Method for determining coverage rate

Abstract

This method for determining the coverage rate of convex part portions on a particle surface in a powder comprises the following steps. (1) A step for acquiring a microscopic image of a powder having a luminance distribution and resolution, the microscopic image being acquired so that the luminance distribution satisfies a specific range. (2) A step for creating a pseudo-binarization model for converting the luminance distribution of the microscope image obtained in (1) to a distribution having peaks at a luminance value of 0 and a luminance value of 255. (3) A step for binarizing and detecting the pseudo-binarization model produced in (2). (4) A step for performing image processing to remove excess noise from the image binarized and detected in (3). (5) A step for calculating, from the image processed in (4), a coverage rate indicating the proportion of the particles covered by the convex parts.

Description

Method for determining coverage

[0001] This invention relates to a method for determining the coverage rate of a powder having two or more protrusions on the surface of a single particle.

[0002] There are specific surface treatment processes that can highly functionalize powders. Examples include methods that create raised areas on the surface of core particles, or methods that create raised areas by coating the surface of core particles with smaller sub-particles. For powders with raised areas on their surfaces as described above, it is preferable to evaluate the powder performance in conjunction with the surface structure. For this purpose, methods for quantitatively and statistically analyzing the surface structure of powders are needed.

[0003] Such powders can be observed using transmission electron microscopes (TEM), scanning electron microscopes (SEM), and optical microscopes. Furthermore, these images can be subjected to detailed analysis through image processing. Image processing includes various operations such as binarization, filtering, dilation, and stenosis, and ImageJ is a well-known image processing software. Image processing using Python libraries is also performed. Regarding binarization, while it is usually done by selecting a threshold from 256 luminance values, in recent years, with the remarkable advancements in AI, attempts are being made to perform binarization by creating models using deep learning and applying them to images.

[0004] Patent Document 1 (Japanese Patent Publication No. 2023-109890) describes an example in which a pigment is physically attached to the surface of a plate-shaped powder. In that document, 10 images showing only the powder surface are taken at 10,000x magnification using a SEM, and the coverage rate (described as "coarse particle area ratio" in the document) is calculated by binarization using a threshold.

[0005] As seen in these examples, conventional methods for calculating coverage rates mainly involve simply selecting a threshold value from 256 luminance levels. The analysis range is limited to a portion of the particle, and the number of analyses is not very large. Therefore, the calculated values ​​are merely examples and cannot be said to represent the coverage rate specific to the sample, raising concerns that the observer's subjectivity may strongly influence the evaluation results.

[0006] To solve the above problem, it is necessary to analyze the range containing the statistic particles. As described later in the analysis method of the present invention, analyzing the range containing the statistic particles requires precise separation and partitioning of the background and particles, and precise separation and partitioning of particles and convex parts. Furthermore, noise reduction is indispensable to improve accuracy. In addition, since changing the analysis operation for each image of a large number of images containing statistic particles requires a great deal of time and effort, it is desirable that the analysis be completed by performing the same operation on all images.

[0007] Japanese Patent Publication No. 2023-109890

[0008] The present invention has been made in view of the above circumstances, and aims to provide a method for statistically valid analysis that eliminates subjectivity by acquiring observation images over a sufficiently wide area for statistical evaluation of a powder having two or more protrusions on the surface of a single particle, accurately recognizing the particles and protrusions, and calculating the percentage of the particle covered by the protrusions (coverage rate).

[0009] As a result of diligent research to achieve the above objective, the present inventors have found that, by following the steps (1) to (5) below, it is possible to accurately calculate the percentage of a particle covered by protrusions (coverage rate) in a powder having two or more protrusions on the surface of a single particle, and to perform a statistically valid analysis that eliminates subjectivity, thus leading to the present invention. A flowchart of the method for determining this coverage rate is shown in Figure 1.

