Complex index of refraction of dental enamel atCO2 laser wavelengths

Gaetan Duplain, Russell Boulay, and P. A. B6Ianger

The reflectance vs angle of incidence method was used to determine the refractive index and absorption

coefficient of dental enamel at CO2 laser wavelengths. A strong wavelength dependence of the optical

constants was observed in this spectral region which corresponds to a well-known absorption band of

hydroxyapatite, the main constitutent of dental enamel. A directional dependence of the optical constants ofdental enamel was also observed. The absorption coefficient reaches a maximum between 9.75 and 10 ,um.This particularity may be important for the main CO2 laser treatments proposed in dentistry up to now:surface treatment of teeth and fusion of dental materials.

1. Introduction

Dentistry is one of the medical specialties where useof the laser is still in the research stage. Many experi-ments have been performed in this area for twentyyears. Stern1 and, more recently, Melcer et al. 2 givereviews of published work in laser experiments in den-tistry.

Applications of CO2 lasers in dentistry include CO2laser treatment of teeth (increase in the resistance ofdental enamel to demineralization) fusion of a biocom-patible dental material,4 and treatment that may in-crease the fluoride uptake of enamel.5 It is importantto determine the optical properties of dental enamel atCO2 laser wavelengths to have better control and un-derstanding of these treatments. Thus the opticalconstants n and k (complex index of refraction) ofdental enamal at CO2 laser wavelengths were deter-mined in this study.

The IR spectra of tooth enamel6 have an absorptionband in a spectral region which corresponds to CO2laser emission. It is very likely that optical propertiesof dental enamel have a strong wavelength dependencein that region. A study of the optical properties ofdental enamel have many implications. It is suspect-

When this work was done all authors were with Laval University,Physics Department (LROL), Quebec, Quebec GlK 7P4, Canada.R. Boulay and G. Duplain are now with National Optics Institute,Sainte-Foy, Quebec G1V 4C5, Canada.

Received 14 March 1987.0003-6935/87/204447-05$02.00/0.© 1987 Optical Society of America.

ed that there is a CO2 laser wavelength at which theabsorption coefficient reaches a maximum. This factcould be important for surface treatment of teethwhere the radiation-matter interaction occurs at thefirst layers of the material. On the other hand, it mayhave consequences on thermal effects that are associ-ated with the vitality of teeth given that the tempera-ture inside a laser radiated tooth is dependent on theabsorption coefficient.

II. Optical Properties of Dental Enamel

Dental enamel is the tissue that covers the outerportion of the tooth crown. It is composed of hydroxy-apatite, a mineral substance [Calo(PO4)6(OH)2] whichforms the principal component of the tooth. The hy-droxyapatite of enamal has a crystalline form and isarranged in prisms or enamel rods. The orientation ofthe prisms tends to be nearly perpendicular to thesurface. In cross section, the prisms have a keyholeshape where the head part or round part points towardthe biting surface of the tooth and the tail part pointstoward the gum. The hydroxyapatite crystals withinone prism have their optics axis (c axis) oriented in adifferent manner. The c axis of the crystals is orientedparallel to the long axis of the prism in its head partand nearly perpendicular in its tail part. Followingthis representation, the hydroxyapatite crystals can beapproximately divided into two groups: one withtheir c axis parallel to the long axis of the tooth and theother with their c axis perpendicular to the long axis ofthe tooth as well as the surface.

Dental enamel is an absorbing material at CO2 laserwavelengths, which can be seen from the IR spectra. 6

The oriented structure of enamel causes a certain anis-tropy of the optical constants. Therefore, n and k may

15 October 1987 / Vol. 26, No. 20 / APPLIED OPTICS 4447

change with the orientation of the electric vector asso-ciated with the polarized CO2 laser beam. This as-sumption has been verified in a previous study.7

I1. Determination of Optical Constants from ReflectanceR Measurements at Oblique Incidence

