Method and apparatus for electron backscatter diffraction sample characterization

Abstract

A method for analyzing a sample imaged by electron backscatter diffraction. The method includes identifying a plurality of Kikuchi bands in an electron backscatter diffraction image of locations on the sample. The method further includes, for each identified Kikuchi band, forming a corresponding vector representation of the Kikuchi band based at least in part on an estimate of the location on the sample. The configuration of the sample is determined by identifying a particular expected vector representation set from a plurality of expected vector representation sets as matching the vector representations of the plurality of identified Kikuchi bands.

Description

Technical Field

[0001] The present invention relates to the characterization of samples using electron backscatter diffraction, and in particular, the analysis of electron backscatter diffraction images, for example to determine the properties of the sample. Background Art

[0002] Electron backscatter diffraction (EBSD) is a widely used technique for characterizing material samples. EBSD allows a variety of crystallographic, microstructural and microstructural properties to be determined for a specific portion of a sample surface or a location on it. The most common EBSD applications include crystal orientation image mapping (OIM) for measuring microstructure, phase analysis, and high-resolution EBSP cross-correlation for strain analysis. In this way, EBSD has proven to be an effective tool for characterizing polycrystalline and / or multiphase materials. In particular, many important properties such as grain size and shape, phase distribution, local deformation, etc. can be measured or estimated using EBSD. By performing EBSD on multiple points on the sample surface, a detailed picture of the properties and composition of polycrystalline and / or multiphase materials can be generated. Such characterization can have a variety of uses, including: failure analysis of components; and quality assurance and control during industrial manufacturing; up to preliminary studies of materials and material structures under various conditions.

[0003] During EBSD analysis, a beam of electrons, usually from an electron microscope, is directed onto a sample in a vacuum chamber. Electrons diffract from crystal planes within the sample to produce a series of overlapping "bright" bands that form the electron backscatter diffraction pattern. A portion of the scattered (diffracted) electrons from the sample strike a screen (usually a phosphor screen) or an imaging sensor (e.g., CMOS or CCD). The electrons collide with the phosphor screen, which fluoresces, and the resulting light can be detected using a lens assembly and camera; or the electrons can be detected directly by the sensor. In either case, the diffraction pattern is converted into a digital signal that measures the angular distribution of the electrons.

[0004] The resulting image produced by the EBSD technique (often referred to as the electron backscatter pattern (EBSP)) typically includes a plurality of intersecting bands defined by a pair of (substantially parallel) edges. These intersecting bands are called Kikuchi bands, and material samples are typically characterized based on these bands. In particular, Kikuchi bands identified in the resulting image are matched to known Kikuchi bands, typically in a process known as indexing. This is typically done by comparing the intersection angles of the identified pairs of Kikuchi bands to a theoretical list of known angles for known materials (typically calculated based on inter-plane angles of a theoretical crystal model).

[0005] At present, a variety of methods are used in the field to automate this indexing process. These schemes usually involve using Hough transform to first identify multiple Kikuchi bands present in the EBSD image, and use a lookup table of inter-plane angles (or less commonly, inter-region angles) to index some of the identified Kikuchi bands (see, for example, "Individual Lattice Orientation Measurements Development and Application of a Fully Automatic Technique", Stuart I.Wright, PhD thesis, Yale University, USA, 1992). However, using an EBSD image that usually contains dozens of Kikuchi bands and tries to fit all the intersection angles of all Kikuchi bands at once may become difficult to manage. This is usually due to the number of inter-plane angle combinations increasing with the square of the number of bands. In this way, automatic indexing techniques usually try to fit only about 3 intersection angles at a time. Since the intersection angle is susceptible to measurement errors in the EBSD process, this limited automatic indexing may miss the correct indexing solution. This may often be the case if one of the original 3 intersection angles happens to contain a significant measurement error, or is from an erroneously detected Kikuchi zone (ie, a Kikuchi zone that is not actually present in the diffraction pattern). This may lead to incorrect or inaccurate results.

[0006] In addition to this, automatic indexing systems typically require external knowledge of the local chemistry or possible phase or lattice type of the sample in order to reduce the number of possible inter-plane angles to be tested against it. This introduces bias into the characterization of the sample which may also lead to incorrect or inaccurate results. Summary of the invention

[0007] An object of the present invention is to provide an improved system for characterizing samples using electron backscatter diffraction, in particular, to improve the accuracy of automated analysis of images produced by electron backscatter diffraction.As such, embodiments of the present invention seek to address the problems described above and other problems of the related prior art.

[0008] In a first aspect, a method (e.g., a computer-implemented method) is provided for analyzing a sample imaged by electron backscatter diffraction (or mapped by electron backscatter diffraction or otherwise subjected to electron backscatter diffraction). The method includes identifying a plurality of Kikuchi bands in an electron backscatter diffraction image (or map or output) of positions on the sample. For each identified Kikuchi band, a corresponding vector representation of the Kikuchi band is formed. Each corresponding vector is based at least in part on an estimate of the position on the sample.

[0009] The method continues by determining a configuration of the sample by identifying a particular expected vector representation set from a plurality of expected vector representation sets as matching the vector representations of the plurality of identified Kikuchi bands.

[0010] In some embodiments, determining a configuration further comprises obtaining a plurality of candidate expected vector representation sets from the plurality of expected vector representation sets by matching angles of the vector representation relative to predetermined coordinate axes with corresponding angles of the expected vector representations. The specific expected vector representation set that matches the vector representations of the plurality of identified Kikuchi bands can then be identified from the plurality of candidate expected vector representation sets.

[0011] In some embodiments, the plurality of expected vector representation sets include one or more primary vector representation sets. For each primary vector representation set, the plurality of expected vector representation sets include one or more rotational expected vector sets generated by applying a corresponding rotation, the applying of the corresponding rotation being equivalent to applying a rotation about the predetermined coordinate axis and then applying a rotation about another coordinate axis. The determining may further include identifying a rotation that matches the particular expected vector representation set with the vector representations of the plurality of identified Kikuchi bands.

[0012] In a second aspect, a method (such as a computer-implemented method) for analyzing a sample imaged by electron backscatter diffraction (or mapped by electron backscatter diffraction or otherwise subjected to electron backscatter diffraction) is provided. The method includes identifying a plurality of Kikuchi bands in an electron backscatter diffraction image (or mapping or output) of locations on the sample. For each identified Kikuchi band, a corresponding point is formed. Each point corresponds to an intersection between a vector representation of the Kikuchi band and a cylindrically symmetric surface (such as a cylindrical surface). Both the vector representation of the Kikuchi band and the cylindrical axis of the surface are determined at least in part based on an estimate of the location on the sample.

[0013] The method continues by identifying a particular expected point set from a plurality of expected point sets as matching the points of the plurality of identified Kikuchi strips. For example, a point may match the expected point when a calculated overlap between a distribution (e.g., a Gaussian distribution) centered at a point and a distribution centered at the expected point exceeds a predetermined threshold. The characteristic width of the distribution may be based on the intensity of the corresponding point.

[0014] This aspect can advantageously provide improved accuracy when matching the experimentally generated Kikuchi bands of a sample with the expected Kikuchi bands. Specifically, this aspect can enable more Kikuchi bands to be matched more effectively compared to prior art methods. As a result, the accuracy or confidence of the generated configuration of the sample can be improved.

[0015] In some embodiments of the first and second aspects, the determined configuration includes any one or more of the following: the crystalline phase in the sample; the unit cell scale of the crystal in the sample; the atoms in the unit cell of the crystal in the sample; the lattice orientation in the sample; the local lattice deformation present in the sample; the strain state.

[0016] In some embodiments, the method further includes obtaining a plurality of expected point sets. Each expected point set corresponds to a corresponding known sample. For each known sample, the expected point corresponds to the intersection between the vector representation of the Kikuchi band of the known sample and another cylindrical symmetric surface (such as a cylindrical surface). The other cylindrical symmetric surface can be the same as the initial cylindrical surface. The Kikuchi band of one or more of the known samples can be identified from simulated and / or experimental EBSD images.

[0017] The determined configuration is based on one or more properties of a particular known sample corresponding to the particular set of expected points that match the points of the plurality of identified Kikuchi bands.

[0018] In some embodiments of the first and second aspects, the vector representation of each respective Kikuchi band is determined based on a plane defined by the Kikuchi band. Typically, the vector representation of the respective Kikuchi band is based on a normal vector of the plane defined by the Kikuchi band.

[0019] In some embodiments, the step of determining the configuration further comprises obtaining a plurality of candidate expected point sets from the plurality of expected point sets. Such obtaining can be performed by matching the relative azimuth angles of the points with the relative azimuth angles of the expected points. Here, the specific expected point set matching the points of the plurality of identified Kikuchi strips is identified from the plurality of candidate expected point sets.

[0020] In some embodiments, the step of determining the configuration further includes: for each expected point set from two or more expected point sets from a plurality of expected point sets, optimizing the estimate of the position on the sample based on the expected point set; and identifying one of the two or more expected point sets as a specific expected point set based at least in part on the optimized estimate of the position on the sample.

[0021] In some embodiments, the step of identifying a particular expected point set from the plurality of expected point sets as matching the plurality of identified Kikuchi strip points is performed by the following steps.

[0022] · plotting in the first image a distribution centered around each of the points of the plurality of identified Kikuchi bands;

[0023] For each point in the specific set of expected points, a second image is obtained which includes a distribution centered at the point.

[0024] Here, a particular expected point set from a plurality of expected point sets is identified as matching the points of the plurality of identified Kikuchi strips based on the intersection of the first image and the second image.

[0025] The present invention also provides apparatus corresponding to or including elements, modules or components arranged to implement the above methods, such as one or more various appropriately configured computing devices, such as those described below.

[0026] Specifically, the present invention therefore provides a first system for analyzing a sample imaged by electron backscatter diffraction (or mapped by electron backscatter diffraction or otherwise subjected to electron backscatter diffraction). The system includes an identification module, the identification module being configured to identify a plurality of Kikuchi bands in the electron backscatter diffraction image of a location on the sample. The system also includes a projection module, the projection module being configured to form, for each identified Kikuchi band, a corresponding vector representation of the Kikuchi band based at least in part on an estimate of the location on the sample.

[0027] The system also includes a matching module configured to determine a configuration of the sample by identifying a particular expected vector representation set from a plurality of expected vector representation sets as matching the vector representations of the plurality of identified Kikuchi bands.

[0028] A second system corresponding to the second aspect outlined above may also be provided. The second system includes an identification module configured to identify a plurality of Kikuchi bands in an electron backscatter diffraction image (or mapping or output) of a position on the sample. The second system also includes a projection module configured to form a corresponding point for each identified Kikuchi band. Each point corresponds to an intersection between: a vector representation of the Kikuchi band and a cylindrically symmetric surface (such as a cylindrical surface). Both the vector representation of the Kikuchi band and the cylindrical axis of the surface are determined at least in part based on an estimate of the position on the sample.

[0029] The second system also includes a matching module configured to determine the configuration of the sample by identifying a particular expected point set from a plurality of expected point sets as matching the points of the plurality of identified Kikuchi bands. For example, a point may be matched to an expected point when a calculated overlap between a distribution (e.g., a Gaussian distribution) centered at a point and a distribution centered at an expected point exceeds a predetermined threshold. The characteristic width of the distribution may be based on the intensity of the corresponding point.

