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Biomedical Optics Express

Biomedical Optics Express

  • Editor: Joseph A. Izatt
  • Vol. 4, Iss. 5 — May. 1, 2013
  • pp: 725–731
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Zirconia dental implants degradation by confocal Raman microspectroscopy: analytical simulation and experiments

Nadia Djaker, Claudine Wulfman, Michaël Sadoun, and Marc Lamy de la Chapelle  »View Author Affiliations


Biomedical Optics Express, Vol. 4, Issue 5, pp. 725-731 (2013)
http://dx.doi.org/10.1364/BOE.4.000725


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Abstract

Subsurface hydrothermal degradation of yttria stabilized tetragonal zirconia polycrystals (3Y-TZP) is presented. Evaluation of low temperature degradation (LTD) phase transformation induced by aging in 3Y-TZP is experimentally studied by Raman confocal microspectroscopy. A non-linear distribution of monoclinic volume fraction is determined in depth by using different pinhole sizes. A theoretical simulation is proposed based on the convolution of the excitation intensity profile and the Beer-Lambert law (optical properties of zirconia) to compare between experiment and theory. The calculated theoretical degradation curves matche closely to the experimental ones. Surface transformation (V0) and transformation factor in depth (T) are obtained by comparing simulation and experience for each sample with nondestructive optical sectioning.

© 2013 OSA

1. Introduction

2. Materials and methods

Experimental zirconia transformation curves were obtained on (20×4×2) mm3 specimens with a pure tetragonal crystalline structure assessed before aging by Raman spectroscopy. The samples were exposed to in vitro aging in Ringer solution at 130°C and 0.6 MPa for 25h and 90h. Raman spectra of transformed zirconia were recorded using a Labram Raman spectrometer (Horiba Jobin Yvon, Kyoto, Japan). The excitation laser was a HeNe laser (633 nm) with 1 mW power. The Raman spectrometer was combined to a confocal microscope (Olympus LX71).

In this study, an objective 10×, NA 0.25 was used. Considering the refraction index of zirconia (n=2.2), the effective numerical aperture (NAeff) as described in [20

20. S. L. Jacques, B. Wang, and R. Samatham, “Reflectance confocal microscopy of optical phantoms,” Biomed. Opt. Express 3(6), 1162–1172 (2012).

] is NA/n=0.11. This gives an axial resolution due to the refractive effect of 70μm ( FWHMz=1.4λ/NAeff2).

Combining the objective with gradually enlarged confocal pinhole apertures, from 30 to 300 μm, allows the control of the probe size and thus of the collection depth (zexp). Pinhole function as rejecting out-of focus signals, enables thin optical sectionning within thick samples [21

21. W. Song, J. Lee, and H. S. Kwon, “Enhancement of imaging depth of two-photon microscopy using pinholes: analytical simulation and experiments,” Opt. Express 20(18), 20605–20622 (2012) [CrossRef] [PubMed] .

].

The principle of the confocal microprobe method is illustrated in Fig. 1. Pinhole size variation leads to different optical slice sizes described theoretically in transparent media by Eq. (1) [22]:
zopt=(0.88λRaman11NA2)2+(2PH2NA)2
(1)
With: λRaman, the emitted Raman wavelength of zirconia at the vibrational frequency of 256 cm−1 (λRaman = 643nm), PH, the object-side pinhole diameter [μm] and NA, the numerical aperture of the objective.

Fig. 1 Schematic presentation of confocal detection principal in the confocal Raman micro-spectroscopy.

Moreover, zirconia is also a highly scattering medium whereas the absorption coefficient of 3Y-TZP can be neglected (μa = 0.135cm−1), in front of the reduced scattering coefficient (μs = 100cm−1 from [23

23. J. Salem and D. Zhu, Ceramic Coatings and Interfaces II, U. Schulz and H. T. Lin eds. (Wiley-Interscience, 2007).

]). The optical slice described previously in transparent media should then be modified according to this scattering effect. The study of in-depth variation in scattering media as phantoms was reported [20

20. S. L. Jacques, B. Wang, and R. Samatham, “Reflectance confocal microscopy of optical phantoms,” Biomed. Opt. Express 3(6), 1162–1172 (2012).

, 24

24. D. Wang, Y. Chen, and J. T. C. Liu, “A liquid optical phantom with tissue-like heterogeneities for confocal microscopy,” Biomed. Opt. Express 3(12), 3153–3160 (2012).

