Annular Beam Shaping in Multiphoton Microscopy to Reduce...

Research ArticleAnnular Beam Shaping in Multiphoton Microscopy to ReduceOut-of-Focus Background

Johan Borglin12 Danni Wang1 Nicholas J Durr3 Dag Hanstorp2

Adela Ben-Yakar4 andMarica B Ericson1

1Biomedical Photonics Group Department of Chemistry and Molecular Biology University of Gothenburg Kemivagen 10412 96 Gothenburg Sweden2Department of Physics University of Gothenburg Kemivagen 9 412 96 Gothenburg Sweden3Department of Biomedical Engineering Johns Hopkins University 3400 N Charles St Baltimore MD 21218 USA4Department of Mechanical Engineering University of Texas 204 E Dean Keeton Street Austin TX 78712 USA

Correspondence should be addressed to Marica B Ericson maricaericsonchemguse

Received 19 January 2017 Accepted 15 March 2017 Published 24 May 2017

Academic Editor Kam-Sing Wong

Copyright copy 2017 Johan Borglin et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Despite the inherent spatial confinement of multiphoton processes that arises from focusing through an objective the maximumimaging depth in conventional multiphoton microscopy is ultimately limited by noise from out-of-focus fluorescence This isparticularly evident when imaging beyond shallow depths in highly scattering tissue as increased laser powers are necessary Theout-of-focus signal originates from multiphoton processes taking place primarily at shallow depths and deteriorates contrast andlimits imaging depth In this paper annular laser beams are explored as a concept to reduce this background signal in multiphotonmicroscopyThe approach is theoretically verified by data from simulations and proof of principle is demonstrated on a custom-builtexperimental multiphoton microscopy platform Annular laser beams were created by adopting wavefront control using a spatiallight modulator and implemented for imaging tissue phantoms simulating turbid media and human skin ex vivo The signal-to-background ratios were calculated and compared to images acquiredwith a traditional filled-apertureGaussian beam Experimentsin tissue phantom show an improvement in signal-to-background ratio of about 30 when using annular beam illumination incomparison to Gaussian illumination at specific depths When laser power is not the limiting factor this approach is expected toprovide even greater benefits

1 Introduction

Multiphoton microscopy (MPM) has evolved from a pho-tonic novelty [1] to a well-established laboratory tool thatallows for noninvasive 3D imaging of tissue [2] Since MPMis operating in the ldquooptical windowrdquo of biological tissue(120582sim600ndash1300 nm) it allows for increased imaging depthscompared to single photon excitationmodalities like confocalmicroscopy [3] MPM utilizes high intensity fs-pulse lasersto generate a high flux of photons necessary for multiphotonabsorption Conventionally these nonlinear processes areassumed to occur only at the focal volume where extremelyhigh photon flux is generated allowing for noninvasive three-dimensional optical sectioning Recently MPM has enabled

powerful applications in life sciences such as high-speedcell mitosis imaging [4] real-time lymphocyte tracking [5]and cell migration monitoring [6] MPM has also beenestablished as a tool for visualization in turbid biologicalmatter such as the human skin [7 8] For dermatologicalpurposes multiphotonmicroscopy has been commercializedfor clinical use (DermaInspect Jenlab Germany) [9] Inaddition in vivo MPM is advancing the field of neuroscienceby allowing for optical visualization of neural architectureand functions [10 11]

Assuming sufficient excitation power and aberrationcontrol the fundamental factor limiting imaging depthwhen performing MPM in tissue is the background fluores-cence originating from out-of-focus areas above the imaging

HindawiInternational Journal of SpectroscopyVolume 2017 Article ID 7560141 10 pageshttpsdoiorg10115520177560141

2 International Journal of Spectroscopy

(a) (b)

(a)(b)F(z)

z

Figure 1 Schematic illustration of the concept of annular laser beamto reduce out-of-focus signal in MPM for the two conditions (a)where Gaussian beam profile is implemented and (b) for annularbeam illumination The figure illustrates the hypothetical relativecontribution of fluorescence signal 119865(119911) as a function of depth119911 While comparing conditions given equal photon fluences in thefocal region the Gaussian illumination (a) is expected to generateelevated levels of out-of-focus signal from the incoming planeswhere the laser power is at a maximum compared to annularillumination (b)

plane [12ndash14] The out-of-focus signal is a result of increas-ingly high excitation powers that are necessary to maintainhigh excitation intensity when the focal volume is locateddeep in the tissue This background signal deteriorates theimaging contrast (signal-to-background ratio) and in turnlimits imaging depth Thus efforts should be made tominimize this undesired signal to improve the signal-to-background ratio and thereby increase the imaging depthThe implementation of a spatial filter such as a confocalpinhole should allow for blocking the out-of-focus sig-nal however the decreased collection efficiency deems thisapproach suboptimal in MPM as previously discussed [14]Instead we here propose an approach based on annularbeam shaping As illustrated in Figure 1 the fluorescenceF generated at a plane 119911 would be more confined tothe focal plane when using an annular laser beam whencompared to Gaussian beam illumination Geometricallythe peak irradiance of the laser light at the sample surfacecan be lowered by distributing the laser energy in a ringinstead of a Gaussian beam profile This lowers the intensityin any given point of the sample while retaining the photonflux in the focal volume and thus reduces the generationof out-of-focus fluorescence contributing to the undesiredbackground Previously annular beam shaping has beeninvestigated for confocal microscopy [15] and multiphotonmicroscopy [16 17] to improve resolution The conceptof using annular beams to reduce out-of-focus signal ispreviously not explored

This study investigates the potential of annular beamsto improve signal-to-background ratio in MPM The imple-mentation of annular beams in optical microscopy gives anelongated focal volume which results in beamprofiles similarto that of a Bessel beamTherefore when explored for MPMthe potential effect on the focal volume should be consideredThis paper investigates the benefits and tradeoffs of using

annular beams by combining theoretical simulations andproof-of-concept experiments using wavefront controllingoptics The work is an extension of our previous approach[18] Here a spatial light modulator (SLM) was introducedin the optical path of a custom-built experimental MPMplatform in order to obtain an annular beam similar to theapproach shown by Nie et al [19] By changing the pattern onthe SLM a systematic comparison of annular versus Gaus-sian illumination could be performed Fluorescent scatteringtissue phantoms simulating the properties of optically densebiological tissue were investigated together with excisedhuman skin tissue in order to demonstrate proof of concept

