CN107590787B - Image distortion correction method of scanning electron microscope - Google Patents

Image distortion correction method of scanning electron microscope Download PDF

Info

Publication number
CN107590787B
CN107590787B CN201710812587.XA CN201710812587A CN107590787B CN 107590787 B CN107590787 B CN 107590787B CN 201710812587 A CN201710812587 A CN 201710812587A CN 107590787 B CN107590787 B CN 107590787B
Authority
CN
China
Prior art keywords
distortion
image
inherent
pixel
time
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN201710812587.XA
Other languages
Chinese (zh)
Other versions
CN107590787A (en
Inventor
李中伟
刘行健
史玉升
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Huazhong University of Science and Technology
Shenzhen Huazhong University of Science and Technology Research Institute
Original Assignee
Huazhong University of Science and Technology
Shenzhen Huazhong University of Science and Technology Research Institute
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Huazhong University of Science and Technology, Shenzhen Huazhong University of Science and Technology Research Institute filed Critical Huazhong University of Science and Technology
Priority to CN201710812587.XA priority Critical patent/CN107590787B/en
Publication of CN107590787A publication Critical patent/CN107590787A/en
Application granted granted Critical
Publication of CN107590787B publication Critical patent/CN107590787B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Landscapes

  • Image Processing (AREA)

Abstract

The invention discloses an image distortion correction method for a scanning electron microscope, which belongs to the field of computer vision and comprises the steps of S1, continuously acquiring images on a preset time sequence and establishing time driftDistortion DdRelation D with image acquisition time td(t); s2 according to D obtained in S1d(t), removing drift distortion in advance, and acquiring sparse image pixel position information and a corresponding distortion vector sample set by using a shooting standard target; s3, establishing the relation between the pixel coordinate u of any pixel point of the image plane and the inherent distortion vector l corresponding to the pixel point, and further calculating to obtain the imaging inherent distortion model Df(ii) a S4: solving a distortion model matrix D by using the sparse position information obtained in S2 and the corresponding distortion vector sample setfIn combination with Df(u) and Dd(t) distortion correcting the image. The method of the invention respectively carries out distortion modeling and correction on two main distortion fields of the scanning electron microscope image, and the method can be applied to actual engineering.

