Rough surface generation method and device

Abstract

The present invention provides a method and apparatus for generating a rough surface. The method is applicable to the field of material surface science. The method comprises: obtaining height data from a plurality of sampling points of a sample to be measured; performing frequency domain analysis and statistical analysis to obtain first height frequency domain data and first height distribution parameters; randomly generating a random Brownian fractal surface based on the sampling resolution; generating a Brownian fractal surface based on the random Brownian fractal surface and the first height distribution parameters; performing frequency domain analysis on the Brownian fractal surface to obtain second height frequency domain data; adjusting the self-similarity parameter of the random Brownian fractal surface to obtain third height frequency domain data; correcting the third height frequency domain data based on the first height frequency domain data to obtain fourth height frequency domain data; and performing an inverse Fourier transform on the fourth height frequency domain data to generate a rough surface that satisfies the statistical laws of the sample to be measured. Through two corrections, the present invention efficiently and accurately obtains a simulated rough surface that is highly consistent with the sample to be measured.

Description

Technical Field

[0001] The present invention relates to the field of material surface science, and in particular to a rough surface generation method and equipment. Background Art

[0002] The study and simulation of surface roughness have always been of paramount importance in the fields of materials science and surface science. It plays a key role in understanding complex processes such as tribology, grinding, polishing, and fine machining. These processes not only involve the microstructure and properties of material surfaces but also directly impact their practical applications and product quality. Atomic force microscopy (AFM), a commonly used and powerful tool, holds an irreplaceable position in the measurement and analysis of surface microstructure. It can capture subtle surface features at extremely high resolution, providing researchers with detailed information about surface roughness. In-depth analysis of AFM data can reveal the statistical laws underlying surface roughness, providing a theoretical basis for evaluating and optimizing material surface properties. Advances in modern computer technology have significantly enhanced fields such as numerical simulation and computational physics. To apply computer science methods to surface science and tribology, modeling of rough surfaces is necessary. This can be achieved by directly using AFM measurements or by generating rough surfaces using other methods.

[0003] During the implementation of this embodiment, the inventors discovered that the prior art has at least the following problems:

[0004] The existing technology obtains models of rough surfaces to conduct simulation and computational research related to rough surfaces more quickly. Among them, the existing method directly uses AFM data for research, which is greatly affected by random errors, has a low sample number, slow sampling, and is non-reproducible, and will introduce random errors into every data using the sample. Other existing methods include simple trigonometric function surfaces, superposition surfaces of trigonometric functions, etc., which meet the definition of "roughness" but do not conform to the statistical laws of real measurement data. Summary of the Invention

[0005] In view of this, the present invention provides a method for generating a rough surface, comprising:

[0006] Obtaining height data of several sampling points of the measured sample;

[0007] Performing frequency domain analysis and statistical analysis on the height data of the plurality of sampling points to obtain first height frequency domain data and first height distribution parameters; and randomly generating a random Brownian fractal surface according to the sampling resolution of the plurality of sampling points;

[0008] generating a Brownian fractal surface according to the height data of a plurality of points in the random Brownian fractal surface and the first height distribution parameter, wherein the height distribution parameter of the Brownian fractal surface is equal to the first height distribution parameter;

[0009] Performing frequency domain analysis on the Brownian fractal surface to obtain second high-frequency domain data;

[0010] The step of randomly generating a random Brownian fractal surface according to the sampling resolutions of the plurality of sampling points is performed again in a manner of adjusting the self-similarity parameter of the random Brownian fractal surface until the second high-frequency domain data overlaps with the high-frequency region of the first high-frequency domain data;

[0011] According to the overlapping area of ​​the high-frequency area, the third high-frequency domain data is obtained;

[0012] Correcting the third height frequency domain data according to the first height frequency domain data to obtain fourth height frequency domain data;

[0013] Performing an inverse Fourier transform on the fourth height frequency domain data to generate a rough surface that meets the statistical laws of the sample being tested.

[0014] Optionally, obtaining height data of several sampling points of the measured sample includes:

[0015] At least two groups of atomic force microscopy data of a measured sample are acquired at the same sampling resolution, wherein the atomic force microscopy data include height data of a plurality of sampling points.

[0016] Optionally, performing frequency domain analysis on the height data of the plurality of sampling points to obtain first height frequency domain data includes:

[0017] Calculating the distances from the plurality of sampling points to the coordinate origin;

[0018] A one-dimensional fast Fourier transform is performed on the height data of each sampling point according to the distance from each sampling point to the coordinate origin to obtain first height frequency domain data.

[0019] Optionally, performing statistical analysis on the height data of the plurality of sampling points to obtain a first height distribution parameter includes:

[0020] Performing statistical analysis on the height data of the plurality of sampling points to obtain statistical analysis results, wherein the statistical analysis results include a mean, a median, a first standard deviation, a first profile arithmetic mean deviation, a kurtosis, and a skewness;

[0021] Determining whether the height data of the plurality of sampling points satisfy a Gaussian distribution law based on the mean, median, kurtosis, and skewness;

[0022] A first standard deviation or a first profile arithmetic mean deviation satisfying a Gaussian distribution law is determined as a first height distribution parameter for describing the measured sample.

