Imaging properties in two-photon excitationmicroscopy and effects of refractive-indexmismatch in thick specimens

Cees J. de Grauw, Jurrien M. Vroom, Hans T. M van der Voort, and Hans C. Gerritsen

The detrimental effects of a refractive-index mismatch on the image formation in a two-photon micro-scope were investigated. Point-spread functions ~PSF’s! were recorded with an oil-immersion objectivenumerical aperture ~NA! of 1.3 and a water-immersion objective NA of 1.2 in an aqueous sample atdifferent depths. For the oil-immersion objective the enlargement of the PSF volume with increasingdepth yields an axial and a lateral loss in resolution of approximately 380% and 160%, respectively, ata 90-mm depth in the sample. For the water-immersion objective no resolution decrease was found.Measurements on a thick aqueous biofilm sample shows the importance of matching the refractive indexbetween immersion fluid and sample. With a good match, no loss in image resolution is observed.© 1999 Optical Society of America

OCIS codes: 180.2520, 110.0180, 120.5710, 190.4180.

1. Introduction

Multiphoton excitation is a comparatively new tech-nique in three-dimensional ~3-D! fluorescence micros-copy.1 The excitation of fluorescent molecules isaccomplished by the simultaneous, absorption of twoor more photons providing the energy to excite themolecule. One of the advantages of multiphoton mi-croscopy is the intrinsic axial resolution, even with-out a confocal pinhole in the detection path. In two-photon excitation ~TPE!, this property arises from thequadratic dependence of the two-photon absorptionprocess on the excitation light intensity. In the focalarea of the microscope objective, the highest intensityis found. This intensity, in combination with thequadratic dependence, leads to a localized volumewith efficient two-photon absorption. The advan-tages of multiphoton imaging over standard confocalmicroscopy include excitation of UV dyes withoutspecial UV optics, reduced photobleaching outside

C. J. de Grauw ~k.degrauw@phys.uu.nl!, J. M. Vroom, and H. C.Gerritsen are with Molecular Biophysics, Utrecht University, P.O.Box 80.000, 3508 TA Utrecht, The Netherlands. H. T. M van derVoort is with Scientific Volume Imaging BV, Alexanderlaan 14,1213 XS Hilversum, The Netherlands.

Received 22 March 1999; revised manuscript received 3 June1999.

0003-6935y99y285995-09$15.00y0© 1999 Optical Society of America

the focal area, and increased penetration depth instrongly scattering specimens.1,2 The latter two areparticularly important during acquisition of large3-D images. Compared with that of single-photonexcitation, the fluorescence yield of the commonlyused fluorescent labels is somewhat low for multipho-ton excitation.3 Therefore, higher intensities are re-quired for yielding a sufficiently strong fluorescencesignal. This high intensity is realized in practice byuse of high numerical aperture ~NA! objectives incombination with ultrashort ~100 fs to 1 ps! laserpulses provided by mode-locked solid-state lasers.Now, a high peak power is present in the focal region,whereas the time-averaged power is comparativelylow.

The increased penetration depth in multiphotonexcitation microscopy can yield images hundreds ofmicronmeters deep into the sample. Consequently,the optical properties of the sample, the refractiveindex in particular, become of great importance forthe image quality. Biological samples are prefera-bly measured at physiological conditions, which nor-mally means aqueous environments. Here, oil-immersion objectives cause a mismatch by thedifference in index of refraction between the immer-sion liquid and the specimen. This mismatch re-sults in a loss of resolution and of signal intensitywith increasing depth4 and an incorrect scaling alongthe optical axis.5

When an immersion objective is used, one can con-

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vert the axial scaling by using the low NA approxi-mation6:

AFP 5 NFPn1yn2.

Here AFP is the actual focus position and NFP thenominal ~apparent! focus position in the sample, andn1 is the refractive index of the immersion liquid andn2 that of the sample. More serious are the effects ofthe refractive-index mismatch on the resolution andsignal intensity through the broadening of the point-spread function ~PSF! by spherical aberration. Thisbroadening increases with depth and is of influenceduring imaging deep inside a sample. In standardone-photon confocal microscopy the detected volumeis limited by a pinhole. The effect of spherical aber-rations results in a loss of signal intensity, whichbecomes substantial, especially at larger depths.One of the advantages of multiphoton microscopy isthat the detection pinhole can be omitted and thatwide-field detection can be used. In this way, theimaging properties become independent of the detec-tion light path, thereby avoiding an important sourceof chromatic aberrations. Moreover, this allows thedetection of ~multiple! scattered fluorescence light,thus improving the detection efficiency. This is par-ticularly important in thick specimens and dense ma-terials in which significant scattering of the emittedlight takes place.

