Prediction of Sublayer Depth in Turbid Media Using Spatially Offset

Sep 12, 2008 - E-mail: [email protected]; [email protected]., † ... monitoring the depth of optically thick layers within turbid media using spat...
0 downloads 3 Views 295KB Size
Download PDF
Anal. Chem. 2008, 80, 8146–8152

Prediction of Sublayer Depth in Turbid Media Using Spatially Offset Raman Spectroscopy N. A. Macleod,*,† A. Goodship,‡ A. W. Parker,† and P. Matousek*,† Central Laser Facility, Science and Technology Facilities Council, Rutherford Appleton Laboratory, Harwell Science and Innovation Campus, Didcot, Oxfordshire, OX11 0QX, United Kingdom, and Institute of Orthopaedics and Musculoskeletal Science UCL, Stanmore Campus, Royal National Orthopaedic Hospital, Brockley Hill, Stanmore, Middlesex, HA7 4LP, United Kingdom We demonstrate experimentally the feasibility of monitoring the depth of optically thick layers within turbid media using spatially offset Raman spectroscopy (SORS) in combination with multivariate analysis. The method uses the deep penetration capability of SORS to characterize significantly thicker (by at least a factor of 2) layers than possible with conventional Raman spectroscopy. Typical relative accuracies were between 5 and 10%. The incorporation of depth information into a SORS experiment as an additional dimension allows pure spectra of each individual layer to be resolved using three-dimensional multivariate techniques (parallel factor analysis, PARAFAC) to accuracies comparable with the results of a twodimensional analysis. In a number of analytical applications involving stratified, diffusely scattering samples, it is a requirement that both the chemical identity and the thickness of a particular layer are quantified; examples include the determination of the thickness of soft tissue above bone and monitoring the penetration of pharmaceutical drugs or cosmetic products into tissue. Although confocal Raman microscopy is used in this area, its penetration depth is severely limited (to depths of several hundred micrometers at best in the case of biological tissue). Deeper zones, where diffuse scattering is dominant, cannot be resolved by this or by other conventional methods. Alternative techniques (e.g., photoacoustic spectroscopy or optical coherence tomography) that offer millimeter (or better) depth penetration suffer from a lack of chemical specificity. For access to such deeply buried regions spatially offset Raman spectroscopy (SORS) 1,2 holds particular promise; the Raman spectra of individual sublayers within a complex multilayer system can be isolated. In SORS, Raman signal is collected from sample areas that are spatially offset (typically by several millimeters) from the point of illumination (see Figure 1). Spectra collected at each spatial offset contain different relative contributions from sample layers located at different depths due * To whom correspondence should be addressed. E-mail: N.MacLeod@ rl.ac.uk; [email protected]. † Rutherford Appleton Laboratory. ‡ Royal National Orthopaedic Hospital. (1) Matousek, P; Clark, I. P.; Draper, E. R. C.; Morris, M. D.; Goodship, A. E.; Everall, N.; Towrie, M.; Finney, W. F.; Parker, A. W. Appl. Spectrosc. 2005, 59, 393–400. (2) Matousek, P.; Morris, M. D.; Everall, N.; Clark, I. P.; Towrie, M.; Draper, E.; Goodship, A.; Parker, A. W. Appl. Spectrosc. 2005, 59, 1485–1492.

8146

Analytical Chemistry, Vol. 80, No. 21, November 1, 2008

Figure 1. Schematic diagram of the experimental arrangement for inverse SORS.

to the wider spread of photons originating from deeper layers emerging onto the sample surface. Consequently, the SORS technique effectively suppresses the interfering Raman (and fluorescence) signals originating from the surface layer. The availability of a set of Raman spectra with varying degrees of surface and subsurface contributions permits complete isolation of the Raman spectrum belonging to each of the individual layers. This can be accomplished using a variety of numerical multivariate methods including band targeted entropy minimization (BTEM).3,4 For a “simple” two-layer system, a manual or automated scaled subtraction of SORS spectra obtained at two different spatial offsets is sufficient to cancel the surface contribution.1,5,6 (3) Chew, W.; Widjaja, E.; Garland, M. Organometallics 2002, 21, 1982–1990. (4) Widjaja, E.; Crane, N. J.; Chen, T. C.; Morris, M. D.; Ignelzi, M. A.; McCreadie, B. R. Appl. Spectrosc. 2003, 57, 1353–1362. 10.1021/ac801219a CCC: $40.75  2008 American Chemical Society Published on Web 09/12/2008