2 Materials and Methods

21 Theoretical Simulations In order to simulate the excita-tion intensity generated in the focal region when switchingfrom Gaussian to annular beam shape the Fresnel-Kirchhoffintegral was calculated for varying beam shape conditionsbased on a previously described approach [18 20] TheFresnel-Kirchhoff integral is stated as

Ψ1015840FK (1199031015840 1205791015840 119911) = 2120587119911120582 intΨ1015840 (119903 120579) 119890(minus2120587119894119877120582)Φ119897119889119878 (1)

corresponding to the total field amplitude in a point (1199031015840 1205791015840)at the distance 119911 from the lens The coordinates are schemat-ically illustrated in Figure 2 Here Ψ1015840(119903 120579) is the fieldamplitude at a point (119903 120579) on the lens (119911 = 0)The integrationis made by summing over the contributions from each areaelement dS on the lens surface The phase retardation of thelens Φ119897 is given by

Φ119897 = 1198901198941205871199032120582119891 (2)

Here 119891 is the focal length of the lens 120582 is the wavelengthand 119877 is the distance vector from the point (119903 120579) on the lensto the point (1199031015840 1205791015840 119911) for which the total field Ψ1015840FK(1199031015840 1205791015840 119911)is calculated using the expression

119877 asymp 119911 + 1199032 + 11990310158402 minus 21199031199031015840 cos (120579 minus 1205791015840)

21199111015840 (3)

The field amplitude at the lens Ψ1015840(119903 120579) was given by theexpression

Ψ1015840 (119903 120579) = 11987501205871198612 (1 minus119887119903) 119890minus2((119903minus119887)119861)

2 (4)

where 1198750 is the laser power at the lens 119861 is the outer radiusof the beam and 119887 is the inner radius of the beam Theouter radius 119861was scaled down with increasing 119887119861 to ensurethat the total energy was kept constant in the comparisonsbetween different conditions The Fresnel-Kirchhoff integral(1) was calculated using MATLAB (MathWorks Natick MAUSA) for a grid around the focus in order to simulate theintensity distribution around the focal volume Each beamshape was characterized by the ratio between the innerradius (b) and outer radius (B) ranging from 119887119861 = 0 for

International Journal of Spectroscopy 3

y

r x

z

b

r998400x998400

y998400

120579998400

120579

(a)

b B

z

r

B998400(z)b998400(z)

(b)

Figure 2 Schematic view of the coordinates for theoretical simulations (a) the coordinates used for calculating the Fresnel-Kirchhoff integralFor every point (1199031015840 1205791015840 119911) located at a distance 119877 from the lens the contribution from each element (119903 120579) on the lens (119911 = 0) is added (b)coordinates for considering the out-of-focus signal generated adopting simplified geometrical focusing conditions

Gaussian illumination up to the extreme annular case with119887119861 approaching 1In addition to exploring the effects on the focal volume

the expected generation of out-of-focus fluorescence wascalculated by a geometric approach using the coordinatesas illustrated in Figure 2(b) This is a simplified modelthat assumes that only the ballistic photons are responsiblefor generating two-photon excitation Though the scatteredsemiballistic photons also contribute to out-of-focus fluores-cence [12] this approach was considered to be a conceptuallysimple and valid model to estimate the potential reductionof out-of-focus fluorescence in relative terms The fieldamplitude Ψ1015840(119911) was calculated as a function of 119911 where theGaussian beam profile is given by

Ψ1015840 (119911) = 119875012058711986110158402 119890minus2(11990310158401198611015840)2 (5)

and the annular beam is given as

Ψ1015840 (119911) = 119875012058711986110158402 (1 minus11988710158401199031015840) 119890minus2((119903

1015840minus1198871015840)1198611015840)2 (6)

1198750 is the peak power at the exit of the lens 1199031015840 is the radialcoordinate and 1198611015840 and 1198871015840 are the beamwidth and inner beam

radius respectively which decrease as a function of depth 119911through the relation according to

1198611015840 (119911) = 119861(1 minus 119911 tan1205721198860 )

1198871015840 (119911) = 119887 (1 minus 119911 tan1205721198860 ) (7)

119861 and 119887 are the beam width and inner radius at the apertureexit 1198860 is the aperture radius and120572 is calculated from theNAdescribed by

NA = 119899 sin120572 asymp 119899 1198632119891 (8)

The generated out-of-focus fluorescence was estimatedto be proportional to the square of the field intensity at thevarying 119911-levels that is at different depths so that the totalbackground fluorescence was calculated as

119865119861 = intΨ1015840 (119911)2119890minus2119911120583119904119889119911 (9)

The attenuation term in (9) was included to account forattenuation of both excitation light and emitted fluorescencein the sample The value of the scattering coefficient 120583119904was set to 150 cmminus1 that is corresponding to approximateparameters of human skin [21ndash23] The value of 119865119861 wascalculated for a Gaussian beam condition and annular beams


TiSapphire laser

Pockels cell

M1

Beam expander

Scanmirrors

M3 DCM

DCM

F1 (52550)

F2 (580150)

PMT1

PMT2

Objective

Sample

M2SLM

L2 L1

Half-wave platePhotodiode

TCSPC

BB

Figure 3 Schematic illustration of the experimentalMPMplatformWe introduced an SLM in the excitation path to form an annulus atthe back aperture of the objective M mirror L lens F filter SLMspatial light modulator BB beam blocker DCM dichroic mirrorPMT photomultiplier tube TCSPC time-correlated single photoncounting data acquisition

with a range of 119887119861 values The implemented parametersused for the simulations were chosen to correspond to theexperimental setup with numerical aperture of the objectiveNA = 08 beam waist at the aperture exit B = 14mmwater immersion with refractive index 119899 = 133 and laserwavelength 120582 = 800 nm The distribution of fluorophoreswithin the sample is assumed to be homogenous The fluo-rescence signal was calculated as being proportional to thelight intensity square dependence as valid for two-photonexcitation processesThe probability of collecting the emittedphotons was adjusted by multiplying by different functionsfor simulating various collection efficiencies Both flat andGaussian shaped collection efficiencies were investigatedFrom these simulations values of the fluorescence generatedwithin the focal volume (119865119891) and outside of the focal volume(119865119861) were computed based on the square dependence of thelight intensity to calculate signal-to-background ratios (SBR)defined as

