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Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 9, Iss. 5 — Apr. 29, 2014
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Spectroscopic measurement of absorptive thin films by Spectral-Domain Optical Coherence Tomography

Tuan-Shu Ho, Pochi Yeh, Cheng-Chung Tsai, Kuang-Yu Hsu, and Sheng-Lung Huang  »View Author Affiliations


Optics Express, Vol. 22, Issue 5, pp. 5675-5683 (2014)
http://dx.doi.org/10.1364/OE.22.005675


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Abstract

A non-invasive method for measuring the refractive index, extinction coefficient and film thickness of absorptive thin films using spectral-domain optical coherent tomography is proposed, analyzed and experimentally demonstrated. Such an optical system employing a normal-incident beam of light exhibits a high spatial resolution. There are no mechanical moving parts involved for the measurement except the transversal scanning module for the measurement at various transversal locations. The method was experimentally demonstrated on two absorptive thin-film samples coated on transparent glass substrates. The refractive index and extinction coefficient spectra from 510 to 580 nm wavelength range and film thickness were simultaneously measured. The results are presented and discussed.

© 2014 Optical Society of America

1. Introduction

Optical coherence tomography (OCT) is a non-invasive morphological technique based on optical interferometry [1

1. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991). [CrossRef] [PubMed]

] involving the employment of a beam of light with a limited coherence length. It provides a micro-scale spatial resolution in both lateral and axial direction, while maintaining a longer scanning depth by using objective lenses of low numerical aperture. The spectroscopic optical coherence tomography further extracts the spectroscopic information from acquired data by analyzing the time-frequency distribution [2

2. U. Morgner, W. Drexler, F. X. Kärtner, X. D. Li, C. Pitris, E. P. Ippen, and J. G. Fujimoto, “Spectroscopic optical coherence tomography,” Opt. Lett. 25(2), 111–113 (2000). [CrossRef] [PubMed]

]. OCT has been proven to be useful for the characterizing of distribution of materials by analyzing the local spectral attenuation. Quantitative identification is also possible with proper calibration [3

3. H. Cang, T. Sun, Z. Y. Li, J. Chen, B. J. Wiley, Y. Xia, and X. Li, “Gold nanocages as contrast agents for spectroscopic optical coherence tomography,” Opt. Lett. 30(22), 3048–3050 (2005). [CrossRef] [PubMed]

5

5. A. Dubois, J. Moreau, and C. Boccara, “Spectroscopic ultrahigh-resolution full-field optical coherence microscopy,” Opt. Express 16(21), 17082–17091 (2008). [CrossRef] [PubMed]

]. Spectral-domain OCT (SD-OCT) configuration is usually preferred for the spectroscopic measurement, since it provides a better phase stability by removing the mechanical scanning in axial direction and with an improved signal to noise ratio [6

6. J. F. de Boer, B. Cense, B. H. Park, M. C. Pierce, G. J. Tearney, and B. E. Bouma, “Improved signal-to-noise ratio in spectral-domain compared with time-domain optical coherence tomography,” Opt. Lett. 28(21), 2067–2069 (2003). [CrossRef] [PubMed]

].

The measurement of optical characteristics such as refractive index and extinction coefficient is important for many applications, including imaging technologies and optics involving integrated devices. Various methods were developed for the non-invasive measurement of refractive index, extinction coefficient and film thickness [7

7. J. C. Manifacier, J. Gasiot, and J. P. Fillard, “A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film,” J. Phys. E Sci. Instrum. 9(11), 1002–1004 (1976). [CrossRef]

10

10. M. T. Fathi and S. Donati, “Thickness measurement of transparent plates by a self-mixing interferometer,” Opt. Lett. 35(11), 1844–1846 (2010). [CrossRef] [PubMed]

]. OCT-based techniques for material characterization were also proposed [11

11. G. J. Tearney, M. E. Brezinski, J. F. Southern, B. E. Bouma, M. R. Hee, and J. G. Fujimoto, “Determination of the refractive index of highly scattering human tissue by optical coherence tomography,” Opt. Lett. 20(21), 2258–2260 (1995). [CrossRef] [PubMed]

13

13. A. Zvyagin, K. K. M. B. Silva, S. Alexandrov, T. Hillman, J. Armstrong, T. Tsuzuki, and D. Sampson, “Refractive index tomography of turbid media by bifocal optical coherence refractometry,” Opt. Express 11(25), 3503–3517 (2003). [CrossRef] [PubMed]

], as they offer the capability to characterize thick layers. Most of them focus on the measurement of either thickness or group refractive index at a specific wavelength.

