Abstract

A theoretical model is developed for the Master/Slave interferometry (MSI) that is used to demonstrate its tolerance to dispersion left uncompensated in the interferometer when evaluating distances and thicknesses. In order to prove experimentally its tolerance to dispersion, different lengths of optical fiber are inserted into the interferometer to introduce dispersion. It is demonstrated that the sensitivity profile versus optical path difference is not affected by the length of fiber left uncompensated. It is also demonstrated that the axial resolution is constant within the axial range, close to the expected theoretical resolution determined by the optical source bandwidth. Then the thickness of a glass plate is measured several times in the presence of dispersion and errors in measurements are evaluated using the MSI method and the conventional Fourier transformation (FT) based method using linearized/calibrated data. The standard deviation for thickness results obtained with the MSI is more than 5 times smaller than the standard deviation for results delivered by the conventional, FT based method.

© 2015 Optical Society of America

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References

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2014 (2)

2013 (1)

2012 (2)

2011 (2)

T. J. Eom, Y. C. Ahn, C. S. Kim, and Z. Chen, “Calibration and characterization protocol for spectral-domain optical coherence tomography using fiber Bragg gratings,” J. Biomed. Opt. 16(3), 030501 (2011).
[Crossref] [PubMed]

B. Liu, E. Azimi, and M. E. Brezinski, “True logarithmic amplification of frequency clock in SS-OCT for calibration,” Biomed. Opt. Express 2(6), 1769–1777 (2011).
[Crossref] [PubMed]

2009 (3)

2008 (2)

P. Hlubina, J. Luňáček, D. Ciprian, and R. Chlebus, “Dispersion error of a beam splitter cube in white-light spectral interferometry,” Opto-Electron. Rev. 16(4), 439–443 (2008).
[Crossref]

A. R. Tumlinson, B. Hofer, A. M. Winkler, B. Považay, W. Drexler, and J. K. Barton, “Inherent homogenous media dispersion compensation in frequency domain optical coherence tomography by accurate k-sampling,” Appl. Opt. 47(5), 687–693 (2008).
[Crossref] [PubMed]

2007 (2)

Z. Hu and A. M. Rollins, “Fourier domain optical coherence tomography with a linear-in-wavenumber spectrometer,” Opt. Lett. 32(24), 3525–3527 (2007).
[Crossref] [PubMed]

M. Mujat, B. H. Park, B. Cense, T. C. Chen, and J. F. de Boer, “Autocalibration of spectral-domain optical coherence tomography spectrometers for in vivo quantitative retinal nerve fiber layer birefringence determination,” J. Biomed. Opt. 12(4), 041205 (2007).
[Crossref] [PubMed]

2005 (2)

2004 (1)

1997 (1)

Adler, D. C.

Ahn, Y. C.

T. J. Eom, Y. C. Ahn, C. S. Kim, and Z. Chen, “Calibration and characterization protocol for spectral-domain optical coherence tomography using fiber Bragg gratings,” J. Biomed. Opt. 16(3), 030501 (2011).
[Crossref] [PubMed]

Akiba, M.

Azimi, E.

Barton, J. K.

Berkovic, G.

Bouma, B. E.

Bradu, A.

Brezinski, M. E.

Cense, B.

M. Mujat, B. H. Park, B. Cense, T. C. Chen, and J. F. de Boer, “Autocalibration of spectral-domain optical coherence tomography spectrometers for in vivo quantitative retinal nerve fiber layer birefringence determination,” J. Biomed. Opt. 12(4), 041205 (2007).
[Crossref] [PubMed]

Chan, K.-P.

Chen, T. C.

M. Mujat, B. H. Park, B. Cense, T. C. Chen, and J. F. de Boer, “Autocalibration of spectral-domain optical coherence tomography spectrometers for in vivo quantitative retinal nerve fiber layer birefringence determination,” J. Biomed. Opt. 12(4), 041205 (2007).
[Crossref] [PubMed]

Chen, Z.

T. J. Eom, Y. C. Ahn, C. S. Kim, and Z. Chen, “Calibration and characterization protocol for spectral-domain optical coherence tomography using fiber Bragg gratings,” J. Biomed. Opt. 16(3), 030501 (2011).
[Crossref] [PubMed]

Chlebus, R.

