WO2017050303A1 - A method of analysis of materials by means of a focused electron beam using characteristic x-rays and back-scattered electrons - Google Patents

A method of analysis of materials by means of a focused electron beam using characteristic x-rays and back-scattered electrons Download PDF

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WO2017050303A1
WO2017050303A1 PCT/CZ2016/000107 CZ2016000107W WO2017050303A1 WO 2017050303 A1 WO2017050303 A1 WO 2017050303A1 CZ 2016000107 W CZ2016000107 W CZ 2016000107W WO 2017050303 A1 WO2017050303 A1 WO 2017050303A1
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memory
particle
map
determined
electron beam
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PCT/CZ2016/000107
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French (fr)
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David Motl
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Tescan Brno, S.R.O.
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N23/00—Investigating or analysing materials by the use of wave or particle radiation, e.g. X-rays or neutrons, not covered by groups G01N3/00 – G01N17/00, G01N21/00 or G01N22/00
    • G01N23/22—Investigating or analysing materials by the use of wave or particle radiation, e.g. X-rays or neutrons, not covered by groups G01N3/00 – G01N17/00, G01N21/00 or G01N22/00 by measuring secondary emission from the material
    • G01N23/225—Investigating or analysing materials by the use of wave or particle radiation, e.g. X-rays or neutrons, not covered by groups G01N3/00 – G01N17/00, G01N21/00 or G01N22/00 by measuring secondary emission from the material using electron or ion
    • G01N23/2251—Investigating or analysing materials by the use of wave or particle radiation, e.g. X-rays or neutrons, not covered by groups G01N3/00 – G01N17/00, G01N21/00 or G01N22/00 by measuring secondary emission from the material using electron or ion using incident electron beams, e.g. scanning electron microscopy [SEM]
    • G01N23/2252—Measuring emitted X-rays, e.g. electron probe microanalysis [EPMA]
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N23/00—Investigating or analysing materials by the use of wave or particle radiation, e.g. X-rays or neutrons, not covered by groups G01N3/00 – G01N17/00, G01N21/00 or G01N22/00
    • G01N23/20—Investigating or analysing materials by the use of wave or particle radiation, e.g. X-rays or neutrons, not covered by groups G01N3/00 – G01N17/00, G01N21/00 or G01N22/00 by using diffraction of the radiation by the materials, e.g. for investigating crystal structure; by using scattering of the radiation by the materials, e.g. for investigating non-crystalline materials; by using reflection of the radiation by the materials
    • G01N23/203—Measuring back scattering
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N23/00—Investigating or analysing materials by the use of wave or particle radiation, e.g. X-rays or neutrons, not covered by groups G01N3/00 – G01N17/00, G01N21/00 or G01N22/00
    • G01N23/22—Investigating or analysing materials by the use of wave or particle radiation, e.g. X-rays or neutrons, not covered by groups G01N3/00 – G01N17/00, G01N21/00 or G01N22/00 by measuring secondary emission from the material
    • G01N23/2206—Combination of two or more measurements, at least one measurement being that of secondary emission, e.g. combination of secondary electron [SE] measurement and back-scattered electron [BSE] measurement
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N23/00—Investigating or analysing materials by the use of wave or particle radiation, e.g. X-rays or neutrons, not covered by groups G01N3/00 – G01N17/00, G01N21/00 or G01N22/00
    • G01N23/22—Investigating or analysing materials by the use of wave or particle radiation, e.g. X-rays or neutrons, not covered by groups G01N3/00 – G01N17/00, G01N21/00 or G01N22/00 by measuring secondary emission from the material
    • G01N23/2206—Combination of two or more measurements, at least one measurement being that of secondary emission, e.g. combination of secondary electron [SE] measurement and back-scattered electron [BSE] measurement
    • G01N23/2208—Combination of two or more measurements, at least one measurement being that of secondary emission, e.g. combination of secondary electron [SE] measurement and back-scattered electron [BSE] measurement all measurements being of a secondary emission, e.g. combination of SE measurement and characteristic X-ray measurement
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N23/00—Investigating or analysing materials by the use of wave or particle radiation, e.g. X-rays or neutrons, not covered by groups G01N3/00 – G01N17/00, G01N21/00 or G01N22/00
    • G01N23/22—Investigating or analysing materials by the use of wave or particle radiation, e.g. X-rays or neutrons, not covered by groups G01N3/00 – G01N17/00, G01N21/00 or G01N22/00 by measuring secondary emission from the material
    • G01N23/225—Investigating or analysing materials by the use of wave or particle radiation, e.g. X-rays or neutrons, not covered by groups G01N3/00 – G01N17/00, G01N21/00 or G01N22/00 by measuring secondary emission from the material using electron or ion
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2223/00—Investigating materials by wave or particle radiation
    • G01N2223/60—Specific applications or type of materials
    • G01N2223/616—Specific applications or type of materials earth materials
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2223/00—Investigating materials by wave or particle radiation
    • G01N2223/60—Specific applications or type of materials
    • G01N2223/66—Specific applications or type of materials multiple steps inspection, e.g. coarse/fine
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01J—ELECTRIC DISCHARGE TUBES OR DISCHARGE LAMPS
    • H01J2237/00—Discharge tubes exposing object to beam, e.g. for analysis treatment, etching, imaging
    • H01J2237/245—Detection characterised by the variable being measured
    • H01J2237/24571—Measurements of non-electric or non-magnetic variables
    • H01J2237/24585—Other variables, e.g. energy, mass, velocity, time, temperature

Definitions

  • Energy-dispersive X-ray spectroscopy is one of the methods for the study of chemical properties of materials using characteristic X-rays, which is another product of the interaction between the accelerated electron beam and the sample material. Electrons are located in a so-called electron shell in the atom. State of the electrons cannot be optional; the electron is in one of its discrete states. The state of electron is described by means of four quantum numbers. Kinetic energy of the electron is determined by on which atomic orbital of which atom is the electron located. According to so-called philosophical principle, the electrons in the ground state are arranged in the shell so that they take places on the orbitals with the lowest energy, wherein only two electrons may be located on the same orbital.
  • Particle classification may be performed using one of the two methods.
  • all the expressions Vk from the set Z or Z' respectively evaluated for each particle and the result of the classification of each particle is the set Cj, which is a subset of the set C of all expressions in the set Z or Z' respectively.
  • the expressions v3 ⁇ 4 evaluated sequentially in the order in which they are arranged before starting the process, and in case any of the expressions has the "true" logical value, the set Q comprises only the class C corresponding to the expression Vk. In case all expressions v3 ⁇ 4 for one of the particles have the "false" logical value, the set Q is empty.
  • the block 115 performs transformation of input maps into one output map with the same dimension in order to select possible measuring points.
  • the first input map, the auxiliary map S of the temporary particles distribution, saved in the memory 112 contains on its coordinates (x, y) values corresponding to the sequence number of the temporary particles located in the point with the coordinate (x, y).
  • the second input map, the auxiliary map T, saved in the memory 114 contains in its coordinates (x, y) values representing the distance of the points with the coordinate (x, y) from the edge of the temporary particle.
  • the output map is determined so that the set of temporary particles is loaded from the memory 109 and for each temporary particle belonging to this set such points are found, which have the largest distance from the edge of this temporary particle.
  • the block 136 updates the script J' of X-ray mapping saved in the memory 133, so that it inserts all measuring points from the set Z of measuring points at the end of the script.
  • the block 131 loads the auxiliary map W of the remaining points from the memory 128 and updates the auxiliary map S of temporary particles distribution saved in the memory 112, and further updates the auxiliary set P of temporary particles.
  • this operation performed so that connected components labeling transformation is applied on the auxiliary map W. Result of the transformation is directly the new auxiliary map S of temporary particles distribution; the new auxiliary set P of temporary particles is determined based on the new auxiliary map S of temporary particles distribution, as a set of unique non-zero values S (x, y).
  • the new auxiliary map S of temporary particles distribution is saved in the memory 112, and the new auxiliary set P of temporary particles is saved in the memory 109.
  • the block 130 loads the auxiliary set P of temporary particles and indicates the state ventilatoff" at its output provided that the set is empty, and cruston" provided that the set is not empty.
  • the block 401 loads the script J' of X-ray mapping from the memory and copies it to the memory 29 on the command of the processing unit 20.
  • the basic block scheme is continued in the fig. 6.
  • Y(x, y) For points with the coordinates (x, y) where Y(x, y) is non-zero (value Y(x, y) corresponds to the sequence number of the measuring point) the value Y (x, y) is used to find the corresponding spectrum, and the value Mi (x, y) is determined based on this spectrum so that the value M,- (x, y) corresponds to the X-ray intensity with the energy belonging to the interval /, emitted in the measuring point (step 703). Resulting X-ray maps Mi are saved in the memory 204.
  • the block 205 loads the X-ray maps M, from the memory 204 and converts them into differential X-ray map DM, where the values DM(X, y) saved in the map DM are related to the points on the sample with the coordinates (x, y) and correspond to the gradient size of the X-ray intensity with the energy in the point with the coordinates (x, y).
  • the block 231. initializes a variable / ' so that it saves the value 1 in the memory 229.
  • the resulting bit map U) is saved in the memory 228.
  • the block 221 reads the bit map U) from the memory 228 and converts it to bit map V'j.
  • the values Vj' (x, y) are zero, provided that the point with the coordinates fx, y) is located outside the particle q,, the positive values V) (x, y) represent the minimum distance of the points with the coordinates fx, y) from the edge of the particle increased by 1. This operation may be performed, for example, using Euclidean distance transformation.
  • the output of the transformation applied on the bit map U is directly the map V'j.
  • the map V) is saved in the memory 222.
  • the block 225 loads the weighted map W) from the memory 224 and the auxiliary map Y from the memory 121 , and creates an accumulated spectrum Xj so that contributions from the points with the coordinates (x, y) multiplied by the weight W'j (x, y) are summed.
  • the block 213 reads the accumulated spectrum Xj from the memory 219, and the set P of chemical elements from the memory 215, and for each element p,- from the set P of chemical elements the relative detection frequency Nij of the X-ray quantums with the energy in the interval /, in the spectrum Xj as a proportion of the number of detected X-ray quantums with the energy in the interval // in the spectrum Xj and the overall number of quantums in the spectrum Xf.
  • the size F of the field of vision is read from the memory 303 and the basic resolution d from the memory 301., and the ratio F / d is calculated; the result is rounded to the nearest positive integer number.
  • the obtained value is used as a number of columns and rows in the regular rectangular grid, for which the block 302 generates the scanning script J based on the request of the processing unit so that the points of the grid are passed along the rows in sequential manner; the scanning script J is saved in the memory 29 (step 502).
  • the control unit 12 reads the scanning script J from the memory 29 and runs the scanning process (step 503).
  • Deflection circuits 5 control the current by means of the deflection coils 3 so that the electron beam 2 gradually impacts on the sample 4 in those points determined by the scanning script J.
  • the control unit 12 further communicates with the analog-to-digital converter 9.
  • a signal from the analog-to-digital converter 9 is sent to the processing unit 20, where it is saved in the memory 27 (map B).
  • the map B is a two-dimensional field of values (x, y), which are related to the points on the sample with the coordinates (x, y).
  • the number of rows and columns of the map is identical with the number of rows and columns of the regular rectangular grid, which has been used for generating the scanning script J.
  • the value ⁇ (x, y) represents the intensity of back-scattered electrons emerging upon the impact of the electron beam 2 on the sample 4 in a point with the coordinates (x, y).
  • Result of such transformation is directly the map R of temporary particles distribution; the set Q is determined based on the map R of temporary particles distribution, as set of unique non-zero values R (x, y).
  • the map R of temporary particles distribution is saved in the memory 110, the set Q of temporary particles is saved in the memory 107.
  • an auxiliary map T is read from the memory 116, the auxiliary map S of temporary particles distribution is read from the memory 112 and the auxiliary set P of temporary particles.
  • one initial point is selected, and the set O of initial points is set as a set of selected initial points (step 605).
  • the resulting new auxiliary map U is saved back in the memory 124.
  • all measuring points from the list Z of measuring points are inserted at the end of the script J' of X- ray mapping, which is saved in the memory 133.