SBR = 119865119891119865119861 (10)

Thus in order to maximize the value of SBR the value of119865119861 should be kept at a minimum

22 Experimental Multiphoton Setup Experimental mea-surements were performed using a custom-built MPM plat-form schematically illustrated in Figure 3 An SLM (X10468-02 LCOS-SLM Hamamatsu Inc) was used for wavefront

control and beammodulationThe annular beamwas createdby shifting the phase of the central part of the beam usinga triangle wave pattern thus diverting the central portionaway from the beam pathThe shape of the annular beamwasvisualized using a beam profiler (Ophir-Spiricon SP90281)A TiSapphire mode locked laser (Tsunami Spectra-Physics)was used as the excitation source The laser is tunable in thewavelength range 700ndash1050 nm and provides a repetition rateof 80MHz with pulse duration of sim100 fs A pump power of6W results in an average laser beam energy of 800mW asthe beam exits the laser cavity Laser power was controlledusing a Pockels cell (350-80LA Conoptics) A beam expander(BE05M-B Thorlabs) was implemented to ensure utilizationof the full SLM area and fill the back aperture of the focusingobjective A water-immersion objective (40x NA 08 coverglass correction Achroplan NIR Carl Zeiss) was used andmounted on a Zeiss Axiovert in an inverted configura-tion The sample was positioned using a combination ofmanual control for the objective height and a piezoelectricstage (MicroStageNanoZL500 Mad City Labs) controllablethrough a LabVIEW program (National Instruments) Dataacquisition was performed using two time-correlated singlephoton counting cards (TCSPC SPC-150 Becker amp Hickl)here operating in intensity mode

23 Tissue Mimicking Fluorescent Phantoms Fluorescentphantoms simulating the optical properties of tissue wereprepared by dissolving 1 weight fraction of agar (VWR PN20767) in 1x PBS (pH 74 Sigma PN P4417) and adding fluo-rescein (Sigma PN 46955) andTiO2 (Acros PN 21358100) toyield 01mMfluorescein and 10mgmLTiO2 in the agar solu-tionThe addition of fluorescein creates a uniformfluorescentbackground in the phantom sample while the addition ofTiO2 serves as the scattering component corresponding to ascattering coefficient of sim40 cmminus1 approximately 3 times lessscattering than normal epidermal layer of skin [22 23] Thelower attenuation was used to ensure that a larger portionof the available 119911-range could be utilized which increasedthe resolution in the 119911-direction A piece of medical gauzewas stained for 5 minutes in a 1mM Rhodamine-B-ITC(Sigma PN R6626) solution at room temperatureThe excessstaining solution was removed through rinsing with 1x PBSThe stained gauze was embedded in the agar gel solution toprovide a localized signal in the red channel and the solutionwas allowed to solidify yielding the final phantom specimen

24 Human Skin Samples A human skin specimen wasobtained as discarded tissue from breast reduction surgery atthe Sahlgrenska University Hospital (University of Gothen-burg Gothenburg Sweden) The specimen was cut into 1times 1 cm2 pieces and stored at minus20∘C Prior to the imagingexperiment the specimen was thawed and mounted onto aglass slide without further processing

25 Experimental Signal-to-Background Ratio (SBR) Fluo-rescence signals from both the red and the green channelswere used to calculate the experimental SBR The pixelintensity of the red channel originates from a combination


of the signals from the RBITC-stained fiber in the focus(119877119891) and the background fluorescence (119877119887) Similarly thepixel intensity of the green channel can be defined as thecombination of the signal from the fluorescein in the focalregion (119866119891) and the background signal from the fluorescenceevenly distributed in the gel (119866119887) The SBR should ideally becalculated as a ratio between the signals from the focus andthe background as

SBR = 119877119891119866119887 (11)

however for practical reasons the SBR was approximated bythe ratio between the total signals in both channels as

SBR asymp 119877119866 = 119877119891 + 119877119887119866119891 + 119866119887 (12)

this simplification is based on the assumption that 119877119891 ≫119877119887 and 119866119887 ≫ 119866119891 As seen from the experimental datathe 119866119891 component cannot be neglected Taking this intoconsideration this formula will give an underestimationof SBR and is thus considered a valid approach The SBRwere extracted from the different 119911-levels by extracting themean fluorescent value of the total 119909 119910 image The data arepresented as bar graphs with standard error

3 Results and Discussion

31 Theoretical Considerations Exploring Annular Beams Inorder to explore the intensity distribution around the focalvolume when changing from Gaussian to annular illumina-tion in MPM the Fresnel-Kirchhoff integral (see (1)) wascalculated on a grid around the focus using MATLAB fordifferent beam ratios 119887119861 As shown in Figure 4 the focalvolume becomes elongatedwhen the ratio 119887119861 gets closer to 1approaching aBessel beamThis elongation can be utilized forother microscopy applications for example in two-photonexcitation light sheet microscopy [4 24] but for the currentapplication the elongation causes a reduction of the axialresolution

To allow for Nyquist sampling at the cellular level thefocal volume should not exceed 2 120583m in the axial directionFrom the data for the theoretical simulations (Figure 4) thefull width at half maximum (FWHM) in the 119911-direction wasextracted as a function of bB as presented in Figure 5 Asdemonstrated by the figure FWHM values below 2 120583m areobtainedwhen the bB ratio is kept below 06 For ratios abovethis value the FWHM rapidly increases the elongation of thefocal volume above 2 120583mThus when implementing annularbeams for MPM bB should be kept below 06 As the bBratio approaches 1 the beam takes the shape of a Bessel beamwith an infinitely long focal volumeThe differentiation of thesame value shows rapid elongation of the focal volume for 119887119861values approaching 1