We have developed a SD-OCT system which is capable of simultaneous measuring the complex refractive index spectrum in the visible range and film thickness of absorptive thin films. With the normal-incident optical system of OCT, film characterization with SD-OCT has the advantage of spatial resolution. Employing the coherence gating effect, the SD-OCT measurement could eliminate the impact from irrelevant layers of the sample under test. In other words, any stray light resulting from unknown layers away from the layer of interest may not affect the measurement result. The algorithm solves the phase ambiguity problem, making it suitable for samples with film thickness much larger than the half detection wavelength.

2. Method

2.1 Thin-film sample modeling

2.2 Identification and separation of signals

The complex interference spectrum, described in Eq. (3), contains both amplitude and phase information at each wavelength. When considering N discrete wavelengths, we have 2N observables in total, which are less than the 2N + 1 unknowns (i.e. refractive index and extinction coefficient at N wavelengths and the sample thickness). To find a set of unique solution of (n, k, l), it is necessary to extract more information from the data. Equation (3) contains all the reflections and multiple reflections of the sample structure of Fig. 1. If the 1st order reflections (Grfront andGtfronttfrontrrearexp[i4π(n+ik)fl/c]) of the two interfaces are isolated to each other and all the other multiple reflections in the temporal domain, the number of observations increases to 4N (2N for each interface), and finding a solution of (n, k, l) becomes possible. To execute such operation, it is important that the signals of each interface is isolated to each other, which requires a better axial resolution for the characterization of thinner films. In addition, system chromatic dispersion compensation via the employment of optical dispersion compensator or digital electronic compensation is needed, since dispersion may also broaden the point spread function. It should be noted that the shape of the light source spectrum is also crucial, since for a spectrum shape away from Gaussian, side lopes arise after the Fourier transform, and prevent the clean separation of signals.

2.3 Model fitting

Once the axial resolution is high enough to separate the first two terms of the multiple reflections due to the front and rear interface of sample, an inverse Fourier transform of the measured interference intensity signal can be performed to each of them. We are interested in the absolute value of these two reflection amplitudes as well as their phase difference. They can be described with following equations:

A=G|rfront|
(4)
B=G|tfronttfrontrrear|exp(4πkfl/c)
(5)
C=(tfronttfrontrrearrfront)+4πnfl/c
(6)

In other words A is the amplitude spectrum of the front interface reflection, B is the amplitude spectrum of the rear interface reflection, and C is the phase difference between these two amplitudes. Note only the phase difference between the two interface signals are used for the calculation. These three spectral attributes are dependent on the complex refractive index and the film thickness. Equations (4)(6) must be inverted to obtain these optical parameters of the film. In our experimental investigation, we measured A, B and C at several wavelengths within the range of 510 nm - 580 nm. The optical parameters (n, k, l) of thin film can then be calculated with Gauss-Newton algorithm by fitting the numerical model to the experimental data. The increment vector (δn, δk, δl) of each wavelength can be determined with the following equation:
(δnδkδl)=(A/nA/kA/lB/nB/kB/lC/nC/kC/l)1(AexpABexpBCexpC)
(7)
where Aexp, Bexp and Cexp are the measured value of A, B and C. An appropriate initial guess of (n, k, l) are (n0, 0, d/ n0), where n0 is the typical refractive index of that sample, d is the optical thickness of the film estimated by the distance between the coherence spikes. Since the film thickness l is known to be wavelength-independent, the actual increment of l for each iteration is the average value of δl derived from Eq. (7) for each wavelength. With the initial condition described above and an accuracy requirement of, for example, 1%, the result usually converges within 100 iterations.

