WO2018042752A1

WO2018042752A1 - Signal analysis device, signal analysis method, computer program, measurement device, and measurement method

Info

Publication number: WO2018042752A1
Application number: PCT/JP2017/016050
Authority: WO
Inventors: 浩行越川
Original assignee: 株式会社堀場製作所
Priority date: 2016-08-31
Filing date: 2017-04-21
Publication date: 2018-03-08
Also published as: JPWO2018042752A1; JP6949034B2

Abstract

Provided are a signal analysis device, signal analysis method, computer program, measurement device, and measurement method for carrying out cluster analysis so as to make it possible to acquire a distribution that has conventionally been difficult to acquire from a spectral distribution. In the present invention, a signal analysis device generates n-dimensional coordinate points defined through the combination of the intensities of n specific signals included in a spectrum; determines a plurality of initial cluster values on an n-dimensional space for the purpose of classifying the plurality of n-dimensional coordinate points; and carries out analysis using the determined initial cluster values. When determining the initial cluster values, the signal analysis device generates an initial cluster value that includes a point on the n-dimensional space that consists of a combination of the representative values for the intensities of the n specific signals and generates initial cluster values that each include an n-dimensional coordinate point where the intensity of one specific signal has deviated from a prescribed standard.

Description

Signal analysis apparatus, signal analysis method, computer program, measurement apparatus, and measurement method

The present invention relates to a signal analysis device, a signal analysis method and a computer program for obtaining a distribution of regions having different combinations of signal intensities from a spectral distribution on a coordinate system, and a measuring device for measuring and analyzing the spectral distribution, and It relates to a measurement method.

X-ray analysis is a technique for irradiating a sample with radiation such as an electron beam or X-ray, and analyzing components contained in the sample from a spectrum of characteristic X-rays generated from the sample. In particular, a spectrum distribution in which a spectrum of characteristic X-rays from each point on a sample is associated with each point on a two-dimensional coordinate system is created, and components in the sample are analyzed using the spectrum distribution. As an example of X-ray analysis using an electron beam as radiation irradiated to a sample, energy dispersive X-ray analysis (EDX: Energy Dispersive X-ray Spectroscopy) is known. As an example of X-ray analysis using X-rays as radiation irradiated to a sample, there is fluorescent X-ray analysis. Moreover, there is an analysis method that can create a spectrum distribution as an analysis method other than the X-ray analysis. For example, in Raman spectroscopic analysis, a spectrum distribution in which the spectrum of Raman light is recorded for each point on the image corresponding to each point on the sample can be created. In addition, for example, it is possible to create a spectral distribution of visible light and infrared light obtained from a sample.

Since characteristic X-rays of specific energy can be obtained from specific elements, the distribution of specific elements can be obtained by examining the signal intensity of specific energy in the spectrum at each point on the sample. Since the sample includes a plurality of elements, a distribution of a plurality of elements can be obtained from the spectral distribution. In general, a sample includes a plurality of components, and each component includes a plurality of elements. For example, when the sample is a rock, the rock is composed of a plurality of mineral components, and each mineral component contains a plurality of elements. Since the same element may be contained even if the components are different, the distribution of the components in the sample and the distribution of the elements generally do not match.

Patent Document 1 discloses a method for obtaining a distribution of components in a sample based on a combination of intensities of a plurality of signals included in a spectrum. In this method, an n-dimensional coordinate point group in which n-dimensional data defined by a combination of n signal intensities is defined for a plurality of points on two-dimensional coordinates is generated, and the n-dimensional coordinate points are classified into a plurality of clusters. Perform cluster analysis. In the cluster analysis, a plurality of clusters are obtained by using an EM (Expectation-maximization) method so that a probability distribution in which n-dimensional coordinate points are included in each cluster is appropriate. After performing the cluster analysis, a distribution of regions corresponding to each cluster is generated. The generated distribution corresponds to a distribution of components including a plurality of elements.

International Publication No. 2013/027553

In order to perform an appropriate cluster analysis by the method disclosed in Patent Document 1, it is necessary to appropriately determine the initial value of the cluster. In the conventional method for determining the initial value of the cluster, first, a cluster composed of an average value of a plurality of signal strengths is set, and a new cluster including an n-dimensional coordinate point having the lowest probability of being included in the set cluster is determined. Set up and repeat the cluster setup to the required number. In such a method, it is easy to set a cluster composed of n-dimensional coordinate points that are out of average for many signals. On the other hand, for an n-dimensional coordinate point where the intensity of a small number of signals deviates greatly from the average value and the intensity of many signals is close to the average value, a cluster composed of the n-dimensional coordinate points is difficult to set. It is likely to be included in the same cluster as the n-dimensional coordinate point. When the initial value of the cluster is determined in this manner and the cluster analysis is performed, it is difficult to obtain a cluster composed of n-dimensional coordinate points in which the intensity of a small number of signals deviates greatly from the average value. For this reason, it is difficult to obtain a distribution of a region where the intensity of a small number of signals deviates from the average value. For example, it is difficult to obtain a distribution of components that exist only in a minute region in a sample.

The present invention has been made in view of such circumstances, and an object of the present invention is to provide a signal for performing cluster analysis so as to enable acquisition of a distribution that has been difficult to acquire from a spectrum distribution in the past. An analysis apparatus, a signal analysis method, a computer program, a measurement apparatus, and a measurement method are provided.

