www.spectroscopyonl ine.com22 Spectroscopy 19(10) October 2004

Raman spectroscopy is useful for studying the chemicalstructure of systems ranging from simple chemicalsand plastics to biological structures. It is equallyinformative on physical properties such as crystal

form, crystal size, molecular orientation, interactions anddynamics, and stress. For this reason, Raman microscopy isone of the techniques of choice for investigating heteroge-neous systems on the micrometer scale. The Raman micro-scope focuses a laser beam down to a small volume (on theorder of 1 µm3 in air) and is operated readily in a confocalmode by placing an aperture at a back focal plane of themicroscope (1). The aperture improves the lateral and axialspatial resolution of the microscope, allowing nondestructivedepth profiling by acquiring spectra as the laser focus is movedincrementally deeper into a transparent sample (2). Thisapproach often is termed “optical sectioning,” as opposed tomechanically cutting a cross-section (microtomy) and scan-ning the laser beam laterally across the section. Because opti-cal sectioning avoids the need for any sample preparation,numerous authors have applied it to the study of layered orgraded systems and of phenomena at buried interfaces (2–10).Its noninvasive character makes it attractive particularly forthe study of biological tissues (3, 10).

Confocal Raman microscopy can be applied in two ways.The first involves plotting the intensity of a component-spe-cific band as a function of the distance from the sample sur-face. This reveals compositional or structural gradients as adepth profile. The second approach is to attempt to acquire apure spectrum of a buried structure for identification purpos-es. Both of these applications require knowledge of the exactsize and position of the microscope focal volume as it movesdeeper into the sample, and this requires a detailed analysisthat has been, until recently, largely ignored in the literature.

The purpose of this two-part article series is to review theissues that must be considered to interpret confocal Ramandata correctly, and to present recent work demonstrating theextent to which depth resolution is degraded when focusingdeep within a sample. The surface specificity of the techniquealso is discussed with particular regard to some unusual inten-sity variations that occur when focusing near a sample surface.

Metallurgical Objectives and RefractionAlmost every basic text or research publication that discussesthe principles of confocal Raman microscopy includes a dia-gram similar to Figure 1 to indicate how a confocal apertureimproves depth resolution. The depth resolution primarilydepends upon two factors — the volume of the laser focus(Figure 1a) and how Raman photons generated within thisvolume are relayed back into the spectrometer via the confocalaperture (Figure 1b). The laser focus appears at point C inFigure 1a. In nontransparent media, scattering makes the focusmore diffuse, spreading from A to B and degrading the depthresolution. Placing an aperture at a back focal plane of the sys-tem should improve the depth resolution by only transmittingthose rays that originate near point C.

According to Juang et al. (11), the limiting resolution DR isgiven by equation 1, where n is the refractive index of theimmersion medium, λ is the laser wavelength, and NA is thenumerical aperture of the focusing lens.

Depth Profiling With ConfocalRaman Microscopy, Part IRaman microscopy is one of the techniques of choice for investigating heterogeneous sys-tems on the micrometer scale. Part I of this two-part article series reviews the issues thatmust be considered to interpret confocal Raman data correctly.

Neil Everall

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OTO

DIS

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Equation 1, taken literally, impliesthat the depth resolution improvesmonotonically as NA increases. Forexample, with a 514.5-nm laser and anobjective with NA = 0.95, the expecteddepth resolution is 0.6 µm (12).Tabaksblat et al. (4) made calculationsand practical determinations of thedepth resolution as a function of thenumerical aperture of the objective, themicroscope magnification, and the sizeof the pinhole, and concluded that a res-olution of ~2 µm was obtained with a100X objective and a 100-µm pinhole.On the basis of this kind of analysis onewould expect that confocal Ramanmicroscopy can be used to obtain depthprofiles with an axial resolution deter-mined only by the objective numericalaperture, the magnification, and thepinhole size, irrespective of how deeplyone focuses below the sample surface.Unfortunately, the simple tests that usu-ally are applied to test the depth resolu-tion reinforce this incorrect assumptionand give misleading results. These testsinvolve measuring the intensity of

Raman scatter of either a very thin oropaque sample as it is translatedthrough the laser focus along the beampropagation axis (usually the surfacenormal). Throughout this paper wedefine the sample displacement alongthis axis by the symbol ∆, which we termthe axial displacement. In practicalterms it corresponds to the displace-ment of the microscope stage, inmicrometers, relative to the positionwhere the laser is focused on the sampletop surface. If ∆ = 0, the laser beam isfocused on the air–sample interface, andpositive values of ∆ imply sample move-ment opposite to the beam propagationdirection (that is, moving the laser focusinto the sample). Figure 1b shows theresponse as a 0.9-µm thick film of PET(polyethyleneterephthalate) was trans-lated through the focus of a 633-nmlaser beam focused by a 0.9-NA, 100Xmetallurgical objective. The full widthat half maximum (fwhm) of the profilewas 1.1 µm, implying excellent depthresolution for this instrumental config-uration. For a very thin or opaque sam-

Raman Microscopy

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Figure 1. (a) Schematic showing opera-tion of a confocal aperture, blockingradiation from points A and B and allow-ing light from point C to pass to thespectrometer, thereby improving axialresolution. (b) Simplified test of axialresolution, translating a thin-film PETsample through the laser focus.

ple, this essentially maps out the axialintensity profile in air (not as it appearsdeep within a transparent sample).