Description

Image distortion correction method of scanning electron microscope
Technical Field
The invention belongs to the field of computer vision, and particularly relates to an image distortion correction method for a Scanning Electron Microscope (SEM).
Background
With the continuous development of micro-nano technology, micro-nano devices are more and more widely applied in the high and new technical fields of chip manufacturing, electronic packaging, biological medicine and the like. The micro-nano device is usually composed of a plurality of different nano materials, the elastic modulus and the thermal expansion coefficient of the materials are different, and cracks are easily generated at the joint of the materials under different load, humidity and temperature conditions to cause the failure of the micro-nano device. Therefore, the deformation analysis of the material and the structure under the micro-nano scale has important significance.
Scanning Electron Microscopy (SEM) has its recognized advantages in image acquisition and acquisition, such as: has larger depth of field, resolution of nanometer scale level, high usability and adjustable magnification from low power (10X) to high power (up to 50000 times). Therefore, the combination of SEM and strain measurement method (such as micro-moire and moire interference technology, digital image correlation technology and the like) in a part of macro scale provides a feasible path for deformation analysis of materials and structures in a micro-nano scale. The above methods all have extremely high requirements for precise image positioning, and the scale of the imaging object and its deformation is extremely small, so distortion-free imaging by a Scanning Electron Microscope (SEM) is required as much as possible. However, the process of taking SEM images is different from the parallel imaging of all pixels in the optical imaging system, the sequential scanning of the observed object by the electron beam needs to be controlled in the SEM imaging process, even in the most advanced current SEM systems, the control of the electron beam is still an open loop system, the scanning process is influenced by the fluctuation of the electromagnetic field, the thermal variation of the sample surface and the mechanical vibration, the taken SEM images have obvious time drift distortion (time-dependent distortion) and space intrinsic distortion (time-independent distortion), and the distortion rule is completely different from the optical images [ Sutton M a, Li N, Joy D C, resyls a P and Li x scanning electron microscopy for obtaining and deformation measurement space I: SEM imaging at least mechanisms 200to 10,000.experimental results, 2007,47 (786): 7757 ],000. experimental results, therefore, it is impossible to model and correct the optical image by using a mature parametric distortion model.
Sutton et al [ Sutton M A, Li N, Garcia D, Cornille N, Orteu J, McNeill SR, Schreier H W & Li X. Metalogy in a scanning electron microscope: the organic observations and experimental evaluation. measurement and Technology,2006,17(10):2613 ] use FEI Quanta-200 type SEM to take a large number of SEM images and perform statistical analysis of their distortion laws, showing that: when the magnification is less than 2000 x, the spatial intrinsic distortion dominates; when the magnification is more than 10000 times, the time drift distortion is dominant; in the middle of 2000X to 10000X, the specific gravities of the two kinds of distortions are equivalent.
In addition, the experiments of m.a. sutton et al also found that when the magnification is 10000 × the average value of the time drift of all pixels in the SEM image is about 0.8 pixel, and the maximum deviation can reach 6 pixels, and under the framework of the deformation analysis technology of materials and structures in the micro-nano scale, the deviation will have a serious influence on the precision of system parameter calibration, displacement calculation, and strain calculation, and must be corrected.
