Non-tissue-like features in the time-of-flight distributions of plastic tissue phantoms

Non-tissue-like features in the time-of-flightdistributions of plastic tissue phantoms

Luca Nardo,1 Adriano Brega,1 Maria Bondani,2,* and Alessandra Andreoni1

1C.N.R.-I.N.F.M.-C.N.I.S.M., Dipartimento di Fisica e Matematica, Università dell’Insubria, Via Valleggio 11, 22100 Como, Italy2National Laboratory for Ultrafast and Ultraintense Optical Science C.N.R.-I.N.F.M., Via Valleggio 11, 22100 Como, Italy

*Corresponding author: [email protected]

Received 25 July 2007; revised 8 February 2008; accepted 27 March 2008;posted 8 April 2008 (Doc. ID 85659); published 29 April 2008

Wemeasure high-temporal-resolution time-of-flight distributions of picosecond laser pulses in the visibleand near-infrared, scattered in the forward direction by solid and liquid phantoms, and compare them tothose obtained by using ex vivo tissues. We demonstrate that time-of-flight distributions from solid phan-tomsmade of Delrin, Nylon, and Teflon aremodulated by ripples that are absent in the biological samplesand disappear when the temporal and/or angular resolution of the measuring apparatus is decreased.This behavior prevents the use of such materials as tissue phantoms when spatial mode and time selec-tion are required, such as in imaging methods exploiting early arriving photons. © 2008 Optical Societyof America

OCIS codes: 170.6930, 170.5280, 170.3660, 170.6920.

1. Introduction

Optical biopsy is one of the most fascinating tasks inmodern biomedical optics and since the late 1980smany studies have been published addressing thisissue [1,2]. The main reason for such a strong inter-est is that the optical biopsy approach offers two sig-nificant potential advantages over the X-ray-baseddiagnostic tools now in use. First of all, optical biopsyis noninvasive; second, as visible and near-infrared(NIR) light absorption and scattering properties ofdifferent soft tissues are distinguishable, it mightallow making assessments on in vivo tissues.Development of reliable diagnostic techniques,

comparison betweennewmethods andprototypes, ca-libration of clinical instrumentations, and even thebasic evaluation of the results of academic researchon this topic can be pursued from a truly scientificstandpoint only if standardized, realistic, and repro-ducible experimental conditions are defined. How-ever, the optical properties of biological tissues areextremely different fromone individual to another de-

pending on age, alimentation, hydration, and healthstatus [3–7]. Substantial variability over time is dis-played even in the same individual. For this reason,there is a need for stable and reproducible tissuelikephantom materials to be used to investigate the pro-pagation of light through tissues, whose optical prop-erties should be easily and deterministically tuned byresearchers to mimic those of biological tissues.

Many different phantom materials have beendesigned and used to investigate the propagation ofradiation through tissues [8,9], including water sus-pensions of milk and ink [10], Intralipid (with orwithout ink) [11–17], microspheres made of latex,polystyrene, or quartz [14,15,18–21], and solid tissue-phantoms made of Agar, Intralipid, and ink [22],Delrin [23–33], Nylon [25,26,33,34], Teflon [33,35],clear plastic, or resin materials with scattering andabsorbing bodies embedded [8]. Threads and beadsof Nylon are also frequently used to simulate lesionsin inhomogeneous tissue phantoms [36]. Liquid phan-toms are usually very easily tunable in their opticalproperties. On the other hand, solid phantoms assurebetter stability against degradation and can be trans-ported, thus being more suitable as standards. More-