[0030] The present invention also provides one or more computer programs suitable for execution by one or more processors, such (one or more) computer programs being arranged to implement the method outlined above and described herein. The present invention also provides one or more computer readable media and / or data signals conveyed over a network, said media and / or data signals comprising (or having stored thereon) such one or more computer programs. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Embodiments of the present invention will now be described, by way of example only, with reference to the accompanying drawings, in which:

[0032] Figure 1 An example of an electron backscatter diffraction (EBSD) system is schematically shown;

[0033] Figure 2 An example of a computer system is schematically shown;

[0034] Figure 3a An example EBSD image analysis system is schematically shown;

[0035] Figure 3b Schematic showing the geometric relationship between the EBSD image, example Kikuchi bands, and pattern center;

[0036] Figure 3c Schematic showing the geometric relationship between the EBSD image, the example Kikuchi zone normal, the pattern center, and the cylindrical surface;

[0037] Figure 3d Different example EBSD image analysis systems are schematically shown;

[0038] Figure 3e The effect of changes in the position of the scintillator screen is schematically shown;

[0039] Figure 4a The schematic diagram shows the EBSD image analysis system (such as Figure 3a Method performed by an EBSD image analysis system;

[0040] Figure 4b The schematic diagram shows the EBSD image analysis system (such as Figure 3dDifferent methods performed by EBSD image analysis systems;

[0041] Figure 5a Schematically shows Figure 3a Variations of the EBSD image analysis system;

[0042] Figure 5b Schematically shows Figure 3d Variations of the EBSD image analysis system;

[0043] Figure 6 The schematic diagram shows the EBSD image analysis system (such as Figure 5a Method performed by an EBSD image analysis system;

[0044] Figure 7a Schematically shows how Figure 3a or Figure 5a A method for matching points representing Kikuchi bands using Kikuchi band mapping performed by an EBSD image analysis system;

[0045] Figure 7b shows how it can be Figure 7a Examples of Kikuchi belt mapping used together with the methods outlined in;

[0046] Figure 8a Example EBSD images are shown along with the effect that changes in the center of the pattern have on the vector representation of the Kikuchi bands;

[0047] Figure 8b Example EBSD images are shown along with the effect of rotation of the diffraction pattern about the pattern center on the vector representation of the Kikuchi zones. DETAILED DESCRIPTION

[0048] In the following description and in the accompanying drawings, certain embodiments of the present invention are described. However, it should be understood that the present invention is not limited to the embodiments described and some embodiments may not include all of the features described below. However, it will be apparent that various modifications and changes may be made herein without departing from the broader spirit and scope of the present invention as set forth in the appended claims.

[0049] Figure 1 Schematically illustrated is an example of an electron backscatter diffraction (EBSD) system 100. The EBSD system 100 includes a beam generator 110 (such as a scanning electron microscope (SEM)) for generating an electron beam 115, and an image capture assembly 130. Also shown is a test sample 120 to be analyzed. The test sample 120 will typically be held in place by a sample holding device, not shown.

[0050] In the EBSD system 100, the beam generator 110, the test sample 120, and the image capture assembly 130 are preferably housed in an evacuated analysis chamber 140. The EBSD system 100 is configured so that at least some of the electrons from the beam generator 110 scattered by the test sample 120 will hit a scintillation screen or imaging sensor 132 of the image capture assembly 130. An electron backscatter diffraction pattern may be formed on the scintillation screen or imaging sensor 132. The scintillation screen or imaging sensor 132 is arranged to convert incident electrons into visible light, and a backscatter diffraction pattern that can be captured by the image capture assembly 130 may thereby be formed on the scintillation screen or imaging sensor 132. For ease of discussion, the EBSD system described below will be discussed from the perspective of a backscatter diffraction pattern generated on the scintillation screen 132. However, it should be understood that the discussion is equally applicable to EBSD systems that perform direct detection of backscatter diffraction patterns. Such systems typically use an imaging sensor 132 instead of a scintillation screen 132. The imaging sensor 132 (which may be, for example, any one of a CCD-type sensor or a monolithic CMOS sensor) is arranged to directly detect the backscattered diffraction pattern. Examples of monolithic CMOS sensors include the MediPix series of sensors and the TimePix series of sensors. Such direct detection is well known in the art (see, for example, PTE Roberts et al. "A CCD-based image recording system for the CTEM", (1982), Ultramicroscopy 8, 385–396, which is incorporated herein by reference in its entirety; or G McMullan et al. "Electron imaging with Medipix2 hybrid pixel detector", (2007), Ultramicroscopy 107(4-5): 401-13, which is incorporated herein by reference in its entirety; or U.S. Patent Application US 2016 / 0054240), and therefore will not be described in detail herein.

[0051] Typically, the image capture assembly 130 will be arranged to capture the pattern formed on the scintillation screen or imaging sensor 132 as an EBSD image 150. Typically, the EBSD image 150 will be a digital image in a suitable format. Such an EBSD image 150 may be referred to as an electron backscatter diffraction pattern (EBSP). The image capture assembly 130 may be arranged to capture a plurality of EBSD images. For example, the EBSD system 100 may be arranged to scan (or move) the electron beam 115 in a predetermined path across the test sample 120. Here, the image capture assembly may be configured to capture EBSD images at predetermined points (or intervals) during scanning. In this way, a plurality of EBSD images corresponding to different regions or points on the surface of the test sample 120 may be generated. The image capture assembly 130 is configured to output (one or more) EBSD images 150 for further processing (analysis as briefly described herein below).

[0052] Figure 1 Also shown in FIG. 1 is an example EBSD image 150. The EBSD image 150 is an image of the location of the sample where it was struck by the electron beam. This location is actually the point of incidence 117 of the electron beam 115 and the test sample 120. A number of features referred to as Kikuchi bands 152 are visible in the EBSD image 150. The Kikuchi bands 152 can be seen as substantially straight, brighter bands in the EBSD image 150, typically bordered by two thinner black lines that show the edges of the Kikuchi bands 152.

[0053] As will be appreciated by those skilled in the art, the Kikuchi bands 152 are generally formed due to the intensity enhancement of electrons scattered from the test sample 120 that strike the scintillating screen or imaging sensor 132. The geometric position of the edges of the Kikuchi bands produced by the scattering of electrons by the test sample 120 is controlled by Bragg diffraction. A particular Kikuchi band 152 generally corresponds to electrons scattered from a particular crystal facet in the test sample 120 at the point of incidence 117 of the electron beam 115. Diffraction causes two electron cones to scatter from the test sample 120 (and specifically, the crystal facets), which then strike the scintillating screen or imaging sensor 132, thereby forming the Kikuchi bands 152. The apex of a pair of coaxial cones is centered at the point of incidence 117, and the cones are generally nearly flat, given that the half-apex angle of the (hkl) plane is 90 degrees minus the Bragg angle.

[0054] As will also be appreciated by those skilled in the art, the Kikuchi zones 152 in the EBSD image 150 can be mapped onto the surface of a sphere 160 centered at the point of incidence 117 of the electron beam 115 and the test sample 120. When mapped onto the surface of such a sphere, the edges of each Kikuchi zone 152 form two circles of the sphere 160. The centerline of the Kikuchi zone forms the great circle of the sphere 160. In fact, each Kikuchi zone 152 can be considered as the intersection between the corresponding scattered electron cone discussed above and the surface of the sphere 160. The representation of the Kikuchi zone 152 on such a sphere 160 is generally referred to as a "spherical map" or "spherical Kikuchi map" of the Kikuchi zone 152. The corresponding EBSD image 150 can be considered as a heart-slice projection of a portion of such a spherical map. Such a projection effectively forms a planar scintillation screen or imaging sensor 132. Specifically, the corresponding EBSD image 150 can be considered as a heart-slice projection of the solid angle of the spherical map subtended by the scintillation screen 132.

[0055] The generation of the Kikuchi bands 152 due to diffraction will be well known to those skilled in the art (see, for example, "Electron Backscatter Diffraction in Materials Science, 2nd edition" (2009), pages 2-3, ISBN 978-0-387-88135-5, which is incorporated herein by reference in its entirety), and as such will not be described in detail herein. Similarly, the generation of a spherical map of the Kikuchi bands 152 will also be well known to those skilled in the art (see, for example, "Spherical EBSD", Austin P Day, Journal of Microscopy, Vol. 230, No. 3, (2008), pages 472-486, which is incorporated herein by reference in its entirety).

[0056] Also shown on the EBSD image 150 is a point 155. Point 155 (often referred to as the "pattern center") corresponds to the point on the scintillation screen 132 that is closest to the point of incidence 117 of the electron beam 115 and the test sample 120. The pattern center 155 can be represented as (or can include) two components that specify a point on the plane defined by the scintillation screen 132. For example, the pattern center 155 can include an x-coordinate PC x and y-coordinate PC yThe pattern center 155 generally includes (or is designated to have) the distance (or spacing) between the scintillating screen 132 and the incident point 117 of the electron beam 115. Thus, the pattern center 155 may be represented as (or may include) three components. Generally, such a pattern center 152 includes an x-coordinate PC x , y-coordinate PC y and z-coordinate PC z Here, the z-coordinate PC z is the distance between the scintillating screen 132 and the point of incidence 117 of the electron beam 115. The pattern center 155 is usually measured (or estimated) before the EBSD image 150 is generated.

[0057] It should be appreciated that the EBSD system 100 outlined above serves merely as an example of how an EBSD image 150 may be generated. Embodiments of the invention presented below may use any suitable EBSD image 150 produced by any EBSD system 100 .

[0058] Figure 2 An example of a computer system 200 is schematically shown. The system 200 includes a computer 202. The computer 202 includes a storage medium 204, a memory 206, a processor 208, an interface 210, a user output interface 312, a user input interface 214, and a network interface 216, all of which are connected together via one or more communication buses 218.

[0059] The storage medium 204 may be any form of non-volatile data storage device, such as one or more of a hard drive, a magnetic disk, an optical disk, a ROM, etc. The storage medium 204 may store an operating system that is executed by the processor 308 to enable the computer 202 to operate. The storage medium 204 may also store one or more computer programs (or software or instructions or codes).

[0060] The memory 206 may be any random access memory (storage unit or volatile storage medium) suitable for storing data and / or computer programs (or software or instructions or code).

[0061] The processor 208 may be any data processing unit suitable for executing one or more computer programs (such as those stored on the storage medium 204 and / or in the memory 206), some of which may be computer programs according to embodiments of the present invention or such computer programs that, when executed by the processor 208, cause the processor 208 to implement a method according to embodiments of the present invention and configure the system 200 into a system according to embodiments of the present invention. The processor 208 may include a single data processing unit or multiple data processing units operating in parallel, individually or in cooperation with each other. The processor 208 may store data to the storage medium 204 and / or the memory 206 and / or read data therefrom when implementing data processing operations for performing embodiments of the present invention.

[0062] The interface 210 may be any unit for providing an interface to a device 222 that is external to the computer 202 or that is detachable from the computer. The device 222 may be a data storage device, such as one or more of an optical disk, a magnetic disk, a solid-state storage device, etc. The device 222 may have processing capabilities—for example, the device may be a smart card. Thus, according to one or more commands received by the device 222 from the processor 208, the interface 210 may access data from the device, provide data to the device, or connect to the device.

[0063] The user input interface 214 is arranged to receive input from a user or operator of the system 200. The user may provide such input via one or more input devices of the system 200 connected to or in communication with the user input interface 214, such as a mouse (or other pointing device) 226 and / or a keyboard 224. However, it should be appreciated that the user may provide input to the computer 202 via one or more additional or alternative input devices, such as a touch screen. The computer 202 may store input received from the input devices via the user input interface 214 in the memory 206 for subsequent access and processing by the processor 208, or may transmit the input directly to the processor 208 so that the processor 208 may react accordingly to the user input.

[0064] The user output interface 212 is arranged to provide graphical / visual output to a user or operator of the system 200. As such, the processor 208 may be arranged to instruct the user output interface 212 to form an image / video signal representing the desired graphical output and to provide this signal to a monitor (or display screen or display unit) 220 of the system 200 connected to the user output interface 212.

[0065] Finally, network interface 216 provides functionality for computer 202 to download data from and / or upload data to one or more data communications networks.

[0066] It should be understood that Figure 2 The architecture of the system 200 described and described above is merely exemplary and may be used in embodiments of the present invention with different architectures (e.g., compared to Figure 2 , with fewer components, or compared to Figure 2 , with additional and / or alternative components). As an example, the computer system 200 may include one or more of the following: a personal computer; a server computer; a laptop computer, a field programmable gate array; etc.

[0067] Figure 3a An example EBSD image analysis system 300 is schematically illustrated. The diagram shows that the system 300 receives as input an EBSD image 150 generated from a test sample 120 to characterize the test sample 120. The EBSD image 150 is as previously described.