2.4 Phase ambiguity issue

For optical thickness of films larger than half optical wavelength, phase ambiguity problem may occur. This ambiguity comes from the fact that the phase retrieved with SD-OCT is always within the principal 2π range. A continuous phase spectrum (proportional to the film thickness) can be obtained via the employment of a phase unwrapping method [15

15. T. R. Judge and P. J. Bryanston-Cross, “A review of phase unwrapping techniques in fringe analysis,” Opt. Lasers Eng. 21(4), 199–239 (1994). [CrossRef]

]. Unwrapped phase spectrum has a 2πm phase shift from the actual phase, where m is an unknown integer, and:
Cexp(m)=Cunwrapped+2πm
(8)
whereCunwrapped is the continuous phase spectrum directly generated from the experimental data. This kind of ambiguity problem generally can be solved by using multiple wavelengths for the detection [16

16. Y. Y. Cheng and J. C. Wyant, “Two-wavelength phase shifting interferometry,” Appl. Opt. 23(24), 4539–4543 (1984). [CrossRef] [PubMed]

]. For low-coherence interference system, removing the ambiguity by introducing an artificial dispersion in low-coherence optical system was firstly proposed by Hitzenberger [17

17. C. K. Hitzenberger, M. Sticker, R. Leitgeb, and A. F. Fercher, “Differential phase measurements in low-coherence interferometry without 2π ambiguity,” Opt. Lett. 26(23), 1864–1866 (2001). [CrossRef] [PubMed]

]. Later Hendargo provided an alternative solution to this problem for SD-OCT system by performing synthetic-wavelength-based phase unwrapping [18

18. H. C. Hendargo, M. Zhao, N. Shepherd, and J. A. Izatt, “Synthetic wavelength based phase unwrapping in spectral domain optical coherence tomography,” Opt. Express 17(7), 5039–5051 (2009). [CrossRef] [PubMed]

]. To solve the phase ambiguity issue with a sample of unknown dispersion properties, a parameter optimization approach was applied. Since the mean square error (MSE) of the model fitting described in Eqs. (4)(7) increases with incorrect m selection, the ambiguity can be resolved by performing the parameter optimization for different m value. The idea is clear for thin layer with zero dispersion (i.e. air spacing) where the C is a straight line crossing the zero, and for incorrect m, Cexp(m) will not cross the zero and perfect fitting becomes impossible. The idea can be extended to thin film with finite dispersion (dn/dλ0) and attenuation (k0) if the minimization of the MSE for all three of Aexp, Bexp and Cexp are processed in the optimization process. The MSE to be considered in this case is defined as:
MSE(m)={1Nj=1N[(AexpjAjAexpj)2+(BexpjBjBexpj)2+(CexpjCjCexpj(m))2]}12
(9)
where N is the number of data points in frequency domain, and the superscript j specifies the discrete frequencies within the light source bandwidth. m0 is defined as the m gives the minimum MSE, Cexp=Cunwrapped+2πm0.

3. Experiment

3.1 System setup

In our experimental investigation the light source of the OCT system is a Ce3+:YAG double-clad crystal fiber (DCF) pumped with a 446-nm laser diode [19

19. C. C. Tsai, T. H. Chen, Y. S. Lin, Y. T. Wang, W. Chang, K. Y. Hsu, Y. H. Chang, P. K. Hsu, D. Y. Jheng, K. Y. Huang, E. Sun, and S. L. Huang, “Ce3+:YAG double-clad crystal-fiber-based optical coherence tomography on fish cornea,” Opt. Lett. 35(6), 811–813 (2010). [CrossRef] [PubMed]

,20

20. S. C. Pei, T. S. Ho, C. C. Tsai, T. H. Chen, Y. Ho, P. L. Huang, A. H. Kung, and S. L. Huang, “Non-invasive characterization of the domain boundary and structure properties of periodically poled ferroelectrics,” Opt. Express 19(8), 7153–7160 (2011). [CrossRef] [PubMed]

]. It emits a broadband spectrum with a 545-nm center wavelength and a bandwidth of 90 nm, as shown in Fig. 2(a), the corresponding axial resolution is about 1.5 μm in free space. The system is an ordinary SD-OCT setup, as shown in Fig. 2(b). The spectrometer we used is an Ocean Optics USB4000, which provides a 1.5-nm spectral resolution.
Fig. 2 (a) Ce:YAG DCF fluorescence spectrum. (b) SD-OCT setup.

