CN-121998817-A - Method for determining deformation characteristics and related system

Abstract

In one example, a method includes determining a characteristic Displacement Gradient (DG) tensor that characterizes a deformation feature. The method includes, in an iterative routine, calculating an objective function value associated with a trial DG tensor, the calculating based at least in part on automatically determined pixel values within a ZOC, wherein the ZOC is based at least in part on the trial DG tensor. In another example, a method includes determining one or more rotational transformation components corresponding to a test image and determining a characteristic DG tensor based at least in part on the rotational transformation components. In another example, a system includes an electron-optical component, a detector component, and a controller programmed to determine a characteristic DG tensor. In another example, a non-transitory computer-readable medium stores instructions that, when executed by a computer, cause the computer to perform a method of determining a deformation characteristic.

Inventors

• J. Caspar
• M - Rick pater
• T. Vistavel
• J Holzer
• M. KAREN

Assignees

• FEI公司

Dates

Publication Date

20260508

Application Date

20251027

Priority Date

20241105

Claims (20)

1. 1. A computer-implemented method for determining deformation characteristics of a test image relative to a reference image, the method comprising: Determining, by a processor and via an iterative routine, a feature Displacement Gradient (DG) tensor characterizing the deformation feature, wherein the determining the feature DG tensor is included in one or more steps of the iterative routine: An objective function value associated with a trial DG tensor is calculated such that the objective function value is based at least in part on pixel values of pixel locations within a region of interest (ZOC) of a test image and a reference image, wherein the ZOC is automatically determined based at least in part on the trial DG tensor.
2. 2. The method of claim 1 wherein calculating the objective function value comprises, for each pixel location of the reference image within the ZOC, calculating the objective function only references the pixel value corresponding to that pixel location once.
3. 3. The method of claim 1, further comprising determining, in each step of the iterative routine, a ZOC such that the ZOC represents a set of maximum overlapping pixel locations between pixel locations of the reference image and offset pixel locations of the test image based at least in part on the trial DG tensor.
4. 4. The method of claim 1, wherein the calculating the objective function values comprises applying respective weighting factors to pixel values within the ZOC.
5. 5. The method of claim 4, further comprising determining the respective weight factors, and the determining the respective weight factors comprises analyzing a test image and/or a reference image.
6. 6. The method of claim 1, wherein the calculating the objective function value comprises calculating such that the objective function value is normalized according to a number of pixel locations within the ZOC.
7. 7. The method of claim 1, further comprising generating an initial DG tensor based at least in part on the test image and/or the reference image prior to determining the characteristic DG tensor, wherein the initial DG tensor is used as a trial DG tensor in at least one step of an iterative routine.
8. 8. The method of claim 7, wherein the generating an initial DG tensor comprises: Generating a set of trial rotation vectors, wherein each trial rotation vector represents one or more corresponding rotation transformation components; calculating a rotation error factor associated with each trial rotation vector, and Selecting an initialization rotation vector from the set of trial rotation vectors based on the rotation error factor, and Wherein the generating an initial DG tensor includes generating an initial DG tensor such that the initial DG tensor represents a rotation corresponding to the initialization rotation vector.
9. 9. The method of claim 1, wherein the determining the characteristic DG tensor comprises determining the characteristic DG tensor such that the characteristic DG tensor corresponds to a test DG tensor associated with an objective function value that meets a convergence criterion.
10. 10. The method of claim 1 wherein said determining a characteristic DG tensor comprises performing a Nelder-Mead minimization algorithm for identifying a trial DG tensor that produces an objective function value that meets a convergence criterion.
11. 11. A computer-implemented method for determining deformation characteristics of a test image relative to a reference image, the method comprising: Determining, with a processor system, one or more rotational transformation components corresponding to the test image; Generating an initial DG tensor based at least in part on the one or more rotational transformation components, and Using the initial DG tensors, determining, by a processor system, a characteristic DG tensor characterizing the deformation characteristic by calculating, in one or more steps of an iterative routine, a respective scalar objective function value for each of one or more trial DG tensors, Wherein in a first step of the iterative routine, one of the one or more trial DG tensors is the initial DG tensor.
12. 12. The method of claim 11, wherein the determining one or more rotational transformation components comprises: Generating a set of trial rotation vectors, wherein each trial rotation vector represents one or more trial rotation transformation components; calculating one or more rotation error factors associated with each trial rotation vector, and Selecting an initialization rotation vector from the set of trial rotation vectors based on the rotation error factor, and Wherein the generating an initial DG tensor includes generating an initial DG tensor such that the initial DG tensor represents a rotation corresponding to the initialization rotation vector.
13. 13. The method of claim 12, wherein the generating the set of trial rotation vectors comprises generating a set of trial rotation vectors such that the trial rotation vectors are distributed in three-dimensional vector space and have one or both of: (i) Vector spacing based at least in part on the expected convergence radius of the objective function value, and (Ii) A maximum vector magnitude based at least in part on an expected rotational magnitude associated with the test image, and The method further includes receiving the desired convergence radius and/or the desired rotation amplitude from a user.
14. 14. The method of claim 11, wherein the calculating the objective function value comprises, at each step of an iterative routine and for each individual trial DG tensor of the one or more trial DG tensors: Determining an offset pixel position of the test image based on the individual trial DG tensors for each pixel position in the ZOC of the reference image, and An objective function value is calculated such that the objective function value represents a weighted average difference between pixel values of pixel locations in a reference image ZOC and pixel values of offset pixel locations of the test image.
15. 15. The method of claim 14, further comprising determining a ZOC based at least in part on each individual trial DG tensor of the one or more trial DG tensors at each step of the iterative routine.
16. 16. The method of claim 15, wherein the determining a ZOC comprises determining a set of maximum overlapping pixel positions between pixel positions such that the ZOC represents the reference image and offset pixel positions of the test image.
17. 17. The method of claim 14, wherein in at least one step of the iterative routine, the number of the one or more trial DG tensors is less than the number of elements of each DG tensor that vary in each step of iteration.
18. 18. A system, comprising: an electron optical assembly configured to direct an electron beam to a selected location on the sample; a detector assembly configured to record a diffraction pattern related to an interaction between the electron beam and the sample, and A controller programmed to: receiving a reference image from the detector assembly when the electron beam is directed to a reference location on the sample; receiving a test image from the detector assembly while the electron beam is directed to a test location on the sample, and Determining, by an iterative routine, a characteristic DG tensor characterizing a deformation characteristic of the test image relative to the reference image, wherein the determining comprises, in each step of the iterative routine, calculating an objective function value corresponding to a trial DG tensor, such that the objective function value is based on pixel values of pixel locations in respective ZOCs of the test image and the reference image, wherein the ZOCs are automatically determined based at least in part on the trial DG tensor.
19. 19. The system of claim 18, wherein the controller is further programmed to determine one or more stress components corresponding to the characteristic DG tensor, and the system comprises an output interface for communicating the one or more stress components to a user.
20. 20. The system of claim 18, further comprising a non-transitory computer readable medium storing instructions that, when executed by the controller, cause the controller to determine the characteristic DG tensor.

