阅读说明：本技术 用于处理晶体材料的衍射图像的方法、装置和程序 (Method, apparatus and program for processing diffraction image of crystalline material ) 是由 费利克斯·拉图尔特 施奇伟 弗朗索瓦·希尔德 斯特凡纳·鲁 于 2018-12-07 设计创作，主要内容包括：本发明涉及一种用于处理由衍射检测器获得的晶体或多晶材料的图像的方法,其中在参考状态下获取材料的第一图像,以及在变形状态下获取材料的第二图像。本发明的特征在于,在计算器中,在第一步骤(E6、E12)期间,赋予当前弹性变形梯度张量F<Sup>e</Sup>以通过计算而确定的值,在第二步骤(E7)期间,计算由张量F<Sup>e</Sup>诱导的当前位移场,在第三步骤(E8)期间,计算由当前位移场校正的变形图像的第三数字值<Image he="83" wi="520" file="DDA0002627030910000011.GIF" imgContent="drawing" imgFormat="GIF" orientation="portrait" inline="no"></Image>以及在迭代算法期间,对修改后的张量F<Sup>e</Sup>执行第一、第二和第三计算步骤(E12、E7、E8)的迭代,直到满足关于F<Sup>e</Sup>的当前值的校正的收敛条件为止。(The invention relates to a method for processing an image of a crystalline or polycrystalline material obtained by a diffraction detector, wherein a first image of the material is acquired in a reference state and a second image of the material is acquired in a deformed state. The invention is characterized in that, in the calculator, during a first step (E6, E12), a current elastic deformation gradient tensor F is assigned e During a second step (E7), the composition F is calculated at the values determined by the calculation e The induced current displacement field, during a third step (E8), is calculated corrected by the current displacement fieldThird digital value of deformed image And during the iterative algorithm, for the modified tensor F e Performing iterations of the first, second and third calculating steps (E12, E7, E8) until a criterion with respect to F is satisfied e Until convergence of the correction of the current value.)

1. A method for processing an image of a crystalline or polycrystalline material obtained by a diffraction detector, wherein the detector is used to:

-measuring a first diffraction image (f) of the material, when the material is in a reference state, giving a first digital pixel value (f (x, y)) as a function of two pixel coordinates (x, y),

-measuring at least a second diffraction image (g) of the material when the material is in a deformed state relative to the reference state, the second image giving a second digital pixel value (g (x, y)) as a function of the pixel coordinates (x, y),

characterized in that, in the calculator,

storing in advance in a memory a displacement field (u) for shifting pixels of the first image to pixels of a deformed image as a function of_x,u_y)：

-the two pixel coordinates (x, y),

-predetermined coordinates (x, y) of a center (O) corresponding to a normal projection of a source point (S) of a light beam diffracted in the material in an image plane of the detector, and

-elastic deformation gradient tensor

During a first calculation step (E6, E12), the elastic deformation gradient tensor is caused

During a second calculation step (E7), according to the current elastic deformation gradient tensor

During a third calculation step (E8), the current displacement field (u) has been added by correction_x,u_y) Of the second image (g) at the pixel coordinates, calculating a third digital pixel value of the deformed image

Modified determination of the tensor by an iterative algorithmPerforming iterations of the first, second and third calculating steps (E12, E7, E8) until the determined values of the elastic deformation gradient tensor are satisfied

2. The method for processing an image of claim 1, wherein the elastic deformation gradient tensor

WhereinIs the elastic deformation gradient tensorThe component (c).

3. Method for processing images according to any of the preceding claims, characterized in that the displacement field u for shifting pixels of the first image to pixels of a deformed image is a function of_x,u_y：

-the two pixel coordinates x, y,

-predetermined coordinates x, y, x of a center (O) corresponding to a normal projection of a source point (S) of a light beam diffracted in said material in an image plane of said detector, and

-said elastic deformation gradient tensorComponent (b) of

Is equal to

4. Method for processing images according to any of the preceding claims, characterized in that said iterative algorithm is performed by a method of the gauss-newton type.

5. Method for processing images according to any of the preceding claims, characterized in that the verification by the iterative algorithm calculation is the followingCorrection vector of equation

Where [ M ] is a Hessian matrix with dimensions of 8 × 8, with coefficients

Wherein f represents the first pixel value of the first image, x represents the two pixel coordinates x and y,

is the displacement field (u)_x,u_y) Tensor of gradient with respect to said elastic deformationSaid component (a) of

{ γ } is a residual with the following terms as coefficients

determined values of the tensorThe convergence condition of (a) is the correction vectorIs less than a specified non-zero positive bound: ()，

In each iteration of the first calculation step (E12), the determined values of the tensor

6. The method for processing an image of claim 5, wherein the elastic deformation gradient tensor

the sensitive field of the displacement field u (x) has as components according to the following equation

Φ_x4＝0

Φ_x5＝0

Φ_x6＝0

Φ_y1＝0

Φ_y2＝0

Φ_y3＝0

7. Method for processing images according to any one of the preceding claims, characterized in that it is performed for most or all pixels of said first image (f) and of said second image (g).

8. Method for processing an image according to any one of the preceding claims, characterized in that said first and second images are obtained after filtering (E4) the value of an overexposed pixel by replacing it with an average value of its neighbours.

9. Method for processing images according to any of the preceding claims, characterized in that said first and second images are obtained after filtering (E4) said pixel values by subtracting a global gray trend represented by a polynomial of degree 2 or 3 obtained with a regression process.

10. Method for processing an image according to any of the preceding claims, wherein said first and second images are obtained after filtering (E5) said pixel values by means of a gaussian smoothing filter.

11. Method for processing images according to any one of the preceding claims, characterized in that it is performed for a plurality of second images (g).

12. Method for processing images according to any of the preceding claims, characterized in that at least one of the following is provided (E13) at an output:

-the elastic deformation gradient tensor calculated to satisfy the convergence condition

-a corrected deformation image calculated as an aspectAnd on the other hand the first digital pixel value (f (x, y)) of the first image (f), wherein the third digital pixel value has been for a respective displacement field (u)_x,u_y) The determined values calculated to satisfy the elastic deformation gradient tensorThe convergence condition of (a) is satisfied,

-mean square values of the residuals (r) calculated for a plurality of second images (g), respectively,

-said determined values calculated to satisfy said elastic deformation gradient tensorOf said convergence condition (u) of the corresponding displacement field (u)_x,u_y)，

-corrected deformed image

13. Method for processing images according to any of the preceding claims, wherein the first and second images are obtained (E3) after subtraction of an image background.