The index of refraction mismatch effects on thesignal attenuation in TPE microscopy have been in-vestigated in homogeneous fluorescent samples of amoderate thickness ~,10 mm!.5 In these experi-ments, the effect of the NA of the objective on thedepth-dependent signal attenuation is similar to thatin single-photon confocal imaging. However, theresolution itself was not directly measured.

During imaging deeper into a sample, the effect ofrefractive-index mismatch becomes more serious.This effect becomes of greater importance when thelarge penetration depth of the two-photon microscopeis used.

In this paper, the experimental PSF was deter-mined at various depths in the sample. The resultsare used to quantify the effects of refractive-indexmismatches ~spherical aberrations! on the optical

erformance of a TPE microscope. The PSF’s wereetermined from 3-D images of small fluorescenteads. The bead images were recorded with an oil-nd a water-immersion objective at several depths inn aqueous sample. The effects of the mismatch onhe observed fluorescence intensity were studied byse of a homogeneous fluorescent sample. A mis-atch in refractive index generally results in a deg-

adation of the PSF, which results in reduceduorescence intensity.The feasibility of 3-D image restoration of a thick

iological sample exhibiting detailed structures wasxamined. The experimentally determined PSF’s ofoth an oil- and a water-immersion objective weresed to restore a 3-D image of a 100-mm-thick modelor dental biofilm containing oral bacteria. Biofilms

996 APPLIED OPTICS y Vol. 38, No. 28 y 1 October 1999

onsist of bacteria, which are embedded in an extra-ellular matrix of proteins and water. The bacterialistribution is an important property of the biofilm.ifferent colonies of aerobic and anaerobic bacteriare believed to develop at different locations in theiofilm. Biofilm is a strongly scattering sample,hich makes imaging at large depths difficult in a

onventional confocal microscope. The dimensionsf the bacteria that form the biofilm are of the orderf 1 mm, which requires a high imaging resolution.hese properties make biofilm very suitable for oururpose.

2. Materials and Methods

A. Sample Preparation

The PSF’s were determined from measurements on220-nm-diameter, latex beads homogeneously filledwith Yellow Green ~FluoresBrite, PolySciences, War-ington USA!. The starting solution of 2.5% solidaterial was diluted approximately 106 times with

distilled water. Drops of this solution were driedonto an object slide and onto a coverslip ~No. 1,Chance Propper, England!. The coverslip was thenreversed and placed on a drop of distilled water on theobject slide. A 170-mm-thick strip of glass served asa spacer on one side of the coverslip to give it a smallfixed inclination of 0.3°. This small inclination isused to obtain images with variable water spacing.The inclination does not yield any measurable opticaleffect. Finally, the sample was sealed with nailenamel. Changing the lateral sample position al-lowed images to be recorded at depths ranging from 0to 100 mm.

To study the signal decay as a function of depth inthe sample, we used a homogeneous fluorescent sam-ple ~fluorescent sea!. We prepared the sample wasprepared by mounting a solution of 50-mM Rhoda-

ine 6G ~Molecular Probes Inc., Eugene, Oregon,SA! in water between a coverslip and an object

lide.The biofilm model was a palette of oral bacteria

onsisting of a dense layer of bacteria embedded in aatrix of extracellular proteins, polysaccharides, andater channels. A mixture of 10 different species ofral bacteria was grown, on a coverslip, in a chemo-tat system in mucin-based growth medium for 10ays to form a biofilm.7 Microscopic examination

shows that these biofilms can serve very well as amodel system for natural oral biofilms.7 The biofilmwas stained for 30 min with a water solution contain-ing 50-mM Rhodamine 6G. After the excess of solu-ion was removed, the biofilm was placed on aoverslip for the imaging experiments.

B. Microscope

The experiments were performed on the home-builttwo-photon microscope that is described in detailelsewhere.8 Briefly summarized, the system con-sists of a light source in the form of a mode-lockedTitanium:Sapphire laser ~Tsunami, Spectra Physics!that produces 80-fs pulses at 800-nm wavelength.