[0068] The EBSD image analysis system 300 includes an identification module 320, a projection module 330, and a matching module 340. The EBSD image analysis system 300 can be implemented in one or more computer systems (such as reference Figure 2 The EBSD image analysis system 300 may be implemented on the computer system 200 described above. The EBSD image analysis system 300 may be communicatively coupled to the EBSD system 100. For example, the EBSD image analysis system 300 may be communicatively coupled to the EBSD system 100 via the network interface 216. The EBSD image analysis system 300 is arranged to receive the EBSD image 150. For example, the EBSD image analysis system 300 may be arranged to receive the EBSD image 150 via any one of the following: the network interface 216; the input interface 210; the user input interface 214; etc. The EBSD image analysis system 300 may be arranged to have the EBSD image 150 stored thereon. For example, the EBSD image 150 may be stored on the storage device 204.

[0069] The identification module 320 is arranged to identify (or detect) a plurality of Kikuchi bands 152 present in the EBSD image 150, thereby forming a plurality of identified Kikuchi bands 354. Typically, the plurality of Kikuchi bands 152 are identified by detecting straight line features in the image. This can be done automatically using conventional techniques in the art. For example, an edge detection algorithm can be applied to the image. Alternatively, a Hough (or Radon) transform can be applied to the image. Here, the image is represented on a polar coordinate plane in which straight lines of high intensity are represented as points of high intensity. In this way, pixels of the EBSD image 150 exceeding a predetermined intensity in the Hough space can be identified as Kikuchi bands 152.

[0070] Additionally or alternatively, the identification module 320 may be arranged to identify one or more Kikuchi bands of the plurality of Kikuchi bands 152 based on user interaction, for example via the user input interface 214. The identification module 320 may be configured to enable a user to place a straight line on a display of the EBSD image 150 that follows the path of the Kikuchi band 152 visually identified by the user.

[0071] The identification module 320 may be arranged to identify the bandwidth of one or more of the identified Kikuchi bands 354. The bandwidth may be identified using the same technique as that used to identify the Kikuchi band 152 itself. For example, an edge detection technique may identify the two outer edges of the Kikuchi band 152. The bandwidth of the Kikuchi band 152 may be calculated based on the interval. Similarly, the bandwidth of the Kikuchi band 152 may be calculated based on the point (and / or size) corresponding to the Kikuchi band 152 in the Hough space. Additionally or alternatively, the user may specify the bandwidth of the Kikuchi band 152, for example, via the user input interface 214.

[0072] Typically, the identified Kikuchi band 152 will be represented (and optionally stored) by the identification module 320 as a straight line. More typically, the identified Kikuchi band 152 will be represented (and optionally stored) by the identification module 320 as a straight line centered on the Kikuchi band 152. Similarly, a line width may also be stored for the identified Kikuchi band 152, thereby indicating the width of the Kikuchi band 152. Additionally or alternatively, the identified Kikuchi band 152 may be represented (and optionally stored) by the identification module 320 as two straight lines, each placed along a respective edge of the Kikuchi band 152. Other parameters may also be calculated and stored, such as any of the following: intensity / strength of the Kikuchi band, asymmetry of the Kikuchi band, gradient of the edge of the Kikuchi band; etc.

[0073] The projection module 330 is arranged to generate a plurality of points 356, each representing a corresponding identified Kikuchi band 152. The plurality of points 356 representing the identified Kikuchi bands 354 are relative to (or have) a common reference (typically the point of incidence 117 of the electron beam 115 and the test sample 120). In view of the above discussion on the relationship between the point of incidence 117 and the pattern center 155, it should be understood that the pattern center 115 can be used instead of the point of incidence 117. Each point can be determined as the intersection between the vector representation of the corresponding Kikuchi band 152 and the cylindrical symmetric surface. The cylindrical symmetric surface is substantially parallel to the line connecting the point of incidence 117 and the pattern center 155.

[0074] For ease of understanding, embodiments of the present invention will be described below using the example of a cylindrical surface that is substantially parallel to the line connecting the incident point 117 and the pattern center 155. However, it should be appreciated that the cylindrically symmetric surface may be any suitable surface rotated about an axis that is substantially parallel to (or coincident with) the line connecting the incident point 117 and the pattern center 155. As such, the projection module 330 is typically arranged to determine a vector representing a corresponding Kikuchi band 152 relative to (or based at least in part on) the incident point 117. In practice, the projection module 330 is typically arranged to map each Kikuchi band 152 to a corresponding vector. It should be appreciated that the Kikuchi band 152 (which is described above in Figure 1 The plane is defined by the sphere 160 described in FIG. 1 . The vector representing the Kikuchi band 152 is generally determined based on the plane defined by the Kikuchi band 152. Specifically, a normal vector of the plane (or relative to the plane) may be used. For example, the vector representation of the corresponding Kikuchi band 152 may be a vector passing through the incident point 117 and normal to the plane defined by the Kikuchi band 152 (or determined based on the vector).

[0075] The projection module 330 may be arranged to associate an intensity (intensity / strength) with (or as part of) each of the plurality of points 356. The intensity generally represents the strength of the detected Kikuchi band. Additionally or alternatively, the intensity may represent (or include) the width of the corresponding Kikuchi band 152, or a weighted combination of the intensity and the width. Similarly, the intensity may represent (or include) some other measured property (such as Kikuchi band asymmetry).

[0076] It should be understood that a variety of variations are possible for determining the vector representation of the corresponding Kikuchi strip 152. For example, in the determination of the vector representation described above, any one or more predetermined injective transformations, such as rotation, vector cross product with a predetermined vector, translation, etc., may be included.

[0077] The cylindrical surface is also determined relative to (or at least partially based on) the incident point 117. The orientation of the cylindrical surface can be selected with the goal of minimizing (or reducing) the spread of the plurality of points 356 representing the identified Kikuchi bands 354 in the axial direction of the cylindrical surface. In the example given above, the cylindrical surface can be perpendicular to the scintillation screen 132. In other words, the cylindrical surface can be along the PC z The direction of the cylindrical surface (or the vector passing through the center of the pattern and the incident point 117) is aligned. Typically, the radius of the cylindrical surface is (or is based on) the spacing PC between the scintillation screen 132 and the incident point 117. z .

[0078] As should be understood, for use Figure 1In the EBSD image 150 formed by the EBSD apparatus described in the above, the pattern center 155 and the extended incident point 117 are measured (or estimated) points. As such, the pattern center 155 (or the incident point 117) used by the projection module 330 as described above is susceptible to measurement and / or estimation errors.

[0079] The matching module 340 is arranged to determine a configuration 360 of the test sample 120 based on the plurality of points 356 representing the identified Kikuchi bands 354. In this way, it can be said that the matching module 340 is arranged to characterize the test sample 120 by the generated configuration 360. Specifically, the matching module 340 is arranged to determine the configuration 360 based on matching the plurality of points 356 representing the identified Kikuchi bands 354 with a plurality of expected point sets 358. Typically, each expected point set 358 corresponds to an EBSD image 150 of a known sample. As explained above with respect to the identification module 320 and the projection module 330, the EBSD image 150 of each expected point set has been processed. In this way, each expected point set 358 is (or includes) a plurality of points representing the identified Kikuchi bands 354 of a known sample (which has a corresponding known configuration).

[0080] It will be appreciated that the EBSD image 150 of a given expected point set 358 may be an experimental image (i.e., a Figure 1 ). Alternatively, the EBSD image 150 may be a theoretical image. Specifically, the EBSD image 150 may be generated by a simulation (such as a kinematic and / or dynamic simulation), in which electron diffraction from a known sample (having a known configuration) is determined according to a computational model and the resulting predicted EBSD image 150. See, for example, "Many-beam dynamical simulation of electron backscatterdiffraction patterns", Aimo Winkelmann, Carol Trager-Cowan, Francis Sweeney, Austin P. Day, Peter Parbrook, Ultramicroscopy 107, 414 (2007). Such simulations of the EBSD image 150 are well known and are therefore not described in detail herein.

[0081] In general, the matching module 340 is arranged to compare the plurality of points 356 representing the identified Kikuchi band 354 with the expected point set 358 to determine whether there is a match between the plurality of points 356 representing the identified Kikuchi band 354 and the expected point set 358. For example, if the two points are within a predetermined distance of each other, then a point in the plurality of points 356 representing the identified Kikuchi band 354 may be said to match (or correspond to) a point in the expected point set. If there are more than a predetermined number (or threshold) of such matching points, then the plurality of points 356 representing the identified Kikuchi band 354 may be said to match (or correspond to) the expected point set.

[0082] Additionally or alternatively, various other criteria may be used when determining (or identifying) a match between the plurality of points 356 representing the identified Kikuchi band 354 and the expected set of points. For example, an overall match score (or goodness of fit metric) may be formed for the plurality of points 356 representing the identified Kikuchi band 354 and the expected set of points. Each match between a point representing the identified Kikuchi band and an expected point may be weighted according to the distance between the two points (or assigned a score based on the distance between the two points). For example, a match between points that are close together may receive a greater weighting than a match between points with a larger spacing. Additionally or alternatively, each match between a point representing the identified Kikuchi band and an expected point may be weighted according to the strength of the one or two points (or assigned a score based on the strength of the one or two points). For example, a match between points of high intensity may receive a greater weighting than a match between points of low intensity. The overall match score may include the sum (or accumulation) of these weights. In this manner, if the overall match score satisfies a predetermined threshold, it may be determined that there is a match between the plurality of points 356 representing the identified Kikuchi zone 354 and the expected set of points. It should be appreciated that various thresholds may be adjusted (or predetermined) to take into account the accuracy of the EBSD image 150 and the method used. It should also be appreciated that different schemes and weightings may be used to calculate the overall match score; for example, an arithmetic or geometric mean or some combination thereof.

[0083] It will be appreciated that by representing the identified Kikuchi bands 354 of the EBSD image 150 and the Kikuchi bands 152 of the known samples as points in the manner described above, a greater number of Kikuchi bands 152 may be considered during the matching process than by using prior art indexing techniques. Specifically, a full match (where all identified Kikuchi bands 354 are taken into account in the match) and analysis of the test sample 120 may be performed. This may improve the accuracy of any determined configuration (or individual property) of the test sample 120 (as briefly described below). Moreover, for situations where the Kikuchi bands 152 of two different known samples or configurations are substantially similar, taking more Kikuchi bands 152 into account may enable better differentiation of the known configurations.

[0084] The configuration 360 of the test sample 120 may be determined by the matching module 340 based on one or more expected point sets identified as matching the plurality of points 356 representing the identified Kikuchi bands 354. Specifically, the determined configuration 360 of the test sample 120 may be determined based on the known sample corresponding to the matched expected point set 358. In general, the determined configuration 360 of the test sample 120 may include one or more properties of the known sample corresponding to the matched expected point set 358. The determined configuration 360 may include any one or more sample properties including: crystalline phase; unit cell dimensions of the crystal; elements present in the crystal; crystal orientation; crystal defects; one or more impurities present; a series of expected reflectors (Kikuchi bands) and their widths and / or approximate intensities, etc. It should be appreciated that in some instances, more than one identified expected point set 358 may be identified as matching the plurality of points 356 representing the identified Kikuchi bands 354. In such cases, more than one configuration 360 of the test sample 120 may be determined. For example, separate configurations 360 may be determined for the test sample 120, each of which is determined based on a different set of matched expected points 358. This may correspond to a situation in which more than one lattice is present in the test sample 120 at or near the incident point 117. Additionally or alternatively, one configuration 360 may be determined based on the matched more than expected point set 358. In this case, typically, the configuration 360 will include one or more properties common to the known samples corresponding to the matched more than expected point set 358. This may correspond to a situation in which a few crystals with different properties produce the same or similar Kikuchi bands 152. An example of such a situation is a face-centered cubic (fcc) crystal of nickel, iron, and aluminum. The matching module 340 may also be arranged to provide (or calculate) a measure of confidence in the determined configuration 360. Specifically, the measure of confidence may include (or be based on) the overall match score (or scores) of the corresponding matched one (or more) expected point set 358. In addition, alternative weighting schemes may be applied to prioritize solutions based on, for example, measured Kikuchi bandwidths.