Reflectance R measurements at oblique incidencewith polarized light for a semi-infinite medium is oneof the photometric methods that can be used to deter-mine n and k. The strong absorption of dental enamelin the spectral region of interest did not allow for theuse of the reflectance-transmittance (R,T) method de-scribed by Nestell and Christy,8 which is, in general,more accurate than the reflectance R method.9 RIand R represent the perpendicular and parallel reflec-tance, respectively. The equations R 1 and R11 for asemi-infinite medium are given by Humphreys-Ow-ens.10 These equations cannot generally be solvedexplicitly for n and k; hence graphic or numericalmeans must be used to solve them.'1 The graphicmethod described by Humphreys-Owen'0 used in thepresent study is based on two reflectance measure-ments at different angles of incidence. This methodgives fairly accurate values for n and k. These valuesserve as starting points for a numerical method thatcalculates the best fit for all the measurements takenat different angles of incidence.

IV. Apparatus

The apparatus used for the measurements is shownin Fig. 1. The laser source is a tunable polarized cwCO2 laser. Laser pulses of 10 ms are obtained with amechanical chopper at a rate of 12 cycles/s. The stateof polarization is rotated by two linear polarizers. Aportion of the chopped CO2 laser beam is reflected by abeam splitter onto a reference detector for normaliza-tion purposes. The remaining radiation is reflectedonto the sample, which is mounted on a goniometerwhose movable arm carries a second detector for re-flectance measurements. The lenses are used to con-trol the size of the laser beam incident on the sampleand detectors. Signals from the detectors are fed to amultichannel peak detector and then processed by ananalog-to-digital converter. The data are processedby an Apple Ie microcomputer. Each measurementis an average of thirty CO2 laser pulses.

V. Samples

Bovine teeth were used to measure the optical con-stants of enamel instead of human teeth; experimentalconstraints dictated this choice. To obtain a flatenamel surface for reflectance measurements, a por-tion of the curved surface of the tooth was polished. Inthis case, the enamel layer of the tooth must be thickenough to obtain a sufficiently large reflecting areafrom the curved surface. Also, the thickness of enamellayer must be so that a semi-infinite medium can beassumed.12 For these reasons, bovine teeth were usedbecause they have a thicker layer of enamel than hu-man teeth. Moreover, the enamel surface must bequite larger than the laser beam, since the effective

DG Co2 M C P P

g-'M-zY -\SBS

Fig. 1. Schematic diagram of the experimental system consisting ofCO2laser: diffraction grating, DG; germanium coupler, M; mechan-ical chopper, OC; polarizers, P; beam splitter, BS; sample S on agoniometer; pyroelectric detectors, D 1, D2; germanium lenses, L1 -L3;

interface, I; and microcomputer MC.

aperture of the reflection surface decreases as the angleof incidence increases. The size of the laser beam canbe reduced by focusing, but other constraints arise. Infact, the energy density at the surface of the tooth hadto be limited to prevent heating that could alter itsstructure or its composition. This limits beam focus-ing. These constraints could be partially eliminatedby reducing the output power of the CO2 laser; howev-er, the signal levels of the detectors were brought closerto the noise level of the data acquisition system.These constraints suggest the use of bovine teeth,whose enamel surface is larger than human teeth.Concerning the similarity between human and bovineteeth, histochemical and comparative anatomicalstudies have shown that all mammalian teeth are es-sentially the same.'3

A plane surface of enamel with dimensions of -8 X11 mm was obtained from polishing the tooth surfacewith diamond paste of 1-,gm grain size. Diffusionoccurred if polishing had been done with larger grainsize. The initial experiments were performed withadult bovine incisors kept in water. After two weeks, aconstant decrease in reflectance was observed. Thiswas probably due to enamel deterioration in water.' 4

This problem was overcome by keeping the bovineincisors in a formaldehyde-glycerol-water solution.

VI. Experimental Procedure

The measurements were obtained according to thefollowing procedure. First, the incident energy wasmeasured, and then the tooth was placed on the goni-ometer table. After its normal incidence position wasdetermined, reflectance measurements were taken forparallel and perpendicular polarizations and for inci-dent angles of 15-70° at 5 increments. This proce-dure was done for the following two orientations of thetooth: the longitudinal axis of the tooth parallel to theplane of incidence and the longitudinal axis perpendic-ular to the plane of incidence. Thus changes in reflec-tance for two different orientations of the tooth couldbe measured.