The signal analysis apparatus according to the present invention is based on a spectrum distribution in which a spectrum is determined for each point on the coordinate system, and n (n is an integer of 2 or more) included in the spectrum for each point in the spectrum distribution. An n-dimensional coordinate point group generation unit that generates an n-dimensional coordinate point on an n-dimensional space defined by a combination of specific signal intensities, and an n-dimensional space on the n-dimensional space for classifying the generated multiple n-dimensional coordinate points In the signal analyzer including an initial setting unit that determines initial values of a plurality of clusters, and a cluster analysis unit that performs cluster analysis using the determined initial values, the initial setting unit includes the intensity of the n specific signals. A first initial cluster generation unit that generates an initial value of a cluster including a point in an n-dimensional space that is a combination of representative values, and an n-dimensional coordinate point in which the intensity of one specific signal deviates from a predetermined reference And having a second initial cluster generator for generating an initial value of Murrell cluster.

In the signal analysis device according to the present invention, the initial setting unit includes a cluster number setting unit that determines the number of a plurality of clusters, and an n-dimensional coordinate point that has the lowest probability of being included in a cluster for which an initial value has already been set. A third initial cluster generating unit that generates an initial value of the cluster to be generated, and a repeating unit that repeats the processing of the third initial cluster generating unit until initial values of the number of clusters determined by the cluster number setting unit are determined. Furthermore, it is characterized by having.

The signal analysis apparatus according to the present invention specifies the distribution in the spectrum distribution of the points corresponding to the n-dimensional coordinate points included in each cluster after the cluster analysis, so that the combination of the strengths of the n specific signals can be obtained. An area distribution generation unit that generates distributions of different types of areas is further provided.

In the signal analysis device according to the present invention, the intensity of the n specific signals indicates a concentration of n elements, and the region distribution generation unit includes a plurality of types of regions having different combinations of n element concentrations. A distribution is generated.

The signal analysis method according to the present invention is based on a spectrum distribution in which a spectrum is determined for each point on a coordinate system by a computer including a calculation unit and a storage unit, and n included in the spectrum for each point in the spectrum distribution. Generating n-dimensional coordinate points on an n-dimensional space defined by a combination of intensities of specific signals (n is an integer of 2 or more), and classifying a plurality of generated n-dimensional coordinate points, n In the signal processing method of performing an initial setting step for determining initial values of a plurality of clusters in a dimensional space and a step of performing cluster analysis using the determined initial values, the initial setting step includes the steps of: A step of generating an initial value of a cluster including a point on an n-dimensional space composed of a combination of representative values of intensity, and the intensity of one specific signal deviates from a predetermined reference Characterized in that it comprises the steps of generating an initial value of clusters included in that n-dimensional coordinate point.

In the signal analysis method according to the present invention, the initial setting step includes a step of determining the number of a plurality of clusters, and a cluster including an n-dimensional coordinate point having the lowest likelihood included in a cluster for which an initial value has already been set. A generating step of generating the initial value of the first and second steps, and repeating the generating step until initial values of a predetermined number of clusters are determined.

In the signal analysis method according to the present invention, by specifying the distribution in the spectrum distribution of the points corresponding to the n-dimensional coordinate points included in each cluster after the cluster analysis, the combination of the strengths of the n specific signals is obtained. The step of generating a distribution of different types of regions is further performed.

The computer program according to the present invention allows a computer to have n (n is an integer of 2 or more) included in a spectrum for each point in the spectrum distribution based on a spectrum distribution in which the spectrum is determined for each point on the coordinate system. ) Generating an n-dimensional coordinate point on the n-dimensional space defined by the combination of specific signal intensities, and classifying the plurality of generated n-dimensional coordinate points to a plurality of clusters on the n-dimensional space. In a computer program for executing processing including an initial setting step for determining an initial value and a step of performing cluster analysis using the determined initial value, the initial setting step includes a representative value of the intensity of the n specific signals. A step of generating an initial value of a cluster including a point on the n-dimensional space formed by the combination, and the intensity of one specific signal is a predetermined reference n-dimensional coordinate point is out of, characterized in that it comprises the steps of generating an initial value of the cluster that contains the.

In the computer program according to the present invention, the initial setting step includes a step of determining the number of a plurality of clusters and a cluster including an n-dimensional coordinate point having the lowest likelihood included in a cluster in which an initial value has already been set. The method further includes a generation step of generating an initial value, and a step of repeating the generation step until initial values of a predetermined number of clusters are determined.

A measuring apparatus according to the present invention includes a measuring unit that measures radiation or electromagnetic waves obtained from each point on a sample, a spectrum distribution generating unit that generates a spectral distribution in which the measured radiation or electromagnetic wave spectrum is associated with each point, and A measurement apparatus comprising: a signal analysis apparatus according to the present invention.

The measurement method according to the present invention includes a signal analysis method according to the present invention in a measurement method for measuring a spectrum obtained from each point on a sample and generating a spectrum distribution in which the measured spectrum is associated with each point. It is characterized by.

In the present invention, for each point included in the spectrum distribution, an n-dimensional coordinate point in an n-dimensional space defined by a combination of n specific signal intensities is generated, and cluster analysis of the n-dimensional coordinate point is performed. When setting an initial value of a cluster for cluster analysis, an initial value of a cluster including points on an n-dimensional space composed of combinations of representative values of n specific signals is generated. An initial value of a cluster including an n-dimensional coordinate point where the intensity of one specific signal deviates from a predetermined reference is generated. By doing so, the intensity of single or a small number of signals deviates from the representative value, and the initial value of the cluster composed of the n-dimensional coordinate point group in which the intensity of other signals is close to the representative value is easily set.

In the present invention, when setting the initial value of the cluster, the initial value of the cluster including the n-dimensional coordinate point having the lowest probability of being included in the existing cluster is further set. As a result, the initial value is set without leaking the cluster which has been able to set the initial value by the conventional method.

In the present invention, by specifying the distribution in the spectrum distribution of the points corresponding to the n-dimensional coordinate points included in each cluster after the cluster analysis, the combination of the intensities of a plurality of specific signals included in the spectrum is obtained. A distribution of different types of regions is generated. Since the cluster analysis is performed after determining the initial value of the cluster including the n-dimensional coordinate point in which the intensity of one specific signal deviates from a predetermined reference, the region where the intensity of a small number of specific signals deviates from the representative value Distribution is obtained.