[0010] Accordingly, the present invention provides a method for determining the following coverage rate. 1. A method for determining the coverage rate of the protruding portions on the surface of a particle having two or more protrusions on the surface of a single particle, comprising the following steps (1) to (5): (1) A step of acquiring a microscopic image of the powder having a brightness distribution and resolution, wherein the brightness distribution when each pixel constituting the microscopic image is displayed with a brightness value of 0 to 255 is and, The following conditions are met, and the resolution is (1) A step to acquire a microscope image that satisfies the following conditions. (2) A step to create the following image analysis models (hereinafter referred to as pseudo-binarization models) (A) and (B) based on the results obtained by machine learning, which convert the brightness distribution of the microscope image obtained in step (1) into a distribution with peaks at brightness values ​​of 0 and 255. (A) A pseudo-binarization model that detects particles based on the results of machine learning using a sample image in which particles have been binarized. (B) A pseudo-binarization model that detects convex parts based on the results of machine learning using a sample image in which convex parts have been binarized. (3) A step to apply the two pseudo-binarization models created in step (2) to the microscope image obtained in step (1), respectively, and independently and completely binarize and detect particles containing noise and convex parts containing noise. (4) A step to perform image processing to remove extraneous noise from the binarized image detected in step (3). (5) A step of obtaining the total area of ​​the particles and the total area of ​​the protrusions on the surface of the particles from the image processed in step (4), and calculating the coverage rate which indicates the proportion that the protrusions cover the particles, wherein the total area of ​​the "particles" is S M Let S be the total area of ​​the "protrusions on the particle surface". C The proportion of the particles covered by the protrusions (coverage rate) is defined as C. R In this case, the coverage C is given by the following formula (X1). R The process of calculating. 2. A method for obtaining the coverage rate of the convex portion described in 1, in which in the acquisition of an image using a scanning electron microscope as the microscope in the step (1), the energy of the signal electrons to be detected, the acceleration voltage, and the irradiation current are selected to adjust the luminance distribution. 3. A method for obtaining the coverage rate of the convex portion described in 1 or 2, in which in the acquisition of an image using a scanning electron microscope as the microscope in the step (1), the resolution is adjusted by selecting the observation magnification, the number of pixels, and the scan time. 4. A method for obtaining the coverage rate of the convex portion described in any one of 1 to 3, in which in the step (2), the sample image is obtained by cutting out a part of the microscope image, filling in the portion to be detected, and binarizing it. 5. A method for obtaining the coverage rate of the convex portion described in any one of 1 to 4, in which the machine learning method in the step (2) is a convolutional neural network. 6. A method for obtaining the coverage rate of the convex portion described in any one of 1 to 5, in which when completely binarizing the image after applying the pseudo-binarization model, the average variance of the distribution having a peak at luminance value 0 and the distribution having a peak at luminance value 255 is minimized, and the threshold value is selected so that the separation degree is maximized. 7. A method for obtaining the coverage rate of the convex portion described in any one of 1 to 6, in which the convex portion of the powder is formed by protruding from the particles. 8. A method for obtaining the coverage rate of the convex portion described in any one of 1 to 7, in which the convex portion of the powder is a sub-particle having an average particle diameter of 0.01 to 50% of the average particle diameter of the particles.

[0011] By using the method of the present invention, in a microscope image of a powder having two or more convex portions on the surface of one particle, the particles and the convex portions can be accurately recognized, and the ratio (coverage rate) of the convex portions covering the particles can be calculated. The analysis target range becomes much wider, and an efficient calculation of the surface coverage rate supported by statistics becomes possible.

[0012] Flowchart of the method Conceptual diagram of the set and its elements in step (4) Conceptual diagram of acquiring set C in step (4)-2-3 Protrusions formed by rising from particles (overall particle diagram) Protrusions formed by rising from particles (enlarged view of protrusions) Example of a SEM linked image of step (1) in the example Enlarged image of a part of the SEM linked image (Figure 6) of step (1) in the example Brightness distribution of the SEM linked image (Figure 6) of step (1) in the example Binarized detection image of "particles containing noise" by the pseudo-binarization model of step (3) in the example Binarized detection image of "protrusions containing noise" by the pseudo-binarization model of step (3) in the example "particle" detection image of step (4) in the example "protrusions on particles" detection image of step (6) in the example R Graph showing the variation within the effective error range of (j) An example of an SEM-linked image in Comparative Example 1 An enlarged image of a part of an example of an SEM-linked image in Comparative Example 1 (Figure 14) Brightness distribution of an example of an SEM-linked image in Comparative Example 1 (Figure 14) Binarized detection image of "particles containing noise" by the pseudo-binarization model of process (3) in Comparative Example 1 Binarized detection image of "convex parts containing noise" by the pseudo-binarization model of process (3) in Comparative Example 1 "particle" detection image of process (4) in Comparative Example 1 "convex parts on particles" detection image of process (4) in Comparative Example 1 Binarized detection image of "particles" by threshold in Comparative Example 2 Binarized detection image of "convex parts" by threshold in Comparative Example 2

[0013] The present invention will now be described in detail. The present invention is a method for determining the coverage rate of a protruding portion having two or more protrusions on the surface of a single particle, and includes the following steps (1) to (5) to determine the coverage rate of the protruding portion on the particle surface. A flowchart of this analysis method is shown in Figure 1.

[0014] The "powder having two or more convex portions on the surface of one particle" to be evaluated is not particularly limited. One particle (powder) can be any one regardless of its material, shape (spherical, needle-like, plate-like, etc.), particle diameter (smoky, fine particle, pigment grade, etc.), or particle structure (porous, non-porous, etc.). Examples of the material of one particle (powder) include inorganic powder, organic powder, surfactant metal salt powder, colored pigment, pearl pigment, metal powder pigment, tar pigment, natural pigment, and the like.

[0015] The shape of the convex portion is not particularly limited, but it is preferably a particle, and is not particularly limited to spherical, needle-like, or plate-like. The method for forming the convex portion is not particularly limited, and it may be formed by protruding from the particle, or a substance for forming the convex portion may be attached or adsorbed to the particle by a chemical or physical method. As the material of the convex portion, the same materials as those listed for the above one particle (powder) can be appropriately used.