Unfortunately, the configurations

shown in Figure 1 are not representativeof confocal Raman microscopy as it isnormally practiced — that is, with ametallurgical objective focused into athick (>1 µm) sample immersed in air.Metallurgical objectives are designed tofocus on the surface of opaque samples,but when focusing beneath the surfaceof a sample with n >1, the light rays are

refracted and the laser intensity distribu-tion becomes shifted and distorted.Figure 2 illustrates the problem. Any raythat passes into a sample immersed inair will suffer refraction through anangle determined by Snell’s Law:sin θi/sin θt = n, where θi and θt are theangles of incidence and transmissionwith respect to the surface normal. Inthe absence of refraction the ray wouldcome to a focus at a distance ∆ below thesample/air interface, but when n >1, the

focal point lies deeper, at z. The ratio ofrefracted and nonrefracted focal depthsis given by z/∆ = tan θi/tan θt, whichtends to n as θi tends to zero. Therefore,z/∆ has a minimum value of n, andincreases as θi becomes larger. To cor-rectly interpret confocal Raman depthprofiles one obviously must take thisspread in focal positions into account.

The first step in analyzing the impor-tance of this effect is to calculate thefocal depth as a function of the radialcoordinate of each ray leaving the objec-tive (see Figure 3). Neglecting diffrac-tion, this has a simple analytical solution(13) (see equation 2).

Here rk is the radius of origin of the kth

ray, NA is the numerical aperture of theobjective (nsin θi), rmax is the maximumradius accessible to a ray, the fractionalradius m = rk/rmax, and ∆ is defined above.

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Figure 2. Schematic showing the shiftin laser focus due to refraction, whichcan be quantified using Snell’s Law.

SEVERAL ISSUES MUST BE CONSIDERED TO INTERPRET

CONFOCAL RAMAN DATA CORRECTLY.

Raman Microscopy

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Equation 2 gives thetrue point of focus zm

for a ray originatingat m. It is obvious thatrays that originate atdifferent radii on theobjective are focusedto a different depth,(spherical aberra-tion). In the paraxiallimit (mÕ0), thenz0/∆ = n, in agree-ment with the discus-sion of Figure 2above. To summarize,the ratio of therefracted and non-refracted focal depths(zm/∆) increases withboth m and NA, soone expects thespherical aberration

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Figure 3. Calculating the depth of focus (z) of a rayas a function of its radial position on the objectivelens. Marginal rays are focused much deeper thanparaxial rays.

Figure 4. Laser axial intensity profiles calculated as a function of ∆ for a 0.9-NA objec-tive and a refractive index of approximately 1.5. (Redrawn with permission from Figure 5of reference 13.)

to be worsened at large NA values.Defining the depth resolution (DR)

as the difference between the maximumand minimum depths of focus,

DR = zm=1 – zm=0

(see equation 3).Equation 3

implies that thedepth resolutionshould degradelinearly as wefocus deeperbelow the surface(∆). It also impliesthat increasing thenumerical aper-ture yields a worsedepth resolution(DR tending toinfinity as NAapproaches 1).This runs counterto the effect of dif-fraction (equation1), and if the NA isreduced too muchthen broadening

due to diffraction will dominate.In brief, the important conse-

quences of equations 2 and 3 are thatwe always are focused deeper than the

microscope scale would indicate, andthe axial laser focus broadens uponmoving deeper into the sample.Assuming a Gaussian laser intensityprofile across the microscope objectivewe can use equation 2 to map the radi-al intensity distribution across the lensinto the axial intensity distribution(I(z)), as a function of ∆ (13). Figure 4shows the broadening of I(z) withincreasing ∆. When focusing to a nom-inal depth ∆ = 10 µm with a 0.9-NAobjective, one actually illuminatesbetween 15 and 27 µm below the sam-ple surface. This means that great caremust be exercised when interpretingconfocal Raman intensity profiles. Theconsequences of neglecting theseeffects have been discussed in detailelsewhere (13, 14).