SORS has been successfully applied to a diverse variety of practical applications that are beyond the reach of conventional Raman, including the noninvasive Raman spectroscopy of bone within the body,5,7 pharmaceutical, forensic investigations,8 and security screening of illicit materials.6 Recently, a refinement of the SORS method, inverse SORS, was developed, which allows higher overall laser powers to be used through the provision of a larger illumination zone on the sample.9-11 In contrast to conventional SORS, scattered light is collected through a group of fibers contained within the center of a probe (typically with an overall diameter of 1-2 mm) while the laser beam is delivered as a ring-shaped beam; the ring radius of the beam defines the SORS spatial offset (see Figure 1). SORS, in both its basic form and in inverse mode, provides information on the chemical composition of individual layers but provides no information on their spatial distribution within a sample. Schulmerich et al.,12 have deployed SORS as a tomographic tool (analogous to NIR absorption tomography) capable of forming highly chemically specific images of subsurface sample components. Recently, this group13 demonstrated the feasibility of 3D tomographic imaging through a canine hind limb section (thickness up to 45 mm) using transmission Raman spectroscopy, which can be considered to be a special case of SORS with extreme separation of the collection and laser deposition zones.14,15 In contrast to full three-dimensional tomographic imaging approaches, here we focus on the conceptually simpler issue of determining the depth of a layer, an application of potentially high practical significance in a number of areas. That SORS and its variants were capable of providing information on the depth/ thickness of a multilayer system was discussed in our earlier theoretical work.2 Similarly, other fundamental sample parameters such as transport length or absorption could also be derived from SORS observables.2 The assumption of a plane two-layer system with infinite side dimensions greatly simplifies the complex problem of tomographic imaging and leads to a more straightforward implementation with a more deterministic outcome. The problem is relevant to cases where the availability of additional information (e.g., the layer depth) can be used to build a calibration model that allows accurate prediction of the thickness of an unknown sample. Accurate depth measurement via a rapid, noninvasive, and nondestructive technique has a number of (5) Schulmerich, M. V.; Dooley, K. A.; Vanasse, T. M.; Goldstein, S. A.; Morris, M. D. Appl. Spectrosc. 2007, 61, 671–678. (6) Eliasson, C.; Macleod, N. A.; Matousek, P. Anal. Chem. 2007, 79, 8185– 8189. (7) Matousek, P.; Draper, E. R. C.; Goodship, A. E.; Clark, I. P.; Ronayne, K. L.; Parker, A. W. Appl. Spectrosc. 2006, 60, 758–763. (8) Eliasson, C.; Matousek, P. Anal. Chem. 2007, 79, 1696–1701. (9) Matousek, P. Appl. Spectrosc. 2006, 60, 1341–1347. (10) Schulmerich, M. V.; Dooley, K. A.; Morris, M. D.; Vanasse, T. M.; Goldstein, S. A. J. Biomed. Opt. 2006, 11, 060502. (11) Schulmerich, M. V.; Morris, M. D.; Vanasse, T. M.; Goldstein, S. A. In Proceedings of SPIE 6430, Advanced Biomedical and Clinical Diagnostic Systems V; Vo-Dinh, T., Grundfest, W. S., Benaron, D. A., Cohn, G. E., Raghavachari, R., Eds.; 2007; 643009. (12) Schulmerich, M. V.; Finney, W. F.; Fredricks, R. A.; Morris, M. D. Appl. Spectrosc. 2006, 60, 109–114. (13) Schulmerich, M. V.; Cole, J. H.; Dooley, K. A.; Morris, M. D.; Kreider, J. M.; Goldstein, S. A.; Srinivasan, S.; Pogue, B. W. J. Biomed. Opt. 2008, 13, 020506. (14) Matousek, P. Chem. Soc. Rev. 2007, 36, 1292–1304. (15) Macleod, N. A.; Matousek, P. Deep Non-invasive Raman Spectroscopy of Turbid Media Appl. Spectrosc. 2008, in press.

