research article resolution improvement in stage-scanning...

Hindawi Publishing CorporationISRN NanotechnologyVolume 2013 Article ID 368671 5 pageshttpdxdoiorg1011552013368671

Research ArticleResolution Improvement in Stage-ScanningElectron Holography Comparison with ConventionalElectron Holography

Dan Lei1 Kazutaka Mitsuishi2 Ken Harada3 Masayuki Shimojo4

Dongying Ju1 and Masaki Takeguchi5

1 Department of Materials Science and Engineering Saitama Institute of Technology 1690 Fusaiji FukayaSaitama 369-0293 Japan

2 Surface Physics and Structure Unit National Institute for Materials Science 3-13 Sakura Tsukuba 305-0003 Japan3 Advanced Measurement and Analysis Center Central Research Laboratory Hitachi Ltd Hatoyama Saitama 350-0395 Japan4Department of Materials Science and Engineering Shibaura Institute of Technology 3-7-5 Toyosu Koto-kuTokyo 135-8548 Japan

5 Transmission Electron Microscopy Station National Institute for Materials Science 3-13 Sakura Tsukuba 305-0003 Japan

Correspondence should be addressed to Dan Lei leidannimsgojp

Received 13 May 2013 Accepted 26 June 2013

Academic Editors I-C Chen C Malagu and B Pignataro

Copyright copy 2013 Dan Lei et al This is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Electron holography provides information on the phase and amplitude of electron wave passing through a specimen The recentlyproposed stage-scanning electron holography technique should improve the spatial resolution of phase and amplitude imagescompared to the conventional electron holography based on the Fourier transformation method To demonstrate the resolutionimprovement cobalt nanoparticles were observed using the stage-scanning holography and the conventional holography andsignificantly sharper images were obtained with the former technique

1 Introduction

Electron holography [1ndash3] is a transmission electronmicroscopy (TEM) technique that uses a biprism to mix anobject wave passing through a specimen with the referencewave passing through vacuum Interaction of the twowaves produces a pattern containing interference fringesIn contrast to conventional TEM techniques which onlyrecord the spatial distribution of image intensity electronholography yields information on both the phase andamplitude of the object wave through reconstruction of theinterference pattern or hologram The phase distributioncan then be used to provide information about the magneticand electrostatic fields in the specimen

To obtain information on the phase and amplitude areconstruction process is necessary such as the Fourier trans-formation method [4 5] in which the electron hologramis Fourier-transformed and then its selected sideband is

inversely Fourier-transformed In this approach the spatialresolution of the reconstructed phase image is limited bythe fringe spacing in the hologram [6ndash10] This spacingdetermines the separation of center band and side bandin Fourier space and thus the resolution of resultant phaseand amplitude images However the use of small fringespacing aiming for higher resolution results in a lowerfringe contrast and signal-to-noise ratio Many efforts havebeen spent to overcome this difficulty For example Ruet al [6 7] developed a phase-shifting electron holographytechnique where the incident beam is tilted to obtain aseries of holograms with different initial phases With thismethod the object wave passing through the specimen canbe determined independently of the fringe spacing withoutrequiring Fourier transformation

We presented an electron holography technique using astage-scanning system [11] In this method line intensitiesare acquired from a series of holograms recorded at different

2 ISRN Nanotechnology

Electron beam

Specimen

Biprism

Hologram

piezo actuatorXYZ-driving

y

x

Figure 1 Schematic of electron holography using a stage-scanningspecimen holder

specimen positions and an interferogram that correspondsto the phase distribution can be obtained directly withoutcomplicated reconstruction such as Fourier transformationWe further improved this method by recording a series ofholograms as a 3-dimensional (3D) data cube at differentspecimen positions [12] Slicing the 3D data cube at differentCCD pixels produces several interferograms By applying theproposed reconstruction procedure to these interferogramsthe phase distribution can be reconstructed with high preci-sionThis technique is expected to overcome the limitation ofspatial resolution due to the fringe spacing