VII. Results

A. Preliminary Results

Figure 2 shows typical reflectance measurementsobtained at 9.209-Am wavelength and parallel polar-

4448 APPLIED OPTICS / Vol. 26, No. 20 / 15 October 1987

I D,

0.5

Li

0

Li

cr

0.4

0.3

0.20 10 20 30 40 50 60 70 80 90

INCIDENCE ANGLE (DEGREES)Fig. 2. Angular reflectance of dental enamel for 9.209-,um radiation

polarized parallel to the plane of the incidence: full line, calculateddata; dots, experimental data.

0.5

Ld

I)Li

Lij

0.4

0.3

0.20 10 20 30 40 50 60 70 80 90

INCIDENCE ANGLE (DEGREES)Fig. 3. Angular reflectance of dental enamel for 9.317-jim radiationpolarized parallel to the plane of the incidence: full and dotted line,

calculated data for two samples; 0 and X, experimental points.

ization. The dots represent experimental data, andthe solid line represents the reflectance curve calculat-ed from n and k. Since these optical constants weredetermined by experimental data, the results fit wellwith the calculated data. Furthermore, Fig. 3 showstwo parallel reflectance measurements obtained fromtwo different samples (two teeth coming from differentindividuals) at 9.317-,gm wavelength. The reflectancemeasurements were repeatable to within +1% absoluteuncertainty, even for different samples.

The near-normal-incidence reflectance of dentalenamel at various CO2 laser wavelengths is shown inFig. 4. These measurements were obtained by sweep-ing the CO2 laser emitting lines while the sample waskept at 150 angle of incidence. The reflectance variesbetween 10 and 50%, depending on the wavelength.These results were compared to the IR spectra of hy-droxyapatite (Fig. 5). Vibrational modes of this mole-cule give rise to an absorption band in the 9-11-Amregion, which has been assigned to three P0 4 stretch-ing modes15 (see arrows in Fig. 4). Small reflectancevariations at those wavelengths were observed. Thisis not unusual since the composition of enamel is 90%hydroxyapatite.

The wavelength dependence of the reflectanceshown in Fig. 4 also indicates the wavelength depen-dence of n and k. This can be qualitatively seen with

0.6

0.5

Li0z60(_1Li

Ld

WAVELENGTH (m)

11.0 10.5 10.0 9.5 9.0

0.4 _

0.2 _

0.1

0 . 0850 900 950 1000 1050 1oo 1150

WAVENUMBER (cm-')Fig. 4. Dental enamel reflectance vs CO2 laser wavelengths (wave-numbers) for an angle of incidence of 150 and radiation polarizedparallel to the plane of incidence. Longitudinal axis of the tooth isparallel to the plane of incidence. Arrows indicate vibrational

modes of hydroxyapatite.

L1Z;

zU

500 '000 1500 2000

WAVENUMBER (cm-')Fig. 5. Infrared spectra of hydroxyapatite.1 5

reference to a well-known model, the Lorentz model.From this model, the classical theory of absorption anddispersion for insulators1 6 can be derived; hence dis-persion curves for n and k were obtained as shown inFig. 6. Maximum attenuation (region II) occurs be-side maximum reflectance (region III). Applying thismodel to the current reflectance results means thatmaximum attenuation will probably occur between the9P and IOR CO2 laser emitting bands. The results forthe optical constants of dental enamel of the presentstudy corrobate this assumption.

B. Optical Constants of Dental Enamel

Optical constants of dental enamel at CO2 laserwavelengths are listed in Table I. All the refractiveindices listed here were derived from reflectance mea-surements taken with radiation polarized parallel tothe plane of incidence as well as the longitudinal axis ofthe tooth. The data are graphically reproduced in Fig.7.