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The fluorescence is separated by a custom-made di-chroic mirror ~Laseroptik, Garbsen, Germany!. Thexcitation light is focused by the objective into theample. The fluorescent light is collected by theame objective, descanned, and directed toward ahotomultiplier ~Hamamatsu R1894! in photon-

counting mode. The remaining excitation light isblocked by a series of 700-nm interference short-passfilters ~Optosigma, Santa Anna, California! in front ofthe photomultiplier tube ~Hamamatsu R1894!. Nopinhole was used, allowing wide-field detection of thefluorescence light. The microscope acquires imagesby scanning either the object or the excitation beam.Between both scanning options no differences in theoptical properties of the microscope were observed.All images presented here were recorded by use ofbeam scanning.

Two different objectives were used: a water-immersion 603 NA of 1.2 plan-apochromatic objec-tive with correction rim for the coverslip thicknessand an oil-immersion 403 NA of 1.3 plan-fluor cover-glass-corrected objective ~both 160-mm tube length,Nikon!. The coverslip correction rim of the water-immersion objective was tuned to its optimal positionbefore the experiments. The immersion oil used had

Fig. 1. XZ planes of the two-photon PSF recorded with the water90-mm depth. XZ planes of the two-photon PSF recorded with thmm depth. Image size: 1.5 3 5 mm.

an index of refraction n 5 1.5118 ~l 5 656 nm at23 °C, DF Oil, Cargille, USA!.

C. Imaging

Images of 220-nm beads were recorded with the twoobjectives at focusing depths of 0, 15, 45, 75, and 90mm ~AFP! in the sample. The depth of the beadswas determined by measurement of the distance be-tween the bead and the coverslip with the water-immersion objective. Its correction collar was set tothe thickness of the coverslip as measured with amicrometer. The measurement at zero depth ~z 50! was performed with fluorescent beads attached tothe coverslip. Three-dimensional images with di-mensions 12 mm 3 12 mm 3 5.2 mm in 256 3 256 30 sample points ~water-immersion objective! and1.4 mm 3 12 mm 3 7.8 mm in 256 3 256 3 60 sampleoints ~oil-immersion objectives! were recorded fromections of the sample containing approximately 4atex beads. The resulting sampling distances of 50m lateral and 130 nm axial ensure ample oversam-ling. The average power on the sample was ap-roximately 3 mW. A pixel dwell time of 256 ms wassed for recording the images. No detectable photo-

ersion objective ~NA of 1.2! ~a! at the surface ~z 5 0! and ~b! at aimmersion objective ~NA of 1.3! ~c! at surface ~z 5 0! and ~d! at 90

-imme oil-

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bleaching of the beads was observed during the ex-periments.

A fluorescent sea was used to measure the signalattenuation as a function of depth, and xz imageswere recorded over a depth range of 95 mm. Theimage pixels were summed in the x direction to givea z profile with a sufficient signal-to-noise ratio.

Three-dimensional image stacks of the bacterialbiofilm were recorded with dimensions of 12 mm 312 mm 3 90.2 mm with both the oil- and the water-mmersion objective. The image stacks consistedf 256 3 256 3 692 sample points, resulting inampling distances equal to the measured beads.pixel dwell time of 64 ms was used, resulting in an

cquisition time of approximately 1 h for a completemage stack. The average excitation intensity onhe sample was approximately 10 mW. To check

998 APPLIED OPTICS y Vol. 38, No. 28 y 1 October 1999

or photobleaching effects, reference xz images werecquired before and after the recording of a stack.he comparison of these images showed no signifi-ant photobleaching. For the measurements withhe oil-immersion objective the imaging depth wasorrected to the AFP. The measurements with thewo objectives were done at a comparable, but notxactly the same, position in same sample for prac-ical reasons. The detected fluorescence intensityecreases during imaging deep into the biofilm. Tollow visualization of the biofilm structure at allepths in the xz images, the images are rescaled toompensate for this signal decrease. To this endhe individual xy images are divided by their totalntegrated intensity. In this way a depth-ependent intensity rescaling that proves to be ad-quate is achieved.

Fig. 2. Lateral- ~3! and axial- ~●! intensity profiles through the PSF’s of Fig. 1.

