Interferometer-based structured-illumination microscopy utilizing complementary phase relationship through constructive and destructive image detection by two cameras.

0.79 MB·English

by  Shao, L

JournalofMicroscopy,Vol.246,Pt32012,pp.229–236 doi:10.1111/j.1365-2818.2012.03604.x
Received2August2011;accepted30January2012
Interferometer-based structured-illumination microscopy utilizing
complementary phase relationship through constructive
and destructive image detection by two cameras
L. SHAO∗,‡, L. WINOTO∗, D.A. AGARD∗,†,
M.G.L. GUSTAFSSON ‡,§ & J.W. SEDAT∗
∗KeckAdvancedMicroscopyLaboratory,DepartmentofBiochemistryandBiophysics,Universityof
California,SanFrancisco,California,U.S.A.
†HowardHughesMedicalInstitute,ChevyChase,Maryland,U.S.A.
‡JaneliaFarmResearchCampus,HowardHughesMedicalInstitute,Ashburn,Virginia,U.S.A.
Keywords. Imagereconstruction,interferometer,I5S,opticaltransfer
function,structured-illumination,widefieldfluorescencemicroscopy.
Summary dimensions.Itcombinesstructured-illuminationmicroscopy
(SIM; Heintzmann & Cremer, 1999; Gustafsson et al.,
Inaninterferometer-basedfluorescencemicroscope,abeam
2000; Gustafsson, 2000; Gustafsson et al., 2008) with
splitter is often used to combine two emission wavefronts
an interferometer using two opposing objective lenses
interferometrically.Therearetwoperpendicularpathsalong
(Hell & Stelzer, 1992; Gustafsson et al., 1999). In SIM,
which the interference fringes can propagate and normally
the sample is illuminated by a periodic pattern, which
only one is used for imaging. However, the other path
mixes with the otherwise undetectable high-resolution
also contains useful information. Here we introduced a
information and, in spatial frequency space, moves it into
secondcameratoourinterferometer-basedthree-dimensional
thepassbandofthemicroscopeintheformofmoire´ fringes.
structured-illumination microscope (I5S) to capture the
The down translated high-resolution information is then
fringesalongthenormallyunusedpath,whichareoutofphase
computationallyrecoveredtoproduceanimagewithextended
byπrelativetothefringesalongtheotherpath.Basedonthis
resolution (Heintzmann & Cremer, 1999; Gustafsson et al.,
complementaryphaserelationshipandthewell-definedphase
2000; Gustafsson, 2000; Gustafsson et al., 2008). SIM can
interrelationships among the I5S data components, we can
double the conventional resolution in all three dimensions,
deduceandthencomputationallyeliminatethepathlength
resultinginaresolutionofabout100nmlaterallyand300nm
errorswithintheinterferometerloopusingthesimultaneously
axially(Gustafssonetal.,2008).I5SisanextensionofSIMin
recorded fringes along the two imaging paths. This self-
whichasecondobjectivelensisusedandplacedontheopposite
correction capability can greatly relax the requirement for
side of the sample, and the two apertures are combined
eliminatingthepathlengthdifferencesbeforeandmaintaining
interferometrically (Hell & Stelzer, 1992; Gustafsson et al.,
thatstatusduringeachimagingsession,whicharepractically
1999;Shaoetal.,2008).Asaresult,theaxialresolutionis
challengingtasks.Experimentaldataisshowntosupportthe
greatlyimprovedbothbecausethesetoflight-gatheringangles
theory.
of the microscope is enlarged and because the highest axial
spatialfrequenciesintheilluminationpatternareincreased
Introduction
due to the interference of the illumination beams coming
Wereportedearlieraresolution-enhancingschemeforthree- fromthetwoopposingobjectives.Anisotropic100-nm-scale
dimensional (3D) widefield fluorescence microscope, I5S resolutionisachievedbythistechniqueinalldimensions(Shao
(Shao et al., 2008), that greatly improves the resolution etal.,2008).
of optical microscopy to nearly 100 nm in all three InI5S,acollimatedlaserilluminationbeamisdiffractedby
atransmissionphasegratingandthecentralthreediffraction
Correspondenceto:JohnW.Sedat,DepartmentofBiochemistryandBiophysics, orders are split by a beam splitter, resulting in six mutually
UniversityofCalifornia,SanFrancisco,CA94158,U.S.A.Tel:[phone]; coherent illumination beams being incident on the sample,
fax:[phone];e-mail:[email protected] one triplet of beams passing through each objective lens
§Deceased (Fig. 1). The illumination pattern that results from the
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230 L. SHAO ET AL.
