Journal of Biomedical Optics 16(2), 026008 (February 2011)

Maximum imaging depth of two-photonautofluorescence microscopy in epithelial tissues

Nicholas J. Durr,a Christian T. Weisspfennig,b Benjamin A. Holfeld,b and Adela Ben-Yakara,caUniversity of Texas at Austin, Department of Biomedical Engineering, Austin, Texas 78712bUniversity of Texas at Austin, Department of Physics, Austin, Texas 78712cUniversity of Texas at Austin, Department of Mechanical Engineering, Austin, Texas 78712

Abstract. Endogenous fluorescence provides morphological, spectral, and lifetime contrast that can indicatedisease states in tissues. Previous studies have demonstrated that two-photon autofluorescence microscopy (2PAM)can be used for noninvasive, three-dimensional imaging of epithelial tissues down to approximately 150 μmbeneath the skin surface. We report ex-vivo 2PAM images of epithelial tissue from a human tongue biopsy downto 370 μm below the surface. At greater than 320 μm deep, the fluorescence generated outside the focal volumedegrades the image contrast to below one. We demonstrate that these imaging depths can be reached with160 mW of laser power (2-nJ per pulse) from a conventional 80-MHz repetition rate ultrafast laser oscillator.To better understand the maximum imaging depths that we can achieve in epithelial tissues, we studied imagecontrast as a function of depth in tissue phantoms with a range of relevant optical properties. The phantom dataagree well with the estimated contrast decays from time-resolved Monte Carlo simulations and show maximumimaging depths similar to that found in human biopsy results. This work demonstrates that the low staininginhomogeneity (∼20) and large scattering coefficient (∼10 mm− 1) associated with conventional 2PAM limit themaximum imaging depth to 3 to 5 mean free scattering lengths deep in epithelial tissue. C©2011 Society of Photo-OpticalInstrumentation Engineers (SPIE). [DOI: 10.1117/1.3548646]

Keywords: nonlinear microscopy; two-photon; autofluorescence microscopy; deep imaging; optical biopsy.

Paper 10479R received Aug. 28, 2010; revised manuscript received Dec. 9, 2010; accepted for publication Dec. 15, 2010; publishedonline Feb. 16, 2011.

1 IntroductionTwo-photon autofluorescence microscopy (2PAM) has emergedas a versatile technique for noninvasive three-dimensional imag-ing of turbid biological samples with subcellular resolution.1–4

Spectral and morphological information obtained from intravital2PAM of unstained epithelial tissues has shown promise for di-agnosing and monitoring of carcinoma.5–9 Typically, carcinomaoriginates and is most clearly distinguished from normal tissueat the basal layer, which can be several hundreds of micrometersbelow the skin surface. Additionally, the quantification of ep-ithelial layer thickness can be used as an indicator of dysplasiaand carcinoma.5 Thus, in 2PAM of carcinoma, it is particularlyimportant to understand and extend the maximum achievableimaging depth.

In general, optical imaging depth in skin can be extendedby using near-infrared (NIR) wavelengths of 700 to 1300 nm,which are minimally attenuated in biological tissues. Confo-cal microscopy can image many hundreds of micrometers intoepithelial tissue using NIR wavelengths and contrast from scat-tering or exogenous contrast agents.10, 11 However, the dom-inant fluorophores naturally present in skin have ultravioletand blue linear absorption bands.4, 12, 13 Confocal autofluores-cence microscopy requires the use of highly scattered excitationand emission light to image these endogenous fluorophores.Though confocal autofluorescence microscopy has been used

Address all correspondence to Adela Ben-Yakar, University of Texas atAustin, Dept. of Mechanical Engineering, 1 University Station C2200,Austin, Texas 78712. Tel: 512 471 7342; Fax: 512 471 1045; E-mail:ben-yakar@mail.utexas.edu.

for imaging shallow regions of epithelial tissue, it has not beendemonstrated more than a few tens of micrometers below thesurface.14 Two-photon imaging, on the other hand, has threeworking principles that make it particularly advantageous fordeep microscopy of endogenous skin fluorescence: 1. the natu-ral fluorophores in epithelial tissues can be excited nonlinearlywith NIR light; 2. fluorescence generation in a sample is inher-ently confined to the focal volume, enabling three-dimensionalsectioning while collecting both ballistic and scattered emissionlight; and 3. resolution is negligibly degraded from scatteringbecause the fluorescence in the perifocal volume is generatedalmost entirely from ballistic photons.15, 16

Deep nonlinear imaging can be achieved by maintaining orincreasing the excitation intensity delivered to the focal spot asthe imaging depth is increased. This can be achieved in biologi-cal samples, where the attenuation of NIR photons is dominatedby scattering processes, by increasing the pulse energy deliv-ered to the sample surface exponentially with imaging depth,with a length constant of approximately one mean free scatter-ing length (ls). In practice, the excitation intensity is increasedat a slightly higher rate to compensate for increased losses fromfluorescence collection and the longer path length encounteredby large-angle excitation photons.15

Although increasing excitation power with imaging depthcan maintain fluorescence generation at arbitrarily large imag-ing depths, the approximation that two-photon excited fluo-rescence is generated only within the perifocal volume doesnot hold beyond ∼3 mean free scattering lengths deep.17

1083-3668/2011/16(2)/026008/13/$25.00 C© 2011 SPIE

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Out-of-focus (background) fluorescence gradually reduces theimage contrast.18, 19 The ratio of collected signal fluorescence(Fs) to background fluorescence (Fb) then decays with increas-ing imaging depth. In cylindrically symmetric tissue, with adistance from the optical axis, r, and an axial distance from thetissue surface, z, this ratio can be expressed as:

Fs

Fb=

∫Vs

∫ ∞−∞ φ(r, z)C(r, z, t)I 2(r, z, t)dt dV∫

Vb

∫ ∞−∞ φ(r, z)C(r, z, t)I 2(r, z, t)dt dV

, (1)

where the signal volume, Vs, is the volume of the feature of inter-est (a fluorescent bead, for instance), the background volume, Vb,

is the volume within the sample but outside of the signal volume,φ is the collection efficiency, C is the fluorophore concentration,and I is the excitation intensity.