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D. Image Processing

Image restoration on the measured biofilm imageswas performed with the iterative maximum likeli-hood estimation restoration method.8 A commercialimplementation of this method ~Huygens System 2,

cientific Volume Imaging, Hilversum, The Nether-ands! running on a Silicon Graphics O2 workstationas used.The emitted fluorescence light is incoherent, and

he recorded image is thus a convolution of the objectunction, f ~r!, and the PSF, h~r!. The image forma-

tion can be written as

g~r! 5 h~r! ^ f ~r!,

m~r! 5 N@g~r!#,

where m~r! is the measured image and N is a functiondescribing the Poisson noise in the signal. The pres-ence of the noise prevents a straightforward determi-nation of h~r! by use of deconvolution in the Fourierdomain.9 Therefore it is necessary to use an itera-tive algorithm. As a result of the restoration proce-dure, image intensities are reallocated under therestriction of energy conservation. Therefore it alsoenhances the contrast and reduces the noise. Thealgorithm computes a new estimate of the object func-tion in each iterative step. Convolution of the objectestimate with the PSF has to match the recordedimage better after each iteration.

The PSF of the microscope was determined from3-D images of fluorescent beads.9 Images of several,

Fig. 3. Lateral and axial width ~FWHM! of the measured PSF’s asfunction of depth for the different objectives. Water-immersionobjective ~NA of 1.2! lateral ~squares! and axial ~circles!, and theoil-immersion objective ~NA of 1.3! lateral ~up triangles! and axial~down triangles!.

Table 1. Theoretical and Experimental FWHM’s of

Objective

Lateral FWHM of PSF

Theoretical

Oil, 403yNA of 1.3 0.20Water, 603yNA of 1.2 0.22

typically four, beads were averaged, resulting in agood signal-to-noise ratio even in the low-intensitytails of distorted PSF’s. The centers of mass ~CM! ofthe individual beads were aligned with subpixel ac-curacy. The averaged bead image is a close approx-imation of the real PSF, which was further improvedby iterative deconvolution with a 220-nm bead object.For the calculation of a PSF from a bead image,knowledge of the object function f ~r! is used. Aand-limited object function f ~r! with the bead diam-ter is generated with the method described by Vaner Voort and Strasters9 and the iterative-restoration

method is applied to obtain the PSF h~r!. In ourcase, when the bead object is sufficiently small, themeasured and the deconvoluted PSF are practicallyidentical.

3. Results and Discussion

A. Point-Spread Function

Figure 1 shows the xz slices through the center of thePSF at the surface ~z 5 0! and at a 90-mm depthrecorded with the water-immersion objective @Figs.1~a! and 1~b!# and the oil-immersion objective @Figs.~c! and 1~d!#. Figure 2 shows the correspondingrofiles through the centers of the PSF’s. For theater-immersion objective no increase in the PSF

ize is observed at larger depths. The PSF, mea-ured with the oil-immersion objective, is clearly ab-rrated at a 90-mm depth. The distortion of thisSF is due to the spherical aberrations that are in-roduced by the mismatch in index of refraction be-ween the specimen and the microscope objective.he deterioration of resolution can be quantified byhe axial and the lateral dimensions ~FWHM! of theSF’s ~Fig. 3!.The measured values at the surface ~z 5 0! are

listed in Table 1, together with the theoretical values.The latter are calculated with the Huygens System 2software and are based on the time-averaged electro-magnetic energy distribution for a two-photon pro-cess in the focus of the objective.10 Reasonableagreement is found between the calculated and theexperimental values of the FWHM’s, although allmeasured values are slightly larger than the theoret-ical values. The discrepancy is somewhat larger forthe oil objective compared with the water objective.This broadening can be ascribed to spherical aberra-tions. As can be seen from Fig. 2, the oil objectiveshows a broadened and asymmetric axial PSF re-sponse that is characteristic for spherical aberra-tions.11,12

In Fig. 3 the FWHM is given as a function of the

at the Sample Surface ~z 5 0! for Both Objectives

5 0 mm Axial FWHM of PSF at z 5 0 mm

asured Theoretical Measured

6 0.01 0.57 0.67 6 0.026 0.01 0.73 0.79 6 0.01

at z

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imaging depth. For the water-immersion objective,constant lateral and axial FWHM’s are observed.From Figs. 1–3 the deterioration of the oil immersionPSF is evident. At a focusing depth of 90 mm themeasured initial axial size of 0.79 mm has increasedby 280% to 2.2 mm. In the lateral direction the in-crease is from 0.27 to 0.44 mm, which is approxi-mately 160%. Clearly, the PSF, and thus theresolution, is more affected in the axial than in thelateral dimension.