  • the auxiliary map Y is also updated as follows: for all measuring points with the coordinates (x, y) from the list Z of measuring points, the values Y (i, j) in the auxiliary map Y are set to the identification number of the measuring point, for all such points with the coordinates (i, j), for which it applies that the point with the coordinates (i, j) is a part of the same temporary particle as the corresponding initial point, to which this measuring point belongs, and at the same time it applies that ⁇ - and y - ⁇ j ⁇ y + , where x and y are coordinates of the measuring point and c is the coefficient defined above.
  • a spectrum map S is created in the processing unit 20 based on the signal from the energy-dispersive detector 10 of X-ray radiation, wherein one spectrum corresponds to each measuring point from the script J' of X-ray mapping (step 702).
  • Spectrum map S refers to two-dimensional field, wherein one dimension corresponds to the identification number of the measuring point from the script J' of X-ray mapping, and the second dimension is the number of the channel corresponding to the narrow interval of photon energy E.
  • Differential X-ray map DM and the differential electron map DB are subsequently merged into resulting differential map D (step 705).
  • This operation may be performed, for example, as follows: a differential map D is created, which has the same dimension as the differential electron map DB.
  • the values D (x, y) are set as a maximum of the values DB (X, y) and DM (X, y).
  • the resulting differential map D is saved in the memory 208.
  • the spectrum Xj enters the block 213, in which the relative detection frequency Nij of the X-ray quantums is determined, with the energy in the interval /, in the spectrum Xj as a proportion of the number of detected X-ray quantums with the energy in the interval // in the spectrum Xj and the overall number of quantums in the spectrum
  • Input of the spectrum analyzer 801 is connected to the memory 219 and the output thereof is connected via the memory 802 to the second input of the controller 25 of the output device.
  • the spectrum analyzer 801 reads the accumulated spectrums Xj from the memory 219 and using the quantitative spectroscopic analysis it determines the percentage of the chemical elements in the particle q).
  • the output values are saved in the memory 802.
  • the result of the quantitative spectroscopic analysis is displayed to the user after highlighting a particle in other part of the displaying device 26 as a table of chemical elements and percentages of each element.
  • FIG. 11 Block scheme of the device in this embodiment is illustrated in the figure 11 , wherein some of the parts which are the same as in the basic embodiment are not shown for better understanding.
  • the particle classifier 810 is connected on its first input via the memory 811. to the sixth output of the controller 23 of the input device, and on its second input it is connected to the memory 214.
  • the output of the particle classifier 810 is connected via the memory 812 to the third input of the controller 25 of the output device.
  • the particle classifier 810 reads the values of relative detection frequencies Njj of X-ray quantums in the interval /, ⁇ for chemical elements p, from the quantity P of the chemical elements from the memory 214 in the particles qj' from the set Q', and reads the set Z from the memory 811 , and for each particle q'j from the set Q' it determines the set Cj of classes, which is saved in the memory 812.
  • no more than one class Ck is allocated to the particle during the classification.
  • Block scheme of this device is illustrated in the figure 12, wherein some of the parts which are the same as in the basic embodiment are not shown for better understanding.
  • the particle classifier 820 is on its first input connected via the memory 822 to the sixth output of the controller 23 of the input device and on its second input it is connected to the memory 214.
  • the output of the particle classifier 820 is connected via the memory 821 to the third input of the controller 25 of the output device.
  • the particle classifier 820 reads the values of relative detection frequencies N,-j of the X-ray quantums from the memory 214 in the interval // for chemical elements p, from the set P of chemical elements in the particles g) from the set Q' , and the ordered set Z is read from the memory 822, and for each particle q from the set Q'it determines the set Cj with the cardinality no more than 1 , which is saved in the memory 821.
  • a number of particles no- is determined as a cardinality of the set Q', and positive integer number ranging from 1 to no' are allocated to the particles according to the order, in which they have been inserted into the set Q'.
  • the set Cy may contain only the element Ck (step 926), and the process continues with the index j (step 929); otherwise, the process continues with another index k (step 928).
  • the set of classes Cy for such a particle q will be empty (step 927) and the device continues with another index j (step 929).
  • the result of the classification is displayed after highlighting the particle in another part of the display device 26 as a name of the class Ck, provided that the set Cj contains the element 3 ⁇ 4, or the text ..unclassified" is shown provided that the set Cy is empty.
  • the particle classification is performed based on the percentages of chemical elements determined by means of quantitative spectrum analysis.
  • Block scheme of the device in this embodiment is illustrated in the figure 13, wherein some of the parts which are the same as in the basic embodiment are not shown for better understanding.
  • the input of the spectrum analyzer 801 connected to the memory 219 and its output is connected via the memory 802 with the second input of the controller 25 of the output device and with the second input of the particle classifier 830.
  • the particle classifier 830 is on its input connected via the memory 831 to the sixth output of the controller 23 of the input device, and on its output it is connected via the memory 832 to the third input of the controller 25 of the output device.
  • nc is the number of classes and each class Ck has its own logical value v3 ⁇ 4, which consists of variable identifiers, numeric constants, arithmetic operators for negation, addition, multiplication, subtraction and division, operators for comparison of two numerical values (equivalence, non-equivalence, greater, greater or equal, less, less or equal) and logical operators for negation, conjunction and disjunction.
  • step 932 the values of percentages of the chemical elements for the particle q) are read from the memory 219 and these values are saved in the variables occurring in the expressions Vk.
  • the result of the evaluation of the truth values of all logical expressions for the particle q is the set Cy, which is a sub-set of the set C and contains those elements Ck from the set C, for which the truth value of the logical expression Vk is comfortabletrue".
  • the set Cj is saved in the memory 832 and the process continues with another index (step 938).
  • the result of the particle classification is displayed to the user after highlighting the particle in another part of the displaying device 26 as a list of classes, to which the highlighted particles has been allocated.
  • the particle classifier 840 reads from the memory 802 the values of percentages of chemical elements in the particles g/from the set Q', and it reads the set Z'from the memory 841 , and it determines the class C, for each particle g from the set Q', which is saved in the memory 842.
  • nc is the number of classes and each class Ck has its own logical expression v3 ⁇ 4, which consists of variable identifiers, numeric constants, arithmetic operators for negation, addition, multiplication, subtraction and division, operators for comparison of two numerical values (equivalence, non- equivalence, greater, greater or equal, less, less or equal) and logical operators for negation, logical conjunction and disjunction.
  • v3 ⁇ 4 consists of variable identifiers, numeric constants, arithmetic operators for negation, addition, multiplication, subtraction and division, operators for comparison of two numerical values (equivalence, non- equivalence, greater, greater or equal, less, less or equal) and logical operators for negation, logical conjunction and disjunction.
  • a number of particles no- is determined as cardinality of the set Q' and positive integer numbers are allocated ranging from 1 to /7Q ⁇ to the particles in the order, in which the particles have been inserted in the set Q'.
  • Particles classification begins with evaluation of the expression Vk for the index k - 1 (step 943).
  • the set Q will contain only the element Ck (step 946) and continues with another index j (step 949); otherwise, the process continues with another index k (step 948).
  • the set C for such particle q,- will be empty (step 947) and the device continues with another index j (step 949).
  • the result of the particle classification is shown to the user after highlighting a particle in another part of the displaying device 26 as a name of the class Ck, provided that the set Q contains the element Ck, or a text ..unclassified" is shown, provided that the set is empty.
  • Figure 1 illustrates a block scheme of the electron microscope with the back- scattered electrons detector, X-ray detector, and control circuits according to the state of the art, wherein some of the basic parts of the electron microscope which are not directly related to the present invention are not shown.
  • Figure 2 illustrates a block scheme of connection of the basic variant of the present device, wherein the internal connection of the processing unit is not shown for better understanding.
  • FIGS 3 to 6 illustrate the basic variant of the connection of blocks and memories inside the processing unit 20.
  • FIGS 7 to 9 illustrate a flowchart of the basic variant of the device.
  • FIG. 15 to 19 illustrate a flowchart of the second to sixth possible embodiment, wherein those steps which are the same as in the basic variant are not shown for better understanding.
  • the provided new method and devices are particularly suitable for use in quantitative analysis in petrography of rocks.
  • the examined sample is usually crushed to fine particles with the size from units to tens of micrometers, it is divided into several fractions using sieves. Several samples are taken from each size fraction. These size fractions are usually mixed with filler and epoxy resin and they are left to cure into cylindrical blocks, which are further polished and subsequently covered with thin conductive layer, usually carbon, for diversion of the surface charge. These block are arranged in the scanning electron microscope, which sequentially collects the data and analyzes the material on their surface.
  • the present device allows to perform a fully automated analysis of these samples, the result of which are not only morphological and chemical properties of the materials, from which the examined sample consists, but mainly the information about mutual spatial distribution of the materials, which is in many cases a crucial information regarding determination of the physical and chemical properties of the rocks. List of reference signs

Abstract

The invention relates to a method of analysis of materials by means of a focused electron beam and a device thereof, where the electron beam is gradually deflected into a number of points on a sample arranged in a regular grid, creating an electron map. A set of temporary particles and a set of new measuring points are determined by means of the electron map, wherein the set of new measuring points comprises less elements than the set of the initial measuring points, and the set of new measuring points comprises at least one measuring point for each particle from the set of temporary particles. The electron beam is deflected along the set of new measuring points, the emitted X-rays are measured and an X-ray spectrum is created, a set of particles is determined, and accumulated spectrums of X-ray radiation for a particle based on the spectrums measured in the points, which are not part of the particle, are created.

Description

A METHOD OF ANALYSIS OF MATERIALS BY MEANS OF A FOCUSED ELECTRON BEAM USING CHARACTERISTIC X-RAYS AND BACK-SCATTERED ELECTRONS
Field of the Invention
The present invention relates to a method and a device for analysis of materials by means of focused electron beam using characteristic X-rays and backscattered electrons.
The present solution allows recognition and analysis of inhomogeneous materials. The term "particles" refers to continuous spatially defined regions near the surface of the sample, which in terms of detection abilities of the device appear to be homogenous. Morphologic analysis of particles means determination of their morphological characteristics, such as shape or area. Qualitative and quantitative spectroscopic analyses are methods of analytical chemistry, which determine the presence of chemical elements contained in the examined compound or their percentage respectively, based on the examination of the characteristic X-rays. The present method is suitable especially for analysis of mutual relations between particular types of materials contained in the examined sample.
State of the Art
Spectroscopic analysis using characteristic X-rays formed during interaction of the focused beam of accelerated electrons, which impact on the surface of the examined sample, with a mass located near the examined sample surface, is an important tool in study of chemical and physical characteristics of materials. This analysis is performed in scanning electron microscope. Scanning electron microscope forms an accelerated electron beam in the electron gun, which is deflected by means of deflection coils so that it consecutively impacts on the sample at various points. Upon the incidence of the accelerated electrons on the sample surface there occur interactions between electrons of the incident beam and the material, which is located near the sample surface and near the place of incidence of beams on the sample surface. During the interactions between accelerated electrons and the material several kinds of products are formed, wherein two of them are especially important for the study of chemical properties of materials, these being the back-scattered electrons (BSE) and X-rays.
Back-scattered electrons are electrons of the incident beam, which after elastic collisions with the atoms of material leave the sample with relatively low energy loss compared to the energy with which they impact on the sample. The probability that an elastic collision will occur depends heavily on the atomic number (Z) of the material. The back-scattered electrons may further undergo various types of interactions with other surrounding atoms, until eventually some of them leave the sample. Interactions therefore occur in a certain volume under the sample surface in a so called interaction volume. The ratio between the number of electrons incident on the sample surface and the number of electrons leaving the sample again with approximately the same energy is called emissivity of the back-scattered electrons, referred to as η. This quantity is also dependent on the atomic number (Z). For materials which consist of more types of atoms applies the following equation published by Heinrich in Proceedings of the 4th International Conference on X-ray Optics and Microanalysis in 1966,
Figure imgf000003_0001
where η is emissivity of the back-scattered electrons in the composite material, Ci is weight percentage of the element in the composite material, and r\, is emissivity of the back-scattered electrons in material consisting only of the element /'. The intensity of the back-scattered electrons is measured by means of back-scattered electron detector, analog signal from the back-scattered electron detector is then converted to numerical value using analog-to-digital converter, and based on its output information, an image representing the distribution of back-scattered electrons intensity in the points of the sample is formed in the computer memory.
