Determination of refractive indices of opaque rough surfaces

Transcription

1 Determination of refractive indices of opaque rough surfaces Nathalie Destouches, Carole Deumié, Hugues Giovannini, and Claude Amra The refractive indices of optical materials are usually determined from spectrophotometric and ellipsometric measurements of specular beams. When the roughness of the interfaces increases, the energy in the specularly reflected and transmitted beams decreases and scattering becomes predominant. For strong roughness compared to the incident wavelength a surface does not exhibit specular reflection or transmission, making difficult the determination of the refractive index. We describe two techniques, based on scattering measurements, that one can use to determine the refractive indices of opaque inhomogeneous media Optical Society of America OCIS codes: , , The authors are with the Institut Fresnel Marseille, Unité Mixte de Recherche 6133, Centre National de la Recherche Scientifique, Ecole Nationale Supérieure de Physique de Marseille, Domaine Universitaire de St Jérôme, Marseille Cedex, France. C. Deumié s address is carole.deumie@fresnel.fr. Received 28 November 2002; revised manuscript received 4 April 2003; accepted 11 June $ Optical Society of America 1. Introduction Determining the refractive index of an optical surface is of overriding importance for many applications including the design and characterization of optical systems. When the surfaces exhibit strong reflection or transmission, the refractive index is usually obtained by goniometric, photometric, or ellipsometric measurements. However, in many other cases the samples are fully diffusive, without any specular reflection or transmission. In these cases, one cannot use standard techniques to determine the refractive indices of optical surfaces, though ellipsometric and total reflectance measurements can still provide interesting results for moderate roughness. For many applications powders and paints, vision, cosmetics, tissues..., these fully diffusive samples exhibit inhomogeneities that are responsible for both bulk and surface scattering. The problem is therefore complex because of the separation of surface and bulk effects, which has been discussed in numerous papers. 1 6 In the research reported here we simplify the approach by working at wavelengths in the absorption domain to reduce bulk scattering. 7 Therefore all samples under study are opaque, so surface scattering is predominant, and we validate the method of index determination for rough surfaces. Notice that other situations may occur in which specular beams exist but are not easy to reach. In these cases off-specular scattering measurements give useful information about the refractive indices of the surfaces. The problem of determining the index of a rough sample can be more or less complex, depending on the profile of the surface and on its roughness and homogeneity. In addition, the refractive index can be complex, with dielectric or metallic behavior. In this paper we limit ourselves to two-dimensional opaque homogeneous surfaces with plane symmetry and an average normal Fig. 1. We present and compare two methods for determining the refractive indices of rough surfaces. The first method, described in Section 2, is based on the conjoint use of light-scattering 1,8 10 and atomic-force microscopy. 11 The advantages and drawbacks of the method are discussed. Several experiments are presented in for both smooth and randomly rough surfaces. Depositing an optical thin film upon a rough surface leads to variations in the amount of scattered light. 8,12,13 In Section 3 we show that the analysis of these variations permits one to determine the refractive index of the bare surface. 13,14 We discuss the sensitivity obtained, and we try to extend the method to metallic surfaces. In this paper all calculations and measurements of scattering have been performed at normal illumination and with nonpolarized light. 756 APPLIED OPTICS Vol. 43, No. 4 1 February 2004