potential applications (e.g., penetration of drugs or cosmetics through tissue); additionally, in combination with theoretical simulations, it yields the dependence between the concentration of each layer in each spectrum as a function of spatial offset. Extraction of pure spectra of each layer via multivariate curve resolution relies on constraints (e.g., signal non-negativity) to limit the otherwise infinite range of mathematically valid solutions to spectrally and chemically sensible regions. In general, concentration factors are forced to be non-negative; any dependence on spatial offset is ignored as long as this constraint is maintained. Incorporation of depth information and subsequent concentration data may provide an additional constraint either singly for each individual layer or combined into more general parameters (e.g., the SORS ratio defined in ref 2). This may be of particular use in cases where the layers are spectrally similar. A good example is diagnosis of bone disease where soft tissue and bone both contain significant amounts of collagen, albeit in very different chemical environments; the Raman spectrum of bone is a good indicator of the presence of various bone diseases (e.g., osteogenesis imperfecta or brittle bone disease) by quantifying the ratio of intensities for spectral bands assigned to different components of the bone matrix.16 Extraction of an accurate spectrum of bone through overlying tissue is only possible via application of suitable constraints to which depth prediction may prove a useful addition. This paper details the use of Raman spectroscopy (both conventional and inverse SORS) to determine the thickness of a surface layer. Multivariate analysis (principal component analysis (PCA) and partial least-squares (PLS) regression) is used to determine the maximum accessible depth and predict the depth over the feasible range. The systems under study include bone with an overlayer of soft tissue and plastic slabs overlain with white paper; in both cases, the surface layer gives rise to intense Raman signals and a broad fluorescence background. METHODOLOGY Experimental Information. The experimental arrangements (see Figure 1) for both SORS and conventional Raman are as follows. The laser source, a continuous-wave, near-infrared cavity tuned diode laser (Sacher TEC Lynx, 830 nm, 120 mW, 2-mm diameter) with a single band-pass filter (Semrock) to remove residual amplified spontaneous emission, was guided onto the sample surface at an angle of 45°. For inverse SORS experiments, a conical lens (axicon) was mounted on a computer-controlled motorized translation stage (Standa) to produce a ring-shaped laser beam; the separation between lens and sample determines the radius of the ring and the spatial offset.9 Scattered light was collected by a lens (50-mm diameter, 75-mm focal length) and imaged (with 1:1 magnification) by an identical lens onto a fiberoptic probe. A notch filter (Kaiser Optical Systems) was placed between the two lenses to remove elastically scattered light. The fiber-optic probe (Ceram-Optec) consisted of 61 fibers (core diameter of 200 µm, outer diameter of 245 µm, numerical aperture 0.28) arranged in a disk shape (2.21-mm diameter). The fibers are rearranged at the output end into a linear formation to match (16) Draper, E. R. C.; Morris, M. D.; Camacho, N. P.; Matousek, P.; Towrie, M.; Parker, A. W.; Goodship, A. E. J. Bone Miner. Res 2005, 20, 1968– 1972.