Description

Method for determining deformation characteristics and related system Technical Field The present disclosure relates generally to methods and related systems for determining deformation characteristics of a test image relative to a reference image. Background In the field of charged particle microscopy, electron Back Scattering Diffraction (EBSD) is a technique for obtaining information about the crystallographic structure of a sample. Specifically, in EBSD, the electron beam is directed to an inclined sample, and the backscattered electrons form a diffraction pattern recorded by the detector. The resulting electron back scattering diffraction pattern (EBSP) may be analyzed to provide information about grain structure, grain orientation, distortion, and other such features. In some examples, material deformation of a sample may be characterized by comparing EBSP recorded in an undeformed "reference" portion of the sample with EBSP of a deformed "test" portion of the sample. However, many existing techniques for performing such analysis have limitations in terms of computational efficiency and/or versatility. Disclosure of Invention In one representative example, a computer-implemented method for determining deformation characteristics of a test image relative to a reference image includes determining, by a processor, a characteristic displacement gradient tensor characterizing the deformation characteristics through an iterative routine. Determining the characteristic displacement gradient tensor includes calculating an objective function value associated with a trial displacement gradient tensor in one or more steps of the iterative routine. The objective function value is based at least in part on pixel values of pixel locations within a considered region of the test image and the reference image. The consideration region is automatically determined based at least in part on the trial displacement gradient tensor. In another representative example, a computer-implemented method for determining deformation characteristics of a test image relative to a reference image includes determining, using a processor system, one or more rotational transformation components corresponding to the test image and generating an initial displacement gradient tensor based at least in part on the one or more rotational transformation components. The method further includes determining, by the processor system, a feature displacement gradient tensor characterizing the deformation feature using the initial displacement gradient tensor. Determining the feature displacement gradient tensor includes calculating scalar objective function values corresponding to the one or more trial displacement gradient tensors in one or more steps of an iterative routine. In a first step of the iterative routine, one of the one or more trial displacement gradient tensors is the initial displacement gradient tensor. In another representative example, a system includes an electron optical assembly configured to direct an electron beam to a selected location on a sample, a detector assembly configured to record a diffraction pattern associated with an interaction between the electron beam and the sample, and a controller. The controller is programmed to receive a reference image from the detector assembly when the electron beam is directed to a reference location on the sample and to receive a test image from the detector assembly when the electron beam is directed to a test location on the sample. The controller is further programmed to determine a feature displacement gradient tensor characterizing a deformation feature of the test image relative to the reference image by an iterative routine. In each step of the iterative routine, the controller is programmed to calculate an objective function value corresponding to one of the trial displacement gradient tensors such that the objective function value is based on the pixel values of the pixel locations within the respective considered areas of the test image and the reference image. The consideration area is determined automatically based in part on the trial displacement gradient tensor. In another representative example, a non-transitory computer readable medium stores instructions that, when executed by a computer, cause the computer to perform a method for determining deformation characteristics of a test image relative to a reference image. The method includes determining a feature displacement gradient tensor characterizing the deformation feature by an iterative routine. The instructions include instructions for determining a characteristic displacement gradient tensor by, in each step of the iterative routine, calculating an objective function value corresponding to one of the trial displacement gradient tensors such that the objective function value is based on pixel values of pixel locations within respective considered regions of the test image and the reference image. The consideration