2 is the angle of the scattered wave from the average sample normal, and is the angle between the scattering plane and the incidence plane. 2,3,8 Inhomogeneous bulk and multilayers can also be addressed with the same theory. 2,3 For surface scattering, the main results can be summarized through the following formula 17 : I, i, j C ij ij j, (1a) Fig. 1. Homogeneous medium bounded by a rough surface. 2. Light Scattering and Atomic-Force Microscopy The first technique is based on the conjoint use of light-scattering and atomic-force microscopy. Consider, for instance, a rough surface seen as a departure from a perfect plane surface Fig. 1. The angular scattering from the rough surface can be predicted from knowledge of the surface s topography and of its refractive index, which are the two unknowns. If the topography is known, for example, from atomic-force microscopy AFM measurements, the angle-resolved scattering ARS can be calculated by electromagnetic theory. Provided that both sensitivity and accuracy are sufficient, the refractive index of the surface can be determined from a comparison of the measured and the calculated ARS. A. ARS Measurements Measurements of the angular scattering are performed with a spectral scatterometer that has been described in numerous papers. 4,5,15 The apparatus, which is ten-axis computer controlled, permits one to investigate the uniformity, the anisotropy, and the polarization of scattering for different incidence angles. Recently the apparatus was modified to permit complete ellipsometry of angular scattering at each direction of space for localization of scatterers and discrimination of surface and bulk effects. 4,5 For optical sources, 15,16 several wavelengths, from the UV 325 nm to the mid infrared 10.6 m, can be used. The apparatus is calibrated with a Lambertian standard of diffuse reflectance in the visible, with absolute accuracy better than 1%. Relative accuracy depends on the stability of the laser source, which is of the order of some percent. The apparatus permits one to measure the ARS with a dynamic range of 7 decades. 15 B. ARS Calculation The angular scattering can be calculated by more than one method. When the surface is slightly rough root mean square much smaller the incident wavelength, first-order vector theory can be used. 2,3,8 In this case angular scattering in whole space can be predicted at normal and polar directions. where I, is the angular scattered intensity and C ij are ideal coefficients 1,8,17 optical factors that do not depend on surface microstructure. These coefficients take into account the amplitudes of waves scattered from the interfaces and the propagation of these waves within the multilayer. They are connected with the design of the multilayer and to illumination and observation conditions. The subscripts i and j are the interface numbers. All structural properties lie in the ij and j terms. j is the Fourier transform of the autocorrelation function of defects at interface j, 8,17 and it is called the roughness spectrum of interface j. The coefficients ij are cross-correlation terms that describe mutual coherence 8,18 between the waves scattered from interfaces i and j. These coefficients are given as 18 ij ij j, (1b) where ij is the Fourier transform of the crosscorrelation function between surfaces i and j. Notice that, in the case of a single rough surface limiting a homogeneous material, Eqs. 1 are reduced to I C s s, (2) where C s is the optical coefficient of the surface and s is its roughness autocorrelation spectrum. Intensity I can be determined from ARS measurements, whereas topography term s can be measured by AFM. Therefore optical factor C s, which depends on the refractive index of the surface, can be recovered from these two measurements. For stronger roughness, rigorous theories based on integral and differential 22 formalisms must be used. In this paper we use a differential method that was presented in previous papers. 13,23 C. Atomic-Force Microscopy The topography of a surface is determined from AFM measurements made with a Topometrix Explorer in contact mode with a standard pyramidal tip whose radius of curvature is of the order of 50 nm. The first issue to address is the apparatus bandpass, which should be identical to the ARS bandpass. The condition is necessary 11 if the AFM data are used for the calculation of scattering. As scattering is measured in the far field, frequency bandpass B ARS of the ARS is given by 11 B ARS sin m, 1, (3) 1 February 2004 Vol. 43, No. 4 APPLIED OPTICS 757

