temporal and spatial resolution in transmission raman spectroscopy

Temporal and Spatial Resolution in Transmission RamanSpectroscopy

NEIL EVERALL,* PAVEL MATOUSEK, NEIL MACLEOD, KATE L. RONAYNE,and IAN P. CLARKIntertek MSG, The Wilton Centre, Wilton, Redcar, TS104RF, UK (N.E.); and Central Laser Facility, Science and Technology Facilities Council,

Rutherford Appleton Laboratory, Harwell Science and Innovation Campus, Didcot, Oxfordshire, OX11 0QX, UK (P.M., N.M., K.L.R., I.P.C.)

Picosecond time-resolved transmission Raman data were acquired for 1

mm thick powder samples of trans-stilbene, and a Monte Carlo model was

developed that can successfully model the laser and Raman pulse profiles.

Photon migration broadened the incident (;1 ps) probe pulse by two

orders of magnitude. As expected from previous studies of Raman photon

migration in backscattering mode, the transmitted Raman pulse was

broader than the transmitted laser pulse and took longer to propagate

through the sample. The late-arriving photons followed tortuous flight

paths in excess of 50 mm on traversing the 1 mm sample. The Monte

Carlo code was also used to study the spatial resolution (lateral and depth)

of steady-state transmission Raman spectroscopy in the diffusion regime

by examining the distribution of Raman generation positions as a function

of incident beam size, sample thickness, and transport length. It was

predicted that the lateral resolution should worsen linearly with sample

thickness (typically the resolution was about 50% of the sample

thickness), and this is an inevitable consequence of operating in the

diffusion regime. The lateral resolution was better at the sample surface

(essentially determined by the probe beam diameter or the collection

aperture) than for buried objects, but transmission sampling was shown to

be biased towards the mid-point of thick samples. Time-resolved

transmission experiments should improve the lateral resolution by

preferentially detecting snake photons, subject to constraints of signal-

to-noise ratio.

Index Headings: Transmission Raman; Photon migration; Time resolved;

Spatial resolution; Sampling volume.

INTRODUCTION

When using optical techniques to characterize highlyscattering turbid materials such as powders, tissues, andemulsions, photons propagate pseudo-randomly through thesample as a result of multiple scattering. The effect iscommonly termed photon migration and has received muchattention regarding its influence on the imaging and analysis ofsemi-transparent materials, particularly biological tissue.1,2 Anextensive body of work exists that discusses time-resolved andsteady-state photon migration; this field is far too large toreview here, but an excellent introduction has been given byDas et al.2

Until recently, Raman photon migration was not recognizedas a specialized technique in its own right; it was simplyregarded as an inevitable consequence of analyzing highlyscattering samples, receiving little attention other than studiesof (predominantly steady-state) reflection and transmission as afunction of scattering and absorption properties.3,4 Nonethe-less, these studies have been extremely important in interpret-ing Raman data obtained in diffusing, absorbing regimes,particularly for biological studies.5–7 In early time-resolved

work, Wu et al.8 used picosecond Raman spectroscopy tolocate a b-carotene inclusion in a turbid latex, but the (80 ps)time resolution limited the depth resolution to the centimeterscale. More recently, picosecond Raman measurementsrevealed the long (multiple centimeter) flight paths that occurwithin thin powder samples (,0.1 cm3),9,10 and nondestructivedepth profiling of stratified systems was performed by temporalfiltering of the backscattered Raman photons.11 Subsequently,time-resolved depth profiling of biological tissue receivedattention because of its nondestructive nature and potential invivo applications,12–16 but the complex equipment requiredputs this approach beyond the resources of most laboratories.Fortunately, it was soon realized that Raman photons generatedat different depths could be discriminated by the distancebetween their point of emission and the laser injection point(spatially offset Raman spectroscopy, or SORS).17,18 (Aconceptually similar approach was previously demonstratedfor in vivo depth-resolved near-infrared spectroscopic analysisof cerebral oxygen content by varying the distance betweensource and collection fibers placed on a patient’s head).19 Thisdevelopment led to a flurry of activity to optimize and applythe technique, primarily by the groups of Matousek20–28 andMorris.29–33 The key result is that by varying the distancebetween the injection and collection points, excellent depthdiscrimination can be obtained using simple continuous wave(cw) lasers at a fraction of the cost of the ultra-fast time-resolved variant, and often with better signal-to-noise ratio (S/N) and reduced peak laser intensities, allowing depth profilingof biological systems and noninvasive analysis of opaque andpackaged materials.

