Abstract

This paper demonstrates that the complex master slave interferometry (CMSI) method used in spectral domain interferometry (SDI) can efficiently be used for accurate refractive index and group velocity dispersion measurements of optically transparent samples. For the first time, we demonstrate the relevance of the phase information delivered by CMSI for dispersion evaluations with no need to linearize data. The technique proposed here has been used to accurately measure the group refractive index and the group velocity dispersion of a strong dispersive sample (SF6 glass), and a weak dispersive one (distilled water). The robustness of the technique is demonstrated through the manipulation of several sets of experimental data.

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  23. http://www.schott.com
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    [Crossref]

2017 (3)

R. Cernat, A. Bradu, N. M. Israelsen, O. Bang, S. Rivet, P. A. Keane, D.-G. Heath, R. Rajendram, and A. Podoleanu, “Gabor fusion master slave optical coherence tomography,” Biomed. Opt. Lett. 8(2), 813 (2017).

C. Photiou, E. Bousi, I. Zouvani, and C. Pitris, “Using speckle to measure tissue dispersion in optical coherence tomography,” Biomed. Opt. Express 8(5), 2528–2535 (2017).
[Crossref] [PubMed]

T. Kitazawa and T. Nomura, “Refractive index tomography based on optical coherence tomography and tomographic reconstruction algorithm,” Jpn. J. Appl. Phys. 56(9S), 09NB03 (2017).
[Crossref]

2016 (3)

2015 (2)

2014 (1)

2013 (1)

2012 (1)

2011 (1)

2010 (1)

2009 (1)

2008 (2)

2007 (1)

2006 (1)

2005 (2)

2003 (1)

J. G. Fujimoto, “Optical coherence tomography for ultrahigh resolution in vivo imaging,” Nat. Biotechnol. 21(11), 1361–1367 (2003).
[Crossref] [PubMed]

2001 (1)

P. Hlubina, “White-light spectral interferometry with the uncompensated Michelson interferometer and the group refractive index dispersion in fused silica,” Opt. Commun. 193(1–6), 1–7 (2001).
[Crossref]

2000 (1)

1999 (1)

1992 (1)

W. V. Sorin and D. F. Gray, “Simultaneous thickness and group index measurement using optical low-coherence reflectometry,” IEEE Photonics Technol. Lett. 4(1), 105–107 (1992).
[Crossref]

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(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Akiba, M.

Bang, O.

R. Cernat, A. Bradu, N. M. Israelsen, O. Bang, S. Rivet, P. A. Keane, D.-G. Heath, R. Rajendram, and A. Podoleanu, “Gabor fusion master slave optical coherence tomography,” Biomed. Opt. Lett. 8(2), 813 (2017).

Beaumont, A.

Belabas, N.

Bijster, J. G.

Bousi, E.

Bradu, A.

Bräuer, B.

Brun, G.

Cernat, R.

R. Cernat, A. Bradu, N. M. Israelsen, O. Bang, S. Rivet, P. A. Keane, D.-G. Heath, R. Rajendram, and A. Podoleanu, “Gabor fusion master slave optical coherence tomography,” Biomed. Opt. Lett. 8(2), 813 (2017).

Chan, K. K. H.

Chan, K.-P.

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(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Choi, E. S.

Choi, H. Y.

Chong, C.

Coen, S.

Daimon, M.

Dorrer, C.

Feuchter, T.

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(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Fujimoto, J. G.

J. G. Fujimoto, “Optical coherence tomography for ultrahigh resolution in vivo imaging,” Nat. Biotechnol. 21(11), 1361–1367 (2003).
[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(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Gillen, G. D.

Gray, D. F.

W. V. Sorin and D. F. Gray, “Simultaneous thickness and group index measurement using optical low-coherence reflectometry,” IEEE Photonics Technol. Lett. 4(1), 105–107 (1992).
[Crossref]

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(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Guha, S.

Hart, C.

Heath, D.-G.

R. Cernat, A. Bradu, N. M. Israelsen, O. Bang, S. Rivet, P. A. Keane, D.-G. Heath, R. Rajendram, and A. Podoleanu, “Gabor fusion master slave optical coherence tomography,” Biomed. Opt. Lett. 8(2), 813 (2017).