3 where m is the minimum measurable scattering angle and is the incident wavelength. In the same way, for a given total scan length L the AFM bandpass that is related to sampling principles Shannon Nyquist criteria is given by B AFM u 1 L, 1 2 u, (4) where u is the sampling interval. Therefore the condition for agreement between ARS and AFM measurements is given by u 2. (5) The roughness spectrum determined from lightscattering measurements is a function of normal angle and polar angle, 11 whereas the roughness spectrum determined from AFM measurements is a function of Cartesian coordinates x and y Fig. 1. Therefore, to compare the results given by the two techniques, a conversion is required. This issue is addressed in Ref. 11, and the conversion allows us to compute one-dimensional curves that are an average of the roughness spectrum over polar angle. These curves are introduced in a numerical code and lead to a one-dimensional function I, which is an average of scattering over polar angle. D. Application to Experiment To validate the technique we used two 5-mm-thick glasses. The glasses were opaque to eliminate scattering from back and lateral faces. The contribution of bulk scattering to scattering in reflection was assumed to be negligible. 1. Polished Sample The first sample was a piece of polished RG 1000 Schott glass whose refractive index was n s 1.55 at wavelength 588 nm and n s 1.53 at wavelength 1014 nm. A linear approximation would give n s at wavelength 633 nm. The root mean square rms of the surface was close to 10 nm. Its topography measured by AFM and shown in Fig. 2 revealed some scratches that created a slight anisotropy of scattering. The scan length was L 50 m, with N data points, with a resultant step x y 0.17 m. In this case, as discussed in Section 1, AFM and ARS had similar bandpasses, provided that the ARS wavelength was close to the AFM step. In the study reported here we used a He Ne laser whose emission wavelength was m and B ARS m 1, 1.58 m 1, whereas B AFM 0.02 m 1,3 m 1. Therefore, as the ARS bandpass was included in the AFM bandpass B ARS B AFM, we could use the AFM data to predict ARS in the whole angular range 0, 90. For this polished sample, first-order theory gave an accurate prediction of angular scattering. Calculations were made of the measured AFM topography for several substrate indices see Fig. 3. The results show that, as is the case for specular reflection, the sensitivity of scattering depends on the refractive index of the surface. Notice that for this kind of glass Fig. 2. AFM image of polished RG1000 Schott glass. Scan length, L 50 m; N data points. the imaginary part of the refractive index was less than As confirmed by numerical experiments, this parameter had negligible influence on the ARS; for this reason no further investigation was made to determine its exact value. To determine the value of a substrate s refractive index n s we compared the numerical results obtained for several values of n s with the experimental values. To obtain results that were not dominated by the near-specular direction we calculated a distance function DF, given by the sum over all the scattering angles i : DF i S 2 m i S c i S c i, (6) where S m i is the measured scattering level at angle i and S c i is the calculated scattering level at angle i. As shown in Fig. 4, the best agreement was obtained for n s The ARS obtained for n s 1.52 is presented in Fig. 5, from which one can see that good agreement between the numerical and the experimental results was found. As the refractive index of the RG 1000 sample from Schott was n s 1.548, this result demonstrates that the method gives Fig. 3. Angular scattering calculated with first-order theory from the AFM data of Fig. 2 as a function of substrate s refractive index. Normal incidence, unpolarized incident beam. Wavelength of illumination, 633 nm. 758 APPLIED OPTICS Vol. 43, No. 4 1 February 2004

4 Fig. 4. Distance function calculated from Eq. 6. the value of the refractive index of the surface with a relative error of 2%. We next applied the same method to rougher surfaces that did not exhibit specular reflection or specular transmission. 2. Rougher Sample In this subsection we consider a sample whose roughness, in terms of the rms of the surface, was much greater than 10, which is commonly considered the limit of validity of first-order theories. The second RG 1000 sample, which was obtained from a partial polishing process, was much rougher and did not exhibit any specular beam. Its AFM topography is shown in Fig. 6. The roughness now lay in the micrometer range, and calculation of the ARS required a computer code based on a rigorous method. As our computer codes for calculation of scattering are based on rigorous electromagnetic theories and require long calculation times and large memory sizes for twodimensional randomly rough surfaces, a rigorous one-dimensional differential method 13,23 was used. This computer code has been shown to give accurate results for the calculation of scattering in the incidence plane. 