Energy-dispersive X-ray spectroscopy (EDS) is one of the methods for the study of chemical properties of materials using characteristic X-rays, which is another product of the interaction between the accelerated electron beam and the sample material. Electrons are located in a so-called electron shell in the atom. State of the electrons cannot be optional; the electron is in one of its discrete states. The state of electron is described by means of four quantum numbers. Kinetic energy of the electron is determined by on which atomic orbital of which atom is the electron located. According to so-called Aufbau principle, the electrons in the ground state are arranged in the shell so that they take places on the orbitals with the lowest energy, wherein only two electrons may be located on the same orbital. The electron of the beam incident on the sample has sufficient kinetic energy to, with certain probability, transfer part of its kinetic energy to one of the electrons located on one of the orbitals. Excited electron leaves the orbital leaving an empty space. In a very short time, in order of picoseconds, the atoms return to ground state so that one of the electrons on the orbital with higher energy fills the empty space, wherein it releases part of its binding energy in the form of photon of X-ray electromagnetic radiation. As the orbitals are discrete, energy of the generated photon cannot be optional, but it corresponds to the difference between the energy of the orbital, where the electron was initially located, and the energy of the orbital, where the empty space was formed during the interaction. Atomic orbital energy is unique for each chemical element, therefore each element when being exposed to an accelerated electron beam emits photons having energies, which are characteristic for the said element. This radiation is therefore called characteristic X-ray radiation. X- ray photons undergo further interactions with the material, some of them leaving the material and being caught by the X-ray detector. In EDS, energy-dispersive X-ray detector is used, in which the output voltage changes upon impact of the X-ray photon on its active surface, wherein this change is proportional to the energy of the photon. Pulse processor is an electronic device, which converts the analog signal from the energy-dispersive X-ray detector output to numerical form. Based on these reports, a histogram is made in the computer's memory, being referred to as spectrum, which indicates the number of detected photons of which the energy falls under pre-defined narrow intervals. As described above, X-ray photons are formed in the material, which are characteristic for the element or elements contained therein, detection frequency of photons with characteristic energies is thus higher than that of the other photons; energy-dispersive spectrum therefore comprises emission lines corresponding to the chemical elements contained in the sample.
Qualitative spectroscopic analysis is a method of analytical chemistry, by means of which the percentage of the chemical elements contained in the examined sample is determined, based on the examination of characteristic X-ray radiation. In quantitative spectroscopic analysis based on energy-dispersive spectrum, a ratio of measured radiation intensity with energy characteristic for the given element and radiation intensity with the same energy for a substance consisting exclusively of the atoms of this element is determined for each chemical element of the examined substance. Corrections have to be applied on the calculated values, which describe the degree of absorption and re-emission (fluorescence) of X-rays, these corrections being referred to in literature as ZAF corrections. To simplify the calculations, it is generally assumed that the examined material is homogenous.
In the analysis of inhomogeneous materials, a technique being referred to as X- ray mapping is used. Mapping is usually done so that the electron beam is gradually deflected to various points on the sample. The control unit provides synchronization of circuits for deflection of the electron beam and the pulse processor; thanks to this synchronization it is possible to determine the region on the sample from which the detected X-rays are emitted. By using this method, it is possible to obtain X-ray spectroscopic data with spatial resolution. The easiest technique of X-ray mapping is a method being referred to as dot mapping. In using this method, the interval of X-ray energies is pre-determined. The mapping result is displayed in form of a two- dimensional image, in which black or white dots respectively correspond to regions on the sample, where the number of detected events for one-time unit falling into determined energy interval is lower or higher than the pre-determined threshold. More accurate information about the chemical composition of heterogeneous samples is provided using a technique being referred to as compositional mapping. Quantitative spectroscopic analysis applied on spectroscopic data obtained for each region on the sample is used in this method. A necessary requirement for using the compositional mapping is sufficient amount of spectroscopic data for quantitative analysis. This requirement is not easy to meet, as the signal from EDS detector is relatively weak in relation to resolution of maps used in particle analysis. A combination of spectroscopic data obtained from more points of the sample belongs among possible solutions.
For example, patent document US 7,490,009 discloses the analysis of inhomogeneous materials in scanning electron microscope. The disclosed device collects spectroscopic data using energy-dispersive spectrometer. By comparing the obtained data with the pre-defined set of spectrum categories, the device firstly assigns the particular measuring points to pre-defined spectrum categories. Subsequently, based on these categories, continuous groups of points and particles thereof are created. A drawback of the said solution is the necessity to define a great amount of spectrum categories because, thanks to the size of the interaction volume for X-ray radiation which is comparable to the distance of adjacent measuring points, emission of X-rays in both particles occurs near the interface of these two particles. In such case, spectroscopic data are distorted, as the detected characteristic X-ray radiation in this point comes from two chemically different materials, and the correct classification is therefore difficult. Moreover, for correct classification it is necessary to collect a sufficient amount of data in each point, which is time consuming. Another drawback of the device is that the particle detection is based on classification made on the basis of spectral data and it does not use information from back-scattered electrons detector.
The analysis of inhomogeneous materials in scanning electron microscope is also disclosed in patent document CZ303228. The method disclosed therein collects information from both types of detector (back-scattered electrons detector and energy- dispersive detector) in each of the measuring points arranged in a regular rectangular grid. Under normal operating conditions, the time period for obtaining such spectrum from EDS detector, which is sufficient for determining the material, is much longer than the time period required for obtaining such information from BSE detector, which is sufficient for good image segmentation. Higher number of measuring points on the grid negatively affects the time period for sample analysis. On the other hand, it is not possible to decrease the number of measuring points freely; in case the distance of adjacent measuring point is lower than half of the shortest length or width of particles, the segmentation cannot function properly (sampling theorem).
Summary of the Invention
Object of the invention is a method of material analysis by means of focused electron beam using characteristic X-rays and back-scattered electrons, comprising consecutive deflection of focused electron beam into a number of initial measuring points on the sample arranged in a regular grid, and measuring of intensity of back- scattered electrons to create an electron map. The above mentioned drawbacks are eliminated by the method, in which a set of temporary particles and a set of new measuring points are determined by means of electron map, wherein the number of new measuring points comprises less elements than the initial number of measuring points, and the set of new measuring points includes at least one measuring point for each particle of the number of temporary particles. The electron beam is deflected along set of new measuring points, wherein at the same time measurement of emitted X-rays in these new measuring points is performed. For each new measuring point an X-ray spectrum Sk is created. The set Q'of particles q is determined using at least one particular X-ray interval in each point of the set of new measuring points, and the X- ray accumulated spectrum Xj is determined for the particle <¾·', as a sum of obtained spectrums Sk obtained in the measuring points, which are part of the temporary particle.
In a preferred embodiment, a value of the coefficient a determined by an expert estimate, and the accumulated spectrum Xj is set for each particle q from the set Q', as a sum of spectrum contributions Sk from particular new measuring points, which are part of the temporary particle, wherein particular contributions have different weight, and the weight of contributions is determined using the coefficient a. This step has an essential impact on the accuracy of the analysis result and on reliability of the subsequent classification. Quantitative spectroscopic analysis works on the presumption that the material in the interaction volume, from which the analyzed spectrum is formed, is homogeneous. In general, this requirement is not met in non- homogeneous materials, as thanks to the significant size of the interaction volume, emission of X-ray radiation occurs on the interface of two particles on both sides of this interface. By using the weighted average, where the points on the edge of the particle have lower weight than the points in the center of the particle, this undesirable phenomenon is significantly reduced.
In another embodiment, the relative detection frequency Ni of X-ray quantums is determined from the accumulated X-ray spectrum Xj for the particle q) from the set Q' for each particle p, from the set P. It is possible to apply quantitative spectroscopic analysis on the accumulated X-ray spectrums Xj in order to find the percentage of the chemical elements in the particle q). Both of the above described types of information may be preferably used in particle classification. It is preferable to use accumulated X- ray spectrum for particle classification because the accumulated spectrum obtained by merging spectrums from several measuring points substantially increases the probability that the particle will be correctly classified. Particle classification requires determination of the set Z of rules for classification of materials by means of expert estimate. The set Z is a set of pairs (Ck, Vk) and in each class Ck a logical expression v¾ consisting of variable identifiers, arithmetic operators, logical operators, operators for comparison and number constants. In some of the preferred embodiments, the variables are replaced by the identified relative detection frequencies Nij of X-ray quantums in evaluation of the expressions v¾.
In other preferred embodiments is the set Z replaced by another set Z', and in evaluation of the expressions v¾ are the variables replaced with the identified percentages of chemical elements.
Particle classification may be performed using one of the two methods. In some preferred embodiments are all the expressions Vk from the set Z or Z' respectively evaluated for each particle, and the result of the classification of each particle is the set Cj, which is a subset of the set C of all expressions in the set Z or Z' respectively. In other preferred embodiments are the expressions v¾ evaluated sequentially in the order in which they are arranged before starting the process, and in case any of the expressions has the "true" logical value, the set Q comprises only the class C corresponding to the expression Vk. In case all expressions v¾ for one of the particles have the "false" logical value, the set Q is empty.
The object of the method is thus substantial reduction of the number of measuring points, in which the measurement of X-ray spectrums is performed, thereby significantly reduces the amount of time needed for sample analysis. At the same time, it does not significantly reduce the quality of the obtained analytical data about the sample, as it would be in case of simple increasing of the spaces between measuring points in regular rectangular grid, as for determining the shape, size and mutual spatial relations of the temporary particles in the first pass, an information obtained in high resolution from BSE detector is used. The temporary particles are used for determining the new set of measuring points, wherein it is also determined that the number of new measuring points is lower than the number of points of regular rectangular grid for collecting the data from BSE detector, and at the same time it is also provided that to each temporary particles at least one new measuring point is assigned. In these new measuring points, the collection of X-ray spectrums is performed. The detection of particles takes place again in the second phase, but this time using information from both types of detectors, wherein the data reduction from BSE detector is prevented, as the X-rays spectrums obtained in new measuring points are transformed to X-ray maps with the same resolution as the map conducted in the first phase using information from the BSE detector. Thanks to the combination of data from both detectors it is possible, in the second phase, to distinguish adjacent particles having similar atomic number, thus similar emissivity values of back-scattered electrons, and therefore are not reliably distinguishable using only information from BSE detector, but having different percentage of chemical elements, as the difference in the chemical composition results into different X-ray spectrum from both particles.
Other advantages and benefits of the invention will be obvious after close reading of the exemplary embodiments of the invention together with the corresponding references to the attached drawings.
Description of Exemplary Embodiments
The state of the art is illustrated in the Fig. 1. Electron microscope 13 creates a beam 2 of accelerated electrons in the electron gun 1 which is deflected by means of two so-called deflection coils 3 so that it consecutively impacts on the sample 4 in different points. The currents in deflection coils 3 are controlled by deflection circuits 5, which generate the deflection signal according to the pre-determined regulation, most commonly a regular rectangular grid. Upon the impacting of the accelerated electron on the surface of the sample 4 interactions between the incident electrons and the material occurs, while back-scattered electrons 6 and X-ray radiation 7 are formed.
Device for material analysis by means of focused electron beam using characteristic X-ray radiation is schematically illustrated in the fig. 2, wherein some of the common parts of the electron microscope, which are not directly related to the present invention, are not shown. The device consists of scanning electron microscope 13, which further contains an electron gun 1 forming the beam of accelerated electrons 2, which is deflected by means of two deflection coils 3 so that it consecutively impacts on the sample 4 in various points. The currents in the deflection coils 3 are controlled using deflection circuits 5 generating the deflection signal according to the pre-determined script, most commonly regular rectangular grid. The electron beam 13 is provided with the deflector 8 of back-scattered electrons and analog-to-digital converter 9, which transfers the analog signal from the detector 8 of back-scattered electrons to numerical value. The device is further provided with an X- ray energy-dispersive detector 10 and a pulse processor 11, which processes the analog signal from the X-ray energy-dispersive detector 10 and transfers it into numerical value. Deflection of the beam and processing of the information from all detectors is synchronized by means of control unit 12; the control unit 12 deflects the beam based on information saved in a memory 29. Information from both types of detectors are saved and processed in the processing unit 20. To the whole processing unit 20 is assigned an input device 21 for entering the input values, and a positioning device 22. The input device 2J. is interconnected via a controller 23 of the input device with the processing unit 20. The positioning device 22 is connected via the controller 24 of the positioning device and controller 25 of displaying device with the processing unit 20. The processing unit 20 is connected via the controller 25 of the displaying device with the displaying device 26. Signal from the analog-to-digital converter 9 is connected to the memory 27 in the processing unit 20, where it is further processed. Signal from the pulse processor 1 is connected to the memory 28 in the processing unit 20, where it is further processed.
