interferometric phasebased dual wavelength...

Interferometric PhaseBased Dual Wavelength Tomography

Changhuei Yang*, Adam Wax, Ramachandra R. Dasari, Michael S. FeldGeorge Haison Spectroseopy Laboratory, Massachusetts Institute of Technology,

Cambridge, MA 02139

ABSTRACT

We describe our phase-sensitive interferometry technique implemented as phase dispersion microscopy(PDM)/ optical tomography (PDOT) The technique is based on measurmg the phase difference betweenfundamental and second harmonic low coherence light in a novel interferometer. We attain high sensitivityto subtle refractive index differences due to dispersion with a differential optical path sensitivity of 5 nm.Usmg PDM we show that ballistic light in a turbid medium undergoes a phase velocity change that isdependent on catterer size. We demonstrate that the microscopy technique performs better than a

conventional phase contrast microscope in imaging dispersive and weakly scattering samples. Thetomographic implementation of the technique (PDOT) can complement Optical Coherence Tomography(OCT) by providing phase information about the scanned object.

Keywords: phase, interferometry, microscopy, tomography

1. INTRODUCTION

We have recently developed a robust and highly sensitive imaging technique which we have implementedas phase dispersion microscopy (PDM) [1] and phase dispersion optical tomography (PDOT) [2]. Thetechnique uses low coherence interferometry to measure the optical phase of light ansmitted through orbackscattered by the target sample. The key feature is the use of a pair ofharmonically related lowcoherence light sources to eliminate motional artifacts in the interferometer and the target, which usuallyprevent accurate measurements ofphase information.

This technique allows measurement of subtle refractive index differences, or equivalently phase velocityvariations, due to dispersion This sensitivity permit us to observe a phase velocity change in the ballisticlight transmitted through a turbid medium that varies with scatterer size [3] This dependence cannot beexplained through the photonic model, which is extensively used in optical tomography [4]. In this model,ballistic propagation is pictured as photons which are undeflected in transmission.

Like phase contrast microscopy (PCM) [5], this technique in its microscopy implementation can be used tostudy unstained tissue sections by rendering subtle refractive index difference visible. In addition, PDM

outperforms PCM m its ability to image weakly scattermg specimens and provide quantitativemeasurements.

The implementation ofthis phase tethnique that provides depth resolution, PDOT, can complement opticalcoherence tomography (OCT) [6] OCT is a valuable technique for imaging m vivo biological tissues,which provides information about the scattering properties of sub-surface structures through measurementofthe amplitude of a backscattered electric field. It has been recently demonstrated that interferometricmethods which measure phase information can provide additional mformation about the birefrmgence [7],dispersion [1] and spatial phase variation [8] of a sample By combrnmg the ability of PDM to measuredispersion related phase information with the capability of OCT to obtain depth-resolved images, PDOTcan reveal dispersion based differences which are otherwise not detectable with OCT.

*chyang1miLedu; phone: 617-253-6203; fax: 617-253-4513

Coherence Domain Optical Methods in Biomedical Science and Clinical Applications V,Valery V. Tuchin, Joseph A. Izatt, James G. Fujimoto, Editors, Proceedings of SPIEVol. 4251 (2001) © 2001 SPIE · 1605-7422/01/$15.00

63

2. THE TECHNIQUE

Our novel phase sensitive technique is based on a modified Iowcoherence Michelson interferometer (Fig.Ia shows setup for 2D imagmg Fig lb shows setup for depth resolved imaging) The input light is a pairof overlapped beams oflaser light at the fundamental and second harmonic frequencies. The source is alow coherence Ti:sapphire laser producing 150 fs pulses at 800 nm, and the second harmonic is generatedby a standard frequency doubler. The composite beam is split into two at the beam splitter. One part isinput to the target sample while the other is reflected by a moving reference mirror. The motion of themirror induces a Doppler shift in the returning beam. The two composite beams then are recombined,separated by their wavelength components with a dichroic mirror, and measured separately byphotodetectors. The resulting heterodyne signals at both wavelengths are measured and digitized. Eachdigitized signal is bandpassed around its center heterodyne frequency, as given by the Doppler shift. Thefiltered signals are then Hubert transformed to yield their respective phases and [9]