The reason for generating the SEM image distortion is complex, the distortion is not obvious and regular, and the modeling and the correction of the SEM image distortion are very difficult, so that the existing research results are few, and only a few research units carry out preliminary research on the problem. Lockwood et al [ Lockwood WD, currents ap. use and verification of digital image correlation for automated 3-d surface characterization in the scanning electronic microscope, 1999,42(23): 123-. Sinram et al [ Sinram O, Ritter M, Kleindick S, Schertel A, Hohenberg H & Albertz J. Calibration of an SEM, using an and a positioning table and a microscopical positioning column 2002ISPRS Commission V Symp. (Corfu, Greece):210 and 214 ] neglect the time-shift distortion at lower magnification, correct the SEM image distortion by referring to the parameterized spatial distortion model in the optical image, but with lower correction accuracy. Sutton et al [ Sutton M A, Li N, Joy D C, Reynolds A P & Li X.Scanningelectrically microscopical for quantitative small and large deformation measured I: SEM imaging at least major distortions from 200to 10,000.Experimental mechanisms, 2007,47(6):775 787 ] set forth from the SEM imaging principle, the Time drift and the spatial distortion are divided into two independent parts, and a Time-based local temporal model (temporal-spatial) and a spatial-based parametric model (SEM-spatial) distortion correction method are proposed to provide a method for correcting image distortion, which is feasible for reducing SEM distortion and SEM distortion.
However, none of the above methods takes into account the continuity constraint on the temporal sequence and between spaces (pixels), i.e. for temporal drift distortion, images of adjacent times have similar temporal drift distortion; for spatial intrinsic distortion, neighboring pixels have similar spatial intrinsic distortion. If the continuity constraint can be parameterized and characterized, a brand new and more effective SEM image distortion correction algorithm can be expected to be formed.
In summary, there are many barriers to the practical application of the conventional Scanning Electron Microscope (SEM) image distortion correction method. Therefore, it is necessary to develop a truly feasible image distortion correction method for a Scanning Electron Microscope (SEM).
Disclosure of Invention
In response to the above-identified deficiencies in the art or needs for improvement, the present invention provides a method for image distortion correction for a Scanning Electron Microscope (SEM). Two major distortions for SEM: drift distortion and inherent spatial distortion, which is based on the continuity principle of an SEM distortion field on a time sequence and a space sequence, respectively establishes a mapping relation between time drift distortion and image acquisition time, establishes an SEM distortion model aiming at the mapping relation between the inherent spatial distortion and image pixel positions and provides a method for correcting a distorted image.
To achieve the above object, according to one aspect of the present invention, there is provided a method for correcting distortion of an image for a Scanning Electron Microscope (SEM), comprising the steps of:
s1: continuously acquiring images in a predetermined time sequence to establish a time-drift distortion DdRelation D with image acquisition time td(t) for time-drift distortion removal for subsequent steps, the time-drift distortion model being as follows:
Dd(t)＝[dx(t),dy(t)]；
dx(t)＝vxt；
dy(t)＝vyy；
wherein d isx(t),dy(t) is the time drift distortion value corresponding to the image t in the x-direction and y-direction of the image at the time of image acquisition, vx,vySolving for continuously acquiring images on preset time sequenceAnd obtaining time drift distortion speed fields corresponding to the x direction and the y direction of the image.
S2 according to D obtained in S1d(t) removing drift distortion in advance, and obtaining sparse image pixel position sample C ═ { C) by using shooting standard targetiI 1.. N and corresponding set of intrinsic spatial distortion vector samples L ═ L ·i,i＝1,...,N}。
S3, establishing the relation between the pixel coordinate u of any pixel point of the image plane and the inherent distortion vector l corresponding to the pixel point, and further calculating to obtain the imaged space inherent distortion model Df；
S4: resolving a space inherent distortion model matrix D by using the sparse position information obtained in S2 and the corresponding inherent space distortion vector sample setfObtaining a full-field inherent distortion model D of the scanning electron microscopef(u), then, the drift distortion model D obtained in S1 is combinedd(t) distortion correcting the image.
Further, in step S1, the time drift distortion velocity field v obtained in the x direction and the y direction of the image is solved by using the images continuously acquired in the preset time sequencex,vyThe specific process is as follows:
setting a first image of continuously acquired images as a reference image, setting the total number of shot images as K, performing feature matching on a subsequent (K-1) image and the reference image by utilizing a digital image correlation and scale invariant operator feature point extraction algorithm, and obtaining a matching set phi ═ phi [ [ phi ] ]iAnd i is 2.. K }, and then obtaining a set of displacement vectors U in the x direction and the y direction of the image, i is { U ═ U ·i,i＝2,...K}，V＝{ViK, and a corresponding set of image capturing times T ═ T ·i,i＝1,...,K}，TiWhich indicates the time at which the reference image was taken,
the time-shifted distortion velocity field v corresponding to the x-direction and the y-direction of the imagex,vyCan be obtained by the following method:
Figure BDA0001404258890000051
Figure BDA0001404258890000052
where num (Φ) represents the number of points of the feature matching set.
Further, in step S3, a relationship between (x, y) and the inherent distortion vector l corresponding to any pixel point of the image plane is established, and the inherent distortion model D of the image is estimated and obtainedfThe specific process is as follows:
the relationship between the inherent distortion vector l and the pixel coordinate u is expressed by adopting a radial basis operator, specifically, two parameters of the inherent distortion vector l in an image coordinate system are respectively expressed by the radial basis operator taking the pixel coordinate u as a variable element as follows:
l＝(l1,l2)＝(s1(u),s2(u))
wherein (l)1,l2) Two parameters(s) representing the intrinsic distortion vector l in the image coordinate system1(u),s2(u)) represents said two parameters expressed using radial basis operators, wherein for(s)1(u),s2(u)) an operator s (u) expressed as follows:
Figure BDA0001404258890000061
wherein, C ═ { C ═ CiN is the sample of the pixel position of the sparse image selected in step S2, ciRepresenting the known pixel position of the sparse image, N representing the number of sample points, | | |. | the 2 norm of the vector, phi being the kernel function of the radial basis operator, a0,auAnd w1,w2,…,wNAll radial basis operators are to be evaluated for(s)1(u),s2(u)) one operator in the expression s (u) in matrix form:
Figure BDA0001404258890000062
wherein, the radial base operatorThe coefficient a is (a)0,au) And w ═ w1,w2,…,wN) The combination is represented as hwaCalled the combining coefficient, Mφ(u)＝[φ(||u-c1||),φ(||u-c2||),...,φ(||u-cN||)]Denotes a kernel function matrix, p (u) ═ 1 u1u2) Wherein u is1,u2Two vector coordinate values being pixel coordinates u,
then, two parameters of the inherent distortion vector l corresponding to the coordinate u of one pixel point on the image plane can be expressed as:
Figure BDA0001404258890000063
then, the estimation can be expressed as:
Figure BDA0001404258890000064
wherein the content of the first and second substances,
Figure BDA0001404258890000065
the matrix to be solved for the intrinsic distortion provided for the space of the present invention, called the spatial intrinsic distortion matrix,
then, for a given sparse image pixel location sample C ═ Ci1, 1.., N }, matrix DfAnd a predetermined kernel function matrix Mφ(u), the inherent distortion vector l corresponding to the coordinate u of a pixel point on the image plane can be expressed as:
l＝(s1(u),s2(u))＝(Mφ(u)p(u))Df。
further, the spatial inherent distortion matrix D is solved in step S4fThe specific process is as follows:
the sparse image pixel position sample C ═ { C ═ C selected by shooting the micro-scale target in step S2iAnd calculating a corresponding inherent spatial distortion vector sample set L { L } by using the imaging characteristic that the central distortion of the image is smalli,i＝1,...,N}。
Then, for a known sparse image pixel location ciAnd its corresponding inherent spatial distortioni＝(lix,liy) The following can be obtained:
Figure BDA0001404258890000071
for the entire collected data sample, with N sets of corresponding points, the above equation can be written as:
Figure BDA0001404258890000072
wherein the content of the first and second substances,
Figure BDA0001404258890000073
the self-properties of the radial basis factors may be constrained as follows:
Figure BDA0001404258890000074
wherein, ci(col),ci(row)Respectively representing sparse image pixel locations ciThe abscissa and ordinate index values.
Combining the above two formulas to obtain:
Figure BDA0001404258890000075