Further, in the present invention, the intensity of the specific signal indicates the concentration of the element contained in the sample, and the distribution of a plurality of types of components having different concentrations of the element in the sample is generated by generating a distribution of a plurality of types of regions. Is generated. According to the present invention, a distribution of components in which the concentration of a small number of elements deviates from the representative value can be obtained.

In the present invention, n-dimensional coordinate points can be appropriately classified by cluster analysis by appropriately setting the initial value of the cluster. Therefore, the present invention has an excellent effect such that it is possible to generate a distribution in a region where the intensity of a small number of specific signals deviates from the representative value from the spectrum distribution.

It is a block diagram which shows the structure of a measuring apparatus. It is a block diagram which shows the structure of a signal analyzer. It is a typical characteristic figure showing an example of a spectrum. It is a flowchart which shows the procedure of the process which a signal analyzer performs. It is a flowchart which shows the procedure of the process which a signal analyzer performs. It is an example of the scatter diagram which plotted the n-dimensional coordinate point on the n-dimensional coordinate. It is a graph which shows the example of the initial value of a cluster, and an n-dimensional coordinate point. It is a schematic diagram which shows the example of distribution of several types of area | region from which the combination of the intensity | strength of a specific signal differs. It is a schematic diagram which shows the example of distribution of several types of area | region from which the combination of the intensity | strength of a specific signal differs. It is a schematic diagram which shows the example of distribution of several types of area | region from which the combination of the intensity | strength of a specific signal differs. It is a schematic diagram which shows the example of distribution of several types of area | region from which the combination of the intensity | strength of a specific signal differs.

Hereinafter, the present invention will be specifically described with reference to the drawings showing embodiments thereof.
FIG. 1 is a block diagram showing the configuration of the measuring apparatus. The measurement apparatus is an EDX apparatus that irradiates the sample 3 with an electron beam, measures characteristic X-rays from the sample 3, and generates a spectrum distribution in which the spectrum of the characteristic X-ray is associated with each point on the sample 3. The measurement apparatus includes an electron gun 11 that irradiates the sample 3 with an electron beam, an electron lens system 12, a sample stage 13 on which the sample 3 is placed, and a detection unit 14 that detects characteristic X-rays generated from the sample 3. It has. The electron lens system 12 includes a scanning coil that changes the direction of the electron beam. The electron gun 11 and the electron lens system 12 are connected to the control unit 16.

In accordance with a control signal from the control unit 16, the electron gun 11 emits an electron beam, the electron lens system 12 determines the direction of the electron beam, and the electron beam is irradiated onto the sample 3 on the X sample stage 13. A characteristic X-ray is generated in the portion irradiated with the electron beam on the sample 3. The characteristic X-ray is detected by the detection unit 14. In FIG. 1, the electron beam is indicated by a solid line arrow, and the characteristic X-ray is indicated by a broken line arrow. The detection unit 14 outputs a signal proportional to the detected characteristic X-ray energy. The electron gun 11, the electron lens system 12, and the detection unit 14 correspond to a measurement unit.

The detection unit 14 is connected to a signal processing unit 15 that processes the output signal. The signal processing unit 15 receives the signal output from the detection unit 14, counts the signal by value, and obtains a characteristic X-ray spectrum in which the characteristic X-ray energy indicated by the signal value is associated with the count number. The count number associated with a certain energy is the intensity of characteristic X-rays having that energy. The signal processing unit 15 is connected to the control unit 16. As the electron lens system 12 sequentially changes the direction of the electron beam, the electron beam scans the sample 3. As the electron beam scans the sample 3, the electron beam is sequentially irradiated to each portion in the scanning region on the sample 3. As the electron beam scans the sample 3, characteristic X-rays generated from the portion irradiated with the electron beam on the sample 3 are sequentially detected by the detection unit 14. The signal processing unit 15 sequentially generates signal spectra of characteristic X-rays generated at a plurality of portions irradiated with the electron beam on the sample 3 by sequentially performing signal processing. The signal processing unit 15 sequentially outputs the generated characteristic X-ray spectrum data to the control unit 16.

The control unit 16 receives the characteristic X-ray spectrum data output from the signal processing unit 15 and stores data in which the position of the portion irradiated with the electron beam on the sample 3 is associated with the characteristic X-ray spectrum. . At the stage when the scanning of the sample 3 by the electron beam is completed, the control unit 16 associates each point on the sample 3 with the spectrum of the characteristic X-ray, so that the characteristic X-ray spectrum becomes each point on the two-dimensional coordinate system. Generate the spectral distribution associated with. The signal processing unit 15 and the control unit 16 correspond to a spectrum distribution generation unit. The control unit 16 is connected to the signal analysis device 2. The controller 16 outputs spectral distribution data to the signal analyzer 2. Note that the signal processing unit 15 and the control unit 16 may be integrally configured.

FIG. 2 is a block diagram showing the configuration of the signal analysis device 2. The signal analyzer 2 is configured using a general-purpose computer such as a personal computer (PC). The signal analysis device 2 includes a CPU (arithmetic unit) 21 that performs calculation, a RAM 22 that stores temporary information generated in accordance with the calculation, and a drive such as a CD-ROM drive that reads information from the recording medium 4 such as an optical disk. Unit 23 and a non-volatile storage unit 24. The storage unit 24 is, for example, a hard disk. The CPU 21 causes the drive unit 23 to read the computer program 41 from the recording medium 4 and stores the read computer program 41 in the storage unit 24. The CPU 21 loads the computer program 41 from the storage unit 24 to the RAM 22 as necessary, and executes processing necessary for the signal analyzer 2 according to the loaded computer program 41.

