Abstract

This paper describes a technique for measuring refractive index and thickness of transparent plates using a fibre-optic low-coherence interferometer. The interferometer is used to independently measure quantities related to the phase and group refractive indices, np and ng, of the material under investigation. Additionally, the dispersion of the phase index dependent quantity is measured by taking advantage of the range of wavelengths available from a broadband source. These three quantities are related to simultaneously yield np and ng as well as the geometrical thickness t of the sample. Measurements are presented for a range of transparent materials including measurements of the ordinary and extraordinary refractive indices of a birefringent sapphire window. The mean percentage errors across all the samples tested were 0.09% for np, 0.08% for np, and 0.11% for t.

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References

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2017 (2)

2015 (2)

2014 (2)

2013 (1)

P. Liu, R. M. Groves, and R. Benedictus, “Signal processing in optical coherence tomography for aerospace material characterization,” Opt. Eng. 52(3), 033201 (2013).
[Crossref]

2012 (1)

2011 (1)

S. J. Park, K. S. Park, Y. H. Kim, and B. H. Lee, “Simultaneous measurements of refractive index and thickness by spectral-domain low-coherence interferometry having dual sample probes,” IEEE Photonic. Tech. L. 23(15), 1076–1078 (2011).
[Crossref]

2009 (1)

J. Na, H. Y. Choi, E. S. Choi, C. S. Lee, and B. H. Lee, “Self-referenced spectral interferometry for simultaneous measurements of thickness and refractive index,” Appl. Opt. 49(13), 2461–2467 (2009).
[Crossref]

2008 (1)

2004 (1)

M. Ohmi, H. Nishi, Y. Konishi, Y. Yamada, and M. Haruna, “High-speed simultaneous measurement of refractive index and thickness of transparent plates by low-coherence interferometry and confocal optics,” Meas. Sci. Technol. 15, 1531–1535 (2004).
[Crossref]

2002 (1)

2000 (1)

H. Maruyama, T. Mitsuyama, M. Ohmi, and M. Haruna, “Simultaneous measurement of refractive index and thickness by low-coherence interferometry considering chromatic dispersion of index,” Opt. Rev. 7(5), 468–472 (2000).
[Crossref]

1998 (1)

1996 (2)

1995 (1)

1991 (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, 1178–1181 (1991).
[Crossref] [PubMed]

1987 (1)

1965 (1)

Adler, D. C.

D. C. Adler, Digital signal processing techniques for optical coherence tomography: spectroscopic OCT and OCT image enhancement, MSc. Thesis, Massachusetts Institute of Technology (Cambridge, MA. 2014).

Ahmed, M.

Aslam Zia, M.

Benedictus, R.

P. Liu, R. M. Groves, and R. Benedictus, “Signal processing in optical coherence tomography for aerospace material characterization,” Opt. Eng. 52(3), 033201 (2013).
[Crossref]

Boettcher, T.

Bouma, B. E.

Brezinski, M. E.

Chang, W.

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, 1178–1181 (1991).
[Crossref] [PubMed]

Cho, S-W.

Choi, E. S.

J. Na, H. Y. Choi, E. S. Choi, C. S. Lee, and B. H. Lee, “Self-referenced spectral interferometry for simultaneous measurements of thickness and refractive index,” Appl. Opt. 49(13), 2461–2467 (2009).
[Crossref]

Choi, H. Y.

J. Na, H. Y. Choi, E. S. Choi, C. S. Lee, and B. H. Lee, “Self-referenced spectral interferometry for simultaneous measurements of thickness and refractive index,” Appl. Opt. 49(13), 2461–2467 (2009).
[Crossref]

Daimon, M.

Danielson, B. L.

Flotte, T.

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, 1178–1181 (1991).
[Crossref] [PubMed]

Fujimoto, J. G.

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]

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, 1178–1181 (1991).
[Crossref] [PubMed]

Fukano, T.

Gregory, K.

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, 1178–1181 (1991).
[Crossref] [PubMed]

Gronle, M.

Groves, R. M.