Conventional
illumination
M4
M3
Obj
m
Sample
CCD 2
Obj
s
M2
M1 CCD 1
Dichroic
m=-2 -1 0 1 2
Fig.2. PrinciplesofI5Sexplainedinfrequencyspace.(A)Thegeneralized
Grating
pupilfunction(GPF)ofanI5S/I5Mmicroscope,i.e.theportionsofthe
wavefrontdetectablethroughthetwoobjectivelenses.Inaconventional
widefieldmicroscope,onlyoneofthetwoshellsisdetectable.Thesupport
Multi-mode fiber
(i.e.regionofnonzerovalue)oftheintensitydetectionOTF,whichisthe
Fig.1. TheschematicdrawingofanI5Smicroscope.Theillumination autocorrelationoftheGPF,isshownin(B).Incomparison,thedetection
OTFofaconventionalmicroscopeisjustthemiddleregion.(C)Thesixdots
lightpassesfirstthroughatransmissiongrating,whichdiffractsitinto
representthesixcollimatedilluminationbeamsbeingincidentuponthe
threebeams(greenlines),andthenthroughabeamsplitter,whichsplits
sample.Theirinterferencecreatesa19-componentilluminationintensity
eachbeamanddirectsthreebeamstoeachofthetwoopposingobjective
pattern(D)organizedintofiveverticallinescorrespondingtom=−2to
lenses. The same beam splitter combines the two beams of emission
light(red)fromthesampleontothecamera.Normally,onlyonecamera 2.(E)TheeffectiveI5SOTFsupportisshowninky–kzcross-section.As
areference,theconventionalOTFsupportisdrawnindashedcontour
(CCD1)isusedtorecordtheemissionlightfromoneofthetwobeamsplitter
in(E).
exitports.HereweintroducedasecondimagingpathtorecordonCCD2
theemissionlightfromtheotherexitport.Themovableobjectivelenscan 3D acquisition, the Fourier transform D˜ of an observed 3D
bepositionedinX,YandZwithrespecttothestationaryobjectivelens.
imageD canbeexpressedasfollows(Gustafssonetal.,2008;
MirrorsM3andM4canbetranslatedtogethertoadjustthepathlength
Shaoetal.,2008):
difference.Thegratingcanberotatedandlaterallytranslatedtocontrol
theorientationandlateralphaseoftheilluminationpattern.MirrorsM3 (cid:2)2
ismadepartiallytransmissivetoletconventionalilluminationcomein D˜(k)= Om(k)S˜(kxy−mp)eimϕ, (2)
fromtheresothatI5SdetectionOTFcanbemeasured. m=−2
where S˜(k)isthesampleinformation, O (Figs3A–C)isthe
m
interference of these six beams consists of 19 frequency
mth-ordereffectiveopticaltransferfunction(OTF)obtainedby
components (Fig. 2D) and can be expressed as (Shao et al.,
convolvingthedetectionOTFwiththeaxialFouriertransform
2008)
of I . The axially extended support, or the nonzero valued
m
(cid:2)2 region, of O in I5S is attributed to both the high axial
m
I(rxy,z)= Im(z)ei(m2πp·rxy+mϕ), (1) illuminationfrequencies(Fig.2D)andadetectionOTFwith
m=−2 twoaxially extendedsupportregions(orthesidebands;Fig.