]. To determine this scattering effect, a calibration of the optical slice sizes is necessary depending on the pinhole size. In case of zirconia, the calibration of collection depth was conducted on a highly-polished knife-shaped specimen as reported by the authors and based on the protocol previously described in [10

10. C. Wulfman, N. Djaker, N. Dupont, D. Ruse, M. Sadoun, and M. Lamy de la Chapelle, “Raman spectroscopy evaluation of subsurface hydrothermal degradation of zirconia,” J. Am. Ceram. Soc. 95(7), 2347–2351 (2012) [CrossRef] .

]. In this study, we have compared the theoretical and experimental optical depths obtained in zirconia.

Figure 2 (left) shows the calculated axial optical slices (zopt) in non-scattering media given by Eq. (1) and the measured experimental depths by knife-edge technique obtained for different pinhole sizes. The ratio between experimental (zexp) and theoretical (zopt) optical slices is due to the scattering effect. In Fig. 2 (right), we see that this ratio is fitted by an exponential law as Beer-Lambert law which describes this scattering effect (I(z) = I0eμz where I(z) is the intensity axial profile). Since the absorption is neglected in zirconia, only the scattering coefficient (μs = 0.01μm−1) is present. A factor of 2 is added in the fit curve due to the fact that, the scattering is considered twice: one time for excitation laser scattering and a second time for Raman diffusion scattering.

Fig. 2 Calculated optical slice thickness given by the optical objective and measured axial depths in zirconia for each pinhole size (left) Ratio between calculated and measured depths.

After depth penetration calibration, Raman spectra were collected from three randomly selected points on the surface of each aged specimen. Raman spectra were measured in 22 probes following the same protocol. The purity of the tetragonal phase was assessed in the control samples. Close to 800 spectra were collected and analyzed. Raman peak positions and intensities were obtained by fitting the Raman spectra with Lorentzian curves. From each spectrum, the monoclinic volume fraction Vfm was calculated. Noise in Raman spectra was very low and the bands picks fittings give errors bars in Vfm calculations which were presented on the experimental graphs.

The spectra of the tetragonal and of the monoclinic phases are sufficiently different to enable qualitative analysis. Each structure exhibits specific features that can be assigned to actual spectral signature of the studied phases. In the tetragonal phase, the most characteristic bands are a sharp band at 142 cm−1 and a broader one at 256 cm−1, whereas, in the monoclinic phase, a doublet is seen at 178 and 190 cm−1. Raman spectra of aged zirconia were reported by the authors in [10

10. C. Wulfman, N. Djaker, N. Dupont, D. Ruse, M. Sadoun, and M. Lamy de la Chapelle, “Raman spectroscopy evaluation of subsurface hydrothermal degradation of zirconia,” J. Am. Ceram. Soc. 95(7), 2347–2351 (2012) [CrossRef] .

]. The zirconia degradation occurs during the tetragonal to monoclinic transformation, which is estimated by calculating the monoclinic volume fraction, Vfm, using Eq. (2) [10

10. C. Wulfman, N. Djaker, N. Dupont, D. Ruse, M. Sadoun, and M. Lamy de la Chapelle, “Raman spectroscopy evaluation of subsurface hydrothermal degradation of zirconia,” J. Am. Ceram. Soc. 95(7), 2347–2351 (2012) [CrossRef] .

, 11

11. C. Wulfman, M. Sadoun, and M. Lamy de la Chapelle, “Interest of Raman spectroscopy for the study of dental material: the zirconia material example,” IRBM 31(5–6), 257–262 (2010) [CrossRef] .

]. The calibration constant of 0.33 included in the ratio between the intensities of the monoclinic and tetragonal peaks taken in this work was widely discussed [13

13. J. A. Munoz-Tabares and M. J. Anglada, “Quantitative analysis of monoclinic phase in 3Y-TZP by Raman spectroscopy,” J. Am. Ceram. Soc. 93(6), 1790–1795 (2010).

], and used to calculate the monoclinic fraction volume:
Vfm=Im178+Im1890.33(It145+It256)+Im178+Im189
(2)
Where Im and It are the intensities of the Raman peaks of the monoclinic and tetragonal phases and 0.33 is the correction factor for the difference of the scattering cross section between the selected peaks of the monoclinic and tetragonal phases. Since the transformation curves (see Fig. 3) are recorded in depth without mechanically cutting the samples but with optical sectioning, their profile is modified by the optical properties of excitation laser (wavelength), the objective used (NA) and the zirconia optical properties (refraction index, absorption and scattering) as explained below.