Internal structure of the processing unit 20 is illustrated in the Figs. 3, 4, 5 and 6. In a preferred embodiment is the controller 23 of the input device connected via the memory 301 (fig. 3) to the first input of the block 302, and via the memory 303 to the second input of the block 302. The input of the block 302 is connected to the input of the memory 29. Output of the memory 27 is connected to the input of the block 102 (fig. 4), wherein the output thereof is connected via the memory 103 to the input of the block 104. The output of the block 104 is connected via the memory 105 to the input of the block 106. First output of the block 106 is connected via the memory 107 to the input of the block 108, wherein the output thereof is connected via the memory 109 to the first input of the block 115, first input of the block 117 and input of the block 130. The second output of the block 106 is connected via the memory HQ to the input of the block HI, wherein the output thereof is connected via the memory 112 with the second input of the block H5, input of the block 113, second input of the lock 119, second input of the block 137, second input of the block VH and with the second input of the block 129. The output of the block 1t3 is connected via the memory 114 to the third input of the block 115. The output of the block 115 is connected via the memory 116 with the third input of the block 117. The output of the block 117 is connected via the memory 1 8 with the third input of the block 119. The first output of the controller 23 of input device is connected via the memory 120 with the first input of the block 119 and with the third input of the block 137. The memory 121 |S connected to the output of the block 122. The memory 124 is connected to the output of the block 123. The memory 133 is connected to the output of the block 132. The output of the block H9 is connected via the memory 134 with the input of the block 135, first input of the block 137 and with the input of the block 136. The memory 124 is connected to the output of the block 135. The memory 133 is connected to the output of the block 136. The output of the block 137 is connected via the memory 121 with the first input of the block 129. The output of the block 129 is connected via the memory 128 with the input of the block 131. The memory 112 is further connected to the output of the block 131 and the memory 109 is further connected to the second output of the block 13_1. The memory 133 is connected to the input of the block 401 (fi9- 5)> wherein the output thereof is connected via the memory 29 with the control unit 12. The fourth output of the controller 23 of the input device is connected via the memory 216 (fig. 6) with the first input of the block 223, the fifth output of the controller 23 of the input device is connected via the memory 201 with the first input of the block 203 and the sixth output of the controller 23 of the input device is connected via the memory 215 with the second input of the block 203. The third input of the block 203 is connected to the memory 121 and the fourth input of the block 203 is connected to the memory 202. The output of the block 203 is connected via the memory 204 to the input of the block 205, wherein the output thereof is connected via the memory 206 to the first input of the block 207. The second input of the block 207 is connected to the memory 103. The output of the block 207 is connected via the memory 208 to the input of the block 217, and the output of the block 217 is connected via the memory 218 to the input of the block 209. The first output of the block 209 is connected via the memory 210 to the first input of the block 221 , and the second output of the block 209 is connected via the memory 211 to the first input of the block 229, wherein the output thereof is connected via the memory 228 to the second input of the block 221. The output of the block 231 is connected via the memory 229 to the input of the block 227, wherein the output thereof is connected via the memory 226 to the second input of the block 229. The input and the output of the block 230 are connected to the memory 229. The output of the block 221. is connected via the memory 222 to the second input of the block 223. The output of the block 223 is connected via the memory 224 to the first input of the block 225. The second input of the block 225 is connected to the memory 202, and the third input of the block 225 is connected to the memory 121. The output of the block 225 is connected via the memory 219 to the input of the block 213, wherein the output thereof is connected via the memory 214 to the controller 25 of the output device.
Block 302 (fig. 3) reads the basic distance d between the measuring points, which is saved in the memory 301 , and the size F of the field of vision, which is saved in the memory 303, calculates the proportion F I d and the result is rounded to the closest positive integer number. The resulting value is used as a number of columns and rows in the regular rectangular grid, for which a script J for rasterizing is determined so that the grid points scan the rows in sequential manner. The scanning script J is saved in the memory 29.
Block 102 performs the transformation of the map B to the differential map DB using operation which is referred to as edge detection. Its purpose is to transform the input image so that the values in the points, in which the transition between two regions with different intensities is located, are higher than the values in the surrounding points in the output image. The transformation result is again a single-channel (grayscale) image with the same dimensions as the input image. In a preferred embodiment it is possible to perform the edge detection process using so-called Sobel operator known in the computer graphics. Description of the Sobel operator was published for example by Shrivakshan and Chandrasekar in „A Comparison of various Edge Detection Techniques used in Image Processing" published in the International Journal of Computer Science Issues, volume 9, issue 5 in 2012. The resulting map DB is saved in the memory 103.
The block 104 performs segmentation of the image so that the bit map £ is created from the differential map DB. The bit map E has the same dimensions as the differential map DB. Values E (x, y) saved in the bit map E differentiate the points, which are parts of the particles (value 1 ), and points which are located outside the particles (value 0). One of the preferred embodiments utilizes transformation, which is referred to as watershed. This transformation is known in the computer graphics, its original idea was presented by Beucher and Lantuejoul in„Use of watersheds in contour detection" published in September 1979 in conference proceedings International Workshop on Image Processing v Rennes. The resulting bit map E is saved in the memory 105.
The block 106 reads the bit map £ from the memory 105 and determines the map R of temporary particles distribution and the set Q of temporary particles. Size of the map R of temporary particles distribution is identical with the size of the map 8. The value R (x, y) is zero, provided that the point with coordinates (x, y) is located outside a valid temporary particle, or it is equal to the sequence number of the temporary particle, to which the sample point with coordinates (x, y) belongs. The set Q of temporary particles is therefore a set of all temporary particles located on the surface. This operation may be performed, for example, so that the transformation known as connected components labeling is applied to the input map. The transformation is known in the computer graphics and description of one of its variants was published by Bailey and Johnston in ..Single Pass Connected Components Analysis" published in Proceedings of Image and Vision Computing New Zealand 2007. The resulting transformation is directly the map R of temporary particles distribution; the set Q is determined based on the map R of temporary particles distribution as a set of non-zero unique values R (x, y). The map R of temporary particles distribution is saved in the memory 10, the set Q of temporary particles is saved to the memory 107.
The blocks 108, 111, 122> 123 and 132 perform initialization (setting initial content) of the memories 109, 112, 121, 124 and 133: the block 108 creates an auxiliary set P of temporary particles so that it copies content of the memory 107 into the memory 109. The block m creates an auxiliary map S of temporary particles distribution so that it copies the content of the memory HO into the memory 112. The block 122 creates an auxiliary map Y so that the auxiliary map Y has the same dimension as the map 8 and all values Y (x, y) are zero, and saves it in the memory 121. The block 123 creates an auxiliary map U of measuring points so that the auxiliary map U of measuring points has the same dimension as the map 8, and all values U (x, y) are zero, and saves it in the memory 124. The block 132 saves an empty script J' of X-ray mapping in the memory 133. The block 113 performs calculation of the dimension between points, which are parts of the particles, and the edge of these particles. One of the possible embodiments utilizes transformation referred to as Euclidean distance transformation. The transformation is applied on the input map and the result is another map with the same dimension. The output map contains on its coordinate (x, y) an integer value, which determines the distance between the point with the coordinates (x, y), which is part of the particle, and the edge of the particles increased by 1 ; values of the input map corresponding to the points located on the edges of the particles are 1 , values corresponding to the points, which are part of the particles, and which are spaced from its edge for 1 point, are 2 etc. Values of the output map corresponding to the points located outside the particles are 0. The input map is loaded from the memory 112, the output map, the auxiliary map T is saved in the memory 114.
The block 115 performs transformation of input maps into one output map with the same dimension in order to select possible measuring points. The first input map, the auxiliary map S of the temporary particles distribution, saved in the memory 112, contains on its coordinates (x, y) values corresponding to the sequence number of the temporary particles located in the point with the coordinate (x, y). The second input map, the auxiliary map T, saved in the memory 114, contains in its coordinates (x, y) values representing the distance of the points with the coordinate (x, y) from the edge of the temporary particle. In one of the preferred embodiments the output map is determined so that the set of temporary particles is loaded from the memory 109 and for each temporary particle belonging to this set such points are found, which have the largest distance from the edge of this temporary particle. These points are tagged in the first input map and the resulting copy of the input map with the selected tagged points - the auxiliary map T - is saved in the memory 116, as it is, for example, illustrated in the fig. 4.
The block 117 performs selection of the output points from the set of possible candidates. The input is the auxiliary map T saved in the memory 116, where a tag determining whether the point is a suitable candidate or not is put on each point. The output is a list O of initial points, wherein one measuring point is selected for each temporary particle from the auxiliary set P of temporary particles saved in the memory 109. In one of the possible embodiments is the initial point selected randomly from the candidates. The result, the list O of initial points, is saved in the memory 118. The block 119 generates a list Z of measuring points based on the list O of output points saved in the memory 118, map S of temporary particles distribution saved in the memory 112, and the coefficient c saved in the memory 120. The block 119 works as follows: for each output point with coordinates (x, y) from the list O of output points a list of measuring points with coordinates (i, j) is determined; the first measuring point is always the initial point (i=x, j=y). Other measuring points are the ones with the coordinates (i, j), which are located in the same column (the same value i=m) or in the same row (j=n) as other measuring points with the coordinates {m, n) belonging to the same initial point as the measuring point with the coordinates (m, n), wherein distance between any of these two measuring points belonging to the same initial point is equal to the coefficient c or higher. It further applies that the measuring points have to be parts of the same temporary particle as the initial point, to which this measuring point belongs, which may be determined based on the auxiliary map S of temporary particles distribution. List of measuring points merges for all initial points of the list O of initial points into one list, and each measuring point is given an identification number, such as sequence number of measuring point. The resulting list Z of measuring points is saved in the memory 134.
The block 135 updates the auxiliary map U of measuring point saved in the memory 124 so that the value U (x, y) is set to the identification number of the measuring point for each measuring point with the coordinates (x, y) from the set Z of measuring points.
The block 136 updates the script J' of X-ray mapping saved in the memory 133, so that it inserts all measuring points from the set Z of measuring points at the end of the script.
The block 137 loads the list Z of measuring points saved in the memory 134, auxiliary map S of temporary particles distribution saved in the memory 112, and values of the coefficient c saved in the memory 120, and updates the auxiliary map Y as follows: for all measuring points with the coordinates (x, y) from the list Z of measuring points, the values Y (i, j) in the auxiliary map Yare set on the identification number of the measuring point for all such points with the coordinates (i, j), for which it applies thatx < i≤ x + ^ and at the same time y - < ; < y + where x and y are coordinates of the measuring point and c is a coefficient defined above. The new auxiliary map Y is saved in the memory 121 .
The block 129 creates an auxiliary map W, in which points which are not covered yet are highlighted, based on the auxiliary map S of temporary particles distribution saved in the memory 112 and the auxiliary map V saved in the memory 121. Resulting auxiliary map Wis saved through the output of the block 129 into the memory 128. The block works as follows: auxiliary map W has the same dimension as the map S of temporary particles distribution; the value W (x, y) with the coordinates (x, y) is set to 1 , provided that the value S (x, y) is a valid particle number, and the value Y (x, y) is not a valid particle identification number of the measuring point. In all other cases is the value W(x, y) zero.
The block 131 loads the auxiliary map W of the remaining points from the memory 128 and updates the auxiliary map S of temporary particles distribution saved in the memory 112, and further updates the auxiliary set P of temporary particles. In a preferred embodiment is this operation performed so that connected components labeling transformation is applied on the auxiliary map W. Result of the transformation is directly the new auxiliary map S of temporary particles distribution; the new auxiliary set P of temporary particles is determined based on the new auxiliary map S of temporary particles distribution, as a set of unique non-zero values S (x, y). The new auxiliary map S of temporary particles distribution is saved in the memory 112, and the new auxiliary set P of temporary particles is saved in the memory 109.
The block 130 loads the auxiliary set P of temporary particles and indicates the state„off" at its output provided that the set is empty, and„on" provided that the set is not empty.