In this paper we demonstrate the resolution enhance-ment by observing Co nanoparticles with the stage-scanningelectron holography and compare the results with the con-ventional holography based on the Fourier transformationmethod We used a low-magnification mode in which theobjective lens of the microscope is switched off To realizethe electron holography configuration the first intermediatelens is also turned off which limits the choice of magni-fication Therefore it may be difficult to have an appro-priate combination of magnification and fringe spacing forperforming conventional electron holography on specimenswith micrometer-scale features The stage-scanning electronholography technique [12] should solve this problem byovercoming the limitation between the spatial resolution andfringe spacing This flexibility is especially important forobserving magnetic specimens which must be located in alow-field region to avoid unwanted magnetic saturation

2 Experimental Methods

Figure 1 shows the electron optics and instruments usedin the stage-scanning holography To acquire an electron

hologram the region of interest on the specimen should bepositioned to cover half the field of view An electron wave isdivided into two an object wave modulated by the specimenand a reference wave passing through vacuum Applicationof voltage to an electrostatic biprism located below thespecimen results in an overlap of the reference wave and theobject wave and in the appearance of interference fringesThe fringe spacing and the width of the interference regionare determined by the biprism voltage A stage-scanningsystem [13ndash15] which comprises a specially designed holderequippedwith a piezo-driven specimen stage a power supplyand control software was used in this experiment Usingthis stage-scanning system the specimen is moved in a fixedelectron-optics configuration and a series of holograms arerecorded at different specimen positions

The object wave is then reconstructed from the recordedseries of holograms The details of the reconstruction pro-cedure are given in our previous paper [12] and are brieflyrepeated here

When the biprism is oriented along the 119910 direction theelectron hologram is obtained as a result of the interferencebetween the object waveΦ

119900and reference waveΦ

119903as

119868 (119899 119909 119910) =1003816100381610038161003816Φ119900 + Φ119903

10038161003816100381610038162

=10038161003816100381610038161206010 (119909 minus 119899Δ119909 119910)

10038161003816100381610038162

+ 1

+ 21206010(119909 minus 119899Δ119909 119910)

times cos [120578 (119909 minus 119899Δ119909 119910) + 2120587 119909119898]

(1)

Here 119909 and 119910 denote the position in a hologram 1206010and 120578

refer to the amplitude and phase respectively Δ119909 is the scanstep along the 119909 direction 119899 is the index of scan steps and119898refers to the fringe spacingThe recorded series of hologramswith different specimen positions can be viewed as a 3D datacube with the dimensions (119909 119910 Δ119909 sdot 119899)

The reconstruction procedure of the stage-scanningholography consists of three steps formation of interfero-grams by slicing the 3D data cube at different 119909 positionsalignment of the specimen positions on the interferogramsand reconstruction of the object wave

Slicing the cube in the (119910 Δ119909 sdot 119899) plane at 119909 = 119909119896extracts

an interferogram

Π119896(119899 119910) =

10038161003816100381610038161206010 (119909119896 minus 119899Δ119909 119910)10038161003816100381610038162

+ 1

+ 21206010(119909119896minus 119899Δ119909 119910)

times cos [120578 (119909119896minus 119899Δ119909 119910) + 2120587

119909119896

119898]

(2)

where the fringe spacing 119898 is set to be an integer and amultiple of CCD pixel sizes and is divided by119873 Thus 119909

119896can

be expressed as 119909119896= (119898119873)119896 (119896 = 0 1 2 119873 minus 1)

ISRN Nanotechnology 3

The specimen positions are offset on the interferogramswith different119909

119896and are aligned using the following equation

Π1015840

119896(119899 119910) = Π

119896((119899 +

119898

119873Δ119909119896) 119910)

=10038161003816100381610038161206010 (minus119899Δ119909 119910)

10038161003816100381610038162

+ 1

+ 21206010(minus119899Δ119909 119910) cos [120578 (minus119899Δ119909 119910) + 2120587 119896

119873]

(3)

The interferogram Π1015840119896(119899 119910) is the one after alignment

Multiplying (3) by exp(minus2120587119894(119896119873)) and summing bothsides over 119896 yields