wherein, P ═ P (c)1) … p(cN)],Lx＝[l1x… lNx]T,Ly＝[l1y… lNy]T，
The space inherent distortion matrix D can be solved by carrying out least square solution on the formulaf。
The invention provides a distortion correction method for scanning electron microscope images, which is based on the continuity principle of SEM distortion fields on time sequences and space sequences and respectively establishes the mapping relation between time drift distortion and image acquisition time; for the mapping relationship between the spatial inherent distortion and the image pixel position. On the basis, an SEM distortion model is established and the distorted image is corrected.
In general, compared with the prior art, the above technical solution contemplated by the present invention can achieve the following beneficial effects:
compared with the traditional parametric distortion model (barrel distortion, pincushion distortion and the like), the method has stronger universality, and is more effective particularly on the irregular distortion of the SEM; meanwhile, the influence of time drift distortion and space inherent distortion on SEM image distortion is considered, and mapping relations between the time drift distortion and image acquisition time are respectively established; aiming at the mapping relation between the inherent distortion of the space and the pixel position of the image, the problems that SEM distortion correction is difficult, measurement is inaccurate and the like is not beneficial to application are solved, the combination of the SEM and a strain measurement method (such as a microscopic moire and moire interference technology, a digital image correlation technology and the like) under a part of macro scale becomes reality, and an implementable path is provided for deformation analysis of materials and structures under the micro-nano scale.
Drawings
FIG. 1 is a flowchart illustrating image distortion correction in a Scanning Electron Microscope (SEM) according to an embodiment of the present invention;
FIG. 2is an artificially prepared speckle plane target for modeling time drift distortion provided by an embodiment of the invention;
fig. 3 is a standard planar target for modeling spatial intrinsic distortion provided by an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
Fig. 1 is a flowchart of image distortion correction for a Scanning Electron Microscope (SEM), according to an embodiment of the present invention, which includes the following specific steps:
first, in a predetermined time sequence (T ═ T)iI 1.., K), K, and one image is set as a reference image. This sequence of images is typically images with more features, such as a natural or artificially fabricated speckle-plane target sample. Fig. 2 shows an artificially prepared speckle planar target used in the present invention.
Secondly, performing feature matching on the subsequent K-1 images and the reference image by using feature point extraction algorithms such as Digital Image Correlation (DIC) and scale invariant operator (SIFT), performing feature extraction and matching by using a digital image correlation algorithm to obtain a denser matching set phi ═ phi { [ phi ]iAnd i is 2, K, and a set of displacement vectors U is { U) in the X direction and Y direction of the image obtained from the matching relationshipi,i＝2,...K}，V＝{ViK and their corresponding image capturing time sets T ═ T · 2i,i＝1,...,K}。
The time-shifted distortion velocity field v corresponding to the X-direction and the Y-direction of the imagex,vyCan be obtained by the following method:
Figure BDA0001404258890000091
Figure BDA0001404258890000092
where num (Φ) represents the number of points of the feature matching set.
A third step of distorting the velocity field v according to the time drift obtained in the second stepx,vyEstablishing a time drift distortion model Dd(t) wherein the model Dd(t) the following:
Dd(t)＝[dx(t),dy(t)]；
dx(t)＝vxt；
dy(t)＝vyy；
wherein d isx(t),dy(t) is a time drift distortion value corresponding to the image t in the X direction and the Y direction of the image at the time of image acquisition, vx,vyAnd solving the obtained time drift distortion speed fields corresponding to the X direction and the Y direction of the image for continuously acquiring the image on a preset time sequence.
Fourthly, shooting the standard target shown in the figure 3, modeling and correcting the time drift distortion by using the time drift distortion model in the third step, and obtaining a sparse image pixel position sample C ═ C by extracting the center of a circle in the targetiAnd calculating a corresponding inherent spatial distortion vector sample set L { L } by using the imaging characteristic that the central distortion of the image is smalli,i＝1,...,N}。