Fig. 3 Measured and calculated averaged monoclinical fraction in depth.

3. Results and discussion

Theoretically, the monoclinic fraction measured depends on the laser intensity Gaussian profile ( ez20.4Dz2 with Dz, the axial resolution of the objective), the optical properties of zirconia (described by Beer-Lambert law: eμsz) and a sigmoid model describing the theoretical monoclinic volume fraction F(z) in depth as proposed by [7

7. J. A. Munoz-Tabares, E. Jimenez-Pique, and M. Anglada, “Subsurface evaluation of hydrothermal degradation of zirconia,” Acta Mater. 59(2), 473–484 (2011) [CrossRef] .

] (see Fig. 4 (left)). The optically modified fraction profile includes the contribution of optical parameters (excitation and beer-Lambert law with zirconia optical parameters) to the real transformation profile described in Eq. (2). This optically modified monoclinic fraction profile OF(z) is then described by Eq. (3):
OF(z)=ez20.4Dz2×eμz×(V0×1+eT.z01+eT(zz0))
(3)
Where V0 is the monoclinic volume fraction on the surface (z = 0), T is the transformation factor in depth and Z0 is the abscissa of the curve inflection point.

Fig. 4 Calculated monoclinic fraction in depth for two different aging times.

A simulation program based on Eq. (3) was developed using Igor software (WaveMetrics, Portland, USA). This program provide a theoretical curve, matching closely to the experimental averaged monoclinic fraction shown in Fig. 3 by variating the parameters: V0, T and z0.

In fact, these experimental curves represent the average monoclinic fraction (AF) measured from the surface down to the depth z for each pinhole size. Indeed, as it was shown, the optical slices represent the collected signal from the surface down to optical depths (z) that are collected by each pinhole size. Thus, the average monoclinic fraction (AF) corresponds to the ratio between the collected monoclinic fraction (OF) and the optical slice thickness (zexp). Theoretically, the experimental design with progressive enlargement of pinhole diameter enables the measurement of monoclinic volume fraction in increasing thickness of material AF (z), which can be written:
AF(z)=0zOF(z)dzzexp
(4)

The average fraction (AF) is the theoretical description of the measured transformation profiles (Vfm calculated using Eq. (2)) by confocal Raman micro-spectroscopy for each optical slice defined for each pinhole size. Figure 3 shows the experimental zirconia transformation AF(z) for two aged times. These experimental curves are compared to the theoretical averaged monoclinic volume fraction inside the collected depth AF(z) obtained by simulation program. Thus, to have the closest profiles, the simulation program fixes the transformation parameters V0, T and z0, such as T=1.1 μm−1 for both aging times, whereas, z0 = 30μm and V0 = 78% for 90h and z0 = 20μm and V0 = 45% for 25h aging time.

This means that the real transformation profile (F(z)) can be determined precisely directly from the simulation of the AF(z) curve and the fit of the experimental AF(z) curve. Figure 4 shows the result of the calculated monoclinic fraction axial profile for the theoretical monoclinic fraction (F(z)) and the optically modified monoclinic fraction (OF(z)) using Eq. (3) depending on pinhole sizes. The transformation parameters, V0, T and z0 have been fixed by the simulation program. In this work, the theoretical monoclinic volume fraction curves (F(z)) are calculated without any sample cross section and are very close to profile curves obtained by sample cut reported before [7

7. J. A. Munoz-Tabares, E. Jimenez-Pique, and M. Anglada, “Subsurface evaluation of hydrothermal degradation of zirconia,” Acta Mater. 59(2), 473–484 (2011) [CrossRef] .

]. F(z) is integrated and averaged in the confocal depth to obtain finally the calculated averaged monoclinic fraction (AF(z)), which corresponds closely to the experimental one measured by confocal Raman microspectroscopy. The transformation parameters (V0, T and z0) are obtained for zirconia hydrothermal degradation in depth which allows the prediction of LTD for different other aging times.

4. Conclusion

In this study, the evolution of transformation (LTD) of 3Y-TZP is simulated and compared with experimentally measured LTD by confocal Raman micro-spectroscopy. The experimental method and the simulation model that we have proposed allow optical sectioning in depth by using different pinhole sizes to avoid any mechanical sectioning. The optical sectioning microscope was used to study a highly scattering media as zirconia used in dental crowns. The developped simulation program allows depths corrections and LTD factors estimation. This leads to the prediction of real transformation factors and profiles for any aging times without any mechanical sectionning which could induce some additional degradations. In addition, this simulation will be useful to model hydrothermal degradation in different dental materials based on zirconia using Raman confocal micro-spectroscopy.