P. Liu, R. M. Groves, and R. Benedictus, “Signal processing in optical coherence tomography for aerospace material characterization,” Opt. Eng. 52(3), 033201 (2013).
[Crossref]

Haruna, M.

M. Ohmi, H. Nishi, Y. Konishi, Y. Yamada, and M. Haruna, “High-speed simultaneous measurement of refractive index and thickness of transparent plates by low-coherence interferometry and confocal optics,” Meas. Sci. Technol. 15, 1531–1535 (2004).
[Crossref]

H. Maruyama, T. Mitsuyama, M. Ohmi, and M. Haruna, “Simultaneous measurement of refractive index and thickness by low-coherence interferometry considering chromatic dispersion of index,” Opt. Rev. 7(5), 468–472 (2000).
[Crossref]

M. Haruna, M. Ohmi, T. Mitsuyama, H. Tajiri, H. Maruyama, and M. Hashimoto, “Simultaneous measurement of the phase and group indices and the thickness of transparent plates by low-coherence interferometry,” Opt. Lett. 23(12), 966–968 (1998).
[Crossref]

Hashimoto, M.

Hee, M. R.

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]

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, 1178–1181 (1991).
[Crossref] [PubMed]

Hernández-Romano, I.

Huang, D.

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, 1178–1181 (1991).
[Crossref] [PubMed]

Huang, J.

Hussain, B.

Iqbal, M.

Kim, C-S.

Kim, G. H.

Kim, M.

Kim, M. J.

Kim, S.

Kim, Y. H.

S. J. Park, K. S. Park, Y. H. Kim, and B. H. Lee, “Simultaneous measurements of refractive index and thickness by spectral-domain low-coherence interferometry having dual sample probes,” IEEE Photonic. Tech. L. 23(15), 1076–1078 (2011).
[Crossref]

Konishi, Y.

M. Ohmi, H. Nishi, Y. Konishi, Y. Yamada, and M. Haruna, “High-speed simultaneous measurement of refractive index and thickness of transparent plates by low-coherence interferometry and confocal optics,” Meas. Sci. Technol. 15, 1531–1535 (2004).
[Crossref]

Larkin, K. J.

Lee, B. H.

S. J. Park, K. S. Park, Y. H. Kim, and B. H. Lee, “Simultaneous measurements of refractive index and thickness by spectral-domain low-coherence interferometry having dual sample probes,” IEEE Photonic. Tech. L. 23(15), 1076–1078 (2011).
[Crossref]

J. Na, H. Y. Choi, E. S. Choi, C. S. Lee, and B. H. Lee, “Self-referenced spectral interferometry for simultaneous measurements of thickness and refractive index,” Appl. Opt. 49(13), 2461–2467 (2009).
[Crossref]

S. Kim, J. Na, M. J. Kim, and B. H. Lee, “Simultaneous measurement of refractive index and thickness by combining low-coherence interferometry and confocal optics,” Opt. Express 16(8), 5516–5526 (2008).
[Crossref] [PubMed]

Lee, C. S.

J. Na, H. Y. Choi, E. S. Choi, C. S. Lee, and B. H. Lee, “Self-referenced spectral interferometry for simultaneous measurements of thickness and refractive index,” Appl. Opt. 49(13), 2461–2467 (2009).
[Crossref]

Lin, C. P.

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, 1178–1181 (1991).
[Crossref] [PubMed]

Liu, P.

P. Liu, R. M. Groves, and R. Benedictus, “Signal processing in optical coherence tomography for aerospace material characterization,” Opt. Eng. 52(3), 033201 (2013).
[Crossref]

Malitson, I. H.

Maruyama, H.

H. Maruyama, T. Mitsuyama, M. Ohmi, and M. Haruna, “Simultaneous measurement of refractive index and thickness by low-coherence interferometry considering chromatic dispersion of index,” Opt. Rev. 7(5), 468–472 (2000).
[Crossref]

M. Haruna, M. Ohmi, T. Mitsuyama, H. Tajiri, H. Maruyama, and M. Hashimoto, “Simultaneous measurement of the phase and group indices and the thickness of transparent plates by low-coherence interferometry,” Opt. Lett. 23(12), 966–968 (1998).
[Crossref]

Masumura, A.