Figure Ia: Phase Dispersion Microscope (2D)

Figure lb: Phase Dispersion Optical Tomography (depth resolved)

It can be seen that a jitter of magnitude, &, in either the signal or reference arm length will vary the

phases, j and , by kx and k2& respectively, with k ( k2) the free space wavenumber of thefundamental (second harmonic) light. As k2 is exactly double Ic,, the effect ofthis jitter can be totallyeliminated by subtracting twice from . Due to the fact that phase measurements are inherently limitedto modulus 2ir, such elimination ofphase artifacts is only possible when one wavelength is an integer

multiple ofthe other. This operation yields OLk21 the optical path length difference experienced by the

two wavelengths in the interferometer, with great sensitivity:

composite800nm /400nm beam

compensator

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targetsample

mirror

composite800nm/400nm beam

compensator

mirror

targetsample

Proc. SPIE Vol. 425164

( 2 2)OLk2,k1 — * (1)

The sensitivity achieved is about S nm in optical path length difference or, equivalently, about 9x1O2 radfor phase difference with respect to the second harmonic light. Note that phase measurements areinherently limited to modulus 27t; therefore measurements of longer path differences require appropriatephase-unwrapping techniques such as those described in Ref. 10.

3 ANOMALOUS PHASE VELOCITY OF BALLISTIC PROPAGATION

The sensitivity ofthe technique to optical path length difference can be exploited to measure subtle phasevelocity changes ofballistic light propagatmg through a turbid medium [3] We modify the mterferometersetup for this purpose by replacing the focusing lens array and sample in Fig Ia with a 10 mm thick cuvettefilled with turbid media The correspondmg compensator arrangement is replaced by a water filled cuvetteofthe same thickness We achieve a differential phase velocity sensitivity of40m/s through thisarrangement Measurements are taken as polystyrene microspheres of a given size are gradually added tothe signal arm cuvette The fractional volume ofmicrospheres i is varied from 8x10 to 33 Therelative refractive index ofthe microspheres is 1.20 at 800 urn and 123 at 400 nm, with respect to that ofwater. Each measurement of optical path difference is then used to find the fractional phase velocity

Av2 Av1difference, — — — , between the two wavelengths in the cuvette:V0 V0

OLk2kL (2)V0 V0 2Ln0

'

with v0 the speed oflight in water, n the refractive index ofwater and L the thickness ofthe cuvette. Notethat the msignificantly small second order corrections due to dispersion ofwater are omittedMeasurements are made for a succession ofmicrospheres varymg m radius, a, from 10 nm to 10 tm Thedata pomts ofFig 2 show the measured fractional difference m phase velocities as a function of scatterersize The experimental observations are best discussed by comparison with the following theoretical phasevelocity analysis ofthe ballistic light.

0.2 —

0.1 5Mie theory

01 vandeHuist /1\ IImodel

oo1 o1 I 10scatterer radius (nm)

Figure 2: Experimental plot ofdifferential phase velocity variation with scatterer size.

The experimental observations can be compared to previously overlooked aspects ofvan de Huist and Mie

Proc. SPIE Vol. 4251 65

scaering theories[I 1]. Van de Huist theo reveals the analytical form as:V0

= I - n = - (ka)2I _ cospV0 2ak LP P

with p = 2/ca(m — 1) the normalized scatterer size, and (rn-i) the relative refractive index differencebetween the scatterers and the surroundmg medium This model is stictly valid only when the scatterer sizeis large compared to the wavelength and the refractive index difference is small. Nevertheless, it providesimportant insights and is a good fit to the experimental data.

