Optical lock-in particle tracking in optical tweezers

0.36 MB·English

by  Michael A Taylor

Optical lock-in particle tracking in
optical tweezers
MichaelATaylor,JoachimKnittelandWarwickPBowen
∗
CentreforEngineeredQuantumSystems,UniversityofQueensland,StLucia,Queensland
4072,Australia
3
[email protected]
1 ∗
0
2
Abstract: We demonstrate a lock-in particle tracking scheme in optical

n tweezersbasedonstroboscopicmodulationofanilluminatingopticalfield.
a
Thisschemeisfoundtoevadelowfrequencynoisesourceswhileotherwise
J
producinganequivalentpositionmeasurementtocontinuousmeasurement.
5
2 This was demonstrated, and found to yield on average 20 dB of noise
suppressioninthefrequencyrange10–5000Hz,wherelowfrequencylaser

] noise andelectronicnoise was significant,and 35 dB of noise suppression
s
c in the range 550–710 kHz where laser relaxation oscillations introduced
i lasernoise.Thesetupissimple,andcompatiblewithanytrappingoptics.
t
p
o © 2013 OpticalSocietyofAmerica
s. OCIScodes:(140.7010)Lasertrapping;(350.4855)Opticaltweezersoropticalmanipulation.
c
i
s
Referencesandlinks
y
h 1. A.AshkinandJ.Dziedzic,“Opticaltrappingandmanipulationofvirusesandbacteria,”Science235,1517–1520
p (1987).
[ 2. M.A.Taylor,J.Knittel,andW.P.Bowen,“Fundamentalconstraintsonparticletrackingwithopticaltweezers,”
arXiv:1208.0657(2012).

1 3. F.GittesandC.F.Schmidt,“Interferencemodelforback-focal-planedisplacementdetectioninopticaltweezers,”
v Opt.Lett. 23,7–9(1998).
5 4. I.Chavez,R.Huang,K.Henderson,E.-L.Florin,andM.G.Raizen,“Developmentofafastposition-sensitive
7 laserbeamdetector,”Rev.Sci.Instrum. 79,105104(2008).
9 5. J.R.Moffitt,Y.R.Chemla,S.B.Smith,andC.Bustamante,“Recentadvancesinopticaltweezers,”Annu.Rev.
5 Biochem.77,205-228(2008).
6. J.T.Finer, R.M.Simmons,andJ.A.Spudich, “Single myosinmolecule mechanics: piconewton forces and
.
1 nanometresteps,”Nature 368,113–119(1994).
0 7. A.Jannasch,A.F.Demiro¨rs,P.D.J.vanOostrum,A.vanBlaaderen, andE.Scha¨ffer, “Nanonewton optical
3 forcetrapemployinganti-reflectioncoated,high-refractive-index titaniamicrospheres,”NaturePhoton.6,469-
1 473(2012).
: 8. K.Svoboda,C.F.Schmidt,B.J.Schnapp,andS.M.Block1993“Direct observation ofkinesinsteppingby
v
opticaltrappinginterferometry,”Nature 365,721–727(1993).
Xi 9. C.Bustamante,Y.R.Chemla,N.R.Forde,andD.Izhaky,“Mechanicalprocessesinbiochemistry,”Annu.Rev.
Biochem.73,705-748(2004).
r 10. C.Bustamante,“UnfoldingsingleRNAmolecules:bridgingthegapbetweenequilibriumandnon-equilibrium
a
statisticalthermodynamics,”Q.Rev.Biophys. 38,291–301(2005).
11. W.J.GreenleafandS.M.Block,“Single-molecule, motion-basedDNAsequencingusingRNApolymerase,”
Science 313,801(2006).
12. P.Kukura,H.Ewers,C.Mu¨ller,A.Renn,A.Helenius,andV.Sandoghdar,“High-speednanoscopictrackingof
thepositionandorientationofasinglevirus,”Nat.Methods6,923–929(2009).
13. M.A.Taylor,J.Janousek,V.Daria,J.Knittel,B.Hage,H.-A.Bachor,andW.P.Bowen,“Biologicalmeasurement
beyondthequantumlimit,”arXiv:1206.6928(2012).
14. S.Yamada, D.Wirtz, andS.C.Kuo,“Mechanics ofliving cells measuredbylasertracking microrheology,”
Biophys.J.78,1736–1747(2000).