14. An apparatus for processing an image of a crystalline or polycrystalline material, comprising a diffraction detector (10) which makes it possible to:

-acquiring a first diffraction image (f) of the material, when the material is in a reference state, giving a first digital pixel value (f (x, y)) as a function of two pixel coordinates (x, y),

-acquiring at least a second diffraction image (g) of the material when the material is in a deformed state relative to the reference state, the second image giving a second digital pixel value (g (x, y)) as a function of the pixel coordinates (x, y),

characterized in that it comprises at least a calculator (12) comprising at least a memory in which is stored a displacement field (u) for shifting pixels of the first image to pixels of a deformed image as a function of_x,u_y)：

-the two pixel coordinates (x, y),

-predetermined coordinates (x, y, z) of a center (O) corresponding to a normal projection of a source point (S) of a light beam diffracted in the material in an image plane of the detector, and

-elastic deformation gradient tensorComponent (b) of

The calculator (12) is configured to:

during a first calculation step (E6, E12), the current elastic deformation gradient tensor is caused toTaking a definite value

During a second calculation step (E7), based on saidCurrent elastic deformation gradient tensor

During a third calculation step (E8), by applying the second image (g) to the current displacement field (u) added_x,u_y) Calculating a third digital pixel value of the deformed image

Determining the tensor value after updating again through an iterative algorithm

15. A computer program comprising code instructions for implementing a method for processing an image of a crystalline or polycrystalline material according to any one of claims 1 to 13 when executed on a computer.

Technical Field

The invention relates to a method for processing an image obtained by a diffraction detector.

Background

The field of application of the invention relates to the analysis of crystalline or polycrystalline materials, in particular by high resolution back-scattered diffraction (HR-EBSD). In particular, the detector may be an electron diffraction detector producing an electron diffraction pattern (called Kikuchi pattern), from the analysis of which the (relative) changes in the crystal unit cell parameters can be calculated very accurately.

In particular, it is desirable to compare the crystal unit cell parameters of one and the same material in different stress states. All the information obtained point by point during the scanning of the sample surface is usually presented in the form of two-dimensional images of the different components of crystallography, even in the form of analytical quality or confidence granted to it.

It is known from the prior art to use cross-correlation based algorithms to compare diffraction patterns between two different states, for example by a software program called crosssort and by a software program called strainorrelator, which is also based on a crosssort software program. This cross-correlation relies on dividing the image into thumbnails (also called regions of interest) whose movement will be tracked in order to obtain a discrete displacement field at the center of each thumbnail.

This cross-correlation of thumbnails has a number of disadvantages.

Each thumbnail provides the average displacement for each cross-correlation. For the process to proceed properly, the thumbnail must be large enough in size to contain a sufficient number of daisy-chain lines. In order to obtain a sufficiently rich displacement field, it is necessary to take a large number of thumbnails, in practice varying between 25 and 100. Because the thumbnails are numerous and equal in size, there is a large amount of overlap between the thumbnails. On the one hand, this slows down the correlation process considerably, since the pixels of the same thumbnail are considered multiple times. On the other hand, this overlap introduces a high degree of spatial correlation between the thumbnails, so that an increase in the number of thumbnails (beyond a certain threshold) cannot reduce neither measurement uncertainty nor system bias.

Furthermore, the choice of thumbnail position may affect the results obtained, which is a non-optimal performance of the method used. In case of large deformations, a significant rotation (more than one degree) of the pattern can be observed.

Since the displacement is looked up in thumbnails by pure translation, the dynamics database is only used approximately for reproducing the transformations observed on the images. Thus, cross-correlation can lead to severe errors, such as calculated stress in regions of greater rotation.

Disclosure of Invention

It is an object of the present invention to obtain a method and a device for processing images which eliminate the drawbacks of the prior art by making it possible to calculate the displacement field between the images with better quality and lower computational cost.

To this end, a first subject of the invention is a method for processing an image of a crystalline or polycrystalline material obtained by a diffraction detector, wherein said detector is used for:

-measuring a first diffraction image of the material when the material is in a reference state, wherein a first digital pixel value is given as a function of two pixel coordinates,

-measuring at least a second diffraction image of said material when said material is in a deformed state with respect to said reference state, said second image giving a second digital pixel value as a function of said pixel coordinates (wherein the digital pixel value of the image may be a grey scale or a luminance value, in particular an intensity value of a diffracted beam at a point of the detector).

According to the invention, in the calculator, a displacement field for shifting the pixels of the first image to the pixels of the deformed image is stored in advance in a memory as a function of:

-the two pixel coordinates are determined by the two pixel coordinates,

-a predetermined coordinate of a center corresponding to a normal projection of a source point of a light beam diffracted in the material in an image plane of the detector, an

-components of the elastic deformation gradient tensor.

During a first calculation step, the elastic deformation gradient tensor is taken as a determined value of the elastic deformation gradient tensor,

during a second calculation step, a current displacement field is calculated from a current elastic deformation gradient tensor and the pixel coordinates of the first image,

during a third calculation step, a third digital pixel value of a deformed image is calculated by correcting the second image at the pixel coordinate to which the current displacement field has been added. The deformed image is thus corrected by the current displacement field and is referred to as a third image or a corrected deformed image having a third pixel value to distinguish the third image from the first and second images.

Performing, by an iterative algorithm, iterations of the first, second and third calculation steps on the modified determined values of the tensor until a convergence condition of the determined values of the elastic deformation gradient tensor is satisfied to calculate the respective displacement field.

The following is a description of embodiments of the different steps of this method.

Thus, according to an embodiment, in particular, the diffraction detector makes it possible to measure a reference configuration of the geometry of the diffraction, associating the direction of the diffracted electron beam with the coordinates of each pixel, and the origin of the coordinates corresponds to the normal projection of the origin of the diffracted beam in the material in the image plane of the detector,

measuring a first diffraction (Kikuchi) map of the material when it is in a reference state, giving a so-called reference image, i.e. a grey-scale image, whose digital values correspond at each pixel to the density of diffracted electrons whose direction is geometrically related to the position of the pixel,

-measuring at least a second diffraction pattern when the material is in a deformed state relative to the reference state, the second image giving a second digital value of the grey scale at each pixel.

According to one embodiment, a displacement field is defined at each pixel in such a way as to make the grey scale of the matching pixels as uniform as possible, so as to match the pixels of the first diffraction image with the pixels of the diffraction image of the anamorphic crystal, this displacement field therefore being associated as far as possible with the direction of the diffracted beam and being in algebraic form, the expression of which is a known function of the elastic deformation gradient tensor.

According to one embodiment, during the first calculation step, the current elastic deformation gradient tensor is initialized to a predetermined tensor value and updated by iteration.

According to one embodiment, during the third calculation step, the third digital pixel values of the above-mentioned third warped image are calculated by interpolating the second image at the pixel coordinates to which the current displacement field has been added.

In the context of the present invention, third pixel values of the warped image are provided, which are corrections to the second image in a shorter time based on the main part of the image. The calculations performed by the present invention also reduce the measurement uncertainty of the displacement field between the first image and the second image. Thus, in various embodiments, the present invention is particularly suited to calculating material deformation between the first image and the second image based on the third image.

According to one embodiment of the invention, the elastic deformation gradient tensor

Is equal to

Wherein

Is the elastic deformation gradient tensor

The component (c).

According to one embodiment of the invention, the displacement field u for shifting the pixels of the first image to the pixels of the deformed image is a function of_x,u_y：

-the two pixel coordinates x, y,

-predetermined coordinates x, y, x of a center corresponding to a normal projection of a source point of a light beam diffracted in said material in an image plane of said detector, and

-said elastic deformation gradient tensorComponent (b) of

Is equal to

According to one embodiment of the invention, the iterative algorithm is performed by a method of the gauss-newton type.