[0016] As described above, the sizes of one particle, the convex portion, and the powder are not particularly limited, and can be applied in a wide range such as an average particle diameter of 1 nm to 10 mm. It may be in the range of 10 nm to 1 mm, or may be in the range of 100 nm to 100 μm. The convex portion is preferably a sub-particle having an average particle diameter of 0.01 to 50% of the average particle diameter of the particle. The method for measuring the average particle diameter shows the value of the volume median diameter (D 50 ). The volume median diameter (D 50 ) is the particle diameter corresponding to 50% cumulative when the volume particle size distribution is represented by a cumulative distribution. In the present invention, the volume median diameter refers to the value measured by a laser diffraction / scattering type particle size distribution measuring device.

[0017] [Step (1)] (1) A step of obtaining a microscopic image of the powder having a luminance distribution and a resolution, wherein when each pixel constituting the microscopic image is displayed with a luminance value of 0 to 255, the luminance distribution satisfies and and a step of obtaining a microscopic image so that the resolution satisfies .

[0018] When acquiring images using a SEM as a microscope in the above process, it is preferable to adjust the brightness distribution by selecting the energy of the signal electrons to be detected, the acceleration voltage, and the irradiation current, and it is also preferable to adjust the resolution by selecting the observation magnification, the number of pixels, and the scan time.

[0019] Let G be the set of q image data obtained in the above process, and let Gr be each image that is an element of the set. However, 1 ≤ r ≤ q, and the same applies hereafter. In this invention, the diameter of the convex portion is defined as follows: If the convex portion is formed of sub-particles having a particle size smaller than that of the powder, the particle size of the sub-particles is defined as the diameter of the convex portion.

[0020] Furthermore, as shown in Figures 4 and 5, if the convex portion is shaped as a protrusion from the powder, the boundary between the space and the convex portion is recognized by a circular arc, the boundary between the particle and the convex portion is recognized by an elliptical arc, the convex portion is detected by a closed curve formed by the combination of these, and the diameter of the circular arc (the major axis of the elliptical arc) is taken as the diameter of the convex portion.

[0021] Regarding the luminance distribution, it refers to the luminance distribution when displayed with luminance values ​​between 0 and 255. If the frequency of luminance values ​​around 0 or 255 is extremely high, it means that a certain area of ​​the image is black or white, which is almost always due to the measurement conditions. Since areas around luminance values ​​of 0 or 255 are difficult to analyze, it is preferable that the frequency of luminance values ​​around 0 or 255 be low. As an example of observation conditions that satisfy the above, when acquiring an image using an SEM, a backscattered electron image with an acceleration voltage of about 1 to 5 kV can be mentioned. However, the above conditions do not limit the observation conditions in this invention.

[0022] When acquiring images using a SEM, the main reason why the brightness of certain areas in the image becomes high, around 255, is the edge effect that occurs when observing the SEM as a secondary electron image. In SEM observation, when incident electrons are irradiated onto the object being observed, the amount of secondary electrons emitted increases at the slanted parts and edges of the object, resulting in high brightness values ​​at the slanted parts and edges of the object in the secondary electron image. On the other hand, since the backscattered electron emission rate of a backscattered electron image depends on the average atomic number of the sample, the image contrast is less affected by the slanted parts and edges of the sample and more affected by the atomic number of the sample. Therefore, the phenomenon of the slanted parts and edges of the object appearing white due to the edge effect, which was a problem with secondary electron images, is resolved. In addition, if the particles and convex parts are different materials, the peaks of their respective brightness values ​​are easier to separate, which has the advantage of facilitating the binarization process performed in subsequent steps.

[0023] Regarding the resolution of the microscope, when acquiring images using a SEM, it is preferable to adjust the observation magnification, number of pixels, and scan time so that one pixel is 3% or less of the particle size of the smallest particle constituting the composite particle. Regarding the particle area ratio, it is preferable that the total projected area of ​​the particles to be analyzed is 20% or more of the total area of ​​the analysis image, and it is also preferable to have a model that can divide and photograph a selected range and stitch the images together. Furthermore, it is preferable that the acquired image contains 200 or more particles.

[0024] [Step (2)] (2) A step to create the following image analysis models (hereinafter referred to as pseudo-binarization models) (A) and (B) based on the results obtained by machine learning, which convert the brightness distribution of the microscope image obtained in step (1) into a distribution with peaks at brightness values ​​of 0 and 255. (A) A pseudo-binarization model that detects particles based on the results of machine learning using a sample image in which particles have been binarized. (B) A pseudo-binarization model that detects convex parts based on the results of machine learning using a sample image in which convex parts have been binarized.

[0025] From the images obtained in (1), sample images necessary for machine learning to create a pseudo-binarization model using machine learning are prepared. Since the machine learning pseudo-binarization detection model will create two models: one for pseudo-binarization detection of particles and another for pseudo-binarization detection of convex areas, the sample images used for training will also be binarized images of particles and convex areas, respectively. The sample images may be obtained by binarizing several images from the images obtained in (1), or by binarizing images of a specific range extracted from several images. There are no restrictions on the size, number of images, or the number of particles and convex areas contained in the images. There are no specific requirements for the binarization method when preparing the sample images, but it is preferable to manually select the area to be binarized using a stylus or mouse and then binarize it. Specifically, one method is to extract a part of the microscope image, fill in the area to be detected, and then binarize it. Machine learning is performed using the prepared binarized images of particles and convex areas to create pseudo-binarization models of particles and convex areas, respectively. Deep learning is preferred as the machine learning method, and among them, convolutional neural networks are preferred. In this invention, an example is shown in which a binarization model was created using machine learning with the image analysis software MIPAR, but the conditions for machine learning and the software used are not particularly limited. Once a model is created, it can be used to analyze other samples using the same material.

