EP-4738256-A1 - METHODS OF DETERMINING A DEFORMATION CHARACTERISTIC AND ASSOCIATED SYSTEMS

EP4738256A1EP 4738256 A1EP4738256 A1EP 4738256A1EP-4738256-A1

Abstract

In an example, a method includes determining a characteristic displacement gradient (DG) tensor that characterizes a deformation characteristic. The method includes, in an iterative routine, calculating an objective function value associated with a trial DG tensor based, at least in part, on pixel values within a zone of consideration (ZOC) that is determined automatically 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 component(s). In another example, a system includes an electron optics assembly, a detector assembly, and a controller programmed to determine a characteristic DG tensor. In another example, a non-transitory computer readable medium stores instructions which, when executed by a computer, cause the computer to perform a method of determining a deformation characteristic.

Inventors

KASPER, Jan
PETREK, Martin
Vystavel, Tomás
HOLZER, JAKUB
KREN, Michal

Assignees

FEI COMPANY

Dates

Publication Date: 20260506
Application Date: 20251027

Claims (13)

A computer-implemented method of determining a deformation characteristic of a test image relative to a reference image, the method comprising: determining with a processor, via an iterative routine, a characteristic displacement gradient (DG) tensor that characterizes the deformation characteristic, wherein the determining the characteristic DG tensor comprises, at one or more steps of the iterative routine: calculating an objective function value associated with a trial DG tensor such that the objective function value is based, at least in part, on pixel values of pixel locations that are within a zone of consideration (ZOC) of the test image and the reference image, wherein the ZOC is determined automatically based at least in part on the trial DG tensor.
The method of claim 1, wherein the calculating the objective function value comprises calculating such that, for each pixel location of the reference image within the ZOC, the objective function is calculated with a calculation that refers to the pixel value corresponding to the pixel location exactly once.
The method of either claim 1 or claim 2, further comprising, at each step of the one or more steps of the iterative routine, determining the ZOC such that the ZOC represents a maximally overlapping set of pixel locations between the pixel locations of the reference image and shifted pixel locations of the test image that are based, at least in part, on the trial DG tensor.
The method of any previous claim, wherein the calculating the objective function value comprises applying respective weight factors to the pixel values within the ZOC.
The method of claim 4, further comprising determining the respective weight factors, and wherein the determining the respective weight factors comprises analyzing one or both of the test image and the reference image.
The method of either claim 1 or claim 2, wherein the calculating the objective function value comprises calculating such that the objective function value is normalized against a number of pixel locations within the ZOC.
The method of any previous claim, further comprising, prior to the determining the characteristic DG tensor, generating an initial DG tensor based, at least in part, on one or both of the test image and the reference image, and wherein the initial DG tensor is used as the trial DG tensor in at least one step of the iterative routine.
The method of claim 7, wherein the generating the initial DG tensor comprises: generating a set of trial rotation vectors, wherein each trial rotation vector represents one or more corresponding rotational transformation components; calculating a rotation error factor associated with each trial rotation vector; and selecting, based on the rotation error factors, an initialization rotation vector from the set of trial rotation vectors, and wherein the generating the initial DG tensor comprises generating such that the initial DG tensor represents a rotation corresponding to the initialization rotation vector.
The method of any one of claims 1-6, wherein the determining the characteristic DG tensor comprises determining such that the characteristic DG tensor corresponds to a trial DG tensor that is associated with an objective function value that satisfies a convergence criterion.
The method of any one of claims 1-6, wherein the determining the characteristic DG tensor comprises performing a Nelder-Mead minimization algorithm that operates to identify a trial DG tensor that yields a corresponding objective function value that satisfies a convergence criterion.
A system comprising: an electron optics assembly configured to direct an electron beam to a selected location on a specimen; a detector assembly configured to record a diffraction pattern associated with an interaction between the electron beam and the specimen; and a controller programmed to: receive a reference image from the detector assembly when the electron beam is directed to a reference location on the specimen; receive a test image from the detector assembly when the electron beam is directed to a test location on the specimen; and determine, via an iterative routine, a characteristic DG tensor that characterizes a deformation characteristic of the test image relative to the reference image by, at 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 that are within a ZOC of each of the test image and the reference image, wherein the ZOC is determined automatically based in part on the trial DG tensor.
The system of claim 11, wherein the controller further is programmed to determine one or more stress components corresponding to the characteristic DG tensor, and wherein the system comprises an output interface for conveying the one or more stress components to a user.
The system of either claim 11 or claim 12, further comprising a non-transitory computer readable medium storing instructions which, when executed by the controller, cause the controller to determine the characteristic DG tensor.