The maximum imaging depth, zm, can be defined as thedepth at which the Fs/Fb ratio falls to one.18 Previous studieshave described the maximum imaging depth in units of opti-cal depths, defined as zm/ls, for homogeneously stained tissuewith similar excitation parameters. Theer and Denk found a zm

of 3 to 4 scattering lengths when ls = 200 μm using an an-alytical model.18 On the other hand, Leray et al. found a zm

of 5 to 6 optical depths when ls = 350 μm using a MonteCarlo model.19 This difference suggests that zm is dependenton ls. Experimentally, zm has also been measured, but only instained brain tissue and phantoms with ls ≈ 200 to 350 μm.18–20

Autofluorescence imaging in epithelial tissues presents a par-ticularly challenging set of optical properties for deep two-photon imaging. First, the scattering length of epithelial tis-sues is much smaller than those considered in previous studies,typically in the range of 40 to 200 μm. Second, endogenous flu-orophores are typically much dimmer and more homogeneouslydistributed than exogenous fluorophores, resulting in inherentlylow contrast imaging. Previous 2PAM reports in epithelial tis-sues have not reached zm, and imaging depths have, to the bestof our knowledge, been limited to 80 to 150 μm below thesurface.2, 3, 6, 8, 21–26

In this paper, we present 2PAM images of a human tonguebiopsy down to and beyond zm. We show that this limit canbe reached with a few hundred milliwatts of excitation poweravailable from conventional, high repetition rate oscillators inphantoms with optical properties in the range typically foundin epithelial tissues. We describe the gradual contrast decay of2PAM for increasing imaging depths as a function of the fluo-rescence staining inhomogeneity and a ratio of integrated inten-sities. We find that zm/ls exhibits a logarithmic dependence on ls.Finally, the Fs/Fb ratio is calculated with time-resolved MonteCarlo simulations and predicted contrast profiles are comparedwith measurements from tissue phantoms and ex vivo humanepithelial tissue.

2 Methods2.1 2PAM ContrastIn the absence of fluorescence saturation, photobleaching, andsample movement, the effective fluorophore concentration is

independent of time. Assuming the concentration of fluo-rophores within Vs is a constant, Cs, and that the out-of-focusfluorophore concentration is diffuse enough to be approximatedby the average fluorophore concentration, Cb, we can removethe concentration terms from the integral in Eq. (1). We definethe staining inhomogeneity, χ , as the ratio of the fluorophoreconcentrations, and R as the ratio of integrated intensities:

χ = Cs

Cb, (2)

R =∫

Vs

∫ ∞−∞ φ(ρ, z)I 2(r, z, t)dt dV∫

Vb

∫ ∞−∞ φ(ρ, z)I 2(r, z, t)dt dV

. (3)

We can then express the ratio of signal to background fluores-cence as the product of χ and R:

Fs

Fb= χ · R. (4)

Though our definition for Fs/Fb is the same as previous reports,our definition of χ and R differ from that described previously.18

Our definition of the staining inhomogeneity relies on the abso-lute concentrations of fluorophores inside and outside a signalvolume and does not depend on the perifocal intensity distri-bution (i.e., the numerical aperture). Additionally, our R valueis defined by the volume of a feature of interest rather than thevolume of the focal spot. Our approach has the distinction thatthe χ value is an intrinsic, system-independent property of thesample that scales linearly with changes in background or signalfluorophore concentration.

In this paper, we explore the gradual decay of image contrast,Q, versus depth due to out-of-focus fluorescence. We define thecontrast in terms of the measured signal (MS) when the focal spotconcentrically overlaps with Vs and the measured background(MB) when the focal spot is in a volume at the same imag-ing depth that produces a relatively weak signal (Fig. 1), suchthat:

Q = MS − MB

MB, (5)

Fig. 1 Diagram of the parameters used in quantifying the contrast in2PAM. The signal and background volumes (Vs and Vb, respectively)and signal and background fluorophore concentrations (Cs and Cb,respectively) are indicated. MS is defined as the fluorescence detectedwhen the geometric focal point of the excitation light is at the centerof Vs . MB is defined as the fluorescence detected when the excitationis focused at the same imaging depth as MS, but outside of the featureof interest.

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where

MS = Cs

∫Vs

∫ ∞

−∞φ(r, z)I 2(r, z, t)dt dV

+Cb

∫Vb

∫ ∞

−∞φ(r, z)I 2(r, z, t) dt dV , (6)

MB = Cb

∫Vs

∫ ∞

−∞φ(r, z)I 2(r, z, t)dt dV

+Cb

∫Vb

∫ ∞

−∞φ(r, z)I 2(r, z, t)dt dV . (7)

Note that our measured background includes a fluorescence con-tribution from within the defined signal volume. This term be-comes important for samples where the fluorophore is relativelyhomogeneously distributed and there are few regions withoutfluorophores, which is typically the case for 2PAM of epithelialtissues. Rearranging Eqs. (5)–(7) and using the definitions inEqs. (2) and (3), we can express the contrast as a function of χ

and R:

Q = χ − 1

1 + 1/R. (8)

This relation shows that the contrast approaches zero as the stain-ing inhomogeneity approaches one (i.e., a uniformly stainedsample), or as R approaches zero. If the fluorophore concen-tration is zero in the focal volume for the MB measurement,Q is exactly equal to Fs/Fb. In the more general case, withsome fluorescent signal present in the focal volume of the MBmeasurement, Q becomes approximately equal to Fs/Fb forsmall values of R. In this paper, we define zm as the depthat which the contrast falls to one, which is approximatelyequal to the maximum imaging depth defined by Theer andDenk.18

2.2 2PAM SystemWe built a two-photon microscope specifically designed for deeptissue autofluorescence imaging. An 80-MHz repetition rate,Ti:Saphire laser oscillator (Spectra Physics, Mai Tai) generatedthe excitation pulses with energies of up to 10 nJ. We used760-nm excitation wavelength because it yielded the brightestautofluorescence signal with minimal excitation light bleed-through in our system. Two half-waveplate/polarizing beamcube pairs attenuated the excitation beam and a pair of gal-vanometer scanning mirrors (Cambridge Technologies, 6215h)scanned the laser into an upright microscope. We used a highnumerical aperture (NA), water dipping objective with a largefield of view and a 2-mm working distance (0.95/20x OlympusXLUMPFL). The large field of view is especially important forhigh collection efficiency at large imaging depths.27 The phys-ical radii of the back aperture, rBA, and front aperture, rFA, ofthis objective are 8.5 and 2 mm, respectively. The measuredbeam 1/e2 radius of the excitation beam, wBA, was 6 mm at the

objective back aperture, giving a fill factor of 0.7. The trans-mission of 760-nm light was measured to be 70% by measuringthe laser power before and after the objective with a powermeter.