[0085] It will be appreciated that in the analysis described above, the expected point set 358 may be determined as needed, for example, using the identification module 320 and the projection module 330. Additionally or alternatively, the expected point set 358 may be pre-computed and stored in a memory (e.g., the storage medium 204) and / or in the device 222. It will be appreciated that the pre-computed expected point set 358 may be stored remotely to the system 300, such as on a server and / or cloud computing platform 390. As such, the matching module 340 may be arranged to retrieve the expected point set 358 from the server and / or cloud computing platform via a suitable data connection 395. Examples of suitable data connections include: via a local area network, via a wide area network, via a direct data connection (e.g., a USB connection, a Thunderbolt connection, a Thunderbolt connection, a direct Ethernet connection, etc.), via the Internet, etc.

[0086] As briefly demonstrated below, both the point 356 representing the identified Kikuchi band 354 and the expected point 358 are relative to the three components PC of the corresponding pattern center 155 in a predictable manner. x 、PC y and PC z In other words, as briefly shown below, a mathematical relationship can be derived between the change in each of the three components of the pattern center 155 and the resulting change in the point of the corresponding Kikuchi band 152.

[0087] In some variations of the system 300 described above, the matching module 340 may be arranged to optimize (or adjust) the estimated pattern center 155 (or the incident point 117) corresponding to the EBSD image 150 relative to the expected set of points 358 for matching. Specifically, optimizing the estimated pattern center 155 may include changing at least one component of the pattern center 155 based on (or dependent on) an objective function. For example, at least one component of the pattern center 155 may be changed with the goal of improving the value of the objective function (such as obtaining an extreme value of the objective function). Optionally, all components of the pattern center 155 may be changed as part of the optimization step, or a subset may be optimized as part of the optimization step. It should be understood that the mathematical relationship discussed above can be used during the optimization to directly calculate the resulting changes in the points 356 representing the identified Kikuchi bands 354 caused by the changes in the pattern center. Therefore, the changes in the value of the objective function caused by the changes in the pattern center 155 can be directly calculated, thereby enabling such optimization. The objective function may include the overall matching score discussed previously. The matching module may be arranged to calculate, for the matched expected point set 358 , an updated goodness-of-fit metric corresponding to the respective optimized pattern center 155 .

[0088] It will be appreciated that the optimization may be performed using numerical optimization techniques (many examples of which are known in the art). For example, the optimization may be performed in whole or in part using any of the following: finite difference methods, such as Newton's method; Quasi-Newton method; conjugate gradient method; steepest descent method; proximal minimization, descent simplex / amoeba; exhaustive search of parameter space at a certain granularity; etc.

[0089] This optimization may be performed separately with respect to each expected point set identified as matching the point 356 representing the identified Kikuchi band 354. It will be appreciated that in this manner, the matching process may be further improved because the matching module 340 may be arranged to distinguish the matched expected point sets 358 (e.g., identify the most likely or best matches) based on the updated goodness of fit metric. Additionally or alternatively, the matching module 340 may be arranged to determine a confidence level for one or more of the matched point sets 358 based on the corresponding optimized pattern center 155. For example, the confidence level of the match may be inversely proportional to the difference between the optimized pattern center 155 and the original estimated pattern center 155.

[0090] The confidence metric may also be weighted using any combination of, for example, measured and predicted values ​​of Kikuchi band strength, Kikuchi band width, Kikuchi band symmetry, the presence and / or absence of critical Kikuchi bands (which may be useful in minimizing pseudo-symmetry effects).

[0091] Figure 3b and 3c The geometric relationship between the EBSD image 150 (eg, an image projected onto the scintillator screen 132 described above), the example Kikuchi band 152, and the pattern center PC is schematically illustrated. Figure 1 The discussion of the EBSD image 150 described above applies equally here.

[0092] exist Figure 3b and 3c In FIG. 1 , a set of axes (labeled x, y, and z) of a Cartesian coordinate system are shown. Here, the xy plane coincides with the EBSD image plane. The z axis is perpendicular to the EBSD image plane. The origin O of the Cartesian coordinate system coincides with the incident point 117 of the electron beam 115 and the test sample 120. In this Cartesian coordinate system, the pattern center PC is at the x, y, z coordinates (PC x 、PC y 、-PC z ) place.

[0093] exist Figure 3b In FIG. 1 , an example Kikuchi zone 152 is also shown as a line connecting points A and B, both of which are on the EBSD image plane. Point A is at the x, y, z coordinates (a x 、a y 、-PC z ). Point B is at the x, y, z coordinates (b x 、b y 、-PC z ) place. Figure 3b (and Figure 3c ) also shows the vector n AB , which is the vector normal to the plane passing through points A, B and the origin O. Thus, it should be understood that the vector n AB is an example of a Kikuchi strip normal as previously described above.

[0094] exist Figure 3c , an example cylindrically symmetric surface 399 is shown (as briefly described in detail above), which in this example is a cylinder aligned along a line connecting the pattern center PC and the origin O. α is the vector n AB The azimuth angle of intersection with cylindrical surface 399. β is the vector n AB The z coordinate of the intersection with cylindrical surface 399.

[0095] Figure 3d A variation of the EBSD image 150 analysis system 300 discussed above is schematically shown. Figure 3a The discussion regarding the EBSD image 150 analysis system 300 is equally applicable here.

[0096] The projection module 330 is arranged to determine a vector representing a corresponding Kikuchi band 152 relative to the incident point 117 (or based at least in part on the incident point). In practice, the projection module 330 is arranged to map each Kikuchi band 152 to a corresponding vector, thereby forming a set of multiple vectors of identified Kikuchi bands. It should be appreciated that the Kikuchi bands 152 (which are as described above in Figure 1 The plane is defined by the sphere 160 described in FIG. 1 . The vector representing the Kikuchi band 152 is generally determined based on the plane defined by the Kikuchi band 152. Specifically, a normal vector of the plane (or relative to the plane) may be used. For example, the vector representation of the corresponding Kikuchi band 152 may be a vector passing through the incident point 117 and normal to the plane defined by the Kikuchi band 152 (or determined based on the vector).

[0097] It should be understood that a variety of variations are possible for determining the vector representation of the corresponding Kikuchi strip 152. For example, in the determination of the vector representation described above, any one or more predetermined injective transformations, such as rotation, vector cross product with a predetermined vector, translation, etc., may be included.

[0098] The matching module 340 is arranged to determine the configuration 360 of the test sample 120 based on the plurality of vectors representing the identified Kikuchi bands 354. In this way, it can be said that the matching module 340 is arranged to characterize the test sample 120 by the generated configuration 360. Specifically, the matching module 340 is arranged to determine the configuration 360 based on matching the plurality of vectors 396 representing the identified Kikuchi bands 354 with a plurality of expected vector sets 398. In general, each expected vector set 398 corresponds to an EBSD image 150 of a known sample. As explained above with respect to the identification module 320 and the projection module 330, the EBSD image 150 of each expected vector set has been processed. In this way, each expected vector set 398 is (or includes) a plurality of vectors representing the identified Kikuchi bands 354 of a known sample (which has a corresponding known configuration).

[0099] It will be appreciated that the EBSD image 150 for a given set of expected vectors 358 may be an experimental image (i.e., a Figure 1 Alternatively, the EBSD image 150 may be a theoretical image as previously discussed above.

[0100] The matching module 340 is arranged to compare the plurality of vectors 396 representing the identified Kikuchi bands 354 with the expected vector set 398 to determine whether there is a match between the plurality of vectors 396 representing the identified Kikuchi bands 354 and the expected vector set 358. For example, if the magnitude of the arithmetic difference of the two vectors is below a predetermined threshold, then a vector in the plurality of vectors 396 representing the identified Kikuchi bands 354 may be said to match (or correspond to) a vector in the expected vector set. If there are more than a predetermined number (or threshold) of such matching vectors, then the plurality of vectors 396 representing the identified Kikuchi bands 354 may be said to match (or correspond to) the expected vector set.

[0101] Additionally or alternatively, various other criteria may be used when determining (or identifying) a match between the plurality of vectors 396 representing the identified Kikuchi band 354 and the expected vector set. For example, an overall match score (or goodness of fit metric) may be formed for the plurality of vectors 396 representing the identified Kikuchi band 354 and the expected vector set. Each match between a point representing the identified Kikuchi band and an expected point may be weighted according to the strength of the one or two vectors (or assigned a score based on the strength of the one or two vectors). For example, a match between vectors of high intensity may receive a greater weighting than a match between vectors of low intensity. The overall match score may include the sum (or accumulation) of these weights. In this way, if the overall match score meets a predetermined threshold, it may be determined that there is a match between the plurality of vectors 396 representing the identified Kikuchi band 354 and the expected vector set. It should be appreciated that various thresholds may be adjusted (or predetermined) to take into account the accuracy of the EBSD image 150 and the method used. It should also be appreciated that different schemes and weightings may be used to calculate the overall match score; for example, an arithmetic or geometric mean, or some combination thereof.

[0102] The configuration 360 of the test sample 120 may be determined by the matching module 340 based on one or more expected vector sets identified as matching the plurality of vectors 356 representing the identified Kikuchi bands 354. Specifically, the determined configuration 360 of the test sample 120 may be determined based on known samples corresponding to the matched expected vector set 398. In general, the determined configuration 360 of the test sample 120 may include one or more properties of the known sample corresponding to the matched expected vector set 398. The determined configuration 360 may include any one or more sample properties including: crystalline phase; unit cell dimensions of the crystal; elements present in the crystal; crystal orientation; crystal defects; one or more impurities present; a series of expected reflectors (Kikuchi bands) and their widths and / or approximate intensities, etc. It should be appreciated that in some instances, more than one expected vector set 398 identified may be identified as matching the plurality of vectors 396 representing the identified Kikuchi bands 354. In such cases, more than one configuration 360 of the test sample 120 may be determined. For example, separate configurations 360 may be determined for the test sample 120, each of which is determined based on a different set of matched expected vectors 398. This may correspond to a situation in which more than one lattice exists in the test sample 120 at or near the incident point 117. Additionally or alternatively, a configuration 360 may be determined based on a set of more than expected vectors 398 that match. In this case, typically, the configuration 360 will include one or more properties common to known samples corresponding to the set of more than expected points 398 that match. This may correspond to a situation in which a few crystals with different properties produce the same or similar Kikuchi bands 152. An example of such a situation is a face-centered cubic (fcc) crystal of nickel, iron, and aluminum. The matching module 340 may also be arranged to provide (or calculate) a measure of confidence in the determined configuration 360. Specifically, the measure of confidence may include (or be based on) the overall match score (or scores) of the corresponding matched one (or more) expected vectors 358. In addition, alternative weighting schemes may be applied to prioritize solutions based on, for example, measured Kikuchi bandwidths.

[0103] It will be appreciated that in the analysis described above, the expected vector set 398 may be determined as needed, for example, using the identification module 320 and the projection module 330. Additionally or alternatively, the expected vector set 398 may be pre-computed and stored in a memory (e.g., the storage medium 204) and / or in the device 222. It will be appreciated that the pre-computed expected vector set 398 may be stored remotely to the system 300, such as on a server and / or cloud computing platform 390. As such, the matching module 340 may be arranged to retrieve the expected vector set 358 from the server and / or cloud computing platform via a suitable data connection 395. Examples of suitable data connections include: via a local area network, via a wide area network, via a direct data connection (e.g., a USB connection, a Thunderbolt connection, a Thunderbolt connection, a direct Ethernet connection, etc.), via the Internet, etc.

[0104] In a further variation, the matching module is arranged to match the plurality of vectors to a desired set or sets of vectors to within a rotation. Specifically, the matching module may be arranged to obtain a rotational transformation that, when applied to the plurality of vectors (or desired set of vectors), minimizes (or is intended to minimize) the difference between the two sets of vectors. This approach may be particularly advantageous when the vectors are related to respective planes defined by their respective Kikuchi bands by a predetermined relationship (e.g., when the vectors are normal to the plane). In this case, EBSD images of the same sample that differ only in the positioning of the scintillation screen 132 may be expected to produce respective plurality of vectors that differ by rotation.

[0105] exist Figure 3e This is schematically illustrated in , which shows a first arrangement 1310 of an EBSD imaging experiment and a second arrangement 1320 of the same EBSD imaging experiment, wherein the scintillation screen 132 screen has been moved relative to the first arrangement.