References and links

1.

M. Hisbergues, S. Vendeville, and P. Vendeville, “Zirconia: established facts and perspectives for a biomaterial in dental implantology,” J. Biomed. Mater. Res. B 88B(2), 519–529 (2009) [CrossRef] .

2.

C. Piconi and G. Maccauro, “Zirconia as a ceramic biomaterial,” Biomaterials 20(1), 1–25 (1999) [CrossRef] [PubMed] .

3.

H. Luthy, F. Filser, O. Loeffel, M. Schumacher, L. J. Gauckler, and C. H. F. Hammerle, “Strength and reliability of four-unit all-ceramic posterior bridges,” Dent. Mater. 21(10), 930–937 (2005) [CrossRef] [PubMed] .

4.

J. S. Schley, N. Heussen, S. Reich, J. Fischer, K. Haselhuhn, and S. Wolfart, “Survival probability of zirconia-based fixed dental prostheses up to 5 yr: a systematic review of the literature,” Eur. J. Oral Sci. 118(5), 443–450 (2010) [CrossRef] [PubMed] .

5.

K. Kobayashi, H. Kuwajima, and T. Masaki, “Phase-change and mechanical properties of ZrO2-Y2O3 solid electrolyte after aging,” Solid State Ionics 3–4 (AUG), 489–493 (1981) [CrossRef] .

6.

S. S. Brown, D. D. Green, G. Pezzotti, T. K. Donaldson, and I. C. Clarke, “Possible triggers for phase transformation in zirconia hip balls,” J. Biomed. Mater. Res. B 85B(2), 444–452 (2008) [CrossRef] .

7.

J. A. Munoz-Tabares, E. Jimenez-Pique, and M. Anglada, “Subsurface evaluation of hydrothermal degradation of zirconia,” Acta Mater. 59(2), 473–484 (2011) [CrossRef] .

8.

H. Toraya, M. Yoshimura, and S. Somiya, “Quantitative-analysis of monoclicnic-stabilized cubic ZrO2 systems by X-ray-diffraction,” J. Am. Ceram. Soc. 67(9), C183–C184 (1984) [CrossRef] .

9.

S. Deville, L. Gremillard, J. Chevalier, and G. Fantozzi, “A critical comparison of methods for the determination of the aging sensitivity in biomedical grade yttria-stabilized zirconia,” J. Biomed. Mater. Res. B 72B(2), 239–245 (2005) [CrossRef] .

10.

C. Wulfman, N. Djaker, N. Dupont, D. Ruse, M. Sadoun, and M. Lamy de la Chapelle, “Raman spectroscopy evaluation of subsurface hydrothermal degradation of zirconia,” J. Am. Ceram. Soc. 95(7), 2347–2351 (2012) [CrossRef] .

11.

C. Wulfman, M. Sadoun, and M. Lamy de la Chapelle, “Interest of Raman spectroscopy for the study of dental material: the zirconia material example,” IRBM 31(5–6), 257–262 (2010) [CrossRef] .

12.

D. Casellas, F. L. Cumbrera, F. Sanchez-Bajo, W. Forsling, L. Llanes, and M. Anglada, “On the transformation toughening of Y-ZrO2 ceramics with mixed Y-TZP/PSZ microstructures,” J. Am. Ceram. Soc. 21(6), 765–777 (2001) [CrossRef] .

13.

J. A. Munoz-Tabares and M. J. Anglada, “Quantitative analysis of monoclinic phase in 3Y-TZP by Raman spectroscopy,” J. Am. Ceram. Soc. 93(6), 1790–1795 (2010).

14.

J. Barbillat, P. Dhamelincourt, M. Delhaye, and E. Dasilva, “Raman confocal microprobing, imaging and fiber-optic remote sensing: a further step in molecular analysis,” J. Raman Spectrosc. 25(1), 3–11 (1994) [CrossRef] .

15.

G. Pezzotti and A. A. Porporati, “Raman spectroscopic analysis of phase-transformation and stress patterns in zirconia hip joints,” J. Biomed. Opt. 9(2), 372–384 (2004) [CrossRef] [PubMed] .

16.