[0026] The number of sample images is preferably 2 to 1,000, and more preferably 4 to 100. These images are used as a sample image set for machine learning. The number of particles in the image set is preferably 5 to 3,000, and more preferably 10 to 300. The number of convex parts in the image set is preferably 10 to 10,000, and more preferably 100 to 1,000.

[0027] [Step (3)] (3) A step in which the two pseudo-binarization models created in step (2) are applied to the microscope image obtained in step (1) to independently and completely binarize and detect particles containing noise and convex parts containing noise. Step (3) is a step in which the microscope image obtained in (1) is transformed so that the brightness distribution has peaks at brightness values ​​of 0 and 255 by applying each pseudo-binarization model, and particles containing noise and convex parts containing noise are detected by selecting the optimal threshold and completely binarizing the image. The mapping corresponding to the pseudo-binarization model for detecting particles created in (2) is denoted as pm, the mapping corresponding to the pseudo-binarization model for detecting convex parts is denoted as pc, and the binarization process is denoted as mapping b. These transformation processes are combined with the element Gr of the image set G obtained in (1) to obtain the element Xr of the set X of "particles containing noise" and the element Yr of the set Y of "convex parts containing noise". If the mapping transformation is represented by ○, it can be expressed by the following mapping transformation formula.

[0028] In pseudo-binarization detection using machine learning, if there are areas where machine learning has difficulty making a detection decision, the brightness values ​​will not be completely classified as black (0) or white (255), but rather the brightness distribution will have peaks at brightness values ​​of 0 and 255. In that case, it is necessary to set a threshold and completely binarize the data. The method of selecting the threshold is not specified, but Otsu's binarization method is preferred, which sets a threshold that minimizes the mean variance of the distribution with a peak at brightness value 0 and the distribution with a peak at brightness value 255, and maximizes the separation of the two peaks (Nobuyuki Otsu (1979). "A threshold selection method from gray-level histograms". IEEE Trans. Sys. Man. Cyber. 9 (1): 62-66. doi: 10.1109 / TSMC. 1979. 4310076).

[0029] [Step (4)] (4) A step of performing image processing to remove extraneous noise from the binarized image detected in step (3). The method is not particularly limited, but specific examples are shown below. A step of removing extraneous noise from the set of "particles containing noise" X by the image processing described in (4)-1-1 to (4)-1-4 below, and a step of removing extraneous noise from the set of "protrusions containing noise" Y by the image processing described in (4)-2-1 to (4)-2-3 below.

[0030] (4)-1-1 Let the mapping e1 be the erosion process that reduces the number of valid pixels. Let the mapping s1 be the transformation process that temporarily deletes the detected area below a specified number of pixels. Combine these transformation processes on the image set element Xr (∈X), and It separates into two parts.

[0031] The purpose of processing by e1 is to remove small noises and to separate noise that is coupled to the detected area. The number of pixels specified in e1 should preferably be about 2 / 3 of the diameter of the protrusion, so as to be able to eliminate the protrusion and not too large. Since Erosis removes the specified number of pixels from the edge of the detected area, circles with a diameter twice the specified number of pixels or squares with sides twice the specified number of pixels or smaller will be removed. This removes small noises and separates noise that is coupled to the detected area.

[0032] The purpose of processing in s1 is to separate the detection image, which has been reduced in size by e1, into "reduced particles (large)" and "reduced particles (small)" + "reduced noise". It is preferable to specify an area equivalent to a circle with a diameter of about 1 / 3 of the smallest particle size of the base material as the area specified in s1.

[0033] (4)-1-2 Let the separation transformation process using Watershed's algorithm be mapped as w1. Let the transformation process that removes the detected area below a valid pixel, which is specified independently of s1, be mapped as s2. Separated by (4)-1-1, By combining these conversion processes, and, It separates into two parts.

[0034] The purpose of w1 is to separate the portion in the image where the "small reduction particles" and "reduction noise" are connected. The purpose of s2 is to separate the "small reduction particles" and "reduction noise" separately. It is preferable to specify an area in s2 that is equivalent to a circle with a diameter of about 2 / 3 of the diameter of the circle with the area specified in s1.

[0035] (4)-1-3 Separated and, Integrating and Create the following. The dilation transformation (DLA) with the same number of pixels as the reduction transformation (e1) is defined as the mapping d1. By performing the expansion transformation process d1, The result is obtained. The purpose of d1 is to restore the "reduced particle (large)" + "reduced particle (small)" that were reduced by the reduction process e1 performed to separate the particles and noise back to their original size.