[0023] Optionally, generating a Brownian fractal surface according to the height data of a plurality of points in the random Brownian fractal surface and the first height distribution parameter, wherein the height distribution parameter of the Brownian fractal surface is equal to the first height distribution parameter, comprises:

[0024] Calculating a second height distribution parameter based on height data of a plurality of points in the random Brownian fractal surface, wherein the second height distribution parameter includes a second standard deviation or a second profile arithmetic mean deviation;

[0025] Calculating height data of a plurality of points in the Brownian fractal surface according to the height data of a plurality of points in the random Brownian fractal surface, the first height distribution parameter, and the second height distribution parameter, wherein the height distribution parameter of the Brownian fractal surface is equal to the first height distribution parameter;

[0026] Generates a Brownian fractal surface based on the height data of several points in the Brownian fractal surface.

[0027] Optionally, the height data of several points in the Brownian fractal surface are calculated according to the height data of several points in the random Brownian fractal surface, the first height distribution parameter, and the second height distribution parameter in the following manner:

[0028] ,

[0029] in, is the height data of several points in the Brownian fractal surface, is the height data of several points in the random Brownian fractal surface, is the first height distribution parameter, is the second height distribution parameter.

[0030] Optionally, correcting the third height frequency domain data according to the first height frequency domain data to obtain fourth height frequency domain data includes:

[0031] Calculating the difference between the third height frequency domain data and the first height frequency domain data in a logarithmic value domain to obtain height frequency domain difference data in a logarithmic value domain;

[0032] Smoothing the height-frequency domain difference data in the logarithmic domain, and fitting the smoothed height-frequency domain difference data in the logarithmic domain to obtain a correction function in the logarithmic domain;

[0033] The third height frequency domain data is corrected according to the correction function to obtain fourth height frequency domain data.

[0034] Optionally, correcting the third height frequency domain data according to the correction function to obtain fourth height frequency domain data includes:

[0035] constructing an exponential function with the correction function as an independent variable, wherein the base of the exponent is the same as the base of the logarithmic domain;

[0036] If the height frequency domain difference data in the logarithmic domain is calculated by subtracting the first height frequency domain data from the third height frequency domain data, the third height frequency domain data is divided by the exponential function to obtain fourth height frequency domain data.

[0037] Optionally, correcting the third height frequency domain data according to the correction function to obtain fourth height frequency domain data includes:

[0038] If the height frequency domain difference data in the logarithmic domain is calculated by subtracting the third height frequency domain data from the first height frequency domain data, the third height frequency domain data is multiplied by the exponential function to obtain fourth height frequency domain data.

[0039] A second aspect of the present invention provides a rough surface generating device, which includes: a processor and a memory connected to the processor; wherein the memory stores instructions that can be executed by the processor, and the instructions are executed by the processor to enable the processor to perform the above-mentioned rough surface generating method.

[0040] The present invention obtains the height data of several sampling points of the sample to be tested. Then, the height data of the several sampling points are subjected to frequency domain analysis and statistical analysis respectively, providing a key data basis for subsequent simulation. Then, a random Brownian fractal surface is randomly generated according to the sampling resolution of the several sampling points, from the calculation of the height distribution parameters to the generation of the Brownian fractal surface that conforms to the specific height distribution, and by adjusting its self-similarity parameters, the height frequency domain data of the randomly generated surface and the height frequency domain data of the sample to be tested are basically overlapped in the high-frequency region, and the randomly generated Brownian fractal surface is gradually adjusted in the direction that conforms to the statistical law of the sample to be tested. Then, the third height frequency domain data obtained by basically coinciding with the high-frequency region according to the first height frequency domain data is corrected to obtain fourth height frequency domain data, and the fourth height frequency domain data is subjected to inverse Fourier transform to obtain a rough surface that finally meets the statistical law of the sample to be tested.

[0041] Compared to traditional methods, this method only requires modifying the self-similarity parameter of the random Brownian fractal surface and calibrating the fourth-degree frequency domain data. These two modifications enable the efficient and accurate generation of a simulated rough surface that closely matches the statistical regularity of the sample being measured. This method avoids the multiple iterations or complex processing steps that traditional methods may require, significantly reducing simulation time and computing resources, and significantly improving simulation efficiency.