Hee, M. R.

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]

Hlubina, P.

P. Hlubina, “White-light spectral interferometry with the uncompensated Michelson interferometer and the group refractive index dispersion in fused silica,” Opt. Commun. 193(1–6), 1–7 (2001).
[Crossref]

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(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Israelsen, N. M.

R. Cernat, A. Bradu, N. M. Israelsen, O. Bang, S. Rivet, P. A. Keane, D.-G. Heath, R. Rajendram, and A. Podoleanu, “Gabor fusion master slave optical coherence tomography,” Biomed. Opt. Lett. 8(2), 813 (2017).

Itoh, M.

Jacquot, M.

Joffre, M.

Kalkman, J.

Keane, P. A.

R. Cernat, A. Bradu, N. M. Israelsen, O. Bang, S. Rivet, P. A. Keane, D.-G. Heath, R. Rajendram, and A. Podoleanu, “Gabor fusion master slave optical coherence tomography,” Biomed. Opt. Lett. 8(2), 813 (2017).

Kim, M. J.

Kim, S.

Kitazawa, T.

T. Kitazawa and T. Nomura, “Refractive index tomography based on optical coherence tomography and tomographic reconstruction algorithm,” Jpn. J. Appl. Phys. 56(9S), 09NB03 (2017).
[Crossref]

Kumar Gupta, P.

Lee, B. H.

Lee, C.

Leick, L.

Likforman, J.-P.

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(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Lippok, N.

Madjarova, V. D.

Makita, S.

Maria, M.

Masumura, A.

Morosawa, A.

Murdoch, S. G.

Na, J.

Nandi, P.

Nielsen, P.

Nomura, T.

T. Kitazawa and T. Nomura, “Refractive index tomography based on optical coherence tomography and tomographic reconstruction algorithm,” Jpn. J. Appl. Phys. 56(9S), 09NB03 (2017).
[Crossref]

Photiou, C.

Pitris, C.

Podoleanu, A.

Podoleanu, A. G.

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(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Rajendram, R.

R. Cernat, A. Bradu, N. M. Israelsen, O. Bang, S. Rivet, P. A. Keane, D.-G. Heath, R. Rajendram, and A. Podoleanu, “Gabor fusion master slave optical coherence tomography,” Biomed. Opt. Lett. 8(2), 813 (2017).

Rao, K. D.

Reolon, D.

Rivet, S.

Sakai, T.

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(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Sharma, M.

Sorin, W. V.

W. V. Sorin and D. F. Gray, “Simultaneous thickness and group index measurement using optical low-coherence reflectometry,” IEEE Photonics Technol. Lett. 4(1), 105–107 (1992).
[Crossref]

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(5035), 1178–1181 (1991).
[Crossref] [PubMed]

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(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Tang, S.

Tedaldi, M.

Tomlins, P. H.

Trull, A. K.

van der Horst, J.

Vanholsbeeck, F.

Veillas, C.

Verma, Y.

Verrier, I.

Woolliams, P.

Yasuno, Y.

Yatagai, T.

Zilio, S. C.

Zouvani, I.

Appl. Opt. (4)

Biomed. Opt. Express (3)

Biomed. Opt. Lett. (1)

R. Cernat, A. Bradu, N. M. Israelsen, O. Bang, S. Rivet, P. A. Keane, D.-G. Heath, R. Rajendram, and A. Podoleanu, “Gabor fusion master slave optical coherence tomography,” Biomed. Opt. Lett. 8(2), 813 (2017).