According to one embodiment of the invention, a correction vector is calculated by the iterative algorithm verifying the following equation

Where [ M ] is a Hessian matrix with dimensions of 8 × 8, with coefficients

Wherein f represents the first pixel value of the first image, x represents the two pixel coordinates (x, y),

is the gradient tensor of the displacement field with respect to the elastic deformationSaid component (a) ofAnd equal to the gradient tensor of said displacement field with respect to said elastic deformationEach component of

The partial derivative of (a) of (b),

{ gamma } is the residual vector with the following terms as components

And is

Is the third digital value of each pixel of the warped image, g represents the second pixel value of the second image,

determined values of the tensor

Is that the norm of the correction vector is less than a specified non-zero positive bound ()，

The determined values of the tensor in each iteration of the first calculation stepAccording to the correction vector

And (4) increasing.

According to one embodiment of the invention, the elastic deformation gradient tensorHas eight componentsAnd a ninth component set to 1 as a component

I.e. according to the following equation:

the sensitive field of the displacement field u (x) has as components according to the following equation

Φ_x4＝0

Φ_x5＝0

Φ_x6＝0

Φ_y1＝0

Φ_y2＝0

Φ_y3＝0

According to one embodiment of the invention, the method for processing an image is performed for most or all pixels of the first image and the second image.

According to one embodiment of the invention, the first and second images are obtained after filtering the overexposed pixel values by replacing them with an average of the neighboring pixels of the overexposed pixel. Outliers are therefore filtered out (for some detectors referred to noise usually defined as "salt and pepper")

According to one embodiment of the invention, the first and second images are obtained after filtering the pixel values by subtracting a global gray scale trend represented by a polynomial of degree 2 or 3 obtained using a regression process.

According to one embodiment of the invention, the first and second images are obtained after filtering the pixel values by a gaussian smoothing filter.

According to one embodiment of the invention, the method is performed for a plurality of second images.

According to one embodiment of the invention, at least one of the following is provided at the output:

-the elastic deformation gradient tensor calculated to satisfy the convergence condition,

-a residual computed as a difference between the third digital pixel values of the corrected deformation image on the one hand and the first digital pixel values of the first image on the other hand, wherein the third digital pixel values have been computed for the respective displacement field as satisfying a convergence condition of the determined values of the elastic deformation gradient tensor,

-mean square values of the residuals calculated for a plurality of second images respectively,

-a respective displacement field calculated as satisfying the convergence condition of the determined values of the elastic deformation gradient tensor,

-a corrected deformed image corresponding to the third digital pixel values that have been calculated based on the respective displacement field calculated to satisfy the convergence condition.

According to one embodiment of the invention, the first and second images are obtained after subtracting the image background.

A second subject of the invention is an apparatus for processing images of crystalline or polycrystalline material, comprising a diffraction detector which makes it possible to:

-acquiring a first diffraction image of the material when the material is in a reference state, wherein a first digital pixel value is given as a function of two pixel coordinates,

-acquiring at least a second diffraction image of the material when the material is in a deformed state relative to the reference state, the second image giving a second digital pixel value as a function of the pixel coordinates,

characterized in that the device comprises at least a calculator comprising at least a memory in which are stored displacement fields for shifting pixels of the first image to pixels of a deformed image as a function of:

-the two pixel coordinates are determined by the two pixel coordinates,

-a predetermined coordinate of a center corresponding to a normal projection of a source point of a light beam diffracted in the material in an image plane of the detector, an

-a component of the elastic deformation gradient tensor,

the calculator is configured to:

during a first calculation step, the current elastic deformation gradient tensor is taken to a determined value,

during a second calculation step, calculating a current displacement field based on the current elastic deformation gradient tensor and the coordinates of each pixel of the first image,

during a third calculation step, a third digital pixel value of the deformed image is calculated by applying the second image (g) to the pixel coordinates to which the current displacement field has been added,

performing, by an iterative algorithm, iterations of the first, second and third calculation steps on the again updated determined tensor values until a convergence condition of the determined values of the elastic deformation gradient tensor is satisfied to calculate the respective displacement fields.

A third subject of the invention is a computer program comprising code instructions for implementing the above-described method for processing an image of a crystalline or polycrystalline material when executed on a calculator.

Drawings

The invention will be better understood when the following description, given purely by way of non-limiting example, is read with reference to the accompanying drawings, in which:

figure 1 schematically shows an apparatus for acquiring and processing images according to an embodiment of the invention,

FIG. 2 shows schematically in a perspective view a projection of a light beam diffracted by an apparatus for processing images according to an embodiment of the invention, and the effect on the diffracted beam resulting from the elastic deformation gradient tensor,

FIG. 3 schematically shows in a side view a projection of a light beam diffracted by an apparatus for processing an image according to an embodiment of the invention,

FIG. 4 schematically shows a block diagram of a method for processing an image according to an embodiment of the invention,

FIG. 5A shows an image of a test piece taken by a scanning electron microscope,

figure 5B shows the image obtained from figure 5A by a software program of the prior art,

FIG. 5C shows the chromaticity of FIG. 5B,

FIGS. 6A and 6B show examples of initial diffraction images of a test piece,

FIG. 6C represents the difference between the images obtained of FIGS. 6A and 6B,

FIG. 6D represents the values calculated for the elastic deformation gradient tensor present in the method and apparatus for processing images according to embodiments of the present invention in the example of FIGS. 6A and 6B,

FIGS. 6E, 6F, 6G, 6H and 6I show the images that appear in the different steps and devices of the method for processing images according to an embodiment of the invention, in the example of FIGS. 6A and 6B,

figures 7A, 7B, 7C, 7D and 7E represent the components of the stress tensors obtained by the method and apparatus for processing images according to an embodiment of the present invention starting from figure 5A,

fig. 8A represents the equivalent von mises stress obtained by the method and device for processing images according to an embodiment of the invention starting from fig. 5A, and fig. 8B represents a histogram of this stress.

Detailed Description

In fig. 1, in the method for processing an image according to the invention, in a previous measurement step, a digital image (or photograph) of the crystalline or polycrystalline material CR is obtained using the diffraction detector 10 (or the sensor 10 or the camera 10). The detector may be a high resolution electron backscatter diffraction (HR-ESBD) detector. Of course, other types of diffraction detectors 10 may be used.

The detector 10 is intended to measure a first image f of the material CR in a reference state, in which first digital pixel values f (x, y) (for example grey-scale or otherwise) are given as two coordinates x, y of a pixel. The EBSD detector is also used to measure one or more second images g of the material CR in a deformed state relative to the reference state. The second image g gives a second digital pixel value g (x, y) (e.g. grey scale) as two coordinates x, y of the pixel. Images f and g are selected in step E2 of fig. 4. In fig. 2 and 3, the three directions x, y and z are mutually orthogonal.

According to one embodiment of the invention, the deformed state and the reference state are obtained by applying different mechanical stresses to the material CR, for example by not applying any mechanical stress to the material CR in the reference state, and by applying a determined mechanical stress to the material CR in the deformed state. In this case, means may be provided for exerting and/or controlling mechanical stresses on the material CR.