[0042] By analyzing the statistical laws of AFM data, this method can ensure that the generated rough surface has a very high similarity with the surface obtained by AFM measurement and does not contain random errors from the sample. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the specific embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0044] Figure 1 is a flow chart of a rough surface generation method in an embodiment of the present invention;

[0045] Figure 2 is a first height frequency domain data s1 graph in an embodiment of the present invention;

[0046] Figure 3 4 is a comparison diagram of the first high-frequency domain data s1 and the updated second high-frequency domain data s2 in an embodiment of the present invention;

[0047] Figure 4 4 is a comparison diagram of the third high-frequency domain data s3 and the first high-frequency domain data s1 in an embodiment of the present invention;

[0048] Figure 5 is a comparison diagram of the fourth high-frequency domain data s4 and the first high-frequency domain data s1 in an embodiment of the present invention;

[0049] Figure 6 Schematic diagram of a random Brownian fractal surface in an embodiment of the present invention. DETAILED DESCRIPTION

[0050] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0051] In the description of the present invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicating orientations or positional relationships, are based on the orientations or positional relationships shown in the accompanying drawings and are intended solely to facilitate and simplify the description of the present invention. They are not intended to indicate or imply that the devices or components referred to must have, be constructed, or operate in a specific orientation, and therefore should not be construed as limitations on the present invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0052] In the description of the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "installed," "connected," and "connected" should be understood in a broad sense. For example, they can refer to fixed connections, detachable connections, or integral connections; mechanical connections or electrical connections; direct connections or indirect connections through an intermediate medium; internal connections between two components; wireless connections or wired connections. Those skilled in the art will understand the specific meanings of the above terms in the present invention based on specific circumstances.

[0053] In addition, the technical features involved in the different embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0054] like Figure 1 As shown, an embodiment of the present invention provides a rough surface generation method, which is executed by an electronic device such as a computer or a server, and specifically includes:

[0055] S1, obtain the height data of several sampling points of the measured sample.

[0056] AFM sampling is performed on the sample under test using an atomic force microscope. The sampling range and sampling resolution can be set by the user. The sampling range is the size of the area scanned by the AFM probe along the X-axis and Y-axis directions on the surface of the sample under test, and the sampling resolution is the distribution density of the sampling points within the sampling range.

[0057] Height data is presented as a two-dimensional digital matrix. The rows and columns of the matrix correspond to the locations of sampling points on the sample surface in the X and Y directions, respectively. Each element in the matrix represents the height of the sample surface at that sampling point relative to a reference plane. For example, a 256×256 matrix indicates 256 sampling points in the X and Y directions, respectively. Each value in the matrix represents the surface height at the corresponding location. The surface represented by the AFM data is the sample surface, i.e., surface1.

[0058] S2, performing frequency domain analysis and statistical analysis on the height data of several sampling points to obtain first height frequency domain data s1 and first height distribution parameters.

[0059] Using the two-dimensional digital matrix of the height values ​​of the surface surface1, frequency domain analysis is performed on the height data of the sampling points to obtain the first height frequency domain data s1; and statistical analysis is performed on the height data of the sampling points to finally obtain the first height distribution parameter.

[0060] S3, randomly generates a random Brownian fractal surface according to the sampling resolution of several sampling points.

[0061] A random Brownian fractal surface surface2 is randomly constructed based on the sampling resolution of several sampling points in step S1. The random Brownian fractal surface includes a self-similarity parameter, namely the Hurst parameter. The Hurst parameter is a parameter of the Brownian fractal algorithm. The higher the Hurst parameter is, the higher the surface self-similarity is. Its value range is usually between 0 and 1. A Hurst parameter can be arbitrarily specified, such as an empirical value. Figure 6 It also contains the XY coordinates of each sampling point and the height of each sampling point.

[0062] S4, generating a Brownian fractal surface according to the height data of a plurality of points in the random Brownian fractal surface and the first height distribution parameter, wherein the height distribution parameter of the Brownian fractal surface is equal to the first height distribution parameter.

[0063] Based on the height data of several points of the random Brownian fractal surface surface2 and the first height distribution parameter, the height distribution parameter of the generated surface is constrained to be equal to the first height distribution parameter, thereby generating the Brownian fractal surface surface3. The Brownian fractal surface surface3 can be as follows: Figure 6 shown.

[0064] S5, performing frequency domain analysis on the Brownian fractal surface to obtain second high-frequency domain data s2.

[0065] The Brownian fractal surface surface3 is subjected to frequency domain analysis in the same manner as in step S2 to obtain second high-frequency domain data s2.

[0066] S6, by adjusting the self-similarity parameter of the random Brownian fractal surface, the step of randomly generating the random Brownian fractal surface according to the sampling resolution of the plurality of sampling points is performed again until the high frequency region of the second high frequency domain data s2 coincides with the high frequency region of the first high frequency domain data s1.

[0067] The self-similarity parameter of the random Brownian fractal surface surface2 is iteratively adjusted, and steps S3-S5 are repeated after each adjustment until the high-frequency region of the updated second high-frequency data s2 substantially overlaps with the high-frequency region of the first high-frequency data s1, i.e., the high-frequency regions overlap, at which point the self-similarity parameter adjustment is stopped. The high-frequency region can be defined by an empirical threshold.

[0068] S7 , obtaining third high-frequency domain data s3 according to the overlapping area where the high-frequency areas overlap.

[0069] The data of the overlapping high-frequency regions are used to obtain the third high-frequency domain data s3.