Figure 5 illustrates the practicalconsequences using the simplest possi-ble system, a single layer of a uniformpolymer film. The raw intensity profileincorrectly indicates that the filmthickness is ~6 µm, rather than thecorrect value of 12 µm. This is in quite

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Figure 5. Measured and calculated intensity response fora 12-µm thick PET film as a function of axial displace-ment ∆. Note the apparent compression of the depthscale compared to the true thickness. (Redrawn withpermission from Figure 3 of reference 14.)

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good agreement with the calculated response curve.Calculated intensity profiles generally have been shown tobe in good agreement with the observed data for a number

of coated films and laminates (13, 14), indicating that thisvery simple model provides a reasonable predictive tool forcomputing the expected profile. This foreshortening of theraw depth profile has been confirmed subsequently by anumber of workers using similar experiments; only a fewexamples are quoted here for reference purposes (8, 15–17).In summary, refraction results in the depth of buried struc-tures being underestimated grossly in a raw intensity depthprofile (typically by a factor of 2 with a 0.9-NA objective,the exact factor can be calculated as a function of NA [13]).

Calculating the thickness of deeply buried layers is not

trivial because we cannot always apply a simple scaling fac-tor to calculate the true thickness. In earlier papers it wasstated that with a high NA objective, both the observedposition and the thickness of buried layers are underesti-mated badly, each by a factor of ~2 (13,14). In fact, as willbe discussed in Part II, this is not always correct; theobserved thickness depends upon the thickness of the layerand its depth below the surface, and can appear to be toothick or too thin. In other words, the apparent depth reso-lution is a function of depth within the sample. Thus prop-er modeling of the confocal profile, rather than simple scalecorrection, is recommended.

References1. P. Dhamelincourt, “Raman Microscopy,” Handbook of Vibrational

Spectroscopy, vol. 2, J.M. Chalmers and P. R. Griffiths, Eds.(John Wiley & Sons, Chichester, 2002), pp. 1149–1428.

2. P.M. Fredericks, “Depth Profiling by Microspectroscopy,”Handbook of Vibrational Spectroscopy, vol. 2, J.M. Chalmersand P. R. Griffiths, Eds. (John Wiley & Sons, Chichester, 2002),pp. 1493–1507.

3. C. Xiao, C.R. Flach, C. Marcott, and R. Mendelsohn, Appl.Spectrosc. 58, 382 (2004).

4. R. Tabaksblat, R.J. Meier, and B.J. Kip, Appl. Spectrosc. 46, 60(1992).

5. S. Hajatdoost and J. Yarwood, Appl. Spectrosc. 50, 558 (1996).6. C. Sammon, S. Hajatdoost, P. Eaton, C. Mura, and J. Yarwood,

Macromol. Symp. 141, 247 (1999).7. K.P.J. Williams, G.D. Pitt, D.N. Batchelder, and B.J. Kip, Appl.

Spectrosc. 48, 232 (1994).8. H. Reinecke, S.J. Spells, J. Sacristan, J. Yarwood, and C. Mijangos,

Appl. Spectrosc. 55, 1660 (2001).9. N. Everall, K. Davis, H. Owen, M.J. Pelletier, and J. Slater, Appl.

Spectrosc. 50, 388 (1997).10. P.J. Caspers, G.W. Lucassen, and G.J. Puppels, Biophys. J. 85,

572 (2003).11. C.B. Juang, L. Finzi, and C.J. Bustamante, Rev. Sci. Instrum. 59,

2399 (1988).12. J. Barbillat, P. Dhamelincourt, M. Delhaye, and E. da Silva, J.

Raman Spectrosc. 25, 3 (1994).13. N.J. Everall, Appl. Spectrosc. 54, 773 (2000).14. N.J. Everall, Appl. Spectrosc. 54, 1515 (2000).15. J. Vyorykka, M. Halttunen, H. Iitti, J. Tenhunen, T. Vuorinen, and

P. Stenius, Appl. Spectrosc. 56, 776 (2002).16. L. Baia, K. Gigant, U. Posset, G. Schottner, W. Kiefer, and J.

Popp, Appl. Spectrosc. 56, 536 (2002).17. O.S. Fleming, K.L.A. Chan, and S.G. Kazarian, Vib. Spectrosc. 35,

3 (2004). n

Neil Everall is a research associate with the MeasurementScience Group at ICI plc (U.K.). E-mail the author at:neil_everall@ici.com.

Raman Microscopy

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BECAUSE A SIMPLE SCALING FACTOR

CANNOT ALWAYS BE APPLIED TO

CALCULATE THE TRUE THICKNESS OF A

SAMPLE’S BURIED LAYERS, PROPER

MODELING OF THE CONFOCAL

PROFILE IS RECOMMENDED.