We optimized the collection optics for maximum collectionof emission photons from the diffusive regime using Zemax-EE (2009 Version), similar to a previous approach.28 Excessstray and scattered excitation light were filtered through twolow pass filters (3-mm thick BG-39, Schott Glass and FF01–750, Semrock). We used a high-sensitivity, cooled, GaAsP pho-tomultiplier tube (PMT) module (Hamamatsu, H7422–40) asour detector. The current from the PMT was sent through a1-MHz bandwidth transimpedance amplifier (Stanford ResearchSystems SR570) and sampled at 1 MHz with 12-bit digitizationon a data acquisition card (National Instruments PCI-6115). Weused a modified version of MPScan software29 to control thelaser power and scanning mirrors, and acquire 512×512 pixelimages at 3 frames/s. All images presented and analyzed in thispaper are the average of 8 frames to minimize other sources ofnoise. In biopsy and phantom measurements, we increased theexcitation power manually with depth to maintain an approxi-mately constant level of collected signal at levels just below thesaturation limit of the system.

We characterized the spatial intensity distribution of the ex-citation light at the focal volume by measuring the intensity-squared point spread function (IPSF2) of our system with100-nm diameter fluorescent beads embedded in agar. A rep-resentative IPSF2 measurement is shown in Fig. 2(a). We foundlateral and axial FWHMs of rFWHM = 460 ± 60 nm and zFWHM

= 1760 ± 130 nm (mean ± standard deviation), respectively, byfitting Gaussian functions to the profiles drawn through the cen-troids of 20 beads. These values are approximately 50% largerthan theoretical values expected with a diffraction-limited spotfrom a 0.95 NA water dipping objective,30 and closer to whatwould be expected from diffraction-limited focusing from anNA of 0.75. The difference between measured and diffraction-limited IPSF2 is too large to be accounted for by our underfillingof the back aperture,31, 32 and is likely due to lens aberrations atNIR wavelengths. Similarly large IPSF2 have been previouslyreported from this objective.27, 33, 34 We found that the IPSF2 wasindependent of imaging depth through the full working distanceof the lens (2 mm) in a sample of 100-nm fluorescent beadsembedded in an agar gel. The constant spot size indicates thatspecimen-induced aberrations negligibly affect the shape of theintensity distribution in the perifocal volume in agar phantoms,which is consistent with other studies.15, 16, 35

We characterized the temporal intensity distribution at thefocal plane by incorporating a Michelson interferometer witha variable delay arm in the excitation path, and measuring theautocorrelation function of the focused excitation beam withina sample of 25-μM fluorescein.36, 37 We calculated the pulseduration at the imaging plane from autocorrelations measuredwith the objective as a focusing lens and also when replacing theobjective lens with a 1 in. diameter singlet lens with a 1 in. focallength. These two measurements [Figs. 2(b) and 2(c)] allow usto estimate the group delay dispersion (GDD) of the objectivelens. We recorded the FWHM of a Gaussian fit, τ FWHM

AC , to themoving average of our interferometric autocorrelation functionover five measurements in each configuration. Assuming theoriginal pulse shape is a Gaussian, the FWHM of the original

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-1.5 -1 -0.5 0 0.5 1 1.50

2

4

6

8

-1.5 -1 -0.5 0 0.5 1 1.50

2

4

6

8

Fig. 2 A representative lateral, r, and axial, z, ISPF2 from a 100-nmfluorescent bead (a), indicating average lateral and axial FWHMs of460 and 1760 nm, respectively. The inset shows the two-photon imageof a typical bead in the rz-plane. Autocorrelation measurements witha 1 in. singlet lens (b) and with a 20x/0.95 objective lens (c) indicatedduration FWHMs of 185 ± 10 and 270 ± 10 fs, respectively. Double-headed arrows in each plot indicate where the FWHM was measured.Fluorescent signal (Fl) is normalized to 1 at the center of the bead in(a), and at 1.5 ps in (b) and (c).

pulse shape, τ FWHMp , is related to the autocorrelation trace by:

τ FWHMp = 0.59 τ FWHM

p , we estimate the pulse duration at thesample plane to be 185 ± 8 fs with the singlet lens and 270± 10 fs with the 20x/0.95 objective lens. Using the measuredspectral bandwidth of 7.5-nm FWHM, and assuming a modestGDD of 250 fs2 from the 1 in. singlet lens, we estimate that theGDD of our objective lens is approximately 4300 fs2 at 760 nm.This GDD is significantly larger than reports of other similar NAobjectives,37 but not unexpected, given the long physical lengthof the lens (75-mm long).

2.3 Monte Carlo ModelWe used two independent Monte Carlo simulations to find thespatiotemporal distribution of the squared excitation intensity,I 2(r, z, t), and the spatial dependence of the collection effi-ciency, φ (r, z). These results were then combined using Eqs. (3)and (8) to calculate R and determine image contrast, Q, as afunction of imaging depth for a variety of sample and systemparameters.

For the excitation simulation, the trajectories of photonpackets were traced through a cylindrically symmetric three-dimensional grid with coordinates for depth z, radius r, and timet. All simulations used a Henyey–Greenstein scattering phasefunction with a scattering anisotropy, g, set to 0.85, which isthe expected value from Mie theory for 760 nm light interacting

with 1-μm diameter polystyrene spheres.38 We used an absorp-tion mean free path length of 5 mm in all simulations.

We modeled the focusing of the excitation light using the hy-perbolic focusing method described by Tycho et al.39 By skew-ing the initial trajectory of each photon off of a z-r plane byan angle depending on r, a focused Gaussian beam is exactlyreconstructed in all three dimensions with photons that travel instraight paths. In a Gaussian beam focused at an imaging depthof z0, the lateral 1/e2 beam radius as a function of depth, w(z),is defined by two parameters: the lateral 1/e2 beam waist at thefocal plane (w0) and the Rayleigh range (zR):

w2 (z) = w20

[1 +

(z − z0

zR

)2]

. (9)

The intensity distribution can then be defined as:

I (z, r ) = 1

w2 (z)e−2r2/w2(z). (10)

We measured three parameters experimentally that characterizethe excitation light distribution: the beam profile at the backaperture, the axial extent of the focal spot, and the lateral ex-tent of the focal spot. With only two parameters that define theshape of a Gaussian focus, all three measurements of our ex-citation beam shape cannot be simultaneously modeled. Sincethe purpose of this model is to simulate the ratio of in-focusto out-of-focus fluorescence, it is important that the simulatedbeam shape matches experimental observations both close andfar from the focal plane. Therefore we choose w0 so that thelateral Gaussian shape is correctly simulated at the focal plane,and zR such that the lateral Gaussian shape is correctly simulatedat the front aperture of the objective.