where r represents the lateral coordinates (x, y), p is the 2B)inadditiontotheusualOTFsupportregion(orthecentral
xy
lateral component of the wave vector of each beam not band) of the single-objective microscopy (Gustafsson et al.,
coincident with the optical axis k (or the side beams), I (z) 1999).Equation(2)showsthatI5Simprovestheresolution
z m
is the mth-order axial illumination pattern in real space laterally via frequency shift of the sample information and
correspondingtothemthaxialrowofilluminationfrequencies axiallyviatheextendedsupportintheeffectiveOTFs.
shownasdotsinFigure2Dandϕisaphaseangle(Gustafsson
et al., 2008; Shao et al., 2008). Given the form of the
Imagereconstructionandpathlengthdifference
illuminationpatterninEq.(1)andtheconditionthattheaxial
positionoftheilluminationpatternisfixedinrelationtothe TherawdataofSIM,includingI5S,isthesummationoffive
focalplaneofthemicroscopeasthesampleisrefocusedduring components (Eq. (2)). These components can be separated
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DUAL-CAMERA I5S MICROSCOPY 231
relationshipbetweenthefringesatthetwobeamsplitterexits
(tobediscussednext),theactualpathlengthdifferencewithin
the interferometer loop can be estimated from a pair of 3D
imagessimultaneouslyacquiredthroughthetwoexits.With
thisquantityknown,onecantheneitherchooseamatching
set of OTFs from a library of OTFs or, in a more attractive
solution, synthesize a set of OTFs that can account for the
estimatedpathlengthdifference,andusethosetoreconstruct
thedataset.Asaresult,therequirementforachievingaspecific
pathlengthdifferenceforeachexperimentcanberelaxed.
Pathlengthdifferenceestimation
First, we discuss how the path length difference can be
Fig.3. ExperimentallymeasuredandrotationallyaveragedI5SOTFsOm estimated from an I5S data set. Given a known path length
ofEq.(2)form=0,±1and±2(A—C).(D)Demonstratesthatm=0 difference δ, the detection OTF of I5S can be divided into
andm=±1componentspartlyoverlapwhentheyareplacedwherethey three regions based on different phases: b, 0 and −b, where
belonginfrequencyspace. b = 2πδ/λem and λem is the emission wavelength (Fig. 4A).
These values are because of the fact that the detection OTF
given a series of images taken with five different lateral isanautocorrelationofthegeneralizedpupilfunction(GPF;
pattern’s phases (ϕ in Eqs (1) and (2); Gustafsson et al., Fig. 2A) and the relative phase difference between the two
2008;Shaoetal.,2008).Becausethelateralpatterninour shellsofGPF(i.e.thetwowavefrontscollectedseparatelyby
implementation is one-dimensional (1D), the same pattern the two objective lenses) is b. Likewise for the illumination
needs to be applied multiple times with different angles (i.e. components(Fig.4B),threegroupscanbedistinguishedbased
p in Eqs (1) and (2) with the same magnitude but different onthecomponents’phases:a,0and−a,wherea=2πδ/λ
ex
orientations)soastoisotropicallyextendthelateralresolution. andλ istheexcitationwavelength.BecausetheeffectiveI5S
ex
Afinalimagewith100nmresolutioninallthreedimensions OTFO istheconvolutionofthedetectionOTFwiththemth
m
(Fig. 2E) is reconstructed by positioning all the separated illumination order I˜ (Eq. (2) and Fig. 3) and phases of the
m
information components back to their original locations in operandsaddinconvolution,thephasesindifferentregions
frequencyspaceandthencorrectingforamplitudedifferences ofI5SeffectiveOTFsarevariousadditivecombinationsof0,
viaageneralizedWienerfilter(Gustafssonetal.,2008;Shao ±aand±b.Thecolour-codedmapsofphaseintheseOTFsare
etal.,2008). showninFigures4C–E.