Meemon, P.

Mitsuyama, T.

H. Maruyama, T. Mitsuyama, M. Ohmi, and M. Haruna, “Simultaneous measurement of refractive index and thickness by low-coherence interferometry considering chromatic dispersion of index,” Opt. Rev. 7(5), 468–472 (2000).
[Crossref]

M. Haruna, M. Ohmi, T. Mitsuyama, H. Tajiri, H. Maruyama, and M. Hashimoto, “Simultaneous measurement of the phase and group indices and the thickness of transparent plates by low-coherence interferometry,” Opt. Lett. 23(12), 966–968 (1998).
[Crossref]

Monzón-Hernández, D.

Moreno-Hernández, C.

Na, J.

J. Na, H. Y. Choi, E. S. Choi, C. S. Lee, and B. H. Lee, “Self-referenced spectral interferometry for simultaneous measurements of thickness and refractive index,” Appl. Opt. 49(13), 2461–2467 (2009).
[Crossref]

S. Kim, J. Na, M. J. Kim, and B. H. Lee, “Simultaneous measurement of refractive index and thickness by combining low-coherence interferometry and confocal optics,” Opt. Express 16(8), 5516–5526 (2008).
[Crossref] [PubMed]

Nawaz, M.

Nishi, H.

M. Ohmi, H. Nishi, Y. Konishi, Y. Yamada, and M. Haruna, “High-speed simultaneous measurement of refractive index and thickness of transparent plates by low-coherence interferometry and confocal optics,” Meas. Sci. Technol. 15, 1531–1535 (2004).
[Crossref]

Ohmi, M.

M. Ohmi, H. Nishi, Y. Konishi, Y. Yamada, and M. Haruna, “High-speed simultaneous measurement of refractive index and thickness of transparent plates by low-coherence interferometry and confocal optics,” Meas. Sci. Technol. 15, 1531–1535 (2004).
[Crossref]

H. Maruyama, T. Mitsuyama, M. Ohmi, and M. Haruna, “Simultaneous measurement of refractive index and thickness by low-coherence interferometry considering chromatic dispersion of index,” Opt. Rev. 7(5), 468–472 (2000).
[Crossref]

M. Haruna, M. Ohmi, T. Mitsuyama, H. Tajiri, H. Maruyama, and M. Hashimoto, “Simultaneous measurement of the phase and group indices and the thickness of transparent plates by low-coherence interferometry,” Opt. Lett. 23(12), 966–968 (1998).
[Crossref]

Osten, W.

Park, K. S.

S. J. Park, K. S. Park, Y. H. Kim, and B. H. Lee, “Simultaneous measurements of refractive index and thickness by spectral-domain low-coherence interferometry having dual sample probes,” IEEE Photonic. Tech. L. 23(15), 1076–1078 (2011).
[Crossref]

Park, S. J.

S. J. Park, K. S. Park, Y. H. Kim, and B. H. Lee, “Simultaneous measurements of refractive index and thickness by spectral-domain low-coherence interferometry having dual sample probes,” IEEE Photonic. Tech. L. 23(15), 1076–1078 (2011).
[Crossref]

Pavlicek, P

P Pavliček and S Svak, “Noise properties of Hilbert transform evaluation,” Meas. Sci. Technol. 26, 085207 (2015).
[Crossref]

Ponting, M.

Puliafito, C. A.

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, 1178–1181 (1991).
[Crossref] [PubMed]

Razzaq, M.

Rolland, J. P.

Saleem, M.

Schuman, J. S.

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, 1178–1181 (1991).
[Crossref] [PubMed]

Shin, B. S.

Southern, J. F.

Stinson, W. G.

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, 1178–1181 (1991).
[Crossref] [PubMed]

Svak, S

P Pavliček and S Svak, “Noise properties of Hilbert transform evaluation,” Meas. Sci. Technol. 26, 085207 (2015).
[Crossref]

Swanson, E. A.