The computer program 41 may be downloaded to the signal analyzer 2 from an external server device (not shown) connected to the signal analyzer 2 via a communication network (not shown) and stored in the storage unit 24. Further, the signal analysis device 2 may be configured such that it does not receive the computer program 41 from the outside, but has recording means such as a ROM in which the computer program 41 is recorded.

The signal analyzer 2 also includes an input unit 25 such as a keyboard or a pointing device for inputting information such as various processing instructions operated by the user, and a display unit 26 such as a liquid crystal display for displaying various information. And. The signal analyzing apparatus 2 includes an interface unit 27 to which the control unit 16 is connected. The signal analyzer 2 receives the spectrum distribution data output from the control unit 16 by the interface unit 27 and stores the data in the storage unit 24.

FIG. 3 is a schematic characteristic diagram showing an example of a spectrum. In general, a spectrum is composed of a combination of a plurality of signals. The horizontal axis in FIG. 3 is energy, and the vertical axis is signal intensity at each energy. In FIG. 3, the peak of one signal included in the spectrum is indicated by an arrow. The signal contained in the spectrum is identified by energy. Each signal included in the characteristic X-ray spectrum is caused by an element included in the sample 3. The spectrum distribution measured by the measuring device is composed of spectra obtained for each point on the two-dimensional coordinate system corresponding to each point on the sample 3. Each spectrum has a different combination of intensity of signals contained therein, and has a different spectrum shape. For example, some spectra may consist of a single signal and some may have zero signal strength. The horizontal axis of the spectrum is not limited to energy, and may be wavelength or wave number. Further, the horizontal axis of the spectrum is not limited to an absolute value, and may be a relative value such as a wavelength shift from a specific wavelength.

Processing performed by the signal analyzer 2 will be described. 4 and 5 are flowcharts showing a procedure of processing performed by the signal analysis device 2. CPU21 performs the following processes according to a computer program. Spectral distribution data from the control unit 16 is received by the interface unit 27, and the CPU 21 stores the spectral distribution data in the storage unit 24 (S1). The spectrum distribution data is data in which two-dimensional coordinates of each point on the sample are associated with spectrum data obtained from each point. The spectrum data is data in which energy or the like is associated with signal intensity.

Next, the CPU 21 generates signal distribution data indicating the intensity distribution of a plurality of specific signals from the spectrum distribution data (S2). Specifically, in S2, the CPU 21 reads out the signal strength of a specific signal identified with a predetermined energy from the spectrum of each point, and associates the read signal strength with each point on the two-dimensional coordinate system. Generated signal distribution data. That is, the signal distribution data is data in which the two-dimensional coordinates of each point on the sample 3 are associated with the signal intensity at a specific energy. The storage unit 24 stores in advance a plurality of energies as specific signal energy, and the CPU 21 generates signal distribution data for each of the plurality of specific signals. That is, in S2, a plurality of signal distribution data are generated. Let n be the number of specific signals that have generated signal distribution data. n is an integer of 2 or more. The signal distribution data is stored in the storage unit 24. The energy of the specific signal may be included in the computer program 41. Further, the specific signal may be identified by a wavelength or a wave number. Further, the specific signal may be identified not from the position of the peak in the spectrum but from the signal waveform in the spectrum. Further, the CPU 21 may accept the designation of the specific signal by operating the input unit 25 by the user, and may generate signal distribution data for the designated specific signal.

Next, the CPU 21 generates n-dimensional data composed of combinations of n specific signal intensities from the signal distribution data (S3). Specifically, for each point on the two-dimensional coordinate system, the CPU 21 generates n-dimensional data defined by a combination of the strengths of n specific signals, thereby obtaining an n-dimensional coordinate point in the n-dimensional space. Generate. Further, the CPU 21 generates data in which the two-dimensional coordinates of each point on the two-dimensional coordinate system are associated with the n-dimensional data representing the n-dimensional coordinates, and stores the data in the RAM 22 or the storage unit 24.

FIG. 6 is an example of a scatter diagram in which n-dimensional coordinate points are plotted on n-dimensional coordinates. FIG. 6 shows a case where n = 2 in which signals a and b are selected as specific signals. In FIG. 6, the horizontal axis indicates the intensity of the signal a, and the vertical axis indicates the intensity of the signal b. For each point on the two-dimensional coordinate system corresponding to each point on the sample 3, n-dimensional coordinate points are plotted on the n-dimensional space. The n-dimensional coordinate points may overlap on the n-dimensional space. The process of S3 corresponds to an n-dimensional coordinate point group generation unit. Note that the signal analysis device 2 may be configured to receive n-dimensional data generated externally and execute the processing after S4.

The signal analyzing apparatus 2 performs cluster analysis that classifies a plurality of n-dimensional coordinate points into a plurality of clusters by an EM (Expectation-maximization) algorithm in S4 and subsequent steps. A cluster is defined by a probability distribution model indicating the probability that each point on the n-dimensional space is included in the cluster. As the probability distribution, a probability distribution such as a mixed Gaussian distribution or a mixed Poisson distribution used in the EM algorithm is used. Each cluster is defined by a product of n probability distribution models.