13,14 The results obtained with the differential method are plotted in Fig. 7. The results obtained for four values of n s n s 1.3, n s 1.44, n s 1.54, and n s 2.04 allow us to point out the sensitivity of scattering to the substrate s refractive index. Fig. 6. AFM image of the rough sample. Scan length, L 50 m; N data points. As expected, for the rough sample a higher level close to 10 2 of scattering was obtained, compared with the level of scattering obtained with the polished sample. The curves of Fig. 7 were obtained in the stochastic case by averaging of 100 calculations. 20 Each measurement was calculated from the AFM data, and each surface corresponds to one horizontal or vertical section of the AFM image. 14 As previously, we calculated the ARS for different values of n s and compared the numerical results with those obtained experimentally see Fig. 8. Here again the best agreement was obtained for n s The corresponding ARS is plotted in Fig. 9 and shows good agreement with experimental data. Here again, the method gave the value of the refractive index of the sample with a relative error of 2%. Notice that the rough sample was obtained by a polishing process that may lead to the presence of a surface transient layer with a refractive index different from the initial refractive index of the RG 1000 Schott glass. The presence of this transition layer may also explain the slight discrepancy between the value obtained for n s and that given by the manufac- Fig. 5. Angular scattering from the RG 1000 polished glass. The measurements were performed at 633-nm wavelength normal illumination and nonpolarized light. A first-order calculation was performed with the AFM data for a substrate refractive index n s Fig. 7. Angular scattering from the rough sample as a function of substrate s refractive index. The calculation was performed for normal incidence by the differential method, and the topography of the surface is given by AFM measurements see Fig. 6. Wavelength of illumination, 633 nm. 1 February 2004 Vol. 43, No. 4 APPLIED OPTICS 759

5 Fig. 10. Deposition of a single thin film upon a rough surface. The two interfaces were assumed to be perfectly correlated. Fig. 8. Distance function calculated from Eq. 6. The sample was rough RG1000 Schott glass. The calculation was performed with the differential method. turer. In this figure we have also plotted the curve calculated from first-order theory. As expected, first-order calculation gave erroneous results at low angles for surfaces with rms values close to the illumination wavelength. To conclude this section, we have shown that this technique can be used to determine the real part of the refractive index of a rough opaque dielectric surface. Notice that the surfaces are opaque with a slight imaginary index less than 10 2 that can be neglected in the calculation. In a general way, care must be taken about measurement s accuracy. The limits of the method are as follows: When the sample is rough, a rigorous method of computation is required for calculating angular scattering. We used a computer code based on a differential formalism. 13,14,23 Because of problems with computer memory size, this method was developed only for one-dimensional surfaces invariant along one axis. However, when scattering was measured in the plane of incidence, it proved to give accurate results. Strictly speaking, the calculation method should be two dimensional, in particular for predicting scattering and polarization effects outside the incidence plane. Fig. 9. Angular scattering from the rough sample. Measurements were performed at 633-nm wavelength normal illumination and nonpolarized light, whereas calculations rigorous and firstorder involved AFM data of Fig. 6. n s 1.52 was the substrate index used for the calculation. The topography of the surface is obtained from AFM measurements. Any lack of accuracy leads to errors on the estimated value of n s. Therefore the AFM calibration must be checked carefully. To overcome this difficulty we used a multiscale approach described in Ref. 11. Depending on the geometrical characteristics shape, rms, and correlation length of the surface, AFM measurements may give erroneous results based on the tip radius and shape. In other words, the apparatus used for AFM must also be checked carefully. Finally, a major difficulty lies in the fact that the surface areas considered in the experiments were different, depending on whether we used AFM L 2 50 m 50 m 2 or ARS illuminated area, 4 mm 2 measurements. Therefore the stationarity of the surface must be taken into account. In particular, the presence of scratches, the anisotropy of the surface, and the degree of cleanliness of the sample may reduce accuracy. 