IEEE Photonics Technol. Lett. (1)

W. V. Sorin and D. F. Gray, “Simultaneous thickness and group index measurement using optical low-coherence reflectometry,” IEEE Photonics Technol. Lett. 4(1), 105–107 (1992).
[Crossref]

J. Opt. Soc. Am. B (2)

Jpn. J. Appl. Phys. (1)

T. Kitazawa and T. Nomura, “Refractive index tomography based on optical coherence tomography and tomographic reconstruction algorithm,” Jpn. J. Appl. Phys. 56(9S), 09NB03 (2017).
[Crossref]

Nat. Biotechnol. (1)

J. G. Fujimoto, “Optical coherence tomography for ultrahigh resolution in vivo imaging,” Nat. Biotechnol. 21(11), 1361–1367 (2003).
[Crossref] [PubMed]

Opt. Commun. (1)

P. Hlubina, “White-light spectral interferometry with the uncompensated Michelson interferometer and the group refractive index dispersion in fused silica,” Opt. Commun. 193(1–6), 1–7 (2001).
[Crossref]

Opt. Express (9)

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]

A. K. Trull, J. van der Horst, J. G. Bijster, and J. Kalkman, “Transmission optical coherence tomography based measurement of optical material properties,” Opt. Express 23(26), 33550–33563 (2015).
[Crossref] [PubMed]

N. Lippok, S. Coen, P. Nielsen, and F. Vanholsbeeck, “Dispersion compensation in Fourier domain optical coherence tomography using the fractional Fourier transform,” Opt. Express 20(21), 23398–23413 (2012).
[Crossref] [PubMed]

D. Reolon, M. Jacquot, I. Verrier, G. Brun, and C. Veillas, “High resolution group refractive index measurement by broadband supercontinuum interferometry and wavelet-transform analysis,” Opt. Express 14(26), 12744–12750 (2006).
[Crossref] [PubMed]

A. G. Podoleanu and A. Bradu, “Master-slave interferometry for parallel spectral domain interferometry sensing and versatile 3D optical coherence tomography,” Opt. Express 21(16), 19324–19338 (2013).
[Crossref] [PubMed]

S. Rivet, M. Maria, A. Bradu, T. Feuchter, L. Leick, and A. Podoleanu, “Complex Master Slave Interferometry,” Opt. Express 24(3), 2885–2904 (2016).
[Crossref] [PubMed]

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

A. Bradu, M. Maria, and A. G. Podoleanu, “Demonstration of tolerance to dispersion of master/slave interferometry,” Opt. Express 23(11), 14148–14161 (2015).
[Crossref] [PubMed]

Y. Yasuno, V. D. Madjarova, S. Makita, M. Akiba, A. Morosawa, C. Chong, T. Sakai, K.-P. Chan, M. Itoh, and T. Yatagai, “Three-dimensional and high-speed swept-source optical coherence tomography for in vivo investigation of human anterior eye segments,” Opt. Express 13(26), 10652–10664 (2005).
[Crossref] [PubMed]

Opt. Lett. (2)

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(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Other (1)

http://www.schott.com

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Figures (10)

Fig. 1
Fig. 1 Block diagram of a spectral domain interferometer. Mr and Ms are respectively the reference mirror and the sample mirror. The mirror Ms can be moved along the optical axis by a linear translation stage. The positions z and z0 correspond to the positions of Ms relatively to the origin 0 of the linear stage. I(x,δ) is the recorded channeled spectrum versus the pixel x of the camera for a given OPD = δ. Ls and Lr are identical achromatic lenses.

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Fig. 2
Fig. 2 Block diagram showing the procedure of extracting the spectral phases ϕvacuum and ϕsample from the channeled spectra Ivacuum and Isample respectively. Masks M, CMSI[Ivacuum] and CMSI[Isample] are complex quantities, only their amplitudes are represented in this diagram.

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Fig. 3
Fig. 3 (a) SLD spectrum as seen by the linear camera. (b) Dependence of the optical angular frequency ω = p(x) versus pixel position on the camera x. The pixel x0 corresponds to the incident position of light from a 0.873 mm-line of the swept-source used for calibration.

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Fig. 4
Fig. 4 (a) Channeled spectrum Ivacuum without sample in the arm of the interferometer, after filtering the DC component. (b) Calculation of CMSI[Ivacuum], where its amplitude is shown only for t>0. (c) Channeled spectrum Isample with sample placed in the sample arm of the interferometer and after filtering the DC component. (d) Calculation of CMSI[Isample], where its amplitude is shown only for t>0. (e) From Eq. (14), Δϕ-Δϕ(ωc) is displayed in black curve between 2.08 and 2.2 rad.fs−1. The red curve corresponds to the fit of Δϕ-Δϕ(ωc) using as numerical values for the constants in Eq. (9) the values shown in the inset.