The potential generation of out-of-focus fluorescence wascalculated for a range of different annular beams (bB =02 to 095) and compared to Gaussian illumination (bB =0) The simulations were implemented by considering the

r

z

000

040

075

095

bB IA IF log IF

Figure 4 The distribution of intensity proportional to the fieldamplitude squared as modeled by the Fresnel-Kirchhoff integralfor different annular scenarios with varying 119887119861 using a maximumbeam waist of 17mm and focal distance of 27mm 119868119860 is the inputbeam profile at aperture exit and 119868119865 is the simulated intensitydistribution around the focal volume Included is also log 119868119865 tovisualize the acquired diffraction pattern

01 02 03 04 05 06 07 08 09 10

bB

0

5

10

15

FW

HM

z(120583

m)

Figure 5 The calculated FWHM119911 (solid line) along the 119911-axis as afunction of bB obtained from the theoretical simulations for a 07NAobjective Tomaintain a focal extentwithin twice the diffraction-limited performance FWHM119911 should be less than 2 120583m (dashedline) Thus annular ratios should be kept lt06 to avoid loss in 119911-resolution

different geometrical distributions of the excitation light forthe varying conditions The results are presented in Fig-ure 6 for two scenarios with different collection efficiencies(Gaussian and flat) assuming the scattering properties of


42

0

minus2

minus4

42

0minus2

minus4

x (mm)y (mm)

0

05

1

pCA

(a)

times1012

10 05

bB

0

5

10

15

FB

(au

)

(b)

4

2

0

minus2

minus4

x (mm)

42

0minus2

minus4 y (mm)

0

05

1

pCA

(c)

times1013

10 05

bB

0

1

2

3

FB

(au

)

(d)

Figure 6 Results from the computer simulations estimating the out-of-focus signal (119865119861) generated for different shapes of the annular beamgiven as the ratio 119887119861 The presented simulations were performed using a mathematical approach considering the varying geometricaldistribution of the excitation light depending on 119887119861 Results are presented for two scenarios assuming different probabilities of collectionefficiency (119901CA) (a) illustrating Gaussian and (c) flat collection efficiency The respective results for simulated out-of-focus signal 119865119861 arepresented in (b) and (d) For both cases the value of the attenuation coefficient (120583119904) was set to 150 cmminus1

human skin It can be seen from the figure that in bothcases the out-of-focus fluorescence is expected to decreaseto a minimum value for annular beams where the ratioof 119887119861 is kept around 04 For larger ratios the generatedout-of-focus fluorescence will increase In the case of amore uniform collection efficiency across the objective atoo narrow annular beam will act contradictorily and elevatethe probability of collecting out-of-focus signal (Figures6(c) and 6(d)) In the case with a more realistic paraxialcollection efficiency with the same waist as the objective exitaperture (Figures 6(a) and 6(b)) the background signal isreduced also for very narrow annulus These computationalsimulations demonstrate that an annular beam with 119887119861

of around 04 should be optimal considering the tradeoffbetween reduction of out-of-focus signal and retaining theimaging resolution In the simulations the background signalcan be reduced by half by switching fromGaussian to annularbeam (119887119861 = 04) assuming paraxial collection efficiency

32 Imaging Tissue Phantoms In order to implement andexperimentally explore how annular beams can reduce theout-of-focus signal inMPM awavefront controlling elementthat is an SLM was included in the optical path of anexperimental MPM setup to allow for versatile control ofthe beam shape and simple switching between Gaussianand annular beam conditions Annular beams were created


120593 = 0 120593 = 0 rarr 120587

(a) (b)

Figure 7 (a) The phase pattern applied at the SLM to generate an annular beam The desired annulus is displayed in reflection mode withno phase shift (120593 = 0) displayed in black while the undesired part of the beam is deflected by applying a phase shift gradient (120593 = 0 rarr 120587)(b) A representative image of the acquired beam profile measured after the SLM Dimensions of beam profiler image 47mm times 63mm

by diverting the central part of the beam uploading aphase pattern to the SLM Figure 7 shows a typical phasepattern applied to the SLM and the corresponding generatedbeam profile obtained as measured in the beam path Asshown by the figure the created annular beam is far fromperfect and future work will involve improvements of thegeneration of the annular beam to optimize the approach Forexample more efficient beam generation may be desirablewhere the central part of the beam is not diverted anddumped to the side to avoid power loss This is of particularimportance for applications requiring deep tissue imagingsince high laser powers are needed to reach deep into thesamples Future efforts could adopt a Fourier plane setupin which iterative Fourier transform algorithms [25] can beimplemented to generate the desired annuli Still the gener-ated beams using the simple diverting setup were sufficientin investigating the hypothesis experimentally Thereforethe present study encourages future refinements of theapproach

According to the theoretical calculations an annularbeamwith ratio bB of around 04 should be optimal in termsof maximum background signal reduction while keeping theaxial resolution in a desired rangeThus experimental effortswere made to generate an annular beam with these condi-tions which were then implemented to image tissue simu-lating fluorescent scattering phantoms The phantoms werecreated so that the RBITC-stained gauze fibers contribute tothe in-focus signal (red channel) while the generation of out-of-focus signal should appear most prominently as fluores-cein fluorescence (green channel) Figure 8 shows data froma side-by-side comparison of representative MPM images ofthe tissue phantom acquired using annular versus Gaussianillumination with matching laser power Both image data (atsim550 120583m subsurface corresponding to 22 scattering lengths)

and the extracted SBR values at different depths are presentedin the figure Similar structures are visualized using bothGaussian and annular beam illumination As expected thebackground signal is reduced when using the annular beamillumination confirming the hypothesis Also seen by thegraph is that the improvement depends on the imaging depthAs expected the improvement in SBR is small at shallowdepths but it increases at greater depths into the samplewith a maximal improvement of 30 at a depth of 550120583mWhen imaging even deeper the signal becomes limited thusreducing the SBR These results imply that annular beam is afeasible approach to reduce out-of-focus signal as validatedin these simplified tissue phantoms