Next, the CPU 21 receives the initial value of the number of clusters by the user operating the input unit 25, and sets the initial value of the number of clusters (S4). The CPU 21 may perform a process of setting an appropriate numerical value as an initial value of the number of clusters in S4. Next, the CPU 21 generates an initial value of a probability distribution model of a cluster including points on an n-dimensional space formed by a combination of representative values of n specific signals (S5). The representative value is a value representing the intensity in the spectrum distribution for each of the n specific signals. For example, the representative value is an average value of the intensity of the specific signal at a plurality of points in the spectrum distribution. The CPU 21 calculates a representative value of intensity for each of the n specific signals, and generates initial values of the parameters of the cluster probability distribution model so that points on the n-dimensional space formed by combinations of the representative values are included. . The parameters of the probability distribution model include the center position of the cluster in the n-dimensional space. For example, the CPU 21 sets the parameters of the probability distribution model so that a point on the n-dimensional space formed by a combination of representative values of n specific signal intensities becomes the center position of the cluster. The representative value is not limited to the average value, and may be another value such as a median value, a mode value, or a specific model value. The model value is stored in advance in the storage unit 24, recorded in advance in the computer program 41, or input through the input unit 25.

Next, the CPU 21 generates an initial value of a probability distribution model of a cluster including n-dimensional coordinate points in which the intensity of one specific signal deviates from a predetermined reference (S6). For example, the signal analyzing apparatus 2 uses the representative value m of the intensity of one specific signal and the parameter α, and considers the intensity less than m + α within the reference and the intensity greater than m + α as being out of the reference. For example, the parameter α is a standard deviation value. The parameter α may be a value other than the standard deviation value, such as a predetermined value. The CPU 21 calculates the representative value m of the intensity of one specific signal and the parameter α, specifies an n-dimensional coordinate point where the intensity of the one specific signal is equal to or greater than m + α among the n-dimensional coordinate points generated in S3, An initial value of a parameter of a new cluster probability distribution model is generated so that the identified n-dimensional coordinate point is included. The form in which the intensity of m + α or more is not a standard is an example, and other standards can be used. For example, the intensity exceeding m + α may be out of the standard. Further, for example, the intensity of m-α or higher or higher may be within the standard, and the intensity of less than or less than m-α may be out of the standard. Further, for example, an intensity that is greater than or equal to a value obtained by adding a predetermined value to the representative value m may be out of the reference. Further, for example, an intensity that is greater than or equal to a predetermined value or less than or less than a predetermined value may be out of the reference. Further, for example, with β as a predetermined value, the strength of the upper β% may be out of the reference and the strength of the lower β% may be out of the reference among the intensities of one specific signal at a plurality of n-dimensional coordinate points. . In S6, for example, the parameters of the probability distribution model are set so that the position of the n-dimensional coordinate point where the intensity of one specific signal deviates from a predetermined reference becomes the center position of the cluster.

In S6, the CPU 21 may generate initial values of a probability distribution model of a plurality of clusters. For example, the CPU 21 excludes the intensity of m−α or less and the intensity of m + α or more from the reference, the cluster including the n-dimensional coordinate point where the intensity of one specific signal is m + α or more, and the intensity of one specific signal An initial value of a probability distribution model is generated for a cluster including an n-dimensional coordinate point that is less than or equal to m−α. Further, for example, the CPU 21 includes an n-dimensional coordinate point in which the intensity of one specific signal is included in m + α to m + 2α and an n-dimensional coordinate point in which the intensity of one specific signal is included in m + 2α to m + 3α in different clusters. Thus, the initial value of the probability distribution model of a plurality of clusters is generated. In addition, for example, a plurality of predetermined reference values are set, and the CPU 21 generates initial values of a probability distribution model of a plurality of clusters corresponding to the intensity of one specific signal. Further, for example, the CPU 21 includes a cluster including an n-dimensional coordinate point in which the intensity of one specific signal is included in the lower β% and an n-dimensional coordinate point in which the intensity of one specific signal is included in the upper β%. An initial value of the probability distribution model may be generated for each cluster. Further, for example, if γ is a predetermined value and β <γ, the CPU 21 determines that the intensity of one specific signal is included in the upper β%, and the intensity of one specific signal is higher β% to γ%. The initial value of the probability distribution model of a plurality of clusters may be generated so that the n-dimensional coordinate point included in is included in another cluster. Further, for example, the CPU 21 determines that the n-dimensional coordinate point where the intensity of one specific signal is included in the lower β% and the n-dimensional coordinate point where the intensity of one specific signal is included in the lower β% to γ% are different. An initial value of a probability distribution model of a plurality of clusters may be generated so as to be included in the cluster. Further, when there is no n-dimensional coordinate point whose intensity of one specific signal deviates from a predetermined reference, the CPU 21 does not need to generate an initial value of a cluster probability distribution model for this specific signal.

Next, the CPU 21 determines whether or not the process of S6 has been executed for all the specific signals (S7). If there is a specific signal that has not yet been subjected to the process of S6 (S7: NO), the CPU 21 returns the process to S6 and executes the process of S6 for one specific signal that has not been subjected to the process of S6. . When the process of S6 is executed for all the specific signals (S7: YES), the CPU 21 generates an initial value of the probability distribution model of the cluster including the n-dimensional coordinate point having the lowest probability of being included in the existing cluster ( S8). In S8, the CPU 21 calculates the likelihood that each n-dimensional coordinate point is included in the cluster that has already generated the initial value of the probability distribution model, and the likelihood included in the nearest cluster in the n-dimensional space is the lowest. An n-dimensional coordinate point is specified, and initial values of parameters of a new cluster probability distribution model are generated so that the specified n-dimensional coordinate point is included. S8 corresponds to a conventional method for generating an initial value of a probability distribution model of a cluster.

Next, the CPU 21 determines whether or not the number of clusters that have generated the initial value of the probability distribution model has reached the initial value of the number of clusters set in S4 (S9). If the number of clusters has not yet reached the initial value (S9: NO), the CPU 21 returns the process to S8. The processes of S4 to S9 correspond to the initial setting unit and the initial setting step. The process of S5 corresponds to the first initial cluster generation unit, the processes of S6 and S7 correspond to the second initial cluster generation unit, the process of S8 corresponds to the third initial cluster generation unit and the generation step, and S9 This processing corresponds to the repetition unit. In the processes of S6 and S7 described above, the process of S6 is executed for all the specific signals, but the signal analyzer 2 performs the process of S6 only for some of the specific signals among the n specific signals. May be executed. In this embodiment, for example, the process of S6 is performed only for a predetermined number of specific signals or specific signals specified in advance, and in S7, whether or not the process of S6 is performed for specific signals that require the process of S6. Determined.