Basic X-ray scheme is continued in the fig. 5. The block 401 loads the script J' of X-ray mapping from the memory and copies it to the memory 29 on the command of the processing unit 20.
The basic block scheme is continued in the fig. 6. The block 203 load the set P of chemical elements from the memory 215, the set of X-ray energy intervals // from the memory 201 and the auxiliary map Y from the memory 121 , and for each element i from the set P of chemical elements an X-ray map Mi is created, where the values Mi (x, y) saved in the map M, are determined as follows: for points with the coordinates (x, y) where Y(x, y) is 0 it applies that M, (x, y) = 0 (points outside the particles). For points with the coordinates (x, y) where Y(x, y) is non-zero (value Y(x, y) corresponds to the sequence number of the measuring point) the value Y (x, y) is used to find the corresponding spectrum, and the value Mi (x, y) is determined based on this spectrum so that the value M,- (x, y) corresponds to the X-ray intensity with the energy belonging to the interval /, emitted in the measuring point (step 703). Resulting X-ray maps Mi are saved in the memory 204.
The block 205 loads the X-ray maps M, from the memory 204 and converts them into differential X-ray map DM, where the values DM(X, y) saved in the map DM are related to the points on the sample with the coordinates (x, y) and correspond to the gradient size of the X-ray intensity with the energy in the point with the coordinates (x, y). In a preferred embodiment, it is possible to perform this operation using transformation of the gradient, which may be applied on multi-channel input image data (differential X-ray map Mi) and the result is one-channel image data (differential X-ray map DM)- Description of the gradient transformation, which operates with multi-channel input image data, may be found, for example, in„A Multichannel Watershed-Based Segmentation Method for Multispectral Chromosome Classification" published by Karvelis in IEEE Transactions on Medical Imaging, volume 27, issue 5, where this method is used for classification of chromosomes in the image obtained using multichannel fluorescence imaging channel. Resulting differential X-ray map DM is saved in the memory 206.
The block 207 merges the differential X-ray map DM, saved in the memory 206, and the differential electron map DB, saved in the memory 103, into resulting differential map D. The values D (x, y) are determined as a maximum of the values DB (X, y) and DM (X, y). The resulting differential map D is saved in the memory 208.
The block 217 performs segmentation of the image so that the differential map D is loaded from the memory 208 and it is converted to bit map E' so that the bit map E' has the same dimension as the differential map D. The values E' (x, y) saved in the bit map £' differentiate the points, which are parts of the particles, and the points located outside the particles. One of the possible embodiments utilizes watershed transformation. The resulting bit map E' is saved in the memory 216. The block 209 loads the bit map E', saved in the memory 216, and determines the map R'of particle distribution and the set Q'of particles. The values R'(x, y) saved in the map R' are related to the points on the sample with the coordinates (x, y) and represent sequence number of the particle, to which the point on the sample with the coordinates (x, y) belongs. The set Q' of particles is therefore the set of all particles detected on the sample. This operation may be performed, for example, using the same transformation as in the block 106. The obtained map R' of particle distribution is saved in the memory 211 , the obtained set Q' of particles is saved in the memory 210.
The block 231. initializes a variable /' so that it saves the value 1 in the memory 229.
The block 230 increments (increases by 1 ) the register value /, saved in the memory 229, based on a command of the processing unit 20.
The block 227 reads the value of the variable / from the memory 229 and this values is saved to a variable j in the memory 226.
The block 229 reads the value from the memory 226 and the map R' of particle distribution from the memory 211 and creates a bit map U), which has the same dimension as the map R'of particle distribution and the values U) (x, y) are 1 , provided that R' (x, y) = j and the values U) (x, y) are 0 for the remaining values R' (x, y). The resulting bit map U) is saved in the memory 228.
The block 221 reads the bit map U) from the memory 228 and converts it to bit map V'j. The values Vj' (x, y) are zero, provided that the point with the coordinates fx, y) is located outside the particle q,, the positive values V) (x, y) represent the minimum distance of the points with the coordinates fx, y) from the edge of the particle increased by 1. This operation may be performed, for example, using Euclidean distance transformation. The output of the transformation applied on the bit map U is directly the map V'j. The map V) is saved in the memory 222.
The block 223 reads the map V) from the memory 222 and the coefficient a from the memory 216, and creates a weighted map W), in which the value W) fx, y) represents the weight of the spectrum contribution to the accumulated spectrum Xj (E). The values W) fx, y) are determined as follows:
Figure imgf000019_0001
0 if V'jix.y) = 0
The resulting weighted map W) is saved in the memory 224.
Coefficient a is determined by one skilled in the art before initializing the analysis based on the knowledge of character of the examined points, this value is saved through the controller of the input device 21 in the memory 216. This step has an essential impact on the accuracy of the analysis result and reliability of the subsequent classification. Quantitative spectroscopic analysis works with the presupposition that the material in interaction volume, from which the analyzed spectrum is formed, is homogeneous. For non-homogeneous materials, this condition is not met in general, as thanks to the significant size of the interaction volume, X-ray emission occurs on both sides of the interface between two particles. Using the weighted average, where the points on the edge of the particle have lower weight than the points in its center, significantly reduces the undesirable phenomenon.
The block 225 loads the weighted map W) from the memory 224 and the auxiliary map Y from the memory 121 , and creates an accumulated spectrum Xj so that contributions from the points with the coordinates (x, y) multiplied by the weight W'j (x, y) are summed. For each point with the coordinates (x, y), where the value W) (x, y) is non-zero the value Y (x, y) is read from the auxiliary map Y, representing the sequence number of the measuring point, and k-th spectrum Sk is read from the spectrum map S, the values Sk (E) in the spectrum Sk are multiplied by the value W) (x, y) and added to the corresponding values Xj (E) of the accumulated spectrum Xj.
Figure imgf000019_0002
Resulting accumulated spectrum Xj is saved in the memory 219.
The block 213 reads the accumulated spectrum Xj from the memory 219, and the set P of chemical elements from the memory 215, and for each element p,- from the set P of chemical elements the relative detection frequency Nij of the X-ray quantums with the energy in the interval /, in the spectrum Xj as a proportion of the number of detected X-ray quantums with the energy in the interval // in the spectrum Xj and the overall number of quantums in the spectrum Xf.
Figure imgf000020_0001
The determined values Ni are saved in the memory 214.
Following description of the device is graphically illustrated in the figs. 7, 8 and 9. The device works as follows: by means of an expert estimate made by one skilled in the art, the basic resolution d, the size F of the field of vision, the value of the coefficient a and the value of the coefficient c are determined. An adequately large set P of chemical elements, which may occur in the examined sample, is further determined by means of an expert estimate. An interval /,· of X-ray photon energies is determined for each element p, from the set P of chemical elements, corresponding to one of the emission lines of the given element. The values d, F, a and c are set by the device operator by means of the input device 2Λ through the controller 23 of the input device; the basic resolution d is saved in the memory 301 , size F of the field of vision is saved in the memory 303, value of the coefficient a is saved in the memory 216 and the value of the coefficient c is saved in the memory 120 (image 7, step 501 ). The set P of chemical elements and intervals // of X-ray photon energies are set by the device operator by means of the input device 21 via the controller 23 of the input device; the set P of chemical elements is saved in the memory 215 and the intervals // of X-ray photon energies are saved in the memory 201. On the command put by the device operator in the input device 21 via the controller 23 of the input device into the processing unit 20, the following process is initialized.
At the beginning of the process, the size F of the field of vision is read from the memory 303 and the basic resolution d from the memory 301., and the ratio F / d is calculated; the result is rounded to the nearest positive integer number. The obtained value is used as a number of columns and rows in the regular rectangular grid, for which the block 302 generates the scanning script J based on the request of the processing unit so that the points of the grid are passed along the rows in sequential manner; the scanning script J is saved in the memory 29 (step 502). The control unit 12 reads the scanning script J from the memory 29 and runs the scanning process (step 503). Deflection circuits 5 control the current by means of the deflection coils 3 so that the electron beam 2 gradually impacts on the sample 4 in those points determined by the scanning script J. The control unit 12 further communicates with the analog-to-digital converter 9. A signal from the analog-to-digital converter 9 is sent to the processing unit 20, where it is saved in the memory 27 (map B). The map B is a two-dimensional field of values (x, y), which are related to the points on the sample with the coordinates (x, y). The number of rows and columns of the map is identical with the number of rows and columns of the regular rectangular grid, which has been used for generating the scanning script J. The value β (x, y) represents the intensity of back-scattered electrons emerging upon the impact of the electron beam 2 on the sample 4 in a point with the coordinates (x, y).
The map B, saved in the memory 27, is converted to a differential map Ds (step 504), by means of edge detection operation. In the preferred embodiment, it is possible to perform the edge detection using so-called Sobel operator. The resulting differential map DB is saved in the memory 103.
The differential map Ds, which is saved in the memory 103, is converted to the bit map £ (step 505). The bit map £ has the same dimension as the differential map Ds. The values £ (x, y) saved in the bit map £ differentiate the points, which are parts of the temporary particles, and the points located outside the temporary particles. One of the possible embodiments utilizes watershed transformation. The resulting bit map £ is saved in the memory 105.
The bit map E, saved in the memory 105, is used for determining the map R of temporary particles distribution and the set Q of temporary particles (step 506). The values R (x, y) saved in the map R are related to the points on the sample with the coordinates (x, y). The value R (x, y) is zero, provided that the point with the coordinates (x, y) is located outside the valid temporary particle, or it is equal to the sequence number of the temporary particle, to which the point with the coordinates (x, y) on the sample belongs. The set Q of temporary particles is therefore the set of all temporary particles detected on the sample. This operation may be performed so that connected components labeling transformation is applied on the input map. Result of such transformation is directly the map R of temporary particles distribution; the set Q is determined based on the map R of temporary particles distribution, as set of unique non-zero values R (x, y). The map R of temporary particles distribution is saved in the memory 110, the set Q of temporary particles is saved in the memory 107.
In the next step, the auxiliary map S of temporary particles distribution is created (figure 8, step 601), as a copy of the map R of temporary particles, and it is saved in the memory 112; further, an auxiliary set P of temporary particles is created as a copy of the set Q of temporary particles, and it is saved in the memory 109. The auxiliary map Y is initialized so that the size of the auxiliary map Y is identical with the size of the map B and all values Y(x, y) are non-zero, the auxiliary map Yis than saved in the memory 121 , and the auxiliary map U of measuring points is initialized in the same manner and saved in the memory 124. An empty script J' of X-ray mapping is created and saved in the memory 133.
Provided that the auxiliary set P of temporary particles is not empty (requirement 602), the following process is repeated.
Based on the auxiliary map S of temporary particles distribution saved in the memory 112, the distance between the points which are parts of the temporary particles and the edge of these particles (step 603); the result is the auxiliary map T, which has the same dimension as the auxiliary map S. The values T (x, y) are zero for points located outside the valid particles, or positive integer numbers representing the distance between the point, which is part of the temporary particle, and the edge of this particles increased by 1. The values T (x, y) are equal to 1 for points located on the edges of the temporary particles, the values T (x, y) are equal to 2 for points, which are parts of the particle and spaced from the edge of this particle by 1 point etc. In one of the possible embodiments Euclidean distance transformation is used. The resulting auxiliary map T is saved in the memory 114.
The obtained auxiliary map T is used for selection of the possible candidates for measuring points (step 604). The auxiliary map S of temporary particles distribution is read from the memory 112, the set P of temporary particles is read from the memory 109, and the auxiliary map T is read from the memory 114. The auxiliary map T is determined so that those points with the coordinates (x, y), for which the value S (x, y) is equal to the sequence number of the temporary particle, are tagged for each temporary particle from the set P of temporary particles, and the value the value T (x, y) is maximum among all the points with the coordinates (i, j), for which the value S (i, j) is equal to the sequence number of the temporary particle. The resulting map T, which is created as a copy of the auxiliary map T with tags on the selected points, is saved in the memory 116.