For I5S reconstruction to work, it is required that the Becausethemth-ordercomponentoftheI5Srawdataisa
raw image is acquired under the same conditions as the subregionofthesample’sFouriertransform—corresponding
measuredeffectiveOTFs.InI5Soranyinterferometricset-up, tothesupportofO shiftedbymp(Eq.(2))—multipliedbyO ,
m m
oneconditionpronetovariationindifferentimagingsessions thiscomponent’sphasemapistheadditionofthesample’sand
isthepathlengthdifferenceoftheinterferometerloop.Before theOTF’sphases.Furthermore,componentsofdifferentorders
everyexperiment,significanttimemustbespentondigitally partiallyoverlapwitheachotherinfrequencyspace(Fig.3D).
adjustingthispathlengthdifferencetoreachzero,whichgives For example, the central line of the m = 1 component (the
the maximum axial fringe contrast. Even if this preimaging dashed line in Fig. 4D) should be placed p distance (Eqs (1)
adjustment is performed very accurately, instrumental drift and (2)) from the central line of the m = 0 component; i.e.
willhavecauseddifferentpathlengthdifferences,i.e.different tothedashedlineinFigure4C.Ifweignoretheportionsof
imagingconditions,intheactualdatasetandinthedataset theeffectiveOTFsderivedfromthesidebandsofthedetection
takenfortheOTFdetermination,resultinginaxiallyringing OTFforthemomentandmovethem=1componenttoits
artefactsinthereconstructionbecauseoftheunmatchedOTF originalpositioninfrequencyspace,asillustratedinFigure5,
used.TomakeI5Seasiertouse,weneedaschemethatcan the green coloured part of the m = 1 component partially
relaxthisverystringentrequirementonpathlengthdifference overlapswiththeredcolouredpartofthem=0component
consistencywithoutinducingartefacts. (shadedareasinFig.5).Withinthisoverlap,therawimage’s
AnotherdisadvantageofthecurrentI5Sset-upisthatonly m=0and1componentsatacertainfrequencykarerelated
theimaginginterferencefringesatoneofthebeamsplitter’s by
two exit ports are recorded, meaning half of the emission
Oˆ (k−p)D˜ (k)= Oˆ (k)D˜ (k−p)eia, (3)
lightisdiscarded.Capturingbothhalvesoftheemissionlight 1 0 0 1
simultaneously would significantly improve the signal-to- where Oˆ and Oˆ are OTFs that are acquired with zero
0 1
noiseratio.Furthermore,becauseofthecomplementaryphase path length difference and D˜ is the mth-order component
m
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232 L. SHAO ET AL.
(a+b a b b-a 0 a b b a a b
Fig.4. ThemapsofphasevaluesinI5SdetectionOTF(A),illuminationstructures(B)andtheeffectiveOTFsform=0(C),±1(D)and±2(E).Thereason
whymostilluminationcomponentsarestretchedaxiallycomparedtoFigure2Dwasexplainedindetailinearlierpublications(Gustafssonetal.,2008;
Shaoetal.,2008).Theregionscoloureddifferentlycorrespondtodifferentphasesequaltovariouslinearcombinationsofaandb,whereaandbarethe
phasedifferencescausedbythepathlengthdifferenceintheinterferometerloopfortheexcitationandemissionwavelengths,respectively.Inreality,the
dashedlinesin(C)and(D)coincide,i.e.theyrepresentthesamelateralfrequency.
Figure 5 before the path length difference can be estimated
usingEq.(3).
Estimationbasedoncomplementaryphaserelation
It can be proved (see Appendix) that in I5S, when the two
emission wavefronts collected from the two objective lenses
are coherently combined at the beam splitter, the phase of
Fig.5. Whenthem=1component(Fig.4D)isplacedwhereitbelongsin
the interference fringes at the primary exit port (i.e. the
frequencyspace,itpartlyoverlapswiththem=0componentasindicated
illuminationentryport,Fig.1)ofthebeamsplitterisexactlyπ
bythe shadedareas. Shownhere areonlythe regionsbecauseof the
differentthanthatattheotherexitport(thesecondaryexit).