From the theory and the experiment, we can see that there are 3 regimes ofballistic light propagation,depending on the scatterer properties:

L__ << I - turhj&iimdiurnasbuIk medium.

In this limit, the phase velocity change, Av , reduces to —iv0(m I) . This change arises only from bulkrefractive index change due to the presence of small scatterers. From another perspective, when the phaselag through each scatterer is small the net result is simply an overall change in phase velocity, asdetermined by the refractive index difference.

1nosim1ificatIon.In this regime Eq. (5) cannot be simplified. The phase velocity is seen to oscillate with changing p. The netchange in phase velocity is strongly dependent on whether the forward scattered light is in phase or out ofphase with the input light. We note the existence of an anomalous phase velocity increase for some valuesofp, despite the fact that the scatterers have higher refractive index than water. Usually, adding a materialwith index higher at 400 nm than at 800 nm (normal dispersion) into water would cause the 400nm light tobe slowed more than at SOOnm. However, in the case of scatterers with p 1, the opposite is observed.Thus, the medium exhibits anomalous dispersive effects.ntofturbidit.In this limit, the phase velocity change, v , is zero. This is the only regime in which the photonic modelprovides a complete description The phase velocity is thus mdependent ofthe presence of turbidityPhysically we can understand this from the fact that when p is large, the phase ofthe transmitted lightvaries rapidly with increasmg distance from the center ofthe sphere The net result is that the phase shift ofthe transmitted light averages to zero, Therefore, large scatterers have no effect on the bulk refractive indexfor ballistic propagation.

This dependency ofthe ballistic light phase velocity on p implies that the ballistic light itself must canyphase infonnation about the structure and composition ofthe turbid medium, The photonic model whichignores all phase considerations simply cannot explain this variation This fmdmg suggests that theincorporation ofphase measurement techniques into optical tomography an obtam more information abouta scanned specimen than a purely intensity based approach can obtain.

4. PHASE DISPERSION MICROSCOPY

As shown in Fig. la, the technique can be implemented in a transmission microscope geometry. In our

implementation, the phase dispersion microscope (PDM), achromatic lOX microscope objectives focus thecomposite beam onto the sample with a FWHM of about 7 tm at both wavelengths, however, difficulty inaligning the returning path to overlap with the incoming path degrades the resolution to about 10 microns.

(Note that finer resolution is achievable by using higher power objectives and improved alignment ) Asimilar lens array and a clear slide is inserted in the other interferometer arm as compensator


For a given sample ofknown thickness L, we can evaluate the refractive index dispersion relative to that of

the compensator medium, (4OOnrn '8OOnm) ' between the wavelengths by.

M400nm 8OOnm = OLk2 kj / L , (2)

where An400flm ( 8OOnm ) iS the difference in refractive index between the sample and the compensator

medium at the wavelength of 400nm (800nm). The sensitivity of our system permits us to detect refractiveindex dispersion as small as 5x106 for a 1 mm sample. This sensitivity improves for thicker samples.

This ability of PDM to provide quantitative information is one of the important differences between PCMand PDM. In addition, PDM can be applied to a wider range of specimens than PCM. PCM forms imagesby phase shifting the scattered light field from a specimen and interfering it with the unscattered light field.Therefore it can be applied only to specimens that scattered a significant amount ofhght In contrast, PDMdirectly measures the small phase shifts ofthe unscattered light and, thus, can be applied to specimens thatare weakly scattering or do not scatter at all. Finally, it is difficult to separate the contributions fromabsorption and phase shift m an PCM image In PDM these two factors can be easily measuredindependently, as absorption affects only the amplitude ofthe detected heterodyne signals while the phaseshift affects only the phase lags ofthe heterodyne signals.