[0070] S8 , correcting the third height frequency domain data s3 according to the first height frequency domain data s1 to obtain fourth height frequency domain data s4 .

[0071] Because the surface surface1 of the sample under test has self-similarity and complex details, a random Brownian fractal surface is first used to simulate its characteristics to generate the second height frequency domain data s2; the self-similarity parameters are adjusted so that the high-frequency region of the second height frequency domain data s2 basically coincides with the high-frequency region of the first height frequency domain data s1 (real surface frequency domain data) to obtain the third height frequency domain data s3; then, based on the real characteristics of the first height frequency domain data s1, the third height frequency domain data s3 is corrected to eliminate the deviation, and finally the fourth height frequency domain data s4 that fits the reality is obtained.

[0072] S9, performing inverse Fourier transform on the fourth height frequency domain data s4 to generate a rough surface that meets the statistical laws of the sample being tested.

[0073] The final simulated real rough surface can be Figure 6 As shown, the horizontal and vertical coordinates are the position of each point of the measured sample, and the grayscale represents the height of the rough surface.

[0074] The present embodiment is by obtaining the height data of several sampling points of the measured sample in step S1.Then, step S2 carries out frequency domain analysis and statistical analysis respectively to the height data of several sampling points, for subsequent simulation provides key data basis.In steps S3-S6, random Brownian fractal surface is randomly generated according to the sampling resolution of several sampling points, from the calculation of height distribution parameter to the generation of Brownian fractal surface that meets specific height distribution, and by adjusting its self-similarity parameter, the height frequency domain data of the randomly generated surface is made to overlap substantially with the height frequency domain data of the measured sample in the high frequency region, progressively the randomly generated Brownian fractal surface is adjusted to the direction that meets the statistical law of the measured sample.Then, steps S7-S8 correct the third height frequency domain data that basically overlaps the high frequency region according to the first height frequency domain data, obtain the fourth height frequency domain data, and step S9 carries out inverse Fourier transform to the fourth height frequency domain data again, can obtain the rough surface that finally generates and meets the statistical law of the measured sample.

[0075] Compared to traditional methods, this method only requires modifying the self-similarity parameter of the random Brownian fractal surface and calibrating the fourth-degree frequency domain data. These two modifications enable the efficient and accurate generation of a simulated rough surface that closely matches the statistical regularity of the sample being measured. This method avoids the multiple iterations or complex processing steps that traditional methods may require, significantly reducing simulation time and computing resources, and significantly improving simulation efficiency.

[0076] In one embodiment, obtaining height data of several sampling points of the sample under test in step S1 specifically includes:

[0077] At least two groups of atomic force microscope data of the measured sample are obtained at the same sampling resolution, where the atomic force microscope data include height data of several sampling points.

[0078] An atomic force microscope is used to take a specific reference point on the surface of the sample to be measured as the origin, and intensive sampling is performed at sampling points determined by the sampling resolution within the sampling range to obtain surface height data of the sample to be measured at least twice under the same sampling range and sampling resolution. Multiple sets of real data are used to eliminate accidental errors caused by environmental equipment, etc.

[0079] In one embodiment, step S2 performs frequency domain analysis on the height data of a plurality of sampling points to obtain first height frequency domain data s1, specifically including:

[0080] S21a, calculating the distances from several sampling points to the coordinate origin.

[0081] Calculate the distance to the coordinate origin based on the XY coordinates of each sampling point.

[0082] S22a, performing a one-dimensional fast Fourier transform on the height data of each sampling point according to the distance from each sampling point to the coordinate origin, to obtain first height frequency domain data s1.

[0083] For example, AFM sampling is performed on a single crystal diamond sample, the sampling range is set to 5μm×5μm, the sampling resolution is set to 256×256 sampling points, and the height data data1 is obtained. Then, 1dlogFFT transformation is performed on the height data data1 to obtain the first height frequency domain data s1. The first height frequency domain data s1 is as follows: Figure 2 As shown, the horizontal axis is the square root of 2 times the original sampling resolution, and the vertical axis is the log intensity of the spectrum. The horizontal and vertical axes of all subsequent height frequency domain data schematic diagrams are the same as those of the first height frequency domain data s1 schematic diagram.

[0084] This embodiment calculates the distance from each sampling point to the coordinate origin and then performs a one-dimensional fast Fourier transform on the height data of the sampling points based on these distances. This can convert the height data from the spatial domain to the frequency domain, revealing the sample surface information contained in the different frequency components in the data. This helps to more clearly observe and analyze the distribution characteristics of the sample surface height changes in the frequency domain, for example, it can identify the periodic structure of the surface and roughness information at different scales.

[0085] In one embodiment, in step S2, statistical analysis is performed on the height data of a plurality of sampling points to obtain a first height distribution parameter, specifically including:

[0086] S21b, performing statistical analysis on the height data of the plurality of sampling points to obtain statistical analysis results, the statistical analysis results including mean, median, first standard deviation, first profile arithmetic mean deviation, kurtosis, and skewness.