Fifthly, establishing the relation between the pixel coordinate u of any pixel point of the image plane (x, y) and the inherent distortion vector l corresponding to the pixel point, and further calculating to obtain the imaged space inherent distortion model Df。
The inherent spatial distortion D provided by the inventionfThe modeling method comprises the following steps:
the relationship between the inherent distortion vector l and the pixel coordinate u is expressed by adopting a radial basis operator, specifically, two parameters of the inherent distortion vector l in an image coordinate system are respectively expressed by the radial basis operator taking the pixel coordinate u as a variable element as follows:
l＝(l1,l2)＝(s1(u),s2(u))
wherein (l)1,l2) Two parameters(s) representing the intrinsic distortion vector l in the image coordinate system1(u),s2(u)) represents said two parameters expressed using radial basis operators, wherein for(s)1(u),s2(u)) an operator s (u) expressed as follows:
Figure BDA0001404258890000101
wherein, C ═ { C ═ CiN is the sample of the pixel positions of the sparse image selected in step S2, where N represents the number of sample points. | | to | vectorIs the kernel function of the radial basis operator, a0,auAnd w1,w2,…,wNAll radial basis operators are to be evaluated for(s)1(u),s2(u)) one operator in the expression s (u) in matrix form:
Figure BDA0001404258890000111
wherein, the radial base operator is to obtain a coefficient a ═ (a)0,au) And w ═ w1,w2,…,wN) The combination is represented as hwaCalled the combining coefficient, Mφ(u)＝[φ(||u-c1||),φ(||u-c2||),...,φ(||u-cN||)]Denotes a kernel function matrix, p (u) ═ 1 u1u2) In u1,u2Two vector coordinate values being pixel coordinates u,
then, two parameters of the inherent distortion vector l corresponding to the coordinate u of one pixel point on the image plane can be expressed as:
Figure BDA0001404258890000112
then, the estimation can be expressed as:
Figure BDA0001404258890000113
wherein the content of the first and second substances,
Figure BDA0001404258890000114
the matrix to be solved for the spatial inherent distortion provided by the invention is called as a spatial inherent distortion matrix.
Solving the spatial inherent distortion matrix DfThe specific process is as follows:
according to the sparse image pixel position sample C ═ { C) selected by shooting the micro-scale target in the fourth stepiI 1.. N } and a corresponding set of intrinsic spatial distortion vector samples L ═ L ·i,i＝1,...,N}。
Then, for a known sparse image pixel location ciAnd its corresponding inherent spatial distortioni＝(lix,liy) The following can be obtained:
Figure BDA0001404258890000115
for the entire collected data sample, with N sets of corresponding points, the above equation can be written as:
Figure BDA0001404258890000121
wherein the content of the first and second substances,
Figure BDA0001404258890000122
the characteristics of the radial basis factor may be constrained as follows:
Figure BDA0001404258890000123
wherein, ci(col),ci(row)Respectively representing sparse image pixel locations ciThe abscissa and ordinate index values.
Combining the above two formulas to obtain:
Figure BDA0001404258890000124
wherein, P ═ P (c)1) … p(cN)],Lx＝[l1x… lNx]T,Ly＝[l1y… lNy]T. The least square solution is carried out on the equation to solve the space inherent distortion matrix Df。
The invention provides a distortion correction method for scanning electron microscope images, which is based on the continuity principle of SEM distortion fields on time sequences and space sequences and respectively establishes the mapping relation between time drift distortion and image acquisition time; for the mapping relationship between the spatial inherent distortion and the image pixel position. On the basis, an SEM distortion model is established and the distorted image is corrected.
The method is based on the principle of continuous change between drift distortion and acquisition time of the scanning electron microscope and the principle of continuous change between inherent distortion and image pixel positions, distortion modeling and correction are respectively carried out on two main distortion fields of the scanning electron microscope image, and the method can be applied to actual engineering.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (1)