V. Presser, M. Keuper, C. Berthold, and K. G. Nickel, “Experimental determination of the Raman sampling depth in zirconia ceramics,” Appl. Spectrosc. 63(11), 1288–1292 (2009) [CrossRef] [PubMed] .

17.

G. Pezzotti, K. Yamada, A. A. Porporati, M. Kuntz, and K. Yamamoto, “Fracture toughness analysis of advanced ceramic composite for hip prosthesis,” J. Am. Ceram. Soc. 92(8), 1817–1822 (2009) [CrossRef] .

18.

A. Gallardo, S. Spells, R. Navarro, and H. Reinecke, “Confocal Raman microscopy: how to correct depth profiles considering diffraction and refraction effects,” J. Raman Spectrosc. 38(7), 880–884 (2007) [CrossRef] .

19.

A. M. Macdonald and A. S. Vaughan, “Numerical simulations of confocal Raman spectroscopic depth profiles of materials: a photon scattering approach,” J. Raman Spectrosc. 38(5), 584–592 (2007) [CrossRef] .

20.

S. L. Jacques, B. Wang, and R. Samatham, “Reflectance confocal microscopy of optical phantoms,” Biomed. Opt. Express 3(6), 1162–1172 (2012).

21.

W. Song, J. Lee, and H. S. Kwon, “Enhancement of imaging depth of two-photon microscopy using pinholes: analytical simulation and experiments,” Opt. Express 20(18), 20605–20622 (2012) [CrossRef] [PubMed] .

22.

http://www.zeiss.de/C1256D18002CC306/0/F99A7F3E8944EEE3C1256E5C0045F68B/$file/60-1-0030_confocal-principles.pdf

23.

J. Salem and D. Zhu, Ceramic Coatings and Interfaces II, U. Schulz and H. T. Lin eds. (Wiley-Interscience, 2007).

24.

D. Wang, Y. Chen, and J. T. C. Liu, “A liquid optical phantom with tissue-like heterogeneities for confocal microscopy,” Biomed. Opt. Express 3(12), 3153–3160 (2012).

OCIS Codes
(170.1850) Medical optics and biotechnology : Dentistry
(170.5660) Medical optics and biotechnology : Raman spectroscopy
(180.1790) Microscopy : Confocal microscopy
(290.5860) Scattering : Scattering, Raman
(160.1435) Materials : Biomaterials

ToC Category:
Dentistry Applications

History
Original Manuscript: February 11, 2013
Revised Manuscript: March 15, 2013
Manuscript Accepted: March 27, 2013
Published: April 12, 2013

Citation
Nadia Djaker, Claudine Wulfman, Michaël Sadoun, and Marc Lamy de la Chapelle, "Zirconia dental implants degradation by confocal Raman microspectroscopy: analytical simulation and experiments," Biomed. Opt. Express 4, 725-731 (2013)
http://www.opticsinfobase.org/boe/abstract.cfm?URI=boe-4-5-725