Transmission Raman spectroscopy can be considered anextreme variant of SORS that places source and detector onopposite sides of the sample. Data can be acquired throughrelatively thick opaque materials such as pharmaceutical tabletsand capsules,34,35 breast tissue,36 and canine bones.37 Foranalytical applications, transmission Raman offers the possi-bility of much improved accuracy and precision, due to the factthat it analyzes a much larger and hence more representativesample volume than backscattering spectroscopy and its abilityto suppress interfering surface-generated Raman and fluores-cence signals. Transmission spectrometers are now commer-cially available and could conceivably become the norm forbulk Raman analysis of opaque materials. Furthermore, thepossibilities for Raman tomographic imaging are exciting. Inshort, SORS and transmission Raman spectroscopy havenumerous practical applications, ranging from noninvasivemedical diagnosis through counterfeit detection and securityscreening of hazardous and illicit materials. Several recentreviews have discussed these applications in detail.38–40

In this work we return to the topic of picosecond time-resolved Raman photon migration, but applied to the

Received 26 August 2009; accepted 8 October 2009.* Author to whom correspondence should be sent. E-mail: [email protected].

52 Volume 64, Number 1, 2010 APPLIED SPECTROSCOPY0003-7028/10/6401-0052$2.00/0

� 2010 Society for Applied Spectroscopy

transmission geometry, which has not, as far as we are aware,been reported previously. This provides additional informationto steady-state measurements because it measures the distribu-tion of path lengths covered by the laser and Raman photons. Itshows how a laser pulse propagates through a turbid samplemore quickly and with a narrower time spread than the Ramanpulse that it generates. An estimate of the scattering length canbe obtained by fitting the temporal transmission profile,allowing Monte Carlo prediction of the spatial resolution of atransmission Raman experiment as a function of samplethickness, probe beam diameter, and the collection aperture.These simulations should be useful when interpreting trans-mission Raman data of samples containing buried features,providing insight into the spatial resolution that can beexpected in imaging experiments and allowing the effectivesampling volume to be estimated in bulk transmissionexperiments. This is important because despite the growingbody of work on transmission Raman spectroscopy, very littlequantitative work has appeared that discusses and predicts thespatial resolution that can be attained or the sample volumesthat are probed. This is vital if one is to correctly interpretanalytical results from, for example, pharmaceutical soliddosage forms; if the sampling is biased to either the surface orthe bulk, this could have significant ramifications whenanalyzing stratified or coated samples.

MONTE CARLO MODELING OF RAMANTRANSMISSION

Consider a short (;1 ps) laser pulse incident at point A andtime t ¼ 0 on a sample cell of thickness T (Fig. 1). Laser and

Raman photons emerging at point D are measured as a functionof time. In a clear sample the laser pulse travels directly from Bto D and emerges un-broadened a short time later (assuming nogroup velocity dispersion or nonlinear optical effects arepresent), along with a simultaneous pulse of Raman photons. Ina turbid sample, multiple scattering causes photons to follow avariety of tortuous routes, delaying pulse propagation andbroadening the transmitted pulse. The temporal profile of thetransmitted laser pulse depends on the likelihood of a flightpath of duration t starting at B and ending at D. One such path(BCPD) is shown in Fig. 1, but there will be many differentpaths with the same transit time that link B and D; the (equal)probabilities of all these different paths of the same length mustbe summed to calculate the pulse profile. This can be calculatedanalytically with differing degrees of rigor using, for example,the diffusion approximation41 and the path integral approach.42

Previously, a simple Monte Carlo model was used tocalculate the temporal variation in backscattered laser andRaman signals from powders.10 This model correctly predictedthe observed result that the backscattered Raman pulse decaysmore slowly than the backscattered laser pulse. For a flight paththat connects the laser injection point with the observationpoint, the probability that the laser photon converts to a Ramanphoton at some point along the path (for example, the pointP(Ygen, Zgen) in Fig. 1) is proportional to the total path length(or time), assuming a sufficiently low probability of conversionat any one point. Therefore, Raman photons tend to originatefrom longer flight paths and on average emerge from thesample later than the laser photons. To a first approximation, ifthe pulse profile of the laser photons at any point in the sampleis P(t), then the Raman pulse profile is t�P(t).