[0106] As can be seen, the plurality of vectors 1315 for the first arrangement and the plurality of vectors 1325 for the second arrangement differ only by rotation about the origin. This is because the Kikuchi strips forming a great circle on a notional sphere centered at the point of incidence are not affected by the movement of the scintillation screen 132. Figure 3e In , vectors are shown by dashed lines terminating in circles, and coordinate axes are shown by solid lines terminating in arrows.

[0107] In this way, by using a further variation in which the matching module is arranged to match a plurality of vectors to a desired set or sets of vectors, within a rotation, fewer expected sets of vectors need to be taken into account.

[0108] It will be appreciated that any suitable known method may be used to obtain the rotational transformation. One such suitable method is to use quaternions as described in "Quaternions in molecular modeling" CFF Kerney (2007), Journal of Molecular Graphics & Modelling, Vol. 25, pp. 595-604, doi: 10.1016 / j.jmgm.2006.04.002, which is incorporated herein by reference in its entirety. For example, take a number of vectors {n l}、Expected vector set {n′ l} and general rotation R q (x), R can be obtained by minimizing the following expression: q (x):

[0109]

[0110] In the quaternion algebra, q = q o 1+q 1 i+q 2 j+q 3 k and (Assume the sign of 1 as the identity element, so that i 2 =j 2 =k 2 =-1)

[0111] The weight w of each Kikuchi band as described above l It can be based on the strength of the Kikuchi band or some other importance measure of the Kikuchi band. Alternatively, they can simply be set to a constant value, such as 1. W is a normalization factor for the weights.

[0112] This leads to the eigenvalue problem:

[0113] E=q T ·B·q

[0114] in is a 4×4 symmetric matrix with real eigenvalue λ 0 ,λ 1 ,λ 2 ,λ 3 , where 0≤λ 0 ≤λ 1 ≤λ 2 ≤λ 3 For completeness, A is annotated here l is a 4×4 skew matrix. l =A(n′ l +nl , n′ l -n l ),in

[0115] Solving the eigenvalue problem can then be done in the usual way and setting q to correspond to the eigenvalue λ 0 This is done by finding the eigenvectors of (given the minimum value of E and hence the initial expression) and providing the required rotation R q .

[0116] It should be appreciated that the above discussion of how to obtain the rotation is merely exemplary, and the skilled person will be aware of other ways in which the rotation between two sets of vectors may be obtained.

[0117] In the above examples, it should be noted that the correspondence between the plurality of vectors and the vectors in the expected vector set is assumed by using a common index l. This can be accomplished by performing the above minimization on all possible correspondences and selecting the correspondence that produces the smallest eigenvalue. As discussed briefly further below, in some cases, a candidate expected vector set is selected, during which the correspondence between the vectors can be inferred or determined.

[0118] Figure 4a The EBSD image 150 analysis system (eg Figure 3a The method 400 is performed by the EBSD image 150 analysis system 300).

[0119] At step 420, a plurality of Kikuchi bands 152 present in the EBSD image 150 are identified. Step 420 may include detecting straight line features in the EBSD image 150 to thereby identify one or more Kikuchi bands 152 in the EBSD image 150. Step 420 may include applying a Hough (or Radon) transform (optionally with filtering and / or peak detection) to the EBSD image 150 to thereby identify one or more Kikuchi bands 152 in the EBSD image 150. Additionally or alternatively, as part of step 420, one or more Kikuchi bands 152 may be identified based at least in part on user interaction. As previously discussed, step 420 may further include identifying a bandwidth of one or more of the identified Kikuchi bands 354.

[0120] At step 430, a plurality of points are generated that each represent a corresponding identified Kikuchi band of the plurality of identified Kikuchi bands 354. Typically, each point is determined as the intersection between a vector representation of a corresponding Kikuchi band 152 (e.g., a Kikuchi band plane normal) and a cylindrical surface or cylindrically symmetric surface (as previously described). Step 430 may include determining a vector representing the corresponding Kikuchi band 152 relative to the incident point 117 (or based at least in part on the incident point). The vector representing the corresponding Kikuchi band 152 may be determined as previously discussed. In step 430, the vector representing the Kikuchi band 152 is typically determined based on a plane defined by the Kikuchi band 152. For example, in step 430, the vector representation of the corresponding Kikuchi band 152 may be determined based on a vector passing through the incident point 117 and normal to the plane defined by the Kikuchi band 152. Step 430 may also include associating an intensity (intensity / strength) with each point (or as part of it). The intensity generally indicates the width of the corresponding Kikuchi band 152 .

[0121] At step 440, the configuration 360 of the test sample 120 is determined based on the plurality of points 356 representing the identified Kikuchi band 354. Step 440 includes identifying one or more expected point sets 358 that match the plurality of points 356 representing the identified Kikuchi band 354. Generally, step 440 is arranged to compare the plurality of points 356 representing the identified Kikuchi band 354 with the expected point set 358 to determine whether there is a match between the plurality of points 356 representing the identified Kikuchi band 354 and the expected point set 358. It should be appreciated that such a comparison may be performed point by point. Alternatively, a comparison may be performed simultaneously across a plurality of points in the plurality of points 356 representing the identified Kikuchi band 354 and the expected point set 358. The determination of the configuration 360 made in step 440 is based on the one or more expected point sets identified as matching the plurality of points 356 representing the identified Kikuchi band 354. Generally, at step 440 a configuration 360 is determined that includes one or more properties corresponding to the matched (or identified) one or more expected point sets 358 .

[0122] It should be appreciated that the configuration 360 determined as part of step 440 may be output or otherwise provided to a user. Additionally or alternatively, the configuration 360 may be stored and / or provided to another analysis tool for further processing or analysis. For example,

[0123] Figure 4b Schematically showing the EBSD images 150 analyzed by different systems (eg Figure 3d Method 409 performed by a different EBSD image 150 analysis system 300). Method 409 is a variation of method 400 discussed above. Figure 4aThe discussion of method 400 is equally applicable here.

[0124] At step 430, a plurality of vectors are generated that each represent a corresponding identified Kikuchi band in the plurality of identified Kikuchi bands 354. Step 430 may include determining a vector representing a corresponding Kikuchi band 152 relative to the incident point 117 (or based at least in part on the incident point). The vector representing the corresponding Kikuchi band 152 may be determined as previously discussed. In step 430, the vector representing the Kikuchi band 152 is generally determined based on a plane defined by the Kikuchi band 152. For example, in step 430, the vector representation of the corresponding Kikuchi band 152 may be determined based on a vector passing through the incident point 117 and normal to the plane defined by the Kikuchi band 152. Although a normal vector is used as an example herein, it should be understood that the vectors may be generated based on any predetermined relationship relative to the plane. Step 430 may also include associating an intensity (intensity / strength) with each vector (or as part of it). The intensity generally represents the width of the corresponding Kikuchi band 152.

[0125] At step 440, the configuration 360 of the test sample 120 is determined based on the plurality of vectors 356 representing the identified Kikuchi band 354. Step 440 includes identifying one or more expected vector sets 398 that match the plurality of vectors 396 representing the identified Kikuchi band 354. Typically, step 440 is arranged to compare the plurality of vectors 396 representing the identified Kikuchi band 354 with the expected vector set 398 to determine whether there is a match between the plurality of vectors 356 representing the identified Kikuchi band 354 and the expected vector set 398. It should be appreciated that such a comparison may be performed vector by vector. Alternatively, a comparison may be performed simultaneously across a plurality of vectors in the plurality of vectors 396 representing the identified Kikuchi band 354 and the expected vector set 398. The determination of the configuration 360 in step 440 is based on one or more expected vector sets identified as matching the plurality of vectors 396 representing the identified Kikuchi band 354. Generally, at step 440 a configuration 360 is determined that includes one or more properties corresponding to the matched (or identified) one or more expected vector sets 398 .

[0126] Figure 5a A variation of the EBSD image 150 analysis system 500 is schematically illustrated. The variation of the EBSD image 150 analysis system 500 is a variation of the EBSD image 150 analysis system 300 discussed above. Figure 3a and Figure 4a The discussion regarding the EBSD image 150 analysis system 300 is equally applicable here.

[0127] The matching module 340 further includes a candidate selection module 545. The candidate selection module 545 is arranged to identify (or determine) one or more candidate expected point sets from the plurality of expected point sets. Specifically, the candidate portion module 545 is arranged to determine whether the expected point set 358 is a candidate expected point set 558 based on matching the azimuth angles of the points in the set 358 with the azimuth angles of the points representing the identified Kikuchi strip 354. As should be appreciated, the azimuth angle of a point is based on the azimuth position of the point on the cylindrical surface discussed previously.

[0128] In accordance with the above Figure 3a In a similar manner to the point matching described above, if the difference in the azimuth angle between a point in the plurality of points representing the identified Kikuchi strip 354 and a point in the expected point set 358 is below a predetermined threshold, the two points can be said to match (or correspond to each other). If there are more than a predetermined number (or threshold) of matching points between the expected point set 358 and the plurality of points representing the identified Kikuchi strip 354, the expected point set 358 can be identified as a candidate set 558.

[0129] Moreover, as mentioned above Figure 3a As with the matching of points described above, various other criteria may be used in determining (or identifying) a match between the plurality of points 356 representing the identified Kikuchi strip 354 and the expected point set 358. For example, a candidate match score (or goodness of fit metric) may be formed for the plurality of points 356 representing the identified Kikuchi strip 354 and the expected point set 358. Each match between a point representing the identified Kikuchi strip 152 and an expected point may be weighted according to the difference in the azimuth angles of the two points (or assigned a score based on the difference in the azimuth angles of the two points). Additionally or alternatively, each match between a point representing the identified Kikuchi strip 152 and an expected point may be weighted according to the strength of one or both points (or assigned a score based on the strength of the one or both points). The candidate match score may include the sum (or accumulation) of these weights. In this manner, if the candidate match score satisfies a predetermined threshold, the expected point set 358 may be identified as the candidate set 558.

[0130] As explained above with respect to FIG. 3 , the matching module 340 is arranged to determine a configuration based on matching the plurality of points 356 representing the identified Kikuchi strips 354 with a plurality of expected point sets, with the modification that only candidate expected point sets 558 identified by the candidate selection module 545 are considered. In this manner, the candidate selection module 545 can be considered to enable pre-filtering of expected point sets and, by extension, possible configurations. It should be appreciated that identifying such candidate sets 558 can advantageously improve the overall efficiency of the process of determining the configuration of the test sample 120, as expected point sets 358 that are not matched due to having incorrect orientation angles can be eliminated early on and not fully matched point by point.

[0131] Determining the candidate point set 558 can be further particularly advantageous because the candidate expected point set 558 is identified based on the azimuth angles of the points. The three components PC representing the azimuth angles of the identified points of the Kikuchi strip 354 and the expected points relative to the center of the pattern as discussed above x 、PC y and PC z Thus, errors in the measurement (or estimation) of the pattern center (or incident point 117) should not affect the identified candidate set. Figure 3b and 3c This is demonstrated as follows. The vector n is obtained by cross-product of the vector connecting the origin and point A with the vector connecting the origin and point B. AB .

[0132] n AB =(AO)×(BO)

[0133] n AB =[a x , a y , -PC z ]×[b x , b y , -PC z ]

[0134]

[0135] By vector n AB The ratio of the y-component to the x-component of gives the tangent to the azimuth angle α, so that the azimuth angle α is given by the following relationship:

[0136]

[0137] As can be seen, this is relative to PC Z The change is constant.