15. E.N.SenningandA.H.Marcus,“ActinpolymerizationdrivenmitochondrialtransportinmatingS.cerevisiae,”
Proc.Natl.Acad.Sci.USA 107,721–725(2010).
16. I.M.Tolic´-Nørrelykke,E.-L.Munteanu,G.Thon,L.OddershedeandK.Berg-Sørensen,“Anomalousdiffusion
inlivingyeastcells,”Phys.Rev.Lett. 93,078102(2004).
17. T.Franosch,M.Grimm,M.Belushkin,F.M.Mor,G.Foffi,L.Forro´,andS.Jeney,“Resonancesarisingfrom
hydrodynamicmemoryinBrownianmotion,”Nature 478,85–88(2011).
18. R.Huang,I.ChavezI,K.M.Taute,B.Lukic´,S.Jeney,M.G.Raizen,andE.-L.Florin,“Directobservationof
thefulltransitionfromballistictodiffusiveBrownianmotioninaliquid,”NaturePhys. 7,576-580(2011).
19. D.E. Chang, C. A.Regal, S.B. Papp, D.J. Wilson, J.Ye, O.Painter, H.J. Kimble, and P.Zoller, “Cavity
opto-mechanicsusinganopticallylevitatednanosphere,”Proc.Natl.Acad.Sci.USA 107,1005–1010(2010).
20. T.Li,S.Kheifets,andM.G.Raizen,“Millikelvincoolingofanopticallytrappedmicrosphereinvacuum,”Nature
Phys. 7,527-530(2011).
21. M.A.Taylor,J.Knittel,M.T.L.Hsu,H.-A.Bachor,andW.P.Bowen,“Sagnacinterferometer-enhancedparticle
trackinginopticaltweezers,”J.Opt. 13,044014(2011).
22. J.W.Tay,M.T.L.Hsu,andW.P.Bowen,“Quantumlimitedparticlesensinginopticaltweezers,”Phys.Rev.A
80063806(2009).
23. P.KweeandB.Willke,“Automaticlaserbeamcharacterization ofmonolithicNd:YAGnonplanarringlasers,”
Appl.Opt.476022–6032(2008)
1. Introduction
In optical tweezers, small particlesare trapped by the electric field gradientat the focusof a
tightlyfocusedlaserbeam[1].Afterthelightinteractswiththeparticle,itencodesinformation
abouttheparticleposition[2],whichistypicallyextractedwithaquadrantdetectorattheback-
focalplaneofacondenserlens[3].Thisallowsparticletrackingwithsub-nanometersensitiv-
ity[4]asforcesrangingfromsubpiconewton[5,6]tonanonewton[7]arecontrollablyapplied.
Suchexperimentshaveuncoveredimportantphenomenainbiophysics,includingboththedy-
namics and magnitudeof the forcesapplied by biologicalmotors [6,8,9], the stretching and
foldingpropertiesofDNAandRNA[9–11],thedynamicsofvirus-hostcoupling[12],thestrain
onanenzymeduringcatalysis[9],andtherheologicalpropertiesofcellularcytoplasm[13–16].
Furthermore,opticaltweezersprovidea significanttoolforstudyingthefundamentalphysics
ofBrownianmotion[17,18]andquantumoptomechanics[19,20].
While shot-noise establishes the fundamental sensitivity limit for optical tweezers based
measurements [2,21,22], real experiments are generally limited by technical noise sources
suchaslasernoise,electronicnoiseinthedetector,ordriftsofmirrorsintheexperiment.These
technical sources of error can be a significant hindrance to precision measurement, so much
efforthasgoneinto reducingthem[4,5,12,21].Recently,an opticallock-inparticletracking
schemewasdevelopedwhichallowedevasionoflow-frequencytechnicalnoisewithoutneed-
ing to remove the noise sources from the experiment. This was applied in conjunction with
quantum correlated light to break the shot-noise limit in particle tracking sensitivity [13]. In
principle,thisopticallock-inparticletrackingschemeoffersnearimmunityto lowfrequency
lasernoiseandelectronicnoise,whichcouldmakeitahighlypracticalmethodforawiderange
of experiments. In the initial demonstration,however,the noise suppression attained through
use of the optical lock-intracking was notcharacterized[13]. Furthermore,the experimental
setupinthatdemonstrationwasmorecomplicatedthannecessaryforclassicalparticletracking
and incompatible with short working distance objectives. Here we demonstrate optical lock-
in particle tracking with a simple optical setup which can be applied with any objectives. It
is shown that lock-in based particle tracking has superior sensitivity to continuous measure-
ment at all frequencieswhere the continuousmeasurementis limited by technicalnoise, and
achievesequivalentsensitivitywherethedominantnoisesourceisfundamentalshot-noise.The
reductionin laser noise and electronicnoise yieldson average20 dB of noise suppressionin
thefrequencyrange10–5000Hz,wherelowfrequencylasernoiseandelectronicnoiseissig-
nificant, and 35 dB of noise suppression in the range 550–710 kHz where the laser crystal
relaxationoscillationsintroducealargenoisefeature.