33 Proof of Principle in Tissue Sample In order to explorethe feasibility of annular beams for MPM in a more complextissue sample specimens of unstained excised human skinwere examined ex vivo Figure 9 shows MPM images ofautofluorescent features of the dermal part of human skinat two different tissue depths acquired using both annularand Gaussian beam illumination As shown by the figurethe fluorescence signal generated by the elastin and collagenfibers of the dermis is clearly visualized At 45 120583m depththe features observed are comparable using power-matchedannular and Gaussian illumination When imaging deeperinto the dermis (around 80 120583m) the imaging contrast for theGaussian illumination is deteriorated as the signal from thefiber structures becomes blurry For the annular illuminationthe overall signal is reduced as expected but the out-of-focussignal has been reduced Even if the demonstrated effect atthis stage in tissue is suboptimal the experiments show proofof principle that (i) annular beams can be applied to performMPM in complex biological tissue and (ii) the hypothesis ofreducing out-of-focus fluorescence by annular beam shape


Red channel Green channelA

nnul

ar

(a)

Red channel Green channel

Gau

ssia

n

(b)

AnnularGaussian

0

20

40

60

80

100

120

140

160

SBR

()

700550350

(120583m)

(c)

Figure 8 MPM images of a tissue mimicking phantom using power-matched (sim15mW at the back aperture) annular (a) and Gaussian(b) beam illumination at sim550 120583m subsurface Field of view sim250 times 250 120583m2 (c) comparison of the signal-to-background ratio (SBR)extracted fromMPM images at different imaging depths The SBR is normalized to the Gaussian SBR at each imaging depth to show relativeimprovement in contrast Each image was divided into 16 nonoverlapping regions of interest of identical size

is confirmed Future work should be undertaken to improvemore efficient generation of the annular beam particularlywith respect to retaining laser power and accounting fordispersion effects

4 Conclusions

This study explores annular beam shaping as a viableapproach to decrease out-of-focus background fluorescencewhen performing MPM in optically turbid media Based onthe findings from computational simulations and mathemat-ical models the optimal regime for background reductionwas found to be a beam ratio bB of around 04 Higherratios degrade axial resolution while lower ratios do noteliminate significant out-of-focus background fluorescenceImaging data from both tissue phantoms and excised tissuespecimens demonstrate proof of principle and support fea-sibility and relevance in translational applications Improvedimaging contrast in annular illuminated MPM enables anincrease in imaging depth which can potentially allow forthe monitoring of tumors and other pathological eventsin the microenvironment within the dermal layer of the

skin which is important in image-guided diagnostics [7]and pharmaceutical development [26] The approach couldpotentially be combinedwith other approaches for improvingimaging depths for example using third-harmonic gen-eration [13 27] Additional quantitative imaging in lightscattering tissue using techniques such as fluorescencecorrelation spectroscopy (FCS) and fluorescence lifetimemicroscopy (FLIM) would significantly benefit from reducedbackground Improved imaging depth is also important tofacilitate neuroscience [11] as it could potentially enable thenoninvasive studies of layer V neurons and provide a betterunderstanding of the neurocircuitryThus future refinementand development are necessary in order to harvest full poten-tial of the technique which in turn could make MPM amorepowerful versatile and indispensable tool in biomedicalresearch

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper


Ann

ular

Gau

ssia

n

z sim45 120583m

(a)

Ann

ular

Gau

ssia

n

z sim80 120583m

(b)

Figure 9 MPM images from the dermis of an excised unstained normal human skin specimen applying annular and Gaussian beamillumination at different tissue depths (sim45 120583m and sim80120583m) using matching laser powers (sim15mW and 20mW resp) at the back apertureScale bar = 50 120583m

Acknowledgments

The authors acknowledge the staff from the Departments ofDermatology and Plastic Surgery at Sahlgrenska UniversityHospital for providing the excised skin specimens and theCentre for Skin Research (SkinResQU) for use of facilitiesFinancial support for this project was obtained from theSwedish Research Council (VR Dnr 621-2011-5189) Vinnova(VINNMER 2008-03414) and Lundberg Research Founda-tion (2013-430)

References

[1] W Denk J H Strickler and W W Webb ldquoTwo-photon laserscanning fluorescence microscopyrdquo Science vol 248 no 4951pp 73ndash76 1990

[2] W R Zipfel R M Williams and W W Webb ldquoNonlinearmagic multiphoton microscopy in the biosciencesrdquo NatureBiotechnology vol 21 no 11 pp 1369ndash1377 2003

[3] C Xu W Zipfel J B Shear R M Williams and W W WebbldquoMultiphotonfluorescence excitation new spectral windows forbiological nonlinear microscopyrdquo Proceedings of the NationalAcademy of Sciences of the United States of America vol 93 no20 pp 10763ndash10768 1996

[4] T A Planchon L Gao D E Milkie et al ldquoRapid three-dimensional isotropic imaging of living cells using Bessel beamplane illuminationrdquo Nature Methods vol 8 no 5 pp 417ndash4232011

[5] J Textor A Peixoto S E Henrickson M Sinn U H VonAndrian and J Westermann ldquoDefining the quantitative limitsof intravital two-photon lymphocyte trackingrdquo Proceedings ofthe National Academy of Sciences of the United States of Americavol 108 no 30 pp 12401ndash12406 2011

[6] W Supatto A McMahon S E Fraser and A Stathopou-los ldquoQuantitative imaging of collective cell migration duringDrosophila gastrulation multiphoton microscopy and compu-tational analysisrdquo Nature Protocols vol 4 no 10 pp 1397ndash14122009

[7] J Paoli M Smedh A-M Wennberg and M B EricsonldquoMultiphoton laser scanning microscopy on non-melanoma


skin cancer morphologic features for future non-invasivediagnosticsrdquo Journal of Investigative Dermatology vol 128 no5 pp 1248ndash1255 2008

[8] B R Masters P T C So and E Gratton ldquoMultiphoton exci-tation fluorescence microscopy and spectroscopy of in vivohuman skinrdquo Biophysical Journal vol 72 no 6 pp 2405ndash24121997

[9] K Konig ldquoClinical multiphoton tomographyrdquo Journal of Bio-photonics vol 1 no 1 pp 13ndash23 2008

[10] U Olcese G Iurilli and PMedini ldquoCellular and synaptic archi-tecture of multisensory integration in the mouse neocortexrdquoNeuron vol 79 no 3 pp 579ndash593 2013