To give a simple example, consider laser and Ramanphotons migrating from a point source within an infinitemedium. At t¼ 0 a fixed number of laser photons are placed atthe origin; the diffusion approximation predicts that the laserphoton density at the origin should decay as t�3/2, so the simplemodel predicts that the corresponding Raman decay will beproportional to t�t�3/2¼ t�1/2. This was exactly the outcome ofthe Monte Carlo simulation. The situation is more complicatedfor measurements on the surface of a finite medium, becausephotons are lost from the sample, increasing the signal decayrate; nonetheless, the temporal exponents of the laser andRaman decay profiles are expected to differ by 1, and this wasobserved in both Monte Carlo simulations and in experimentaldata.10

For our current work the Monte Carlo model was modifiedfor the transmission geometry, shown in Fig. 2, where thesample was assumed to consist of an infinite slab of thicknessT. A Gaussian distribution of laser photons was placed at onesurface at t ¼ 0 and allowed to propagate on a random walkthrough the sample. Any photons emerging from the oppositesurface within a rectangular aperture, defined by the back-projected image of the spectrometer entrance slit, werecounted. No account was taken of the collection solid angle;any photons that left the sample within the defined aperturewere counted, irrespective of trajectory. This has the advantageof maximizing the number of Raman photons counted,improving the S/N. Modeling the solid angle of acceptancewill mainly reduce the number of photons accepted by thespectrometer by a common factor in each experiment.

The random walk was simulated using the diffusionapproximation, i.e., with a step length equal to the transport

FIG. 1. Schematic showing flight path through turbid sample of thickness T.The temporal profile of the transmitted laser pulse yields the probabilitydistribution of paths with flight time t, which begin at A and end at D. Thetransmitted Raman pulse profile gives the probability distribution of paths thatsatisfy the above criterion and that yield a laser to Raman conversion at somepoint on the path. Such a conversion can occur at any point on the path, forexample at point P(Xgen,Ygen, Zgen).

APPLIED SPECTROSCOPY 53

length lt. Under the diffusion approximation, lt is the meandisplacement required to fully randomize the photon direction.For isotropic scattering, lt is the distance between successivescattering events, while for anisotropic scattering the photonrequires multiple events to randomize its direction, and thescattering mean free path, ls, gives the average distancebetween successive scattering events. Defining the anisotropy(g) as the mean cosine of the scattering angle, the relationbetween the two scattering lengths is given by lt¼ ls/(1� g).2

For isotropic scatter g ¼ 0 and lt ¼ ls.In this work we assumed a single transport length rather than

a statistical distribution; every photon performed a randomwalk with step length lt, and if it emerged from the samplewithin the detection zone, the number of steps (and hence time)taken up to this event was recorded. At each step a smallprobability of converting the laser photon into a Raman photonwas allowed (equivalent to 1 conversion every 50 cm traveled).This ensures a low probability that a given laser photon willconvert to a Raman photon on traversing the cell; too high aprobability biases the generation process to shorter flight paths.It is still several orders of magnitude too high compared withphysical reality, but this does not matter for the purposes of thesimulation; lower scattering probabilities were evaluated andfound to make no significant difference to the computedresolutions. No possibility of secondary Raman photonconversion was allowed in the simulation. No depletion ofthe Raman signal by this mechanism would be expected tooccur given the small probability of this secondary process (theprimary process (Raman scattering) did not deplete signifi-cantly the laser beam itself). Furthermore, no possibility ofabsorption (laser or Raman) was allowed. This will beimportant in some situations, such as studies of biologicaltissues, since absorption would statistically tend to eliminatethe longer flight paths, mitigating against detection of longerlived photons, which in turn should improve the lateral spatialresolution. However, the attenuation would reduce the signalintensity and so worsen the signal-to-noise ratio. Overall, thesignificance of absorption must be investigated on a case-by-case basis for which the optical parameters are known.

Typically 109 laser photons were injected into the sample.The maximum number of steps allowed before photontermination depended on sample thickness and scatteringlength and was selected to ensure that the pulse intensity hadfully decayed. For example, with a 1 mm sample and lt ¼ 40lm, the maximum number of steps per photon was 2000(equivalent to 374 ps), whereas for a 4 mm sample with thesame scattering length, 20 000 steps were allowed beforetermination. If a Raman photon was generated, the generationposition (Xgen, Ygen, Zgen) was recorded and its subsequentprogress tracked through the sample. If it emerged within thecollection zone, the time of emission was noted and correlatedwith the generation position, giving the detected photonintensity versus number of steps. The time taken to traverseone transport length is lt/v, where v is the effective speed oflight in the sample. This is determined by the refractive indexof the particles and their packing density. The refractive indexof the compound used in these studies, trans-stilbene, was notknown at the probe wavelength (400 nm), so it was assumed tohave the value measured using the sodium D-line (1.63). Thepacking density was also unknown. Making the sweepingassumption that the sample consists of randomly packedmonodisperse spheres, a maximum packing fraction F ; 0.64

would be expected, although the fraction could easily exceedthis value for other shapes and size distributions. Assumingrefractive indices of 1.63 and 1.0 for stilbene and air, theeffective refractive index of the scattering medium is given by1.63F þ (1 � F) ¼ 1.4, so v ;214 lm/ps. Therefore, theaverage time required to traverse one transport length is ; lt/214, with the transport length expressed in lm and time inpicoseconds.