As shown in fig. 1, the detector 10 is part of a measurement apparatus 1, the measurement apparatus 1 comprising an internal source 2 emitting a beam of incident particles 3 and a backscatter diffraction detector 10. The source 2 and the incident particle beam 3 are positioned relative to the material CR so that the material CR emits one or more diffracted particle beams 4 by interaction of the material CR with the incident particle beam 3. The beam 3 may be or include an X-ray beam, an electron beam or others. The diffracted beam 4 may also correspond to Kossel-type diffraction, Laue-type diffraction or diffraction in a transmission electron microscope (in particular in a transmission electron microscope using TKD or transmission chrysanthemum pool diffraction). The detector is positioned relative to the source 2, the incident particle beam 3 and the material CR to receive or intercept one or more diffracted particle beams 4 from the material CR in response to the incident particle beam 3. The detector 10 for example comprises a screen 11 for receiving the diffracted particle beam 4. The receiving screen 11 has a certain range, such as two-dimensional and planar or other ranges. The receiving screen 11 is connected to a unit 12 (which may be an automatic calculation unit 12) which records and generates images f, g based on the diffracted particle beam 4 received or intercepted by the receiving screen 11. The incident particle beam 3 may be or comprise incident monochromatic radiation of a certain wavelength, or a plurality of incident monochromatic radiation of different certain wavelengths. The detector 10 may be part of an electron microscope, in particular a transmission and/or scanning electron microscope, for example. The screen 11 may be, for example, a phosphor screen or otherwise.

According to one embodiment of the invention, in the case where the incident particle beam 3 is an X-ray beam, the diffraction phenomenon of the incident particle beam 3 by the material CR results in a Laue diagram on the detector 10; in case the incident particle beam 3 is an electron beam, a Kikuchi picture is caused on the detector 10.

According to bragg's law, incident monochromatic radiation 3 of wavelength λ will diffract on the crystallographic plane hkl (or diffraction plane hkl) of material CR, complying with:

nλ＝2d_hklsinθ (1)

where n is the diffraction order, d_hklIs the gap distance of the plane hkl. The angle θ is the half angle between the incident beam 3 and the diffracted beam 4. The crystalline material CR described by the reference system (a, b, c) of the unit cell has a reciprocal lattice whose reference system is (a, b, c). By definition, a is such that a · a ═ 1, b · a ═ c · a ═ 0. By cyclic permutation, the same is true for b and c.

Let k_iIs the wave vector, k, of the incident beam_fWave vector of diffracted beam. Since diffraction is the result of elastic processes (no energy loss), the norm of the vectors is the same, | k_f|＝|k_i|＝λ^-1Thus k is_fDescribes a radius equal to k_iIs the norm of (d). The diffraction vector q is defined as:

q＝k_f-k_i(2)

thus a vector if its origin is located at vector k_iThe end point of (1) is defined by the vector k_iIs centered at the origin of (a) and propagates on a circle of radius 1/lambda.

In this same reciprocal lattice space, the Bragg condition can be defined by the vector q of the hkl family of facets^(hkl)The coincidence condition with the diffraction vector q is expressed. Only a few favorable directions cause coherent diffraction.

According to one embodiment of the present invention, the electron beam used in EBSD has a very short wavelength λ, and θ is typically less than 2 °. Thus, as shown in fig. 1, the electrons in the diffraction state remain close to the trajectory of the crystal plane 40 diffracted thereon.

According to one embodiment of the invention, in the case of a divergent source 2, the diffracted beam 4 is distributed over two Kossel cones CO symmetrical with respect to the trajectory of the facet 40. The Kossel cone CO captured by the detector 10 may have the shape of two highly open hyperbolas, as shown in fig. 1.

According to one embodiment of the invention, during one acquisition, a first image f in the reference state and a second image g in the deformed state are obtained by scanning the sample surface of the material CR. A reference state is then taken at the center of the grain (assuming the stress is minimal) and then compared to the diffraction pattern taken at the periphery of the grain.

In fig. 2 and 3, the center O of the normal projection in the image plane 110 of the screen 11 of the detector 10, corresponding to the source point S of the light beam 4 diffracted in the material CR, has two predetermined coordinates (x, y) in the plane 110 of the screen 11, according to an embodiment of the invention. In the non-limiting example in fig. 2 and 3, the projection of the diffracted beam 4 onto the detector 10 is shown. The detector 10 is chosen as a reference in the rest of the text. In fig. 2, taking the corner B of the lower left corner of the flat screen 11 as the origin, the axis x is a horizontal axis in the plane of the screen 110, the axis y is a vertical axis in the plane of the screen 110, and the axis z is an axis perpendicular to the plane of the screen 110. The incident particle beam 3 is directed onto the test piece at an angle inclined at 70 ° to the normal, and the "central" point S in the interaction volume of the material CR is considered as the "effective" source of diffracted electrons 4. The projection center O is the normal projection of the point S on the plane 110 of the screen 11 (relative to the plane of the screen 11). The coordinates are expressed as (x, y, 0). z denotes the distance between the source point S and the center O, so S has the coordinates (x, y, -z).

According to one embodiment of the invention, F denotes the deformation gradient tensor according to the following equation, applied to the current point X in the initial configuration of the reference material CR, so that the position X of the current point X in the deformed configuration can be obtained:

by way of example, figure 1 shows the diffraction of a light beam in a microscope cavity, projecting itself onto the screen of an EBSD camera, representing two crystalline states, and the associated transition gradient tensor that passes from one state to the other. Fig. 3 illustrates the projection in detail and shows the source point S and the center of the projection.

According to one embodiment of the invention, the deformation gradient tensor F is two components: elastic part F^e(elastic deformation gradient tensor) and plastic part F^pThe product according to the following equation:

F＝F^eF^p

according to one embodiment of the invention, the plastic deformation has the effect of making the tanzan line less sharp, which is difficult to quantify and does not allow measuring the plastic deformation by analyzing the diffraction image. If hydrostatic elastic deformation occurs, a change in the width of the cell line on the detector can be observed. In contrast, a deviation from elastic deformation changes the shape of the crystal lattice, i.e., the relative orientation of the crystal planes, and thus the angular relationship within the crystal. A projection on the screen away from the light source will magnify the angular separation between the two beams and produce a measurable change between the diffraction patterns.

According to one embodiment of the invention, since only F can be measured^eEight components, it is therefore necessary to define a convention for setting the missing degree of freedom. According to one embodiment, a single tensor is selected

It has eight components

And a ninth component set to 1, i.e. according to the following equation:

according to one embodiment of the invention, the true elastic deformation gradient is then according to the following equation:

factor(s)Not measurable, but can be determined by other assumptions, such as choosing the frequently used planar stress state.

According to one embodiment of the invention, the element Δ X is taken into account in the reference lattice of the material CR. It is assumed that this particular direction results in a diffracted beam 4 which intersects the detector 10 at a point P with coordinates (x, y, 0). In the remainder of this document, p denotes a vector SP. This gives (p) ═ Δ x, Δ y, Δ z)^T＝(x-x*,y-y*,z*)^Tα Δ X, where α is the projection scale.