When the number of clusters has reached the initial value (S9: YES), the CPU 21 next includes each n-dimensional coordinate point on the n-dimensional space based on the probability distribution model of each cluster. Probability is calculated (S10). The process of S10 corresponds to the E (Expectation) step in the EM algorithm. Next, the CPU 21 performs a process of updating the probability distribution model parameters of each cluster so as to increase the overall likelihood (S11). Specifically, parameters of probability distribution such as the center position of each cluster in the n-dimensional space are updated. The process of S11 corresponds to the M (maximization) step in the EM algorithm.

Next, the CPU 21 determines the convergence of the EM algorithm (S12). As the convergence index, an index generally used in the EM algorithm, such as a likelihood value, a change amount or a change rate, or a parameter value of the probability distribution model, a change amount or a change rate, is used. For example, the CPU 21 determines that the likelihood has converged when the likelihood change amount is less than or equal to a predetermined value, and determines that the likelihood has not yet converged when the likelihood change amount is greater than the predetermined value. The signal processing unit 2 may be configured such that when the user operates the input unit 25, the input of the convergence condition can be received and the convergence condition can be changed. The processes of S10 to S12 correspond to the cluster analysis unit. The signal analysis device 2 may be configured to perform cluster analysis using a maximum likelihood method or maximum a posteriori probability estimation algorithm other than the EM algorithm in S10, S11, and S12. For example, the signal analyzer 2 may perform processing using an algorithm of the k-means method (K-means method), the Ward method, or the Newton-Raphson method. Depending on the algorithm, clusters may be defined by other than probability distribution models. Regardless of which algorithm is used, the signal analyzer 2 calculates which cluster each n-dimensional coordinate point belongs to in the processing corresponding to S10, S11, and S12. Further, the signal analysis device 2 may perform cluster analysis using clusters defined by a method other than the method using the probability distribution model.

If not converged yet in S12 (S12: NO), the CPU 21 returns the process to S10. If it is determined that they have converged (S12: YES), the CPU 21 determines whether or not there are a plurality of clusters in which the distance between each other in the n-dimensional space is a predetermined distance or less. Is determined (S13). For example, in S13, the CPU 21 calculates the Mahalanobis distance between the centers between the two clusters, and determines based on whether the calculated Mahalanobis distance is equal to or less than a predetermined value. Further, for example, the CPU 21 calculates the inner product of the vectors to the center between the two clusters, and determines that the mutual distance is equal to or smaller than the predetermined distance when the calculated inner product is closer to 1 than a predetermined threshold. CPU21 performs the process which determines the distance between two clusters about the combination of all the clusters. In S <b> 13, the CPU 21 may make a determination by other methods. When there are a plurality of clusters close to each other (S13: YES), the CPU 21 combines the plurality of clusters close to each other (S14). Specifically, the CPU 21 performs a process of determining a plurality of cluster ranges as a new one cluster range. In FIG. 6, the cluster range is indicated by a solid line. In the example shown in FIG. 6, five clusters are obtained.

After step S14 is completed, or when there are no clusters close to each other in step S13 (S13: NO), the CPU 21 specifies a point in the spectrum distribution corresponding to the n-dimensional coordinate point included in each cluster. Then, distributions of a plurality of types of regions having different combinations of n specific signal intensities on the two-dimensional coordinate system are individually generated (S15). The distribution of the generated region is a distribution of a region including points where the intensities of n specific signals included in the spectrum are a combination of specific intensities among the points included in the spectral distribution. A distribution of regions in which the intensity of specific signals is a combination of specific intensities is generated for each cluster. The process of S15 corresponds to a region distribution generation unit. Next, the CPU 21 stores the generated distribution data representing the distribution of each region in the storage unit 14 (S16), and ends the process.

Note that the signal analysis device 2 may be configured to perform the process of determining the number of repetitions of the processes of S10 and S11 instead of performing the convergence determination in S12. In this embodiment, the signal analyzer 2 stores in advance the predetermined number of repetitions of S10 and S11 in the storage unit 24. In S12, the CPU 21 determines whether or not the number of repetitions of the process has reached the predetermined number. If the number of repetitions of the process has not yet reached the predetermined number, the process returns to S10, and the number of repetitions of the process is the predetermined number. If reached, the process proceeds to S13. As the predetermined number of repetitions of processing, the number of times that the likelihood of the entire plurality of clusters is sufficiently large from experience is determined. The predetermined number of times is 100, for example. The signal analyzer 2 can shorten the calculation time by ending the repetition of the process a predetermined number of times regardless of whether or not the convergence condition is satisfied. Further, the signal analyzer 2 may perform both the convergence determination and the number determination, and perform the process of proceeding to S13 when the convergence condition is satisfied before the number of repetitions of the process reaches the predetermined number. Good.

In FIG. 6, the cluster range is indicated by a solid line. Further, in FIG. 6, each of the average values of the intensities of the signals a and b is indicated by a broken line. FIG. 7 is a chart showing examples of initial values of clusters and n-dimensional coordinate points. In the figure, the intensity of each specific signal at the center position of a certain cluster 1 is shown, and the intensity of each specific signal at an n-dimensional coordinate

point

1, 2, 9, and 10 is shown. The specific signals are signals a, b, c, d, e, f, and g. The center position of the cluster 1 is assumed to be a representative value of each specific signal. In the n-dimensional coordinate point 1 shown in FIG. 7, the intensity of each specific signal is substantially the same as the representative value. For this reason, the n-dimensional coordinate point 1 is included in the cluster 1. In the n-dimensional coordinate point 10 shown in FIG. 7, the intensity of the signal c is significantly different from the representative value, and the intensity of other specific signals is the same as the representative value.