Analytical Chemistry, Vol. 80, No. 21, November 1, 2008

8147

the input port of the detection system. The scattered light was dispersed through a spectrograph (Kaiser Optical Systems Holospec 1.8i) onto a back-thinned, deep-depletion thermoelectrically cooled CCD detector (Andor Technology, DU434-BR-DD, 1024 by 1024 pixels). Due to the large curvature imposed by the spectrograph and the finite vertical height of the internal slit, only the central strip (600 pixels, corresponding to ∼35 individual fibers) of the CCD chip was binned. Complete control of the experiment was provided by a LABVIEW (National Instruments version 8.2) interface. For inverse SORS experiments, spectra were collected in random order across the selected range of spatial offsets (typically 1-4 mm). Acquisition times were of the order of 10-100 s per spatial offset. Data Analysis. Data were analyzed using MATLAB (The Mathworks Inc., version 2007b) with in-built and user-defined scripts. Additional multivariate methods were from the PLS Toolbox (eigenvector Research, version 4.1). Spectra were baseline corrected for background fluorescence by a polynomial fitting routine with a non-negative spectral constraint.17 Additional preprocessing consisted of normalization of spectra to unit length (division by the sum of squares). Multivariate methods used included PCA, PLS regression, parallel factor analysis (PARAFAC) and multivariate curve resolution using the BTEM method with non-negative constraints on spectra and concentrations.3 Multivariate analysis18 is based on the assumption that the relationship between spectral response and concentration follows the Beer-Lambert law (eq 1); the observed spectra (Y, m samples measured at n wavelength points) are the linear product of submatrices of concentration (C, m by k) and spectra (S, n by k) of each distinct analyte (k) present in the sample set. Y ) CST ) ABT

(1)

In the absence of external information, the data set Y can be decomposed into an infinite set of bilinear matrices (A and B); PCA selects the submatrices such that the variance about the principal axes is maximized. In general, the axes (eigenvectors or loadings) do not correspond to “pure” spectra of individual components. For a two-dimensional matrix, pure component spectra and concentrations can only be obtained by supplying additional information (e.g., reference concentrations or spectra) or by applying specific constraints (non-negativity, unimodality, or closure). External information (commonly concentration) can be used to build regression models to quantitatively predict unknown samples; PLS, for example, constructs a regression vector (b, 1 by n), which is applied to the unknown data set (Y, n by 1) to extract the required value (eq 2). c ) bY

(2)

Multivariate curve resolution encompasses a wide variety of methods.18-26 Commonly, a mixing (or rotation) matrix is applied (17) Lieber, C. A.; Mahadevan-Jansen, A. Appl. Spectrosc. 2003, 57, 1363–1367. (18) Gemperline,P. Practical Guide to Chemometrics; Taylor & Francis Group: Boca Raton, FL, 2006. (19) Widjaja, E.; Li, C.; Garland, M. Organometallics 2002, 21, 1991–1997. (20) Widjaja, E.; Garland, M. J. Comput. Chem. 2002, 23, 911–919. (21) Widjaja, E.; Garland, M. J. Magn. Reson. 2005, 173, 175–182.

8148

Analytical Chemistry, Vol. 80, No. 21, November 1, 2008

to the data to produce an estimate of the pure spectra and concentrations; a metric (including constraints) is applied to this estimate and minimized by variation of the mixing scheme. Metrics applied include measures of spectral simplicity (entropy and area under spectra) and independence of each spectrum (mutual information). Recently, Garland and co-workers3,19-22 developed a scheme (based on differential entropy) that removes the need to specify the precise number of distinct components by targeting a specific spectral band for retention. BTEM has been successfully applied to data from diverse sources including FTIR, Raman, NMR, and mass spectrometry.3,5,10,19-22 The success of deconvolution routines in reliably extracting spectra of individual components is, in part, due to the number and manner (“hard” or “soft”) of constraints applied during optimization that limit the solution to spectroscopically and chemically feasible regions. Alternatively, expanding the data set to include an additional dimension provides a means of extracting pure component spectra. For a three-dimensional data set (or cube), decomposition in a fashion analogous to PCA on simpler data sets results in three submatrices (eq 3). Y ) ABC

(3)