[0036] (4)-1-4 Let the dilation process d1 be mapped to a map d2, which is a dilation process with a number of pixels greater than the number of pixels specified in the dilation process d1. Let the erosion process e2 be mapped to a map d2, which is a reduction process with the same number of pixels as the number of pixels specified in the dilation process d2. (4)-1-3 obtained By combining these transformation processes, undetected areas within the particles are reconstructed. To obtain.

[0037] The closing process involves performing a reduction transformation for the same number of pixels following the expansion transformation to restore undetected areas within the particle (fill in defects).

[0038] (4)-2-1 Let map e3 be a reduction transformation process (Erosion) of a valid number of pixels, specified independently of maps e1 and e2. Let map s3 be a transformation process that temporarily deletes detected areas smaller than or equal to a valid pixel, specified independently of maps s1 and s2. Then, combine these transformation processes on the image set element Yr (∈Y), and, It separates into two parts.

[0039] e3 aims to remove small noises and separate the noises connected to the convex part detection area. The number of pixels specified by e3 is preferably a value that does not eliminate the convex part and reduces the diameter of the detected convex part to about 2 / 3. s3 aims to remove the noises that were separated from the convex part detection area by e3 but have not yet been removed. The area specified by s3 is preferably specified as about 2 / 3 of the area of one particle of the reduced convex part so that the reduced convex part by e3 does not disappear. Here, by performing the reduction conversion process first, the specified area can be made smaller, and it is not necessary to eliminate what is not intended to be eliminated.

[0040] (4)-2-2 Let the dilation process with the same number of pixels as the number of pixels specified by the reduction conversion process e3 be the mapping d3. Separated by (4)-2-1 By performing the dilation process (mapping) d3 on, is obtained. d3 aims to restore the convex part reduced by the reduction conversion process e3 performed to separate and remove noises from the convex part detection image to its original size.

[0041] (4)-2-3 Let the set of "particles" obtained by (4)-1-4 be M, and of the set M be M r and denote it as M r is t r rows, u r columns of pixel arrays, and the minimum unit element constituting M r be Mr tu and denote it as Mr. Mr tu is t r rows, u r columns, which means the pixel at the t-th row and u-th column in the image Mr consisting of pixel arrays. However, assume 1 ≤ r ≤ q, 1 ≤ t ≤ tr, 1 ≤ u ≤ ur, and the same applies hereinafter. The relationship between the set and the element is shown in Figure 2. Let the set of "convex parts" obtained by (4)-2-2 be B, and of the set B be B r and denote it as B r is t r rows, u r columns of pixel arrays, and the minimum unit element constituting B r be Br tu and denote it as Br.tu t r row, u r This refers to the pixel in the tth row and uth column of the image Br, which consists of an array of pixels in a column. The set C of "convex parts on particles" and its image set Cr are derived from sets M and B, and are the smallest unit elements of that set. tu We obtain (∈C). However, Mr tu , Br tu In this case, if elements determined to be detected are assigned a value of 1, and elements not determined to be detected are assigned a value of 0, then the smallest unit element of the image set is Cr tu teeth Figure 3 shows a conceptual diagram of acquiring aggregate C using the above process. Since the convex detection image after d3 processing also detects convexities that do not exist on the particles, by extracting the common detection portion of the particle detection image and the convex detection image, only the convexities on the particles necessary for calculating the coverage rate are detected.

[0042] [Step (5)] (5) A step of calculating the coverage rate, which indicates the proportion of the particles covered by the convex portion, from the image processed in step (4), wherein the total area of ​​the "particles" is S M Let S be the total area of ​​the "protrusions on the particle surface". C The proportion of the particles covered by the protrusions (coverage rate) is defined as C. R In this case, the coverage C is given by the following formula (X1). R The process of calculating.

[0043] Specifically, the total area of ​​the image set "particles" and the total area of ​​the image set "convex parts on particles" are calculated from the images, and the total area of ​​the image set "particles" is S M The total area of ​​the image set "convex parts on particles" is S C That's what I decided.

[0044] Measurable coverage C R This is not particularly limited, and 0 < C R It can measure in the range of ≤100, and 5 ≤ C R The range ≤95 is also acceptable, or 10 ≤ C R The range ≤90 is also acceptable.

[0045] In the method for analyzing surface shape from the coverage rate of the convex portion on the particle surface of the present invention, the obtained "coverage rate CR The statistical validity of " can be confirmed by the following method [Step (6)]. [Step (6)] (6) A step in which the statistical validity of the coverage rate is evaluated by the following formula (X5) based on the following formulas (X2) to (X4) using the microscope images and "particle" detection images obtained in Steps (1) to (4) above, and the "protrusions on the particles" detection images. Let U be a set of n unit images of the acquired microscope images, and rearrange the elements of the set randomly, so that the i-th image is U(i) (i = 1, 2, ..., n). The image in which "particles" are detected from image U(i) is U M (i) Image U(i) in which "protrusions on the particle" were detected. C (i) Let S be the area of ​​the detected "particle". M (i) The area of ​​the "convex part on the particle" is S C (i) Based on the coverage formula, the cumulative coverage C up to the jth sheet is R (j) This is defined as C. R To evaluate the sample size such that (j) fluctuates within a valid error range, the starting sample size for convergence determination is set to α (<n), and the coverage C R Let ε be the effective error. At j satisfying α ≤ j ≤ n (X3), the average coverage of that interval C' R Defined below, Coverage C R For the effective error ε, C R (j) The statistical validity of the coverage rate is evaluated by confirming that the above condition (X5) is satisfied. R The statistical validity of the formula is evaluated. Preferably, the unit image used is the image before image stitching, obtained by dividing and photographing a specified area with a microscope. Furthermore, by requiring that equation (X5) satisfies ε ≤ 5, more preferably ε ≤ 2.5, and evaluating the statistical validity of the coverage rate, a more accurate formula can be selected.