[0087] Statistical analysis was performed on the height data of several sampling points (covering the calculation of indicators such as mean, median, first standard deviation, first profile arithmetic mean deviation, kurtosis and skewness), and finally the calculation results of these parameters were obtained.

[0088] S22b, judging whether the height data of the plurality of sampling points satisfy the Gaussian distribution law based on the mean, median, kurtosis and skewness.

[0089] Generally, normalizing the height data results in a mean close to 0. The median is then determined to be close to the mean. If so, the height data distribution is likely symmetrical, consistent with the symmetric nature of a Gaussian distribution. The skewness is then determined to be close to 0. If so, the height data conforms to the symmetric nature of a Gaussian distribution. The kurtosis is then determined to be close to 0. If so, the peaked state of the height data distribution closely matches that of a Gaussian distribution. This ensures that the height data at several sampling points adhere to the Gaussian distribution, effectively reducing errors in subsequent calculations. Conversely, failure to adhere to the Gaussian distribution can negatively impact subsequent calculations.

[0090] S23b, determining a first standard deviation or a first profile arithmetic mean deviation that satisfies a Gaussian distribution law as a first height distribution parameter for describing the measured sample.

[0091] When the height data distribution of the measured sample is judged to basically meet the Gaussian distribution law based on the mean, median, skewness and kurtosis, the standard deviation and the arithmetic mean deviation of the profile become the key indicators for describing the roughness of the measured sample. Therefore, the first standard deviation std1 or the first arithmetic mean deviation Ra1 of the profile can be used to roughly describe the height distribution of the measured sample.

[0092] Specifically, taking the height data data1 as an example, the mean, median, first standard deviation std1, first profile arithmetic mean deviation Ra1, kurtosis and skewness of the height data data1 are obtained, and mean=0.000, median=0.029, std1=0.346, Ra1=0.277, skewness=-0.387, kurtosis=-0.249 are obtained, and the units are all nm.

[0093] The mean is 0, and the median is 0.029, which is close to the mean, indicating that the height data distribution conforms to the symmetric characteristics of a Gaussian distribution. The skewness is -0.387, close to 0, indicating that the height data distribution conforms to the symmetric characteristics of a Gaussian distribution. The kurtosis is -0.249, close to 0, indicating that the kurtosis of the height data distribution is close to that of a Gaussian distribution, neither too sharp nor too flat. Therefore, the first standard deviation (std1) and the first profile arithmetic mean deviation (Ra1) can be used as the first height distribution parameters to describe the measured sample.

[0094] Furthermore, step S4 generates a Brownian fractal surface based on the height data of a plurality of points in the random Brownian fractal surface and the first height distribution parameter, wherein the height distribution parameter of the Brownian fractal surface is equal to the first height distribution parameter, specifically including:

[0095] S41 , calculating a second height distribution parameter according to height data of a plurality of points in the random Brownian fractal surface, where the second height distribution parameter includes a second standard deviation or a second profile arithmetic mean deviation.

[0096] Since it is concluded above that the first standard deviation std1 or the first profile arithmetic mean deviation Ra1 can be used to roughly describe the height distribution of the measured sample, the second height distribution parameter is calculated based on the height data of several points in the random Brownian fractal surface in step S41, and the second standard deviation or the second profile arithmetic mean deviation can be calculated based on the height data of several points in the random Brownian fractal surface. Taking the second standard deviation as an example, the second standard deviation std2 of the random Brownian fractal surface surface2 is calculated.

[0097] S42, calculating the height data of several points in the Brownian fractal surface according to the height data of several points in the random Brownian fractal surface, the first height distribution parameter, and the second height distribution parameter, wherein the height distribution parameter of the Brownian fractal surface is equal to the first height distribution parameter.

[0098] In step S42, the height data of several points in the random Brownian fractal surface are calculated based on the height data of several points in the random Brownian fractal surface, the first height distribution parameter, and the second height distribution parameter. Then, the height distribution parameter of the Brownian fractal surface can be made equal to the first height distribution parameter based on the first standard deviation std1 and the second standard deviation std2.

[0099] S43, generating a Brownian fractal surface according to height data of a plurality of points in the Brownian fractal surface.

[0100] In fact, the Brownian fractal surface surface3 is generated by scaling surface2 according to the first standard deviation std1 and the second standard deviation std2, so that the standard deviation of the Brownian fractal surface surface3 is equal to the first standard deviation std1 of the height data data1.

[0101] Furthermore, the height data of several points in the Brownian fractal surface are calculated according to the height data of several points in the random Brownian fractal surface, the first height distribution parameter, and the second height distribution parameter in the following manner:

[0102] ,

[0103] in, is the height data of several points in the Brownian fractal surface surface3, is the height data of several points in the random Brownian fractal surface surface2, is the first height distribution parameter, is the second height distribution parameter.