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, 1178–1181 (1991).
[Crossref] [PubMed]

Tajiri, H.

Tearney, G. J.

Villatoro, J.

Whittenberg, C. D.

Yamada, Y.

M. Ohmi, H. Nishi, Y. Konishi, Y. Yamada, and M. Haruna, “High-speed simultaneous measurement of refractive index and thickness of transparent plates by low-coherence interferometry and confocal optics,” Meas. Sci. Technol. 15, 1531–1535 (2004).
[Crossref]

Yamaguchi, I.

Yao, J.

Zilio, S. C.

S. C. Zilio, “Simultaneous thickness and group index measurement with a single arm low-coherence interferometer,” Opt. Express Opt. Express 22(22), 27392–27397 (2014).
[Crossref] [PubMed]

Appl. Opt. (4)

IEEE Photonic. Tech. L. (1)

S. J. Park, K. S. Park, Y. H. Kim, and B. H. Lee, “Simultaneous measurements of refractive index and thickness by spectral-domain low-coherence interferometry having dual sample probes,” IEEE Photonic. Tech. L. 23(15), 1076–1078 (2011).
[Crossref]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Meas. Sci. Technol. (2)

M. Ohmi, H. Nishi, Y. Konishi, Y. Yamada, and M. Haruna, “High-speed simultaneous measurement of refractive index and thickness of transparent plates by low-coherence interferometry and confocal optics,” Meas. Sci. Technol. 15, 1531–1535 (2004).
[Crossref]

P Pavliček and S Svak, “Noise properties of Hilbert transform evaluation,” Meas. Sci. Technol. 26, 085207 (2015).
[Crossref]

Opt. Eng. (1)

P. Liu, R. M. Groves, and R. Benedictus, “Signal processing in optical coherence tomography for aerospace material characterization,” Opt. Eng. 52(3), 033201 (2013).
[Crossref]

Opt. Express (4)

Opt. Express Opt. Express (1)

S. C. Zilio, “Simultaneous thickness and group index measurement with a single arm low-coherence interferometer,” Opt. Express Opt. Express 22(22), 27392–27397 (2014).
[Crossref] [PubMed]

Opt. Lett. (3)

Opt. Rev. (1)

H. Maruyama, T. Mitsuyama, M. Ohmi, and M. Haruna, “Simultaneous measurement of refractive index and thickness by low-coherence interferometry considering chromatic dispersion of index,” Opt. Rev. 7(5), 468–472 (2000).
[Crossref]

Science (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, 1178–1181 (1991).
[Crossref] [PubMed]

Other (4)

D. C. Adler, Digital signal processing techniques for optical coherence tomography: spectroscopic OCT and OCT image enhancement, MSc. Thesis, Massachusetts Institute of Technology (Cambridge, MA. 2014).

M. N. Polyanskiy, “Refractive index database,” https://refractiveindex.info

Schott, Optical glass datasheets, (July2015).

Schott UK, Skan House, Stratford Road, Shirley, Solihull, West Midlands. B90 4AE, UK (personal communication, December 2016).

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Figures (9)