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References

  1. M. Hisbergues, S. Vendeville, and P. Vendeville, “Zirconia: established facts and perspectives for a biomaterial in dental implantology,” J. Biomed. Mater. Res. B88B(2), 519–529 (2009). [CrossRef]
  2. C. Piconi and G. Maccauro, “Zirconia as a ceramic biomaterial,” Biomaterials20(1), 1–25 (1999). [CrossRef] [PubMed]
  3. H. Luthy, F. Filser, O. Loeffel, M. Schumacher, L. J. Gauckler, and C. H. F. Hammerle, “Strength and reliability of four-unit all-ceramic posterior bridges,” Dent. Mater.21(10), 930–937 (2005). [CrossRef] [PubMed]
  4. J. S. Schley, N. Heussen, S. Reich, J. Fischer, K. Haselhuhn, and S. Wolfart, “Survival probability of zirconia-based fixed dental prostheses up to 5 yr: a systematic review of the literature,” Eur. J. Oral Sci.118(5), 443–450 (2010). [CrossRef] [PubMed]
  5. K. Kobayashi, H. Kuwajima, and T. Masaki, “Phase-change and mechanical properties of ZrO2-Y2O3 solid electrolyte after aging,” Solid State Ionics3–4 (AUG), 489–493 (1981). [CrossRef]
  6. S. S. Brown, D. D. Green, G. Pezzotti, T. K. Donaldson, and I. C. Clarke, “Possible triggers for phase transformation in zirconia hip balls,” J. Biomed. Mater. Res. B85B(2), 444–452 (2008). [CrossRef]
  7. J. A. Munoz-Tabares, E. Jimenez-Pique, and M. Anglada, “Subsurface evaluation of hydrothermal degradation of zirconia,” Acta Mater.59(2), 473–484 (2011). [CrossRef]
  8. H. Toraya, M. Yoshimura, and S. Somiya, “Quantitative-analysis of monoclicnic-stabilized cubic ZrO2 systems by X-ray-diffraction,” J. Am. Ceram. Soc.67(9), C183–C184 (1984). [CrossRef]
  9. S. Deville, L. Gremillard, J. Chevalier, and G. Fantozzi, “A critical comparison of methods for the determination of the aging sensitivity in biomedical grade yttria-stabilized zirconia,” J. Biomed. Mater. Res. B72B(2), 239–245 (2005). [CrossRef]
  10. C. Wulfman, N. Djaker, N. Dupont, D. Ruse, M. Sadoun, and M. Lamy de la Chapelle, “Raman spectroscopy evaluation of subsurface hydrothermal degradation of zirconia,” J. Am. Ceram. Soc.95(7), 2347–2351 (2012). [CrossRef]
  11. C. Wulfman, M. Sadoun, and M. Lamy de la Chapelle, “Interest of Raman spectroscopy for the study of dental material: the zirconia material example,” IRBM31(5–6), 257–262 (2010). [CrossRef]
  12. D. Casellas, F. L. Cumbrera, F. Sanchez-Bajo, W. Forsling, L. Llanes, and M. Anglada, “On the transformation toughening of Y-ZrO2 ceramics with mixed Y-TZP/PSZ microstructures,” J. Am. Ceram. Soc.21(6), 765–777 (2001). [CrossRef]
  13. J. A. Munoz-Tabares and M. J. Anglada, “Quantitative analysis of monoclinic phase in 3Y-TZP by Raman spectroscopy,” J. Am. Ceram. Soc.93(6), 1790–1795 (2010).
  14. J. Barbillat, P. Dhamelincourt, M. Delhaye, and E. Dasilva, “Raman confocal microprobing, imaging and fiber-optic remote sensing: a further step in molecular analysis,” J. Raman Spectrosc.25(1), 3–11 (1994). [CrossRef]
  15. G. Pezzotti and A. A. Porporati, “Raman spectroscopic analysis of phase-transformation and stress patterns in zirconia hip joints,” J. Biomed. Opt.9(2), 372–384 (2004). [CrossRef] [PubMed]
  16. V. Presser, M. Keuper, C. Berthold, and K. G. Nickel, “Experimental determination of the Raman sampling depth in zirconia ceramics,” Appl. Spectrosc.63(11), 1288–1292 (2009). [CrossRef] [PubMed]
  17. G. Pezzotti, K. Yamada, A. A. Porporati, M. Kuntz, and K. Yamamoto, “Fracture toughness analysis of advanced ceramic composite for hip prosthesis,” J. Am. Ceram. Soc.92(8), 1817–1822 (2009). [CrossRef]
  18. A. Gallardo, S. Spells, R. Navarro, and H. Reinecke, “Confocal Raman microscopy: how to correct depth profiles considering diffraction and refraction effects,” J. Raman Spectrosc.38(7), 880–884 (2007). [CrossRef]
  19. A. M. Macdonald and A. S. Vaughan, “Numerical simulations of confocal Raman spectroscopic depth profiles of materials: a photon scattering approach,” J. Raman Spectrosc.38(5), 584–592 (2007). [CrossRef]
  20. S. L. Jacques, B. Wang, and R. Samatham, “Reflectance confocal microscopy of optical phantoms,” Biomed. Opt. Express3(6), 1162–1172 (2012).
  21. W. Song, J. Lee, and H. S. Kwon, “Enhancement of imaging depth of two-photon microscopy using pinholes: analytical simulation and experiments,” Opt. Express20(18), 20605–20622 (2012). [CrossRef] [PubMed]
  22. http://www.zeiss.de/C1256D18002CC306/0/F99A7F3E8944EEE3C1256E5C0045F68B/$file/60-1-0030_confocal-principles.pdf
  23. J. Salem and D. Zhu, Ceramic Coatings and Interfaces II, U. Schulz and H. T. Lin eds. (Wiley-Interscience, 2007).
  24. D. Wang, Y. Chen, and J. T. C. Liu, “A liquid optical phantom with tissue-like heterogeneities for confocal microscopy,” Biomed. Opt. Express3(12), 3153–3160 (2012).

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