119873minus1

sum

119896=0

Π1015840

119896(119899 119910) exp(minus2120587119894 119896

119873)

= 1198731206010(minus119899Δ119909 119910) cos [120578 (minus119899Δ119909 119910)]

+ 1198941198731206010(minus119899Δ119909 119910) sin [120578 (minus119899Δ119909 119910)]

(4)

Then the phase image and amplitude image can be obtainedrespectively as

120578 (minus119899Δ119909 119910) = tanminus1 ( ImRe)

1206010(minus119899Δ119909 119910) =

1

119873

radic(Im)2 + (Re)2(5)

where Im and Re denote the imaginary and real parts of theterm sum119873minus1

119896=0Π1015840

119896(119899 119910) exp(minus2120587119894(119896119873)) in (4) respectively

An important improvement of this technique is thatthe spatial resolution of the reconstructed phase image isdetermined not by the interference fringe spacing but by thescan step and by the microscope resolution or the pixel sizealong the 119910 directionThis is the principal difference from theconventional holography as mentioned in the introductionBecause the Fourier transformation method is unnecessaryto reconstruct the phase coarse fringes with high contrastcan be used which would also be helpful for improving theprecision of the reconstructed phase image

Experiments were carried out in the low-magnificationmode with a JEOL JEM-ARM200F microscope (200 kV)equipped with a biprism and a stage-scanning system Conanoparticles with a diameter of 10ndash20 nm deposited on acarbon film were used as a sample

3 Results and Discussion

Figure 2 shows a bright-field TEM image of Co particlesdispersed on the edge of a carbon film Holograms wereacquired at different specimen positions by moving thespecimen with the stage-scanning system and saved as a3D data cube with dimensions of 155 pixels times 260 pixels times90 steps The total acquisition time was about 1min 40 sincluding data transfer and 1 second exposure for eachscan step Two holograms recorded at different specimen

20nm

Figure 2 TEM image of Co particles

positions and extracted from the 3D data cube are shownin Figures 3(a) and 3(b) In this case the fringe spacingwas 26 nm or 10 pixels which is wider than the diameterof the particles In the extracted holograms (a) and (b) theparticles cannot be distinguished but only the fringe shifton the specimen can be seen We reconstructed the phasedistribution of the particles (Figure 3(c)) using 10 lines ofCCD pixels as a fringe 90 holograms and stage-scanningdistance of 230 nm The Co particles are well distinguishedin Figure 3(c)

Figure 4 shows the line profile across a Co particle indi-cated by the white line in Figure 3(c) The profile shows theshape of the particle with a phase change of about 12 radiansand a diameter of about 155 nm which is close to 141 nmmeasured from the TEM image of Figure 2 Comparing withthe results of the conventional holography shown next theproposed technique yields higher precision in measuring theparticle sizeThe phase change on both sides of the particle isdue to the thickness variation of the carbon film

For comparison the same Co particles were observedwith the conventional holography technique based on theFourier transformation method In this case fine fringespacing was necessary to attain a high resolution Otherwisewindowing the sideband in the Fourier space might induceartifacts in the real space [16] Therefore a fringe spacingof 17 nm was used in the same optical configuration with ahigher biprism voltage which was the finest fringe spacingconsidering the fringe contrast and signal-to-noise ratio ofthe holograms given the limited freedom of magnification inthis experiment Figures 5(a) and 5(b) show the hologramand the phase distribution of the Co particles retrievedvia Fourier transformation respectively It is difficult todistinguish the phase of eachCo particle in this reconstructedphase image because of the low spatial resolution In Fouriertransformation method the size of the selected sidebandregion should be small enough for avoiding the mixture ofthe sideband and the center bandThis requirement limits thenumber of pixels of the reconstructed image and reduces thespatial resolution of the reconstructed image Comparing the


50nm

(a) (b)

50nm

(c)

Figure 3 Two extracted holograms of the Co particles (a) and (b) with a fringe spacing of 26 nm The specimen moved from the positionin hologram (a) to the position in hologram (b) due to the movement of the specimen stage (c) The phase image obtained with the stage-scanning technique