3. Technique Based on Surface Overcoating In previous papers 12,13,18,24,25 it was shown that depositing a single thin film upon a rough surface modifies the angular scattering of the surface. Such an effect occurs when the vertical correlation is strong between the two interfaces of the film. 18 Because the variation in scattering that is obtained depends on the value of substrate s refractive index, a second technique for determining the value of n s can be proposed. 14 Notice that the variation of scattering results from the presence of two rough interfaces that are two secondary scattering sources. When these surfaces are correlated see Fig. 10, the scattering sources are coherent and interfere. The result is an increase or reduction of scattering, depending on the substrate s index and on the optogeometrical parameters refractive index, thickness of the deposited thin film. As previously, first we validated the method on a polished sample and then we applied it to the case of a rougher surface. A. Polished Sample Here again the sample was a polished piece of black RG 1000 Schott glass that scatters a small amount of energy compared with that of the reflected beam. First-order theory was used to predict the difference 760 APPLIED OPTICS Vol. 43, No. 4 1 February 2004

6 Before coat- in scattering before and after coating. ing, the ARS was given by I s, C s, s,, (7) where s, is the substrate s roughness spectrum and C s is the substrate s scattering coefficient. After multilayer coating was applied we obtained, for correlated surfaces identical to that of the substrate, I, s, ij C ij,. (8) This result was valid only when the cross-correlation coefficients were unity ij 1, which caused all surfaces and roughness spectra to be identical i j s in the stack. From an experimental point of view, this assumption was proved 12,18,26 when coatings were produced with high-energy deposition technologies ion-assisted deposition, ion plating, ion beam sputtering.... Therefore Eq. 8 shows that scattering can be reduced or enhanced by the coating, and this modification can be described, for a single thin film, by the scattering ratio with, I I s C C s, (9) C C 00 C 11 2Re C 01, (10) Fig. 11. Ratios of angular scattering to normal angle and substrate index n s. The curve was calculated for normal illumination for a single correlated SiO 2 layer with optical thickness 5 4at633 nm. The calculation is the result of first-order theory. Wavelength of illumination, 633 nm. where C 00 and C 11 are the optical factors of interfaces 0 and 1, respectively Fig. 10, and C 01 is a crossed term for which interference between waves scattered by the two interfaces was taken into account. The refractive index and the thickness of the deposited films were controlled and determined with errors of less than 1% because of classic in situ optical monitoring and ex situ spectrophotometric measurements. Moreover, a high energy deposition technique ion-assisted deposition was used to guarantee perfect replication of the substrate s surface. 17,26 In this case the assumption of perfect correlation between the interfaces within the structure was valid. All these conditions make the substrate s refractive index n s the unique unknown to be determined. In Fig. 11 we show the variations of scattering ratio n s, versus substrate refractive index and scattering angle. The film was a single low-index SiO 2 layer n SiO of optical thickness 5 4 at633 nm. We noticed a strong reduction of scattering at low angles when n s This result originates from the fact that the SiO 2 layer is a perfect antireflection coating when the substrate s index follows the condition n s n 2 SiO2, which also causes an antiscattering effect. 12 As shown in Fig. 11, two different values of n s may lead to the same value of, for which reason we now prefer to consider a high-index layer. Results obtained with a single high-index TiO 2 deposited layer n TiO whose optical thickness was 5 4 at 633 nm are given in Fig. 12. Numerical results indicate that, for a given value of n s, the angular variations of are negligible for angles smaller than 40. Depending on whether the substrate s refractive index was greater or lower than the refractive index of TiO 2, scattering was reduced or increased. This was so because correlated scattering is quasi-proportional to specular reflection, 18 which also explains the results of Fig. 11. Notice that scattering varied by a factor greater than 100 Fig. 12 when the substrate index lay in the interval 1.2, 3.2. The measurements presented in Fig. 13 were taken before and after coating of a rough surface by a TiO 2 layer of optical thickness 5 4. The deposition technique was ion-assisted deposition. The mean value of ratio was 7.8. The corresponding value of n s, determined from the curve of Fig. 12, was n s Such a result shows that this method is successful for slightly rough surfaces and can be used to determine the refractive index of a dielectric smooth opaque surface. The relative error calculated from the theoretical n s value was 2%. Fig. 12. Ratio of angular scattering at 10 to substrate index n s. Normal incidence. The curve was calculated for a single correlated TiO 2 layer whose optical thickness was 5 4 at 633 nm. Wavelength of illumination, 633 nm. 1 February 2004 Vol. 43, No. 4 APPLIED OPTICS 761