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over, solids lend themselves to better reproduction ofinhomogeneous structures [10,22].Many studies concerning the development of opti-

cal tissue-imaging techniques make use of time-resolved photon-detection methods and are basedon the acquisition and analysis of the time-of-flight(TOF) distribution of the photons emerging fromthe sample [10,11,15,17,18,22,28,37,38]. It is a com-mon opinion that the best imaging results could beobtained by discriminating the early arriving, un-scattered, and marginally scattered photons fromthe multiply scattered ones [1,2,20,39]. Thus, be-tween the end of the 1980s and the first half ofthe 1990s, encouraged by the outstanding technolo-gical advances pursued by lasers and light detectors,many groups have devoted their studies (see reviewarticles by Dunsby and French [1] and by Hebden etal. [2]) at performing optical imaging through thickscattering media by selecting the early arrivingphotons by means of either time-resolved transmit-tance imaging methods [20,21,37,39,38] or optical co-herence tomography [19,21]. As none of theseattempts have managed to get rid of the problemof extracting the negligible fraction of early arrivingphotons out of the overwhelming multiply scatteredone, many authors have concluded that performingoptical imaging of biological tissues thicker than afew millimeters by exploiting the early arrivingphotons is simply impossible [1,19]. Instead, theyhave concentrated on strategies implying the analy-sis of the multiply scattered photons, which repre-sent the dominant part of the emerging light[13,17,18]. Not surprisingly, these methods providevery poor spatial resolution (of the order of manymillimeters) [13,17,18,40]. However in 2004 [12],we managed to distinguish a measurable fractionof nearly unscattered photons in the TOF distribu-tions of NIR picosecond laser pulses emerging froma scattering medium with values of its optical para-meters similar to those of tissues. This result waspursued by performing timecorrelated single-photoncounting (TCSPC) measurements with a home-assembled, state-of-the-art excitation detection ap-paratus endowed with <35ps temporal resolutionand with a fiber-guided collection ensuring an angu-lar acceptance single-mode selection at NIR wave-lengths. In a subsequent work [11], we presentedone-dimensional scanning patterns of opaque, light

diffusing, and transparent objects, embedded inIntralipid suspensions featuring clinically relevantoptical parameters, and managed to localize and dis-tinguish the different optical properties of obstacleswith spatial resolutions as small as ≈180 μm. In bothRefs. [11,12] we show that early arriving photons canbe directly revealed in the collimated transmittancesignal of light emerging from tissue-phantoms,whose scattering, anisotropy and absorption para-meters are comparable with those of living tissues,only provided that ultimate mode selection and ex-treme time resolution are combined.

Here, we present high-temporal-resolution TOFdistributions of photons transmitted within a 0:6mrag angle around the incident beamdirection by so-lid (Delrin, Nylon, and Teflon slabs and Intralipid/inksuspensions hardened by the addition of Agar) and li-quid (Intralipid suspensions) phantoms, all illumi-nated with picosecond laser pulses in the visibleand NIR. We compare these TOF distributions tothose obtained by using ex vivo biological tissue tar-gets such as chicken, pork, or turkeymuscle, and porkor turkey fat. We show that the TOF distributions ob-tained by using all the plastic phantoms we have con-sidered as the targets are significantly different fromthose obtained with either Intralipid/ink suspensionsin water or with the solid Intralipid/ink phantom ob-tained by adding Agar. The TOF distributions of thelast samples are found to be the most similar to thoseof ex vivo tissues.

2. Materials and Methods

A. TCSPC Setup

The TCSPC experimental setup we used is describedin more detail elsewhere [11,12] and sketched inFig. 1. As the light source, we use either the funda-mental (1064nm) or the second harmonic outputpulses (113MHz repetition rate, 9ps duration) of aNd:VAN continuous-wave mode-locked laser (GE-100-1064-VAN, Time-Bandwidth Products). The lightemerging from the sample is selected by a single-mode fiber for the specific wavelengthwith a couplinglens at the input (OZ Optics) and focused, at the fiberoutput, by means of a 20×microscope objective on thesensitive area of the TCSPC detector, which is a sin-gle-photon avalanche diode (SPAD) of original design[41]. The avalanche current pulse from the SPAD

Fig. 1. Experimental setup.