y y
c c
n n
e e
u u
q q
e e
ser fr ser fr Msidoed-ublaantidosn
a a
L L
Particle
Laser noise
motion
Frequency Frequency
Fig.1. Aprobeopticalfieldismodulatedbyitsinteractionwiththeparticle(red).Inorder
tomeasurethis,itismixedwithanotherbrightlocaloscillatorfield(darkblue).However,
thelocaloscillatoralsohassomelow-frequencynoisepresent.Iftheprobefieldfrequency
matchesthelocaloscillatorfrequency,asshownontheleft,thenthelow-frequencynoise
competeswiththelow-frequencyparticlemotionsignal.However,iftheprobeisinampli-
tudemodulatedside-bands,asshownontheright,thenthelow-frequencyparticlemotion
canbeisolatedfromthelow-frequencynoise,therebyimprovingthemeasurementsensi-
tivity.
2. Basicconcept
Thelock-inbasedparticletrackingmeasurementdemonstratedhereisqualitativelysimilarto
acontinuouspositiontrackingexperiment.Inopticaltweezersbasedmeasurements,scattering
particlesareilluminatedandthespatialdistributionoftheresultingscatteredfieldismeasured
to infer particle position [2,3]. Any modulation on the incident illumination is carried onto
the scattered field, shifting some of the optical power from the laser carrier frequency into
modulationside-bands.Oncethescatteredfieldismeasured,theopticalmodulationtranslates
intoamodulationontheelectricalsignal,withtheparticlepositioninformationcenteredabout
themodulationfrequency(seeFig.1).Theparticlepositioncanberecoveredbydemodulating
thissignal.
We mayaskhowthe expectedsensitivity ofsucha measurementcomparesto a usualcon-
tinuousmeasurement.Whenopticalfieldsaremeasured,theresultingphotocurrentattimet is
givenby
I(t)=G U(X,Y)E(t)2dXdY+N (t) (1)
Z | | E
whereN istheelectronicnoise,Gisthedetectorgain,Eisthetotalelectricfieldatthedetector
E
atthecoordinatesX andY,andU(X,Y)representsthespatialgainofthedetector;forinstance,
if the photocurrent from two halves of a split detector are subtracted from one another, this
isrepresentedasU(X,Y)=sign(X),whileabulkdetectorhasU(X,Y)=1.Hereweassume
that the fields presentare a scattered field E which dependson particle position, and a local
s
oscillatorE withwhichthescatteredfieldinterferes,suchthatE=E O+E .Inmostoptical
LO L s
tweezers experiments, the local oscillator is simply given by the component of the trapping
fieldwhichhasnotscatteredfromtheparticle.Forlock-inexperiments,thefieldsareseparated
to allow the particle illumination to be modulated independently of the local oscillator. The
scattered field is assumed to be much smaller than the local oscillator (E E ) as is
s LO
| |≪| |
typicallythecase,suchthatthemeasuredphotocurrentisgivenby
I(t)=G U(X,Y)E (t)2+2U(X,Y)Re E (t)E (t) dXdY+N (t). (2)
Z | LO | { LO s∗ } E
The explicit time dependence of the scattered field may be separated from the spatial mode
shape as E =(A (t)+x (t))y (X,Y), where A (t) and x (t) are respectively the real expec-
s s s s
tation value of the field amplitude from which the particle tracking signal originates, and its
fluctuationswhichcontributenoisesuchasshotnoise. y (X,Y)isthecomplexspatialmode-
s
shapeofthescatteredfield;thisdoesnothaveexplicittimedependence,butismodifiedasthe
particlemoves.Itisthisspatialmodificationwhichisultimatelymonitoredtoretrieveaparticle
trackingsignal.Tofindthedependenceofthescatteredfield onasmallparticledisplacement
x(t),itcanbeexpandedtofirstorderas
dE dy (X,Y)
E =E +x(t) s =(A (t)+x (t))y (X,Y) +x(t)(A (t)+x (t)) s .