7 Fig. 13. Scattering measurements of the rough surface before and after coating with a 5 4 TiO 2 layer. Normal incidence. Wavelength of illumination, 633 nm. Next we compared this accuracy with the theoretical accuracy. If we denote by p n s the local slope of the n s curve, we could obtain the relative accuracy in n s from the equation n s n s p ns 2 I p n s I, (11) where I I is the measurement accuracy, with a relative error of 1%. With the slope value p 30 near n s 1.53, we found the refractive index of substrate with an accuracy greater than 99.7%, which was much better than the preceding 98% value. There may be several reasons for this difference, such as a lack of uniformity and isotropy of roughness and the fact that scattering was measured only in the incidence plane. B. Rougher Sample We then used a sample that consisted of RG 1000 Schott glass whose roughness was close to the illumination wavelength rms 0.6 m. In this case there was no specular reflection. The refractive index was determined by the same technique as that described in Subsection 3.A, but, as was done in Subsection 2.D.2, the calculation was performed by the differential method. 13,23 Figure 14 shows the average value of calculated over scattering angle for Fig. 14. Ratio of angular scattering averaged over a 20 angular range centered about 10 to substrate index n s filled circles. The curve was calculated by the differential method for a single TiO 2 layer whose optical thickness was 5 4 at 633 nm. The dashed horizontal curve is given for comparison and was calculated by first-order theory. Wavelength of illumination, 633 nm. The two curves are quasi-identical. Fig. 15. Ratio calculated versus correlation length by the differential method for a single TiO 2 layer deposited upon the substrate. The optical thickness of the layer was 5 4 at 633 nm, and n s The surface has Gaussian statistics, with rms 0.6 m. Wavelength of illumination, 633 nm. several values of n s. A curve calculated with the first-order theory has also been drawn in this same figure for comparison and is superimposed upon the curve obtained with the rigorous calculation. One can see that the ratio seem to be independent of the calculation method, which can be of strong practical interest. In other words, with this technique based on the measurement of the scattering ratio, firstorder calculation seem to give accurate results for determining the value of n s. However, this result is due to the large value of the correlation length rms ratio of the surface considered in the experiment. AFM measurements show that this ratio was greater than 3. To go further in this comparison of the calculation methods, we have plotted in Fig. 15 the calculated value of as a function of the correlation length of the surface. The surface was assumed to have Gaussian statistics with a rms equal to 0.6 m. One can see that for large values greater than 2.5 of the correlation length and for a refractive index of the substrate equal to 1.52, scattering ratio is constant and equal to the value given by first-order theories. This result seems to prove that, when the correlation length of the sample is greater than 2.5, determining n s requires no AFM measurement. The experimental results are plotted in Fig. 16; a value of 5.6 was obtained. From the curve of Fig. 14 we found an n s value of 1.59, to be compared with the theoretical value n s of the RG 1000 glass s refractive index. We can conclude that the relative error is 3%. Such result is rather encouraging, because the surface roughness results from a partial polishing process that may introduce a transition layer. In addition, all calculations were performed for perfectly correlated surfaces, whereas the sensitivity to correlation was high See Fig. 17. Indeed, any lack of vertical correlation ij 1 can explain our discrepancies, because the scattering ratio varies by a factor of 2 when the correlation is varied from unity to zero. 762 APPLIED OPTICS Vol. 43, No. 4 1 February 2004