Vil. Discussion

Figure 7 shows that the dispersion behavior of n andk tends to be as the Lorentz model suggested earlier.The dispersion curves (dashed lines) that could bederived from the Lorentz model have been traced onthis figure. Maximum absorption or attenuation oc-curs between the 9P and 1OR bands or more precisely

15 October 1987 / Vol. 26, No. 20 / APPLIED OPTICS 4449

fo266,P1

t

,' 'Il

11-1.111111-1

4.TREFLECTANCE

n,k

T ' R

WAVENUMBER -Fig. 6. Dispersion curves (full lines) for n and k and reflectivitycurve (dashed line) given by the Lorentz model. The regions I, II,III, and IV are seen to be primarily transmitting T, absorbing A,

reflective R, and transmitting T, respectively.16

Table I. Optical Constants of Dental Enamel; a (4irk)/X

Spectralline MgUm) n k a(jml)

9R32 9.209 0.62 + 0.02 1.19 0.03 1.629R30 9.219 0.64 + 0.02 1.20 + 0.03 1.649R28 9.229 0.63 + 0.02 1.21 + 0.03 1.659R26 9.240 0.65 0.02 1.23 0.03 1.679R24 9.250 0.66 0.02 1.22 0.03 1.669R22 9.261 0.66 4 0.02 1.26 0.03 1.719R20 9.272 0.65 E 0.02 1.26 + 0.03 1.719R18 9.282 0.63 0.02 1.25 0.03 1.699R16 9.294 0.68 E 0.02 1.34 0.03 1.819R14 9.306 0.68 0.02 1.37 0.03 1.859R12 9.317 0.68 0.02 1.39 0.03 1.879R10 9.329 0.68 4 0.02 1.41 0.03 1.909R8 9.341 0.68 4 0.02 1.44 ± 0.03 1.949P8 9.458 0.97 0.04 1.92 0.04 2.559P10 9.473 0.98 0.04 1.91 0.04 2.539P12 9.488 1.00 + 0.04 1.92 + 0.04 2.549P14 9.505 1.05 0.04 1.97 0.04 2.609P16 9.520 1.12 0.04 2.05 0.04 2.719P18 9.536 1.16 4 0.04 2.09 0.04 2.759P20 9.552 1.20 0.04 2.17 0.04 2.859P24 9.586 1.39 E 0.04 2.29 0.04 3.009P28 9.621 1.48 0.04 2.31 0.04 3.139P34 9.677 2.25 0.04 2.52 0.04 3.27

1OR32 10.171 2.43 0.03 0.46 0.06 0.57lOR26 10.208 2.27 d 0.03 0.59 0.06 0.731OR20 10.247 2.26 0.03 0.46 0.06 0.561OR10 10.319 2.11 d 0.03 0.53 0.06 0.651OR8 10.333 2.12 0.03 0.49 0.06 0.6010R6 10.350 2.10 0.03 0.48 ± 0.06 0.581OP6 10.457 2.12 4 0.03 0.51 0.06 0.611OP12 10.514 2.10 0.03 0.46 0.06 0.551OP18 10.571 2.07 4 0.03 0.48 0.06 0.571OP24 10.632 2.02 0.03 0.44 0.06 0.521OP30 10.697 1.96 0.03 0.46 0.06 0.541OP32 10.719 1.94 0.03 0.48 0.06 0.561OP34 10.742 1.95 0.03 0.43 0.06 0.501OP36 10.765 1.93 0.03 0.48 0.06 0.56

between 9.75 and 10 gim. The optical constants havenot been measured in this region since the gain of theCO2 laser with 16012C160 isotope was too weak to per-mit a laser emission. However, another isotope of theCO2 molecule might be used. It is then possible tochange the wavelength emission of the CO2 laser bandsto have a laser emission in the region mentioned. Itseems to be the 18013C180 isotope that would provide

4

3

n,k 2

L85C

WAVELENGTH (/.Lm)

11.0 10.5 10.0 9.5 9. 0

900 950 1000 1050 1100 1150

WAVENUMBER (cm-')Fig. 7. Real and imaginary parts of the complex indices of refrac-tion of dental enamel at CO2 laser wavelengths. Dashed lines repre-

sent dispersion curves from the Lorentz model.