Fig. 4. Axial fluorescence intensity profiles of the homogeneousfluorescent sample for ~a! the water-immersion objective ~NA of.2! and ~b! the oil-immersion objective ~NA of 1.3!. The edge

between cover glass and fluorescent solution is near 0 mm. Dotsindicate the integrated intensity of the PSF’s measured with theoil-immersion objective at various depths, normalized to the valueat a 0-mm depth.

Fig. 5. XZ planes from the 3-D data sets of biofilm. ~a! Meascorresponding image after image restoration. ~c! Measured datacentral PSF; ~e! restored image with three, depth-dependent PSF’sz direction to correct for the depth-dependent intensity decrease.

000 APPLIED OPTICS y Vol. 38, No. 28 y 1 October 1999

Comparable theoretical values were found for thebroadening of the confocal ~single-photon! PSF byacobsen and Hell.13 The FWHM’s were calculated

at a depth of 95 mm for a confocal setup with anoil-immersion objective ~NA of 1.3! at an excitation

avelength of 488 nm and with an aqueous fluores-ein isothiocyanate solution. The authors find anncrease in FWHM from 0.45 to 1.75 mm axially androm 0.16 to 0.255 mm laterally. The axial broaden-ng ~278% of the width at the surface! and the lateralroadening ~163%! are similar to the values pre-ented here. In the two-photon microscope used forhe experiments described here, wide-field detections employed, making it insensitive to chromatic ef-ects and other aberrations in the detection lightath. The optical response of this system is mainlyetermined by the properties of the illumination lightath. Therefore the degradation of the PSF can bettributed to aberrations of the excitation path. Inontrast, the conventional confocal geometry is alsoensitive to aberration in the detection path.In addition to scattering and absorption, a mis-atch in refractive index between sample and im-ersion fluid results in a reduction of the measureduorescence intensity at larger depths. In Fig. 4 theuorescence intensity as a function of depth in a flu-rescent water sample is shown for the different ob-ectives. No correction was applied for theifferences in transmission and pulse broadening ofhe individual objectives. In general, scattering, ab-orption, and enlargement of the PSF due to aefractive-index mismatch are the causes of signal

data, recorded with the water-immersion objective and ~b! therded with the oil objective; ~d! restored image, restored with oneage size 11 mm 3 90 mm. The image intensities are scaled in theface ~z 5 0! is located at the bottom of the images.

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decrease deep in a sample. The water-immersionobjective shows no signal attenuation at increasingdepth. This is consistent with the observed depth-independent PSF and implies a negligible scatteringand absorption in this sample. For this aqueoustransparent sample, no attenuation due to scatteringis expected. No absorption is observed, confirmingthat for two-photon microscopy, no absorption isfound outside the focal region. For the oil-immersion objective a clear signal decrease is found.At an 80-mm depth the signal intensity has decreasedto 20% of the value at the surface. This is consistentwith earlier findings for TPE microscopy5 and withthe enlargement of the PSF. Since absorption andscatting are negligible, this decrease is attributedonly to enlargement of the PSF volume. The mea-sured PSF’s can be used to verify this. The inte-grated intensity of the measured PSF’s at 0, 16, 49,and 95 mm depth with the oil-immersion objective areplotted in Fig. 4. Overlapping between signal ob-tained from the fluorescent sea and the signal con-tained in the PSF confirms that the dependence of thesignal with depth arises from the enlargement of thePSF volume only.

B. Axial Scaling

The axial scaling was determined by comparison ofthe observed depth of beads measured at a knownposition with both the water- and the oil-immersionobjectives. Here the depth observed with the water-immersion objective served as the reference depth.Analysis of the observed values at various depths ~notshown! showed that the scaling effect is linear withdepth. Linear regression of the data results in ascaling factor of 0.866 for the oil objective. This scal-ing factor is also close to the geometric approximationof n1yn2, which is 0.878. It is also in good agreementwith both experimental and theoretical values foundin the literature.4,13,14

C. Large-Depth Imaging

Three-dimensional images of biofilm were recordedwith both the water- and the oil-immersion objec-tives. The detected fluorescence decreases with thedepth. The xz images presented in Fig. 5 are cor-ected for this decrease by a depth-dependent inten-ity rescaling.A mismatch in refractive index between the immer-

ion fluid and the biofilm is of direct influence on themaging quality. To investigate the effects of a mis-

atch, we mixed a small amount of 220-nm beadsith unstained biofilm material. Images of theeads were recorded at various depths in the biofilmith the water-immersion objective ~not shown!.