convolutionofcentralbandofthedetectionOTF(Fig.4A,green)and
thecentralthreeandtwofrequenciesofthem=0and1illumination This results in the following relation between the detection
structure,respectively(Figs2Dand4B). OTFsacquiredattheprimaryandthesecondaryexits:when
thephasesare±binthesidebandsoftheformer,thephases
are±(b+π)inthesidebandsofthelatter.ThenifI5Seffective
O (k)S˜(k−mp)separatedfromEq.(2)(thezeropathlength OTFsareacquiredthroughthetwoexits,thesameπ phase
m
differencerequirementon Oˆ canbesatisfiedevenforOTFs differenceexistsbetweenthetwosetsofOTFsinthoseregions
m
acquiredwithnonzeropathlengthdifference,tobediscussed because of the convolution of the illumination components
inOTFseparationandsynthesis).Linearregressioncanthenbe withthesidebandsofthedetectionOTF.Furthermore,asan
appliedtosolveEq.(3)forausingallthefrequencieswithin image in frequency space is a multiplication of the object’s
the overlap. This seems to be a straightforward method to Fourier transform by the OTF, this π phase difference in
estimate the path length difference, except that it requires thosesideband-derivedregionsisalsotherebetweentwoI5S
a clean overlap between only the two central band-derived datasetsacquiredsimultaneouslythroughthetwoexitsfor
regions of the m = 0 and 1 components pointed to by the any sample. Consequently, the addition (or subtraction) of
arrows in Figure 5. Unfortunately, superimposed on those thesetwodatasetsresultsinonlythecentral(orside)band-
two central band-derived regions are other signals derived derived regions being nonzero in frequency space, provided
from the sidebands of the detection OTF (Figs 3 and 4C–E), thatcorrectintensitynormalizationbetweenthetwoimages
which make Eq. (3) invalid. Hence, we first need a solution hasbeenapplied.Iftheadditionimageisusedforextracting
for obtaining the uncontaminated overlaps as depicted in the overlap shown in Figure 5, the overlap would not be
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DUAL-CAMERA I5S MICROSCOPY 233
with each other to compensate the residual misalignment
between the imaging paths. The misalignment, mainly
becauseoflateralshift,rotationandmagnification,onlyneeds
tobecalibratedonceeveryfewmonthsusingscatteredbeads
samples.Theresultofthecalibration,atwo-dimensionalaffine
transform matrix, was saved for aligning the image pairs
in subsequent experiments. The intensity ratio between the
imagepairafterbackgroundsubtractionwasalsocalibrated
and saved for future use. After alignment and intensity
correction, each raw image was separated into the five
information components (Eq. (2)), each corresponding to a
differentmofEq.(2)(Shaoetal.,2008),andthem=0and1
componentsoftheimagesacquiredbyonecamerawereadded
totheircounterpartsacquiredbytheother,resultinginthe
new m = 0 and 1 components with little sideband-derived
contamination. The overlap between the red subregion of
the m = 0 component and the green subregion of the m =
1 component (Fig. 5) was then extracted and used for the
estimationofthepathlengthdifferencebasedonEq.(3).
OTFseparationandsynthesis
Given the estimated path length difference, we still need a
schemeforimagereconstructiontotakeadvantageofit.Here
weintroducesuchaschemebasedonthefactthatI5Seffective
OTFsaretheconvolutionofthedetectionOTFOwiththe1D
axialilluminationstructuresI˜ (Eq.(2)).Supposeameasured
m
I5S OTF can be decomposed into O and I˜ . Once the path
m
length difference is estimated from a raw image, then it is
trivialtomodifythephasesofOandI˜ bymultiplyinge±ia to
m
theI˜ componentsofnonzerophases(Fig.4B)ande±ibtothe
m
Fig.6. TheeffectiveI5SOTFswereacquiredthroughtheprimaryand sidebandsof O(Fig.4A).Thephase-modulatedOand I˜m can
secondarybeamsplitterexitandrotationallyaveraged,andtheiradditions then be convolved together to synthesize a set of OTFs that
andsubtractions,form=0,±1and±2,areshownin(A)–(C)and(D)–(E), canaccountforthepathlengthdifferencespecifictotheraw
respectively.TheregionsderivedfromthesidebandsofthedetectionOTF image.
aremostlymissingintheadditions,althoughthosefromthecentralband ToseparateI5SOTFsintotwoconvolvingparts,oneofthe
aremissinginthesubtractions,astheoreticallypredicted.