[0104] In this embodiment, the randomly generated random Brownian fractal surface is calculated to have the same height distribution parameters as the actual AFM measured height data data1, so that the simulated random Brownian fractal surface is preliminarily matched with the actual sample surface in terms of the key feature of roughness, which establishes a reasonable basis for the subsequent comparison and matching of frequency domain features, avoids interference in the frequency domain feature analysis due to excessive roughness differences, and more accurately simulates the actual sample surface conditions.

[0105] Furthermore, in step S5, the Brownian fractal surface is subjected to frequency domain analysis to obtain second high-frequency domain data s2, including: performing the same processing as step S2 on the Brownian fractal surface surface3, converting the XY coordinates of each sampling point on the Brownian fractal surface surface3 into the distance from the coordinate origin, performing 1dlogFFT transformation on the distance, and obtaining second high-frequency domain data s2.

[0106] This embodiment calculates the distances from sampling points in the Brownian fractal surface surface3 to the coordinate origin, and then performs a one-dimensional fast Fourier transform on the height data of the sampling points based on these distances. This can convert the height data from the time domain to the frequency domain, revealing the surface information of the Brownian fractal surface surface3 contained in the different frequency components in the data, which helps to more clearly observe and analyze the distribution characteristics of the height changes of the Brownian fractal surface surface3 in the frequency domain.

[0107] In one embodiment, steps S6-S7 specifically include:

[0108] Self-similarity affects the shape of the frequency domain distribution. Ra or std affects the height of the frequency domain but does not affect the shape. The parameter, Hurst, changes the Hurst specified in the random Brownian fractal surface surface2. Starting from the randomly specified Hurst value, a relatively large step size, such as 0.1, can be selected to quickly narrow the possible parameter range. When approaching the target, the step size is further reduced, such as 0.01 or smaller, to improve the accuracy of the adjustment. Each time the Hurst value is changed, the random Brownian fractal surface is updated according to the updated Hurst value, that is, steps S3-S5 are repeated to obtain the updated second high-frequency domain data s2. The Hurst value and the second height frequency domain data s2 are continuously changed until the updated second height frequency domain data s2 coincides with the high frequency area of ​​the first height frequency domain data s1. The high frequency area can be preset within a range through an empirical threshold. To determine whether the updated second height frequency domain data s2 coincides with the high frequency area of ​​the first height frequency domain data s1, an error evaluation indicator can be used to calculate the degree of difference between the two, such as the mean square error (MSE), root mean square error (RMSE) or mean absolute error (MAE). When the error is less than a preset value, it can be determined that the updated second height frequency domain data s2 coincides with the high frequency area of ​​the first height frequency domain data s1.

[0109] The overlapping area within the preset high frequency range is used to obtain the third high frequency domain data s3, such as Figure 3 As shown in , the horizontal axis is the square root of 2 times the original sampling resolution, the vertical axis is the log intensity of the spectrum, the blue curve represents the first height frequency domain data s1, and the red curve represents the updated second height frequency domain data s2. The high-frequency area range can be set according to the vertical axis, and the overlapping area can be found to obtain the third height frequency domain data s3, and the corresponding surface is surface4.

[0110] Because the random Brownian fractal surface generated in step S3 is an uncorrected rough surface and does not conform to the statistical laws of real sample roughness, the Hurst value needs to be corrected. The Hurst parameter plays a key role in controlling the roughness of the Brownian fractal surface. By correcting the Hurst value, the surface roughness characteristics can be adjusted so that the height-frequency domain data of the corresponding Brownian fractal surface approaches that of the real sample, making its statistical characteristics closer to those of the real sample.

[0111] In one embodiment, step S8 corrects the third height frequency domain data s3 according to the first height frequency domain data s1 to obtain fourth height frequency domain data s4, specifically including:

[0112] S81 , calculating the difference between the third height frequency domain data s3 and the first height frequency domain data s1 in the logarithmic value domain to obtain height frequency domain difference data in the logarithmic value domain.

[0113] The comparison diagram of the third high-frequency data s3 and the first high-frequency data s1 is as follows: Figure 4 As shown, the horizontal axis is the square root of 2 times the original sampling resolution, the vertical axis is the log intensity of the spectrum, the blue curve represents the first height frequency domain data s1, and the red curve represents the third height frequency domain data s3. The difference of the vertical axis is calculated according to the horizontal axis in the logarithmic domain to obtain the height frequency domain difference data.

[0114] S82 , smoothing the height-frequency domain difference data in the logarithmic domain, and fitting the smoothed height-frequency domain difference data in the logarithmic domain to obtain a correction function f1 in the logarithmic domain.

[0115] Based on the distribution pattern of the difference between the first and third height-frequency domain data in the logarithmic domain, an appropriate correction function type is selected and fitted to obtain correction function f1. Options include polynomial function (power function), generalized logarithmic function, generalized exponential function, and generalized negative power function (a polynomial that converts positive n-th powers to -n-th powers). The correction function to be used should be selected based on the actual situation. For each correction function, the smoothed height-frequency domain difference data is fitted, and the root mean square error (RMSE) between the fit result and the height-frequency domain difference data is calculated. The correction function with the lowest RMSE is selected as correction function f1. Smoothing can use moving average or Gaussian smoothing to reduce noise in the data.