In contrast to PCA, the decomposition can (under suitable conditions) provide unique submatrices consisting of pure spectra (A) and pure concentrations (B and C). Generally, trilinear decomposition (also known as PARAFAC) to a unique solution (except for the trivial effects of permutation and multiplicative scaling) is possible if the submatrices are distinct, thus avoiding the need for subsequent matrix rotation to derive “real spectra” from abstract eigenvectors.27-30 In practical terms, this requires the implementation of an additional source of variation with an influence on spectral response and concentration distinct from that caused by spatial offset; a convenient variable is the thickness of the surface layer. Samples. Two systems were used in this study. First, a model system composed of plastic slabs (Teflon) with an overlayer of multiple white paper sheets; each paper sheet was ∼100 µm thick and provided a clear Raman signal on top of a broad background fluorescence. A more challenging system was bone with an overlayer of soft tissue. Porcine rib bone and porcine tissue were purchased from local butchers; the thickness of each surface layer was ∼1 mm. RESULTS AND DISCUSSION Representative spectra of plastic slabs (Teflon) with a surface layer of white paper (100-1300 µm thick) obtained using both conventional Raman and inverse SORS (spatial offset ∼3 mm) are shown in Figure 2. The principal band of Teflon (“subsurface”) (22) Zhang, H.; Garland, M.; Zeng, Y.; Wu, P. J. Am. Soc. Mass Spectrom. 2003, 14, 1295–1305. (23) de Juan, A.; Tauler, R. Crit. Rev. Anal. Chem. 2006, 36, 163–176. (24) Stognauer, H.; Kraskov, A.; Astakhov, S. A.; Grassberger, P. Phys. Rev. E 2004, 70, 066123. (25) Astakhov, S. A.; Stogbauer, H.; Kraskov, A.; Grassberger, P. Anal. Chem. 2006, 78, 1620–1627. (26) Hyvarinen, A.; Oja, E. Neural Networks 2000, 13, 411–430. (27) Pedersen, H. T.; Bro, R.; Engelsen, S. B. J. Magn. Reson. 2002, 157, 141– 155. (28) Bro, R. Crit. Rev. Anal. Chem. 2006, 36, 279–293. (29) Alm, E.; Bro, R.; Engelsen, S. B.; Karlberg, B.; Torgrip, R. J. O. Anal. Bioanal. Chem. 2007, 388, 179–188. (30) Liangfeng, G.; Garland, M. Appl. Spectrosc. 2007, 61, 148–156.

Figure 2. Representative conventional Raman (a) and inverse SORS (b) spectra of plastic slabs (Teflon) with a surface layer of white paper. Black trace, thickness 100 µm; gray trace, thickness 300 (conventional) or 600 µm (SORS).

lies in the region of 730 cm-1 while that of paper (“surface”) occurs at ∼1100 cm-1. For each thickness of overlayer, 10 duplicate spectra were collected. For both experimental arrangements, the intensity of the Teflon band drops rapidly with increasing thickness of the surface layer. On visual inspection, the SORS experiment offers substantially higher penetration than conventional Raman, a conclusion that is confirmed and quantified by PCA. The scores on the second principal axis (Figure 3) indicate that SORS has approximately twice the penetration depth of conventional Raman (800 versus 400 µm) under these conditions, a direct consequence of the ability of SORS to suppress interfering surface Raman and fluorescence signals, which restrict the “visibility” of signals from deeper layers. At thicknesses beyond these limits, the scores (and the spectra) are essentially invariant. The second principal axis (not shown) displays an inverse relationship between the surface and subsurface spectra. It should also be noted that the arrangement used here for conventional Raman is significantly less sensitive to surface effects than a commercial Raman spectrometer in which the laser is far more tightly focused on the sample,31 a geometry resulting in a substantial bias toward surface born Raman and fluorescence signals. Hence, the estimate for the penetration depth of conventional Raman quoted here represents an upper limit. (31) Pelletier, M. J. Analytical Applications of Raman Spectroscopy;Blackwell Science: Oxford, 1999.

Figure 3. Principal component analysis of conventional Raman (a) and inverse SORS (b) spectra of plastic slabs (Teflon) with white paper overlayer. Plot of score on second principal component versus thickness of surface layer. The spectra were baseline corrected and normalized to unit length.

