deviation of the discrete gradient moduli of all undersampled points. Step S32: construct a loop and slowly increase the sampling rate through iterative steps to make the PSNR of the image exceed 37dB; Step S33: Then, a new loop is constructed to halve the step size through bisection to find a suitable sampling rate so that the image PSNR just reaches 37 dB. The sampling rate of each sub-block of 37 dB is obtained through this iterative step; Step S34: Load the above data into the BP neural network and train the PSNR. When the PSNR reaches 37dB, the weights between GTV, Lu, SD and the output sr are input. After the training process is completed, the values ​​of the characteristic parameters GTV, Lu and SD obtained by pre-scanning are input into the trained BP neural network model to adaptively obtain the appropriate sampling rate for each sub-block. The step S5 specifically includes the following steps: Step S51: construct a measurement matrix of a compressed sensing method, the mathematical form of which is as follows: Step S52: Combine the sampled low-resolution image and the measurement matrix Φ m×n Substitute the following compressed sensing formula and use the TVAL3 algorithm to obtain the reconstructed high-resolution image X*; Y=ΦX Where Y is the sampled image; Step S53: reconstruct the 25 reconstructed sub-blocks according to the overlapping block mode during the block division to obtain a high-quality AFM image.

2. The adaptive atomic force microscope (AFM) imaging method based on block-based compressed sensing according to claim 1 is characterized in that: The step S1 specifically includes the following steps: Step S11: Divide the sample surface into 25 sub-blocks of the same size using an overlapping block pattern, and set the total sampling rate of some sub-blocks, with an overlapping ratio k=0.

25.

3. The adaptive atomic force microscope (AFM) imaging method based on block-based compressed sensing according to claim 1, characterized in that: The step S4 specifically includes the following steps: Step S41: for a sample block with a sampling rate greater than 0.125 required by the sub-block, a continuous random scanning mode is used to implement adaptive scanning; Step S42: searching for the shortest broken line distance by continuous random scanning, and connecting all random sampling points in one direction; Step S43: Calculate the nearest broken line using the simulated annealing algorithm.

4. The adaptive atomic force microscope (AFM) imaging method based on block-based compressed sensing according to claim 1, characterized in that: In step S22 , the tip of the scanning device is a probe.

5. The adaptive atomic force microscope (AFM) imaging method based on block-based compressed sensing according to claim 1, characterized in that: When training PSNR in step S34, the input layer is set to three neurons, the hidden layer is set to four neurons, and the output layer is set to one neuron.

6. The adaptive atomic force microscope (AFM) imaging method based on block-based compressed sensing according to claim 5, characterized in that: When training PSNR in step S34, the maximum number of iterations is set to 50,000 times, and the learning rate is set to 0.00093; a normal distribution is used to generate noise with an intensity of 0.01 to prevent overfitting.

7. The adaptive atomic force microscope (AFM) imaging method based on block-based compressed sensing according to claim 3, characterized in that: In step S34, if the obtained appropriate sampling rate is greater than 0.125, the sub-block must be additionally scanned, and sufficient sampling points must be added through the adaptive scanning mode of step S41.

Images