Fig. 1
Fig. 1 Schematic showing the optical arrangement of the interferometer. SLD is the 840 nm centre wavelength super-luminescent diode, BC is the broadband coupler, RM is the reference mirror, and AD are 8 mm aperture achromatic doublets (20 mm focal length to collimate, 15 mm focal length to focus). The blue shading indicates which components are mounted on the translation stages in each arm.
Fig. 2
Fig. 2 Plots showing the spectra of the three SLDs present in the Superlum M-T-850-HP-I SLD system measured on (a) a Yokogawa AQ6370C optical spectrum analyser (0.2 nm resolution bandwidth) and (b) the BaySpec CMOS spectrometer (0.1 nm resolution bandwidth) used in the present work.
Fig. 3
Fig. 3 Calibration procedure for the spectrometer: (a) Signals obtained after a two minute integration time for a range of wavelengths from 805 nm – 855 nm plotted against pixel number. Peaks were obtained sequentially but are shown here plotted on the same graph. The black curves are polynomial fits to the signal data. (b) Interpolation and extrapolation of the measured data to cover the entire 4,096 pixel array of the line-scan camera (only a section shown in the plot for illustration). ID = interpolated data, MW = measured wavelengths, ED = extrapolated data.
Fig. 4
Fig. 4 Plots showing the measured quantities (a) Δz, the separation between the reflection peaks in the confocal arrangement, and (b) ΔD, the separation between the low-coherence fringe envelopes. These measurements were obtained using a CaF2 window with a thickness of approximately 2 mm.
Fig. 5
Fig. 5 Plots showing low-coherence fringe envelopes obtained with the system: (a) shows the influence of the spectral intensity distribution (shown in Fig. 2(b)) on the fringe pattern obtained using the SLD, (b) shows a fringe pattern obtained with each individual spectrometer acquisition multiplied by a Gaussian function and the demodulated fringe envelope (MS = mean integrated signal, HE = Hilbert envelope, PF = polynomial fit). The highlighted region near the centre shows the section of the fringe pattern used to plot (c), which shows that the noise in the Hilbert envelope corresponds with noise in the integrated signal.
Fig. 6
Fig. 6 Multi-wavelength confocal measurement of a BK7 window: (a) plot showing the reflected signal from both surfaces of the BK7 window as the object is scanned through the focus of the sample arm lens. (b) The path traversed by the stage. (c) The top of the reflected peak associated with the front surface at 850 nm and the polynomial fit to the data.
Fig. 7
Fig. 7 (a) Plots showing the variation in peak position with wavelength for the front and rear surfaces. (b) The difference between peak locations at each wavelength, the gradient of which provides the dispersion term dΔz/dν.
Fig. 8
Fig. 8 The impact of etalon fringes present when measuring a thin BK7 window on the dispersion measurement and improvement through Fourier filtering: (a) a typical spectrometer acquisition at a confocal peak and (b) the associated dispersion measurement, (c) and (d) are similar plots obtained after using Fourier filtering to reduce the etalon fringes. Note the more readily discernible gradient of (d) relative to (b).
Fig. 9
Fig. 9 Plot showing the fringe burst associated with the rear surface of a sapphire window. The integrated spectrometer data is plotted along with the polynomial fit to the demodulated Hilbert envelope. The arrows indicate the peak separations (from the fringe burst associated with the front surface) used to determine Δl for the ordinary and extraordinary refractive indices.

Tables (5)

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Table 1 Summary of phase and group refractive index measurements for four different optical materials.

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Table 2 Summary of thickness measurements for four different materials given in millimetres. The reference values were obtained using a micrometer gauge and were measured ten times, hence they have an associated standard deviation.

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Table 3 Measurements of the phase and group refractive indices for the ordinary and extraordinary optical paths of a birefringent sapphire window.

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Table 4 Measurements of the thickness of a sapphire window given in millimetres.

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Table 5 Summary of mean percentage errors in np, ng, and t from various publications based on quoted data. ‘S’ represents the number of samples tested.

Equations (7)

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Δ z = t × n air 2 N A 2 n p 2 N A 2 t n p
Δ l = Δ D + Δ z = t × n g
n g ( ν ) = n p ( ν ) + ν d n p ( ν ) d ν
t 2 = Δ l Δ z 1 ν Δ z d Δ z d ν
A t 2 + B t 4 + C t 6 = 0
A = ( n air 2 N A 2 ) 2 Δ z 4 + ν 2 ( n air 2 N A 2 ) 2 Δ z 6 ( d Δ z d ν ) 2 2 ν ( n air 2 N A 2 ) 2 Δ z 5 d Δ z d ν B = 2 ( n air 2 N A 2 ) Δ z 2 N A 2 2 N A 2 ν ( n air 2 N A 2 ) Δ z 3 d Δ z d ν C = N A 4 Δ l 2 Δ z 2 ( n air 2 N A 2 ) D = Δ l 2 N A 2
N A = n air 2 t 2 n p 2 Δ z 2 t 2 Δ z 2

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