0 20 40 60

minus20

minus15

minus10

minus05

00

05

Phas

e (ra

ds)

Distance (nm)

Figure 4 Profile of phase change of the Co particle indicated by thewhite line in Figure 3(c)

results from these two techniques we conclude that the stage-scanning holography yields higher resolution with a widerfringe spacing than the conventional holography based onthe Fourier transformation method The former techniqueis useful when fine fringes cannot be obtained but a highresolution is needed

The major difference between the stage-scanning holog-raphy and conventional holography based on Fourier trans-formation is the necessity of fine fringe spacing In theconventional holography the fringe spacing should be aboutthree times finer than the desired spatial resolution [6ndash10] Thus many studies focused on decreasing the fringespacing although this will also decrease the fringe contrastIn our stage-scanning holography the spatial resolution isdetermined by the scan step width but not the fringe spacingTherefore we can use awide fringe spacing for reconstructionand then obtain a high-contrast interference pattern Also in

the conventional electron holography method if the speci-men has sharp edges or large phase variations the Fourierspectrum of the specimen will extend widely hampering theseparation of the sidebands from the central band Imperfectseparation will distort the overall area of the reconstructedimage The stage-scanning holography does not suffer fromthis problem

In practice several factors can introduce artifacts intothe reconstructed phase image For example the drift ofthe specimen andor of the biprism may introduce phaseerrors or distortions to the specimen shape These effects canhopefully be reduced in the future by improving the biprismstage and the specimen stage Moreover the stage-scanningsystem is driven by a piezo which results in inconsistent stepsdue to hysteresis effects and in the concomitant errors in thephase calculation

4 Summary

The stage-scanning electron holography allows retrievingphase distribution without Fourier transformation As aresult the spatial resolution can be determined indepen-dently of the fringe spacing of the holograms In this studywe applied the stage-scanning electron holography in a low-magnificationmode to Co particles Higher spatial resolutionwas achieved compared with that of conventional electronholography based on the Fourier transformationmethodThestage-scanning electron holography is thus useful in a low-magnification mode when fine fringes cannot be obtaineddue to the limited TEMmagnification

Acknowledgments

The authors are grateful to Dr Iakoubovskii for proofreadingthe paper Apart of this studywas financially supported by theBudgets for ldquoDevelopment of Environmental Technologies


100nm

(a)

100nm

(b)

Figure 5 Hologram taken with a fine fringe spacing of 17 nm by conventional electron holography (a) and the reconstructed phase image(b) The area within the blue box is the same area that was observed by the stage-scanning holography

Utilizing Nanotechnologyrdquo and ldquothe Low-Carbon ResearchNetwork in Japan (LCnet)rdquo of the Ministry of EducationCulture Sports Science and Technology

References

[1] D Gabor ldquoMicroscopy by reconstructed wave-frontsrdquo Proceed-ings of the Royal Society London vol 197 pp 454ndash487 1949

[2] H Lichte and M Lehmann ldquoElectron holography-basics andapplicationsrdquoReports on Progress in Physics vol 71 no 1 ArticleID 016102 2008

[3] A Tonomura Electron Holography Springer Berlin Germany1993

[4] M Takeda H Ina and S Kobayashi ldquoFourier-transformmethod of fringe-pattern analysis for computer-based tomog-raphy and interferometryrdquo Journal of the Optical Society ofAmerica vol 72 no 1 pp 156ndash160 1982

[5] T Fujita K Yamamoto M R McCartney and D J SmithldquoReconstruction technique for off-axis electron holographyusing coarse fringesrdquo Ultramicroscopy vol 106 no 6 pp 486ndash491 2006

[6] Q Ru J Endo T Tanji and A Tonomura ldquoPhase-shiftingelectron holography by beam tiltingrdquo Applied Physics Lettersvol 59 no 19 pp 2372ndash2374 1991

[7] G Lai Q Ru K Aoyama and A Tonomura ldquoElectron-wave phase-shifting interferometry in transmission electronmicroscopyrdquo Journal of Applied Physics vol 76 no 1 pp 39ndash451994