[0138] A formula for the out-of-plane (or tilt) angle β can be derived:

[0139]

[0140] Because points A and B are in the plane of image 150, the range of β is limited. Typically, in particular, β rarely exceeds 60°. It should be understood that other mapping functions can also be used for β, such as:

[0141]

[0142] or

[0143]

[0144] Here, c 0 It can be an angle scaling factor. Other mapping functions will be known to those skilled in the art, and it should be understood that the present invention is not necessarily limited to

[0145] Azimuth angle α relative to PC X and PC Y For example, if the pattern center is offset by [Δx, Δy, Δz], this effectively changes the coordinates of points A and B relative to the offset pattern center (which will be used as the origin of the x and y axes). The offset points A and B, now labeled A' and B' respectively, are given by:

[0146] A′=[(a x -Δx), (a y -Δy),-(PC z +Δz)]

[0147] B′=[(b x -Δx), (b y -Δy),-(PC z +Δz)]

[0148] As a result, the vector n AB It is concluded from the following:

[0149] n AB = ±(A′-O)^(B′-O)

[0150]

[0151]

[0152] As can be seen, α is still given by:

[0153]

[0154] However, β depends on the change in the center of the pattern, as it is given by:

[0155]

[0156] It should be appreciated that the Kikuchi strip plane normal fitting algorithm can be split into two parts - the first part uses α (insensitive to the pattern center position) and the second part uses both α and β. This reduces the overall sensitivity of the fitting algorithm to pattern center errors. In addition, as briefly described below Figure 8b, any rotation of the EBSD image 150 about the pattern center 155 should simply result in a constant azimuthal offset for all points representing the Kikuchi zone 152 in the EBSD image 150, as calculated using the system 300 and the system 500 described above. It should be appreciated that the Kikuchi zone normal can point in either direction. In some cases, wrapping of the azimuthal angle (e.g., to force the angle to fall within the range of 0 to 180 degrees) can be accommodated by reversing the sign of B.

[0157] Thus, it will be appreciated that the expected point sets 358 that differ only by rotation of the corresponding EBSD images 150 about the center of the pattern (and therefore are the same within a constant offset of the azimuthal angle of the points) can be reduced to a single expected point set 358. In this manner, it will be appreciated that in some variations of the systems 300 and / or systems 500 described above, the plurality of points 356 representing the identified Kikuchi zones 354 and the expected point set 358 can be matched or compared based on the relative azimuthal angles of the corresponding points.

[0158] Similarly, in some variations of the system 500 described above, the candidate portion module may be arranged to determine whether the expected point set is a candidate expected point set based on matching the relative azimuth angles of points in the set with the relative azimuth angles of points representing the identified Kikuchi strip 354 .

[0159] It should be understood that no matter the vector (such as n AB ) are correctly matched, the above discussion applies equally to the variants discussed above. As can be seen, these vectors can always be expressed in a coordinate system in which one component (the azimuth angle in the above example) is invariant with respect to rotation about the center of the pattern, and one component (the tilt angle in the example given above) is invariant with respect to PC X and PC Y The change is constant.

[0160] Figure 5b The above schematically shows Figure 3d A variation of the discussed EBSD image 150 analysis system 300. The above referenced Figure 5a The discussion regarding the EBSD image 150 analysis system 500 applies equally here.

[0161] The matching module 340 further includes a candidate selection module 545. The candidate selection module 545 is arranged to identify (or determine) one or more candidate expected vector sets from a plurality of expected vector sets. Specifically, the candidate portion module 545 is arranged to determine whether the expected vector set 398 is a candidate expected vector set 598 based on matching the tilt angle of the vectors in the set 398 with the tilt angle of the vector representing the identified Kikuchi band 354. Here, the tilt angle of the vector is the angle of the vector relative to a first predetermined coordinate axis. In the example discussed herein, this axis is considered to be perpendicular to the image and passing through the incident point. Additionally or alternatively, the candidate selection module may be arranged to determine whether the expected vector set 398 is a candidate expected vector set 5958 based on matching the azimuth angle of the vectors in the set 398 with the azimuth angle of the vector representing the identified Kikuchi band 354. Here, the azimuth angle may be considered to be an angle around a predetermined coordinate axis. This may be considered to be equivalent to matching the azimuth angles of the points discussed in other variations above. It should be understood that the azimuth angles of the points discussed above may be matched based on the above description of the azimuth angles of the vectors. Figure 5a The predetermined threshold discussed and the matching of the azimuth angles of the points are used to perform such matching of the angles.

[0162] The above text about Figure 5a In a similar manner to the point matching described, if there are more than a predetermined number (or threshold number) of matching vectors between the expected vector set 398 and the plurality of vectors representing the identified Kikuchi bands 354 , the expected vector set 398 may be identified as a candidate set 598 .

[0163] Moreover, as mentioned above Figure 3d As with the vector matching described above, various other criteria may be used when determining (or identifying) a match between the plurality of vectors 396 representing the identified Kikuchi bands 354 and the expected vector set 398. For example, a candidate match score (or goodness of fit metric) may be formed for the plurality of vectors 396 representing the identified Kikuchi bands 354 and the expected vector set 398. Each match between a vector representing the identified Kikuchi band 152 and an expected vector may be weighted according to the difference between the angles (one or more) of the two vectors (or assigned a score based on the difference between the angles (one or more) of the two vectors). Additionally or alternatively, each match between a vector representing the identified Kikuchi band 152 and an expected vector may be weighted according to the strength of the corresponding Kikuchi band of one or both vectors (or assigned a score based on the strength of the corresponding Kikuchi band of the one or both vectors). The candidate match score may include the sum (or accumulation) of these weights. In this manner, if the candidate match score satisfies a predetermined threshold, the expected vector set 398 may be identified as a candidate set 598. It should be understood that the above matching will also provide a corresponding relationship (or mapping) between the corresponding vectors of the plurality of vectors and the corresponding vectors in each candidate vector set. Figure 3d As discussed, such correspondence may be further used to determine a rotation connecting multiple vectors to a given set of candidate vectors.

[0164] As mentioned above about Figure 3d As illustrated, the matching module 340 is arranged to determine a configuration based on matching the plurality of vectors 396 representing the identified Kikuchi bands 354 with a plurality of expected vector sets, with the modification that only the candidate expected vector sets 558 identified by the candidate selection module 545 are considered. In this way, the candidate selection module 545 can be considered to enable pre-filtering of the expected vector sets and, by extension, possible configurations.

[0165] It will be appreciated that the expected vector set may be generated by applying a rotation to an existing expected vector set. Figure 3e As discussed, for a given EBSD experiment (whether actual or simulated), changing the position of the screen 132 results in a rotation of the vectors representing the Kikuchi zones. Thus, from the expected set of vectors, additional expected sets of vectors, each associated with a corresponding position of the screen 132, can be generated by applying the appropriate corresponding rotations.

[0166] Therefore, in another variation, the expected vector set may include one or more primary expected vector sets each corresponding to a corresponding sample in a corresponding orientation, and for each primary expected vector set, a plurality of rotated expected vector sets are included, each rotated expected vector set corresponding to the primary expected vector set with a corresponding rotation applied.

[0167] It should be understood that any general rotation of a vector set can be equivalent to three consecutive rotations about the coordinate axes. Specifically, a general rotation of a vector v can be written as in is the angular rotation about the first axis (Z in this example) R x (Φ) is the angular rotation Φ about the second axis, and is another angle of rotation about the first axis Thus, in a coordinate system where one of the coordinates of a vector is the angle between the vector and the first axis, the value of this coordinate is relative to the resulting rotation about the first axis Thus, it should be appreciated that when the expected vector set includes multiple rotated primary vector sets, determining the candidate expected vector set by matching the tilt angles set forth above may be advantageous because such matching is invariant with respect to one of the degrees of freedom of a general rotation.

[0168] Thus, in another variation, each rotation expected vector set can be generated from the corresponding main set by applying a corresponding rotation, which is equivalent to applying a rotation around a predetermined coordinate axis and then applying a rotation around another coordinate axis. The number of rotation sets and the amplitude of the rotation can vary according to the accuracy of the match and / or the desired sampling of the rotation space. Once a candidate set is determined based on the above tilt angle, other candidate sets that are different from the identified candidate set only by rotation around a predetermined axis may be included in subsequent matches.

[0169] A sample implant is provided in the steps below to aid understanding.

[0170] For a given Kikuchi strip, the pattern constructs the set of vectors normal to the plane defined by the Kikuchi strip Each vector corresponds to a respective Kikuchi zone and can be expressed in terms of a tilt angle β and an azimuth angle α.

[0171] For multiple potential samples, the most significant crystallographic reflections are calculated using, for example, kinematic simulations. The expected vector set n for each sample is generated based on the simulated Kikuchi bands i , each vector is normal to the plane defined by the corresponding Kikuchi strip.

[0172] For each rotation according to multiple selected values ​​of the rotation angle Construct a set of rotated expected vectors for each expected vector set

[0173]

[0174] Spin Sets Each vector can be expressed as a pair of azimuth angle and tilt angle

[0175] ·exist Search in space to detect This results in a list of candidate sets

[0176] By performing a third rotation again with the selected value of the rotation angle Add to the candidate set any sets related to the existing candidate set:

[0177]

[0178] Only use candidates from previous steps in Search in space to detect The best match for the angle.

[0179] · In cases where multiple candidates come from previous steps, validate the solution. Optimize for required accuracy angle.

[0180] To aid understanding, a further more detailed solved example is provided below. It should be understood that the values ​​given in this solved example are not intended to be limiting, but are merely illustrative.

[0181] Consider an initial setting of, for example, 40 precomputed expectation vectors n i , each vector corresponds to a separate reflector plane of a given crystal.

[0182] At an inclined angle To begin with, we can The rotation space is sampled to obtain, for example, 32,400 points. The values ​​of are quantized into, for example, 120 bins with steps of 1°, since β typically spans only +-60°. A 120×32,400 point array of slots is then created.

[0183] Then, make 40 pre-computed expectation vectors n i The vector rotates every 32,400 points Therefore, for each such rotation, 40 β j，k angle, and the bit field is incremented accordingly, i.e., the bit field stored in the The value of the bit in the position defined by the value (usually 1).

[0184] Assuming there are 8 measured Kikuchi zones, we can obtain the corresponding 8 angles vector. Now we can The values ​​select eight 32,400-bit long vectors. These vectors can be pre-filled with 1 second that may correspond to the measured orientations. value.

[0185] Candidates are identified by summing all eight 32,400-bit long vectors and identifying points with values ​​greater than a predetermined threshold that indicates the number of matching vectors in a given rotation. The number of values.

[0186] This process can be repeated to consider only the angle of Rotate space, because is invariant under such rotations. Moreover, now only the candidates from the previous step need to be considered In this way, it is possible to identify (one or more) final candidates.

[0187] Figure 6A method 600 is schematically illustrated which is performed by a different EBSD image 150 analysis system (such as the different EBSD image 150 analysis system 500 of FIG. 5 ). The method 600 is a variation of the method 400 discussed above. Figure 4a The discussion of method 400 is equally applicable here.

[0188] Step 440 includes step 642. At step 642, one or more candidate expected point sets are identified from the plurality of expected point sets. Step 642 includes determining whether the expected point set 358 is a candidate expected point set 558 based on matching the azimuth angles of the points in the set 358 with the azimuth angles of the points representing the identified Kikuchi strip 354. Step 642 may include determining that the two points match (or correspond to each other) if the difference between the azimuth angles of a point in the plurality of points representing the identified Kikuchi strip 354 and a point in the expected point set 358 is below a predetermined threshold. Step 642 may include identifying the expected point set 358 as a candidate set 558 if there are more than a predetermined number (or threshold) of matching points between the expected point set 358 and the plurality of points representing the identified Kikuchi strip 354. As described above with respect to Figure 5a As discussed, it should be appreciated that various other criteria may be used in determining (or identifying) a match between the plurality of points 356 representing the identified Kikuchi strip 354 and the expected set of points 358 .

[0189] Additionally, step 642 may include forming (computing) a candidate matching score (or goodness-of-fit metric) for the plurality of points 356 representing the identified Kikuchi strips 354 and the expected point set 358 , as discussed above.

[0190] Step 440 includes step 644. Figure 4a The discussion of step 440 is equally applicable to step 644, with the modification that only candidate prospective point sets 558 identified by the candidate selection module 545 are considered. As such, step 644 includes identifying one or more candidate prospective point sets 558 that match the plurality of points 356 representing the identified Kikuchi strip 354. Step 644 also includes determining a configuration based on the matches.

[0191] In this way, step 642 may be considered to enable pre-filtering of the set of expected points and, by extension, possible configurations.