3.2 Sample

4. Result and discussion

Fig. 4 Axial scan and calculated spectral attributes. (a) Axial scan of Sample 1. (b) Axial scan of Sample 2. (c) Calculated spectral attribute A, B and C of sample 1. (d) Calculated spectral attribute A, B and C of sample 2.
In the data analysis of the experimental results, the measured signals of the interference intensity at various wavelengths form an interference spectrum. This spectrum is then transformed into temporal domain via a Fourier transform. Figure 4 shows the results of the Fourier transform (axial scans) and corresponding spectral attributes (A, B, and C versus wavelength). Note the phase spectra C shown here are the continuous phase spectra directly unwrapped from the experimental value. To determine the m0 value for each case, the MSE versus m relation were calculated, as shown in Fig. 5.
Fig. 5 MSE versus m plot. The m is equal to zero if Cexp is within the principal interval [-π,π] at 545 nm. The insets show the zoomed portions of the figures around the minimum of MSE. (a) Sample 1. (b) Sample 2.

The MSE versus m relation suggests the m0 is 27 for sample 1 and 16 for sample 2, respectively. In both figures asymmetry was found centering m0. With the m0 known via the optimization process using Eq. (9), the phase ambiguity in Eq. (8) is resolved. Using Eqs. (4)-(6) in conjunction with the Gauss-Newton algorithm, we are able to obtain the unknowns n, k and l. A starting condition of (n, k) is set to be (1.6, 0) for all wavelength, and the initial guess of film thickness is the estimated optical thickness of thin film divided by 1.6. The optical thickness was estimated with the distance between coherence spikes in Fig. 4, which are 8.2 μm for sample 1 and 5.4 μm for sample 2, and the corresponding guesses of l are 5.1 μm and 3.4 μm, respectively. The calculation results for (n, k, l) are shown in Fig. 6.
Fig. 6 The derived optical properties. From left to right: refractive index, extinction coefficient, uniqueness test of film thickness. (a) Sample 1. (b) Sample 2.
The derived refractive indices of both samples show negative dispersion, as expected for this kind of polymer film in the spectral regime where absorption occurs. The calculation precision is discussed by performing the uniqueness test that commonly used for spectroscopic ellipsometry [21

21. J. N. Hilfiker, N. Singh, T. Tiwald, D. Convey, S. M. Smith, J. H. Baker, and H. G. Tompkins, “Survey of methods to characterize thin absorbing films with spectroscopic ellipsometry,” Thin Solid Films 516(22), 7979–7989 (2008). [CrossRef]

]. As shown in Fig. 6, the minima of MSE appear at 4.44 μm and 2.73 μm for sample 1 and sample 2. The corresponding uniqueness range is 6.4 nm and 3.5 nm, respectively.

To further verify the calculated optical properties, the transmittance of the samples is calculated using the measured optical parameters (n, k, l) of the samples with the following equation:
T=|tsubstratetfronttrearexp[i2π(n+ik)fl/c]1rfrontrrearexp[i4π(n+ik)fl/c]|2
(10)
where tsubstrateis the transmission coefficient of the back interface of substrate. The transmission spectra of samples within the same spectral range were measured with a commercial transmission spectrometer, JASCO V670, which uses a halogen lamp as probe to measure the transmittance within a slit-shaped area. To calculate the transmission spectrum within that area, cross-sectional tomographic images of samples were measured, as shown in Fig. 7.
Fig. 7 Cross-sectional tomographic images of the thin film samples measured with SD-OCT in the substrate-incident scheme. The figures show tomographic images within 20 μm (axial) X 5 mm (lateral) area. The figures are plotted in logarithmic scale and stretched in the longitudinal direction. Light is incident from the top of figures. (a) Sample 1. (b) Sample 2.
Slight inhomogeneity (film thickness variation) in lateral direction can be seen for both samples, and standard deviation of optical thickness of sample 1 and sample 2 are around 21.5 nm and 10.3 nm, respectively. The characterization process was applied for each sample, and the transmittances were calculated according to Eq. (10). The overall transmission curves were generated by averaging the transmittances, and the comparison to the value measured by a commercial transmission spectrometer is shown in Fig. 8, which shows good agreement for both samples.
Fig. 8 Comparison of the derived transmittance based on SD-OCT data (with a 50-nm standard deviation of optical thickness) and the value measured with commercial transmittance spectrometer. Black solid line: derived from the optical constants measured with the OCT. Red dash line: measured with transmittance spectrometer. (a) Sample 1. (b) Sample 2.