partshastobeknown.Thereisawaytomeasurethedetection
OTFandI5SeffectiveOTFsalmostsimultaneouslyaslongas
contaminatedbythesuperimposedsideband-derivedsignals the mirror M3 in Figure 1 also transmits partially (20% is
and therefore, the path length difference can be cleanly whatweused)sothataconventionalilluminationpathcanbe
estimatedasdescribedinEq.(3). introducedthroughthatmirror.Withthisnewset-up(Fig.1),
Toimplementtheaboveidea,asecondimagingpathwas the3DI5SeffectivePSFanddetectionPSFcanbeacquiredinan
addedtoI5Stocapturetheinterferencefringesthroughthe interleavedmannerbyalternatingbetweentheconventional
secondaryexitofthebeamsplitter(CCD2inFig.1).Apairof andthestructured-illuminationpathateachdefocusstep.We
I5Spointspreadfunctions(PSF)wasacquiredsimultaneously canthenobtainrotationallyaveragedI5SeffectiveOTFsand
bythetwoCCDsandtherotationallyaveragedeffectiveOTFs detectionOTFfromthesePSFs.
were generated (Gustafsson et al., 2008; Shao et al., 2008). The OTF separation problem is formulated as solving
Thesummations and subtractionsof thesetwosetsof OTFs for I˜ (k ) in O (k)= O(k)⊗I˜ (k ) given O (k) and O(k).
m z m m z m
areshowninFigure6,which,asexpected,containmostlythe Because I˜ (k ) is a 1D function, this problem is equivalent
m z
subregionsderivedonlyfromthecentralbandandsidebands to solving it in a series of 1D deconvolution problems
ofthedetectionOTF,respectively. O (k ,k )= O(k ,k )⊗I˜ (k ) for each lateral frequency
m z xy z xy m z
To estimate the path length difference in each data set, a k . Linear convolution can be transformed into a circular
xy
pairofrawdatasetswasacquiredsimultaneouslybythetwo convolution, which can then be formulated as a vector (in
cameras. The image pair was then computationally aligned this case the unknown I˜ (k )) being multiplied by a cyclic
m z
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234 L. SHAO ET AL.
I5S illumination structure (Fourier space) described above can be applied to the I5S effective OTFs
measured by the two cameras. The estimated path length
order 0 differencecanthenberemovedfromOandI˜mand,therefore,
1 order 1 wecansynthesizetheI5SeffectiveOTFswithzeropathlength
e 0.8 order 2 difference (Oˆm in Eq. (3)) by convolving the zero phase-
plitud 0.6 mpaotdhulelantgetdhOdiaffnerdenI˜mc,ewinheiachchaIr5eSndeaetdaesdetto(Ecqo.r(r3e)c).tlFyoersetaimchatoef
m
A 0.4 thethreelateralpatternorientations,data-specificI5Seffective
OTFs are synthesized based on the estimated path length
0.2
differenceasdescribedaboveandthenusedinreconstructing
0 thenormalI5Sdatasetacquiredthroughtheprimarybeam
−10 −5 0 5 10
splitterexit.
k (µm−1)
z
Fig. 7. I5S illumination structure axial profiles in frequency space,
obtained by deconvolving measured I5S detection OTF from the I5S Results
effectiveOTFs.Black,redandbluecurvescorrespondtoorderm=0,
Figure 7 shows the results of separating I5S illumination
±1and±2components,respectively.
structuresfromthemeasuredI5SeffectiveOTFsasdiscussed
above.ThethreecurvesinFigure7aretheamplitudesofI5S
matrix, if the vectors have a sufficiently short support or illuminationstructureversusk infrequencyspaceform=0,
z
are padded with enough zeros (Bertero & Boccacci, 1998, ±1and±2(Eqs(1)and(2)).