[0046] The present invention provides a method for determining the coverage rate of the protruding portions, specifically a method for determining the coverage rate of the protruding portions on the particle surface. Furthermore, it may also be possible to analyze properties and characteristics. According to the analytical method of the present invention, the scope of analysis is significantly broadened, and efficient calculation of surface coverage rate supported by statistics becomes possible. Such an analytical method is also effective for evaluating the properties and characteristics of powders in fields such as cosmetics, food, pharmaceuticals, electrical and electronic materials, and paints.

[0047] The present invention will be described in more detail below with reference to examples, but the present invention is not limited to these. In this example, the coverage rate of a powder in which silica (protrusions) is attached to titanium mica (particles) was determined by the following steps (1) to (5). The scheme of this analysis is shown in Figure 1. (1) Step of acquiring an SEM image of the powder having brightness distribution, resolution and particle area ratio Conductive carbon double-sided tape was attached to the SEM sample stage, a small amount of powder was taken with the tip of a cosmetic brush and attached to the double-sided tape, and excess powder was removed by air blowing. After that, Au-Pt deposition was performed. The prepared sample stage was set in the measuring jig of the apparatus and observed under the following conditions. <Observation Conditions> Equipment used: FEI Helios NanoLab 600i Detected electrons: Backscattered electrons Acceleration voltage: 5kV Irradiation current: 0.17nA Magnification: 20,000x Pixel count: 1536 pixels × 1024 pixels Scan time: 3μs Automatic acquisition and image stitching software: FEI MAPS Automatic acquisition and image stitching conditions: 11 vertical × 11 horizontal (total 121 images) Number of stitched images acquired: 10 (converted to 10 × 121 = 1,210 images)

[0048] Wide-area observation was performed using automated imaging and image stitching software FEI's MAPS. The magnification was set to 20,000x, and 11x11 images of 1,536 pixels × 1,024 pixels (10.35 μm × 6.90 μm) were automatically observed and stitched together. Ten stitched images were acquired under these conditions. Approximately 20 to 60 powder particles could be identified in each stitched image, and it was confirmed that there were more than 200 powder particles in the 10 stitched images. An example of a stitched image acquired by SEM is shown in Figure 6, and a magnified cropped portion of the stitched image is shown in Figure 7 to illustrate the analysis flow of the present invention. Furthermore, the brightness distribution of the stitched image shown in Figure 1 is shown in Figure 8.

[0049] Regarding the brightness distribution of the image in Figure 1 obtained under the above conditions, and The following conditions are met. Regarding resolution, 1 pixel = 6.7 nm, the diameter of the smallest protrusion on the powder surface = 300 nm, and (diameter of the smallest protrusion on the powder surface) × 3 / 100 = 9 nm, It satisfies the condition.

[0050] (2) A step to create two types of pseudo-binarization models that convert the brightness distribution of the SEM image obtained in step (1) into a distribution with peaks at brightness values ​​of 0 and 255, based on the results obtained by machine learning. (A) A pseudo-binarization model for detecting particles was created using the following procedure, based on the results of machine learning using a sample image set in which particles were binarized. Four images of approximately 3,000 pixels × 3,000 pixels (20.22 μm × 20.22 μm, including 2 or 3 particles) were cut out from the image obtained in (1), and the particles were manually filled in using a stylus to prepare binarized images for training. Deep learning (CNN: Convolutional Neural Network) was performed using the images before and after binarization to create a pseudo-binarization model for detecting particles. The corresponding mapping was p m (B) A pseudo-binarization model for detecting convex areas was created using the following procedure, based on the results of machine learning with a sample image set in which the convex areas were binarized.

[0051] (1) From the image obtained in (1), a 500 pixels x 500 pixels (3.37 μm x 3.37 μm, 1 μm) 2Six images were extracted (each image having approximately 6 convex areas, and about 70 convex areas in total). Using a stylus, only the convex areas were manually filled in to prepare binarized images for training. Using the images before and after binarization, deep learning (CNN: Convolutional Neural Network) was performed to create a pseudo-binarization model that detects convex areas. The corresponding mapping was p c The image analysis software MIPAR was used to create the pseudo-binarization model.