5. Conclusion

We have proposed, analyzed and experimentally demonstrated an OCT technique that is capable of characterizing the refractive index, extinction coefficient and physical thickness of absorptive thin layers. The experimental investigation was demonstrated using two absorptive polymer films coated on transparent glass substrate. The 510~580-nm measurement bandwidth is limited by the Ce:YAG DCF emission spectrum. This technique provides a convenient method for the characterization of film with a micro-scale thickness, with high spatial resolution in both axial and lateral direction, making it useful in imaging technology and integrated optics.

Acknowledgment

This work was partially supported by the National Science Council.

References and links

1.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991). [CrossRef] [PubMed]

2.

U. Morgner, W. Drexler, F. X. Kärtner, X. D. Li, C. Pitris, E. P. Ippen, and J. G. Fujimoto, “Spectroscopic optical coherence tomography,” Opt. Lett. 25(2), 111–113 (2000). [CrossRef] [PubMed]

3.

H. Cang, T. Sun, Z. Y. Li, J. Chen, B. J. Wiley, Y. Xia, and X. Li, “Gold nanocages as contrast agents for spectroscopic optical coherence tomography,” Opt. Lett. 30(22), 3048–3050 (2005). [CrossRef] [PubMed]

4.

C. Xu, C. Vinegoni, T. S. Ralston, W. Luo, W. Tan, and S. A. Boppart, “Spectroscopic spectral-domain optical coherence microscopy,” Opt. Lett. 31(8), 1079–1081 (2006). [CrossRef] [PubMed]

5.

A. Dubois, J. Moreau, and C. Boccara, “Spectroscopic ultrahigh-resolution full-field optical coherence microscopy,” Opt. Express 16(21), 17082–17091 (2008). [CrossRef] [PubMed]

6.

J. F. de Boer, B. Cense, B. H. Park, M. C. Pierce, G. J. Tearney, and B. E. Bouma, “Improved signal-to-noise ratio in spectral-domain compared with time-domain optical coherence tomography,” Opt. Lett. 28(21), 2067–2069 (2003). [CrossRef] [PubMed]

7.

J. C. Manifacier, J. Gasiot, and J. P. Fillard, “A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film,” J. Phys. E Sci. Instrum. 9(11), 1002–1004 (1976). [CrossRef]

8.

R. M. A. Azzam, “Simple and direct determination of complex refractive index and thickness of unsupported or embedded thin films by combined reflection and transmission Ellipsometry at 45° angle of incidence,” J. Opt. Soc. Am. 73(8), 1080–1082 (1983). [CrossRef]

9.

F. Yang, M. Tabet, and W. A. McGahan, “Characterizing optical properties of red, green, and blue color filters for automated film-thickness measurement,” Proc. SPIE 3332, 403–410 (1998). [CrossRef]

10.

M. T. Fathi and S. Donati, “Thickness measurement of transparent plates by a self-mixing interferometer,” Opt. Lett. 35(11), 1844–1846 (2010). [CrossRef] [PubMed]

11.

G. J. Tearney, M. E. Brezinski, J. F. Southern, B. E. Bouma, M. R. Hee, and J. G. Fujimoto, “Determination of the refractive index of highly scattering human tissue by optical coherence tomography,” Opt. Lett. 20(21), 2258–2260 (1995). [CrossRef] [PubMed]

12.

A. Knüttel and M. Boehlau-Godau, “Spatially confined and temporally resolved refractive index and scattering evaluation in human skin performed with optical coherence tomography,” J. Biomed. Opt. 5(1), 83–92 (2000). [CrossRef] [PubMed]

13.