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Fig. 5
Fig. 5 (a) Relative error of GVD according to the position of the mirror Ms with and without the sample in the interferometer’s arm. The white circle corresponds to the specific configuration zv = 20.1 mm and zs = 3.695 mm used at the beginning of Section 4.1. (b) Δϕ-Δϕ(ωc) for the configuration zv = 20.1 mm and zs = 3.745 mm. (c) Δϕ-Δϕ(ωc) for the configuration zv = 20.1 mm and zs = 3.645 mm.

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Fig. 6
Fig. 6 Measurement of GVD for SF6 sample according to the position of the mirror Ms in the case δs = δv. The white circle corresponds to the specific configuration zv = 20.1 mm and zs = 3.695 mm used in the beginning of Section 4.1.

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Fig. 7
Fig. 7 (a) Relative error of ng according to the position of the mirror Ms with and without the sample. The white circle corresponds to the specific configuration zv = 20.1 mm and zs = 3.695 mm used in the beginning of Section 4.1. (b) Measurement of ng for SF6 sample according to the position of the mirror Ms in the case δs = δv. The thickness of the glass is assumed to be equal to 20 mm for the calculation of ng.

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Fig. 8
Fig. 8 Δϕ is displayed in black curve between 2.08 and 2.2 rad.fs−1. The red curve corresponds to the fit of Δϕ.

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Fig. 9
Fig. 9 (a) Relative error of GVD according to the position of the mirror Ms with and without water. The white circle corresponds to the specific configuration zv = 20.1 mm and zs = 16.68 mm used in the beginning of Section 4.2. (b) Δϕ-Δϕ(ωc) for the configuration zv = 20.1 mm and zs = 16.63 mm. (c) Δϕ-Δϕ(ωc) for the configuration zv = 20.1 mm and zs = 16.68 mm.

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Fig. 10
Fig. 10 (a) Measurement of GVD for water according to the position of the mirror Ms in the case δs = δv. The white circle corresponds to the specific configuration zv = 20.1 mm and zs = 16.68 mm used in the beginning of Section 4.2. (b) Measurement of ng according to the position of the mirror Ms in the case δs = δv. The thickness of the cuvette is assumed to be equal to 10 mm for the calculation of GVD and ng.

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Equations (14)

Equations on this page are rendered with MathJax. Learn more.

I( x,δ )= I 0 ( p( x ) ) ( 1+cos[ ϕ( p( x ),δ )+ ϕ 0 ( p( x ) ) ] ),
M( x,t )= dp dx  Exp[ −i( ( p( x )−p( x c ) ) t+ ϕ 0 ( p( x ) )− ϕ 0 ( p( x c ) ) ) ].
CMSI[ I( x,δ ) ]= ∑ i=1 N I( x i ,δ )   M * ( x i ,t )=F T −1 [ I without chirp ( ω,δ ) ],
I without chirp ( ω,δ )= I 0 ( ω ) Exp[ i ϕ( ω,δ ) ].
ϕ( ω,δ )=Arg[ FT[ CMSI[ I( x,δ ) ] ] ].
ϕ vacuum ( ω,δ )= ω c   δ v = ω c  2 ( z v − z 0v ),
ϕ sample ( ω,δ )= ω c   δ s = ω c  2 ( z s − z 0s ),
Δϕ( ω )=2  ω c  [ z s − z v +( n( ω )−1 ) e ].
Δϕ( ω )=α+β ( ω- ω c )+γ  ( ω- ω c ) 2 ,
β= dΔϕ dω | ω c = 2 c  ( z s − z v −e )+ 2 c  e  n g ( ω c ),
γ= 1 2 d 2 Δϕ d ω 2 | ω c =GDD( ω c ),
n g ( ω c )= c β/2+ z v − z s e +1,
GVD( ω c )= GDD( ω c ) e = γ e .
Δϕ=Arg[ FT[ CMSI[ I sample ( x, δ s ) ] ]×FT [ CMSI[ I vacuum ( x, δ v ) ] ] ∗ ].

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