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ResearchNote
OpticsandLaserTechnology
journalhomepage: www.elsevier.com/locate/optlastec
Unconventionalmagnificationbehaviourinmicrosphere-assisted microscopy
StephanePerrin⁎,HongyuLi,SylvainLecler,PaulMontgomery ICubeLaboratory,UniversityofStrasbourg – CNRS,67412Illkirch,France
HIGHLIGHTS
• Magnificationinmicrosphere-basedmicroscopybehavesdifferentlythaninopticalmicroscopy.
• Lateralmagnificationincreasesalongthemicrosphereimagingdepth.
• Magnificationfactordependsonthemicrospheresizeandilluminationconditions.
• Reducingthespectralbandwidthofthelightsourcenarrowsthemagnificationrange.
ARTICLEINFO
Keywords:
Microscopy
Super-resolution
Microsphere
Magnification
Imageformation


ABSTRACT
Microsphere-assistedmicroscopyisanoriginalsub-diffraction-limitimagingtechniqueallowingtoreachafew hundrednanometresoflateralresolutioninaironlybyplacingamicrobeadinaclassicalopticalmicroscope. Thisworkaimstohighlightthemagnificationprocessinmicrosphere-assistedmicroscopywhichbehavesdifferentlyfromthecaseinopticalmicroscopy.Asamatteroffact,thelateralmagnificationofanopticalmicroscopedoesnotchangeaccordingtofocusplanepositions.Experimentsonthesuper-resolutionimaging technique,performedinairthroughsoda-lime-glassmicrospheresandattestedbysimulations,demonstratea significantincreaseinthemagnificationfactoralongthemicrosphereimagingdepth, i.e. atdifferentobjectfocal-planepositionoftheobjective.Moreover,itisshownthatthemagnificationrange,aswellasitsslope, dependonthesizeofthemicrosphere.Additionally,theinfluenceofthespectralwidthoftheilluminationlight sourceonthemagnificationrangeishighlighted.
1.Introduction
Resolvingpowerinclassicalopticalmicroscopyislimitedbydiffractionoflight,resultinginaminimaldistancebetweentwodistinct objectdetailsofhalfofthewavelengthinairusingalow-coherentillumination [1].Theideaofsub-diffraction-limitimagingtechniques appearedwiththeneedtovisualizeincreasinglysmallerelements [2], andwiththenotionof ultra-microscopy [3].Severalsuper-resolution imagingtechniqueshavethenbeendevelopedinthelastcenturysuch asconfocalmicroscopy [4,5] (enhancedfurtherusingadouble-pass configuration [6] andthephotonicjetphenomenon [7]),scanning near-fieldopticalmicroscopy [8,9],structuredilluminationmicroscopy [10,11] andmetamaterials-basedsuperlenses [12,13].Theycontributedtobringingopticalnanoscopytotheforefront,reinforcedby theNobelPrizeforChemistryin2014withsuper-resolved fluorescence microscopy [14] andsinglemoleculelocalizationmicroscopy [15].
⁎ Correspondingauthor.
E-mailaddress: stephane.perrin@unistra.fr (S.Perrin).
https://doi.org/10.1016/j.optlastec.2019.01.030
Nevertheless,thesesuper-resolutionimagingtechniquesrequirehigh stabilitysystems,complexalignmentorlongacquisitiontime.
In2011,Wangetal.experimentallydemonstratedfull-fieldlabelfreesuper-resolutionmicroscopyusinglow-refractive-indexmicrospheres(silicamicrosphereswithn 1.46) [16].Relativelyeasy-toimplement,thisapproachconsistsinintroducingatransparentmicrosphereinaclassicalwhite-lightmicroscope, i.e. betweenthesample andthemicroscopeobjective.Amagnifiedimage,providingsub-diffraction-limitinformation,isthengeneratedandcollectedbythemicroscope.Inthepastyears,severalpapershavefocusedontheperformanceofthesuper-resolutionimagingtechnique.In2012, Darafshehetal.suggestedplacinghigh-refractive-indexmicrospheres (barium-titanate-glasswithn ∼ 2.0)inanimmersionliquid [17] and, morerecently,embeddinginanelastomerlayer [18].Studiesofthe immersionmediuminfluenceontheimagecontrast [19,20] andonthe imagenature [21,22],aswellasoftheroleofthecoherenceoflighton
Received7August2018;Receivedinrevisedform7December2018;Accepted15January2019
Availableonline25January2019
0030-3992/©2019ElsevierLtd.Allrightsreserved.
thelateralresolution [23,24],leadtoabetterunderstandingofthe imagingtechnique.Inaddition,themanipulationofthemicrospheres hasbeenstudied,makingitpossibletoperformcontact-lesssuper-resolutionmeasurements [25–28];methodswhichcould,forexample, avoiddamagingbiologicalsamplesduringtheacquisitions [29–31]. Thesecontributionsarepromisingasregardsthefabricationofnovel opticaldevices(e.g.,microsphere-embeddedmicroscopeaccessories), enablingtoimproveopticalmicroscopy.
Experimentally,microsphere-assistedmicroscopyisabletoreacha lateralresolutionhigherthanconfocalmicroscopyandsolidimmersion lens [32],andsimilartostructuredilluminationmicroscopyandnegative-indexsuperlenses [33].However,beingarecentimagingtechnique,somephenomenaarestillnotfullyexplainedsuchastheorigin ofthesuper-resolutionresolvingpower.Duetothemicron-scalesizeof thespheres,theirimagingpropertiesdonotexactlyfollowgeometrical optics [34,35] andtheoreticalanalysesthusremaincomplex.Apossible collectionoftheevanescentwavesbythemicrospherefollowedbytheir conversioninthefar fieldyetappearsrelevanttoexplainthesuperresolvingpower [36,37].Inmicrosphere-basednanoscopy,itisnotonly thesuper-resolutionphenomenonisstillnotfullyexplained,butalso theimageprocessinvestigatedinthiswork.Unlikeopticalmicroscopy, microsphere-assistedmicroscopyprovideslongaxialfocusingranges, thereforetheimagingfactorwithintheimagingdepthbehavesinan unconventionalway.Asamatteroffact,thelateralmagnificationdiffersaccordingtotheaxialpositionofthemicroscopeobjective.Asan example, SupplementaryMovie illustratesthechangeinthemagnificationalongtheopticalaxisusingasoda-lime-glassmicrospherewitha diameterof29 μm.Thiseffectcouldleadtodivergentinterpretationsof results(e.g.,themagnificationfroma4.7 μm-diametermicrosphere equals × 4.1andeven × 8inRef. [16],and × 2.8,inRef. [28]).Therefore, arangeofmagnificationfactorissometimespreferredinordertoavoid anyposition-dependent-magni ficationconfusions [29,38]
Thisworkexposesafundamentalpropertyinmicrosphere-assisted microscopybyhighlightingthenon-classicalevolutionofthelateral magnificationalongtheimagingdepth.Throughexperimentalmeasurementsandnumericalanalyses,theinfluenceofthemicrosphere diameter,aswellasthebandwidthofthelightsource,onthemagnificationbehaviourisshowninair.
2.Methods
Aclassicalopticalmicroscopeinreflectingmodehasthusbeen enhancedbyintroducingglassmicrospheres(CosphericLLC, California)havingdifferentdiameters.Thesoda-lime-glassmicrosphereshavearefractiveindexof1.52.Theilluminationpartconsistsof awhite-lightsource( λ 0 =650nm, λΔ =400nm)wheretheemitting beampassesthroughaKöhlerarrangementtoprovideamorehomogeneousintensitydistribution.The fielddiaphragmwasclosedtoimprovetheimagingcontrast [39].Inaddition,wavelength filters(acyan filterwith λ 0 =567nmand λΔ =90nm,andablue-line filterwith λ 0 =445nmand λΔ =11nm)canbeintroducedinordertolimitthe spectralwidthofthelightsource.Theobjectbeamisthendirected towardstheimagingpartandpassesthroughthetransparentmicrosphereandthemicroscopeobjective(Zeiss, × 50,NA=0.55),asshown in Fig.1(a).Here,theobjectisacontrastgratingtargethavingaperiod of400nm(fabricatedattheMIMENTOTechnologyCentre,FEMTO-ST Institute,France).Itcanbenotedthattheopticalmicroscopealoneis notabletovisualizethe200-nm-groove-widthfeatures(Fig.1(b)).Indeed,consideringthetransferfunctionofthewholewhite-lightmicroscope,theresolvingpowerequalsonly840nm.Themicrosphereis thusplacedinaironthesurfaceoftheobject,allowingthesuper-resolutionphenomenontooccur.Acamera finallyrecordsthesuper-resolutionimage(Fig.1(c))fromtheobjectivelensandarelaylens.In ordertocapturethevirtualimagesatdifferentpositionsalongthe opticalaxis,apiezoelectricdeviceisverticallydisplaced.Thedepthof fieldofthemicroscopeobjective( 1 μ m)definestheaxialsamplingof


Fig.1. (a)Layoutofopticalheadofthemicrosphere-basednanoscope.Amicroscopeobjective(MO)collectsthevirtualimage(VI)oftheobject(OB)which wasmagnifiedbeforebya25-μ m-diameterglassmicrosphere(MS).Apiezoelectricdevice(PZT)allowstheMOtofocusondifferentaxialVIplanesalong theimagingdepth(ID)bydisplacingOBandMS.Comparisonofperformance between(b)theMOaloneand(c)theMS-basednanoscope,byimaginga200nm-line-widthgrating.

Fig.2. (a)Experimental(redsolidline)andnumerical(bluedottedline)evolutionsofthelateralmagnificationfroma25-μ m-diametermicrosphereplaced inairusingawhite-lightsource,alongthemicrobeadimagingdepth(Zaxial position).(b.i),(b.ii)and(b.iii)arethevirtualimagesofthe400nmperiodic objectatZpositionsof30 μ m,55 μ mand90 μ m,respectively.Scalebarsrepresent1 μ m.(c)Simulationofthevirtualimageformation.Theobjectistwo pointsourcesplacedagainstthemicrosphere.Thewhitedottedlineillustrates theinitialmicrospherelocation.(Forinterpretationofthereferencestocolour inthis figurelegend,thereaderisreferredtothewebversionofthisarticle.)
themeasurements.Duringtheexperiments,themeasurementswere repeatedusingtensimilarmicrospheres.Forexample,experimental curverepresentedin Fig.2(a)resultsthusofanaveragingofthemagnificationfactorsthroughten25-μ m-diametermicrospheres.Moreover, ateachaxialposition,themagnificationmeasurementswereperformed tentimes.
3.Resultsanddiscussion
Thelateralmagnificationgeneratedbythemicrosphere,definedas theratiobetweenthegratingperiodsintheimageplaneandtheobject plane,was firstmeasuredaccordingtotheaxialpositionwherethe objectivefocuseson(Fig.2(a)).Asoda-lime-glassmicrospherehavinga
diameterof25 μ mwasusedtodemonstratetheinfluenceoftheaxial imagepositiononthemagnificationfactor.Alinearevolutionalongthe microsphereimagingdepth(∼60 μ m)isshown,changingfrom × 4to × 8whilemaintainingthesuper-resolutionphenomenon.Thiseffectis significantlydifferenttoconventionalfull-fieldopticalsystem.Indeed, themagnificationofaconventionalopticalmicroscoperemainsconstantovertheclearestimagingdepth.Obviously,thevirtualimagesat positionsdeeperthan60 μ mhaveacontrastdecreased(Fig.2(b.iii)).In ordertoconfirmtheexperimentalresults,arigorous2Delectromagneticmodelwasalsoimplementedbyusinga finiteelement method(ComsolMultiphysics).Thesimulationofsuper-resolution virtualimagingconsistsintwosteps [23,40,41]: firstly,theelectric fieldsfromtheobject, i.e. twopointsources,interactswithamicrosphere.Then,thetransmittedelectric fieldistime-reversepropagated infree-space, i.e. propagatedintheoppositeaxialdirectionwithoutthe microsphere,inordertoretrievethetwoimages.Thebroadbandilluminationofthelightsourceisconsideredbyrepeatingthetwosteps overthevisiblespectralrange( λΔ =400nm,step=50nm)andthen thewavelength-dependantirradiancedistributionsaresummed (Fig.2(c)).Thesimulatedmagnificationfactor, i.e. thetransversedistanceratiobetweenthetworesultingimagesandthetwopointsources, isrepresentedbythebluedottedlinein Fig.2(a)accordingtothe longitudinalpositionoftheimageplane,showingmagnificationvalues ingoodagreementwiththeexperiments.
Afterwards,theinfluenceofthemicrospherediameterontheposition-dependentmagnificationwerestudied.Eightglassmicrospheres havingdifferentdiameterswerehenceplacedonthe400-nm-period grating.Inordertobereadable, Fig.3(a)representsthelinearevolution ofthemagnificationfactorforonlythreemicrospherediameters, i.e. 7 μ m,46 μ mand125 μ m.Thecurvesallowtoaffirmthat,atagiven axialimageposition,thelargemicrospheresprovideamagnification factorlowerthanwhenusingsmallmicrospheres.Moreover,themicrosphere-diameterdependenceonthemagnificationcurveslope α has
Fig.3. (a)Evolutionofthelateralmagnificationinairfrommicrospheres havingdiametersof7 μ m(inred),46 μ m(inorange)and125 μ m(inblue),asa functionofaxialpositionZ.Themicrospheresareilluminatedbyawhite-light source.(b)Evolutionofthemagnificationinclination α (inred)andtheinitial imageposition(inblue)fordifferentdiameters D.Acurve fitting1/D function issuperimposedtothecalculatedvalues α .(Forinterpretationofthereferences tocolourinthis figurelegend,thereaderisreferredtothewebversionofthis article.)
Whitelight Cyan-filteredwhitelight Blue-filteredwhitelight
Axialposition ( m) 7 6 5 4
Fig.4. Evolutionofthelateralmagnificationfroma25-μ m-diametermicrosphereplacedinairasafunctionofaxialpositionunderthreetypesoflight sourcehaving400nm(inredline),90nm(incyanline)and11nm(inblue line)ofbandwidth.(Forinterpretationofthereferencestocolourinthis figure legend,thereaderisreferredtothewebversionofthisarticle.)
beenestimatedandisrepresentedin Fig.3(b)(red-colorcurve).A fittingcurveisjuxtaposed,highlightingtheinverseproportionalityofthe slope α accordingtothediameter D ofthesoda-lime-glassmicrospheres.Inairandusingsoda-lime-glassmicrospheres,thisrelationis expressedas:
= α D [inμm] 1.83 [inμm] 1
Inaddition, Fig.3(a)showsthatthesmallerthediameter,thenarrower theimagingdepth.Indeed,notonlythemagnificationfactorbutalso theimagingdeptharehighlyaffectedbythesizeofthemicrosphere. Largemicrospheresareabletoformvirtualimagesatdeeperpositions, requiringfocuswiththemicroscopeobjectiveatfurtherpositions.The linearproportionalityoftheinitialpositionoftheimagingdepthasa functionofthediameterofsoda-lime-glassmicrospheresisshownin Fig.3(b)(blue-colorcurve).
Finally,theroleofthespectralbandwidthofthelightsourceonthe magnificationwasinvestigated.Forthispurpose,theperformanceof the25-μ m-diametermicrosphereusingthewhitelightsource(representedbytheredlinein Fig.4)iscomparedwithtwospectrallygatedilluminations, i.e. usingthecyan filter(cyanline)andtheblueline-filter(blueline).Themagnificationfactorremainslinearlyproportionalaccordingtotheaxialpositionandthemagnificationvalues donotdiffer,regardlessofthespectralbandwidthofthelightsource. However,onlythemagnificationrangeappearslimited.Asamatterof fact,thesmallerthespectralbandwidthis,thenarrowerthemicrosphereimagingdepthis.Thisspectralwidthdependenceshowsthatthe unconventionalmagnificationbehaviourismainlyduetoasignificant contributionofthechromaticaberrations.Wavelength-dependent beamsarefocusedindifferentimageplanes,eachhavingadifferent magnification.Thisleadstodifficultiestodefineauniquemagnification.Nevertheless,thisyieldsadegreeoffreedomduringthemeasurement, i.e. thepossibilitytoadjusttherequiredmagnification.This assumptioncanberetrievedthroughglassmicrosphereshavinganother diameter.
Inthiswork,theunconventionalbehaviourofthelateralmagnificationinmicrosphere-assistedmicroscopyhasbeenachievedinair usingsoda-lime-glassmicrospheres.Itshouldhoweverbementioned thatthiseffectoccursalsousingmicrosphereshavingahigherrefractiveindexandinadifferentimmersionconfiguration [35,42].
4.Conclusions
Thisworkexposesafundamentalpropertyinmicrosphere-assisted microscopy:thenon-classicalbehaviourofthelateralimagemagnification.Contrarilytoclassicalopticalmicroscopy,themagnification factorissubjecttoalinearevolutionalongthemicrosphereimaging depth,andbothgeometricalandopticalparametershaveaninfluence ontheposition-dependentmagnificationslopeandrange.Indeed, throughexperimentsandnumericalsimulations,itwasshownthatthe
microspheresizeisinverselyproportionaltothemagnificationgrowth andislinearlyproportionaltotheinitialpositionoftheaxial fieldof view.Furthermore,thereductionofthespectralbandwidthoftheilluminationlightsourceindeedlimitsthemagnificationrange.
Acknowledgements
TheauthorsthankA.Leong-Hoiforherfruitfulcontribution.This workreceivedfundingfromSATTConectusAlsaceandwaspartly supportedbytheFrenchRENATECHnetwork(FEMTO-STInstitute, Besançon)andtheUniversityofStrasbourg.
AppendixA.Supplementarymaterial
Supplementarydataassociatedwiththisarticlecanbefound,inthe onlineversion,at https://doi.org/10.1016/j.optlastec.2019.01.030
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Title: Kyllikki ja Lemminkäinen Laulurunoja
Author: Hilja Liinamaa-Pärssinen
Release date: April 1, 2024 [eBook #73309]
Language: Finnish
Original publication: Helsinki: E. E. Sundvall, 1902
Credits: Tapio Riikonen *** START OF THE PROJECT GUTENBERG EBOOK KYLLIKKI JA LEMMINKÄINEN ***