s s|x=0 dx x=0 s s |x=0 s dx x=0
(cid:12) (cid:12)
(cid:12) (cid:12) (3)
SubstitutingthisexpressionintoEq.2,thecomponentofthephotocurrentwhichgivesalinear
particletrackingsignalcanbeseentobe
dy (X,Y)
I = 2Gx(t)A (t) U(X,Y)Re E s∗ dXdY, (4)
sig s Z { LO dx x=0}
(cid:12)
= gx(t)A (t) (cid:12) (5)
s
whereforbrevitywedefineagaing=2G U(X,Y)Re E dy s∗(X,Y) dXdY.Theposition
{ LO dx x=0}
sensitivityisoptimizedwhenthisgainismRaximized,asoccurswhen(cid:12)boththephaseandshape
(cid:12)
ofthelocaloscillatorfieldareoptimizedtoperfectlyinterferewiththescatteredfieldcompo-
nent dEs [13,22].SubstitutingthisintoEq.2,wecanrepresentthemeasuredphotocurrent
dx x=0
as (cid:12)
(cid:12)
I(t)=N (t)+N (t)+gA (t)x(t), (6)
opt E s
whereallthetermsintheintegrandwhichdidnotcontributetothetrackingsignalareincluded
asopticalnoiseN .Foracontinuousmeasurement,theexpectationvalueofthescatteredfield
opt
amplitudeA (t)shouldbeconstant.Alternatively,wecanperformlock-inmeasurementifwe
s
modulatethescatteredfieldamplitudeatfrequencyw suchthatA (t)=√2A¯ cos(w t),where
s s
themodulatedamplitudehasanRMSvalueofA¯ .Providedthemodulationfrequencyismuch
s
fasterthanthemechanicalmotion,thepositioncanthenbeextractedbydemodulation;
I =√2Icos(w t)=√2 N (t)+N (t) cos(w t)+gA¯ x+gA¯ xcos(2w t). (7)
lock in opt E s s
− (cid:0) (cid:1)
Thus, the effect of the lock-in is to shift the low frequency noise to high frequencies, and
generate a second harmonic term proportionalto x while leaving the signal term unchanged.
The second harmonic term and the low frequencynoise can then be removedvia a low-pass
filter, such that only the noise originally near the modulation frequency enters the measure-
ment.Whereverlow-frequencynoiseisdominant,lock-inmeasurementallowssuppressionof
thenoisefloor.Thisdoesnotinfluencewhitenoisesourcessuchasshot-noise,sincetheseare
equallypresentatlowfrequenciesandaroundthemodulationfrequency.Thus,thefundamen-
talshot-noiselimitonpositionsensitivityisnotinfluencedbyachoicebetweencontinuousor
lock-in measurement. The two schemes have equivalentshot-noise limits to sensitivity when
thelock-inscatteredamplitudeA¯ matchestheamplitudeA ofathecontinuousmeasurment,
s s
orequivalently,whenthesamenumberofscatteredphotonsinmodulationside-bandsarecol-
lectedforthelock-inmeasurementasarecollectedforacontinuousmeasurement.
3. Experiment
Theopticallock-inparticletrackingexperimentshowninFig.2wasbuilt,andthesensitivity
attainable with continuous and lock-in measurements characterized. A particle is trapped in
waterbetweentwoobjectiveswith0.4numericalaperture(NA)by1064nmlightproducedby
alownoise[23]InnolightPrometheusNd:YAGlaser.DuetothelowNAobjectivesused,trap-
pingisnotpossiblewithasinglebeam.Twoorthogonallypolarizedcounter-propagatingfields
Fiber out-coupler
Imaging
Detector
CCD field
e
b
o Trapping field
r DM DM
p
M
A λ/2 Phase plate
50/50 PBS Local PBS
PBS λ/2
Oscillator
Fig.2. Layoutoftheopticallock-intrackingschemeusedhere.PBS:polarizingbeamsplit-
ter,DM:dichroicmirror.Thelocaloscillatorisshapedwithaphaseplatewhichimpartsap
phaseshifttoonehalfofthespatialprofile.Particlesaretrappedbythecounter-propagating
probeandtrapfields.Thetrapfieldisisolatedfromthedetection,andifitisnotrequired
forstabletrapping,canberemovedaltogether.Theprobefieldscattersfromtrappedpar-
ticles,andtheparticlemotiontrackedviatheinterferencebetweenthisscatteredlightand
thelocaloscillator.Theprobeisamplitudemodulatedat2MHzinafiberMach-Zehnder
modulator.Aseparategreenfieldisusedtoimagetheparticlesinthetrap.