8 Fig. 16. Angular scattering of the rough surface measured before and after deposition of a single 5 4 TiO 2 film. Wavelength of illumination, 633 nm. C. Metallic Layer The index-determination problem is more complex in the case of a metallic surface because we have two parameters to determine, i.e., the real part n s and the imaginary part n s of the substrate s complex index: n s n s jn s. (12) To determine these two unknowns we used two thin-film depositions that gave two ratios of scattering, H and L, depending on whether the deposited layer was a TiO 2 film high index or a SiO 2 film low index. Because the surface considered in this subsection was smooth, we used a method similar to that described in Subsection 3.A to determine the complex value of the substrate s index. Figure 18 shows the variations of ratios H and L versus n s and n s for a 4 TiO 2 layer and for a 4 SiO 2 layer. The experiments were made with a thick opaque chromium thin film layer used as the substrate. The roughness was much smaller than the wavelength. The angular scattering was measured for each layer. Experimental data indicate that scattering was reduced by the factor H 0.52 after deposition of a 4 TiO 2 layer and by the factor L 0.68 after deposition of a 4 SiO 2 layer. From these measured values and the theoretical results of Fig. 18. a Ratio of scattering at 10 to the real and the imaginary parts of the refractive index of the substrate. The calculation was performed for a single correlated SiO 2 layer whose optical thickness was 4 at 633 nm. b Same as a for a single correlated TiO 2 layer whose optical thickness was 4 at 633 nm. Fig. 17. Angular scattering as a function of the cross-correlation coefficient between interfaces of a single layer, calculated a by the first-order vector theory and b by the differential method. Wavelength of illumination, 633 nm. 1 February 2004 Vol. 43, No. 4 APPLIED OPTICS 763

9 In a more general way, and although numerous tests remain to be done with different kinds of rough surfaces of different materials, we believe that these techniques can aid the optical community in extracting indices of opaque surfaces that are fully diffusive. For transparent surfaces, the problem is more complex because of the additional presence of bulk scattering. 7 Fig. 19. Relationships between real and imaginary parts of metal complex indices. Each curve was obtained from the ratios measured after deposition of a high- and of a low-index layer upon a metal see text. The intersection of the curves gives the complex index. Fig. 19, we could determine the complex value of n s. The result is given by n s 2.4 j4.3. This value appears to be acceptable with respect to the refractive indices that can be found in the literature for Cr material n 2 j3.5 Refs. 28 and 29 to n 3.6 j4.4 Ref. 27. Indeed, the value of Cr may vary from one reference to another, depending on whether the Cr had been produced in thin-film or bulk form and also on the deposition technique. In addition, this material is known to be strongly inhomogeneous with a vertical gradient index. It is clear that complementary experiments should be performed with other materials, such as nickel and aluminum. 4. Conclusions We have shown that scattering of light can be used for determining the refractive indices of opaque surfaces. The two techniques described in this paper are helpful for characterizing optical surfaces that do not exhibit specular reflection or transmission. Both techniques can be used when surfaces are smooth or randomly rough and have a relative error of 3% in most cases. The nondestructive technique presented in Section 2 is based on the conjoint use of ARS and AFM. It was shown to be successful for both slightly and randomly rough surfaces, provided that the optical and nanoprobe bandpasses were adjusted. However, care must be taken with the calibration procedures and the stationarity anisotropy of the surface. The technique described in Section 3 is based on the measurement of the variation of scattering caused by a film deposited upon a bare surface. It was first shown to be successful for slightly and randomly rough surfaces. Some discrepancies can be explained by the lack of vertical correlation caused by the strong roughness and by the possible presence of a transition layer upon the substrate. This technique was also applied to slightly rough metallic samples. In this case, depositing two different layers upon a bare surface gave information about both real and imaginary parts of the complex index of the metallic surface. References 1. C. Amra, From light scattering to the microstructure of thin film multilayers, Appl. Opt. 32, C. Amra, C. 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