[0192] Figure 7a Schematically shows how Figure 3a Or the method 700 performed by the EBSD image 150 analysis system of FIG. 5 to match points representing the Kikuchi band 152 using the Kikuchi band 152 mapping. Specifically, Figure 4aMethod 700 is used in step 440 of method 400 described in , to identify whether the expected point set 358 matches the plurality of points 356 representing the identified Kikuchi band 354. Similarly, Figure 6 Method 700 is used in step 644 of method 600 described in to identify whether the candidate prospective point set 558 matches the plurality of points 356 representing the identified Kikuchi strip 354 .

[0193] In step 720, a first image (or map) is drawn for a plurality of points of a plurality of identified Kikuchi bands 152. For each of a plurality of points of a plurality of identified Kikuchi bands 152, a distribution centered on the point can be drawn (or included) in the first image. In this manner, it should be understood that the first image typically includes an array of pixels, such as a bitmap image (or raster image or array), thereby allowing the distribution to be drawn as varying pixel values ​​(or intensities). Of course, it should be understood that any suitable image or array representation can be used. For a given point, the distribution can be based on (or represent or calculate based on) the expected error or confidence interval on the position of the point. For example, the characteristic width of the distribution can be (or be proportional to) one or more standard errors of the point. Additionally or alternatively, the distribution can be based on (or represent or calculate based on) the intensity and / or bandwidth of the identified Kikuchi band 152 corresponding to the point. For example, the characteristic width of the distribution can be (or be proportional to) the bandwidth of the identified Kikuchi band 152 corresponding to the point. The maximum value (or height) of the distribution may be (or be proportional to) the intensity of the identified Kikuchi band 152 corresponding to the point. Additionally or alternatively, negative intensity values ​​may be given (or assigned) to Kikuchi bands that are not expected to exist. This may be advantageous for resolving pseudo-symmetric mis-indexing issues (e.g., in triangular quartz patterns).

[0194] In step 730, a second image (or map) is obtained for a given expected set of points. In a manner similar to the first image, for each point in a given expected set of points, a distribution centered on the point can be drawn (or included) in the second image. In this manner, it should be understood that the second image typically includes an array of pixels, such as a bitmap (or raster) image, allowing the distribution to be drawn as varying pixel values ​​(or intensities). Of course, it should be understood that any suitable image or array representation can be used, or the data can be kept as discrete points. For a given point, the distribution can be based on the expected error or confidence interval on the location of the point (or represent it or calculate it based on it). For example, the characteristic width of the distribution can be one or more standard errors of the point (or be proportional to it). Additionally or alternatively, the distribution can be based on the intensity and / or bandwidth of the Kikuchi band 152 corresponding to the point (or represent it or calculate it based on it). For example, the characteristic width of the distribution can be the bandwidth of the identified Kikuchi band 152 corresponding to the point (or be proportional to it). The maximum value (or height) of the distribution can be the intensity of the identified Kikuchi band 152 corresponding to the point (or be proportional to it).

[0195] It should be appreciated that in step 730 described above, the second image may be directly drawn by the matching module 340 as part of the method 700. Likewise, it should be appreciated that the second image may be pre-drawn (or pre-computed) by a separate system in a manner similar to the pre-computation of the expected point set described previously. For example, for the expected point set, the corresponding second image may be pre-computed and stored in a memory (such as the storage medium 204) and / or in the device 222. It should be appreciated that the second image may be stored remotely to the system 300, such as on a server and / or cloud computing platform 390. Thus, step 730 may include the matching module 340 retrieving the second image from the server and / or cloud computing platform via a suitable data connection 395. Examples of suitable data connections include: via a local area network, via a wide area network, via a direct data connection (such as a USB connection, a Thunderbolt connection, a Thunderbolt connection, a direct Ethernet connection, etc.), via the Internet, etc.

[0196] At step 740, it is determined whether the plurality of points of the plurality of identified Kikuchi strips 152 match the given expected point set. In step 740, the match between the particular expected point set and the plurality of points of the identified Kikuchi strips 354 is determined based on the intersection (or overlap) of the first image and the second image. The intersection of the first image and the second image can be calculated (or determined or formed) by combining pixels or elements of the first image with corresponding pixels or elements of the second image. In this way, another image including the overlap between the distribution in the first image and the distribution in the second image can be formed. The elements of the first image and the second image can be combined using a multiplication operator and / or a binary AND operator. Additionally or alternatively, one or more images can be binarized using a suitable threshold value, and the first image elements and the second image elements are combined only for these threshold regions. These matching processes are well known in image processing and are not described in detail herein. Step 740 can include calculating an overall matching score (as previously discussed) for the plurality of points of the plurality of identified Kikuchi strips 152 and the given expected point set. The overall match score typically includes (or is based on) a combination (e.g., a sum) of elements at the intersection of the first image and the second image. In this manner, it will be appreciated that the overall match score may be equivalent to an overall match score obtained by summing the overlap of the distributions centered on the corresponding points as previously discussed. Typically, a match between the plurality of identified points of the plurality of Kikuchi strips 152 and a given set of expected points is identified (or determined) if the overall score reaches a predetermined threshold. Alternatively, a match between the plurality of identified points of the plurality of Kikuchi strips 152 and a given set of expected points may be identified only for the set of expected points with the highest overall score.

[0197] In step 740 described above, calculating the intersection between the first image and the second image and calculating the overall match score based on the intersection are described as separate sub-steps. However, it should be appreciated that these sub-steps may be combined so that the calculation of the overall match score is performed in series with the calculation of the intersection between the first image and the second image. Thus, in some instances, a complete intersection between the first image and the second image may not be explicitly generated at any point.

[0198] It should be appreciated that a different distribution may be used to plot the plurality of points of the plurality of identified Kikuchi strips 152 in step 720 than the distribution used in the plotting of the expected set of points 358 in step 730. In some cases, the plurality of points in the plurality of identified Kikuchi strips 152 or the expected set of points 358 may be plotted as simple points (e.g., points generated by a Dirac delta distribution).

[0199] Figure 7b An example image (or map) is shown, as may be seen by Figure 7aThose images (or maps) produced by the method 700. Figure 7b , an example first image 760 (corresponding to the first image described above with respect to step 720), an example second image 770 (corresponding to the first image described above with respect to step 730), and a drawing of the intersection 780 of the example first image 760 and the example second image 770 (such as the drawing that may be produced in step 740 above) are shown.

[0200] Example first image 760 shows a plurality of identified Kikuchi bands 152 points from an EBSD image 150 of silicon. As can be seen, the axes of first image 760 correspond to the cylindrical coordinates of the cylindrical surface used in determining the points. Cylindrical surface 799 is also shown to provide reference. The points in first image 760 have been plotted as Gaussian functions in a grayscale bitmap.

[0201] The example second image 770 shows points in the expected point set corresponding to silicon. As with the first image 760, the axes of the second image 770 correspond to the cylindrical coordinates of the cylindrical surface used when confirming the points of the plurality of identified Kikuchi strips 152. The points in the second image 770 have been plotted as Gaussian functions in a grayscale bitmap.

[0202] The Gaussian used may be asymmetric horizontally and / or vertically. In this particular example, a 2 degree Gaussian expansion is used for both axes.

[0203] The plot of the intersection 780 shows the intersection between the example first image 760 and the example second image 770. As can be seen, some points from the example second image 770 are missing in the first image 760, so they appear as dark areas in the intersection 780. For points in the two example images 760, 770 that overlap, there are overlapping bright areas, showing the degree of overlap.

[0204] Figure 8aAn example 800 of an EBSD image 150 as described above and the effect of a change in the pattern center 155 on the vector representation of the previously described Kikuchi band 152 is shown. An EBSD image 800 is shown. The description of the example EBSD image 150 above also applies to this EBSD image 800. The Kikuchi band 152 present in the image 800 has been identified as by using the identification module 320 described previously. The identified Kikuchi band 354 is shown as an overlay solid line in the EBSD image 800. Corresponding dashed lines indicating the bandwidth of the corresponding Kikuchi band 152 are also shown. These bandwidths have been identified as by using the identification module 320 described previously. Four estimated pattern centers of the EBSD image 800 are shown in the EBSD image 800: 802; 804; 806; 808. The pattern center 802 represents the true pattern center of the image. The other pattern centers 804; 806; 808 are incorrect pattern centers. The fourth pattern center 808 is shown to be overlapped by the third pattern center 806 because the two pattern centers are only in the component PC z These other pattern centers 804; 806; 808, which are very different from the true pattern center, have been deliberately chosen to clearly illustrate the effect of errors in the pattern center. Typically, the error in the estimate or measurement of the pattern center is smaller than that shown in FIG8 , and is typically in the order of a few percent. It has been observed that subsequent indexing has an effect on the PC x and PC y Mean error compared to PC z More sensitive to errors in.

[0205] Figure 8a Four spherical volumes are shown: 812; 814; 816; 818, each corresponding to a respective pattern center: 802; 804; 806; 808. A plan view and a side view of each spherical volume are shown.

[0206] The first spherical volume corresponds to the true pattern center 802. The first spherical volume shows vector representations of the identified Kikuchi bands 354 calculated based on the true pattern center 802 as previously discussed with respect to the projection module 340. Specifically, in this example, each vector representation is a vector normal to the plane defined by the corresponding Kikuchi band 152, passing through the estimated point of incidence 117 (as defined by the pattern center 802). The second spherical volume 814 is the same as the first spherical volume 812, except that the second pattern center 804 is used instead of the true pattern center. The third spherical volume 816 is the same as the first spherical volume 812, except that the third pattern center 806 is used instead of the true pattern center. Similarly, the fourth spherical volume 818 is the same as the first spherical volume 812, except that the fourth pattern center 808 is used instead of the true pattern center. As can be seen, across the four spherical volumes 812; 814; 816; 818, errors in the estimation of the pattern center appear to result in changes in the vector representations of the identified Kikuchi bands 354.

[0207] Figure 8a Again, four plots are shown: 822; 824; 826; 828, each corresponding to a corresponding pattern center: 802; 804; 806; 808. The first plot corresponds to the true pattern center 802. The first plot shows a plurality of points each representing a corresponding identified Kikuchi band 152. Specifically, as previously discussed with respect to the projection module 340, each point in the first plot is an intersection point between a cylindrical surface and a vector representation of a corresponding Kikuchi band 152. In practice, the first plot can be considered to be an unfolded or flattened cylindrical surface. As such, the horizontal axis of the first plot corresponds to the azimuth angle of the cylindrical surface. The second plot 824 is the same as the first plot 822, except that the second pattern center 804 is used instead of the true pattern center. The third plot 816 is the same as the first plot 812, except that the third pattern center 806 is used instead of the true pattern center. Similarly, the fourth plot 818 is the same as the first plot 812, except that the fourth pattern center 808 is used instead of the true pattern center. As can be seen, across the four plots 822;824;826;828, while errors in the estimation of the center of the pattern will change the relative vertical position of the points in the plots 822;824;826;828, the azimuth angle (or horizontal position) of the points remains constant. This can be seen in the four bars 832;834;836;838 also shown. Each bar corresponds to a respective plot 822;824;826;838. The bars 832;834;836;838 simply show the line corresponding to each point in the plots 822;824;826;828 at the azimuth angle of the point. As can be seen, the bars 832;834;836;838 are identical.

[0208] Figure 8b An example 800 of an EBSD image 150 as described above is shown, along with the effect that rotation of the image 150 about a pattern center 802 has on the vector representation of the Kikuchi zones 152 previously described. Figure 8b As shown above, Figure 8a Depicted are an EBSD image 800 , a pattern center 802 , a corresponding plot 822 , and a corresponding bar 832 .

[0209] Figure 8b Also shown is a rotated image 800' corresponding to the image 800 rotated about the pattern center 802. The plot 800 is shown relative to the rotated image 800' in a dashed rectangle. There is also a plot 822' corresponding to the rotated image 800' and showing a plurality of points each representing a corresponding identified Kikuchi band 152. Again, the plot 822 corresponding to the image 800 is shown relative to the plot 822' in a dashed rectangle. As can be seen, the two rightmost points of the plot 822 corresponding to the image 800 have been wrapped to the left hand side of the plot 822' corresponding to the rotated image 800'. Also shown is a bar 832' corresponding to the rotated image 800', which itself shows the same wrapping.