[8] W J De Ruijter and J KWeiss ldquoDetection limits in quantitativeoff-axis electron holographyrdquoUltramicroscopy vol 50 no 3 pp269ndash283 1993

[9] K Yamamoto T Hirayama and T Tanji ldquoOff-axis electronholography without Fresnel fringesrdquo Ultramicroscopy vol 101no 2ndash4 pp 265ndash269 2004

[10] H Lichte ldquoPerformance limits of electron holographyrdquo Ultra-microscopy vol 108 no 3 pp 256ndash262 2008

[11] D Lei K Mitsuishi K Harada M Shimojo D Y Ju andM Takeguchi ldquoMapping of phase distribution in electron

holography with a stage-scanning systemrdquo Materials ScienceForum vol 750 pp 152ndash155 2013

[12] D Lei K Mitsuishi K Harada M Shimojo D Y Ju andM Takeguchi ldquoDirect acquisition of interferogram by stagescanning in electron interferometryrdquoMicroscopy 2013

[13] M Takeguchi M Shimojo M Tanaka R Che W Zhang andK Furuya ldquoElectron holographic study of the effect of contactresistance of connected nanowires on resistivity measurementrdquoSurface and Interface Analysis vol 38 no 12-13 pp 1628ndash16312006

[14] M Takeguchi A Hashimoto M Shimojo K Mitsuishi andK Furuya ldquoDevelopment of a stage-scanning system for high-resolution confocal STEMrdquo Journal of Electron Microscopy vol57 no 4 pp 123ndash127 2008

[15] M Takeguchi K Mitsuishi D Lei and M Shimojo ldquoDevelop-ment of sample-scanning electron holographyrdquoMicroscopy andMicroanalysis vol 17 supplement 2 pp 1230ndash1231 2011

[16] H Lichte D Geiger A Harscher et al ldquoArtefacts in electronholographyrdquo Ultramicroscopy vol 64 no 1ndash4 pp 67ndash77 1996

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Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research



MetallurgyJournal of


BioMed Research International

MaterialsJournal of


Nano

materials


Journal ofNanomaterials


Electron beam

Specimen

Biprism

Hologram

piezo actuatorXYZ-driving

y

x

Figure 1 Schematic of electron holography using a stage-scanningspecimen holder

specimen positions and an interferogram that correspondsto the phase distribution can be obtained directly withoutcomplicated reconstruction such as Fourier transformationWe further improved this method by recording a series ofholograms as a 3-dimensional (3D) data cube at differentspecimen positions [12] Slicing the 3D data cube at differentCCD pixels produces several interferograms By applying theproposed reconstruction procedure to these interferogramsthe phase distribution can be reconstructed with high preci-sionThis technique is expected to overcome the limitation ofspatial resolution due to the fringe spacing

In this paper we demonstrate the resolution enhance-ment by observing Co nanoparticles with the stage-scanningelectron holography and compare the results with the con-ventional holography based on the Fourier transformationmethod We used a low-magnification mode in which theobjective lens of the microscope is switched off To realizethe electron holography configuration the first intermediatelens is also turned off which limits the choice of magni-fication Therefore it may be difficult to have an appro-priate combination of magnification and fringe spacing forperforming conventional electron holography on specimenswith micrometer-scale features The stage-scanning electronholography technique [12] should solve this problem byovercoming the limitation between the spatial resolution andfringe spacing This flexibility is especially important forobserving magnetic specimens which must be located in alow-field region to avoid unwanted magnetic saturation

2 Experimental Methods

Figure 1 shows the electron optics and instruments usedin the stage-scanning holography To acquire an electron

hologram the region of interest on the specimen should bepositioned to cover half the field of view An electron wave isdivided into two an object wave modulated by the specimenand a reference wave passing through vacuum Applicationof voltage to an electrostatic biprism located below thespecimen results in an overlap of the reference wave and theobject wave and in the appearance of interference fringesThe fringe spacing and the width of the interference regionare determined by the biprism voltage A stage-scanningsystem [13ndash15] which comprises a specially designed holderequippedwith a piezo-driven specimen stage a power supplyand control software was used in this experiment Usingthis stage-scanning system the specimen is moved in a fixedelectron-optics configuration and a series of holograms arerecorded at different specimen positions