In the next step, an auxiliary map T is read from the memory 116, the auxiliary map S of temporary particles distribution is read from the memory 112 and the auxiliary set P of temporary particles. For each particle from the auxiliary set P of temporary particles one initial point is selected, and the set O of initial points is set as a set of selected initial points (step 605). In one of the possible embodiments is the initial point selected as follows: a list of initial point candidates is determined as a list of points with the coordinates (x, y) by passing all the values T (x, y) of the map T'for each temporary particle from the auxiliary set P of temporary particles, where the value S (x, y) is equal to the sequence number of the temporary particle and the tag on the value V (x, y) is set. After passing, one initial point is chosen for each temporary particle from the list of the possible candidates from the auxiliary set P of temporary particles; in one of the possible embodiments is the initial point chosen randomly. The resulting set O of initial points is saved in the memory 118.
For each initial point from the set O of the initial points, a list of measuring point is generated (step 606) as follows: a list of measuring points with the coordinates (i, j) is created for each initial point with the coordinates (x, y) from the list O of initial points so that the first measuring point is the initial point (i=x, j=y). Other initial points are all points with the coordinates (i, j), which are located in the same column (i=m) or in the same row (J=n) as any other measuring point with the coordinates (m, n) belonging to the same initial point as a measuring point with the coordinates (m, n), wherein the distance between any two measuring points belonging to the same initial point is equal to the coefficient c or higher. It further applies that all measuring points have to be part of the same temporary particle as the initial point, to which this measuring point belongs, which may be determined based on the auxiliary map S of temporary particles distribution. The list of measuring point is merged into one list for all initial points from the list O of initial points, and a unique positive identification number is allocated to each measuring point, for example, a sequence number of the measuring point. The resulting list Z of measuring points is saved in the memory 134. The list Z of measuring points saved in the memory 134 is used for updating the auxiliary map U (step 607). This is illustrated in the fig. 8. The value U fx, y) is set to the identification number for all measuring points from the list Z of measuring points; the coordinates fx, y) are the coordinates of the measuring point. The resulting new auxiliary map U is saved back in the memory 124. At the same time, all measuring points from the list Z of measuring points are inserted at the end of the script J' of X- ray mapping, which is saved in the memory 133. Based on the list Z of measuring points, the auxiliary map Y is also updated as follows: for all measuring points with the coordinates (x, y) from the list Z of measuring points, the values Y (i, j) in the auxiliary map Y are set to the identification number of the measuring point, for all such points with the coordinates (i, j), for which it applies that the point with the coordinates (i, j) is a part of the same temporary particle as the corresponding initial point, to which this measuring point belongs, and at the same time it applies that χ -
Figure imgf000024_0001
and y - < j≤y + , where x and y are coordinates of the measuring point and c is the coefficient defined above. The new auxiliary map Yis saved in the memory 121.
Based on the new auxiliary map Y saved in the memory 121 and the auxiliary map S of temporary particles distribution, which is read from the memory 112, the auxiliary map Wis determined as follows (step 608): the auxiliary map Whas the same dimension as the new auxiliary map Y. The values W(x, y) in the auxiliary map Ware set to 1 , provided that the value S (x, y) in the auxiliary map S of temporary particles distribution is a valid number of some of the temporary particles, and the value Y (x, y) in the new auxiliary map Y is 0. For all other measuring points with the coordinates fx, y) is the value W(x, y) in the auxiliary map Wset to 0. The auxiliary map W is saved in the memory 128.
In the next step, new temporary particles are determined in the auxiliary map W; a new auxiliary map S of temporary particles distribution is generated as well as a new set P of temporary particles (step 609). In a preferred embodiment, this operation is performed so that connected components labeling transformation is applied on the auxiliary map W. Result of the transformation is directly the new auxiliary map S of temporary particles distribution; a new auxiliary set P of temporary particles is determined based on the new auxiliary map S of temporary particles distribution, as a set of unique non-zero values S (x, y). A new auxiliary map S of temporary particles distribution is saved in the memory 112, and a new auxiliary set P of temporary particles is saved in the memory 109.
Subsequently, the set P of temporary particles is tested in order to determine whether it is empty (requirement 602). Provided that the set is not empty, the above described process is repeated.
In case the set P of temporary particles is empty, the content of the memory 133 is copied to the memory 29 and the processing unit 20 gives command to the control unit 12, which runs the X-ray mapping (fig. 9, step 701 ). The deflection circuits 5 control the current by means of the deflection coils 3 so that the electron beam 2 consecutively impacts on the sample 4 in the points determined by the script J' of X-ray mapping saved in the memory 29. The control unit 12 further communicates with the pulse processor 11 A signal from the pulse processor J is sent to the processing unit 20, where it is further processed.
A spectrum map S is created in the processing unit 20 based on the signal from the energy-dispersive detector 10 of X-ray radiation, wherein one spectrum corresponds to each measuring point from the script J' of X-ray mapping (step 702). Spectrum map S refers to two-dimensional field, wherein one dimension corresponds to the identification number of the measuring point from the script J' of X-ray mapping, and the second dimension is the number of the channel corresponding to the narrow interval of photon energy E. Scalar values Sk (E) saved in the spectrum map S correspond to the number of detected X-ray photons with the given energy E in the point on the of the sample 4 with the coordinates (x, y) = J' (k) for time, during which the electron beam remained at this point.
After the X-ray mapping is finished, the set P of chemical elements is read from the memory 215, the intervals // of X-ray energy are read from the memory 201 and the auxiliary map Y is read from the memory 121 , and for each element p,- from the set P of chemical elements an X-ray map is created, where the values M, (x, y) saved in the map M, are related to the points on the sample with the coordinates (x, y), and they are determined as follows: for points with the coordinates (x, y) where Y(x, y) is 0, it applies that M, (x, y) = 0 (points outside the particle). For points with the surroundings (x, y) where Y(x, y) is non-zero (value Y (x, y) of the sequence number of the measuring point), the value Y (x, y) is used for finding the corresponding spectrum, and the value M, (x, y) is determined based on this spectrum so that the value Mi (x, y) corresponds to the X-ray intensity with energy in the interval /, emitted in the measuring point (step 703). Resulting X-ray maps M,- are saved in the memory 204.
Subsequently, the X-ray maps Mi, saved in the memory 204, are converted to differential X-ray map DM, in which the values DM (X, y) saved in the differential X-ray map DM are related to the points on the sample with the coordinates (x, y) and they correspond to the size of the X-ray intensity gradient in the point with the coordinates (x, y) (step 704). In a preferred embodiment, it is possible to perform this transformation using transformation of the gradients. The resulting X-ray map DM is saved in the memory 206.
Differential X-ray map DM and the differential electron map DB are subsequently merged into resulting differential map D (step 705). This operation may be performed, for example, as follows: a differential map D is created, which has the same dimension as the differential electron map DB. The values D (x, y) are set as a maximum of the values DB (X, y) and DM (X, y). The resulting differential map D is saved in the memory 208.
The differential map D, which is saved in the memory 208, is converted to bit map E' (step 706). The bit map E' has the same dimension as the differential map D. The values E' (x, y) saved in the bit map E' differentiate the points, which are part of the particle, and the points located outside the particle. One of the possible embodiments utilizes watershed transformation. The resulting bit map E'is saved in the memory 218.
The bit map E', saved in the memory 218, is used for determining the map R' of particle distribution and the set Q' of particles (step 707). The values R' (x, y) saved in the map R' are related to the points on the sample with the coordinates (x, y). The value R' (x, y) is zero, provided that the point with the coordinates (x, y) is located on the valid temporary particle, or it is equal to the sequence number of the temporary particle, to which the point on the sample with the coordinates (x, y). The set Q' of the particles is therefore the set of the particles detected on the sample. This operation may be, for example, performed so that the connected components labeling transformation is applied on the input map. The result is directly the map R'of particle distribution; the set Q' of particles is determined based on the map R' of particle distribution, as a set of unique non-zero values R' (x, y). The map R' of particle distribution is saved in the memory 211, the set Q' of particles is saved in the memory 210.
In the next step, the X-ray spectrum Xj is determined for each particle q from the set Q' of particles. In a preferred embodiment, it is possible to perform this operation so that, at first, register /' is initialized so that the value 1 is saved therein. The identification number j of the /-th particle q, from the set Q' of particles is read, and the identification number j of the particle qj is saved in the memory 226. The bit map U) with the same dimension as the map R' of particle distribution is created, and the values U (x, y) are 1 , provided that R' (x, y) = j and values U (x, y) are 0 for other values R' (x, y), the bit map U is saved in the memory 228. Subsequently, the bit map LI) is converted using Euclidean distance mapping to the map V), the values V) (x, y) are zero, provided that the point with the coordinates (x, y) is located outside the particle q,, the positive values V) (x, y) represent the minimum distance of the point with the coordinates (x, y) from the edge of the particle, increased by 1. The map V) is further transformed to the weighted map W using the coefficient a, saved in the memory 216.
As it has been mentioned above, the coefficient a is determined by an expert estimate before initializing the analysis based on the knowledge of the examined samples character. This step has an essential impact on the accuracy of the analysis result as well as on the reliability of the subsequent classification. Quantitative spectroscopic analysis works with the presupposition that the material in the interaction volume, from which the analyzed spectrum is formed, is homogeneous. In general, this requirement is not met in homogeneous materials, as thanks to the significant size of the interaction volume, emission of X-ray radiation occurs near the interface of two particles on both sides of this interface. Using the weighted average, where the points on the edge of the particles have lower weight than the points in its center, significantly reduces this undesirable phenomenon.
The values W) (x, y) are calculated as follows:
Figure imgf000028_0001
0 if V'j(x,y) = 0
The resulting weighted map W) is saved in the memory 224.
Based on the weighted map W) (x, y) saved in the memory 224, the auxiliary map Y saved in the memory 121 , and the spectrum map S saved in the memory 202, the accumulated spectrum Xj of the particle q, is determined as follows: all points with the coordinates (x, y) where the value W (x, y) is non-zero are sequentially passed, the value Y (x, y) from the auxiliary map Y is read for each of these points, the value V (x, y) represents the sequence number k of the measuring point. The spectrum S is read from the spectrum map S, which has been obtained from the sample 4 with the coordinates (x, y). The values Sk (E) are multiplied by W (x, y) and are added to the accumulated spectrum Xj.
Figure imgf000028_0002
The spectrum Xj enters the block 213, in which the relative detection frequency Nij of the X-ray quantums is determined, with the energy in the interval /, in the spectrum Xj as a proportion of the number of detected X-ray quantums with the energy in the interval // in the spectrum Xj and the overall number of quantums in the spectrum
Figure imgf000028_0003
The determined values Nij are saved in the memory 214 and are displayed to the user on the displaying device 26 connected to the processing unit 20 in a form of two-dimensional image, in which the spatial distribution of the detected particles is illustrated, based on the map R' of the particle distribution, saved in the memory 211. User is allowed, using the positioning device 22 preceding the processing unit 20, for example a mouse, to highlight one of the particles in the image, and subsequently, relative detection frequencies of the X-ray quantums for chemical elements p, from the set P are displayed in the another part of the display. In another (second) possible embodiment is the device according to the above mentioned description supplemented with the spectrum analyzer 801. The block scheme of the device in this embodiment is illustrated in the figure 10, wherein some of the parts which are the same as in the basic embodiment are left out for better understanding. Input of the spectrum analyzer 801 is connected to the memory 219 and the output thereof is connected via the memory 802 to the second input of the controller 25 of the output device.
The spectrum analyzer 801 reads the accumulated spectrums Xj from the memory 219 and using the quantitative spectroscopic analysis it determines the percentage of the chemical elements in the particle q). The output values are saved in the memory 802. The result of the quantitative spectroscopic analysis is displayed to the user after highlighting a particle in other part of the displaying device 26 as a table of chemical elements and percentages of each element.
Description of the device operation in this embodiment is graphically illustrated in the figure 15, wherein some of the steps which are the same as in the basic embodiment are not shown for better understanding. Device in this embodiment operates in the similar manner as the basic device described above, except that after saving the accumulated spectrum Xj for the particle q) (step 708). a percentage of chemical elements in this particle is determined using quantitative spectroscopic analysis (step 901 ).
In another (third) possible embodiment is the device according to the description provided above supplemented with the particle classifier 8_10. Block scheme of the device in this embodiment is illustrated in the figure 11 , wherein some of the parts which are the same as in the basic embodiment are not shown for better understanding. The particle classifier 810 is connected on its first input via the memory 811. to the sixth output of the controller 23 of the input device, and on its second input it is connected to the memory 214. The output of the particle classifier 810 is connected via the memory 812 to the third input of the controller 25 of the output device.