2478 APPLIED OPTICS / Vol. 47, No. 13 / 1 May 2008

gives the start signal to the time-to-amplitude conver-ter (TAC) (2145, Canberra). The stop is given by a fastPIN photodiode monitoring the laser excitation pulsevia a constant fraction discriminator (CFD) (2126,Canberra). The pulse-height spectra of the TAC out-put are provided by amultichannel analyzer (MCA) ina 10ns acquisition time window with a 2:14ps bin-width and a 19 bit resolution (Acuspec B-Genie2000, Canberra).A small fraction of the incidentpulses is delivered to

theSPADvia amultimode optical fiber (Fsync)withoutbeing scattered, to provide a time-reference [11,12]represented by two detected subsequent excitationpulses that is stable against electronic drifts. Allthe TOF distributions displayed in this paper havebeen synchronized by superposing their time-reference peaks. Immediately after themeasurementof each TOF distribution, we made a measurement ofthe excitation pulses upon removing the sample: thepeak channel of this reference TOF is taken as t ¼ 0 s.

B. Phantom Media

As the phantommedia we first considered three plas-tic materials we found in the literature to be used tosimulate tissue in laboratory experiments: Delrin[23–33], Nylon [25,26,33,34], and Teflon [33,35]. Foreach of these materials, four discs of 6 cm diameterwere cut using a precisionmilling cutter, at the thick-nesses of 190 μm, 0:5 cm, 1 cm, and 2 cm. The cuttingprocedure assured the disks surfaces to be smooth towithin ≤10 μm accuracy. As to the optical parametersof the plastic materials, Delrin has been reported tohave an absorption coefficient μa ¼ 0:0017mm−1, ascattering coefficient μs ¼ 2:34mm−1, and an aniso-tropy factor g ¼ 0:87mm−1 at 632:8nm [23], whileGannot et al. [29] reported the values μa ¼0:008mm−1 for the absorption coefficient and μ0s ¼1:6mm−1 for the reduced scattering coefficient at488nm, and the values μa ¼ 0:004mm−1 for the ab-sorption coefficient and μ0s ¼ 2:7mm−1 for the reducedscattering coefficient at 553nm. Finally, at 785nmthe values μa ¼ 0:002mm−1 and μ0s ¼ 1:2mm−1 havebeen reported [16]. Nylon slabs with surfaces assmooth as ours have been reported [34] to haveμa ≅ 0:0017mm−1, slightly depending on the slab sur-face roughness, and μ0s ¼ 1:65mm−1, at 632:8nm. Te-flon optical parameters have been reported [42] to beμ0s ¼ 6:2mm−1 at 500nm and μ0s ¼ 5:5mm−1 at1650nm, with μa < 0:1mm−1 in both cases. To esti-mate the optical parameters of the plastic materialsat the relevantwavelengths,532nmand1064nm, thetransmittance spectra of light passing through the190 μm discs were measured in the range between500 and 1100nm by using a spectrophotometer(Lambda 2, Perkin Elmer). For such a thin layer,the Beer–Lambert law applies, and the extinctioncoefficient μ ¼ μa þ μs is given by the equationμðλÞ ¼ lnð10ÞAðλÞ=l, where AðλÞ is the absorbance va-lue at the wavelength λ and l is the thickness of theattenuating target. If we make the reasonable as-sumption that, as observed at a number of visible

and NIR wavelengths, μa ≪ μs also at the relevantwavelengths 532 and 1064nm, then μ ≅ μs. We ob-tained the following values: for Delrin μs ≅31:7mm−1 (at 532nm) and μs ≅ 28:4mm−1 (at1064nm); for Teflon μs ≥ 37mm−1 (at 532nm) (be-cause the spectrophotometer’s maximum absorbanceis 3, a value reached at 565nm) and μs ≅ 21:6mm−1

(at 1064nm); for Nylon μs ≅ 25:3mm−1 (at 532nm)and μs ≅ 15:9mm−1 (at 1064nm).