As an illustration ofthe capabilities of PDM, we compare the performance of PDM to PCM on similarlyprepared samples comprismg a drop ofwater and a drop of DNA solution (1 O% vol conc ) sandwichedbetween two cover slips (Fig. 3). The separation between the cover slips is 170 jtm. As evident in Fig. 3,PDM can easily distinguish the two drops and provides a refractive index dispersion value for the DNAsolution In contrast, PCM does not distmguish between the two nearly transparent droplets nor does itprovide any quantitative data. Interestingly, the refractive index dispersion measured in this experiment byPDM (1 3±0 2)x104, differs from the value, 1 6x10 extrapolated from an experiment with more dilutesamples ofDNA, based only on the ratio ofthe sample concentrations This difference can be attributed tothe fact that the refractive index depends on scatterer size, as well as concentration, Thus, at higherconcentration the formation ofDNA aggregates, which behave as scatterers, effectively alters therefractive index The above study on ballistic light propagation [3] has experimentally verified that therefractive index depends strongly on scatterer size.

Figure 3 : Images of a drop of 1.0% vol. conc, DNA solution and water, We measure thedispersion contribution due to DNA as (1 ,3±O,2)x1O.

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Figure 5: Phase Dispersion Optical Tomograph' ii iage of a simp'e samJe

6. CONCLUSiONS

In suiimary, we have developed a robust phase sensitive technique which coniplete! eliminaLs phasenoise due o interferoniterk jitters. our tee ini']ue is highly sensitive and can be used to provide quantitativephase information about the aret. ihe 2D implementation. PDM can pet form better tI n the curt enstandard — phase contrast micioscop". The advantages of PDYI ii ( lude its ability to prcvirie qualitita ivedata and its \;deI ran,c of nnagmg taige s which iicludes non o weaki)' scatet ing pecimen. Ti etomogiaphic implementatioi of t1e phase technique can complement OCT by vovidiig dispersion basedin formation

ACKNOWLEDGEMENTS

Wewould like to acknowledge the assistance of Irene Georgakoudi, Eugene B. Hanlon and KamranBadizadegan with sample preparation and analysis. This work was carried out at the MIT Laser BiomedicalResearch Center and was supported by NIH grant P41-RR02594, NSF grant 9708265-CHE and a grantfrom Hamamatsu Corporation. Adam Wax is supported by NIH National Research Service Award I F32RR05075-O I.

REFERENCES

1. C. Yang, A. Wax, I. Georgakoudi, E. B, Hanlon, K. Badizadegan, R. R. Dasari, M. S. Feld,"Interferometric phase-dispersion microscopy", Opt. Left. 25, 1526 (2000).2. C. Yang, A. Wax, R. R. Dasari, M, S. Feld, "Phase dispersion optical tomography",submitted toOpt. Left. (2000),3, C. Yang, A. Wax, M. S. Feld, "Measurement of anomalous phase velocity ofballistic light in arandom medium using a novel interferometer", submitted to Opt. Left. (2000).4, D. A. Benaron and D. K. Stevenson, "Optical time-of-flight and absorbance imaging of biologicmedia", Science 259, 1463 (1993).5, K. F. A. Ross, Phase Contrast andinterference Microscopyfor Cell Biologists (St. Martin's Press,New York, 1967).6. W. Drexler, U. Morgner, F. X. Kartner, C. Pitris, S. A. Boppart, X. D. Li, F. P. Ippen and J. G.Fujimoto, "In vivo ultrahigh-resolution optical coherence tomography", Opt. Left. 24, 1221 (1999).

phas dispersion image

800nm OCT Image


7. J F deBoer, T. E. Milner, M. J. C. van Gemert, and I S. Nelson, "Two-dimensional birefringenceimaging in biological tissue by poIarizationsensitive optical coherence tomography, " Opt. Left. 22, 934(1997)8. F. Cuche, F. Bevilacqua and C. Depeursine Opt. Lett, 24, 291 (1999).9. A. B. Carison, Communication Systems 3' Edition (McGraw-Hill, New York 1986).10 G Fornaro G Franceschetti, R Lanan E Sansosti 3 Opt Soc Am A 13 2355 (1999)


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