[11] O Garaschuk R-I Milos C Grienberger N Marandi HAdelsberger and A Konnerth ldquoOptical monitoring of brainfunction in vivo From neurons to networksrdquo Pflugers ArchivEuropean Journal of Physiology vol 453 no 3 pp 385ndash3962006

[12] N J Durr C T Weisspfennig B A Holfeld and A Ben-YakarldquoMaximum imaging depth of two-photon autofluorescencemicroscopy in epithelial tissuesrdquo Journal of Biomedical Opticsvol 16 no 2 article 026008 2011

[13] DKobatM EDurstNNishimuraAWWongC B Schafferand C Xu ldquoDeep tissue multiphoton microscopy using longerwavelength excitationrdquoOptics Express vol 17 no 16 pp 13354ndash13364 2009

[14] P Theer and W Denk ldquoOn the fundamental imaging-depthlimit in two-photon microscopyrdquo Journal of the Optical Societyof America A Optics and Image Science and Vision vol 23 no12 pp 3139ndash3149 2006

[15] C J R Sheppard ldquoUse of lenses with annular aperture inscanning optical microscopyrdquoOptik vol 48 no 3 pp 329ndash3341977

[16] S W Hell P E Hanninen A Kuusisto M Schrader and ESoini ldquoAnnular aperture two-photon excitation microscopyrdquoOptics Communications vol 117 no 1-2 pp 20ndash24 1995

[17] C J R Sheppard and A Choudhury ldquoAnnular pupils radialpolarization and superresolutionrdquo Applied Optics vol 43 no22 pp 4322ndash4327 2004

[18] J Borglin N J Durr S Guldbrand et al ldquoImproving mul-tiphoton microscopy using annular beam shaping focusingon imaging of human skinrdquo in Proceedings of MultiphotonMicroscopy in the Biomedical Sciences XIV vol 8948 SPIEFebruary 2014

[19] Y Nie X Li J Qi et al ldquoHollow gaussian beam generatedby beam shaping with phase-only liquid crystal spatial lightmodulatorrdquoOptics and Laser Technology vol 44 no 2 pp 384ndash389 2012

[20] Y Liu P He and D Cline ldquoVacuum laser acceleration testsrdquo inProceedings of the 1999 Particle Accelerator Conference vol 5 pp3639ndash3641 1999

[21] I V Meglinski and S J Matcher ldquoQuantitative assessment ofskin layers absorption and skin reflectance spectra simulationin the visible and near-infrared spectral regionsrdquo PhysiologicalMeasurement vol 23 no 4 pp 741ndash753 2002

[22] A N Bashkatov E A Genina V I Kochubey and V V TuchinldquoOptical properties of human skin subcutaneous and mucoustissues in thewavelength range from400 to 2000 nmrdquo Journal ofPhysics D Applied Physics vol 38 no 15 pp 2543ndash2555 2005

[23] E Salomatina B Jiang J Novak andAN Yaroslavsky ldquoOpticalproperties of normal and cancerous human skin in the visibleand near-infrared spectral rangerdquo Journal of Biomedical Opticsvol 11 no 6 article 064026 2006

[24] F O Fahrbach P Simon and A Rohrbach ldquoMicroscopy withself-reconstructing beamsrdquo Nature Photonics vol 4 no 11 pp780ndash785 2010

[25] MWalde A Jost KWicker and R Heintzmann ldquoEngineeringan achromatic Bessel beam using a phase-only spatial lightmodulator and an iterative fourier transformation algorithmrdquoOptics Communications vol 383 pp 64ndash68 2017

[26] V Kirejev S Guldbrand J Borglin C Simonsson and M BEricson ldquoMultiphoton microscopymdasha powerful tool in skinresearch and topical drug delivery sciencerdquo Journal of DrugDelivery Science andTechnology vol 22 no 3 pp 250ndash259 2012

[27] M Yildirim N Durr and A Ben-Yakar ldquoTripling themaximum imaging depth with third-harmonic generationmicroscopyrdquo Journal of Biomedical Optics vol 20 no 9 2015

Submit your manuscripts athttpswwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 201

International Journal ofInternational Journal ofPhotoenergy


Carbohydrate Chemistry

International Journal ofInternational Journal of


Journal of

Chemistry


Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of


Chromatography Research International


Applied ChemistryJournal of



Theoretical ChemistryJournal of


Journal of

Spectroscopy

Analytical ChemistryInternational Journal of


Journal of


Quantum Chemistry


Organic Chemistry International

ElectrochemistryInternational Journal of



CatalystsJournal of


(a) (b)

(a)(b)F(z)

z

Figure 1 Schematic illustration of the concept of annular laser beamto reduce out-of-focus signal in MPM for the two conditions (a)where Gaussian beam profile is implemented and (b) for annularbeam illumination The figure illustrates the hypothetical relativecontribution of fluorescence signal 119865(119911) as a function of depth119911 While comparing conditions given equal photon fluences in thefocal region the Gaussian illumination (a) is expected to generateelevated levels of out-of-focus signal from the incoming planeswhere the laser power is at a maximum compared to annularillumination (b)

plane [12ndash14] The out-of-focus signal is a result of increas-ingly high excitation powers that are necessary to maintainhigh excitation intensity when the focal volume is locateddeep in the tissue This background signal deteriorates theimaging contrast (signal-to-background ratio) and in turnlimits imaging depth Thus efforts should be made tominimize this undesired signal to improve the signal-to-background ratio and thereby increase the imaging depthThe implementation of a spatial filter such as a confocalpinhole should allow for blocking the out-of-focus sig-nal however the decreased collection efficiency deems thisapproach suboptimal in MPM as previously discussed [14]Instead we here propose an approach based on annularbeam shaping As illustrated in Figure 1 the fluorescenceF generated at a plane 119911 would be more confined tothe focal plane when using an annular laser beam whencompared to Gaussian beam illumination Geometricallythe peak irradiance of the laser light at the sample surfacecan be lowered by distributing the laser energy in a ringinstead of a Gaussian beam profile This lowers the intensityin any given point of the sample while retaining the photonflux in the focal volume and thus reduces the generationof out-of-focus fluorescence contributing to the undesiredbackground Previously annular beam shaping has beeninvestigated for confocal microscopy [15] and multiphotonmicroscopy [16 17] to improve resolution The conceptof using annular beams to reduce out-of-focus signal ispreviously not explored