We also fitted the experimental TOF distributionsobtained for the 1 cm and the 2 cm thick discs to sev-eral analytical isotropic diffusion models, as ex-plained in [11], upon suitably smoothing the MCApulse-height spectra by adjacent averaging on 60bins, and obtained estimations of μ0s: for Delrin μ0s ¼ð3; 9� 0:6Þmm−1 (at 532nm) and μ0s ¼ ð2:5� 0:1Þmm−1 (at 1064nm); for Teflon μ0s ¼ ð8� 2Þmm−1 (at532nm) and μ0s ¼ ð2:45� 0:05Þmm−1 (at 1064nm);for Nylon μ0s ¼ ð2:8� 0:6Þmm−1 (at 532nm) and μ0s ¼ð1:5� 0:3Þmm−1 (at 1064nm). The values of the ani-sotropy factor g, calculated according to g ¼ 1 − μ0s=μswere: forDelring ¼ 0:875� 0:015 (at532nm)andg ¼0:910� 0:001 (at 1064nm); for Teflon g ≥ 0:79� 0:06(at 532nm) and g ¼ 0:885� 0:005 (at 1064nm); forNylon g ¼ 0:89� 0:03 (at 532nm) and g ¼0:905� 0:015 (at 1064nm). Neglecting the contribu-tion of absorbance to the measured extinction coeffi-cient value leads to a slight overestimation of the μs.The μ0s values obtained by fitting the smoothed TOFsto approximate solutions of the time dependent diffu-sion equation, which do not account for the observedripples, are also overestimated although in substan-tial qualitative agreement with those reported in theliterature at similarwavelengths,measured by eitheroblique angle illumination [23] or integrating spheres[29] techniques. Nevertheless, some fundamental in-formation canbe safely derived fromour data. First, itshould be noted that all the considered plastics havevalues of the anisotropy factor comparable to those ofseveral soft human tissues [3–7] and indicate astrongly forward scattering of both visible and NIRlight. Secondly, the scattering coefficient values aresuch that the average number of scattering events ex-perienced by a photon transmitted through a 1 cmthick slab of phantom is equal to the average numberof scattering events experienced by a photon trans-mitted through a several-centimeter-thick layer ofhuman soft tissue. Finally, the TOF data could be de-cently fittedby fixing theabsorption coefficient valuesto those found in the literature at other wavelengths.The fits were not significantly improved by eitherincreasing or decreasing the absorption coefficientvalues by as much as 1 order of magnitude. This con-sideration suggests the conclusion that, for the con-sidered plastic phantoms, absorption is negligibleas compared to scattering, similarly to what isobserved for biological tissues.

We then tested a liquid phantom consisting in a2.5% weight-to-volume (w=v) concentrated Intralipidsuspension in bidistilled water, to which 10−5

volume-to-volume (v=v) concentrated black Indian


ink was added to mimic tissue absorption, and asolid phantom made of Agar (1%w=v), Intralipid(2:5%w=v), and ink (10−5 v=v) diluted with bidistilledwater, prepared as described in Ref. [22], wherein theoptical parameters for such phantoms are reportedat varying Intralipid concentration values. The scat-tering coefficient values are such that, once again,the average number of scattering events experiencedby a photon transmitted through a 1 cm thick slab ofphantom is equal to the average number of scatter-ing events experienced by a photon transmittedthrough a several-centimeter-thick layer of humansoft tissue. Moreover, the absorption coefficientvalues are negligibly small in comparison to the scat-tering coefficient values. In detail, a 2%w=v Intra-lipid, 10−5 v=v ink concentrated suspension isreported to have μa ¼ 0:006mm−1 and μ0s ¼ 2:3mm−1 at 650nm, while a solid phantom obtainedby adding 1% Agar to that suspension has μa ¼0:006mm−1 and μ0s ¼ 1:7mm−1 at 650nm. On thecontrary, the anisotropy coefficient of Intralipid sus-pensions is reported to stay constant against wave-length and Intralipid concentrations at the valuegðIntralipidÞ ≅ 0:49, which is much lower than thosetypically measured for biological tissues. For an ex-tensive discussion on the optical properties of Intra-lipid suspensions in the NIR, see Ref. [11] and thereferences therein.The Delrin, Nylon, and Teflon slabs were directly

positioned in the light pathway, while the Intralipid/ink suspension and the solid phantom obtained byadding Agar to the Intralipid/ink sample were heldin a 1 cm-thick, 5 cm-wide, 4 cm-high cuvette.