The particle classifier 810 reads the values of relative detection frequencies Njj of X-ray quantums in the interval /,· for chemical elements p, from the quantity P of the chemical elements from the memory 214 in the particles qj' from the set Q', and reads the set Z from the memory 811 , and for each particle q'j from the set Q' it determines the set Cj of classes, which is saved in the memory 812.
Description of the operation of the device in this embodiment is graphically illustrated in the figure 16, wherein some of the steps which are the same as in the basic embodiment are not shown for better understanding. The device in this embodiment works in the similar manner as the basic device described above, except that before initialization of the operation the operator sets the set Z using the input device 21 via the controller 23 of the input device and the set Z is saved in the memory 811. (step 910). The set Z is set in the form of a set of ordered pairs, where Z = { (Ck, Vk); k = 1 , 2, ... nc }, where r?c is the number of classes and each class Ck has its own logical expression v¾, which consists of variable identifiers, numeric constants, arithmetic operators for negation, addition, multiplication, subtraction and division, operators for comparison of two numerical values (equivalence, non-equivalence, greater, greater or equal, less, less or equal) and logical operators for negation, conjunction and disjunction.
After determining the relative detection frequencies Nij of the X-ray quantums (step 709) and saving the values Nij in the memory 214, the classification of the particles follows. A set of variables occurring in the expressions v¾ is found. A number of particles /IQ I'S determined as a cardinality of the set Q', and positive integer numbers ranging from 1 to no- are allocated to the particles according to the order, in which the particles have been inserted into the set Q'. Classification begins with the particle qj' for the index j = 1 (particles with the sequence number 1 ) (step 911 ). In case the index value is less than or equal to /7Q- (step 912), relative detection frequencies of X-ray quantums are read from the memory 214 for the particle qj', and these values are saved in the variables occurring in the expressions v¾. Particle classification begins by evaluation of the expression v¾ for the index k = 1 (step 913). In case the truth value of the expression is„true", the class Ck is inserted to the set Q (step 916). Regardless of the truth values of the expression, the process continues with the next index k (step 917). Evaluation of the truth values of all logical expressions for the particle q) results into the creation of the set Q, which is a sub-set of the set C and contains those particles Qcfrom the set C, for which the truth value of the logical expression ¾ is„true". The set Cj is saved in the memory 812 and the process continues with another index j (step 918). The result of the particle classification is displayed to the user after highlighting the particle in another part of the displaying device 26 as a list of classes, to which the particle has been allocated.
In another (fourth) possible embodiment, no more than one class Ck is allocated to the particle during the classification. In this embodiment, the set Z is an ordered set (the elements of the set Z have their defined order) Z = { (Ck, Vk), k = , 2, ... nc}; in the similar manner, the set C is an ordered set of classes ¾. Block scheme of this device is illustrated in the figure 12, wherein some of the parts which are the same as in the basic embodiment are not shown for better understanding. The particle classifier 820 is on its first input connected via the memory 822 to the sixth output of the controller 23 of the input device and on its second input it is connected to the memory 214. The output of the particle classifier 820 is connected via the memory 821 to the third input of the controller 25 of the output device.
The particle classifier 820 reads the values of relative detection frequencies N,-j of the X-ray quantums from the memory 214 in the interval // for chemical elements p, from the set P of chemical elements in the particles g) from the set Q' , and the ordered set Z is read from the memory 822, and for each particle q from the set Q'it determines the set Cj with the cardinality no more than 1 , which is saved in the memory 821.
Description of the device in the fourth embodiment is graphically illustrated in the figure 17, wherein some of the steps which are the same as in the basic embodiment are not shown for better understanding. The device in this embodiment works in the similar manner as the basic device described above, except that before initialization of the operation, the operator sets the ordered set Z using the input device 21 through the controller 23 of the input device (step 920); the ordered set Z is saved in the memory 822. The set Z is set in the form of an ordered set of ordered pairs, in which Z = { (Ck, Vk); k = 1 , 2, ... nc}, where nc is the number of the classes and each class ¾ has its logical expression v¾, which consists of variable identifiers, numeric constants, arithmetic operators for negation, addition, multiplication, subtraction and division, operators for comparison of two numerical values (equivalence, non-equivalence, greater, greater or equal, less, less or equal) and logical operators for negation, conjunction and disjunction. After determining the relative detection frequencies N,j of the X-ray quantums (step 709) and saving the values A/;,y in the memory 214, particle classification follows. A set of variables occurring in the expressions Vk is found. A number of particles no- is determined as a cardinality of the set Q', and positive integer number ranging from 1 to no' are allocated to the particles according to the order, in which they have been inserted into the set Q'. Classification begins with the particle q) for the index j = 1 (particle with the sequence number 1 ) (step 921 ). In case the index value is less than or equal to no- (step 922), relative detection frequencies of X-ray quantums for the particle q) are red from the memory 214, and these values are saved in the variables occurring in the expressions i¾. Particle classification begins with evaluation of the expression v¾ for the index k = 1 (step 923). In case the value of the index k is less or equal to nc (step 924) and the truth value of the expression v¾ is„true" (step 925), the set Cy may contain only the element Ck (step 926), and the process continues with the index j (step 929); otherwise, the process continues with another index k (step 928). In case none of the expressions is„true" for the particle <¾■', the set of classes Cy for such a particle q, will be empty (step 927) and the device continues with another index j (step 929). The result of the classification is displayed after highlighting the particle in another part of the display device 26 as a name of the class Ck, provided that the set Cj contains the element ¾, or the text ..unclassified" is shown provided that the set Cy is empty.
In another (fifth) possible embodiment, the particle classification is performed based on the percentages of chemical elements determined by means of quantitative spectrum analysis. Block scheme of the device in this embodiment is illustrated in the figure 13, wherein some of the parts which are the same as in the basic embodiment are not shown for better understanding. In this embodiment is the input of the spectrum analyzer 801 connected to the memory 219 and its output is connected via the memory 802 with the second input of the controller 25 of the output device and with the second input of the particle classifier 830. The particle classifier 830 is on its input connected via the memory 831 to the sixth output of the controller 23 of the input device, and on its output it is connected via the memory 832 to the third input of the controller 25 of the output device.
The particle classifier 830 reads the values of the percentages of chemical elements in the particles q 'from the set Q'from the memory 802, and the set Z' is read from the memory 831 , and for each particle g from the set Q' it determines the set C, of classes, which is saved in the memory 832.
Description of the operation of the device in this embodiment is illustrated in the figure 18, wherein the steps which are the same as in the basic embodiment are not shown for better understanding. The device in this embodiment operates in a similar manner as the basic embodiment described above, except that before initialization of the operation the operator sets the ordered set Z' using the input device 21 via the controller 23 of the input device (step 930); the ordered set Z' is saved in the memory 831. The set Z' is set in a form of an ordered set with ordered pairs, in which Z' = { {ck, Vk); k = 1 , 2, ... nc}, where nc is the number of classes and each class Ck has its own logical value v¾, which consists of variable identifiers, numeric constants, arithmetic operators for negation, addition, multiplication, subtraction and division, operators for comparison of two numerical values (equivalence, non-equivalence, greater, greater or equal, less, less or equal) and logical operators for negation, conjunction and disjunction.
After determining the percentage of chemical elements p,- from the set P of chemical elements (step 901 ) and saving the values in the memory 219, the particle classification follows. A set of variables occurring in the expressions v¾ is found. The number of particles no- is determined as cardinality of the set Q' and positive integer numbers ranging from 1 to HQ- are allocated to the particles in the order, in which the particles have been inserted into the set Q'. Classification begins with the particle q) for the index j = 1 (particle with the sequence number 1 ) (step 931 ). In case the index value is less or equal to no- (step 932), the values of percentages of the chemical elements for the particle q) are read from the memory 219 and these values are saved in the variables occurring in the expressions Vk. Particle classification begins with evaluation of the expression Vk for the index k = 1 (step 933). In case the truth value of the expression is„true", the class Ck is inserted into the set Q (step 936). Regardless the truth values of the expression, the process continues with another index k (step 937). The result of the evaluation of the truth values of all logical expressions for the particle q is the set Cy, which is a sub-set of the set C and contains those elements Ck from the set C, for which the truth value of the logical expression Vk is„true". The set Cj is saved in the memory 832 and the process continues with another index (step 938). The result of the particle classification is displayed to the user after highlighting the particle in another part of the displaying device 26 as a list of classes, to which the highlighted particles has been allocated.
In another (sixth) possible embodiment, no more than one class ¾ is allocated to the particle during the classification. In this embodiment is the set Z an ordered set (elements of the set Z have their defined order) Z = { (¾, v¾); k = 1 , 2, ... nc}; in similar manner, the set C is an ordered set of classes ¾. Block scheme of the device in this embodiment is illustrated in the figure 14, wherein some of the parts which are the same as in the basic embodiment are not shown for better understanding. In this embodiment is the input of the spectrum analyzer 801 connected to the memory 219 and its output is connected via the memory 802 to the second input of the controller 25 of the output device and to the second input of the particle classifier 840. The particle classifier 840 is connected on its first input via the memory 841 to the sixth output of the controller 23 of the input device, and it is connected on its output via the memory 842 to the third input of the controller 25 of the output device.
The particle classifier 840 reads from the memory 802 the values of percentages of chemical elements in the particles g/from the set Q', and it reads the set Z'from the memory 841 , and it determines the class C, for each particle g from the set Q', which is saved in the memory 842.
Description of the device in the sixth embodiment is illustrated in the figure 19, wherein some of the steps which are the same as in the basic embodiment are not shown for better understanding. The device in this embodiment operates in a similar manner as the basic embodiment described above, except that before initialization of the operation the operator sets the ordered set Z' using the input device 2J. through the controller 23 of the input device (step 940); the ordered set Z' is saved in the memory 841. The set Z is defined in a form of an ordered set with ordered pairs, in which Z = { (Ck, Vk); k = 1 , 2, ... nc }, where nc is the number of classes and each class Ck has its own logical expression v¾, which consists of variable identifiers, numeric constants, arithmetic operators for negation, addition, multiplication, subtraction and division, operators for comparison of two numerical values (equivalence, non- equivalence, greater, greater or equal, less, less or equal) and logical operators for negation, logical conjunction and disjunction. After determining the percentages of chemical elements p, from the set P of chemical elements (step 502) and saving the values in the memory 219, classification of the particles follows. A set of variables occurring in the expressions v¾ is found. A number of particles no- is determined as cardinality of the set Q' and positive integer numbers are allocated ranging from 1 to /7Q< to the particles in the order, in which the particles have been inserted in the set Q'. Classification begins with the particle q) for the index y = 1 (particle with the sequence number 1 ) (step 941 ). In case the value of the expression is less or equal to no (step 942), percentages of the chemical elements for the particle q) are read from the memory 214, and these values are saved in the variables occurring in the expressions v¾. Particles classification begins with evaluation of the expression Vk for the index k - 1 (step 943). In case the value of the index k is less or equal to nc (step 944) and the truth value of the expression v¾ is„true" (step 945), the set Q will contain only the element Ck (step 946) and continues with another index j (step 949); otherwise, the process continues with another index k (step 948). Provided that none of the expressions Vk is„true" for some of the particle q , the set C, for such particle q,- will be empty (step 947) and the device continues with another index j (step 949). The result of the particle classification is shown to the user after highlighting a particle in another part of the displaying device 26 as a name of the class Ck, provided that the set Q contains the element Ck, or a text ..unclassified" is shown, provided that the set is empty.
Description of the Drawings
Figure 1 illustrates a block scheme of the electron microscope with the back- scattered electrons detector, X-ray detector, and control circuits according to the state of the art, wherein some of the basic parts of the electron microscope which are not directly related to the present invention are not shown.
Figure 2 illustrates a block scheme of connection of the basic variant of the present device, wherein the internal connection of the processing unit is not shown for better understanding.
Figures 3 to 6 illustrate the basic variant of the connection of blocks and memories inside the processing unit 20.
Figures 7 to 9 illustrate a flowchart of the basic variant of the device.
Figures 10 to 14 illustrate a block scheme of the connection of the second to sixth possible embodiment, wherein those blocks which are the same as in the basic variant are not shown for better understanding.
Figures 15 to 19 illustrate a flowchart of the second to sixth possible embodiment, wherein those steps which are the same as in the basic variant are not shown for better understanding.