P. Hlubina, J. Luňáček, D. Ciprian, and R. Chlebus, “Dispersion error of a beam splitter cube in white-light spectral interferometry,” Opto-Electron. Rev. 16(4), 439–443 (2008).
[Crossref]

Chong, C.

Ciprian, D.

P. Hlubina, J. Luňáček, D. Ciprian, and R. Chlebus, “Dispersion error of a beam splitter cube in white-light spectral interferometry,” Opto-Electron. Rev. 16(4), 439–443 (2008).
[Crossref]

Coen, S.

de Boer, J. F.

M. Mujat, B. H. Park, B. Cense, T. C. Chen, and J. F. de Boer, “Autocalibration of spectral-domain optical coherence tomography spectrometers for in vivo quantitative retinal nerve fiber layer birefringence determination,” J. Biomed. Opt. 12(4), 041205 (2007).
[Crossref] [PubMed]

DeRose, P.

K. Gaigalas, L. Wang, H.-J. He, and P. DeRose, “Procedures for wavelength calibration and spectral response correction of CCD array spectrometers,” J. Res. Natl. Inst. Stand. Technol. 114(4), 215–228 (2009).
[Crossref]

Drexler, W.

Duker, J.

Eom, T. J.

T. J. Eom, Y. C. Ahn, C. S. Kim, and Z. Chen, “Calibration and characterization protocol for spectral-domain optical coherence tomography using fiber Bragg gratings,” J. Biomed. Opt. 16(3), 030501 (2011).
[Crossref] [PubMed]

Fujimoto, J.

Fujimoto, J. G.

Gaigalas, K.

K. Gaigalas, L. Wang, H.-J. He, and P. DeRose, “Procedures for wavelength calibration and spectral response correction of CCD array spectrometers,” J. Res. Natl. Inst. Stand. Technol. 114(4), 215–228 (2009).
[Crossref]

He, H.-J.

K. Gaigalas, L. Wang, H.-J. He, and P. DeRose, “Procedures for wavelength calibration and spectral response correction of CCD array spectrometers,” J. Res. Natl. Inst. Stand. Technol. 114(4), 215–228 (2009).
[Crossref]

Hillman, T.

Hlubina, P.

P. Hlubina, J. Luňáček, D. Ciprian, and R. Chlebus, “Dispersion error of a beam splitter cube in white-light spectral interferometry,” Opto-Electron. Rev. 16(4), 439–443 (2008).
[Crossref]

Hofer, B.

Hu, Z.

Itoh, M.

Iyer, S.

Kim, C. S.

T. J. Eom, Y. C. Ahn, C. S. Kim, and Z. Chen, “Calibration and characterization protocol for spectral-domain optical coherence tomography using fiber Bragg gratings,” J. Biomed. Opt. 16(3), 030501 (2011).
[Crossref] [PubMed]

Ko, T.

Kowalczyk, A.

Liu, B.

Lunácek, J.

P. Hlubina, J. Luňáček, D. Ciprian, and R. Chlebus, “Dispersion error of a beam splitter cube in white-light spectral interferometry,” Opto-Electron. Rev. 16(4), 439–443 (2008).
[Crossref]

Madjarova, V. D.

Makita, S.

Morosawa, A.

Mujat, M.

M. Mujat, B. H. Park, B. Cense, T. C. Chen, and J. F. de Boer, “Autocalibration of spectral-domain optical coherence tomography spectrometers for in vivo quantitative retinal nerve fiber layer birefringence determination,” J. Biomed. Opt. 12(4), 041205 (2007).
[Crossref] [PubMed]

Park, B. H.

M. Mujat, B. H. Park, B. Cense, T. C. Chen, and J. F. de Boer, “Autocalibration of spectral-domain optical coherence tomography spectrometers for in vivo quantitative retinal nerve fiber layer birefringence determination,” J. Biomed. Opt. 12(4), 041205 (2007).
[Crossref] [PubMed]

Podoleanu, A. G.

Považay, B.

Rollins, A. M.

Sakai, T.

Sampson, D.

Shafir, E.