A. Zvyagin, K. K. M. B. Silva, S. Alexandrov, T. Hillman, J. Armstrong, T. Tsuzuki, and D. Sampson, “Refractive index tomography of turbid media by bifocal optical coherence refractometry,” Opt. Express 11(25), 3503–3517 (2003). [CrossRef] [PubMed]

14.

P. Yeh, Optical Waves in Layered Media (John Wiley, 1998), Chap. 4.

15.

T. R. Judge and P. J. Bryanston-Cross, “A review of phase unwrapping techniques in fringe analysis,” Opt. Lasers Eng. 21(4), 199–239 (1994). [CrossRef]

16.

Y. Y. Cheng and J. C. Wyant, “Two-wavelength phase shifting interferometry,” Appl. Opt. 23(24), 4539–4543 (1984). [CrossRef] [PubMed]

17.

C. K. Hitzenberger, M. Sticker, R. Leitgeb, and A. F. Fercher, “Differential phase measurements in low-coherence interferometry without 2π ambiguity,” Opt. Lett. 26(23), 1864–1866 (2001). [CrossRef] [PubMed]

18.

H. C. Hendargo, M. Zhao, N. Shepherd, and J. A. Izatt, “Synthetic wavelength based phase unwrapping in spectral domain optical coherence tomography,” Opt. Express 17(7), 5039–5051 (2009). [CrossRef] [PubMed]

19.

C. C. Tsai, T. H. Chen, Y. S. Lin, Y. T. Wang, W. Chang, K. Y. Hsu, Y. H. Chang, P. K. Hsu, D. Y. Jheng, K. Y. Huang, E. Sun, and S. L. Huang, “Ce3+:YAG double-clad crystal-fiber-based optical coherence tomography on fish cornea,” Opt. Lett. 35(6), 811–813 (2010). [CrossRef] [PubMed]

20.

S. C. Pei, T. S. Ho, C. C. Tsai, T. H. Chen, Y. Ho, P. L. Huang, A. H. Kung, and S. L. Huang, “Non-invasive characterization of the domain boundary and structure properties of periodically poled ferroelectrics,” Opt. Express 19(8), 7153–7160 (2011). [CrossRef] [PubMed]

21.

J. N. Hilfiker, N. Singh, T. Tiwald, D. Convey, S. M. Smith, J. H. Baker, and H. G. Tompkins, “Survey of methods to characterize thin absorbing films with spectroscopic ellipsometry,” Thin Solid Films 516(22), 7979–7989 (2008). [CrossRef]

OCIS Codes
(110.4500) Imaging systems : Optical coherence tomography
(310.3840) Thin films : Materials and process characterization

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: July 24, 2013
Revised Manuscript: February 22, 2014
Manuscript Accepted: February 27, 2014
Published: March 5, 2014

Virtual Issues
Vol. 9, Iss. 5 Virtual Journal for Biomedical Optics

Citation
Tuan-Shu Ho, Pochi Yeh, Cheng-Chung Tsai, Kuang-Yu Hsu, and Sheng-Lung Huang, "Spectroscopic measurement of absorptive thin films by Spectral-Domain Optical Coherence Tomography," Opt. Express 22, 5675-5683 (2014)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-22-5-5675