C. Ex-Vivo Tissue Samples

Slices of fresh ex vivo muscular tissue from chicken,pork, and turkey, and adipose tissue from pork andturkey have been crammed into the 1 cm-thick,5 cm-wide, 4 cm-high cuvette, taking care to not leaveempty spaces.

3. Results

In Figs. 2(a) and 2(b) we show the TOF distributionsof pulses at 532nm and 1064nm, respectively, whichwe obtained by using either the Delrin (empty cir-cles), the Nylon (full dots), or the Teflon (line) slabas the target. The TOF distributions display almostperiodical ripples that cannot be described by meansof the time dependent diffusion equation.InFigs. 3(a) and3(b)we show theTOFdistributions

ofpulses (circles) at532nmand1064nm,respectively,whichwe obtained byusing the Intralipid/ink suspen-sion as the target. We also show the correspondingTOF distributions (line) measured by using the solidIntralipid/Agar phantom. Notably, the TOF intensitydistributions obtained for these targetshaveanasym-metric bell-shaped trend, andvary smoothlyasa func-tion of flight time, displaying one maximum only, aspredicted by the time dependent diffusion equation.We also note that photons emerging from the Intrali-pid/ink suspension are, on average, delayed with re-

spect to photons emerging from the solid Intralipid/Agar phantom. In fact, at both wavelengths, theTOF distribution peak occurs at a later time afterexcitation for the liquid as compared to the solid phan-tom. This observation is consistent with the conclu-sion, made by Cubeddu et al. [22], that addition ofAgar causes a 30% decrease in the reduced scatteringcoefficient value.

The TOF distributions measured by using slices ofdifferent real tissues as the targets are reported inFig. 4(a) (532nm pulses) and Fig. 4(b) (1064nmpulses). We tested muscular tissue from chicken(black line), pork (circles) and turkey (gray line),and adipose tissue from pork (triangles) and turkey(squares).Wenote that all theTOFdistributionsmea-sured with tissue targets have the smooth singlypeaked shape predicted by the time dependent diffu-sion equation, and are qualitatively similar to thoseobtained with either the Intralipid/ink suspensionor the Intralipid/ink solid phantom.We also note thatphotons typically emerge much later from fat than

Fig. 2. (a) Experimental TOF distributions at 532nm for the1 cm-slabs of Delrin (empty circles), Nylon (gray full dots), andTeflon (line). (b) Corresponding TOF distributions at 1064nm.

Fig. 3. (a) Experimental TOF distributions at 532nm for the li-quid phantom made of Intralipid and ink (empty circles) and forthe solid phantom made of Agar, Intralipid, and ink (line). (b) Cor-responding TOF distributions at 1064nm.


from muscle tissues. This behavior is consistent withpublished data assigning higher transport coefficientvalues to fat tissues [14,38].

4. Discussion

The TOF distributions obtained for each of the plastictissue-phantoms at both wavelengths resulted to besubstantially different from those obtained for the tis-sues that they were supposed to mimic. Among theconsidered plastic materials, Delrin has been themost widely used as a tissue phantom and, untilnow, has been reported to faithfully reproduce tissuescattering [16,23–33]. The ripples modulating itsTOF distributions have never been detected. The rea-son canbedue to somedifferences in the experimentalconditions, with respect to ours, in which previousmeasurements were performed. In particular, herewe show that both temporal resolution and modeselection play a key role in revealing the ripples. Tomimic a worse temporal resolution we calculatedthe convolution of the TOF distribution measuredby us for Delrin with IR excitation (empty circles inFig. 2(b), also reported as empty circles in Fig. 5) withaGaussian pulse response of 100ps full-width at half-maximum (FWHM). The resulting TOF distribution(gray line in Fig. 5) is indistinguishable from thatof a purely diffusive medium. Regardless, we founddata in the literature showing that high-temporal-resolution (e.g., ∼50 ps in Ref. [30] and ∼70ps inRef. [31]) without mode selection is not enough todetect the ripples.To test the dependence of the TOF on mode selec-

tion, we substituted the single-mode collecting fiberwith a 250 μm pinhole located in front of the micro-scope objective at a distance of 25 cm from the slab,thus increasing the acceptance angle up to 1mrad.This distribution measured at 1064nm, which isshown as black line in Fig. 5, displays less neat(but still evident) peaks. Finally, we also acquired aTOF distribution with no spatial filtering betweenthe slab and the microscope objective, which exhibitsno peaks as shown by the gray fulldot plot in Fig. 5.The same experiments performed with Delrin at

532nm and with the Nylon and Teflon slabs gavesimilar results (data not shown).