Excitation photons were launched to a w0 equal to√

2 timesthe 1/e2 radius of the measured IPSF2 at the focal plane. Tofind the zR to match the profile of the excitation beam at thefront aperture, we assume that the fill factor at the back apertureof the objective is linearly transferred to the front aperture ofthe objective—that is that wBA/rBA = wFA/rFA [Fig. 3(a)]. Theresulting parameters describing the Gaussian distribution of theexcitation photons are:

w0 = rFWHM√ln 2

and zR = WD√(0.7rF A)2

/ (w2

0

) − 1. (11)

In our simulations, w0 = 552 nm and zR = 0.78 μm for work-ing distance of WD = 2 mm and r f a = 2.04 mm. The FWHMof the axial dimension of the two-photon excited focal spotis linearly related to the Rayleigh range by zFWHM = 1.29 · zR

= 1.06 μm. Thus the axial resolution of our simulation is 40%smaller than the measured resolution. The effect of this discrep-ancy in calculating the R value is shown in Fig. 3(b). For atransparent medium, the R value calculated by these parametersis approximately twice that if the IPSF2 is exactly simulated.In our application, we are studying the change in signal whenimaging many mean free scattering lengths deep in turbid media.Imaging five mean free scattering lengths deep, for instance, wewill see that the signal decays by over 4 orders of magnitude.So this inaccuracy in R value has a small effect on calculatingthe maximum imaging depth.

We obtained the temporal impulse response of the system bysetting initial photon times such that ballistic photons intercept

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m][ µµµµsr0.1 0.5 1

10-3

10-2

10-1

100

101

Fig. 3 (a) Schematic of parameters used in modeling signal and back-ground fluorescence generation for a focused Gaussian beam in turbidmedia. (b) The ratio of signal fluorescence to background fluorescencein a homogeneously stained, R, is a function of the signal volume size,defined here as the volume of a sphere with radius rs . The lines shownare exact analytical solutions and solid points are Monte Carlo resultsfor focusing to a spot size equal to the measured ISPF2 of our system(blue line), and for focusing to the conditions used in our model (redline) in the limiting case where the scattering and absorption of themedia are zero.

the focal plane at exactly the same instant. The intensity distri-bution was determined by convolving the impulse response withthe Gaussian pulse envelope measured in Sec. 2.2. Finally, thefluorescence generated per voxel was calculated by multiplyingthe integrated intensity squared by the volume of the voxel.

A second, time-independent, Monte Carlo simulation wasused to model the effect of heterogeneous collection efficiencyon maximum imaging depth. We implemented the approach out-lined by Beaurepaire and Mertz, where the maximum radius andexiting angle of a photon escaping the tissue are coupled to con-serve beam etendue.40 We used an effective field of view radiusof rf = 1 mm.27 We created a set of collection efficiency mapsby launching photons with an isotropic initial angle distributionand a wavelength of 515 nm. The ratio of scattering length at760 and 515 nm found to be 1.7 by Mie simulations for 1-μmpolystyrene beads (see Sec. 2.5). Thus, for each excitation simu-lation set, we then used a scattering length of lcollection

s = ls/1.7 tocreate a matching collection efficiency map. We used an lcollection

aof 2 mm. To calculate R, the fluorescence grid created from theexcitation simulation was integrated over time and every ele-ment was multiplied by an interpolated value from the spatialcollection efficiency grid.

2.4 Analytical ModelWe applied the analytical model developed by Theer and Denk tocalculate the fluorescence distributions for different optical sys-tem and sample parameters.41 In short, we consider the ballisticand scattered light distributions in turbid media independentlyand then combine the resulting intensities to calculate total flu-orescence. The intensity from ballistic photons assumes an in-cident beam with Gaussian spatial and temporal distributions.The scattered light is modeled using a small angle approxima-tion and statistical methods to calculate an effective temporal

and transverse spatial beam width. We used an NA of 0.75,which produces a similar spot size to that measured from ourIPSF2. All other parameters used in the analytical model werethe same as those used in the Monte Carlo model.

2.5 Tissue Phantom Preparation

To measure the experimental contrast decay of two-photon imag-ing in a turbid media, we prepared 12 scattering agar phan-toms with a range of optical properties similar to what is typi-cally observed in epithelial tissues. Low melting point agarose(1.0%, Sigma) was prepared with 0.95-μm diameter polystyrenebeads (Bangs Labs, PS03N) to vary scattering coefficient, 1-μm diameter fluorescent polystyrene beads (Invitrogen F-8823)to provide features for contrast measurements, and fluorescein(Fluka 46955) to control staining inhomogeneity. Polystyrenebeads were ultrasonicated for 30 min to reduce aggregationsbefore they were mixed into the agar phantoms. To increasethe two-photon action cross-section of fluorescein, we mixedthe agar solution with 2% pH 12 buffer. Polystyrene concen-trations of 1.7×1010, 0.9×1010, and 0.6×1010 particles per mLprovided scattering mean free paths of 40, 80, and 120 μm at760 nm excitation, and 23, 46, and 69 μm at 515 nm emission,respectively. We determined the scattering coefficient with aMie calculation using polystyrene sphere and agar gel refractiveindices of 1.58 and 1.33, respectively.42 To verify the scatteringlengths of our polystyrene solution matched Mie predictions, wemeasured attenuation of collimated 760-nm light through dilutesolutions of polystyrene beads in a cuvette. Fluorescent beadswere added at a constant concentration of 3.5×108 particles permL in all phantoms.