Chapter2.7).Astackoflinearequations,oneforeachk ,can Two pairs of dual-camera I5S images of a single-bead
xy
thusbeformulatedintoanoverdeterminedsystemforsolving samplewereacquired.Nonzeropathlengthdifferenceswere
I˜ (k ).Theaxialilluminationstructuresthussolvedandthe intentionallyintroducedwhenacquiringthesedatasets.The
m z
measureddetectionOTFarestillmodulatedbyanunknown reconstructionsusing astandard setofeffective OTFstaken
phasebecauseoftheunknownpathlengthdifferenceduring with little path length difference present show the expected
dataacquisition.Toestimatethispathlengthdifference,the ringing artefacts in the axial intensity profile through the
same summation–subtraction and overlap extraction steps bead centre (Figs 8A and C). The different polarities of the
A B
1 1
0.8 0.8
y 0.6 y 0.6
sit sit
n n
e 0.4 e 0.4
nt nt
I I
0.2 0.2
0 0
−50 0 50 −50 0 50
Z Z
C D
1 1
0.8 0.8
Fig. 8. Results showing the effects of path length y 0.6 y 0.6
difference estimation and correction. (A) and (C) sit sit
n n
The axial profiles of I5S reconstruction of a single nte 0.4 nte 0.4
bead,imagedwithintentionalpathlengthdifferences I I
0.2 0.2
estimatedtobe0.15and−0.9radians,respectively.
(B)and(D)ResultsusingsynthesizedOTFsbasedon 0 0
theestimatedpathlengthdifferencescorresponding
to(A)and(C),respectively.Therearesignificantlyless −50 0 50 −50 0 50
ringingartefactsin(B)and(D)thanin(A)and(C). Z Z
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DUAL-CAMERA I5S MICROSCOPY 235
significantly enhance the real-world applicability of I5S to
Secondary exit
Is biology. The basic principle demonstrated in this paper lays
thegroundworkforaschemethatcanachievesuchagoal.It
I
p doesnot,however,affectotherfactorslimitingtheapplication
Primary exit of I5S to biology, including the requirement of refractive
indexmatchingamongthemountingmedium,theimmersion
medium and the sample itself, and the requirement that
thetwoobjectivelensesarecloselymatchedintheiroptical
properties. In our demonstration, the fluorescent bead was
I2 (A2) I1 (A1) mounted in the same medium as the high refractive index
Point (1.51)immersionmedium.
source As mentioned earlier, the image pair recorded on two
camerascanalsobeusedsimplyforimprovingthesignalto
Fig.9. Proofofπphasedifferencebetweentheinterferencefringesatthe noise.Thiscanbeaccomplishedbyincludinginthegeneralized
primaryandthesecondarybeamsplitterexits.SeeAppendixfordetails. Wiener filter (Gustafsson et al., 2008) the additional terms
correspondingtotheimagesandOTFsacquiredbythesecond
asymmetryinthoseplotsindicateeitherpositiveornegative cameraoncetheimagepairisaligned.
path length difference in the loop. For each data set, we
performed phase difference estimation (the results are 0.15 Acknowledgements
and –0.9 radians for data set shown in Figs 8A and C,
We dedicate this paper to the late Dr. Mats Gustafsson.
respectively)anddataset-specificOTFsynthesisasdescribed
This work was supported in part by the Keck Laboratory
above,andthenreconstructedtheimagesacquiredthrough
for Advanced Microscopy, the National Institutes of Health
theprimarybeamsplitterexitusingthesynthesizedOTFs.The
(GM25201toJ.W.S.andGM31627toD.A.A.),theHoward
resultsarealsodisplayedasaxialintensityprofilesinFigures
HughesMedicalInstitute(D.A.A.)andbytheNationalScience
8BandD,whichexhibitmuchlessringingthanFigures8A
Foundation through the Center for Biophotonics, an NSF
andC.
Science and Technology Center that is managed by the
UniversityofCalifornia,Davis,underCooperativeAgreement
Discussion No.PHY0120999.