In addition to the pulse profile, the simulation producesstatistics on the distribution of Raman generation positions fordetected photons. The standard deviations of Xgen, Ygen, andZgen were computed as a function of time; a similar analysiswas carried out for all detected photons irrespective of time.These parameters enable quantification of the spatial resolutionof the transmission Raman experiment.

EXPERIMENTAL

Figure 2 illustrates the experimental arrangement. Time-resolved transmission data were recorded from a sample ofpowdered trans-stilbene, which was held in a 1 mm path-length, 1 cm wide transmission cell. The powder was simplypoured into the cell, without compacting. A pulsed laser beam(the probe beam) was focused onto the sample surface and thetransmitted photon pulses were collected and relayed to thespectrometer for temporal and spectral analysis. Both the laserand Raman intensities were measured simultaneously as afunction of time by curve-fitting the Rayleigh band and thestilbene doublet near 1600 cm�1 to Gaussians. This waspermitted by selecting a spectral range spanning the laser lineand the Raman doublet and attenuating the laser line using anappropriately angled holographic notch filter placed in front ofthe spectrograph in a collimated region of the beam. The filterwas rotated so as to reduce the Rayleigh line to about the sameintensity as the Raman doublet, the adjustment being made

FIG. 2. Schematic of sampling geometry: the pulsed laser beam, of diameter500 lm, travels in theþz direction along the spectrometer axis (normal to thesample surface); photons that emerge within a rectangular collection zone onthe opposite side are collected and transmitted to the Kerr Cell for temporalfiltering. The collection zone is the back-projected image of the spectrometerentrance slit; the zone size was estimated to be ;100 lm 3 2000 lm. Diagramnot drawn to scale.

54 Volume 64, Number 1, 2010

with the Kerr gate held open by aligning both polarizers in thesame direction. The probe beam diameter at the sample wasabout 500 lm, assessed using a knife-edge to define the pointsthat contain 10–90% of the beam intensity, and a 60 mm focallength lens (f/#¼ 1.2) was used to collect the transmitted light.The back-projected image of the spectrometer entrance slit onthe sample (approximately 100 lm wide by 2000 lm high)defined the photon collection zone W 3 H. There was no lateraloffset between the probe beam and the collection zone.

The picosecond-gated Raman spectrometer used a highthroughput optical Kerr shutter (CS2), which has beendescribed in detail in other publications.43–45 Briefly, the KerrGate was driven by a high-power (;0.5 mJ) short (1 ps) 800nm laser pulse operating at 1 kHz, providing a temporalresolution of approximately 4 ps. Raman scatter was inducedusing a synchronized 400 nm probe pulse of ; 1 ps width and15 lJ energy, giving a maximum average power of 15 mW. Bycontrolling the delay between the probe pulse and the gatingpulse using an optical delay line, the Kerr Gate can be openedat any specified time relative to the arrival of the probe pulse atthe sample. About 15 sampling times were selected over thetime range�10 to 200 ps, and these were accessed as a randomsequence to avoid errors due to systematic variations in laserpower during a run.

RESULTS AND DISCUSSION

Time-Resolved Transmission. Figure 3 shows the laser andRaman pulses transmitted through 1 mm of stilbene powder.The observed laser and Raman signals are shown as solidsquares and triangles, respectively, while the Monte Carloresults are depicted by the dashed and solid lines. Time zerowas defined as the point when the ‘‘snake’’ photons weredetected; these are the earliest arriving diffusely scatteredphotons, which happen to have traveled directly across thesample in an almost straight line. No discrete pulse due tocoherent ballistic (undeviated) photons was observed. For anon-turbid sample of index 1.6, we would expect all photons topass straight through the sample in a 1 ps wide pulse with amaximum transit time of ;5 ps, but photon diffusion had threeobserved consequences, in line with the expectations discussedabove: both the Raman and transmitted laser pulses were two