We added increasing amounts of fluorescein to get final con-centrations of 0, 4, 10, and 25 μM for each scattering lengthtested, creating a total of 12 phantoms. This approach allows theformation of phantoms with low staining inhomogeneities with-out an increase in scattering coefficient that would result fromadding high concentrations of fluorescent polystyrene beads. Anadditional benefit of using this method is that we can increase thebackground fluorescence immediately adjacent to the fluores-cent beads. In contrast, previous studies that varied fluorescentbead concentration could control the fluorescence only in vol-umes many micrometers away from the signal volume.18 Thusour approach provides a more appropriate model for studyingautofluorescence contrast decay, where the local staining inho-mogeneity changes rapidly in short distances from the nucleus tocytoplasm to extracellular matrix. The disadvantage of this ap-proach is that the out-of-focus background fluorescence cannotbe measured directly because there is no region without somefluorescent signal—when the focal spot does not overlap with afluorescent bead, the measured background still includes somecontribution from the fluorescein in the focal volume.

We obtained lateral phantom images at 1 μm depth incre-ments from the surface to the depth where the image con-trast fell to approximately 0.1. The contrast for each of the16 phantoms was analyzed using an automated bead-findingscript written in MATLAB (Mathworks, Inc.). The MS for eachbead was then calculated as the average of the maximum 4 vox-els (150×150×1000 nm/voxel) within each region and the MBwas calculated as the average pixel value of the nonconnectedregions at the depth determined by the centroid of the bead.

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2.6 Biopsy PreparationHuman oral cavity biopsies were obtained from the Universityof Texas M. D. Anderson Cancer Center as part of an ongoingproject for two-photon diagnosis of oral malignancies. The studywas reviewed and approved by the internal review boards atM. D. Anderson Cancer Center and the University of Texasat Austin. Biopsies were excised from suspicious regions andcontralateral normal tissue in the oral cavity and submitted forhistopathology. We present two-photon images from the normalbiopsy in this paper. The biopsy was approximately 3 mm indiameter and 5-mm thick, delivered in chilled culture media(Phenol Red-free DMEM High, Fisher Scientific), and imagedwithin 6 h of excision. The biopsy was stabilized on a Petri dishwith low melting point agar and imaged at room temperature ina culture media bath.

3 Results and Discussion3.1 Monte Carlo SimulationsTo validate our Monte Carlo model, we verified that for a trans-parent tissue, in the absence of scattering and absorption, theexpected Gaussian profile is maintained from the sample sur-face to the full working distance of the lens. The value of Rcalculated from Monte Carlo simulations and the exact solutionare shown in good agreement in Fig. 3(b). Select Monte Carlosimulations were rerun with half the chosen grid spacings of r, z,and t (and corresponding eight times more grid elements for con-stant grid size), to verify the grid spacing was sufficiently smallto capture the spatiotemporal changes in fluence. No significantchanges were found in R calculations for smaller grid spacings,indicating the grid choice was sufficiently small to capture dy-namic and spatial changes in intensity distribution. Finally, weverified that focal plane fluorescence generation scales inverselywith pulse duration.

We used our Monte Carlo model to calculate R as a func-tion of depth for each phantom. For these calculations, Vs wasset to the volume of the 1 μm diameter fluorescent beads whichprovide the signal in the phantoms. Figure 4 presents the fluores-cence distribution for imaging 400 μm deep in a homogeneouslylabeled sample with an ls of 80 μm. In this case, the collectedbackground fluorescence overwhelms the signal fluorescenceby approximately 30 times. When the fluorescence is integratedcircumferentially, we observe that the cumulative backgroundfluorescence generation peaks slightly off-axis because the off-axis fluorescence is generated in larger volumes [Fig. 4(a)].Finally, integration of this fluorescence radially shows that thetotal fluorescence generation at each transverse plane is rela-tively constant through the first two ls, and monotonically de-creasing at larger depths [Fig. 4(b)].

The contributions from ballistic (B) and scattered (S) flu-ence were separated by tagging scattered photons in the MonteCarlo simulations [Fig. 4(b)]. The fluorescence generation ateach voxel will then be proportional to (S + B)2. These resultscan provide some insight into how certain parameters affect thegeneration of background fluorescence. For instance, previousstudies have shown that the R value can be increased by usingshorter pulses.18, 19 Looking at the individual components, as thepulse duration is decreased, it is entirely the scattered (S2) andcombined (2BS) terms that show a relative reduction in contri-

bution of background fluorescence. Scattering can be thought ofas a source of temporal dispersion from the sample on the scat-tered fluence. Furthermore, as the pulse duration is decreased,the dispersion from scattering reduces the fluorescence gener-ated from scattered photons relative to the peak fluorescencegenerated within the focal volume, resulting in an increase in Rfor shorter pulse durations.

Though high collection efficiency is important for reachinglarge imaging depth with limited excitation power, we foundthat heterogeneous collection efficiency generally had a smalleffect on our calculations of R. In the ls = 80-μm simulation(lemission

s = 46 μm), the collection efficiency only reduced R by12% at z0 = 400 μm, and by 60% at z0 = 800 μm. The radialdependence of the collection efficiency had an especially weakeffect on R, since the majority of the fluorescence generated inthe excitation simulations was within 200 μm of the optical axis.

3.2 Phantom ImagingFor all phantoms, we had sufficient power to reach contrast levelsbelow one. Typically, excitation powers smaller than 1 mW weresufficient to image at the surface, while several hundreds ofmegawatts were required at the largest depths. For the phantomwith ls = 80 μm and χ = 300, for example, the excitation powerwas increased from 0.7 mW at the sample surface to 483 mW atthe sample surface when imaging 510-μm deep. We identifiedan average of 190 beads per 77×77×100 μm3 field of viewin each of the 12 phantoms using the automated bead-findingscript. This number of beads corresponds to a bead concentrationof 3.2×108 beads per mL, slightly less than the expected valueof 3.5×108 beads per mL.

Figure 5 shows XZ images of the ls = 80 μm phantom set fordifferent staining inhomogeneities. Each XZ reconstruction iscreated from a maximum projection through 15 μm (45 pixels)of Y. The accompanied biopsy images are discussed in Sec. 3.5.We estimated the staining inhomogeneity of phantoms using themeasured contrast at the surface of each phantom and the R val-ues found from Monte Carlo simulations. The R value since itonly changes slightly for shallow imaging depths in our MonteCarlo model—a decrease from 0.51 at the surface to approx-imately 0.46 at one ls deep. Substituting an R value of 0.5 inEq. (8), the staining inhomogeneity, χ , becomes approximatelyequal to three times the measured contrast at shallow depths,for large values of χ . Using this approximation, we estimate theaverage staining inhomogeneities to be χ = 300, 62, 25, and10, by using the average contrast from beads identified withinthe first 20 to 40 μm of the three phantoms at each staininginhomogeneity.

