Signal Processing Tools for Electron Microscopy

62 Pages·2017·0.7 MB·English

Digital Comprehensive Summaries of Uppsala Dissertations
from the Faculty of Science and Technology 1672
Signal Processing Tools for
Electron Microscopy
JAKOB SPIEGELBERG
ACTA
UNIVERSITATIS
ISSN 1651-6214
UPSALIENSIS
ISBN 978-91-513-0345-1
UPPSALA
urn:nbn:se:uu:diva-348264
2018
Dissertation presented at Uppsala University to be publicly examined in Å2001,
Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, Tuesday, 12 June 2018 at 09:00 for
the degree of Doctor of Philosophy. The examination will be conducted in English. Faculty
examiner: Professor Johan Verbeeck (EMAT, University of Antwerp).
Abstract
Spiegelberg, J. 2018. Signal Processing Tools for Electron Microscopy. Digital
Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and
Technology 1672. 60 pp. Uppsala: Acta Universitatis Upsaliensis. ISBN 978-91-513-0345-1.
The detection of weak signals in noisy data is a problem which occurs across various disciplines.
Here, the signal of interest is the spectral signature of the electron magnetic chiral dichroism
(EMCD) effect. In principle, EMCD allows for the measurement of local magnetic structures in
the electron microscope, its spatial resolution, versatility and low hardware requirements giving
it an eminent position among competing measurement techniques. However, experimental
shortcomings as well as intrinsically low signal to noise ratio render its measurement challenging
to the present day.
This thesis explores how posterior data processing may aid the analysis of various data
from the electron microscope. Following a brief introduction to different signals arising in
the microscope and a yet briefer survey of the state of the art of EMCD measurements, noise
removal strategies are presented. Afterwards, gears are shifted to discuss the separation of
mixed signals into their physically meaningful source components based on their assumed
mathematical characteristics, so called blind source separation (BSS).
A data processing workflow for detecting weak signals in noisy spectra is derived from these
considerations, ultimately culminating in several demonstrations of the extraction of EMCD
signals. While the focus of the thesis does lie on data processing strategies for EMCD detection,
the approaches presented here are similarly applicable in other situations. Related topics such
as the general analysis of hyperspectral images using BSS methods or the fast analysis of large
data sets are also discussed.
Jakob Spiegelberg, Department of Physics and Astronomy, Materials Theory, Box 516,
Uppsala University, SE-751 20 Uppsala, Sweden.
© Jakob Spiegelberg 2018
ISSN 1651-6214
ISBN 978-91-513-0345-1
urn:nbn:se:uu:diva-348264 (http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-348264)
ThereisaT-rexinthisthesis!

List of papers
Thisthesisisbasedonthefollowingpapers,whicharereferredtointhetext
bytheirRomannumerals.
I Detectingmagneticorderingwithatomicsizeelectronprobes
J.C.Idrobo,J.Rusz,J.Spiegelberg,M.A.McGuire,C.T.Symons,R.
R.Vatsavai,C.CantoniandA.R.Lupini
Adv. Struct. Chem. Imag. 2,5(2016).
II Magneticmeasurementswithatomic-planeresolution
J.Rusz,S.Muto,J.Spiegelberg,R.Adam,K.Tatsumi,D.E.Bürgler,
P.M.OppeneerandC.M.Schneider
NatureCommunications7,12672(2016).
III CanweusePCAtodetectsmallsignalsinnoisydata?
J.SpiegelbergandJ.Rusz
Ultramicroscopy172,40-46(2017).
IV AnalysisofElectronEnergyLossSpectroscopyDatausing
GeometricExtractionMethods
J.Spiegelberg,J.Rusz,T.ThersleffandK.Pelckmans
Ultramicroscopy174,14-26(2017).
V TensorDecompositionsfortheAnalysisofAtomicResolution
ElectronEnergyLossSpectra
J.Spiegelberg,J.RuszandK.Pelckmans
Ultramicroscopy175,36-45(2017).
VI Localizationofmagneticcirculardichroicspectraintransmission
electronmicroscopyexperimentswithatomicplaneresolution
J.Rusz,J.Spiegelberg,S.Muto,T.Thersleff,K.Tatsumi,M.Ohtsuka,
K.LeiferandP.M.Oppeneer
Phys. Rev. B95,174412(2017).
VII Towardssub-nanometerreal-spaceobservationofspinandorbital
magnetismattheFe/MgOinterface
T.Thersleff,S.Muto,M.Werwin´ski,J.Spiegelberg,Y.Kvashnin,B.
Hjörvarsson,O.Eriksson,J.RuszandK.Leifer,
ScientificReports7,44802(2017).
VIII Theusageofdatacompressionforthebackgroundestimationof
electronenergylossspectra
J.Spiegelberg,J.Rusz,K.LeiferandT.Thersleff
Ultramicroscopy181,117-122(2017).
IX Fullynon-localinelasticscatteringcomputationsforspetroscopical
TEMmethods
J.Rusz,A.Lubk,J.SpiegelbergandD.Tyutyunnikov
Phys. Rev. B96,245121(2017).
X UnmixingHyperspectralDatabyusingSignalSubspaceSampling
J.Spiegelberg,S.Muto,M.Ohtsuka,K.PelckmansandJ.Rusz
Ultramicroscopy182,205-211(2017).
XI Locallowrankdenoisingforenhancedatomicresolutionimaging
J.Spiegelberg,J.C.Idrobo,A.Herklotz,T.Z.Ward,W.ZhouandJ.
Rusz
Ultramicroscopy187,34-42(2018).
XII OntheusageofICAfortheanalysisofEELSandEDXdata
J.Spiegelberg
Ultramicroscopy,submitted.
XIII LowdoseSTEMimagingviainpaintingofregularlyundersampled
images
J.Spiegelberg,J.Hachtel,J.C.IdroboandJ.Rusz
ScientificReports,submitted.
XIV Realspacemappingofmagnetismatatomicresolutionusing
APR-EMCD
J.Spiegelberg,S.Muto,M.Ohtsuka,andJ.Rusz
Microscopy,submitted.
XV Blindidentificationofmagneticsignalsinelectronmagneticchiral
dichroismusingindependentcomponentanalysis
J.Spiegelberg,D.Song,R.E.Dunin-Borkowski,J.Zhu,andJ.Rusz
Ultramicroscopy,submitted.
XVI Datafusionapproachesforelectronmicroscopy
J.Spiegelberg,Y.Yamamoto,S.Muto,M.Ohtsuka,andJ.Rusz
Ultramicroscopy,submitted.
Papersthatwere(co-)authoredbyme,butarenotincludedinthis
thesis:
XVII Validityoftherotatingwaveapproximationinnonadiabatic
holonomicquantumcomputation
J.SpiegelbergandE.Sjökvist
Phys. Rev. A88,054301(2013).
XVIII Amultislicetheoryofelectronscatteringincrystalsincluding
backscatteringandinelasticeffects
J.SpiegelbergandJ.Rusz
Ultramicroscopy159,11-18(2015).
Reprintsweremadewithpermissionfromthepublishers.