The equally spaced ripples modulating the inten-sity profiles of the TOF distributions might, in princi-ple, be originated by some systematic fault of themeasuring apparatus. The possible sources of arti-facts in TOF distributions acquired with a TCSPC de-vice are [43]: differentialnonlinearity in the electronicchain, pile-up effects, and detector after-pulsing. Dif-ferential nonlinearity causes nonuniformity of thechannel width and may arise either from the TAC/ADC intrinsic differential nonlinearity or by parasiticcoupling of the start and stop pulses. The TAC/ADCnonlinearity has permanent effects on the timing,which should be equally visible in any TOF distribu-tion acquired with the same setup. The fact that theTOFdistributionswemeasuredwith either Intralipidphantoms or ex vivo tissue as the targets are totallyfree of ripples proves that this kind of nonlinearityhas no substantial effect in our setup. Moreover,coupled measurements have been performed by ac-quiring “twin TOFs” with the electronic chain de-scribed above and immediately after by connectingthe SPAD directly to a PC board (SPC 152, Becker& Hickl), featuring integrated CFD, TAC, and ADC,whoseoperationandperformances are completelydif-ferent. The twin TOFs were equal within the experi-mental errors. On the contrary, parasitic coupling ofstart–stop pulses can change over time, dependingon the presence of synchronous noise picked up bythe SPAD, on the presence of electromagnetic noise(e.g., radio signals from outside the laboratory), andon the electronic coupling between the cable connect-ing the SPAD to the TAC and the cable connecting theinternal PIN photodiode to the CFD. Our setup hasbeen optimized to minimize the probability of parasi-tic coupling, and all the cables have been carefullyshielded.Moreover, theSPADhasbeendesignedtoas-sure optimal electrical shielding. Finally, the cablesconnecting the SPAD with the TAC and the PIN with

Fig. 4. (a) Experimental TOF distributions of pulses at 532nmfor slices of ex vivo tissues. (b) Corresponding TOF distributionsat 1064nm.

Fig. 5. Experimental TOF distributions for Delrin at 1064nm col-lected with the single-mode fiber (empty circles) and its convolu-tion with a Gaussian pulse response of 100ps FWHM (gray line).TOF distributions for Delrin at 1064nm collected with the 250 μmpinhole (black line) and without spatial filtering (gray full dots).


the CFD have been kept spatially separated. Regard-less, measurements were repeated on different daysby changing the cables and their relative positions.Theresultshavealwaysshownthedetectionof ripplesonly with the use of the plastic targets. Pile-up effectscan be easily reduced by keeping the count rate signif-icantly lower than the repetition rate of the excitationpulses. We performed all the measurements pre-sented in this paper in strict single-photon regime,that is, at count rates ≤50kHz. However, it has beenreported that even at count rates ≈20%of the laser re-petition rate (in our case ≈23MHz), pile-up effects arestill negligible [43]. The after-pulsing probability of aSPADmostly depends on themode of quenching of theavalanche pulses. For our SPAD it has beenmeasuredby thegroup ofCova (Politecnico diMilano, Italy) to be≈2% (private communication). This very low value al-lows us to exclude that the measurements can be sig-nificantly affected by occurrence of after-pulses.Moreover after-pulses are typically generated severalmicroseconds after the detection of real photons, andthey should equally affect the TOFmeasured for plas-tic phantoms and Intralipid phantoms. Finally,coupled measurements have been performed by ac-quiring twin TOFs with the SPAD we used to acquirethe TOFs presented above, which was endowed withan integrated active quenching circuit (AQC), and im-mediately afterwith an oldSPADprototype quenchedby an external AQC with a much slower reset time.The twin TOFs were equal within the experimentalnoise. Finally, none of the electronic faults we exam-ined abovewould be reduced by simply reducingmodeselection. For these reasons, we can safely concludethat the ripples in the TOF distributions of the plasticphantoms are not generated by artifacts of the tim-ing setup.Alternatively, the peaks could be due to a margin-