Weintroducedamethodtoestimatethepathlengthdifference
present in each I5S data set with the assistance of a
References
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information,thenewsecondarybeamsplitterexitwillhave microscopywithbetterthan100nmaxialresolution.J.Microsc.195,
destructive interferences information. With the estimated 10–16.
phase difference, a data set specific set of OTFs can then Gustafsson,M.G.,Shao,L.,Carlton,P.M.etal.(2008)Three-dimensional
be synthesized, because I5S effective OTFs are separable resolutiondoublinginwidefieldfluorescencemicroscopybystructured-
intoadetectionOTFconvolvingwiththeaxialillumination illumination.Biophys.J.94,4957–4970.
structures, and used for reconstructing the data set. We Gustafsson,M.G.L.,Agard,D.A.&Sedat,J.W.(2000)Doublingthelateral
resolution of wide-field fluorescence microscopy using structured-
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principle. Reconstruction using a synthesized, as opposed
Hecht,E.(1998)Optics,3rdedn.Addison-Wesley,Reading,MA.
to a standard, set of OTFs successfully removes most of the
Heintzmann, R. & Cremer, C. (1999) Laterally modulated excitation
axialringingartefactsthatarebecauseofanunknownpath
microscopy:improvementofresolutionbyusingadiffractiongrating.
length difference. One major difficulty of I5S or any other
Proc.SPIE.3568,185–196.
interferometricmicroscopeisthestrictrequirementonpath Hell,S.&Stelzer,E.H.K.(1992)Propertiesofa4piconfocalfluorescence
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(cid:3)C 2012TheAuthors
JournalofMicroscopy(cid:3)C 2012RoyalMicroscopicalSociety,246,229–236
236 L. SHAO ET AL.
Shao,L.,Isaac,B.,Uzawa,S.,Agard,D.A.,Sedat,J.W.&Gustafsson,M.G. Thereflectedhalfofwavefront1interferesattheprimaryexit
(2008)I5S:widefieldlightmicroscopywith100-nm-scaleresolutionin withthetransmittedhalfofwavefront2,whosephaseisϕ2+
threedimensions.Biophys.J.94,4971–4983. θ,andthustheinterferenceintensityis(Born&Wolf,1980,
Chapter7.2)eitherI =I /2+I /2+(I I )1/2·cos(ϕ1+π –
p 1 2 1 2
ϕ2 – θ), denoted Case 1a, or I = I /2 + I /2 + (I I )1/2·
Appendix p 1 2 1 2
cos(ϕ1+θ –ϕ2),denotedasCase1b.Likewise,thereflected
Hereweprovetheπphasedifferencebetweentheinterference half of wavefront 2 either has phase ϕ2 + π or ϕ2 +
fringes at the primary and secondary exit port of the beam 2θ, depending on where the reflection occurs, and when it
splitter. Two parts of a wavefront with intensities I1 and I2 interferes with the transmitted half of wavefront 1 at the
combineatthebeamsplitteraftertraversingthetwoarmsof secondary exit, whose phase is ϕ1 + θ, the interference
the interferometer. Each of them is split into halves by the intensityiseitherI =I /2+I /2+(I I )1/2·cos(ϕ1+θ–ϕ2
s 1 2 1 2
beam splitter, with one-half transmitting through and the –π),denotedCase2a,orI =I /2+I /2+(I I )1/2·cos(ϕ1–
s 1 2 1 2
otherhalfreflectedbythebeamsplitter(Fig.9).Thereflected ϕ2–θ),denotedCase2b.Becauseofenergyconservation,i.e.
halfofwavefront1eitherhasphaseϕ1+π,whereϕ1isthe thatI +I mustequalI +I ,itismandatorythatCase1aand
1 2 p s
phasebeforethesplit,ifthereflectionoccursattheglass–glue 2borCase1band2aco-occursothatthecos(·)termscancel
interface, or ϕ1 + 2θ if the reflection occurs at the glue– out. In either case, it means the phases of the interference
glassinterfaceaccordingtotheStokesrelations(Hecht,1998, fringes at the primary and secondary exit port are different
Chapter4.10),whereθisthephasedelaybecauseoftheglue. byπ.
(cid:3)C 2012TheAuthors
JournalofMicroscopy(cid:3)C 2012RoyalMicroscopicalSociety,246,229–236