[0210] If you can Figure 8b As can be seen in FIG. 8 , the relative positions of the points in plot 822 and plot 822 ′ remain unchanged, and the effect of the rotation is to impose a constant azimuthal offset on the points.

[0211] Revise

[0212] It should be understood that the described methods have been shown as individual steps performed in a particular order. However, the skilled person will appreciate that these steps can be combined or performed in a different order while still achieving the desired result.

[0213] For ease of understanding, in the above discussion, the system and method for matching by directly matching vector sets has been described separately from the matching by which the projected points have been matched. However, it should be understood that the matching described with respect to the point sets also achieves matching between the vector sets, given the corresponding relationship between the separate point sets and the separate vector sets.

[0214] It should be appreciated that a variety of different information processing systems can be used to implement embodiments of the present invention. Specifically, although the figure and its discussion provide exemplary computing systems and methods, these are presented only for providing useful references when discussing aspects of the present invention. Embodiments of the present invention can be performed on any suitable data processing device, such as personal computers, laptop computers, personal digital assistants, mobile phones, set-top boxes, televisions, server computers, etc. Of course, for the purpose of discussion, the description of system and method has been simplified, and they are only one of many different types of systems and methods that can be used for embodiments of the present invention. It should be appreciated that the boundaries between the logic blocks are only illustrative and alternative embodiments can merge logic blocks or elements, or the alternative decomposition of functions can be applied to various logic blocks or elements.

[0215] It should be understood that the above functionality can be implemented as hardware and / or software as one or more corresponding modules. For example, the above functions can be implemented as one or more software components executed by a processor of the system. Alternatively, the above functionality can be implemented as hardware such as on one or more field programmable gate arrays (FPGAs), and / or one or more application specific integrated circuits (ASICs) and / or one or more digital signal processors (DSPs) and / or other hardware arrangements. The method steps implemented according to the flowcharts contained herein or as described above can each be implemented by a corresponding corresponding module; multiple method steps implemented according to the flowcharts contained herein or as described above can be implemented together by a single module.

[0216] It should be understood that, in the scope of the embodiment of the present invention being implemented by a computer program, the storage medium and transmission medium carrying the computer program form aspects of the present invention. The computer program may have one or more program instructions or program codes, which execute embodiments of the present invention when executed by a computer. As used herein, the term "program" may be an instruction sequence designed to be executed on a computer system, and may include subroutines, functions, programs, modules, target methods, target implementation schemes, executable applications, applets, server applets, source codes, object codes, shared libraries, dynamic link libraries, and / or other instruction sequences designed to be executed on a computer system. The storage medium may be a disk (such as a hard disk drive or a floppy disk), a solid-state drive, an optical disk (such as a CD-ROM, a DVD-ROM or a BluRay disk) or a memory (such as a ROM, a RAM, an EEPROM, an EPROM, a flash memory or a portable / removable memory device), etc. The transmission medium may be a communication signal, a data broadcast, a communication linked between two or more computers, etc.

[0217] Example methods and systems are set forth in the following paragraphs (NP):

[0218] NP 1. A method for analyzing a sample imaged by electron backscatter diffraction, the method comprising:

[0219] a plurality of Kikuchi bands in an electron backscatter diffraction image identifying locations on the sample;

[0220] for each identified Kikuchi band, forming a respective point corresponding to an intersection between: a vector representation of the Kikuchi band and a cylindrically symmetric surface, wherein both the vector representation of the Kikuchi band and the cylindrical axis of the surface are determined based at least in part on an estimate of the location on the sample;

[0221] The configuration of the sample is determined by identifying a particular expected point set from a plurality of expected point sets as matching points of the plurality of identified Kikuchi bands.

[0222] NP 2. The method according to NP 1, further comprising:

[0223] The plurality of expected point sets are obtained, each expected point set corresponding to a respective known sample, wherein for each known sample, the expected point corresponds to an intersection between a vector representation of a Kikuchi band of the known sample and a cylindrically symmetric surface, wherein the determined configuration is based on one or more properties of a particular known sample corresponding to the particular expected point set that matches the points of the plurality of identified Kikuchi bands.

[0224] NP 3. The method according to NP 2, wherein the Kikuchi bands of one or more of the known samples are identified from simulated EBSD images.

[0225] NP 4. The method according to NP 2 or 3, wherein the Kikuchi bands of one or more of the known samples are identified from experimental EBSD images.

[0226] NP 5. The method according to any one of the preceding NPs, wherein for each Kikuchi band, the vector representation of the corresponding Kikuchi band is determined based on a plane defined by the Kikuchi band.

[0227] NP 6. The method according to NP 5, wherein for each Kikuchi band, the vector representation of the corresponding Kikuchi band is a normal vector based on the plane defined by the Kikuchi band.

[0228] NP 7. The method according to any one of the preceding NPs, wherein determining the configuration further comprises:

[0229] A plurality of candidate expected point sets are obtained from the plurality of expected point sets by matching the relative azimuth angles of the points with the relative azimuth angles of the expected points, wherein the specific expected point set matching the points of the plurality of identified Kikuchi belts is identified from the plurality of candidate expected point sets.

[0230] NP 8. The method according to any one of the preceding NPs, wherein determining the configuration further comprises:

[0231] for each expected point set of two or more expected point sets from a plurality of expected point sets, optimizing the estimate of the position on the sample based on the expected point set;

[0232] One of the two or more expected point sets is identified as a particular expected point set based at least in part on the optimized estimate of the location on the sample.

[0233] NP 9. The method according to any one of the preceding NPs, wherein the certain point is matched with the expected point when an overlap calculated between a distribution centered at a certain point and a distribution centered at an expected point exceeds a predetermined threshold.

[0234] NP 10. The method of any one of NPs 1-8, wherein identifying a particular expected point set from a plurality of expected point sets as matching the points of the plurality of identified Kikuchi strips comprises:

[0235] plotting in the first image a distribution centered at each of the points of the plurality of identified Kikuchi bands;

[0236] For each point in the specific expected point set, obtaining a second image including a distribution centered at the point;

[0237] A particular expected point set from a plurality of expected point sets is identified as matching the points of the plurality of identified Kikuchi strips based on intersections of the first image and the second image.

[0238] NP 11. The method according to NP 9 or 10, wherein the characteristic width of the distribution is based on the intensity of the corresponding point.

[0239] NP 12. The method according to any one of NP 9-11, wherein at least one of the distributions is a Gaussian distribution.

[0240] NP 13. A method according to any one of the preceding NPs, wherein the determined configuration comprises any one or more of the following:

[0241] crystalline phase in the sample;

[0242] The unit cell dimensions of the crystals in the sample;

[0243] atoms in a unit cell of a crystal in the sample;

[0244] lattice orientation in the sample;

[0245] The local lattice deformation present in the sample; the strain state.

[0246] NP 14. An apparatus arranged to perform a method according to any one of NP 1 to 13.

[0247] NP 15. A computer readable medium storing a computer program which, when executed by a processor, causes the processor to perform the method according to any one of NP 1 to 13.

Claims

1. A method for analyzing a sample imaged by electron backscatter diffraction, the method comprising: a plurality of Kikuchi bands in an electron backscatter diffraction image identifying locations on the sample; for each identified Kikuchi band, forming a corresponding vector representation of the Kikuchi band based at least in part on the estimate of the position on the sample; The configuration of the sample is determined by identifying a particular expected vector representation set from a plurality of expected vector representation sets as matching the vector representations of the plurality of identified Kikuchi bands.

2. The method of claim 1, wherein determining a configuration further comprises: obtaining a plurality of candidate expected vector representation sets from the plurality of expected vector representation sets by matching angles of the vector representation relative to predetermined coordinate axes with corresponding angles of the expected vector representation, The specific expected vector representation set matching the vector representations of the plurality of identified Kikuchi bands is identified from the plurality of candidate expected vector representation sets.

3. The method according to claim 2, wherein obtaining a plurality of candidate expected vector representation sets further comprises: The relative angle of the vector representation about the predetermined coordinate axis is matched to the relative angle of the expected vector representation about the predetermined coordinate axis.

4. A method according to any one of claims 2 to 3, wherein the multiple expected vector representation sets include one or more primary vector representation sets, and wherein for each primary vector representation set, the multiple expected vector representation sets include one or more rotated expected vector sets generated by applying a corresponding rotation, wherein applying the corresponding rotation is equivalent to applying a rotation around the predetermined coordinate axis and then applying a rotation around another coordinate axis.

5. The method of any one of claims 1 to 3, wherein the determining comprises identifying a rotation that matches the particular set of expected vector representations with the vector representations of the plurality of identified Kikuchi strips.

6. The method of claim 1, further comprising, for each identified Kikuchi band, forming a respective point corresponding to an intersection between: the vector representation of the Kikuchi band and a cylindrically symmetric surface, wherein a cylindrical axis of the surface is determined based at least in part on an estimate of the location on the sample; Wherein identifying a particular expected vector representation set from a plurality of expected vector representation sets as matching the vector representations of the plurality of identified Kikuchi bands comprises matching an expected point set corresponding to the particular expected vector representation set with points of the plurality of identified Kikuchi bands.

7. The method of claim 6, wherein determining a configuration further comprises: for each expected point set of two or more expected point sets from a plurality of expected point sets, optimizing the estimate of the position on the sample based on the expected point set; One of the two or more expected point sets is identified as a particular expected point set based at least in part on the optimized estimate of the location on the sample.

8. The method according to any one of claims 6 to 7, wherein the certain point is matched with the expected point when an overlap calculated between a distribution centered at the certain point and a distribution centered at the expected point exceeds a predetermined threshold.

9. The method of any one of claims 6 to 7, wherein identifying a particular expected point set from a plurality of expected point sets as matching the points of the plurality of identified Kikuchi strips comprises: plotting in the first image a distribution centered at each of the points of the plurality of identified Kikuchi bands; For each point in the specific expected point set, obtaining a second image including a distribution centered at the point; A particular expected point set from a plurality of expected point sets is identified as matching the points of the plurality of identified Kikuchi strips based on intersections of the first image and the second image.

10. The method of claim 8, wherein a characteristic width of the distribution is based on an intensity of a corresponding point. The method of claim 8 , wherein at least one of the distributions is a Gaussian distribution.

12. The method according to claim 1 or any one of claims 6 to 7, further comprising: obtaining the plurality of expected vector representation sets, each expected vector representation set corresponding to a corresponding known sample, wherein for each known sample, the expected vector representation corresponds to a vector representation of the known Kikuchi band, Wherein the determined configuration is based on one or more properties of particular known samples corresponding to the particular set of expected vector representations that match the vector representations of the plurality of identified Kikuchi bands.

13. The method of claim 12, wherein the Kikuchi zones of one or more of the known samples are identified from simulated EBSD images.

14. The method of claim 12, wherein the Kikuchi zones of one or more of the known samples are identified from experimental EBSD images.

15. The method according to any one of claims 1 to 3, wherein for each Kikuchi band, the vector representation of the respective Kikuchi band is determined based on a plane defined by the Kikuchi band.

16. The method of claim 15, wherein for each Kikuchi band, the vector representation of the corresponding Kikuchi band is based on a normal vector of the plane defined by the Kikuchi band.

17. The method according to any one of claims 1 to 3, wherein determining the configuration further comprises: for each expected vector representation set of two or more expected vector representation sets from the plurality of expected vector representation sets, optimizing the estimate of the position on the sample based on the expected vector representation set; One of the two or more expected vector representation sets is identified as the particular expected vector representation set based at least in part on the optimized estimate of the location on the sample.

18. The method according to any one of claims 1 to 3, wherein the determined configuration comprises any one or more of the following: crystalline phase in the sample; The unit cell dimensions of the crystals in the sample; atoms in a unit cell of a crystal in the sample; lattice orientation in the sample; The local lattice deformation present in the sample; the strain state.

19. An apparatus arranged to perform a method according to any one of claims 1 to 18.

20. A computer readable medium storing a computer program which, when executed by a processor, causes the processor to perform the method according to any one of claims 1 to 18.

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