these wavelengths.'7 For example, an increase in theabsorption in the 9P band of the CO2 laser can bemeasured since the attenuation coefficient a is muchhigher in the 9P than in the 1OR band. At 9.68 ,gm, theattenuation is about sixteen times (e3 3Ie0 .52) greaterthan the one at 10.6 gum, and a factor of "30 times canbe expected with the use of a different isotope CO2laser. This comparison is important since 10.6 gm isthe standard wavelength used in the CO2 laser becauseit has its highest gain at this wavelength. The litera-ture of experimental studies on CO2 laser applicationsin dentistry shows this laser was used at 10.6 gim. It ispossible that different effects may be produced onteeth, depending on the CO2 laser wavelength. Specif-ically, better surface treatment is possible due to agreater attenuation coefficient for a specific wave-length. It might also have consequences in other ap-plications like fusion of dental materials and fluorideuptake of enamel.

The optical properties of dental enamel also dependon the orientation of its structure. Figure 8 shows thereflectance measurements obtained for two differenttooth orientations of both parallel and perpendicularpolarizations. The variations in reflectance can be asgreat as 10%. The highest variation was observed inthe 9P band. The resulting changes in optical con-stants are mainly attributed to a variation in n; a moredetailed discussion can be found in Duplain.7 Kravitzet al.' 8 give the polarized reflectance spectra of fluor-oapatite [Cajo(PO4)6F2] crystal in the infrared regionof the corresponding vibrational modes of P0 4. Theirresults show that reflectance taken with radiation po-larized parallel to the c axis of the crystal is higher thanthat taken with radiation polarized perpendicular tothe c axis. Given the near-normal-incidence results ofFig. 8, it can be seen that the reflectance of the teethfollows the same behavior if the crystal orientationdescribed previously is taken into account. Fowlerand Kuroda'9 also discuss the possibility of wavelengthselective reaction by CO2 lasers and the possible direc-tional dependence of the optical properties of dentalenamel. The results of the present study confirm theirassumptions.

4450 APPLIED OPTICS / Vol. 26, No. 20 / 15 October 1987

.I

, 1 I

I I

n i i~

00110 0 ,

I I

I # II¢¢ f t

B

. . . .

I

o

0.8 ,--

0.7 _

W

a)U~-W

W

O.6 F

0.5 -

0.4 _

0.3 F

0.2

0.8

0.7

b)

WU-z8-C-,Uj-JU-Ur

0.6

0.5

0.4

0.3

0.2

1 10 20 30 40 50 60 70 B0 90

INCIDENCE ANGLE (DEGREES)

tI

* I

t I

* *II 8 8

. I + + 8

l l l l l l l8

0 10 20 30 40 50 60 70 80 90

INCIDENCE ANGLE (DEGREES)Fig. 8. Reflectance vs incidence angle for 9.272-Am radiation polar-ized parallel (a) and perpendicular (b) to the plane of incidence: X,longitudinal axis of the tooth perpendicular to the plane of inci-

dence; 0, parallel to the plane of incidence.

IX. Conclusion

The optical constants n and k of dental enamel atCO2 laser wavelengths were determined using a reflec-tance method. A strong wavelength dependence of nand k was obtained in this spectral region which corre-sponds to a well-known absorption band of hydroxyap-atite, the main constituent of dental enamel. Thismay be important for updating the main CO2 lasertreatments in dentistry: surface treatment and fusionof dental materials. The attenuation is much higherin the 9Pband than at 10.6 gim. The attenuation couldbe optimized if one uses a proper isotopic species ofCO2 laser which can emit between 9.75 and 10 gim,where attenuation reaches a maximum. A directionaldependence of the optical properties of dental enamelwas also observed. The results of this study may con-tribute to better control of CO2 laser treatments indentistry. Fowler and Kuroda's recent paper'9 aboutthe properties of CO2 lasers in reducing caries and theiruse at a particular wavelength gives more weight to theresults of our work.