If the interactor around the source point S experiences a gradient tensor F due to elastic deformation^eWhen elastic deformation is expressed, the reference element Δ X is converted into Δ X ═ F^eΔ X. The light beam 4, which is initially diffracted in the direction P, is redirected to a point P ", such that

p”＝αF^eΔX

Where the vector SP "is denoted as p" as previously described. Line SP "intersects detector 10 at point P'. The apparent displacement u on the detector 10 is u-p '-p (i.e., the vector PP') according to the following equation:

a displacement function giving a displacement field (u) for shifting (or "shifting" or matching) the pixels of the first image f to the pixels of the deformed image g as a function of_x,u_y)：

Two pixel coordinates (x, y),

predetermined coordinates x, y of a center O corresponding to the normal projection of the source point S of the light beam diffracted in the material in the image plane 110 of the detector 10, an

-elastic deformation gradient tensorComponent (b) of

Of course, the expression "each said pixel" or "said pixel" may be replaced by a "pixel" to designate a part of the pixels of the image.

According to one embodiment of the present invention, the displacement field (u) is according to equation (9) below_x,u_y) Equal to:

displacement field (u) between first diffraction image f (referred to as reference image) and second diffraction image g (referred to as deformation image)_x,u_y) Reflecting the elastic deformation of the CR crystal unit cell of the material at the point of investigation.

The following is the tensor for calculating the elastic deformation gradientA description of the algorithm of (c). For example, the algorithm may iterate through steps E7, E8, E9, E10, and E11 described below, as shown in fig. 4.

The method for processing images is performed by an automatic computing unit 12, for example one or more electronic calculators and/or one or more computers, and/or one or more processors and/or one or more servers and/or one or more machines, pre-programmed by a pre-stored computer program.

During a first calculation step E6, the current elastic deformation gradient tensor is causedTaking the determined value of the elastic deformation gradient tensorFor example the initial value INIT before the first iteration. According to one embodiment of the invention, the initial value INIT before the first iteration may be, for example, a unit tensor.

During a second calculation step E7, following step E6, the gradient tensor of the current elastic deformation will be relied uponIs applied to the two coordinates x, y of each pixel of the first image f to calculate the current displacement field (u)_x,u_y). Thus, a current displacement field caused by the current elastic deformation gradient tensor at the pixel coordinates of the first image is calculated.

During a third calculation step E8, following step E7, by adding the current displacement field (u)_x,u_y) To calculate a third digital value of the warped image by applying or interpolating the second image g at the two pixel coordinatesWhere x denotes the two coordinates x, y of the pixel. Thus, during the second calculation step E8, the gradient tensor is calculated as the current elastic deformationAnd the current displacement field (u) of the function of the coordinates of each pixel of the first image_x,u_y)。

According to one embodiment of the invention, the third digital pixel value based on the already calculated deformed image

The quadratic difference of most or all pixels between the first digital pixel value f (x) of the first image f, a cost function a (see below) is calculated,

calculating a current elastic deformation gradient tensor

Thereby minimizing a third digital pixel value from the deformed image that has been calculatedA cost function a calculated from the difference of most or all pixels between the first digital pixel values f (x) of the first image f.

By iterative algorithms, via modification of the tensor at each iterationDefinite value (called definite tensor value after modification)

) Iterating the first, second and third calculation steps E7, E8, E9, E10, E11 until the determined value of the elastic deformation gradient tensor is satisfiedUntil the convergence condition of (a), in other words,until it is satisfiedUntil convergence of the correction of the current value. In step E7, the determined values corresponding to these tensors are calculated by a displacement functionDisplacement field (u)_x,u_y)。

In the prior art, the global correlation of digital images consists in associating two images f and g. According to one embodiment of the invention, the method implements integrated digital image Correlation (CINI). In the case of electron diffraction, the method according to the invention can be named ADDICTED in short (substitute specific digital image correlation tailored for electron diffraction).

According to one embodiment of the invention, by using the displacement field in step E8Correcting the deformed image g to search for a displacement field (u)_x,u_y) So as to be as close as possible to the reference imageI.e. equivalent to minimizing the residual error accumulated over the whole region of interest

The region of interest may be the entire image f and g. In the following, the displacement field has been passed in step E8

The corrected deformed image g is referred to as a corrected deformed image

Therefore, the method for processing an image according to the present invention may be a method for correcting the second image g, and thus, the apparatus for processing an image according to the present invention may be an apparatus for correcting the second image g.

The cost function a to be minimized is written according to the following equation:

whereinIs by means of a displacement field (u)_x,u_y) Corrected deformed image

(by means of a digital resolution algorithm, this will be the current determination), the minimization of the cost function a will result in a continuous correction of the determination until convergence.

According to one embodiment of the invention, the displacement field (u) is searched_x,u_y) (or corrections thereof) as a linear (or affine) combination of fields forming a "kinetic database". They tend to have any medium and then require global processing of all kinetics. Furthermore, if the so-called kinetic database is derived from a physical model and is therefore limited to well-defined mechanisms with displacement field characteristics, it is referred to as "integration". The correlation of the resulting digital image is also described as the integrated correlation.

In the case of the ADDICTED method, CINI is the tool chosen for analyzing the diffractogram (f and g are the corresponding diffractograms of the crystalline or polycrystalline reference material CR (unstressed for image f) and the observed crystal (for image g)). According to one embodiment of the invention, the displacement field (u) observed in the diffraction pattern is given_x,u_y) Depending on diffractionThe manner of elastic deformation of the material CR. Finally, other parameters P may influence the measured displacement field (u)_x,u_y) E.g. projection parameters P, e.g. test piecesThe tilt with respect to the sensor 10, the physical size of the pixels and the scanning pitch of the scanning electron microscope, the latter two being summarized by the beam induced displacement.

According to one embodiment of the present invention, the displacement field (u) is explained according to the following equation_x,u_y)：

Finally, in general, these fields may be pairedOr P has a non-linear dependence. According to one embodiment of the invention, these dependencies are formed around the current determination of parameters to access affine expressions suitable for the CINI method. Thus, according to one embodiment of the invention, it is written according to the following equation:

where Φ i corresponds to the gradient tensor with respect to deformation

Component (b) of(e.g., i ranges from 1 to 8) and Ψ j is a sensitive field relative to parameter P_iOf the sensor element. Thus, for example, Φ is a size of (2N)_pixel) × 8, respectively.

According to one embodiment of the invention, the sensitive field of the displacement field u (x)Having components according to the following equation

And

as components:

Φ_x4＝0

Φ_x5＝0

Φ_x6＝0

Φ_y1＝0

Φ_y2＝0

Φ_y3＝0

according to one embodiment of the invention, the iterative algorithm is of the gauss-newton type. For example, it attempts to iteratively minimize the cost function a by a gaussian-newton algorithm.

According to one embodiment of the invention, during a step E8 following the step E7, a calculation is madeThis value is the third digital pixel value of the corrected warped image.

According to one embodiment of the invention, during a step E8 following the step E7, a calculation is made

This value is the third digital pixel value of the corrected warped image.