areusedinsteadtoconfineparticles,withonlyoneofthesecontributingtothemeasurement.It
isimportanttonotethatalthoughadualbeamopticaltrapisusedhere,lock-inparticletracking
isfullycompatiblewithsingle-beamtraps.Oneofthetrappingfields(referredtoastheprobe)
is amplitudemodulatedat 2 MHz, which is sufficientlyhigh that the resulting modulationof
the trap strength does not measurably disturb the particle motion. The back-scatterfrom this
modulatedprobefieldiscombinedwithalocaloscillatorfieldwhichalsopropagatesthrough
the trap. The local oscillator is shaped with a phase plate so that particle motion modulates
thespatialoverlapbetweenthelocaloscillatorandscatteredfield.Providedthephasebetween
thelocaloscillatorandscatteredfieldiscorrectlychosen,theinfluenceoftheparticlemotion
on the interference between these fields directly maps the position onto the transmitted light
intensity [13], which is then measuredon a New Focus1811bulk detector.Demodulationof
theresultingsignalattheamplitudemodulationfrequencyallowsbothtrackingofascattering
particleandalsomonitoringoftherelativeopticalphases.Thescatteredlightincludesalarge
stationaryterm(E inEq.2),andthephasebetweenthisandthelocaloscillatorcanbede-
s x=0
|
terminedfromtheamplitudeofthemeasuredmodulation.Thismeasuredphasewasprocessed
with a PID controller and locked by feedback to a piezo-mounted mirror in the path of the
probefield.Thisapproachextendstheschemefirstdevelopedforopticallock-inparticletrack-
ing[13]toamoretypicalopticaltrappingsetup.Therethescatteredfieldwasproducedfrom
side-illuminationwhereasherethemodulatedprobeactsasatrappingfield.Side-illuminationis
onlypossibleifthereisroomforafree-spaceprobefieldtoreachthetrapcenter,whichrequires
useoflongworkingdistanceobjectives(inRef.[13],6mm)whicharenottypicallyusedfor
optical trapping. Furthermore, the probe can only be weakly focused with side-illumination.
Focusing the probe field through the objective increases its intensity by approximately 103,
whichresultsinacorrespondingincreaseinthescatteredfieldamplitudeandanimprovement
inthepositionsensitivityasdescribedinEq.7.
The amplitude modulation on the probe is chosen to leave approximately equal power in
the central laser frequency and the first modulation side-band. This allows the continuous
andpulsedmeasurementsto occursimultaneouslywitha singledetector,andwith equivalent
10−16 a: Continuous b: Lock-in
Hz)10−18
2m /
nt (10−20
e
m
e
ac10−22
pl
s
Di
10−24
101 102 103 104 105 106 102 103 104 105 106
Frequency (Hz) Frequency (Hz)
c d
104
nt
or improveme 110032 anical signal
o h
e fl 101 Mec
s
oi
N 100
101 102 103 104 105 106 0 2 4 6 8 10
Frequency (Hz) Time (ms)
Fig.3. Particletrackingspectraareshownfromsimultaneouscontinuous(a)andlock-in
(b)measurements.Thelightyellowtraceshowsthenoisefloorpresentintheabsenceofa
trappedparticlewhichcorrespondstothemeasurementimprecision,andtheblueshowsthe
measuredsignalwitha1m mpolystyrenebeadheldinthetrap.Thethickdarkerblueline
fitsthebeadmotionandtheflatshot-noisefloor.Thismatchesthelock-indatawellsince
itisshot-noiselimitedfrom500Hz,butdoesnotfollowthecontinuousspectraasthiswas
limitedby low frequency lasernoise until 1MHz. Thisnoise includes averyprominent
spectral peak around 630 kHz from the laser diode relaxation oscillations. Because the
fittedfloorcorrespondstotheshot-noiselevel,itdropsbelowthemeasureddatabetween
10 kHzand1 MHz.Thetrapwasveryweak, asweused 0.4NA objectiveswithatotal
of 30 mWtrapping field.Assuch, thecorner frequency isslightlybelow 10 Hzand not
visibleinthedisplayeddata.Byexcludinglowfrequencynoise,thelock-inmeasurement
yields a measurement precision which is improved by the factor shown in c. Subplot d
shows the continuous (light) and lock-in (medium) time-traces after a low-pass filter at
1MHz,revealingtheclearnoiseimprovementfromlock-inmeasurement,andalsoshows
thecontinuousdatawithalow-passfilterat10kHz(dark),whichcloselyfollowsthehigher
bandwidthlock-inresults.