∙ For proper cluster analysis, it is necessary to set the initial value of the cluster appropriately. In the conventional method for setting the initial value of the cluster, the initial value of the cluster including the point on the n-dimensional coordinate system, which is a representative value such as an average value, is set first, and the probability of being included in the existing cluster is low. An initial value of a new cluster is set so as to include an n-dimensional coordinate point. For this reason, as in the cluster indicated by 51 in FIG. 6, the initial value of a cluster composed of n-dimensional coordinate points in which the intensity of many specific signals is separated from the representative value is easily set. On the other hand, although the intensity of a single specific signal or a small number of specific signals deviates from the representative value, an initial value is set in the conventional method for clusters composed of n-dimensional coordinate points whose intensities of other specific signals are close to the representative value. Hateful. For example, it is unlikely that the initial value of the cluster composed of the n-dimensional coordinate points 10 shown in FIG. In the conventional method, the n-dimensional coordinate point 10 is included in the cluster 1.

In the present embodiment, the initial value of the cluster is set so as to include an n-dimensional coordinate point where the intensity of one specific signal deviates from a predetermined reference, for example, an n-dimensional coordinate point whose intensity of one specific signal is equal to or greater than m + α. To do. For this reason, it is easy to set an initial value of a cluster composed of n-dimensional coordinate points whose intensities of single or a small number of specific signals deviate from the representative value but whose intensity of other specific signals is close to the representative value. For example, the initial value of the cluster composed of the n-dimensional coordinate points 10 shown in FIG. In the present embodiment, since the initial value of the cluster is set in S8 in the conventional method, the initial value can be set even for the cluster in which the initial value can be set by the conventional method. As described above, by appropriately setting the initial value of the cluster, it is possible to appropriately classify the n-dimensional coordinate points in the cluster analysis and appropriately generate the distribution of a plurality of types of regions having different combinations of specific signal intensities. It becomes possible.

8A, 8B, 8C, and 8D are schematic diagrams illustrating examples of distributions of a plurality of types of regions having different combinations of specific signal intensities. The signal analyzing apparatus 2 can display an image showing the distribution of each region as shown in FIGS. 8A to 8D on the display unit 26. It is assumed that the spectrum included in the spectrum distribution is composed of signals a, b and c. FIG. 8A shows a distribution of regions where the intensity of the signal a is average and the intensity of the signals b and c is small. FIG. 8B shows a distribution of regions where the intensity of the signals a and b is average and the intensity of the signal c is small. FIG. 8C shows a distribution of regions where the intensity of the signals a and b is average and the intensity of the signal c is large. FIG. 8D shows a distribution in a region where the intensity of the signal a is average, the intensity of the signal b is small, and the intensity of the signal c is large. Assuming that signals a, b, and c correspond to elements A, B, and C, respectively, FIG. 8A shows the distribution of components that contain element A and almost no elements B and C, and FIG. The distribution of a component containing almost no element C is shown. Further, FIG. 8C shows the distribution of the component in which the element C is concentrated among the components including the elements A and B, and FIG. 8D is the concentration of the element C in the component that includes the element A and hardly includes the element B. The component part is shown. It is also possible to obtain other types of distributions of regions according to combinations of the strengths of signals a, b, and c, such as distributions of regions where the strengths of signals a and b greatly exceed the average.

The distributions shown in FIGS. 8C and 8D are distributions of regions that were difficult to separate from other regions by the conventional method. As described above, in this embodiment, when generating a distribution of a plurality of types of regions having different combinations of specific signal intensities from the spectrum distribution, a region in which the intensity of a small number of specific signals deviates from a representative value such as an average value. It is possible to obtain a distribution of. The distribution of a plurality of types of regions having different combinations of specific signal intensities represents the distribution of a plurality of types of components having different concentrations of elements contained in the sample 3. That is, according to the present embodiment, it is possible to obtain a distribution of components in which the concentration of a small number of elements deviates from the representative value. In particular, as shown in FIGS. 8C and 8D, it is possible to obtain a distribution of components that exist only in a minute region in the sample 3.

In this embodiment, the signal analysis device 2 is connected to the control unit 16. However, the signal analysis device 2 may be integrated with the control unit 16. In this form, the signal analysis device 2 executes a process to be executed by the control unit 16. Further, the signal analysis device 2 may be separated from the measurement device. In this embodiment, the signal analysis device 2 receives externally generated signal distribution data and executes the processes after S3.

Further, in the present embodiment, the form of analyzing the spectrum distribution obtained by EDX is shown, but the signal analyzer 2 may be the form of analyzing the spectrum distribution obtained by other measurement methods. Good. The measuring device may be a device other than the EDX device as long as it can measure the spectral distribution. For example, the signal analyzer 2 may be configured to analyze a spectrum distribution composed of a fluorescent X-ray spectrum. Also in this form, the signal analyzer 2 can obtain a distribution of a plurality of types of components having different concentrations of elements contained in the sample. Further, the signal analysis device 2 may be configured to analyze a spectrum distribution including a Raman spectrum. Further, the signal analysis device 2 may be configured to analyze a spectrum distribution composed of visible light and / or infrared light spectrum from the measurement target. Visible light and infrared light are light reflected from the surface of the measurement object or light transmitted through the measurement object. For example, the signal analysis device 2 calculates an n-dimensional coordinate point group composed of a combination of R (red), G (green), B (blue), and infrared intensities from a spectral distribution obtained by measuring reflected light from a measurement target. Generate and perform cluster analysis, and generate distributions of a plurality of types of regions on the measurement target according to the combination of RGB and infrared intensity. For example, a plurality of types of tree distributions are generated from a captured image of a forest. Further, the signal analysis device 2 may be configured to analyze other spectral distributions.