According to one embodiment of the invention, the correction vector is calculated by an iterative algorithm during a step E10 following the step E9

Thereby verifying the following equation:

wherein [ M ] is]Is a Hessian matrix with dimension 8 × 8 according to one embodiment of the invention, during step E9 after step E8, the Hessian matrix [ M ] is calculated according to the following formula]Coefficient of (2)

Where f is the pixel value of the reference image and x represents the two coordinates x and y of the pixel.Is a displacement field (u)_x,u_y) Tensor gradient with respect to elastic deformationComponent (b) of

And is equal to the displacement field (u)_x,u_y) Tensor gradient with respect to elastic deformationEach component of

Partial derivatives of (a). Thus, the sensitive field is a two-dimensional vector whose component along x is equal toAnd the component along y is equal to

{ gamma } is a second member of the Newton-Raphson method, and is a residual vector with the following as components

Is the gradient of f (x), i.e., the gradient of f (x, y).

According to one embodiment of the present invention, during step E9, which follows step E8, a second component is calculated according to the following equationCoefficient of member [ gamma ]

According to an embodiment of the invention, the determined tensor valuesIs that the correction vector has been calculatedIs less than a specified non-zero positive bound。

According to one embodiment of the invention, during a step E11 following the step E10, after each iteration of the steps E7, E8, E9 and E10, the correction vector is checked

Is less than a specified non-zero positive bound. For example, the limit may be equal to 10^-7Or otherwise. After the calculated correction vectorIs not less than a specified positive boundIn the case of (no in fig. 4), the update step E12 described below is executed.

According to one embodiment of the invention, during the calculation step E12, the current elastic deformation gradient tensor is caused to be

Taking the determined tensor value

For example, during the update calculation step E12, the determined tensor values are based on the following equation for updating the determined values

According to the correction vector

Increment:

step E12 is followed by a first step E7 of computing a subsequent iteration.

According to one embodiment of the invention, the correction vector is calculated after the correction vector has been calculatedIs less than a specified positive boundIn the case of (yes in fig. 4), step E13 described below is performed.

According to one embodiment of the invention, in step E13, the elastic deformation gradient tensor calculated during step E12 of the last iteration is takenDetermined values (verification of convergence conditions) and displacement field (u) calculated during the last step E7_x,u_y) (by corresponding to the extracted tensor

Of the determined values of (a) and (b)_x,u_y) Calculation).

According to one embodiment of the invention, in step E13, one or more of the following is provided at an output (which may be, for example, an on-screen display and/or a storage device in memory, and/or sent on an output or otherwise):

-determined values calculated to satisfy the elastic deformation gradient tensor

Corresponding displacement field (u) of the convergence condition of_x,u_y)，

-quilt countingCalculated as a determination of the elastic deformation gradient tensor satisfying the convergence condition

The determined values calculated in step E8 as satisfying the elastic deformation gradient tensor

Has passed through a corresponding displacement field (u)_x,u_y) Corrected image corresponding to deformed image g or corrected deformed image

That is, the determined value calculated to satisfy the elastic deformation gradient tensor

Has been based on the corresponding displacement field (u)_x,u_y) The calculated third digital pixel value is calculated,

-a corrected deformation image calculated as an aspectAnd on the other hand the first digital pixel value f (x, y) of the first image f, wherein the third digital pixel value has been for the respective displacement field (u)_x,u_y) Is calculated as a determination value satisfying the elastic deformation gradient tensorConvergence condition of (2)

-mean square values of the residuals r calculated for several second images g, respectively.

According to one embodiment of the invention, the method is performed for a majority (e.g. at least 50%, at least 60%, at least 70%, at least 80% or at least 90% of the pixels of the first image f and the second image g) or all pixels of the first image f and the second image g and is done by one traversal for each image.

According to one embodiment of the invention, the method is performed for several second images g.

The residual field r collects all artifacts of image formation and acquisition and therefore may contain very rich information from the image being analyzed. A signal in the residual that is not white noise typically indicates incomplete utilization of the information or an inappropriate model of the kinetic transformation between images. Therefore, the residual may include a signal or white noise. If the reference image f is assumed to be a perfect noise-free reference image f_pAnd these noise-free reference images are superimposed on white noise b which should be normally distributed, has no spatial correlation and is known as "white gaussian noise_fThe method comprises the following steps: then image f is equal to:

f＝f_p+b_f

according to one embodiment of the invention, a series g of diffraction images g is deformedⁱEach image g is according to the following equationⁱEqual to:

wherein

Is pure noise.

After applying the method according to the invention, it is given according to the following equation:

according to the following equation, when the reference image and the deformed image perfectly correspond after registration (in this case,

) Then the residual is:

according to one embodiment of the invention, the same reference image is used within one and the same die, which thus corresponds to a single image f, rather than multiple images g. It is then observed that the residuals with convergence obtained for all images g can be averaged and by representing them as <. >, this average value of the different measurement points within the grain, the average value of the residuals r, is equal to the following equation:

thus, according to one embodiment of the invention, the average of the residuals r provides the noise b_fAnd the noise b calculated therefrom_fIs taken from a reference image f_pAnd (4) subtracting. This can reduce measurement uncertainty by reducing the residual (variance divided by 2).

According to one embodiment of the invention, during a step E5 preceding step E6, the pixel values f (x, y) of the first image f and the pixel values g (x, y) of the second image g are filtered by a gaussian filter. Since the original image is corrupted by a large amount of white noise, performing a minimum gaussian smoothing process on the diffraction image greatly facilitates subsequent calculations. The gaussian smoothing process involves convolving the initial image f (and, where applicable, G) with a softening function G.

In practice, the selected length ξ may be 1 to 2 pixels. The choice depends on the level of noise on the image, which itself is a function of acquisition time, pixel count, beam parameters, and imaging material. The gaussian smoothing process can effectively eliminate the high-frequency noise of the diffraction image.

According to one embodiment of the invention, in step E4, which precedes step E5, the pixel values f (x, y) of the first image f and the pixel values g (x, y) of the second image g are filtered by replacing the overexposed pixel values with average values of neighboring pixels of the overexposed pixel to filter the overexposed pixel values. If the phosphor screen 110 used to capture the electrons is not uniform, the acquired images f, g typically have overexposed pixels at fixed points. These very bright pixels can adversely affect the image correlation calculation and it is recommended to replace the gray values of these "bad pixels" with the average gray of the neighboring pixels.

According to one embodiment of the invention, in step E4, which precedes step E5, the pixel values f (x, y) of the first image f and the pixel values g (x, y) of the second image g are filtered by subtracting the global gray scale trend represented by a 2 or 3 degree polynomial obtained by means of a regression process. In particular, images f and g may exhibit global gray level variations related to fluctuations in diffraction average energy. For global image correlation, the global gray scale trend is preferably subtracted in this case.