Description

FIELD The present disclosure relates generally to methods of determining a deformation characteristic of a test image relative to a reference image, and associated systems. BACKGROUND In the field of charged particle microscopy, electron backscatter diffraction (EBSD) represents a technique for obtaining information regarding the crystallographic structure of a specimen. In particular, in EBSD, an electron beam is directed to a tilted specimen, and the backscattered electrons form a diffraction pattern that is recorded by a detector. The resulting electron backscatter diffraction patterns (EBSPs) may be analyzed to provide information regarding crystal grain structure, grain orientation, deformations, and other such features. In some examples, a material deformation of the specimen may be characterized through comparison of the EBSP recorded at an undeformed "reference" portion of the specimen and a deformed "test" portion of the specimen. Many prior techniques for performing such analysis, however, suffer from limited computational efficiency and/or versatility. SUMMARY In a representative example, a computer-implemented method of determining a deformation characteristic of a test image relative to a reference image includes determining with a processor, via an iterative routine, a characteristic displacement gradient tensor that characterizes the deformation characteristic. The determining the characteristic displacement gradient tensor comprises, at one or more steps of the iterative routine, calculating an objective function value associated with a trial displacement gradient tensor. The objective function value is based, at least in part, on pixel values of pixel locations that are within a zone of consideration of the test image and the reference image. The zone of consideration is determined automatically based at least in part on the trial displacement gradient tensor. In another representative example, a computer-implemented method of determining a deformation characteristic of a test image relative to a reference image includes determining, with 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, using the initial displacement gradient tensor, determining, with the processor system, a characteristic displacement gradient tensor that characterizes the deformation characteristic. Determining the characteristic displacement gradient tensor includes determining by, in one or more steps of an iterative routine, calculating a scalar objective function value corresponding to each of one or more trial displacement gradient tensors. One of the one or more trial displacement gradient tensors in the first step of the iterative routine is the initial displacement gradient tensor. In another representative example, a system includes an electron optics assembly configured to direct an electron beam to a selected location on a specimen, a detector assembly configured to record a diffraction pattern associated with an interaction between the electron beam and the specimen, 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 specimen and to receive a test image from the detector assembly when the electron beam is directed to a test location on the specimen. The controller additionally is programmed to determine, via an iterative routine, a characteristic displacement gradient tensor that characterizes a deformation characteristic of the test image relative to the reference image. At each step of the iterative routine, the controller is programmed to calculate an objective function value corresponding to a trial displacement gradient tensor such that the objective function value is based on pixel values of pixel locations that are within a zone of consideration of each of the test image and the reference image. The zone of consideration is determined automatically based in part on the trial displacement gradient tensor. In another representative example, a non-transitory computer readable medium stores instructions which, when executed by a computer, cause the computer to perform a method of determining a deformation characteristic of a test image relative to a reference image. The method includes determining, via an iterative routine, a characteristic displacement gradient tensor that characterizes the deformation characteristic. The instructions include instructions for determining the characteristic displacement gradient tensor by, at each step of the iterative routine, calculating an objective function value corresponding to a trial displacement gradient tensor such that the objective function value is based on pixel values of pixel locations that are within a zone of consideration of