The measured bead size remained constant with imagingdepth for all phantoms. Figure 6 shows a representative case forthe measured bead size versus depth for ls = 80 μm, χ = 300phantom. We determined the FWHMs of bead sizes by fittinga Gaussian function through the centroid of each bead found inthe phantom. We found a slightly smaller bead sizes in the direc-tion of our fast moving mirror (horizontal), indicating a slightlysmaller resolution in that direction, possibly due to a slight el-lipticity of the beam shape at the back aperture of the objective.The apparent axial resolution measured from the 1-μm beadswas noticeably larger than that measured from the IPSF2 with100-nm beads. We attribute this increased measured axial

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Fig. 4 Monte Carlo simulations are used to calculate the expected fluorescence distribution for an imaging depth of 400 μm in a sample with a460-nm FWHM lateral spot size, τp = 270 fs, ls = 80 μm, and g = 0.85. These parameters resulted in an R value of 1/30. (a) shows the lateral andaxial distribution of the circumferentially integrated background fluorescence distribution. In this case, most of the background fluorescence comesfrom above the imaging plane and within 200 μm of the optical axis. (b) shows the contributions from ballistic (B2), scattered (S2), and combined2(B + S) photons separately. The total fluorescence generation per transverse slice is relatively constant through the first three ls deep. The solid anddotted lines represent simulations with excitation pulse durations of 270 and 135 fs, respectively. (a) is normalized so that the maximum out-of-focusfluorescence is one, (b) is normalized so the maximum fluorescence is one.

resolution to sparse sampling (axial spacing between imageswas 1 μm) and long times between imaging the top and bottomof the beads (the time elapsed between the first image and thelast image 3-μm apart was approximately 10 s). Nonetheless,the constant lateral and axial size of the measured beads doesindicate minimal specimen-induced aberrations with increas-

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Fig. 5 Comparison of XZ images of phantoms with constant scatteringlength of ls = 80 μm for increasing staining inhomogeneity, χ , and ahuman tongue biopsy. Phantom cross sections are maximum projec-tions through 15 μm of Y. Biopsy cross-sections shown are a max-imum projection “max Biopsy” and a standard deviation projection“σ Biopsy” through 15 μm of Y. The standard deviation projection isnormalized so that the maximum value is white.

ing imaging depth. This result is in contrast to studies with-out index matching, where spherical aberrations are commonlyobserved.43, 44

3.3 Fluorescence DecayWe measured the decay of the signal, background, and total flu-orescence with increasing imaging depth in our 12 phantoms.By increasing the excitation power exponentially with imag-ing depth and normalizing the measured signal at each imagingdepth by the expected quadratic increase with the excitationpower, P(z = 0)2/P(z = z0)2, we could accurately measure

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Fig. 7 Plots of normalized fluorescence decays versus imaging depthfor constant staining inhomogeneity (χ = 62). Points are data fromphantom measurements and lines are the decays predicted by ourMonte Carlo simulation with homogeneous (solid lines) and heteroge-neous (dashed lines) collection efficiency. (a) The average fluorescencedecay, 〈M〉, represents the average pixel value of a 512×512 pixelimage recorded at each imaging depth. For comparison, the averagefluorescence decay of the biopsy is also shown. (b) Examining relativedecays for the MS, MB, and difference (MS-MB) versus depth for theχ = 62, ls = 80 μm phantom, we found a maximum imaging depth ofzm = 390 μm. (c) The background-subtracted fluorescence decay ex-hibits exponential decay for the entire measured range. Monte Carlosimulations agree well with experiments for homogeneous collectionefficiency (dashed lines) and heterogeneous collection efficiency (solidlines). Decays are normalized to one at 20-μm deep in (a) and (c). In(b), the background is normalized to one at 20-μm deep.

fluorescence decays far beyond the limited dynamic range ofour detection system.

Figure 7 shows the measured and calculated fluorescence de-cays of the three χ = 62 phantoms. Looking at the χ = 62, ls= 80 μm phantom, Fig. 7(a) shows the decays of the averagevalue of the measured background at each imaging plane (MB),the measured signal for each fluorescent bead (MS), and thedifference (MS-MB). Note that the slopes of the (MS-MB) andMB decays are approximately equal for imaging depths down tothree mean free scattering lengths. This result suggests that the

contrast, defined as the ratio of (MS-MB) to MB, is relativelyconstant for shallow depths. At larger imaging depths (z > 4ls)the measured signal, which decays exponentially, is overcomeby the background, which decays with z−1

0 .18 Comparing the flu-orescence decay in phantoms with different scattering lengths,we found good agreement between the measured data and theMonte Carlo predictions [Figs. 7(b) and 7(c) ]. The decay of thefluorescent signal from the biopsy is discussed in Sec. 3.5.

The effect of heterogeneous collection efficiency has littleeffect on the calculated decay curves, indicated by the overlapof the Monte Carlo results for shallow and moderate imagingdepths. We also found that changing the staining inhomogeneityhad little effect on the observed fluorescence decay rate, assummarized in Table 1. As expected, the staining inhomogeneityhad the effect of raising or lowering the initial MB value relativeto the MS values.

Table 1 summarizes the measured length constants, lms , ob-

tained from the exponential decay rates of the background-subtracted fluorescence in each phantom, and the correspondingdecay constants predicted by Monte Carlo models. In all phan-toms, the actual scattering length could be estimated to within10% accuracy by using the approximation: ls = 2.3lm

s . This re-sult is reasonable considering a previous report, which found afactor of 2.5 relation between lm

s and ls using an NA of 1.2.15

3.4 Contrast DecayThe measured contrast decay from tissue phantoms showed sim-ilar trends to those predicted by Monte Carlo and analyticalmodels (Fig. 8). The Monte Carlo model matches the analyticalmodel relatively well for the higher χ values tested. For the χ

= 10 phantom, the measurements demonstrate shorter zm than

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Fig. 8 Contrast decays of phantoms with (a) constant staining inho-mogeneity and (b) constant scattering length. Monte Carlo simulations(solid lines) agree well with the analytical model (dashed lines) and thephantom contrast measurements (solid dots). Both models slightly over-estimate the maximum imaging depth, increasingly at lower staininginhomogeneities.