Contents
1 Introduction 11
................................................................................................
2 Signalsintheelectronmicroscope 13
...........................................................
2.1 Thespectraltrinity 14
.........................................................................
2.1.1 Cathodoluminescence 14
.....................................................
2.1.2 EnergydispersiveX-rayspectroscopy 14
...........................
2.1.3 Electronenergylossspectroscopy 15
..................................
2.2 Theholygrail 17
.................................................................................
2.2.1 BrieftheoreticalbackgroundofEMCD 17
.........................
2.2.2 Surveyofexperimentsettings 19
.........................................
2.3 Apocryphalsignals 21
.........................................................................
3 Aselectionofdataprocessingtoolsforamicroscopist 22
..........................
3.1 Noiseremovalapproaches 22
.............................................................
3.1.1 PrincipalComponentAnalysis 23
.......................................
3.1.2 Imagedenoising 25
...............................................................
3.2 MatrixfactorizationsI-ICAandNMF 25
........................................
3.2.1 IndependentComponentAnalysis 26
..................................
3.2.2 Non-negativeMatrixFactorization 27
.................................
3.3 MatrixfactorizationsII-usinggeometry 28
.....................................
3.3.1 Findingpurepixels 28
..........................................................
3.3.2 Estimatingpurepixels 29
.....................................................
3.4 MatrixfactorizationsIII-beyondmatrices 30
..................................
3.4.1 Tensorfactorizations 31
.......................................................
3.4.2 Coupledfactorizations 34
....................................................
4 Lookingfortheholygrail 36
.........................................................................
4.1 Findingsignalsinnoisyhyperspectralimages 36
.............................
4.1.1 DetectingsignalswithPCA 36
............................................
4.1.2 MappingsignalswithMLSVDandLLR 38
.......................
4.2 LearninghowtofindEMCD 39
.........................................................
4.2.1 GeometricblindsourceseparationforEMCD 40
..............
4.2.2 EMCDandICA 41
...............................................................
4.2.3 ExtractingEMCDstraightfromthetensor 41
....................
4.3 FindingEMCD 42
...............................................................................
4.3.1 EMCDwithabberatedprobes 42
........................................
4.3.2 APR-EMCD 42
.....................................................................
4.3.3 EFTEM-EMCD 43
...............................................................
4.3.4 DD-EMCD 43
.......................................................................
4.4 WhathasbeenlearnedfromthequestforEMCD 43
.......................
4.4.1 Afasterwayoffindingpurepixels 44
................................
4.4.2 Analysisofcompressedsignals 45
......................................
4.4.3 Exploringthesignalsubspace 45
........................................
4.4.4 Unmixinghyperspectraldatabyexploitingspatial
periodicity 46
........................................................................
4.4.5 Inpaintinginsteadofdenoising 47
.......................................
5 Conclusions 50
................................................................................................
6 Sammanfattningpåsvenska 51
......................................................................
7 Acknowledgements 52
...................................................................................
References 53
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