Within the limits of penetration depth, it was possible to quantitatively predict the thickness of the surface layer using regression analysis. Partial least-squares regression models were constructed using the points below the maximum thickness (100-400 (conventional) and 100-800 µm (SORS)); typically one or two latent variables (selected using cross-validation of randomly selected subsets) were required. Regression vectors (not shown) show an inverse correlation between the principal bands of the surface (∼1100 cm-1) and subsurface (∼730 cm-1) components. Predicted and measured thicknesses for both conventional Raman and SORS are shown in Figure 4. For both methods, good agreement is found between predicted and measured values; rootmean-square errors of cross-validation (RMSECV) using random subsets were 3 (conventional) and 26 µm (SORS). Surface thicknesses beyond the observable limits (400 or 800 µm) gave essentially the same value when the model was applied. The greater accuracy of conventional Raman (∼2 versus 7% relative accuracy) is a consequence of the superior signal-to-noise ratio (see Figure 2) since both SORS and conventional spectra were recorded using the same laser power and acquisition times; degradation of the predictive accuracy (or increased signal collection times) comes with the potential to explore deeper into the sample. Analytical Chemistry, Vol. 80, No. 21, November 1, 2008

8149

Figure 5. Inverse SORS spectra (middles traces) of bone with a tissue (porcine) overlayer (1-4 mm thick) recorded using a spatial offset of 3 mm. The spectra were baseline corrected and normalized to unit length. The upper and lower traces show reference spectra of pure tissue and bone. The arrows indicate the relative change in peak height of bands representative of the surface (∼1450 cm-1) and subsurface (∼950 cm-1) layers with respect to surface layer thickness.

Figure 4. Partial least-squares regression analysis of conventional Raman (a) and inverse SORS (b) spectra of plastic slabs (Teflon) with white paper overlayer. Plot of predicted versus measured thickness; the dotted line indicates the diagonal. The spectra were baseline corrected, normalized to unit length, and mean centered. Calibration models were constructed using the ranges 100-400 (conventional) and 100-800 µm (SORS) and applied to the full data set. The number of latent variables (1 or 2) was selected using crossvalidation of random subsets.

Similar results are found for samples of bone with an overlayer of soft tissue.10 Inverse SORS spectra (spatial offset ∼3 mm) collected with varying thicknesses of surface layer are shown in Figure 5. Also shown are reference spectra of bare bone and tissue. The characteristic band of bone (the phosphate ν1 mode at ∼950 cm-1) decreases rapidly with increasing thickness while bands due to the overlying tissue (principally collagen, e.g., phenylalanine ring breathing mode at ∼1000 cm-1 and CH2 bending/deformation modes at ∼1450 cm-1), display an increase in relative intensity. PCA and PLS analyses indicate quantifiable (RMSECV ) 0.3 mm, ∼10% relative accuracy) results up to a thickness of 5 mm of overlying soft tissue (Figure 6). This limit on penetration depth is similar to that obtained by Schulmerich et al.5,10 using a similar experimental arrangement in combination with multivariate curve resolution using BTEM. The BTEM algorithm was applied to both systems; resolved spectra (surface thickness of 400 µm (Teflon) and 3 mm (bone)) 8150

Analytical Chemistry, Vol. 80, No. 21, November 1, 2008

are shown in Figure 7 (upper traces) while the middle traces show reference spectra of bare Teflon and bone. The targeted bands were ∼730 cm-1 (Teflon) and the phosphate stretch (∼950 cm-1) of bone. For the bone samples, excellent agreement (crosscorrelation ratio ∼0.98) between reference and reconstructed spectra is observed. However, visual inspection reveals that separation of the tissue and bone spectra is not fully accomplished, i.e., the band at 1450 cm-1 (CH2 wagging of collagen). Similar results were observed by Schulmerich et al.10 and result from the substantial spectral overlap caused by the presence of collagen in both tissue and bone material. The metric used to obtain the spectra included non-negative constraints (imposed as a penalty function) on both spectra and concentrations. Spectra of similar quality (lower traces of Figure 7) can also be obtained via PARAFAC analysis of three-dimensional data (i.e., wavenumber by spatial offset by surface layer thickness) requiring no additional rotation of eigenvectors. The difference in the signal-to-noise ratio between the two reconstructed spectra (Figure 7) is partially due to the total acquisition times used in the individual data sets. For example, for the bone measurements, the total acquisition time for PARAFAC was 5 times longer than for BTEM. In addition, unlike BTEM, which used a 3-mm layer, the PARAFAC method utilized spectral data covering a range of thicknesses (1-5 mm) including thinner ones, where the ratio between the surface and subsurface components was more favorable. Both deconvolution methods have their own particular strengths and weaknesses.3,4,19-22,27-30 BTEM requires no information on the number of distinct layers in the system (the primary requirement is selection of a spectral band known to be specific to the layer of choice). Such information is essential for PARAFAC analysis; in contrast, however, constraints are essential to the success of BTEM but are unnecessary for PARAFAC. Addition of a third dimension necessitates an expansion in the total time for data collection, the benefit is a reduced level of noise (see