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Table 1 Summary of fluorescence signal decay length constants from exponential fits to measured phantom data (from z0 = 0 to 3ls ) and predictedin Monte Carlo data, with and without including the effect of heterogeneous collection efficiency.

Measured length constants, lms / ls

Phantom measurements Monte Carlo data

ls (μm) χ = 10 χ = 25 χ = 62 χ = 300 Homogeneous collection Heterogeneous collection

40 0.43 0.45 0.43 0.45 0.50 0.48

80 0.40 0.43 0.41 0.41 0.46 0.44

120 0.43 0.45 0.45 0.43 0.46 0.43

predicted, likely due to the high concentration of fluoresceinin these phantoms beginning to absorb significant amounts ofemission (the “inner filter” effect). If the absorption mean freepath length is known at the emission wavelength, this effectcould be accounted for using a shorter mean free absorptionlength in our collection efficiency calculations.

We observed that for the χ = 300 phantoms, the contrast washigher than the expected values at shallow depths [Fig. 8(b)].We attribute this large contrast to an effective increase in χ atshallow depths. Because no fluorescein was added in this set ofphantoms, the staining inhomogeneity was determined by theinfluence of background fluorescent beads. For the shallowestbeads, there are no background fluorescent beads directly abovethem, effectively increasing their apparent staining inhomogene-ity. For deeper beads, the fluorescent beads that are present abovethe imaging plane produce background fluorescence.

3.5 Human Biopsy ImagingFigure 9 presents a summary of the 200 autofluorescence imagescollected at 2-μm depth increments from a biopsy of healthyhuman tongue tissue. The water-dipping objective allowed usto visualize the natural surface roughness of the tissue, whichplays a role in collection efficiency40 [Fig. 9(a)]. We defined thesurface (z = 0 μm) as the depth at which half of the field ofview had signal. We increased the excitation power delivered tothe tissue surface gradually from 3 mW at the surface to 30 mWat 170-μm deep. At larger imaging depths, we could maintainconstant signal detected while increasing the excitation powerless rapidly. We used a maximum of 160 mW of excitation powerdelivered to the sample surface when imaging 380-μm deep.

Lateral images show subcellular resolution and cellularmorphology with bright cytoplasm to dark nucleus contrast[Fig. 9(b)]. Contrast is presumably due to high concentrationsof NADH, NAD, and FAD in the cytoplasm, which have beenshown to be the dominant endogenous fluorophores in con-focal autofluorescence imaging of cervical and oral epithelialtissues,45, 46 and are efficiently excited in 2PAM at 760-nmexcitation.4 We found especially high signal levels from the stra-tum corneum, which, based on our Monte Carlo model, wouldstrongly contribute to the out-of-focus fluorescence found atlarge imaging depths.

A maximum XZ projection through 15 μm of Y shows thatat large depths, bright pixels in the background substantiallydegrade the contrast beyond 300 μm [Fig. 5]. A normalized

standard deviation projection through 15 μm of Y gives valuessimilar to the measured contrast—it shows bright regions wherethere are large changes in pixel values. At shallow depths, thisprojection shows large values where there is variation betweenthe bright cytoplasm signal and dark nuclei. At large depths,the increase in low-spatial-frequency, out-of-focus backgroundfluorescence reduces the lateral variation in signal, and the cor-responding standard deviation along Y decreases.

We examined the total fluorescence decay with imaging depthto estimate the scattering coefficient of the biopsy. Though flu-orescence decay accurately predicted the scattering coefficientin phantoms, extending this method to the biopsy can be com-plicated by several effects. 1. The scattering length and fluo-rophore concentrations are likely to change with depth. Pre-vious studies have observed brighter signal coming from thestratum corneum and basal membrane than at the intermediateepithelial layers.46, 47 2. As the excised tissue dies, the autofluo-rescence signal levels gradually decay with time. We observedthat the superficial regions of the tissue begin losing fluorescencesignal more rapidly than the interior regions, creating a time-dependent change in relative fluorescence density. 3. Specimeninduced aberrations typically become more severe with increas-ing imaging depths,48 and would result in a higher apparent rateof fluorescence decay. Though we verified aberrations playeda minimal role in degradation of signal in the phantom, with-out a constant-size point source in our biopsy, we were unableto monitor our excitation spot size with depth in the biopsy.Nevertheless, we can obtain an estimate of the biopsy scatteringcoefficient by comparing our measured biopsy fluorescence de-cay to phantom experiments [Fig. 7(a)]. We fit an exponentialcurve to the first 200 μm of fluorescence decay obtained fromthe biopsy and found a length constant of 39 μm, correspondingto a scattering length of 89 μm, assuming ls = 2.3lm

s . At largerdepths, the fluorescence decayed less rapidly, showing a similarslope to the ls = 120-μm phantom.

Figure 9(c) presents typical contrast levels obtained at dif-ferent imaging depths. We examined the contrast in line profilesdrawn through manually identified epithelial cells marked bythe lines drawn in the lateral images displayed in Fig. 9(b).At 40-μm deep, the brightest signal from the cytoplasm is ap-proximately 20 to 40 times larger than the minimum signalfrom within the nucleus, while the average signal from the cyto-plasm is approximately 5 to 10 times the average signal from thenucleus [Fig. 9(c)]. Using averaged signal and background ascontrast, and employing the same method used with the

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Fig. 9 (a) Three-dimensional rendering of a sequence of 200 lateral 2PAF images acquired from healthy human tongue biopsy. (b) Selection oflateral images from an imaging depth of 40 to 360 μm. Field of view in all lateral images is 170 μm. (c) Normalized signal profile from manuallyidentified cells at imaging depths of 40, 120, 240, and 360 μm. Profiles are taken from lateral lines indicated in (b).

phantoms, we estimate the χ of the biopsy to be 15 to 30.The contrast falls to 1 in our biopsy around 320 μm below thetissue surface, approximately 3 to 4 mean free scattering lengthsdeep.

3.6 Fluorescence Saturation and PhotobleachingThe analysis presented in this paper has assumed that the inten-sity ranges used in our experiments are low enough to assumenegligible fluorescence saturation and photobleaching—that is,that the fluorescence generation is quadratically dependent onthe excitation intensity and is time-independent. However, athigh intensities, these assumptions no longer hold. We per-formed a series of tests to verify that we do not experienceany saturation and photobleaching in our experiments.