The object wave is then reconstructed from the recordedseries of holograms The details of the reconstruction pro-cedure are given in our previous paper [12] and are brieflyrepeated here

When the biprism is oriented along the 119910 direction theelectron hologram is obtained as a result of the interferencebetween the object waveΦ

119900and reference waveΦ

119903as

119868 (119899 119909 119910) =1003816100381610038161003816Φ119900 + Φ119903

10038161003816100381610038162

=10038161003816100381610038161206010 (119909 minus 119899Δ119909 119910)

10038161003816100381610038162

+ 1

+ 21206010(119909 minus 119899Δ119909 119910)

times cos [120578 (119909 minus 119899Δ119909 119910) + 2120587 119909119898]

(1)

Here 119909 and 119910 denote the position in a hologram 1206010and 120578

refer to the amplitude and phase respectively Δ119909 is the scanstep along the 119909 direction 119899 is the index of scan steps and119898refers to the fringe spacingThe recorded series of hologramswith different specimen positions can be viewed as a 3D datacube with the dimensions (119909 119910 Δ119909 sdot 119899)

The reconstruction procedure of the stage-scanningholography consists of three steps formation of interfero-grams by slicing the 3D data cube at different 119909 positionsalignment of the specimen positions on the interferogramsand reconstruction of the object wave

Slicing the cube in the (119910 Δ119909 sdot 119899) plane at 119909 = 119909119896extracts

an interferogram

Π119896(119899 119910) =

10038161003816100381610038161206010 (119909119896 minus 119899Δ119909 119910)10038161003816100381610038162

+ 1

+ 21206010(119909119896minus 119899Δ119909 119910)

times cos [120578 (119909119896minus 119899Δ119909 119910) + 2120587

119909119896

119898]

(2)

where the fringe spacing 119898 is set to be an integer and amultiple of CCD pixel sizes and is divided by119873 Thus 119909

119896can

be expressed as 119909119896= (119898119873)119896 (119896 = 0 1 2 119873 minus 1)




Π1015840

119896(119899 119910) = Π

119896((119899 +

119898

119873Δ119909119896) 119910)

=10038161003816100381610038161206010 (minus119899Δ119909 119910)

10038161003816100381610038162

+ 1


119873]

(3)



119873minus1

sum

119896=0

Π1015840

119896(119899 119910) exp(minus2120587119894 119896

119873)



(4)



1206010(minus119899Δ119909 119910) =

1

119873



119896=0Π1015840






20nm






50nm

(a) (b)

50nm

(c)


0 20 40 60

minus20

minus15

minus10

minus05

00

05

Phas

e (ra

ds)

Distance (nm)






4 Summary


Acknowledgments



100nm

(a)

100nm

(b)



References

























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials






Π1015840

119896(119899 119910) = Π

119896((119899 +

119898

119873Δ119909119896) 119910)

=10038161003816100381610038161206010 (minus119899Δ119909 119910)

10038161003816100381610038162

+ 1


119873]

(3)



119873minus1

sum

119896=0

Π1015840

119896(119899 119910) exp(minus2120587119894 119896

119873)



(4)



1206010(minus119899Δ119909 119910) =

1

119873



119896=0Π1015840






20nm






50nm

(a) (b)

50nm

(c)


0 20 40 60

minus20

minus15

minus10

minus05

00

05

Phas

e (ra

ds)

Distance (nm)






4 Summary


Acknowledgments



100nm

(a)

100nm

(b)



References

























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




50nm

(a) (b)

50nm

(c)


0 20 40 60

minus20

minus15

minus10

minus05

00

05

Phas

e (ra

ds)

Distance (nm)






4 Summary


Acknowledgments



100nm

(a)

100nm

(b)



References

























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




100nm

(a)

100nm

(b)



References

























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials










CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials



research article resolution improvement in stage-scanning...

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