Analysis of the images showed no significant changein the dimensions. This indicates that the refractiveindex of the biofilm material is close to that of water.Since most of the biofilm matrix consists of water,this is expected.

Figures 5~a! and 5~c! show an xz plane from the 3-Dimage measured with the water- and the oil-immersion objectives, respectively. Figure 6 shows

xy planes at a 4- and an 80-mm depth from the imagestacks. Comparison of Figs. 5~a! and 5~b! with Figs.6~a!, 6~b! ~oil and water immersion at a 4-mm depth,espectively!, 6~c!, and 6~d! ~oil and water immersiont a 80-mm depth! shows the effect of the mismatch inefractive index on the image quality. The imagesecorded with the oil-immersion objective show alear degradation of details with increasing depth inhe sample. In the xy image measured with the oil-

Fig. 6. XY images ~parallel to the biofilm surface! from the 3-Data set of biofilm. Left panels show the measured data, and theight panels show the images after restoration. ~a! and ~c! Water-mmersion objective recorded at a 4- and a 80-mm depth, respec-ively, in the biofilm. ~b! and ~d! Oil-immersion objective recordedt a 4- and a 80-mm depth, respectively, and restored with theirorresponding depth-dependent PSF. All images are 11 mm 3 11m. Arrows show some of the oral bacteria Fusobacterium nu-leatum.

1 October 1999 y Vol. 38, No. 28 y APPLIED OPTICS 6001

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Table 2. Diameter ~FWHM! of Fusobacterium nucleatum Bacteria and Their Characteristic Signal Noisea in the Biofilm Images at Two

6

immersion objective at a 4-mm depth @Fig. 6~b!, leftanel#, bacterial structures can be distinguished. Atn 80-mm depth @Fig. 6~d!# structures appear largernd details are blurred, demonstrating a loss of res-lution at larger depths. With the water-immersionbjective, detailed structures remain visible over thentire scan depth. At a large depth @Fig. 6~c!, leftanel# the loss in signal intensity results in a lowerignal-to-noise ratio, but the resolution does not vis-bly decrease. These results, again, indicate thathe refractive index of the biofilm is comparable withhat of water. They also indicate that the loss ofignal with increasing depth is due to scattering andbsorption.To quantify the results, we analyzed the character-

stics of the images of oral bacteria Fusobacteriumucleatum in the xy images. Of all the bacteria, onlyhis bacteria has a hairlike phenotype and can thuse unambiguously identified ~see arrows in Fig. 6!.heir diameter and fluorescent signal noise were an-lyzed at two different depths in the biofilm. Atach depth several bacteria were analyzed at severalpots ~typically 5 to 10!, and the averaged results arehown in Table 2. The diameter of these bacteria isnown to be approximately 0.5 mm.15 The observed

diameter results from a convolution of the PSF andthe bacteria. Therefore the average diameter in theimages can serve as a measure for the image resolu-tion and thus for the imaging quality, although it isnot a linear dependence. The standard deviation ofthe signal strength measured over these bacteriagives an indication of the signal noise in the images.

At a 4-mm depth the diameter and the signal noiseare rather similar for both objectives. At 4 mm the.59-mm diameter measured with the oil-immersionbjective is slightly larger than the 0.52 mm mea-ured with the water-immersion objective. At aarger depth, however, the image diameter increaseor the oil objective is 140% of its original value.his is of the order of the enlargement of 160% found

or the PSF at an 80-mm depth ~Fig. 3!. The diam-eter measured with the water-immersion objectivestays constant. Deeper in the biofilm a lower fluo-rescence intensity is detected owing to absorptionand scattering. Therefore the signal noise in-creases. The signal noise increases with a factor of2.7 for the water-immersion objective, which is

Differe

Objective,Depth ~mm!