Figure 7. Deconvoluted spectra of Inverse SORS spectra of (a) plastic (Teflon) slabs with white paper overlayer and (b) bone with tissue overlayer. Upper trace: spectra decomposed using BTEM. Middle trace: reference spectra of pure sublayer. Lower trace: spectra decomposed from PARAFAC. Spectra were baseline corrected.

Figure 6. Multivariate analysis of inverse SORS spectra of bone with tissue overlayer (1-7 mm thick). (a) PCA; plot of score on the second principal axis versus thickness of surface layer and (b) PLS regression; plot of predicted versus measured thickness of surface layer, the dotted line indicates the diagonal. The calibration model was constructed using thicknesses of 1-5 mm and applied to the full data set. The number of latent variables (2) was selected using cross-validation of random subsets. Spectra were baseline corrected, normalized to unit length, and mean centered.

Figure 7) in the reconstructed spectra. In a previous study,30 Garland and co-workers found a similar agreement between twoand three-dimensional methods for absorption and fluorescence data of aromatic amino-acids; Rayleigh and Raman scattering superimposed upon the fluorescence data did not demonstrate a trilinear structure and could not be analyzed by PARAFAC. Variation across spatial offset and surface-layer thickness provides the variation necessary for trilinear behavior of Raman data. In some practical applications, however, alteration of the thickness of a surface layer may be difficult, if not impossible to achieve (for example, in vivo examination of bone through overlying skin and subcutaneous tissues). However, alternative sources of variation (e.g., the compression of soft, flexible surface layers, the enhancement effects of dielectric optical elements,32 or alteration of the focusing conditions of the laser beam onto (32) Matousek, P. Appl. Spectrosc. 2007, 61, 845–854.

the sample33) may provide the means of adding a third dimension to SORS experiments. It should be noted that the penetration depth of the technique depends on a variety of sample parameters including scattering properties and absorption as discussed in earlier theoretical work.2 To determine the thickness of the top layer none of these properties has to be known in the proposed methodologies. However, a training sample set, containing samples of known layer thicknesses, is required to establish appropriate calibration points for the technique. Alternatively, numerical simulations can be used to deduce the sample thickness by assuming knowledge of the scattering and absorption properties of the sample.2 CONCLUSIONS Raman spectroscopy has been applied for the accurate prediction of the thickness of stratified, turbid samples. Multivariate analysis (PCA and PLS regression) shows that SORS has a penetration depth at least twice that available using conventional backscattering Raman spectroscopy. The incorporation of a third, distinct dimension to a SORS experiment allows pure spectra of each layer to be extracted using parallel factor analysis. Excellent agreement is found between the extracted spectra and reference spectra of pure samples; the agreement is similar to that found via two-dimensional deconvolution methods (BTEM). The inher(33) Eliasson, C.; Claybourn, M.; Matousek, P. Appl. Spectrosc. 2007, 61, 1123– 1127.

Analytical Chemistry, Vol. 80, No. 21, November 1, 2008

8151

ent qualities of a trilinear, three-dimensional data set result in greatly reduced noise levels without the need for constraints.

contribution of CLIK Knowledge Transfer and the EPSRC (grant EP/D037662/1) is also acknowledged.

ACKNOWLEDGMENT The authors thank Dr. Darren Andrews, Dr. Tim Bestwick, and Professor Mike Dunne of the Science and Technology Facilities Council for their support of this work. The financial

Received for review June 16, 2008. Accepted August 18, 2008.

8152

Analytical Chemistry, Vol. 80, No. 21, November 1, 2008

AC801219A