The average powers used for surface imaging in the phan-toms and biopsy were 1 to 3 mW, respectively. Using our mea-sured spot size and pulse duration, these powers correspond topeak intensities of 5 to 15 GW/cm2 generated at the focal spot.These intensities and the estimated ∼320 overlapping pulsesper spot used in our study, are well below imaging conditionsfound in the literature to have no affect cell viability, as sum-marized by Hoy et al.49 Furthermore, we found in phantomexperiments and Monte Carlo simulations that the rate of powerincrease necessary for maintaining constant fluorescence de-tected is close to that required to deliver constant fluence tothe focal point. Though when imaging deep inside scatteringmedia, average powers greater than 100 mW are delivered tothe sample surface, it is unlikely that the fluence delivered tothe imaging plane at large depths is significantly greater thanthat delivered to the imaging plane when imaging the samplesurface.

Fluorescence saturation can broaden the point spread func-tion, as fluorophores in the highest intensity regions no longergenerate a greater emission signal than fluorophores further

away. The resulting decrease in resolution has been previ-ously demonstrated, but is expected to have a significant ef-fect only under a combination of high intensities and especiallylarge two-photon action cross-section50 (>1000 GM cross-section at 1 mW of excitation power delivered to the imag-ing plane, where 1 GM unit equals 10− 50 cm4 s). Our obser-vation of constant measured bead size with increasing imag-ing depth indicates a negligible influence of fluorescence sat-uration in our phantom experiments [Fig. 6]. To test for flu-orescence saturation in our biopsy experiments, we verifiedthat our detected signal scales quadratically with excitation atselect imaging depths. We measured power dependencies of1.94, 2.00, 1.97, and 1.99 at increasing imaging depths of z0

= 290, 300, 326, and 356 μm, respectively. In phantoms, wealso observed that the signal from the identified beads scaledto the power of 1.98 ± 0.05 at each 100 μm imaging depthincrement.

We also tested for the presence of photobleaching in 2PAMof the biopsy by measuring the ratio of the average signal ofthe first and last image taken at every image plane. Each imag-ing plane was raster scanned 8 times at 3 frames per second.We found an average ratio of 1.00 ± 0.02 for the biopsy,and no trend for photobleaching at larger imaging depths. Inconclusion, we expect that fluorescence saturation and photo-bleaching did not appreciably influence the results presentedherein.

3.7 Maximum Imaging DepthFigure 10(a) summarizes the maximum imaging depth found inphantom experiments, Monte Carlo simulations, and the analyti-cal model for samples with different scattering lengths and stain-ing inhomogeneities. We found reasonable agreement betweenthe three approaches, with experiments matching the modelsslightly better for longer scattering lengths and higher staining

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Fig. 10 (a) The maximum imaging depth determined by the depth atwhich Q = 1. (b) Expressing the maximum imaging depth in termsof scattering mean free paths, we observed a linear dependence ofmaximum imaging depth on log(ls ). Data are plotted from phantommeasurements, as well as analytical and Monte Carlo models, withhomogeneous collection, and real heterogeneous collection.

inhomogeneities. This difference is likely due to the increas-ing influence of small heterogeneities in our shorter scatter-ing length phantoms, such as spatial variations in fluoresceinand polystyrene bead concentrations. The Monte Carlo modelshowed a slightly weaker dependence of maximum imagingdepth on scattering length, partially due to the effect of inhomo-geneous collection efficiency.

The approximate position of our biopsy is also indicated,based on extraction of optical properties from biopsy im-ages. The maximum imaging depth achieved in the biopsy was320 μm, which was approximately 20% less than that expectedfrom phantoms with similar ls and χ . This difference is likelydue to greater specimen-induced aberrations in biopsy imaging.

Normalizing the maximum imaging depth by znm = zm/ ls ,

we find a logarithmic dependence on ls [Fig. 10(b)]. Thoughthis is a reasonable approximation for small fractional changesin ls, it leads to an overestimate of maximum imaging depthby 1 scattering length when extrapolating maximum imagingdepths found in samples with ls = 200 μm to samples with anls of 40 μm. The origin of the dependence of zm on ls is that asthe distances are scaled down by ls, the photons responsible forthe background fluorescence are confined to smaller volumeswhile the photons generating focal volume signal pass througha constant size signal volume.

4 ConclusionsWith recent technological advances in 2PAM, including the de-velopment of 2PAM systems more relevant for in vivo opticalbiopsy,49, 51, 52 it is increasingly important to understand how out-of-focus background fluorescence affects image contrast andultimately limits imaging depth. In this paper, we presentedexperimental data and a computation model that describes thegradual contrast decay of two-photon fluorescence imaging withincreasing imaging depth for samples with a variety of scatter-ing lengths and staining inhomogeneities relevant to 2PAM ofepithelial tissues. We found the maximum imaging depth, evenwhen normalized by scattering length, is significantly smallerin epithelial tissue than those observed brain tissue, due to adependence on maximum imaging depth on scattering lengthand very low staining inhomogeneities. Based on this analysis,we expect that given a range of optical properties typical of ep-ithelial tissue, the 2PAM image contrast decays to 1 at imagingdepths of 3 to 5 ls, or, approximately 150 to 400 μm.

In this paper, we only considered conventional 2PAM.However, more sophisticated approaches could extend 2PAMimaging depth and contrast by temporal focusing,53, 54 differ-ential aberration imaging,55 optical clearing,56 and/or spatialfiltering.18 It would conceivably also be possible to extend imag-ing depth by using longer wavelength excitation light57 to probedimmer intrinsic fluorophores that have higher wavelength ab-sorption bands, or by using higher order excitation (e.g., three-photon excited fluorescence).

AcknowledgmentsWe would like to thank Dr. Anne Gillenwater and LeslieZachariah from the University of Texas M. D. Anderson CancerCenter for providing the tissue biopsy. We also thank Dr. QuocNguyen for providing the source code for the MPScan programand Christopher Hoy and Dr. Frederic Bourgeois for their helpin implementing our 2PAM and autocorrelation systems, anduseful discussions. We acknowledge support by the National In-stitutes of Health NIH Grant RO3 CA125774–01 and NationalScience Foundation Grants BES-0508266 and Career Award:CBET-0846868. N. J. Durr was partially supported by an NSFIGERT fellowship.

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