[0116] S83 , correcting the third height frequency domain data s3 according to the correction function f1 to obtain fourth height frequency domain data s4 .

[0117] The third height frequency domain data s3 is adjusted using the correction function f1 to finally obtain fourth height frequency domain data s4 that is more consistent with the physical characteristics of the actual surface.

[0118] This embodiment first calculates the difference between the third height frequency domain data s3 and the first height frequency domain data s1 in the logarithmic domain to obtain the height frequency domain difference data in the logarithmic domain, which can intuitively reflect the difference between different height frequency domain data and provide a basis for subsequent correction processing. Then, the height frequency domain difference data in the logarithmic domain is smoothed to effectively remove noise interference in the data, making the data more stable and reducing the impact of outliers on subsequent fitting. Afterwards, the height frequency domain difference data in the logarithmic domain is fitted and the root mean square error (RMSE) is used as an evaluation indicator to select the most suitable correction function f1 in the logarithmic domain, thereby improving the accuracy and reliability of the correction function.

[0119] In one embodiment, step S83 corrects the third height frequency domain data s3 according to the correction function f1 to obtain the fourth height frequency domain data s4, specifically including:

[0120] S831, construct an exponential function f2 with the correction function f1 as an independent variable, where the base of the exponent is the same as the base of the logarithmic domain.

[0121] For example, the base of the logarithm can be chosen arbitrarily, as long as the base is a real number greater than 0 and the base of the exponential function is also this value, and is not limited to e, 2, or 10. For example, if the common logarithm (base 10) is used in the logarithmic domain, then the exponential function f2=10 f1 ; If the natural logarithm with base e is used, then the exponential function is f2=e f1The purpose of this is to ensure that when the correction result of the logarithmic domain is converted back to the linear domain, the mathematical relationship between the data can be accurately restored, thereby achieving correct correction of the third height frequency domain data s3 and obtaining the fourth height frequency domain data s4 that conforms to the actual physical meaning.

[0122] S832: If the height-frequency domain difference data in the logarithmic domain is calculated by subtracting the first height-frequency domain data s1 from the third height-frequency domain data s3, the third height-frequency domain data s3 is divided by the exponential function f2 to obtain fourth height-frequency domain data s4.

[0123] If the height frequency domain difference data calculated in the logarithmic domain in step S81 is based on At this time, the third high-frequency data in the logarithmic domain minus the correction function f1 basically coincides with the first high-frequency data in the logarithmic domain, that is, , then when calculating the fourth height frequency domain data s4, the third height frequency domain data s3 should be divided by the exponential function f2, that is, the exponential function f1 is used to correct and convert it into a linear value domain to obtain the fourth height frequency domain data s4.

[0124] Correcting the third high-frequency domain data s3 according to the correction function f1 is equivalent to adding a correction term (correction function f1) to the surface surface4, and dividing the function value of f1 in the frequency domain to obtain the fourth high-frequency domain data s4, such as Figure 5 The red curve in the middle shows the surface 5, where the horizontal axis is the square root of 2 times the original sampling resolution, the vertical axis is the log intensity of the spectrum, and the blue curve represents the first height frequency domain data s1. The surface 5 can then be obtained by inverse Fourier transform.

[0125] In another embodiment, step S83 corrects the third height frequency domain data s3 according to the correction function f1 to obtain fourth height frequency domain data s4, further comprising:

[0126] If the height frequency domain difference data in the logarithmic domain is calculated by subtracting the third height frequency domain data s3 from the first height frequency domain data s1, the third height frequency domain data s3 is multiplied by the exponential function f2 to obtain the fourth height frequency domain data s4.

[0127] If the height frequency domain difference data calculated in the logarithmic domain in step S81 is based on At this time, the third high-frequency domain data in the logarithmic domain plus the correction function f1 basically coincides with the first high-frequency domain data in the logarithmic domain, that is, , then when calculating the fourth height frequency domain data s4, the third height frequency domain data s3 should be multiplied by the exponential function f2, that is, the exponential function f1 is used to correct and convert it into a linear value domain to obtain the fourth height frequency domain data s4.

[0128] The above two methods further improve the accuracy and reliability of the data by re-calibrating the data of the surface roughness characteristics corrected in step S8, so that the data is more consistent with the physical properties of the actual surface.

[0129] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0130] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0131] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0132] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0133] Obviously, the above embodiments are merely examples for clarity of explanation and are not intended to limit the implementation methods. Those skilled in the art will readily appreciate that other variations or modifications based on the above descriptions are possible. It is not necessary and impossible to enumerate all implementation methods here. Obvious variations or modifications arising therefrom remain within the scope of protection of the present invention.