orders of magnitude broader than the incident laser pulse, thelaser pulse centroid passed through the cell slightly morequickly than the Raman pulse, and the Raman pulse wasbroader than the transmitted laser pulse. Reasonable agreementwas attained between the observed and modeled pulse profileswhen a transport length of ;40 lm was assumed, although adifferent estimate of the packing density or the refractive index,or the introduction of a finite probability for absorption, wouldrequire a different transport length to optimize the fit. There is,therefore, a significant uncertainty in the assumed value of lt.However, it is shown below that lt does not need to be knownaccurately in order to predict the spatial resolution of thetransmission Raman experiment, provided it is sufficientlysmall relative to the sample thickness and the collectionaperture (in other words, under conditions where the diffusionapproximation is valid).

The most interesting feature of Fig. 3 is the breadth of thetransmitted pulses, which spanned more than 250 ps, indicatingthat the late-arriving photons traveled ;50 mm further than thesnake photons. This implies an extremely convoluted path andraises the interesting question of just how far, on average, theflight paths meandered laterally within the cell while stillexiting through the collection zone. This will determine thelateral resolution of the transmission Raman experiment, sincephoton conversion can occur anywhere along the flight path.Winn et al.42 considered the distribution of flight paths in anelastically scattering medium using the diffusion approxima-tion and the path integral approach, showed how the lateralspread in flight paths could be predicted, and discussed itsinfluence on the lateral resolution of tomographic imaging. Weare not aware of similar calculations being reported for thetransmission Raman equivalent.

Spatial Resolution. Because the simulation records theposition at which each Raman photon is generated, it isstraightforward to compute the distribution of generationpositions both as a function of detection time and averagedover all detection times. For example, Fig. 4 shows thefrequency distributions of Xgen, Ygen, and Zgen for a 1 mmthick sample, 0.5 mm diameter probe beam, 100 lm 3 2000lm collection zone and lt¼ 40 lm, averaged over all detectedRaman photons irrespective of time. The spread in the xdirection (61r) was 550 lm, roughly equal to the probediameter or 53 the width of the collection zone. The y spreadwas bigger, approximately 800 lm, presumably due to the slitaspect ratio. Bearing in mind that the maximum flight paththrough the sample was ;50 mm, it is interesting that morethan half of the detected Raman photons were generated withina zone width that was less than 2% of the total maximum flightpath length. This is intuitively reasonable and stems from theconstraint of the considered photons to the entrance and exitapertures (many photons deviating significantly laterally arealso more likely to miss the exit aperture and consequently donot deteriorate the spatial resolution). Consider all possiblerandom walks with a large (fixed) number of steps, and whichlink points B and D (Fig. 1). Each of these walks has exactlythe same probability, but there are many more walks that stayfairly close to the line B-D and very few that deviate a longway laterally. Even so, the lateral spread was quite a largefraction of the sample thickness; for a sample thickness of 25transport lengths, the X and Y resolutions were approximately14 and 20 transport lengths, respectively. Again, this isreasonable; since we are assuming isotropic diffusion, it is

FIG. 3. Transmitted laser and Raman signals as function of time andnormalized to the same maximum height, compared with Monte Carlosimulations. A reasonable fit was obtained to both profiles assuming lt¼ 40 lmand no absorption.


unlikely that a photon would travel through ‘‘n’’ transport

lengths in order to traverse a sample without deviating laterally

though a similar distance; otherwise, the diffusion would be

anisotropic.

The Zgen distribution shows that the Raman response was

biased towards the center of the sample, presumably because

laser photons near either surface are more likely to be lost

before they can convert to a Raman photon The same effect

was predicted in Monte Carlo simulations of transmission

Raman scattering for a 3.9 mm thick tablet with lt¼ 200 lm.34

The fact that the distribution was symmetrical and centered at

the mid-point of the sample is encouraging; if too high a

probability of Raman generation is used in the code, the Zgen

distribution becomes biased towards the z ¼ 0 surface, forobvious reasons of fast laser photon depletion.

Figure 5 plots the computed Raman resolution (2r(Xgen)and 2r(Ygen)) versus sample thickness assuming a 100 32000 lm rectangular collection zone, a 500 lm probe beam,and lt¼ 40 lm. The distribution is close to normal, so the 61rrange accounts for approximately 68% of the total Ramanintensity, while 95% of the detected photons originate within62r about the collection axis. The simulation predicts thatincreasing sample thickness for a fixed aperture and beamdiameter should linearly degrade the spatial resolution in eachdirection. For thin samples the predicted X resolution is betterthan the Y resolution, but the difference diminishes withthickness. Because a large number (thousands) of Ramanphotons were counted in each simulation, r could bedetermined with high precision; when the standard error wascomputed for each value of r, the largest relative error wasabout 1%. This was the case for every simulation that was run.