ally scattered component of the incident beam beingreflected back and forth from the slabs surfaces. Be-cause of the very high μs values that we measuredat both wavelengths for all the plastics, this hypoth-esis is very unlikely. To be reflected back and forth,onephotonwould supposedly travel2 cm into thescat-tering medium without being scattered, while itsmean free path is in any case ≤63 μm.Even taking intoaccount that the scattering is highly forward, photonswould be on the average deflected after having tra-veled<0:7mm into the scatteringmedium. The prob-ability for a photon to travel N times back and forthacross the medium without being appreciably de-flected (and thus delayed) is ≈ expð−2Nμ0slÞ, whichmeans that even the probability of traveling one timeonlyacross themediumwouldbe inanycase≤10−13. Inour TOFs we can count as many as 15 ripples [see theTeflon TOF in Fig. 2(a)]. If the ripples were generatedby a marginally scattered component of the incidentbeam being reflected back and forth from the slabssurfaces, the 15th ripple in the TOF measured forTeflon at 532nm would be formed by photons travel-ing 15 times back and forth through the 1 cm-thickTeflon disc. Only one photon every ≈10−200 would be

able to make such a trip. Moreover, the time delay be-tween two subsequent ripples is in any case ≤65ps.The refractive index of Delrin is nDelrin ≈ 1:48, whilethat of Teflon is nTeflon ≈ 1:35, and Nylon hasnNylon ≈ 1:53. Were the ripples generated by margin-ally scattered component of the incident beam beingreflected back and forth from the slabs surfaces, thedelay between two subsequent ripples would begiven by Δt ≅ nΔl=c0, which means ΔtDelrin ≈ 99ps,ΔtTeflon ≈ 90ps, and ΔtNylon ≈ 102ps. Therefore, toeliminate any doubt that the ripples are due to backand forth reflections, we acquired the TOF distribu-tions of both 532nm and 1064nm pulses emergingfrom the 0:5 cm-thick and from the 2 cm-thick discs.The TOF obtained at 532nm in the case of Delrinare reported in Fig. 6(a). The delay between subse-quent ripples does not scale linearly with the thick-ness of the target. Moreover, the ripples are moreevident in the TOF obtained for the 2 cm-thick discthan in that obtained for the 1 cm-thick disc. On thecontrary, the marginally scattered component shouldbe most efficiently depressed in the thickest target.With the very weakly scattering 0:5 cm-thick disc,the ripples are not even observed [see black line inFigs. 6(a) and 6(b)]. Anyway, some substructures ap-pear in the TOF pertaining to the 0:5 cm-thick disc[see dots inFig. 6(b)] if the fiber is tilted to select a pro-pagation direction different to that of the unscatteredlaser beam, thus preventing the collection of margin-ally scattered photons.Well-defined ripples are recov-ered only if the multiply-scattered photons areconveyed to the detector, e.g., by displacing the fiberwith respect to the laser beam path. In Fig. 6(b) (grayline) the TOFobtainedwith a 0:65 cm displacement isdisplayed. Similar results were obtained with Delrinin the NIR, and with Teflon and Nylon at both 532and 1064nm.

As the surface of our milling cutter-smoothed discsis not assured to be smooth on the impinging lightwavelength scale, interference effects generated by

Fig. 6. (a) Experimental TOF distributions at 532nm for slabs ofDelrin of thickness 0:5 cm (black line), 1 cm (black full dots) and2 cm (gray line). (b) Experimental TOF distributions at 532nmfor the same slab of Delrin of thickness 0:5 cm in (a) (black line)along with that obtained by misaligning the fiber (black full dots)and by displacing the fiber of 0:65 cm (gray line).