1. An image distortion correction method for a scanning electron microscope, comprising the steps of:
s1: continuously acquiring images in a predetermined time sequence to establish a time-drift distortion DdRelation D with image acquisition time td(t) time-drift distortion removal for subsequent steps, time-drift distortion model Dd(t) the following:
Dd(t)＝[dx(t),dy(t)]；
dx(t)＝vxt；
dy(t)＝vyy；
wherein d isx(t),dy(t) is the time drift distortion value corresponding to the image t in the x-direction and y-direction of the image at the time of image acquisition, vx,vyIn order to solve the time drift distortion velocity field corresponding to the x direction and the y direction of the image obtained by continuously acquiring the images on the preset time sequence,
s2: from the time-drift distortion model D obtained in S1d(t) removing drift distortion in advance, and obtaining sparse image pixel position sample C ═ { C) by shooting standard targetiI 1.. N and corresponding set of intrinsic spatial distortion vector samples L ═ L ·i,i＝1,...,N}，
S3: establishing a relation between a pixel coordinate u ═ of (x, y) of any pixel point of an image plane and an inherent distortion vector l corresponding to the pixel point, and further calculating to obtain an imaged space inherent distortion model matrix Df，
S4: calculating a space intrinsic distortion model matrix D by using the sparse image pixel position sample obtained in S2 and the corresponding intrinsic space distortion vector sample setfFurther obtain the full-field inherent distortion model D of the scanning electron microscopef(u)，
Finally, the drift distortion model D obtained in S1 is combinedd(t) distortion correcting the image,
in step S1, the time drift distortion velocity field v obtained in the x direction and the y direction of the image is solved by using the images continuously acquired in the preset time sequencex,vyThe specific process is as follows:
setting a first image of continuously acquired images as a reference image, setting the total number of shot images as K, performing feature matching on a subsequent (K-1) image and the reference image by utilizing a digital image correlation and scale invariant operator feature point extraction algorithm, and obtaining a matching set phi ═ phi [ [ phi ] ]iAnd i is 2.. K }, and then obtaining a set of displacement vectors U in the x direction and the y direction of the image, i is { U ═ U ·i,i＝2,...K}，V＝{ViK, and a corresponding set of image capturing times T ═ T ·i,i＝1,...,K}，TiWhich indicates the time at which the reference image was taken,
the time-shifted distortion velocity field v corresponding to the x-direction and the y-direction of the imagex,vyCan be obtained by the following method:
Figure FDA0002355020360000021
Figure FDA0002355020360000022
where num (Φ) represents the number of points of the feature matching set,
in step S3, an arbitrary image plane is createdThe pixel coordinate u of a pixel point is (x, y) and the relation between the inherent distortion vector l corresponding to the pixel point, and then the inherent distortion model D of the imaging is calculated and obtainedfThe specific process is as follows:
the relationship between the inherent distortion vector l and the pixel coordinate u is expressed by adopting a radial basis operator, specifically, two parameters of the inherent distortion vector l in an image coordinate system are respectively expressed by the radial basis operator taking the pixel coordinate u as a variable element as follows:
l＝(l1,l2)＝(s1(u),s2(u))
wherein (l)1,l2) Two parameters(s) representing the intrinsic distortion vector l in the image coordinate system1(u),s2(u)) represents said two parameters expressed using radial basis operators, wherein for(s)1(u),s2(u)) an operator s (u) expressed as follows:
Figure FDA0002355020360000031
wherein, C ═ { C ═ CiN is the sample of the pixel position of the sparse image selected in step S2, ciRepresenting the known pixel position of the sparse image, N representing the number of sample points, | | |. | the 2 norm of the vector, phi being the kernel function of the radial basis operator, a0,auAnd w1,w2,…,wNAll the coefficients to be solved are radial basis operators,
for(s)1(u),s2(u)) one operator in the expression s (u) in matrix form:
Figure FDA0002355020360000032
wherein, the radial base operator is to obtain a coefficient a ═ (a)0,au) And w ═ w1,w2,…,wN) The combination is represented as hwaCalled the combining coefficient, Mφ(u)＝[φ(||u-c1||),φ(||u-c2||),...,φ(||u-cN||)]Representing a kernel function matrix，p(u)＝(1 u1u2) Wherein u is1,u2Two vector coordinate values being pixel coordinates u,
then, two parameters of the inherent distortion vector l corresponding to the coordinate u of one pixel point on the image plane can be expressed as:
Figure FDA0002355020360000033
then, the estimation can be expressed as:
Figure FDA0002355020360000041
wherein the content of the first and second substances,
Figure FDA0002355020360000042
in the form of a matrix of spatially inherent distortions,
step S4 of solving a spatial inherent distortion matrix DfThe specific process is as follows:
the sparse image pixel position sample C ═ { C ═ C selected by shooting the standard target in step S2iAnd calculating a corresponding intrinsic spatial distortion vector sample set L { L } by using the imaging attribute with small image center distortioni,i＝1,...,N}，
Then, for a known sparse image pixel location ciAnd its corresponding inherent spatial distortion vector li＝(lix,liy) The following can be obtained:
Figure FDA0002355020360000043
for the entire collected data sample, with N sets of corresponding points, the above equation can be written as:
Figure FDA0002355020360000044
wherein the content of the first and second substances,
Figure FDA0002355020360000045
the self-properties of the radial basis factors may be constrained as follows:
Figure FDA0002355020360000051
wherein, ci(col),ci(row)Respectively representing sparse image pixel locations ciThe abscissa and ordinate index values of (a),
combining the above two formulas to obtain:
Figure FDA0002355020360000052
wherein, P ═ P (c)1)…p(cN)],Lx＝[l1x…lNx]T,Ly＝[l1y…lNy]TAnd solving the space inherent distortion matrix D by carrying out least square solution on the formulaf。
CN201710812587.XA 2017-09-11 2017-09-11 Image distortion correction method of scanning electron microscope Active CN107590787B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201710812587.XA CN107590787B (en) 2017-09-11 2017-09-11 Image distortion correction method of scanning electron microscope