Industrial applicability
The provided new method and devices are particularly suitable for use in quantitative analysis in petrography of rocks. In this analysis, the examined sample is usually crushed to fine particles with the size from units to tens of micrometers, it is divided into several fractions using sieves. Several samples are taken from each size fraction. These size fractions are usually mixed with filler and epoxy resin and they are left to cure into cylindrical blocks, which are further polished and subsequently covered with thin conductive layer, usually carbon, for diversion of the surface charge. These block are arranged in the scanning electron microscope, which sequentially collects the data and analyzes the material on their surface. The present device allows to perform a fully automated analysis of these samples, the result of which are not only morphological and chemical properties of the materials, from which the examined sample consists, but mainly the information about mutual spatial distribution of the materials, which is in many cases a crucial information regarding determination of the physical and chemical properties of the rocks. List of reference signs
1 - electron gun
2 - accelerated electron beam
3 - deflection coils
4 - sample
5 - deflection circuits
6 - back-scattered electrons
7 - X-ray radiation
8 - back-scattered electrons detector
9 - analog-to-digital converter
10 - X-ray radiation detector
11 - pulse processor
12 - control unit
13 - electron microscope
20 - processing unit
21 - input device
22 - positioning device
23 - controller of the input device
24 - controller of the positioning device
25 - controller of the displaying device - displaying device
- memory (data from the analog-to-digital converter, map B) - memory (data from the pulse processor, map S)
- memory (scanning script J )
- block (creates differential map DB)
- memory (differential map DB)
- block (converts DB to E)
- memory (bit map £)
- block (converts E to Q and R)
7 - memory (set Q of temporary particles)
8 - block (copies Q to P)
9 - memory (auxiliary set P of temporary particles)
- memory (map R of temporary particles distribution)
- block (copies R to S)
- memory (auxiliary map S of temporary particles distribution)3 - block (converts S to T)
4 - memory (auxiliary map 7)
5 - block (creates T1)
6 - memory (auxiliary map T1)
7 - block (selection of initial points)
8 - memory (set O of the initial points)
9 - block (determining the set Z of measuring points) 120 - memory (coefficient c)
121 - memory (auxiliary map Y)
122 - block (initialization of the auxiliary map Y)
123 - block (initialization of the auxiliary map U of measuring points)
124 - memory (auxiliary map U of measuring points)
128 - memory (auxiliary map W)
129 - block (converts Yto W)
130 - block (test if P is empty)
131 - block (updating P and S)
132 - block (initialization of the script J' of X-ray mapping)
133 - memory (script J'of X-ray mapping)
134 - memory (list Z of measuring points)
135 - block (updates the auxiliary map U of measuring points)
136 - block (inserts the list Z of measuring points to the scanning script J')
137 - block (creates the auxiliary map Y)
201 - memory (intervals /; of X-ray photon energy)
202 - memory (spectrum map S)
203 - block (converts the map S to the X-ray maps Mi)
204 - memory (X-ray maps Mi)
205 - block (converts M to DM)
206 - memory (differential X-ray map DM)
207 - block (merges DB and DM into D) 208 - memory (differential map D)
209 - block (converts E'to Q' and
210 - memory (set Q'of particles)
211 - memory (map f?' of particle distribution)
213 - block (converts Xj to values Ni,j)
214 - memory (values N,j of relative detection frequency of X-ray quantums)
215 - memory (set P of chemical elements)
216 - memory (coefficient a)
217 - block (converts D to £*)
218 - memory (bit map E*)
219 - memory (accumulated spectrum Xj)
221 - block (transformation U to V'j)
222 - memory (auxiliary map Vj')
223 - block (converts V'j to W'j)
224 - memory (weighted map Wj')
225 - block (determining the accumulated spectrums Xj)
226 - memory (value of the variable j)
227 - block (saving the value of the variable j to the variable i)
228 - memory (bit map Uj')
229 - block (creating the bit map U'j)
230 - block (increasing the value of the variable / for 1 )
231 - block (initialization of the value of the variable i) 301 - memory (basic resolution d)
302 - block (generates the scanning script J)
303 - memory (size F of the field of vision)
401 - block (copies J' to J)
501 - step (setting and saving F, d, a, c, P and /)
502 - step (setting the scanning script J)
503 - step (obtaining the map B)
504 - step (conversion of B to De)
505 - step (conversion of DB to E)
506 - step (conversion of E to Q and R)
601 - step (initialization of the memories S, P, Y, L/ and J1)
602 - step (testing the emptiness of the set P)
603 - step (setting the 7)
604 - step (conversion of the Tto Γ)
605 - step (setting the set O of initial points)
606 - step (setting the Z)
607 - step (updating the U, J' and V)
608 - step (conversion of the Y to W)
609 - step (updating the S and P)
701 - step (copies J'to )
702 - step (creating the map S)
703 - step (converting the map S to Mi) 704 - step (conversion of the M, to DM)
705 - step (conversion of the DM and Ds to D)
706 - step (conversion of the D to E1)
707 - step (conversion of the E'to Q' and R )
708 - step (determining the accumulated spectrums Xj)
709 - step (setting the value j)
801 - spectrum analyzer
802 - memory (percentage of the chemical elements in the particle q'j)
810 - particle classifier
811 - memory (set Z)
812 - memory (set Cj)
820 - particle classifier
821 - memory (set Cj)
822 - memory (set Z)
830 - particle classifier
831 - memory (set Z')
832 - memory (set Cj)
840 - particle classifier
841 - memory (set Z1)
842 - memory (set Cj)
901 - step (quantitative spectrum analysis)
910 - step (setting and saving F, d, a, c, P, / and Z) 11 - step (initialization of the index j = 1 )
912 - step (comparing the indexes and /IQ )
913 - step (initialization of the index k = 1 )
914 - step (comparing the indexes k and nd)
915 - step (allocating the values to the variable and evaluation of the expression
Vk)
916 - step (inserting Ck to Cy)
917 - step (increasing the index k by 1 )
918 - step (increasing the index by 1 )
920 - step (setting and saving F, d, a, c, P, I and 2)
921 - step (initialization of the index j = 1 )
922 - step (comparing the indexes j and 7Q )
923 - step (initialization of the index k = 1 )
924 - step (comparing the indexes k and nd)
925 - step (allocation of the values to the variables and evaluation of the expression Vk)
926 - step (allocation of the Ck to Q)
927 - step (allocation of the empty set to Q)
928 - step (increasing the index k by 1 )
929 - step (increasing the index j by 1 )
930 - step (setting and saving F, d, a, c, P, I and Z1)
931 - step (initialization of the indexes j = 1 ) 932 - step (comparing the indexes j and no)
933 - step (initialization of the index k = 1 )
934 - step (comparing the indexes k and nc)
935 - step (allocating the values to the variables and evaluation of the expression Vk)
936 - step (inserting Ck to Cj)
937 - step (increasing the index k by 1 )
938 - step (increasing the index by 1 )
940 - step (entering and saving of F, d, a, c, P, I and Z1)
941 - step (initialization of the index j = 1 )
942 - step (comparing the indexes and no)
943 - step (initialization of the index k = 1 )
944 - step (comparing the indexes k and nc)
945 - step (allocation of the values to the variables and evaluation of the expression Vk)
946 - step (allocation of the Ck to Q)
947 - step (allocation of the empty set to Cj)
948 - step (increasing the index k by 1 )
949 - step (increasing the index j by 1 )

Claims

1. Method of material analysis by means of a focused electron beam using characteristic X-rays and back-scattered electrons, the method including consecutive deflection of the focused electron beam onto a set of initial measuring points on the sample in regular grid, measurement of intensity of back-scattered electrons in order to create an electron map, characterized in that a set of temporary particles and a set of new measuring points are established by means of the electron map, the set of new measuring points comprising less particles than the set of initial measuring points, and the set of new measuring points comprising at least one measuring point for each particle from the set of temporary particles, deflection of the electron beam along the set of new measuring points, measurement of emitted X-ray radiation from these new measuring points, and creation of an X-ray spectrum Sk from each point of the set of new measuring points, determining the set Q' of particles q'j using at least one particular interval of X-ray energy in each point of the set of new measuring points, determining an X-ray spectrum Xj for the particle qj' based on spectrum SR measured in those points, which are part of the particle.
2. Method of material analysis by means of a focused electron beam according to claim 1 , characterized in that for each particle q'j from the set Q' the spectrum Xj is determined as a sum of contributions of particular new measuring points, which are part of the particle, wherein the particular points have different weight, the weight of contribution is determined by means of a pre-determined coefficient a.
3. Method of material analysis by means of a focused electron beam according to claim 2, characterized in that a coefficient a is determined by the user.
4. Method of material analysis by means of a focused electron beam according to claim 1 or 2, characterized in that relative detection frequency of X-ray quantums is determined for the particle cy' from the set Q' using the X-ray spectrum Xj.
5. Method of material analysis by means of a focused electron beam according to claim 1 or 2, characterized in that percentage of chemical elements in the particle q'j is determined by means of the quantitative spectroscopic analysis of X-ray spectrums Xj for the particles q'j.
6. Method of material analysis by means of a focused electron beam according to claim 4, characterized in that a set Z of pre-determined rules is used for classification, where Z is a set of pairs (CK, VR) and each class Ck has a logical expression Vk consisting of variable identifiers, arithmetic operators, logical operators, operators for comparison, and numerical constants, subsequently a set of variable occurring in the expression in the set Z is determined, for each particle q'j from the set Q' the relative detection frequencies of X-ray events are allocated to these variables and subsequently the logical value of each expression Vk is determined, in order to create a set Q, where the set Q comprises those classes Ck from the set C, where C is a set of all classes from the set Z, for which the corresponding expression Vk is "true".
7. Method of material analysis by means of a focused electron beam according to claim 6, characterized in that the set Z is determined by the user.
8. Method of material analysis by means of a focused electron beam according to claim 4, characterized in that the predetermined set Z of rules is used for material classification, where Z is a set of pairs (ck, Vk) and a logical expression Vk consisting of variable identifiers, arithmetic operators, logical operators, operators for comparison and numerical constants is allocated to each class Ck, than a set of variable occurring in the expressions in the set Z is determined, the determined relative frequencies of X-ray events for each particle q'j from the set Q' are allocated to these variables, and subsequently the expressions Vk are evaluated, subsequently one of the following facts is evaluated: a) in case the expression Vk is "true" for some k, than the set Q contains only the element Ck, or b) in case all of the expressions are "false", the set Q is empty.
9. Method of material analysis by means of a focused electron beam according to claim 8, characterized in that the set Z of rules is determined by the user.
10. Method of material analysis by means of a focused electron beam according to claim 5, characterized in that a predetermined set Z' of rules is used for material classification, where Z' is a set of pairs (Ck, Vk) and a logical expression Vk consisting of variable identifiers, arithmetic operators, logical operators, operators for comparison and numerical constants is allocated to each class Ck, subsequently a set of variables occurring in the expressions saved in the set Z' is determined, the determined percentage of chemical elements for each particle q'j from the set Q' is allocated to these variables and subsequently the logical value of each expression Vk is evaluated, in order to create a set Q, where the set Q contains those classes Ck from the set C, where C is a set of all classes from the set Z', for which the corresponding expression Vk is "true".
11. Method of material analysis by means of a focused electron beam according to claim 10, characterized in that the set Z of rules is determined by the user.
12. Method of material analysis by means of a focused electron beam according to claim 5, characterized in that the predetermined set Z' of rules is used for particle classification, where Z' is a set of pairs (Ck, Vk) and a logical expression Vk consisting of variable identifiers, arithmetic operators, logical operators, operators for comparison and numerical constants is allocated to each class Ck, subsequently a set of variables occurring in the expressions saved in the set Z' is determined, the determined percentage of chemical elements for each particle q'j from the set Q' is allocated to these variables and subsequently the following expression Vk are evaluated, and then one of the two following facts is determined: a) in case the expression vk is "true" for some k, than the set Q contains only the element Ck, or b) in case all of the expressions are "false", the set Q is empty.
13. Method of material analysis by means of a focused electron beam according to claim 12, characterized in that the set Z' of rules is determined by the user.
PCT/CZ2016/000107 2015-09-22 2016-09-22 A method of analysis of materials by means of a focused electron beam using characteristic x-rays and back-scattered electrons WO2017050303A1 (en)

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