Claims

1. A rough surface generation method, characterized in that: include: Obtaining height data of several sampling points of the measured sample; Performing frequency domain analysis and statistical analysis on the height data of the plurality of sampling points to obtain first height frequency domain data and first height distribution parameters; and randomly generating a random Brownian fractal surface according to the sampling resolution of the plurality of sampling points; generating a Brownian fractal surface according to the height data of a plurality of points in the random Brownian fractal surface and the first height distribution parameter, wherein the height distribution parameter of the Brownian fractal surface is equal to the first height distribution parameter; Performing frequency domain analysis on the Brownian fractal surface to obtain second high-frequency domain data; The step of randomly generating a random Brownian fractal surface according to the sampling resolutions of the plurality of sampling points is performed again in a manner of adjusting the self-similarity parameter of the random Brownian fractal surface until the second high-frequency domain data overlaps with the high-frequency region of the first high-frequency domain data; According to the overlapping area of ​​the high-frequency area, the third high-frequency domain data is obtained; Correcting the third height frequency domain data according to the first height frequency domain data to obtain fourth height frequency domain data; Performing an inverse Fourier transform on the fourth height frequency domain data to generate a rough surface that satisfies the statistical laws of the sample being tested; The step of generating a Brownian fractal surface according to the height data of a plurality of points in the random Brownian fractal surface and the first height distribution parameter, wherein the height distribution parameter of the Brownian fractal surface is equal to the first height distribution parameter, includes: Calculating a second height distribution parameter based on height data of a plurality of points in the random Brownian fractal surface, wherein the second height distribution parameter includes a second standard deviation or a second profile arithmetic mean deviation; Calculating height data of a plurality of points in the Brownian fractal surface according to the height data of a plurality of points in the random Brownian fractal surface, the first height distribution parameter, and the second height distribution parameter, wherein the height distribution parameter of the Brownian fractal surface is equal to the first height distribution parameter; Generates a Brownian fractal surface based on the height data of several points in the Brownian fractal surface.

2. The method according to claim 1, characterized in that Obtain height data of several sampling points of the sample being tested, including: At least two groups of atomic force microscopy data of a measured sample are acquired at the same sampling resolution, wherein the atomic force microscopy data include height data of a plurality of sampling points.

3. The method according to claim 1, characterized in that Performing frequency domain analysis on the height data of the plurality of sampling points to obtain first height frequency domain data includes: Calculating the distances from the plurality of sampling points to the coordinate origin; A one-dimensional fast Fourier transform is performed on the height data of each sampling point according to the distance from each sampling point to the coordinate origin to obtain first height frequency domain data.

4. The method according to claim 1, wherein Statistically analyzing the height data of the plurality of sampling points to obtain a first height distribution parameter includes: Performing statistical analysis on the height data of the plurality of sampling points to obtain statistical analysis results, wherein the statistical analysis results include a mean, a median, a first standard deviation, a first profile arithmetic mean deviation, a kurtosis, and a skewness; Determining whether the height data of the plurality of sampling points satisfy a Gaussian distribution law based on the mean, median, kurtosis, and skewness; A first standard deviation or a first profile arithmetic mean deviation satisfying a Gaussian distribution law is determined as a first height distribution parameter for describing the measured sample.

5. The method according to claim 1, wherein Calculate the height data of several points in the Brownian fractal surface according to the height data of several points in the random Brownian fractal surface, the first height distribution parameter, and the second height distribution parameter in the following manner: ； in, is the height data of several points in the Brownian fractal surface, is the height data of several points in the random Brownian fractal surface, is the first height distribution parameter, is the second height distribution parameter.

6. The method according to claim 1, characterized in that Correcting the third height frequency domain data according to the first height frequency domain data to obtain fourth height frequency domain data includes: Calculating the difference between the third height frequency domain data and the first height frequency domain data in a logarithmic value domain to obtain height frequency domain difference data in a logarithmic value domain; Smoothing the height-frequency domain difference data in the logarithmic domain, and fitting the smoothed height-frequency domain difference data in the logarithmic domain to obtain a correction function in the logarithmic domain; The third height frequency domain data is corrected according to the correction function to obtain fourth height frequency domain data.

7. The method according to claim 6, characterized in that Correcting the third height frequency domain data according to the correction function to obtain fourth height frequency domain data includes: constructing an exponential function with the correction function as an independent variable, wherein the base of the exponent is the same as the base of the logarithmic domain; If the height frequency domain difference data in the logarithmic domain is calculated by subtracting the first height frequency domain data from the third height frequency domain data, the third height frequency domain data is divided by the exponential function to obtain fourth height frequency domain data.

8. The method according to claim 7, characterized in that Correcting the third height frequency domain data according to the correction function to obtain fourth height frequency domain data includes: If the height frequency domain difference data in the logarithmic domain is calculated by subtracting the third height frequency domain data from the first height frequency domain data, the third height frequency domain data is multiplied by the exponential function to obtain fourth height frequency domain data.

9. A rough surface generating device, characterized in that: include: A processor and a memory connected to the processor; wherein the memory stores instructions that can be executed by the processor, and the instructions are executed by the processor to enable the processor to execute the rough surface generation method according to any one of claims 1 to 8.

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