References1. R. H. Stern, "The Laser in Dentistry: A Review of Literature,"

J. Dent. Assoc. S. Afr. 29, 173 (1974).2. J. Melcer, F. Melcer, R. Merard, R. Hasson, C. Freche, and J.

Gautier, "Utilisation du laser en odontologie," Innov. Tech.Biol. Med. 2, 67 (1981).

3. R. H. Stern and R. F. Sognnaes, "Laser Inhibition of DentalCaries Suggested by First Test In Vivo," J. Am. Dent. Assoc. 85,1087 (1972).

4. L. Stewart, G. L. Powell, and S. Wright, "Hydroxyapatite At-tached by Laser: A Potential Sealent for Pits and Fissures,"Oper. Dent. 10, 2 (1985).

5. R. Boehm, T. Baechler, J. Webster, and S. Janke, "Laser Pro-cesses in Preventive Dentistry," Opt. Eng. 16, 493 (1977).

6. S. Kuroda and B. 0. Fowler, "Compositional, Structural andPhase Changes in In Vitro Laser-Irradiated Human Tooth Ena-mel," Calcif. Tissue Int. 36, 361 (1984).

7. G. Duplain, "D6termination des indices de refraction de l'6maildentaire aux longueurs d'onde du laser C0 2," Master of ScienceThesis, Laval U., Quebec City, Canada (Oct. 1986).

8. J. E. Nestell, Jr., and R. W. Christy, "Derivation of OpticalConstants of Metals from Thin-Film Measurements at ObliqueIncidence," Appl. Opt. 11, 643 (1972).

9. L. Ward, "The Accuracies of Photometric, Polarimetric andEllipsometric Methods for the Optical Constants of ThinFilms," Opt. Laser Technol. 263 (Oct. 1985).

10. S. P. F. Humphreys-Owens, "Comparison of Reflection Meth-ods for Measuring Optical Constants without PolarimetricAnalysis, and Proposal for New Methods Based on the BrewsterAngle," Proc. Phys. Soc. 77, 949 (1961).

11. W. R. Hunter, "Errors in Using the Reflectance vs Angle ofIncidence Method for Measuring Optical Constants," J. Opt.Soc. Am. 55, 1197 (1965).

12. W. R. Hunter and G. Hass, "Thickness of Absorbing FilmsNecessary to Measure Their Optical Constants Using the Re-flectance vs Angle of Incidence Method," J. Opt. Soc. Am. 64,429 (1974).

13. I. Nakamichi, M. Iwaku, and T. Fusayama, "Bovine Teeth asPossible Substitutes in the Adhesion Test," J. Dent. Res. 62,1076 (1983).

14. S. Smith, School of Dental Medicine, Laval U.; private commu-nication (1986).

15. B. 0. Fowler, "Infrared Studies of Apatites. I. VibrationalAssignments for Calcium, Strontium and Barium Hydroxyapa-tite Utilizing Isotopic Substitution," Inorg. Chem. 13, 194(1974).

16. F. Wooten, Optical Properties of Solids (Academic, New York,1972).

17. L. C. Bradley, K. L. Soohoo, and C. Freed, "Absolute Frequen-cies of Lasing Transitions in Nine CO2 Isotopic Species," IEEEJ. Quantum Electron. QE-22, 234 (1986).

18. L. C. Kravitz, J. D. Kingsley, and E. L. Klein, "Raman andInfrared Studies of Couple P04 -3 Vibrations," J. Chem. Phys.49, 4600 (1968).

19. B. 0. Fowler and S. Kuroda, "Changes in Heated and in Laser-Irradiated Human Tooth Enamel and Their Probable Effects onSolubility," Calcif. Tissue Int. 38, 197 (1986).

This project was funded by federal (NSERC) andprovincial (FCAR) research agencies.

We are grateful to S. Smith from the School of Den-tal Medicine (Laval University) for basic informationin dental anatomy and for his continuous support ofthe project.

15 October 1987 / Vol. 26, No. 20 / APPLIED OPTICS 4451

8 8.~~~~~~~~~~~~~

888 8