This study investigates the potential of annular beamsto improve signal-to-background ratio in MPM The imple-mentation of annular beams in optical microscopy gives anelongated focal volume which results in beamprofiles similarto that of a Bessel beamTherefore when explored for MPMthe potential effect on the focal volume should be consideredThis paper investigates the benefits and tradeoffs of using

annular beams by combining theoretical simulations andproof-of-concept experiments using wavefront controllingoptics The work is an extension of our previous approach[18] Here a spatial light modulator (SLM) was introducedin the optical path of a custom-built experimental MPMplatform in order to obtain an annular beam similar to theapproach shown by Nie et al [19] By changing the pattern onthe SLM a systematic comparison of annular versus Gaus-sian illumination could be performed Fluorescent scatteringtissue phantoms simulating the properties of optically densebiological tissue were investigated together with excisedhuman skin tissue in order to demonstrate proof of concept

2 Materials and Methods

21 Theoretical Simulations In order to simulate the excita-tion intensity generated in the focal region when switchingfrom Gaussian to annular beam shape the Fresnel-Kirchhoffintegral was calculated for varying beam shape conditionsbased on a previously described approach [18 20] TheFresnel-Kirchhoff integral is stated as

Ψ1015840FK (1199031015840 1205791015840 119911) = 2120587119911120582 intΨ1015840 (119903 120579) 119890(minus2120587119894119877120582)Φ119897119889119878 (1)

corresponding to the total field amplitude in a point (1199031015840 1205791015840)at the distance 119911 from the lens The coordinates are schemat-ically illustrated in Figure 2 Here Ψ1015840(119903 120579) is the fieldamplitude at a point (119903 120579) on the lens (119911 = 0)The integrationis made by summing over the contributions from each areaelement dS on the lens surface The phase retardation of thelens Φ119897 is given by

Φ119897 = 1198901198941205871199032120582119891 (2)

Here 119891 is the focal length of the lens 120582 is the wavelengthand 119877 is the distance vector from the point (119903 120579) on the lensto the point (1199031015840 1205791015840 119911) for which the total field Ψ1015840FK(1199031015840 1205791015840 119911)is calculated using the expression

119877 asymp 119911 + 1199032 + 11990310158402 minus 21199031199031015840 cos (120579 minus 1205791015840)

21199111015840 (3)

The field amplitude at the lens Ψ1015840(119903 120579) was given by theexpression

Ψ1015840 (119903 120579) = 11987501205871198612 (1 minus119887119903) 119890minus2((119903minus119887)119861)

2 (4)

where 1198750 is the laser power at the lens 119861 is the outer radiusof the beam and 119887 is the inner radius of the beam Theouter radius 119861was scaled down with increasing 119887119861 to ensurethat the total energy was kept constant in the comparisonsbetween different conditions The Fresnel-Kirchhoff integral(1) was calculated using MATLAB (MathWorks Natick MAUSA) for a grid around the focus in order to simulate theintensity distribution around the focal volume Each beamshape was characterized by the ratio between the innerradius (b) and outer radius (B) ranging from 119887119861 = 0 for


y

r x

z

b

r998400x998400

y998400

120579998400

120579

(a)

b B

z

r

B998400(z)b998400(z)

(b)




Ψ1015840 (119911) = 119875012058711986110158402 119890minus2(11990310158401198611015840)2 (5)


Ψ1015840 (119911) = 119875012058711986110158402 (1 minus11988710158401199031015840) 119890minus2((119903

1015840minus1198871015840)1198611015840)2 (6)



1198611015840 (119911) = 119861(1 minus 119911 tan1205721198860 )

1198871015840 (119911) = 119887 (1 minus 119911 tan1205721198860 ) (7)


NA = 119899 sin120572 asymp 119899 1198632119891 (8)


119865119861 = intΨ1015840 (119911)2119890minus2119911120583119904119889119911 (9)



TiSapphire laser

Pockels cell

M1

Beam expander

Scanmirrors

M3 DCM

DCM

F1 (52550)

F2 (580150)

PMT1

PMT2

Objective

Sample

M2SLM

L2 L1


TCSPC

BB



SBR = 119865119891119865119861 (10)









SBR = 119877119891119866119887 (11)


SBR asymp 119877119866 = 119877119891 + 119877119887119866119891 + 119866119887 (12)






r

z

000

040

075

095

bB IA IF log IF


01 02 03 04 05 06 07 08 09 10

bB

0

5

10

15

FW

HM

z(120583

m)




42

0

minus2

minus4

42

0minus2

minus4

x (mm)y (mm)

0

05

1

pCA

(a)

times1012

10 05

bB

0

5

10

15

FB

(au

)

(b)

4

2

0

minus2

minus4

x (mm)

42

0minus2

minus4 y (mm)

0

05

1

pCA

(c)

times1013

10 05

bB

0

1

2

3

FB

(au

)

(d)






120593 = 0 120593 = 0 rarr 120587

(a) (b)








nnul

ar

(a)


Gau

ssia

n

(b)

AnnularGaussian

0

20

40

60

80

100

120

140

160

SBR

()

700550350

(120583m)

(c)



4 Conclusions






Ann

ular

Gau

ssia

n

z sim45 120583m

(a)

Ann

ular

Gau

ssia

n

z sim80 120583m

(b)


Acknowledgments


References







































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


y

r x

z

b

r998400x998400

y998400

120579998400

120579

(a)

b B

z

r

B998400(z)b998400(z)

(b)




Ψ1015840 (119911) = 119875012058711986110158402 119890minus2(11990310158401198611015840)2 (5)


Ψ1015840 (119911) = 119875012058711986110158402 (1 minus11988710158401199031015840) 119890minus2((119903

1015840minus1198871015840)1198611015840)2 (6)



1198611015840 (119911) = 119861(1 minus 119911 tan1205721198860 )

1198871015840 (119911) = 119887 (1 minus 119911 tan1205721198860 ) (7)


NA = 119899 sin120572 asymp 119899 1198632119891 (8)


119865119861 = intΨ1015840 (119911)2119890minus2119911120583119904119889119911 (9)