The resolution is expected to depend on the dimensions ofthe collection zone, but Fig. 5 is limited to the specific case of afixed high-aspect ratio slit. Figure 6 plots resolution versus

FIG. 4. Monte Carlo simulation of distributions of Raman generation positionsaveraged over all detected photons for W¼ 100 lm, H¼ 2000 lm, T¼ 1 mm,and laser beam diameter of 500 lm. The range 6r, which contains ;68% ofall detected Raman photons, was taken as an estimate of the spatial resolution.

FIG. 5. Plot of X and Y resolutions versus sample thickness assuming a 100 32000 lm collection zone and a 500 lm beam diameter. The working measureof resolution was twice the standard deviation of the X and Y distributions.

FIG. 6. Plot of resolution (average of 2r(Xgen) and 2r(Ygen)) versus samplethickness, assuming 1 mm diameter circular collection zone, 0.5 mm probebeam and either 40 lm or 80 lm transport length. Under these conditions thediffusion approximation holds and the transport length has little effect on thepredicted resolution, which worsened linearly with thickness.


sample thickness assuming a circular collection zone, in orderto model the sampling geometry of practical transmissionRaman instruments, which employ fiber-optic collectionsystems with bundles of circular fibers. (For example,Srinivasan et al.37 carried out transmission Raman tomographyon canine bone, and on TeflonTM inclusions in Intralipid TM

tissue phantoms, using a rectangular array of collection fibers,with the projected image of each fiber being ;1 mm diameteron the sample, and Matousek and Parker used a fiber bundle tocollect transmission data of pharmaceutical tablets from a 3mm circular collection zone.)34 Simulations were run assuminga 500 lm diameter probe beam and a 1000 lm diametercircular collection zone, and two transport lengths weremodeled (40 lm and 80 lm). In the latter case the minimumsample thickness used was 1000 lm, in an attempt to satisfythe diffusion approximation, but we note that even a thickness/transport length ratio of 103 does not assure operation wellwithin the diffusion regime, and in fact a ratio of 303 isrequired for the diffusion equation to accurately modeltransmitted pulse profiles.41 However, a numerical value ofT/lt¼ 10 should give only a 10% difference between observedand transmitted pulse profiles, which is adequate for ourwork.41

Figure 6 shows that the predicted resolution (taken as theaverage of 2r(Xgen) and 2r(Ygen)) worsened linearly from;450 to 1900 lm as the thickness increased from 1 to 4 mm. Itconfirms the result from Fig. 5 that even though the lateralresolution is a very small fraction of the total flight path, it is alarge fraction (;50%) of the sample thickness. The resolutiondid not depend strongly on the transport length, presumablybecause in each case lt was sufficiently small compared withthe sample thickness to satisfy the diffusion approximation. Fora 1 mm collection aperture and a 4 mm thick sample, the lateralresolution was very similar to that calculated for a 100 3 2000lm aperture, showing that the slit geometry conveyed noadvantage in preserving lateral resolution for a thick sample.

Figure 7 summarizes the effect of probe beam diameter for a1 mm circular aperture and 2 mm or 4 mm thick samples.According to the simulation, the resolution was fairlyinsensitive to the size of the probe beam, particularly in the 1to 500 lm range. This suggests that the photons diffuselaterally so rapidly that selecting a very narrow probe beam

makes little difference. Furthermore, because the 1 mmcollection zone only transmits Raman photons that aregenerated within a fairly small lateral spread relative to thecollection zone, illuminating with a large beam did not severelydegrade the resolution; a 6 mm probe beam gave a resolutionthat was only ;50% worse than that predicted for a 0.5 mmprobe. This suggests that global illumination and detection withfiber bundles should retain some degree of spatial resolution,because the resolution in this case is determined by thedetection fibers, a result that was observed by Morris’ group.30

Resolution versus Depth. The results so far have beenbased on all detected photons, irrespective of the depth atwhich they were generated, but it is important to know how theresolution varies with sampling depth. Figure 8 shows thecorrelation between Xgen and Zgen for a 4 mm thick samplewith a 0.5 mm probe beam, a 1 mm diameter collectionaperture, and lt¼ 80 lm; the dashed lines show the 61r rangeaveraged over all photons. The distribution was not symmet-rical about the sample mid-point, being slightly tighter on theprobe side of the sample, particularly at the surface; this ispresumably because the probe beam was narrower than thecollection aperture. One could widen the probe beam to makethe distribution symmetrical, but in fact the asymmetricaldistribution could feasibly be a useful feature, since if onerecorded two images or maps from the same sample, with theprobe beam incident on different sides for each image, then thechange in apparent size of a buried feature would give some(albeit limited) information on its depth. An alternative andprobably preferable strategy to deduce the depth of a buriedfeature would be the use of SORS.