According to one embodiment of the invention, in step E3, which precedes step E4, the already calculated image background is subtracted from the pixel values f (x, y) of the first image f and the pixel values g (x, y) of the second image g. In particular, the acquired images f and g may be stained by the background, in particular because of the energy distribution of the diffracted electrons. This correction by subtracting the background eliminates the average intensity variation of the image, which can increase the contrast and make the tanacetum line clearer. For example, to achieve this, the acquisition is performed at a low magnification of the crystalline or polycrystalline material CR, so as to scan a large number of grains of different orientations. The diffraction images thus obtained are averaged and an estimate of the background can be obtained. In principle, the background image is unique to the entire investigation region acquired HR-EBSD.

Of course, in other embodiments of the present invention, the order of steps E3, E4, and E5 may be modified, or one or more of these steps E3, E4, and E5 may be deleted. Before step E2, step 1 may be entered to input the chrysanthemum pool image, the center O and the parameter P. At step E13A post-processing step may then be performed, for example obtaining other quantities calculated on the basis of the quantities obtained in step E13, for example a deformation component according to direction y_yyOr otherwise.

According to one embodiment of the invention, the apparatus 1 for processing images of crystalline or polycrystalline material according to the invention comprises means for implementing the apparatus 1 for processing images according to the invention. The device 1 for processing images according to the invention comprises a diffraction detector 10 which makes it possible to obtain:

a first image f of the material in a reference state, in which first digital pixel values f (x, y) are given as a function of two pixel coordinates (x, y),

one or more second images g of the material in a deformed state with respect to the reference state, the second images giving second digital pixel values g (x, y) as a function of the pixel coordinates (x, y),

the device 1 for processing images comprises at least a calculator 12 comprising at least a memory in which is stored a displacement field (u) for making the pixels of the first image become the pixels of the deformed image as a function of_x,u_y)：

Two pixel coordinates (x, y),

-predetermined coordinates (x, y) of a center (O) corresponding to a normal projection of a source point S of the light beam diffracted in the material in an image plane of the detector, and

-elastic deformation gradient tensor

Component (b) of

The calculator 12 is configured to:

during a first calculation step E6 or E12, the current elastic deformation gradient tensor is caused to

Taking a definite value

During a second calculation step E7, a tensor is calculated corresponding to the elastic deformation gradient

And the current displacement field (u) of the pixel coordinates x, y of the first image f_x,u_y)，

During a third calculation step E8, by correcting the current displacement field (u)_x,u_y) A second image g at pixel coordinates of (a), calculating a third digital pixel value of the deformed image

By means of an iterative algorithm, the modified definite tensor valuePerforming iterations of the first, second and third calculation steps E12, E7, E8 until a determined value is metUntil the convergence condition of (c) to calculate the corresponding displacement field (u)_x,u_y)。

The invention also relates to a computer program comprising code instructions for implementing the method for processing images of crystalline or polycrystalline material according to the invention when executed on a computer. The computer program is stored in a memory of the calculator 12.

According to an embodiment of the invention, the image is corrected according toAndthe following equations, after correcting the overall translation of the image by interpolating the image, obtain the first and second images f and g:

where x denotes the two coordinates x and y of the image pixel. The translation w may be obtained based on calibration of the detector with a standard test piece and a known scan direction relative to the screen 110 and the physical dimensions of the pixels of the screen 110. Therefore, before starting the integration correlation calculation, the image drift due to the movement of the emission point (i.e., the scanning movement of the electron beam) can be corrected in advance.

According to one embodiment of the present invention, the first and second images f and g are obtained after performing correction centering on the projection center O. For example, in HR-EBSD, the test piece (material CR) may be tilted by 70 °. The acquisition location and screen 110 may also be offset by a few degrees. If the acquisition is performed over a large area, the distance z between the emission point S and the screen varies. The value of z has an effect on the magnification of the diffraction image. According to the equations of the corrected images ˇ f and ˇ g below, the center of projection O ═ (x, y ═ can be adjusted by adjusting before initiating image correlation^TThe size of the diffraction image as a centre corrects this effect, especially when the measurement area exceeds 100 μm:

ˇg(x-x*)≡g^[(z_g*/z_f*)(x-x*)]

ˇf(x-x*)≡f^[(z_g*/z_f*)(x-x*)]

wherein z is_gIs the distance between the "deformed" image emission points, and z_fIs the distance between the reference image emission points. As a result, the projection parameters P can be preprocessed and corrected for the sensitive field Ψ_jAnd may be to tensors

The resolution is performed.

The tests carried out on a polycrystalline traction test piece are described below by way of non-limiting example with reference to fig. 5A, 5B, 5C, 6A to 6I.

A first image f of the test piece is produced in the reference state and a second image g of the test piece is produced in the deformed state. To create the deformed state, test pieces made of coarse-grain AISI 316L stainless steel were polished and subjected to a traction load in the scanning electron microscope chamber using an in-situ test plate. In fig. 5A and 5B, the load direction is horizontal. In the first elastic phase of loading, HR-EBSD was obtained by considering the region of interest focused on three points of the microstructure (i.e. separating three grains G1, G2 and G3). The algorithm according to the invention has been used to process data.

Fig. 5A shows an image made of secondary electrons taken by a scanning electron microscope in a region of interest of a test piece. Fig. 5B shows the inverse pole figure obtained by standard EBSD analysis in the region of interest of the test piece of fig. 5A. Fig. 6A shows a reference image f obtained at a point of interest, as a function of coordinates in the detector plane, x on the abscissa and y on the ordinate. Fig. 6B shows the second image g in a deformed state as a function of the x-coordinate on the horizontal axis and the y-coordinate on the vertical axis. Fig. 6C shows the initial difference ECI between the image of fig. 6B and the image of fig. 6A as a function of the x-coordinate on the horizontal axis and the y-coordinate on the vertical axis. FIG. 6D illustrates the elastic deformation gradient tensor obtained by the ADDICTED method in accordance with the present invention based on the images f and g of FIGS. 6A and 6BFig. 6E shows on the gray level ECH represented on the right hand side the component u of the displacement field calculated by the ADDICTED method according to the invention on the basis of the images of fig. 6A and 6B_xAs a function of the x-coordinate on the horizontal axis and the y-coordinate on the vertical axis. Fig. 6F shows on the gray scale (digital pixel values) represented on the right hand side the component u of the displacement field that has been calculated by the ADDICTED method according to the invention on the basis of the images of fig. 6A and 6B_yAs a function of the x-coordinate on the horizontal axis and the y-coordinate on the vertical axis. FIG. 6G shows a deformed and corrected imageI.e. having passed the displacement field (u) of fig. 6E and 6F_x,u_y) Correction was made based on FIG. 6B, and the field (u) was displaced_x,u_y) Has been calculated by the ADDICTED method according to the invention based on the images of fig. 6A and 6B as a function of the x-coordinate on the horizontal axis and the y-coordinate on the vertical axis. FIG. 6H shows a residual field r equal to the corrected warped image of FIG. 6G obtained by the ADDICTED method according to the present inventionAnd image f of fig. 6A. Fig. 6I shows a diffraction image of crystal grain G3, in which the signal contained in image 6H is visible.

As shown in fig. 6C, there is rotation that is not easily perceived by the naked eye between the two images of fig. 6A and 6B, but the rotation becomes apparent when the initial difference between them is calculated. From fig. 6H and 6C it can be concluded that due to the ADDICTED method according to the invention in fig. 6H, the main initial difference shown in fig. 6C disappears and that the "dashed" line field becomes visible in the residual of fig. 6H.