TiSapphire laser

Pockels cell

M1

Beam expander

Scanmirrors

M3 DCM

DCM

F1 (52550)

F2 (580150)

PMT1

PMT2

Objective

Sample

M2SLM

L2 L1


TCSPC

BB



SBR = 119865119891119865119861 (10)









SBR = 119877119891119866119887 (11)


SBR asymp 119877119866 = 119877119891 + 119877119887119866119891 + 119866119887 (12)






r

z

000

040

075

095

bB IA IF log IF


01 02 03 04 05 06 07 08 09 10

bB

0

5

10

15

FW

HM

z(120583

m)




42

0

minus2

minus4

42

0minus2

minus4

x (mm)y (mm)

0

05

1

pCA

(a)

times1012

10 05

bB

0

5

10

15

FB

(au

)

(b)

4

2

0

minus2

minus4

x (mm)

42

0minus2

minus4 y (mm)

0

05

1

pCA

(c)

times1013

10 05

bB

0

1

2

3

FB

(au

)

(d)






120593 = 0 120593 = 0 rarr 120587

(a) (b)








nnul

ar

(a)


Gau

ssia

n

(b)

AnnularGaussian

0

20

40

60

80

100

120

140

160

SBR

()

700550350

(120583m)

(c)



4 Conclusions






Ann

ular

Gau

ssia

n

z sim45 120583m

(a)

Ann

ular

Gau

ssia

n

z sim80 120583m

(b)


Acknowledgments


References







































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


TiSapphire laser

Pockels cell

M1

Beam expander

Scanmirrors

M3 DCM

DCM

F1 (52550)

F2 (580150)

PMT1

PMT2

Objective

Sample

M2SLM

L2 L1


TCSPC

BB



SBR = 119865119891119865119861 (10)









SBR = 119877119891119866119887 (11)


SBR asymp 119877119866 = 119877119891 + 119877119887119866119891 + 119866119887 (12)






r

z

000

040

075

095

bB IA IF log IF


01 02 03 04 05 06 07 08 09 10

bB

0

5

10

15

FW

HM

z(120583

m)




42

0

minus2

minus4

42

0minus2

minus4

x (mm)y (mm)

0

05

1

pCA

(a)

times1012

10 05

bB

0

5

10

15

FB

(au

)

(b)

4

2

0

minus2

minus4

x (mm)

42

0minus2

minus4 y (mm)

0

05

1

pCA

(c)

times1013

10 05

bB

0

1

2

3

FB

(au

)

(d)






120593 = 0 120593 = 0 rarr 120587

(a) (b)








nnul

ar

(a)


Gau

ssia

n

(b)

AnnularGaussian

0

20

40

60

80

100

120

140

160

SBR

()

700550350

(120583m)

(c)



4 Conclusions






Ann

ular

Gau

ssia

n

z sim45 120583m

(a)

Ann

ular

Gau

ssia

n

z sim80 120583m

(b)


Acknowledgments


References







































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of



SBR = 119877119891119866119887 (11)


SBR asymp 119877119866 = 119877119891 + 119877119887119866119891 + 119866119887 (12)






r

z

000

040

075

095

bB IA IF log IF


01 02 03 04 05 06 07 08 09 10

bB

0

5

10

15

FW

HM

z(120583

m)




42

0

minus2

minus4

42

0minus2

minus4

x (mm)y (mm)

0

05

1

pCA

(a)

times1012

10 05

bB

0

5

10

15

FB

(au

)

(b)

4

2

0

minus2

minus4

x (mm)

42

0minus2

minus4 y (mm)

0

05

1

pCA

(c)

times1013

10 05

bB

0

1

2

3

FB

(au

)

(d)






120593 = 0 120593 = 0 rarr 120587

(a) (b)








nnul

ar

(a)


Gau

ssia

n

(b)

AnnularGaussian

0

20

40

60

80

100

120

140

160

SBR

()

700550350

(120583m)

(c)



4 Conclusions






Ann

ular

Gau

ssia

n

z sim45 120583m

(a)

Ann

ular

Gau

ssia

n

z sim80 120583m

(b)


Acknowledgments


References







































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


42

0

minus2

minus4

42

0minus2

minus4

x (mm)y (mm)

0

05

1

pCA

(a)

times1012

10 05

bB

0

5

10

15

FB

(au

)

(b)

4

2

0

minus2

minus4

x (mm)

42

0minus2

minus4 y (mm)

0

05

1

pCA

(c)

times1013

10 05

bB

0

1

2

3

FB

(au

)

(d)






120593 = 0 120593 = 0 rarr 120587

(a) (b)








nnul

ar

(a)


Gau

ssia

n

(b)

AnnularGaussian

0

20

40

60

80

100

120

140

160

SBR

()

700550350

(120583m)

(c)



4 Conclusions






Ann

ular

Gau

ssia

n

z sim45 120583m

(a)

Ann

ular

Gau

ssia

n

z sim80 120583m

(b)


Acknowledgments


References







































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


120593 = 0 120593 = 0 rarr 120587

(a) (b)








nnul

ar

(a)


Gau

ssia

n

(b)

AnnularGaussian

0

20

40

60

80

100

120

140

160

SBR

()

700550350

(120583m)

(c)



4 Conclusions






Ann

ular

Gau

ssia

n

z sim45 120583m

(a)

Ann

ular

Gau

ssia

n

z sim80 120583m

(b)


Acknowledgments


References







































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of



nnul

ar

(a)


Gau

ssia

n

(b)

AnnularGaussian

0

20

40

60

80

100

120

140

160

SBR

()

700550350

(120583m)

(c)



4 Conclusions






Ann

ular

Gau

ssia

n

z sim45 120583m

(a)

Ann

ular

Gau

ssia

n

z sim80 120583m

(b)


Acknowledgments


References







































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


Ann

ular

Gau

ssia

n

z sim45 120583m

(a)

Ann

ular

Gau

ssia

n

z sim80 120583m

(b)


Acknowledgments


References







































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of
































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of

Annular Beam Shaping in Multiphoton Microscopy to Reduce...

Documents

Transcript of Annular Beam Shaping in Multiphoton Microscopy to Reduce...