Figure 8 shows that the resolution is improved near eithersurface compared with the bulk, suggesting that the probebeam and the collection aperture both play an important role indetermining the apparent size of features near their respectivesurfaces. This is intuitively reasonable; when a small object ison the probe surface, the majority of the Raman photons aregenerated when the laser beam directly strikes the object, so theprobe beam size effectively determines the resolution.Likewise, when the object is on the collection surface, thecollection aperture limits the resolution, since most of the

FIG. 7. Resolution versus probe beam diameter assuming 1 mm collectionzone, 80 lm transport length and either 2 mm or 4 mm sample thickness.

FIG. 8. Correlation of Xgen and Zgen computed for 4 mm thick sample, 0.5mm diameter probe beam, 1 mm collection aperture, and 80 lm transportlength. Resolution is better near the surface than in the bulk and is best at theprobe beam surface since the probe was about half the diameter of thecollection aperture.


detected photons do not undergo significant migration but areinstead emitted directly from the object into the collectionaperture. In the center of the sample migration is important,because the laser beam has been diffused and the collectionaperture ‘‘views’’ a wide sample region.

Time-Resolved Resolution Enhancement. The resultsabove show that if all detected photons are counted irrespectiveof arrival time, the best expected lateral resolution for a 4 mmthick sample and a 1 mm collection aperture is approximately 2mm. On the basis of the computed trends, we expect this toworsen linearly with sample thickness. It is well known that byapplying ultra-fast gating it is possible to improve imagesharpness in transmission tomography, since this preferentiallyselects the photons that have experienced minimal lateraldeviation.42,46 In principle, a similar effect is expected withtime-resolved transmission Raman imaging. At this stage noexperimental data are available to test this assertion, but Fig. 9shows the correlation of 2r(Xgen) versus detection time for a0.5 mm probe beam, a 1 mm circular collection zone, a 2 mmthick sample, and 80 lm transport length. The horizontaldashed line shows 2r(Xgen) averaged over all detectedphotons. As expected, the early-arriving photons werepredicted to have a smaller lateral spread. In this case,positioning a moderate (e.g., 50 ps) detection gate near t ¼ 0would improve the lateral resolution by a factor of ;2, signal-to-noise permitting. In principle, shorter gates could improvethe resolution such that it is ultimately limited only by probebeam size and collection aperture. In practice there is aminimum achievable spatial resolution, determined by spectralS/N, as discussed by Moon et al. for time-resolved imaging ofturbid samples.47 This will be a more serious issue for Ramanimaging, owing to the paucity of Raman photons. We intend toinvestigate the effect of gating on Raman lateral resolution infuture studies. However, it is likely that the experimental timerequired to obtain acceptable quality data would restrict theapplicability of the time-gated approach to all but the mostspecialized situations, where the time to acquire the data is nota critical factor.

DISCUSSION AND FUTURE WORK

These calculations suggest that for Raman tomography witha simple coaxial illumination and collection geometry and witha collection aperture of the order of 1 mm diameter, lateralresolution will degrade linearly for samples that are thickcompared with the transport length, and the resolution shouldbe of the order of half the sample thickness. This is aninevitable consequence of isotropic diffusion. Imagine a sourceobject in the middle of a sample of thickness T, emittingRaman photons that spread isotropically; by the time theRaman photon cloud has traversed the distance T/2 and reachedthe collection surface, it will have spread laterally to a similarextent, which suggests that the resolution will always be asignificant fraction of the sample thickness. Under the diffusionapproximation, the transport length has little effect on theresolution, which is useful because it implies that one does notneed to measure an accurate transport length in order to modelthe resolution. However, we have not computed the effect ofoptical absorption, which could be very important in manypractical circumstances. Also, forward-biased scatteringthrough a sufficiently thin sample will result in less lateraldeviation and better resolution, but we have not yet modeled

this situation, which will be important for some biomedicalapplications.