Moreover, in this embodiment, although the form which analyzes the spectrum distribution in which the spectrum was linked | related with each point on a two-dimensional coordinate system was shown, the signal analysis apparatus 2 is a point where a spectrum is each point on a three-dimensional coordinate system. It is also possible to perform an analysis of the spectral distribution associated with. In this form, the signal analyzer 2 can obtain the distribution of components existing on the surface of a three-dimensional sample, for example. Similarly, the measurement device may be configured to generate a spectrum distribution in which a spectrum is associated with each point on a three-dimensional coordinate system.

DESCRIPTION OF SYMBOLS 11 Electron gun 12 Electron lens system 13 Sample stand 14 Detection part 15 Signal processing part 16 Control part 2 Signal analyzer 21 CPU
24 Storage Unit 3 Sample 4 Recording Medium 41 Computer Program

Claims

The spectrum is defined by a combination of the intensity of n specific signals (n is an integer of 2 or more) included in the spectrum for each point in the spectrum distribution based on the spectrum distribution determined for each point on the coordinate system. An n-dimensional coordinate point group generation unit for generating n-dimensional coordinate points in the n-dimensional space;
In order to classify the plurality of generated n-dimensional coordinate points, an initial setting unit that determines initial values of a plurality of clusters in the n-dimensional space;
In a signal analyzer comprising a cluster analysis unit that performs cluster analysis using a predetermined initial value,
The initial setting unit includes:
A first initial cluster generation unit that generates an initial value of a cluster including a point on an n-dimensional space that is a combination of representative values of the intensity of the n specific signals;
And a second initial cluster generation unit configured to generate an initial value of a cluster including an n-dimensional coordinate point whose intensity of one specific signal deviates from a predetermined reference.
The initial setting unit includes:
A cluster number setting unit for determining the number of a plurality of clusters;
A third initial cluster generation unit for generating an initial value of a cluster including an n-dimensional coordinate point having the lowest probability of being included in a cluster for which an initial value has already been set;
The signal analyzer according to claim 1, further comprising: a repeating unit that repeats the processing of the third initial cluster generation unit until an initial value of the number of clusters determined by the cluster number setting unit is determined. .
By identifying the distribution in the spectral distribution of the points corresponding to the n-dimensional coordinate points included in each cluster after cluster analysis, the distribution of multiple types of regions with different combinations of n specific signal intensities is generated. The signal analysis device according to claim 1, further comprising a region distribution generation unit that performs the processing.
The intensity of the n specific signals indicates the concentration of n elements,
The signal analysis apparatus according to claim 3, wherein the region distribution generation unit generates a plurality of types of regions having different combinations of n element concentrations.
By a computer having a calculation unit and a storage unit,
The spectrum is defined by a combination of the intensity of n specific signals (n is an integer of 2 or more) included in the spectrum for each point in the spectrum distribution based on the spectrum distribution determined for each point on the coordinate system. Generating n-dimensional coordinate points on the n-dimensional space,
An initial setting step for determining initial values of a plurality of clusters on the n-dimensional space in order to classify the plurality of generated n-dimensional coordinate points;
In a signal processing method for performing cluster analysis using a predetermined initial value,
The initial setting step includes:
Generating an initial value of a cluster including points on an n-dimensional space composed of combinations of representative values of the intensity of the n specific signals;
Generating an initial value of a cluster including n-dimensional coordinate points in which the intensity of one specific signal deviates from a predetermined reference.
The initial setting step includes:
Determining the number of multiple clusters;
A generating step for generating an initial value of a cluster including an n-dimensional coordinate point having the lowest likelihood included in a cluster in which an initial value is already set;
The signal analysis method according to claim 5, further comprising: repeating the generating step until initial values of a predetermined number of clusters are determined.
By identifying the distribution in the spectral distribution of the points corresponding to the n-dimensional coordinate points included in each cluster after cluster analysis, the distribution of multiple types of regions with different combinations of n specific signal intensities is generated. The signal analyzing method according to claim 5 or 6, further comprising the step of:
On the computer,
The spectrum is defined by a combination of the intensity of n specific signals (n is an integer of 2 or more) included in the spectrum for each point in the spectrum distribution based on the spectrum distribution determined for each point on the coordinate system. Generating n-dimensional coordinate points on the n-dimensional space,
An initial setting step for determining initial values of a plurality of clusters on the n-dimensional space in order to classify the plurality of generated n-dimensional coordinate points;
In a computer program for executing processing including a step of performing cluster analysis using a predetermined initial value,
The initial setting step includes:
Generating an initial value of a cluster including points on an n-dimensional space composed of combinations of representative values of the intensity of the n specific signals;
Generating an initial value of a cluster including an n-dimensional coordinate point whose intensity of one specific signal deviates from a predetermined reference.
The initial setting step includes:
Determining the number of multiple clusters;
A generating step for generating an initial value of a cluster including an n-dimensional coordinate point having the lowest likelihood included in a cluster in which an initial value is already set;
The computer program according to claim 8, further comprising: repeating the generating step until initial values of a predetermined number of clusters are determined.
A measurement unit for measuring radiation or electromagnetic waves obtained from each point on the sample;
In a measurement apparatus comprising a spectrum distribution generation unit that generates a spectrum distribution in which a spectrum of a measured radiation or electromagnetic wave is associated with each point,
A measuring apparatus comprising the signal analyzing apparatus according to claim 1.
In a measurement method for measuring a spectrum obtained from each point on a sample and generating a spectrum distribution in which the measured spectrum is associated with each point,
A measurement method comprising the signal analysis method according to claim 5.