recordingconditions.Somenon-linearityinthemodulatorresultedinanumberofhigherhar-
monicsbeinggenerated,whichweresuppressedinthedataacquisitionwithanalogelectronic
filters.
Usingthissetup,theBrownianmotionofa1m mpolystyrenebeadwassimultaneouslymeas-
uredbothcontinuouslyandfromside-bandsaroundthe2MHzmodulation,withspectrashown
in Fig. 3a and b respectively.The backgroundnoise was characterizedby performingequiv-
alent measurementsin the absence of a trapped bead. As expected, the lock-in measurement
isverysimilartothecontinuousmeasurement,butwithareductionintheincludedelectronic
and laser noise. The reduction in included noise (shown in Fig. 3c) causes the measurement
imprecisiontoimprovemarkedlyatthefrequencieswherelaserandelectronicnoisearedomi-
nant.Between10and5000Hz,theimprecisionisimprovedbyanaverageof20dB,witheven
greatersuppressionof35dBinthefrequencyrange550–710kHzwherethelasercrystalrelax-
ation oscillationsproducea prominentlasernoise peakcentredat630kHz.A comparisonof
thetwomeasurementsinthetimedomainalsorevealsboththeclearsuppressionofnoiseonthe
lock-intraceandtheotherwisecloseagreementbetweenthemeasureddisplacements(Fig.3d).
Theseresultsverifythatthelock-inmeasurementisequivalentto acontinuousmeasurement,
exceptthatitevadeslowfrequencytechnicalnoise.
Withtheopticallayoutusedhere,particlemotionwastrackedinaself-homodynemeasure-
mentonasinglebulkdetectorratherthanaquadrantphotodiode.Thisisnotrequiredforlock-in
particletracking,whichshouldworkwithanydetectionapparatus.However,itcanbeveryad-
vantageous;quadrantdetectorsareavoidedinsomehigh-speedexperimentsbecausetheytyp-
icallyhavelowbandwidth[4,20].Furthermore,thequantum limitonsensitivityisaccessible
onlywithperfectinterferencebetweenthelocaloscillatorandscatteredfields,whichrequires
the local oscillator to be spatially engineered, as it is in a homodyne measurement such as
this [2,22]. A difficulty with the layout used here was that some of the probe field reflected
fromthesamplechamberintothedetector.Thisback-reflectionwasofagreaterintensitythan
the back-scatterfrom the particle, and phase shifts between the local oscillator and scattered
fields generateda measured signal, but this was primarily below 5 Hz. In that low frequency
range,ourlock-inmeasurementperformedworsethanthecontinuousmeasurement,although
eliminatingtheback-reflectionwithanti-reflectioncoatingswouldresolvethis.Also,itshould
be noted that evasion of laser noise and electronic noise can only improve sensitivity to the
particle position relative to the opticalfields. As with all otherparticle trackingexperiments,
thismeasurementremainssensitivetomirrordriftsoraircurrentsoutsidethetrapwhichcause
thetrapcentertodrift,andconventionalmethodsareneededtostabilizethesenoisesources.
We have demonstrated that a lock-in measurement scheme provides a simple and robust
technique to reduce technical noise in an optical tweezers setup. This can yield a substantial
improvementinsensitivitywhichcouldbepracticalformanyopticaltweezersapplications.
Acknowledgments
ThisworkwassupportedbytheAustralianResearchCouncilDiscoveryProjectContractNo.
DP0985078.