[0052] (3) Steps to independently and completely binarize and detect particles containing noise and protrusions containing noise by applying the two pseudo-binarization models created in step (2) to the SEM image obtained in step (1). - Particle detection step containing noise The pseudo-binarization model for particle detection created in (2) was applied to the SEM image acquired in (1), and "particles containing noise" were detected by binarization by Otsu's binarization. An enlarged image after detection is shown in Figure 9. - Protrusion detection step containing noise The pseudo-binarization model for protrusion detection created in (2) was applied to the SEM image acquired in (1), and "particles containing noise" were detected by binarization by Otsu's binarization. An enlarged image after detection is shown in Figure 10.

[0053] (4) Image processing to remove extra noise from the binarized image detected in step (3) Extra noise was removed from the "particles containing noise" in the following procedure: (4)-1-1 A 30-pixel reduction transformation e1 was performed on the 10 "particles containing noise" detection images obtained in step (3) above. Subsequently, a transformation process s1 was performed to delete the detection area of ​​200,000 square pixels or less, thereby separating the images into "reduced particles (large)" and "reduced particles (small)" + "reduced noise".

[0054] (4)-1-2 The "small reduced particles" + "reduced noise" obtained above were subjected to a separation and transformation process w1 using Watershed's algorithm. Subsequently, a transformation process s2 was applied to delete detection areas with an area of ​​80,000 square pixels or less, thereby separating them into "small reduced particles" and "reduced noise 1".

[0055] (4)-1-3 The separated "Reduced Particle (Large)" and "Reduced Particle (Small)" were combined to obtain "Reduced Particle (Large)" + "Reduced Particle (Small)". Subsequently, by performing the expansion transformation process d1 at 30 pixels as specified in the reduction transformation process e1, "Particle (Large)" + "Particle (Small)" were obtained.

[0056] (4)-1-4 The "large particle" + "small particle" obtained above is subjected to an expansion transformation d2 at 50 pixels, which is larger than the 30 pixels specified in the expansion transformation d1, followed by a reduction transformation e2 at the same 50 pixels. This restores the undetected parts within the particle and obtains a "particle". Thus, by performing image processing on the "particle containing noise" detection image, a noise-free "particle" detection image (Figure 11) is obtained.

[0057] Extraneous noise was removed from the "noisy protrusions" using the following procedure: (4)-2-1 Ten images of the "noisy protrusions" detected in (3) above were subjected to a 7-pixel reduction transformation process e3. Subsequently, a transformation process s3 was performed to delete detection areas of 50 square pixels or less, separating them into "reduced protrusions" and "reduced noise 2". (4)-2-2 The "reduced protrusions" obtained above were subjected to an expansion transformation process d3 of 7 pixels as specified in the reduction transformation process e3 to obtain "protrusions". (4)-2-3 "Protrusions on particles" were obtained, consisting of the common detection portion of the "particles" obtained in (4)-1-4 and the "protrusions" obtained in (4)-2-2. As a result, by performing image processing on the "noisy protrusions" detection images, a noise-free "protrusion on particle" detection image (Figure 12) was obtained.

[0058] (5) A step to calculate the coverage rate, which indicates the proportion of the particle covered by the protrusions, from the noise-removed detection image processed in step (4) above. The total area of ​​the image set "particle" consisting of the 10 noise-removed detection images obtained above is S M The total area of ​​the image set "convex parts on particles" is S C The following formula was used to calculate the percentage of the particles covered by the protrusions (coverage rate) of 49.8%. Note that the volume median diameter (D) of the powder was used. 50 The diameter was 23.4 μm.

[0059] (6) A step to evaluate the statistical validity of the coverage rate using the SEM images and "particle" detection images and "protrusions on particles" detection images obtained in steps (1) and (5) above. A set of 1,210 unit images of the acquired SEM images is called U, and the elements of the set are randomly rearranged, and the i-th image is called U(i) (i = 1, 2, ..., 1210). Based on the coverage rate formula, the cumulative coverage rate C up to the j-th image is calculated. R (j) This was defined as C. R To evaluate the sample size for which (j) fluctuates within a valid error range, the starting sample size α for convergence determination is set to 400 (<1210), and the coverage C R The case where the effective error ε is 2.5% is shown below. For j satisfying 400 ≤ j ≤ 1210, the average coverage C' of that interval. R The following calculations were made. Furthermore, for j satisfying 400 ≤ j ≤ 1210, C R The maximum and minimum values ​​of (j) are: And, Therefore, C R (j) is Satisfying C R (j) was shown to fluctuate within a valid error range of ±2.5% (Figure 13). Therefore, in this analysis, it was determined that the evaluation of coverage rate was statistically valid within this valid error range.

[0060] [Comparative Example 1] As a comparative example of binarization analysis of SEM images using machine learning with secondary electron images, the acquisition conditions for the SEM image in step (1) of the example are changed as follows, and an example is shown where the conditions of (1) are not met. Detected electrons: Secondary electrons Acceleration voltage: 15kV An example of a stitched image acquired by SEM is shown in Figure 14, and a cropped and enlarged image of a part of the stitched image is shown in Figure 15 to explain the analysis flow of the present invention. Also, the brightness distribution of the stitched image shown in Figure 10 is shown in Figure 16. The image obtained above has a very strong peak at a brightness value of 255 in the brightness distribution, and as can be seen from Figures 10 and 11, white, bright areas are scattered throughout the image. Regarding the brightness distribution, the peak intensity ratio of the brightness value 255 is as follows, and the conditions of (1) above were not met. That is,

[0061] Therefore, the peak intensity ratio of the luminance value 255 in this comparative example 1 is as follows: It did not meet the requirement.