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201710812587.XA CN107590787B (en) 2017-09-11 2017-09-11 Image distortion correction method of scanning electron microscope

Publications (2)

Publication Number Publication Date
CN107590787A CN107590787A (en) 2018-01-16
CN107590787B true CN107590787B (en) 2020-06-02

Family

ID=61051403

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201710812587.XA Active CN107590787B (en) 2017-09-11 2017-09-11 Image distortion correction method of scanning electron microscope

Country Status (1)

Country Link
CN (1) CN107590787B (en)

Families Citing this family (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111024739B (en) * 2019-12-31 2023-03-21 长江存储科技有限责任公司 Characterization method and characterization device for image distortion of transmission electron microscope
CN112697062A (en) * 2021-01-26 2021-04-23 湖南北斗微芯数据科技有限公司 Railway roadbed deformation monitoring system and method
CN113331809B (en) * 2021-05-20 2023-02-14 浙江大学 Method and device for imaging three-dimensional blood flow in cavity based on MEMS micro galvanometer

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106815871B (en) * 2016-12-26 2019-12-17 华中科技大学 Modeling method of scanning electron microscope imaging system

Also Published As

Publication number Publication date
CN107590787A (en) 2018-01-16

Similar Documents

Publication Publication Date Title
Sutton et al. Scanning electron microscopy for quantitative small and large deformation measurements part II: experimental validation for magnifications from 200 to 10,000
CN107590787B (en) Image distortion correction method of scanning electron microscope
Li et al. Full-field thermal deformation measurements in a scanning electron microscope by 2D digital image correlation
US10885647B2 (en) Estimation of electromechanical quantities by means of digital images and model-based filtering techniques
Chen et al. Two-step digital image correlation for micro-region measurement
Lord et al. A good practice guide for measuring residual stresses using FIB-DIC
Wang et al. A vision-based fully-automatic calibration method for hand-eye serial robot
CN111127613A (en) Scanning electron microscope-based image sequence three-dimensional reconstruction method and system
CN106815871B (en) Modeling method of scanning electron microscope imaging system
Chen et al. Digital image correlation of SEM images for surface deformation of CMOS IC
Moretti et al. Assessment of surface topography modifications through feature-based registration of areal topography data
Rodriguez et al. Optical analysis of strength tests based on block‐matching techniques
CN114078114A (en) Method and system for generating calibration data for wafer analysis
CN112525085A (en) Node displacement and strain measurement method based on triangular gridding image technology
Miyamoto et al. Bootstrapping de-shadowing and self-calibration for scanning electron microscope photometric stereo
CN108983702B (en) Computer microscopic visual slice scanning technology-based microscopic visual field digital extension method and system for microscopic visual system
Cui et al. Scanning electron microscope calibration using a multi-image non-linear minimization process
Gu et al. Non-uniform illumination correction based on the retinex theory in digital image correlation measurement method
Liu et al. Calibration of a stereo microscope based on non-coplanar feature points with iteratively weighted radial alignment constraint
Lu et al. High-efficiency and high-accuracy digital speckle correlation for full-field image deformation measurement
US8989511B1 (en) Methods for correcting for thermal drift in microscopy images
Wang et al. Space quantization between the object and image spaces of a microscopic stereovision system with a stereo light microscope
Li et al. Application of adaptive Monte Carlo method to evaluate pose uncertainty in monocular vision system
Li et al. Study of natural patterns on digital image correlation using simulation method
CN109579731B (en) Method for performing three-dimensional surface topography measurement based on image fusion

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant