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Optics and Lasers in Engineering
journalhomepage:www.elsevier.com/locate/optlaseng
Resolution enhancement of confocal fluorescence microscopy via two illumination beams
Vannhu Le
a,c,+, Xiaona Wang
a,+, Cuifang Kuang
a,b,∗, Xu Liu
a,baState Key Laboratory of Modern Optical Instrumentation, College of Optical Science and Engineering, Zhejiang University, Hangzhou 310027, China
bCollaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
cDepartment of Optical Engineering, Le Quy Don Technical University, Hanoi, Vietnam
a r t i c le i n f o
Keywords:
Confocal fluorescence microscopy Superresolution
Digital processing
a b s t r a ct
Confocalfluorescencemicroscopyisaneffectiveimagingtechnique,butitsresolutionislimitedbythediffraction- limit.Fluorescenceemissiondifference(FED)methodisausefulwaytoimprovetheresolutionofconfocalflu- orescencemicroscopy,butthenegativevaluesgeneratedduringsubtractionprocessmightcauselossofvalid information.Inthispaper,weproposeoneeffectivemethodtoenhancetheresolutionofconfocalfluorescence microscopywithoutgeneratingsignificantnegativevalues.Theproposedmethodcombinesdigitalprocessing andFEDmethod,obtainingthefinalimageswithhigherresolutionandlessinformationloss.
1. Introduction
Confocalscanningmicroscopyisaroutinetoolinthelifesciences.
Thisimagingsystemcanbeusedtoimproveresolutionofconventional microscopybyafactorof√
2[1,2],andcouldacquirehigh-resolution opticalimageswithacertaindepth[3].Asaresult,confocalscanning microscopyhasbeenusedwidelyinthree-dimensionalspecimenanal- ysis.However,itsspatialresolutionisrestrictedto∼200nmduetothe diffractionlimitundercommonexperimentalconditions[4]. Thede- mandforhigherspatialresolutioninopticalmicroscopyhaspromoted thedevelopmentofnovelsuper-resolutionmicroscopy,whichiscapable ofbreakingthediffractionlimit.Multi-beamcombinationisoneofthe mostcommonwaystoachievesubcellularimagesandthesetechniques havedevelopedrapidly,suchasstimulatedemissiondepletion(STED) microscopy [5, 6], ground-state depletion(GSD) microscopy, [7–9], reversiblesaturable/switchableopticaltransitions(RESOLFT)[10]and soon.STEDisatwo-beammicroscopythatcanimprovetheresolution ofconventionalfluorescencemicroscopysignificantly,withaGaussian beamexcitingfluorescence,andadonutbeamdepletingsurrounding fluorescence.Thespotsizecanbe reducedbymatchingtheGaussian pumping and donut depletion beams, so that the spatial resolution canbeimproved.Itisarelativelyfastwaytoachievesuper-resolution and requires no data post processing. GSD is another two-beam super-resolutionmicroscopywithasimilarprinciplebutdifferenttime sequences.Thismethodexcitesthesamplewithrelativelylow-power
∗Correspondingauthorat:StateKeyLaboratoryofModernOpticalInstrumentation,CollegeofOpticalScienceandEngineering,ZhejiangUniversity,Room418, AcademicBuilding#3,#38ZhedaRoad,XihuDistrict,Hangzhou310027,China.
E-mailaddress:[email protected](C.Kuang).
+Authorshavecontributedequallytothiswork.
continuous wave,sothatthephoto-bleachingandphoto-damageare slightlyreduced.RESOLFTisathree-beamsuper-resolutionmicroscopy.
InRESOLFT,aGaussianbeamisusedtoactivatethesample,adonut beam turnsoff theactivation ofthe sample, andasecond Gaussian beam excites the fluorophore that is still active. Although these super-resolutionmicroscopysystemsmentionedabovehavebeencom- merciallyavailableandtheyareattractiveforbiologicalimaging,the applicationofthesesystemsisstilllimited,becauseoftheintricateopti- calsystem,specialspecimenpreparation,expensiveinstrument,higher powersource,time-consumingdataprocessing,andhighphoto-damage.
Fluorescenceemissiondifference(FED)method[11–13]providesa newpossibilitytoimprovespatialresolutionofconfocalmicroscopy.In FED,thesampleisilluminatedbyasolidbeamanddonutbeam,re- spectively,toobtaintwoimages,calledsolidimageanddonutimage.
Thefinalimageisobtainedbysubtractingtheacquiredsolidimageand thedonutimage.FEDmethodhasthefollowingadvantages.First,its calculationis simplesinceweonlyneed toperformsubtraction.Sec- ond,thecostofFEDsystemislow,andtherequiredbeampathscan beassembledeasilyinthelaboratory.Third,therequiredlaserpower ofFEDmethodislowerthanthatofSTEDandGSD,whichminimizes photo-damageduringtheimagingprocess.However,negativeintensity valuesareinevitablygeneratedduringsubtractionprocessing[14].Al- thoughthesenegativevaluesarezeroedinthefinalresult,theywould stillleadtoinformationloss.Thereisatrade-off betweenthenegative valuesandresolution: thehighertheresolution,themoreseriousthe
https://doi.org/10.1016/j.optlaseng.2019.05.018
Received11January2019;Receivedinrevisedform19April2019;Accepted17May2019 0143-8166/© 2019PublishedbyElsevierLtd.
Fig.1. Opticalschemesviatwoillumination beamsinconfocalfluorescencemicroscopy.
effectofnegativevalues[15].Tosuppressthegenerationofnegative valueswithoutreducingtheresolution,Researchershavemadegreat effortsandachievedsomeresults[16,17].However,thenegativeval- uesonthefinalimageisstillaprobleminthesemethods.Inthisarticle, weproposedanewmethodcombiningthedigitalprocessingandFED methods,toobtainimageswithhighresolutionandlowerinformation loss.Theproposedmethodincludestwosteps.First,weobtainthere- storedimagewithhigherresolutionbydigitalprocessing.Then,remove thebackgroundoftherestoredimagebyintroducingFEDmethod.After thesetwosteps,wecanachievehighqualityimages.
2. Method 2.1. Rawimagedata
Therawimagedataacquiredbytheproposedmethodisthesame asthatoftheFEDmethod:asolidimageexcitedbysolidbeamanda donutimageexcitedbydonutbeam.SimilartotheFEDmethod,the donutbeamisobtainedbyphasemodulationof0–2𝜋vortexpattern.
InFig.1,weindicatetwofeasibleimagingschemesfortheproposed method.InFig.1(a),therearetwoilluminationpaths:onepathissolid beam,theotherpathisdonutone.ThedonutPSFismodulatedby0–2𝜋 vortexphasemask.Thetwoilluminationpathsshouldbeadjustcare- fully,toensurethatthesolidanddonutspotsareinthesameposition onthesample.InFig.1(b),aspatiallightmodulator(SLM)isaddedto theilluminationpathtocontrolphasemodulation.Thephasepattern ontheSLMisswitchedbetween0and0–2𝜋vortexphasemask.When thepatternontheSLMissetto0,theilluminationbeamissolid;when thepatternontheSLMissetto0–2𝜋vortexphasemask,theillumina- tionbeamisdonut.Inthedetectionpath,thereisonepinhole,working asthespatialfilter.TheilluminationpartshowninFig.1(b)issimpler thanthatinFig.1(a).Besides,thereisnoneedtoadjustthesolidand donutbeamtoensurethespotoverlaponthesample.So,weusethe SLMtomodulatetheilluminationbeam.
ThetwoimagesexcitedbysolidanddonutPSFscanbepresented by,
𝐼𝑠(𝑥,𝑦)=𝑜(𝑥,𝑦)⊗ 𝑃𝑆𝐹𝑠(𝑥,𝑦) (1)
𝐼𝑑(𝑥,𝑦)=𝑜(𝑥,𝑦)⊗ 𝑃𝑆𝐹𝑑(𝑥,𝑦) (2) whereoistheobject;PSFs,PSFdarethepointspreadfunctionsofsolid beamanddonutbeamsinthecross-sectionperpendiculartotheoptical axis;Is,IdaretheimagesexcitedbysolidanddonutPSFs,respectively;
⊗istheconvolutionoperator.
Fig.2. Modeloftheproposedmethod.
The procedure of theproposed method is shown in Fig. 2. This methodincludestwomainparts:digitalprocessingandFEDmethod.
Firstly,thedigitalprocessingisappliedtorestorethehigh-resolution imagefromtwooriginalimagesexcitedbysolidanddonutPSFs.Then, FEDmethodisintroducedtoremovethebackgroundinrestoredimage.
Thisistheproposedmethodtogetahighqualityfinalimage.
2.2. Digitalprocessing
ThetworawimagesexcitedbydifferenttwoPSFsaredigitallypro- cessedtoreconstructahigh-resolutionimage.Inthisarticle,weusethe blindpostprocessingtoachievethehigh-resolutionimage.Asshownin Ref.[18],theblindpostprocessingcancorrecttheeffectoftheoptical aberrations.Inthisarticle,weusetheRichardson-Lucydeconvolution toachievetheblindpostprocessing,andtheiterativeformulacanbe presentedby,
𝑜𝑡+1=𝑜𝑡×
( 𝐼
𝑜𝑡⊗ 𝑃𝑆𝐹𝑡⊗ 𝑃𝑆𝐹𝑟𝑡 )
(3)
𝑃𝑆𝐹𝑡+1=𝑃𝑆𝐹𝑡×
( 𝐼
𝑜𝑡+1⊗ 𝑃𝑆𝐹𝑡⊗ 𝑜𝑡𝑟 )
(4)
whereoistheobject;oristheflippedobject;Iistheinputimage;PSF isthepointspreadfunctionofilluminationbeam;PSFr istheflipped pointspreadfunction;tisthenumberofiterations;⊗istheconvolution operator.
Sincethere aretworawimages, theiterative processcan bepre- sentedby,
𝑜𝑡𝑠+1=𝑛𝑜𝑟𝑚 [
𝑜𝑡× ( 𝐼𝑠
𝑜𝑡⊗ 𝑃𝑆𝐹𝑠𝑡⊗ 𝑃𝑆𝐹𝑠𝑟𝑡 )]
(5)
𝑃𝑆𝐹𝑠𝑡+1=𝑛𝑜𝑟𝑚 [
𝑃𝑆𝐹𝑠𝑡×
( 𝐼𝑠
𝑜𝑡+1⊗ 𝑃𝑆𝐹𝑠𝑡⊗ 𝑜𝑡𝑟 )]
(6)
𝑜𝑡𝑑+1=𝑛𝑜𝑟𝑚 [
𝑜𝑡× ( 𝐼𝑑
𝑜𝑡⊗ 𝑃𝑆𝐹𝑑𝑡 ⊗ 𝑃𝑆𝐹𝑑𝑟𝑡 )]
(7)
Fig.3.Thesimulationresultsofspoke-likesamplewiththesizeof10𝜆×10𝜆.(a)Thespoke-likesample.(b)Theimagingresultofconventionalconfocalfluorescence microscopy.(c)TheimagingresultimagedbydonutPSF.(d)ThevaluesofevaluationfunctionC(𝛼)ofthespoke-likesampledependingondifferent𝛼values.(e) Theimagingresultofproposedmethodinthisarticle,andthesubtractionfactorissetto0.06.Thesizeoftheimagesis10𝜆×10𝜆.
𝑃𝑆𝐹𝑑𝑡+1=𝑛𝑜𝑟𝑚 [
𝑃𝑆𝐹𝑑𝑡×
( 𝐼𝑑
𝑜𝑡+1⊗ 𝑃𝑆𝐹𝑑𝑡⊗ 𝑜𝑡𝑟 )]
(8)
𝑜𝑡+1=𝑛𝑜𝑟𝑚(
𝑜𝑡𝑠+1+𝑜𝑡𝑑+1)
(9) whereoistheobjectrestoredfromthetworawimages;oristheflipped o;os is theobjectrestoredfrom therawimageexcitedbysolidPSF;
odistheobjectrestoredfromtherawimageexcitedbydonutPSF;Is istherawimageexcitedbysolidPSF;Idistherawimageexcitedby donutPSF;PSFsisthepointspreadfunctionofsolidbeam;PSFsristhe flippedPSFs; PSFdis thepointspreadfunctionof donutbeam;PSFdr istheflippedPSFd;norm()representsnormalizedcalculation;tisthe numberofiterations;⊗istheconvolutionoperator.
2.3. FEDmethod
Thereisalsobackgroundintherestoredimage.Toremovetheback- ground,wecansubtracttherestoredimageanddonutimage,whichcan bepresentedby,
𝐼(𝑥,𝑦)=𝐼𝑟𝑒𝑠(𝑥,𝑦)−𝛼⋅𝐼𝑑(𝑥,𝑦) (10) whereIresistherestoredimage,afterthedigitalprocessing;Idisthe imageexcitedbydonutPSF;𝛼isthesubtractionfactor.
Thesubtractionfactorinaboveformulaismuchsmallerthanthat inconventionalFEDmethod,sothenegativevaluesinthesubtraction resultaregreatlyreduced.
Toobtainanoptimalsubtractionfactor,we analysistheimaging resultsofdifferentsubtractionfactorswithanevaluationfunction[19]:
𝐶(𝛼)= ∑ |||𝐹𝑇{
𝑃𝑆𝐹𝑟𝑒𝑠−𝛼⋅𝑃𝑆𝐹𝑑}|
||( 𝑟∕𝑟𝑚𝑎𝑥)
∑ |||𝐹𝑇{
𝑃𝑆𝐹𝑟𝑒𝑠−𝛼⋅𝑃𝑆𝐹𝑑}|
|| (11)
whereƩ representsthesummationoperation;FTrepresentstheFourier transform;PSFres istherestoredsolidpointspreadfunction(PSF)af- terthedigitalprocessing;PSFdisthedonutPSF;𝛼isthesubtraction factor;risthepolarradiusoffrequencyspace;𝑟𝑚𝑎𝑥=(𝜉𝑚𝑎𝑥2 +𝜂2𝑚𝑎𝑥)1∕2=
√
1∕(2𝛿𝜉)2+1∕(2𝜂𝜉)2,and𝛿𝜉,𝜂𝜉 representthelengthandwidthofthe pixel,respectively.
Inthefollowingsimulationandexperiment,thesubtractionfactoris calculatedbythisfunction.Asthecalculationresultsshowinthefollow- ingsimulationandexperiments,thesubtractionfactorinourproposed methodisgreatlyreduced.Therefore,thenegativevaluegeneratedin theimageisalsoreducedinthesubtractionprocess.
Then,thefinalimageisobtainedbyzeroingthenegativevalueofthe subtractionresult.Becausethenegativevaluesinthesubtractionresult arereduced,thezeroingprocesswouldnotcauseasmuchinformation lossastheconventionalFEDmethod.
3. Simulationresults
Inordertoshowtheeffectivenessoftheproposedmethod,thesimu- lationresultsarepresentedinthissection.Inthesimulation,thenumer- icalaperture(NA)ofobjectivewassetto1.49,andwavelengthwasset to640nm,whichweretheparametersusedinexperiments.Asisshown inFig.3(a),thesampleisaspoke-likesamplewiththesizeof10𝜆×10𝜆.
ThevaluesofC(𝛼)areshowninFig.3(d),andthepeakvalueofC(𝛼)is
Fig.4. Thesimulationresultsofcellmicrotubules.(a)Theoriginalcellmicrotubulesintensitysimulatedbycomputer.(b)Theimagingresultsofcellmicrotubules withconventionalconfocalfluorescencemicroscopy.(c)TheimagingresultsofcellmicrotubulesimagedbydonutPSF.(d)ThevaluesofevaluationfunctionC(𝛼) ofcellmicrotubulesdependingondifferent𝛼values.(e)TheimagingresultsofcellmicrotubuleswithconventionalFEDmethod.Thesubtractionfactorissetto0.6.
(f)Theimagingresultsofcellmicrotubuleswiththeproposedmethodinthisarticle,andthesubtractionfactorissetto0.08.Thesizeoftheimagesis6𝜆×6𝜆.
takenwhen𝛼isequalto0.06.Therefore,thesubtractionfactorofthe proposedmethodissetto0.06inthesimulationofspoke-likesample.
The imaging results of conventional confocal fluorescence mi- croscopyandproposedmethodinthisarticleareshowninFig.3(b)and (e),respectively.Bycomparingtheunresolvedareaincentralpartofthe imagingresults,wecannoticethattheproposedmethodcanimprove resolutionoftheconventionalconfocalfluorescencemicroscopy.
Furthermore, we alsosimulate cellmicrotubules by computer to demonstratethattheproposedmethodcanproducebetterimagingre- sult.Theparametersof themicrotubulessimulationarethesameas those of spoke-like simulation. The simulated cell microtubules are showninFig.4(a).Thewidthofsinglemicrotubuleis13nm,andthesize ofthewholesampleis6𝜆×6𝜆.AsisshowninFig.4(d),thepeakvalue oftheevaluationfunctionC(𝛼)istakenat𝛼equalto0.08,sothesubtrac- tionfactorissetto0.08inthesimulationofcellmicrotubules.Fig.4(b, eandf)showtheimagingresultsofconventionalconfocalfluorescence microscopy,conventionalFEDmethod,andtheproposedmethod,re- spectively.AsisshowninFig.4(bandf),therearemoredetailsinthe imagingresultofproposedmethod,provingthattheproposedmethod canenhancetheresolutionofconventionalconfocalmicroscopy.
Besides,theinformationlossofconventionalFEDmethodhasalso beenalleviatedintheproposedmethodduetothesmallersubtraction factorintheproposed.ComparingFig.4(e)and(f),itisobviousthat theimagingresultof proposedmethodisbetterthanthatofconven- tionalFEDmethod.AsisshowninFig.4(e),thewidthofmicrotubules isnotuniformintheimagingresultofconventionalFEDmethod.Atthe positionindicatedbythearrowsof1and2inFig.4(e),thereisnoin- tensityinformationwheremicrotubulesactuallyexist.Itisobviousthat theinformationlossisveryseriousinconventionalFEDmethod.
However,becauseofthereductionofsubtractionfactor,theinfor- mationlossissignificantlysuppressedthroughtheproposedmethodin thisarticle.WecanseefromFig.4(f)thatthemicrotubulesarecontin- uouswhentheyareimagedbytheproposedmethod,andtheintensity informationexistsatthepositionindicatedbythearrowsof1and2.
4. Experiments
Inexperiment,weuse200nmsphericalfluorescenceparticlestoper- form theexperiment.Thelaserwavelengthis640nm,theNAof the objectiveissetto1.49,100X.Theexperimentalresultsofconventional confocal fluorescencemicroscopy,conventionalFEDmethod andthe proposedmethodareshownbelow.
AsisshowninFig.5(b),thepeakvalueoftheevaluationfunction C(𝛼)istakenat𝛼equalto0.19,sothesubtractionfactorinthisexperi- mentissetto0.19.Theimagingresultofconventionalconfocalfluores- cencemicroscopyisshowninFig.5(a),andtheimageoftheproposed methodisdepictedinFig.5(c).AsFig.5shows,theresolutionofthe proposedmethodishigherthanthatofconventionalconfocalfluores- cencemicroscopy.At thepositionsindicatedby thewhitearrowsin Fig.5(aandc),theproposedmethodcanresolvetwofluorescencepar- ticles,whiletheconventionalconfocalfluorescencemicroscopycannot resolvethem.Thismeansthattheproposedmethodcanachievehigher resolutionthanconventionalconfocalfluorescencemicroscopy.
Inordertocomparetheeffectivenessoftheproposedmethodand conventionalconfocalfluorescencemicroscopyclearly,wedrawthein- tensity profilesalong thegreenlineinFig.5(aandc). Theintensity profilesoftheconventionalconfocalfluorescencemicroscopyandthe proposedmethodareshowninFig.5(d).Intheintensityprofiles,there
Fig.5. Theimagingresultsof200nmsphericalflu- orescence particles. (a) The fluorescence particles imaged by conventional confocal fluorescence mi- croscopy.(b)Thevalueofevaluation functionC(𝛼) dependingondifferent𝛼values.(c)Thefluorescence particlesimagedbytheproposedmethodinthearti- cle,withsubtractionfactorsetto0.19.(d)Theinten- sityprofileofthetwomethodsalongthegreenline in(a)and(c).(Thebluedottedlinerepresentsthere- sultofconventionalconfocalfluorescencemicroscopy, andtheblacklinerepresentstheresultoftheproposed method.Thedistancebetweentwopeakintensitiesis 210nm.Thesizeof(a,c)is5𝜇m×5𝜇m.
Fig.6. Theimagingresultsoffluorescenceparticlesfor(a)theconventional FEDmethod(α =0.6)and(b)theproposedmethod(α =0.19).Thenegative valuesstillexistonthesubtractionresults.Thesizeoftheimageis5𝜇m×5𝜇m.
aretwointensitypeaksincurveoftheproposedmethod(blacklinein Fig.5(d)),whilethereisonlyoneintensitypeakinconventionalconfo- calmicroscopy(bluedottedlineinFig.5(d)).AsisshowninFig.5(d), thelateralresolutionoftheproposedmethodisashighas210nm,which ismuchhigherthanthatofconventionalconfocalmicroscopy.
Next,wecomparetheimagingresultsofconventionalFEDmethod andproposedmethod.ThesubtractionfactoroftheconventionalFED methodissetto0.6,thisisthecommonlyusedvalue[12].Thesub- tractionfactoroftheproposedmethodismuchsmallerthanthatofthe conventionalFEDmethod,whichissetto0.19accordingtothepeak positionofC(𝛼)inFig.5(b).Thesubtractionresultsofthesetwometh- odsareshowninFig.6.TheresultoftheconventionalFEDmethodis showninFig.6(a),whiletheresultoftheproposedmethodisdepicted inFig.6(b).Itisobviousthatthenegativevalueshaveworseeffecton theconventionalFEDmethodthanthatonproposedmethod.Therefore,
wecaninferthattheproposedmethodwiththesubtractionfactorequal to0.19wouldproducelessinformationlossafterzeroingnegative.
Furthermore,theresolutionoftheproposedmethodishigherthan thatofconventionalFEDmethod.Atthepositionindicatedbythear- rowsof1and2inFig.6(a),theconventionalFEDmethodcan’tresolve twofluorescenceparticles,butthesetwofluorescenceparticlesarere- solvedbytheproposedmethodinFig.6(b).AtthepositionsinFig.6in- dicatedbythearrow of3,theconventionalFEDmethodcanresolve thetwofluorescenceparticles,buttheresolutionisnotashighasthe proposedmethod.
5. Conclusion
Inthisarticle,weproposedanewmethodbasedoncombinationof digitalprocessingandFEDmethodtoobtainimageswithhigherresolu- tion.Becauseofthedigitalprocessing,thesubtractionfactorofproposed methodismuchsmallerthanthatofconventionalFEDmethod.There- fore, theinformationlossis alsoalleviatedin theproposed method.
Thesimulationandexperimentalresultsarepresented.Comparedwith conventional confocalfluorescencemicroscopyandconventionalFED method,theproposedmethodshowshigherresolutionandreducesthe lossofvalidinformationinconventionalFEDmethodsignificantly.
Acknowledgments
This work is supported by the National Key Research and De- velopment Programof China(2016YFF0101400); NationalBasic Re- searchProgramofChina(973Program)(2015CB352003);NationalNat- ural Science Foundation ofChina (NSFC)(61851110762, 61427818, 61827825, 61735017); Natural Science Foundation of Zhejiang Province(LR16F050001),andtheFundamentalResearchFundsforthe CentralUniversities(2018FZA5005);VietnamNationalFoundationfor ScienceandTechnologyDevelopment(NAFOSTED)underGrantnum- ber(103.03-2018.08).
Supplementarymaterials
Supplementarymaterialassociatedwiththisarticlecanbefound,in theonlineversion,atdoi:10.1016/j.optlaseng.2019.05.018.
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