As far as we are aware, no precise measurements of thelateral resolution of transmission Raman spectroscopy havebeen reported to date. There have been statements to the effectthat the shape of fairly large (;9 mm) buried objects can berecovered accurately when immersed 10 mm inside a scatteringmedium, but precise details of the apparent size were notgiven.48 Morris and co-workers have reported studies inreflection mode using SORS ‘‘ring-disk’’ illumination-collec-tion geometries and showed how by varying the radius of theilluminating ring one can improve the lateral resolution suchthat boundaries can still be resolved up to depths of ;5 to 6mm beneath a highly scattering overlayer.29 The same groupshowed how global illumination and a bundled fiber collectionprobe could be used in reflection mode to image the boundarybetween two abutted polymer blocks buried under 13 mm ofTeflonTM, but no quantitative measure of the degree of blurringwas given.30 A full three-dimensional tomographic reconstruc-tion of a bone through soft tissue was also performed intransmission Raman geometry by Srinivasan et al.37

A detailed study of the lateral resolution of steady-statetransmission Raman spectroscopy using single crystals ofstrong Raman scatterers buried in opaque powders has recentlybeen conducted and will be reported in the future; however, atthis stage the initial results appear to be broadly consistent withthe predictions reported above, i.e., the resolution apparentlydegrades linearly with sample thickness, and the resolution ateither surface is much better than in the bulk.49 It is clear thatgiven the rapidly increasing use of Raman photon migration forcharacterizing complex structures, much more work is requiredto establish the fundamental performance parameters, usingboth simulation and experimental techniques.

This work is clearly at a preliminary stage and the currentexperimental data set is not adequate for proper modelvalidation. First, it would be useful to have time-resolved datafrom thicker samples to study the change in the pulse profile

FIG. 9. Monte Carlo correlation of lateral resolution with detection time for 2mm sample, 0.5 mm probe beam, 1 mm circular collection zone, and lt ¼ 80lm. The dashed line is the time-averaged resolution. Counting only the early-arriving photons would significantly improve the lateral resolution, but at theexpense of worsened S/N.


and compare with simulations, but reliable data are notavailable at present, owing to problems with obtainingreproducible results from thicker samples. Second, powderedstilbene is not a well-defined reference material because of theconsiderable uncertainties in the particle size, the effectiverefractive index, and the scattering length. The reason it wasused in this work is that it is an extremely strong Ramanscatterer and a robust material, making the observation ofpicosecond-resolved transmission Raman data quite easy andenabling straightforward demonstration of the main concepts. Itwould be much more useful to study a material where thescattering length, the absorption length, and the anisotropy canbe controlled, such as a polymer latex of known concentrationand particle size, as used by previous workers.8,42 This wouldalso permit insertion of objects of defined size into the latex inorder to test the lateral spatial resolution and to assess whethertime-resolved measurements can improve the resolution. Theseexperiments will be carried out in future work, although theywill require significant instrumental modifications, for examplethe introduction of stirred or flowing cells to avoid possibledecomposition of the latex on the cell wall (a factor that was anissue in preliminary attempts).

CONCLUSION

As far as we are aware these are the first picosecond time-resolved transmission Raman studies of highly scatteringsamples. A simple Monte Carlo model successfully simulatedthe temporal profiles of both the laser and Raman pulsestransmitted through a 1 mm thick sample of powdered stilbene.The transmitted Raman pulse was broader than the transmittedlaser pulse and took longer to traverse the cell, as expectedfrom previous backscattering experiments. The temporal datashowed that for some photons, flight paths in excess of 50 mmwere required to traverse the 1 mm thick sample.

The lateral resolution of steady-state transmission Ramanspectroscopy was simulated for a variety of probe beamdiameters, sample thicknesses, collection apertures, andtransport lengths, ensuring that in each case the transportlength was an order of magnitude smaller than the samplethickness. Despite the extremely long flight paths through thesamples (many cm), it was predicted that approximatelymillimeter-scale lateral resolution would be maintained becauseonly those Raman photons generated close to the collectionaxis can pass through the collection zone. This assertion iscurrently being tested by imaging buried objects in transmis-sion mode. Nonetheless, the lateral resolution was predicted tobe quite poor, typically half the sample thickness in the casesstudied. This is an inevitable consequence of working in theisotropic diffusion regime, because (isotropic) spreadingphoton clouds originating from deeply buried objects willinevitably overlap before they leave the sample. Calculationssuggest that temporal gating should improve the lateralresolution, but S/N will be a key limiting factor.

ACKNOWLEDGMENT

The authors acknowledge Intertek Group plc for granting permission topublish this work.

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temporal and spatial resolution in transmission raman spectroscopy

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