[0062] Figure 17 shows the particle detection image and Figure 18 shows the convexity detection image, which were obtained by performing pseudo-binarization and complete binarization on the SEM image using the same steps (2) and (3) as in the example. While the particles were detected fairly well, it was difficult to detect the white, glowing parts of the convexity. Next, noise reduction was performed on the particle detection image and the convexity detection image using the same step (4) as in the example. Figure 19 shows the particle detection image after noise reduction, and Figure 20 shows the convexity detection image. Regarding the convexity, the silica in the white, glowing parts in the original SEM image could not be detected. Because detection could not be performed with sufficient accuracy, it was not possible to calculate the coverage rate.

[0063] [Comparative Example 2] As a comparative example of the main analysis of binarization of SEM images using backscattered electron images by threshold, step (1) is performed in the same way as in the example, step (2) of the example is omitted, and in step (3) of the example, the pseudo-binarization model is not applied, and binarization using a normal threshold is applied. For the SEM concatenated image obtained in the example (Figure 1), a threshold that could best binarize the particles was searched by visual inspection, but the background was detected before the particles could be fully detected, making particle detection impossible. The binarized image with a threshold of 122 is shown in Figure 21. Similarly, a threshold that could best binarize the convex parts was searched by visual inspection, but the background and particle parts were detected before the convex parts could be fully detected, making accurate detection impossible. The binarized image with a threshold of 130 is shown in Figure 22. With binarization using thresholds, neither particles nor convex parts could be detected accurately, and the calculation of coverage could not be performed.

[0064] Table 1 below summarizes the differences between the example and Comparative Examples 1 and 2. Explanation of symbols in Table 1: ○: Same process as the example ×: Different process from the example -: The process was not performed because it could not be analyzed.

Claims

1. A method for determining the coverage of the protruding portions on the surface of a particle having two or more protrusions on the surface of a single particle, comprising the following steps (1) to (5): (1) A step of acquiring a microscopic image of the powder having a luminance distribution and resolution, wherein the luminance distribution when each pixel constituting the microscopic image is displayed with a luminance value of 0 to 255 is and, The following conditions are met, and the resolution is (1) A step to acquire a microscope image that satisfies the following conditions. (2) A step to create the following image analysis models (hereinafter referred to as pseudo-binarization models) (A) and (B) based on the results obtained by machine learning, which convert the brightness distribution of the microscope image obtained in step (1) into a distribution with peaks at brightness values ​​of 0 and 255. (A) A pseudo-binarization model that detects particles based on the results of machine learning using a sample image in which particles have been binarized. (B) A pseudo-binarization model that detects convex parts based on the results of machine learning using a sample image in which convex parts have been binarized. (3) A step to apply the two pseudo-binarization models created in step (2) to the microscope image obtained in step (1), respectively, and independently and completely binarize and detect particles containing noise and convex parts containing noise. (4) A step to perform image processing to remove extraneous noise from the binarized image detected in step (3). (5) A step of obtaining the total area of ​​the particles and the total area of ​​the protrusions on the surface of the particles from the image processed in step (4), and calculating the coverage rate which indicates the proportion that the protrusions cover the particles, wherein the total area of ​​the "particles" is S M Let S be the total area of ​​the "protrusions on the particle surface". C The proportion of the particles covered by the protrusions (coverage rate) is defined as C. R In this case, the coverage C is given by the following formula (X1). R The process of calculating.

2. A method for determining the coverage of a convex portion according to claim 1, wherein the brightness distribution is adjusted by selecting the energy of the signal electrons to be detected, the acceleration voltage, and the irradiation current when acquiring an image using a scanning electron microscope as the microscope in step (1).

3. A method for determining the coverage of a convex portion according to claim 1, wherein the resolution is adjusted by selecting the observation magnification, the number of pixels, and the scan time when acquiring an image using a scanning electron microscope as the microscope in step (1).

4. A method for determining the coverage of a convex portion according to claim 1, wherein in step (2) above, the sample image is obtained by cutting out a part of a microscope image, filling in the area to be detected, and binarizing it.

5. The method for determining the coverage of a convex portion according to claim 1, wherein the machine learning method in step (2) is a convolutional neural network.

6. The method for determining the coverage of a convex portion according to claim 1, wherein in step (3) above, when completely binarizing the image after applying the pseudo-binarization model, a method is used to select a threshold such that the mean variance of the distribution having a peak at a brightness value of 0 and the distribution having a peak at a brightness value of 255 is minimized and the degree of separation is maximized.

7. A method for determining the coverage rate of a protruding portion according to claim 1, wherein the protruding portion of the powder is formed by being raised from the particles.

8. A method for determining the coverage of a protruding portion according to claim 1, wherein the protruding portion of the powder is a sub-particle having an average particle diameter of 0.01 to 50% of the average particle diameter of the main particle.

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