Measured Rest

Diameter@mm#

Signal Noise%

Dia@

Water, 4 0.52 6 0.05 9 0.47Oil, 4 0.59 6 0.05 10 0.58Water, 80 0.52 6 0.08 24 0.47Oil, 80 0.76 6 0.12 31 0.63

aSignal noise in percentage of the signal strength.

002 APPLIED OPTICS y Vol. 38, No. 28 y 1 October 1999

smaller than for the oil-immersion objective ~a factorof 3.1!.

D. Image Restoration

The measured 3-D image stacks were restored withthe maximum likelihood estimation restorationmethod with the earlier measured PSF’s. The im-age stack measured with the water-immersion objec-tive was restored with the PSF measured at a 45-mmdepth ~halfway the biofilm!. In fact, for this objec-tive the choice of PSF is irrelevant since its dimen-sions are constant over the imaging depth ~Figs. 1–3!.The image stack recorded with the oil-immersion ob-jective was restored with one PSF measured at a45-mm depth and also with three PSF’s recorded atdifferent depths in the water sample. The latter res-toration was carried out by division of the imagestack axially into three overlapping segments of 36.5mm ~AFP!. Each of these segments was then re-tored with the maximum likelihood estimation algo-ithm with the corresponding PSF at 15, 45, and 75m depth ~AFP!. Figures 5~b!, ~d!, and ~e!, show xzlanes of the restored image stacks. In all cases alear improvement in image detail and a reduction inoise is observed. The quality of the restored oil

mage appears to be not as good as that of the water-mmersion objective. This is confirmed by the anal-sis of bacteria sizes as presented in Table 2. Theateral diameter of the bacteria identified improvesith restoration. For the water-immersion objec-

ive a small decrease in diameter is observed. A twoo four times improvement in axial resolution wasbserved by Kano et al.10 Their decrease in lateral

direction appears to be much less than that. In ourcase the object diameter is approximately 0.5 mm, so

o substantial decrease in diameter below that isxpected.For the oil-immersion objective at a large depth

Fig. 6~b!#, much more details are visible in the re-tored image than in the original image. This is aesult of the 3-D restoration to which also the planesbove and below the presented one contribute. Theignal noise, after restoration, is strongly reduced forll restorations.Comparing the diameters in Table 2 it can be con-

luded that, for the oil-immersion objective, restora-ion with three different PSF’s leads to a small

pths

with One Central PSFRestored with

Depth-Dependent PSF’s

r Signal Noise%

Diameter@mm#

Signal Noise%

03 2 — —04 2 0.56 6 0.08 203 4 — —04 4 0.62 6 0.08 4

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increase in image quality. With the oil-immersionobjective, it remains obvious that at a large depth areduced measured image quality cannot be compen-sated for by image restoration. The image qualityfor the water-immersion objective is better in allcases than that found for the oil-immersion objective.

4. Conclusions

The detrimental effects of a refractive-index mis-match on the image formation in a two-photon mi-croscope were investigated. Point-spread functions~PSF’s! were recorded with both oil- and water-mmersion objectives ~NA of 1.3 and NA of 1.2, re-

spectively! in an aqueous sample at depths rangingform 0 to 90 mm below the sample surface. Theresults show a strong depth dependence of the PSF’srecorded with the oil-immersion objective. Axialand lateral resolution losses of approximately 280%and 160% respectively were found at a depth of 90 mmor an oil-immersion objective ~NA of 1.3!. For theater-immersion objective the PSF’s are, in good ap-roximation, independent of the measuring depth.he enlargement of the PSF at larger depth due toefractive-index mismatch causes a substantial at-enuation of the signal.

Measurements on a thick aqueous biofilm samplehow that with the water-immersion objective no lossn resolution is found during imaging as deep as 90m into the sample. For the oil-immersion objectivemismatch in refractive index between immersion

uid and sample results in a decrease in resolutionuring imaging deeper into the sample. The de-rease in resolution is of the order of the enlargementf the PSF. Also, with the latter objective, at largerepth, a lower signal, and consequently, a higherelative noise is obtained.

Restoration of the image stacks improved the res-lution, image details, and noise in all cases. Res-oration with three PSF’s measured at three differentepths gave only a minor improvement comparedith restoration with one central PSF. The reduced

mage quality with the oil-immersion objective, owingo refractive-index mismatch, cannot completely beompensated for by image restoration. Matchinghe immersion fluid with the refractive index of theample is of great importance for the imaging quality,

specially during deep measurement into deep sam-les.

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