It was observed that the diffraction image of fig. 6I showed a similarity in the chrysanthemi line with the "dashed" line present in the residual shown in fig. 6H. This phenomenon indicates that a "background image" has not been acquired in a sufficiently accurate and robust manner, and therefore the diffraction signal of grain G3 is still contained in this image. By interpreting the residual field provided in fig. 6H by the ADDICTED method according to the invention, it is possible to reveal information hidden so far, which may be useful for constructing a better background picture.

In order to initialize the first estimation in step E6(first "deformed" diffraction image g), the identity matrix is a tensor, since less deformation is expected, and there is no other informationIs not a wrong choice. To is coming toThe tensors at the other pixels are initialized in step E6, it is usually better to take the value that has been calculated for one of its neighbors, since the degree of deformation should be small between neighboring points in the material.

Table 1 below summarizes the convergence speed versus the calculation conditions:

table 1: number of iterations for different calculation conditions

It can be concluded that gaussian smoothing of the diffraction image greatly reduces the number of iterations required for convergence, and that smoothing using a larger kernel (2 pixels) leads to faster convergence than using a smaller kernel (1 pixel). By adjacent pixel tensorThe initialization of the estimate of (a) also speeds up the convergence speed, especially for the calculation of diffraction images that are not smoothed. The tensor obtainedFor values of (a), the different calculation conditions do not result in a tensor

Are the same, resulting in rather close values. The obtained tensorHas a standard deviation of less than 10^–4。

The calculations shown below are based on the image g of the pressed material of fig. 5A. The image is smoothed using a 2-pixel Gaussian kernel and the tensors of the neighboring pixels are usedThe value of (c) is initialized. The plane stress assumption has been applied to the tensorThus having been converted into (valued as) a tensor F^e(elastic part F of deformation gradient tensor F^e). The depth of the emitting area (interacting with the electron beam) is about 25nm, which makes the plane stress assumption reasonable. It should be noted that this plane stress assumption is based on the assumption that the surface normal is well known, but not generally after deformation. Irregularities on the surface can reduce the accuracy of the HR-EBSD measurement. The acquisition of HR-EBSD is performed at the onset of plasticity, so the effect of the relief is negligible. It is assumed here that the rotation can be large, but that the net deformation is small (elastic state). Then it is recommended to keep F^eA formalism of large deformations and calculation of the rotation R by polar decomposition, which makes it possible to estimate the stress-related linear Green-Lagrange elastic pure deformation tensor U according to the following formula^eEquation:

F^e＝R U^e

with respect to pure deformation, the assumption of small perturbations is reasonable, | I-U^e||<<1, therefore, the Green-Lagrange deformation tensor is approximately equal to the infinite deformation tensor, according to the following equation:

in the elastic state, the complete stress tensor σ is calculated by hooke's law according to the following equation:

σ＝J^-1F^eC:(F^e)^T

wherein J is F^eDeterminant (c). The elastic constant is: c₁₁＝206GPa，C₁₂＝133GPa，C₄₄119GPa and is taken for the hooke tensor C, which is assumed to be Cubic for the ADDICTED method according to the present invention.

Component σ of the stress tensor σ obtained by the ADDICTED method according to the present invention_xx、σ_yy、σ_xy、σ_yzAnd σ_xzExpressed as coordinates x on the horizontal axis and coordinates on the vertical axis in fig. 7A, 7B, 7C, 7D, and 7E, respectivelyy is a function of. Stress tensor σ obtained by ADDICTED method according to the invention_zzToo small to distinguish from 0 and is therefore not shown.

Furthermore, to verify the plane stress assumption, the free surface σ_izThe shear stress on the steel must be close to zero. These shear stresses are small in the ADDICTED method according to the present invention and therefore approach an in-plane stress regime.

Fig. 8A shows the equivalent von mises stress obtained by the ADDICTED method according to the invention as a function of the x-coordinate on the horizontal axis and the y-coordinate on the vertical axis, in terms of the gray scale ECH indicated on the right. Fig. 8B shows a histogram of the equivalent von mises stress of fig. 8A. For the ADDICTED method according to the invention, the limit value for von mises stress is 2.7 GPa. In terms of computation time, for a program using MATLAB code, the automatic execution of the method according to the invention requires 40 hours on a portable computer using two i7 kernels. On a desktop (and therefore more powerful, faster machine) running 8 i7 cores, the CrossCourt program takes about 40 hours to perform the first calculation, whereas the remapping takes about 100 hours. Thus, the method according to the invention greatly reduces the computation time (by 75% or 90%) by using the program in an interpreted language of uncompiled and unoptimized code.

The invention makes it possible to measure deformations and to evaluate stresses accurately. The invention has the following advantages:

easy to implement. The pre-rotation operation is incorporated into the resolution by what is inherent in the ADDICTED method according to the present invention.

Robustness of the calculation, since the deformation gradient tensor is directly measured by integrating most or all of the diffraction image8 components of (a). This effect has been demonstrated on degraded chrysanthemum pool images. The exploitation of the image correlation is done in a complete way and does not lead to spatial correlation between neighboring computation points. Thus, the physical significance of the results is improved.

The global correlation strategy according to the invention also makes it possible to avoid redundancy in the calculations performed (the cross-correlation methods of the prior art produce overlaps in the thumbnails), thus making it possible to save considerable calculation time (75% to 90% savings, depending on the test case).

The global correlation strategy reduces the measurement uncertainty. The easily understandable test case shows a 40% reduction. This strategy occupies a large and unique region of interest, i.e. it samples a large number of pixels with one traversal. By avoiding the sampling bias inherent in cross-correlation, the ADDICTED method according to the present invention is optimal with respect to white Gaussian noise affecting the diffraction image.

In an embodiment, improvements are proposed, such as applying a gaussian smoothing process on the diffraction pattern to attenuate high frequency noise, or again initializing the calculation based on the results of neighboring elements.

In case of large deformations, the standard correlation of the prior art does not evaluate the deformation of the image well, but based on the projection equation the deformation of the image can be well described by the formula according to the invention. The accuracy is thus improved, which can be seen from the result of the reduction of the ultimate stress value.

In an embodiment, the relevant residual field is inherently obtained by the method according to the invention, whereas the relevant residual field is not calculated by prior art techniques, and when one wishes to obtain it by these techniques, the calculation cost is high, because a large amount of interpolation is required. In an embodiment, by analyzing all calculated residuals, all of the image of the tanacetum can be "denoised", or any error present in the background noise detected.

Finally, the ADDICTED method according to the invention, which is suitable for HR-EBSD images, can be extended to other types of images obtained by diffraction, for example Kossel diffraction, Laue diffraction or TEM (transmission electron microscope) diffraction. These techniques are based on the same principles as the diffracted beam projection. The ADDICTED method according to the invention can be applied to these techniques. The ADDICTED method for Laue and TEM diffraction according to the invention, with all the advantages described above, provides a significant improvement in its development.

Of course, the above embodiments, features and examples may be combined with each other or selected independently of each other.