simple surface wave phenomena might be at the ori-gin of the ripples. This hypothesis was probed bymea-suring the TOFdistributions of both 532 and 1064nmlaser pulses emerging from slabs made of Delrin, thesurfaces of which were made either rougher orsmoother than those of the milling cutter-smootheddiscs. We first compare [Fig. 7(a)] the TOF distribu-tions obtained at 1064nm with the 1 cm-thick Delrindisc (gray line) and with a 0:8 cm-thick Delrin slab,whose surface was made rough by removing a 1mmlayer from both surfaces with sandpaper (black dots).TheTOFdistributions are very similar and both showripples spaced by ∼62ps. We now compare [Fig 7(b)]the TOF distributions obtained at 1064nm with the0:5 cm-thick Delrin disc (gray line) and with a0:58 cm-thick Delrin slab (black dots), whose surfacewas smoothed by leaving it immersed in a 15%w=vsolution of HCl in water for one week (the slab was4mm thinner after exposure to HCl, the surfacewas homogeneously abraded). Once again, the TOFdistributions are very similar and both show ripplesspaced by ∼50ps. The results obtained with the532nm pulses are similar (data not shown). Thusthe influence of the surface roughness seems to bemarginal.In conclusion, the observation that ripples are

formed only by multiply scattered photons [seeFig. 6(b)] is not easily interpreted in the frame of sur-face wave phenomena, and suggests that they wouldrather be caused by bulk phenomena. These last maybe connected to the presence of residual orderedmicrodomains in the plastics. If the plastics werenot totally amorphous, coherent scattering of lightby the residualmicrodomainswould occur, in contrastto the randomized scattering occurring in tissues.This would advise not to use tissue-phantoms madewithDelrin, Teflon, andNylon. In fact, the three plas-tics we considered are made of polymeric substitutedhydrocarbons. Specifically, there are many slightly

different plastics called Delrin, which are all madeof polyoxymethylenes. In the same way, Nylons aremade of polyamides, and Teflons of polytetrafluor-oethylenes. Among the possible crystalline structuresto be formed by variants of these polymers, the mostwidely studied are those made by polyamides(Nylons). It has been observed that the variantNylon-6 can crystallize at room temperature in anα− and a γ− form, with a crystallinity around 30%[44]. The variant Nylon 5,6 also crystallizes in anα−anda γ− form [45],whileNylon10,14 is able to crys-tallize in two different α− and two different β− formsandNylon-66 adopts the structure of a triclinic lattice[46]. Commercial Nylons are mixtures of these andmany other highly pure variants of the polymer,and thus they are very likely to contain at least sometraces of all the cited crystal structures, even if crys-tallinity is expected to be loweredby the coexistence ofmultiple variants of polyamide. Also polyoxymethy-lenes (Delrin) [47] and polytetrafluoroethylenes(Teflon) [48] can arrange into crystals.

5. Conclusion

Based on the experimental data presented here, wecan assess that light interacts with tissue-phantomsmadeofeitherDelrin,Nylon,orTefloninaremarkablydifferent way as compared to real tissues. Such differ-ences are revealed by the presence of ripples in TOFdistributions that become evident in measurementsperformed by combining high-temporal-resolutionand extrememode selection. On the other hand, morerealistic solid tissue-phantoms can be obtained byadding Agar to Intralipid/ink suspensions [22].

It is well known that the best results in humantissue optical imaging for diagnostic purposes canbe obtained by discriminating the early arrivingphotons in time-resolved transmittance imagingmethods [1,2,20,39]. However, early arriving photonscan be directly revealed in the TOF distributions ofphotons emerging from samples with absorptionandscatteringparameters comparable to those of sev-eral-cm thick slices of human tissue only by means ofexperimental techniques in which extreme mode se-lection and short time response are concurrent [11].In such crucial experiments using Delrin, Nylon, orTeflon phantoms is expected to affect the resultsrather seriously.

This work has been supported by MIUR-PRIN2005027857. The authors are grateful to S. Covaand his group (Politecnico di Milano, Italy) for theirsupport with the TCSPC instrumentation.

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Non-tissue-like features in the time-of-flight distributions of plastic tissue phantoms

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