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References

  1. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991). [CrossRef] [PubMed]
  2. U. Morgner, W. Drexler, F. X. Kärtner, X. D. Li, C. Pitris, E. P. Ippen, J. G. Fujimoto, “Spectroscopic optical coherence tomography,” Opt. Lett. 25(2), 111–113 (2000). [CrossRef] [PubMed]
  3. H. Cang, T. Sun, Z. Y. Li, J. Chen, B. J. Wiley, Y. Xia, X. Li, “Gold nanocages as contrast agents for spectroscopic optical coherence tomography,” Opt. Lett. 30(22), 3048–3050 (2005). [CrossRef] [PubMed]
  4. C. Xu, C. Vinegoni, T. S. Ralston, W. Luo, W. Tan, S. A. Boppart, “Spectroscopic spectral-domain optical coherence microscopy,” Opt. Lett. 31(8), 1079–1081 (2006). [CrossRef] [PubMed]
  5. A. Dubois, J. Moreau, C. Boccara, “Spectroscopic ultrahigh-resolution full-field optical coherence microscopy,” Opt. Express 16(21), 17082–17091 (2008). [CrossRef] [PubMed]
  6. J. F. de Boer, B. Cense, B. H. Park, M. C. Pierce, G. J. Tearney, B. E. Bouma, “Improved signal-to-noise ratio in spectral-domain compared with time-domain optical coherence tomography,” Opt. Lett. 28(21), 2067–2069 (2003). [CrossRef] [PubMed]
  7. J. C. Manifacier, J. Gasiot, J. P. Fillard, “A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film,” J. Phys. E Sci. Instrum. 9(11), 1002–1004 (1976). [CrossRef]
  8. R. M. A. Azzam, “Simple and direct determination of complex refractive index and thickness of unsupported or embedded thin films by combined reflection and transmission Ellipsometry at 45° angle of incidence,” J. Opt. Soc. Am. 73(8), 1080–1082 (1983). [CrossRef]
  9. F. Yang, M. Tabet, W. A. McGahan, “Characterizing optical properties of red, green, and blue color filters for automated film-thickness measurement,” Proc. SPIE 3332, 403–410 (1998). [CrossRef]
  10. M. T. Fathi, S. Donati, “Thickness measurement of transparent plates by a self-mixing interferometer,” Opt. Lett. 35(11), 1844–1846 (2010). [CrossRef] [PubMed]
  11. G. J. Tearney, M. E. Brezinski, J. F. Southern, B. E. Bouma, M. R. Hee, J. G. Fujimoto, “Determination of the refractive index of highly scattering human tissue by optical coherence tomography,” Opt. Lett. 20(21), 2258–2260 (1995). [CrossRef] [PubMed]
  12. A. Knüttel, M. Boehlau-Godau, “Spatially confined and temporally resolved refractive index and scattering evaluation in human skin performed with optical coherence tomography,” J. Biomed. Opt. 5(1), 83–92 (2000). [CrossRef] [PubMed]
  13. A. Zvyagin, K. K. M. B. Silva, S. Alexandrov, T. Hillman, J. Armstrong, T. Tsuzuki, D. Sampson, “Refractive index tomography of turbid media by bifocal optical coherence refractometry,” Opt. Express 11(25), 3503–3517 (2003). [CrossRef] [PubMed]
  14. P. Yeh, Optical Waves in Layered Media (John Wiley, 1998), Chap. 4.
  15. T. R. Judge, P. J. Bryanston-Cross, “A review of phase unwrapping techniques in fringe analysis,” Opt. Lasers Eng. 21(4), 199–239 (1994). [CrossRef]
  16. Y. Y. Cheng, J. C. Wyant, “Two-wavelength phase shifting interferometry,” Appl. Opt. 23(24), 4539–4543 (1984). [CrossRef] [PubMed]
  17. C. K. Hitzenberger, M. Sticker, R. Leitgeb, A. F. Fercher, “Differential phase measurements in low-coherence interferometry without 2π ambiguity,” Opt. Lett. 26(23), 1864–1866 (2001). [CrossRef] [PubMed]
  18. H. C. Hendargo, M. Zhao, N. Shepherd, J. A. Izatt, “Synthetic wavelength based phase unwrapping in spectral domain optical coherence tomography,” Opt. Express 17(7), 5039–5051 (2009). [CrossRef] [PubMed]
  19. C. C. Tsai, T. H. Chen, Y. S. Lin, Y. T. Wang, W. Chang, K. Y. Hsu, Y. H. Chang, P. K. Hsu, D. Y. Jheng, K. Y. Huang, E. Sun, S. L. Huang, “Ce3+:YAG double-clad crystal-fiber-based optical coherence tomography on fish cornea,” Opt. Lett. 35(6), 811–813 (2010). [CrossRef] [PubMed]
  20. S. C. Pei, T. S. Ho, C. C. Tsai, T. H. Chen, Y. Ho, P. L. Huang, A. H. Kung, S. L. Huang, “Non-invasive characterization of the domain boundary and structure properties of periodically poled ferroelectrics,” Opt. Express 19(8), 7153–7160 (2011). [CrossRef] [PubMed]
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