Srinivasan, V.

Tearney, G. J.

Tsai, T.-H.

Tumlinson, A. R.

Vanholsbeeck, F.

Wang, L.

K. Gaigalas, L. Wang, H.-J. He, and P. DeRose, “Procedures for wavelength calibration and spectral response correction of CCD array spectrometers,” J. Res. Natl. Inst. Stand. Technol. 114(4), 215–228 (2009).
[Crossref]

Winkler, A. M.

Wojtkowski, M.

Yasuno, Y.

Yatagai, T.

Zhou, C.

Adv. Opt. Photon. (1)

Appl. Opt. (1)

Biomed. Opt. Express (2)

J. Biomed. Opt. (2)

M. Mujat, B. H. Park, B. Cense, T. C. Chen, and J. F. de Boer, “Autocalibration of spectral-domain optical coherence tomography spectrometers for in vivo quantitative retinal nerve fiber layer birefringence determination,” J. Biomed. Opt. 12(4), 041205 (2007).
[Crossref] [PubMed]

T. J. Eom, Y. C. Ahn, C. S. Kim, and Z. Chen, “Calibration and characterization protocol for spectral-domain optical coherence tomography using fiber Bragg gratings,” J. Biomed. Opt. 16(3), 030501 (2011).
[Crossref] [PubMed]

J. Microsc. (1)

A. G. Podoleanu, “Optical coherence tomography,” J. Microsc. 247(3), 209–219 (2012).
[Crossref] [PubMed]

J. Res. Natl. Inst. Stand. Technol. (1)

K. Gaigalas, L. Wang, H.-J. He, and P. DeRose, “Procedures for wavelength calibration and spectral response correction of CCD array spectrometers,” J. Res. Natl. Inst. Stand. Technol. 114(4), 215–228 (2009).
[Crossref]

Opt. Express (5)

Opt. Lett. (4)

Opto-Electron. Rev. (1)

P. Hlubina, J. Luňáček, D. Ciprian, and R. Chlebus, “Dispersion error of a beam splitter cube in white-light spectral interferometry,” Opto-Electron. Rev. 16(4), 439–443 (2008).
[Crossref]

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Figures (6)

Fig. 1
Fig. 1

Diagram of the Sp-SDI system, and of the Processing Block showing the signal processing steps to deliver a point in the A-scan for a given mask. DC: directional coupler; L1-5: achromatic lenses; TG: diffraction grating; LSC: line-scan camera; SMF: single mode fiber; CL: camera link cable; PCIe 1429: image acquisition board; HPF: high pass filter; W: wavenumber window the correlation signal is integrated over; FR: flat mirror in the reference arm; FO: flat mirror when the interferometer is used as Master, with switches K1 and K2 in position 1; O: object to be investigated when the interferometer is used as Slave, switches K1 and K2 in position 2 and O replaces FO.

Fig. 2
Fig. 2

Sensitivity decay versus z for different lengths of extra SMF in the object arm. (a) 0.0 m; (b) 0.5 m; (c) 1.0 m; (d) 1.5 m. Continuous plots show the sensitivity profiles obtained using the FT method, while filled circles, connected by dashed lines show the values of the sensitivity obtained with the MSI technique.

Fig. 3
Fig. 3

Sensitivity decay versus z for different lengths of extra SMF in the object arm. (a) 0 m; (b) 0.5 m (c) 1.0 m (d) 1.5 m. Continuous plots show the sensitivity profiles obtained using the FT method, where data were re-sampled using a phase based technique with calibration coefficients calculated for z = 0.4 mm. Filled circles connected by a dashed line show the values of the sensitivity obtained with the MSI technique.

Fig. 4
Fig. 4

Axial resolution vs. z, with (a) no data re-sampling and (b) data re-sampled using the FT technique (SMF = 1.5 m (open circles), 1.0 m (open squares), 0.5 m (open triangles), 0.0 m (open diamonds) and the MSI technique (filled circles).

Fig. 5
Fig. 5

Example of normalized axial reflectivity profiles obtained when a microscope slide is used as an object and employing the FT technique (left) and the MSI method (right) for four cases: (a1) and (b1) 0 m, (a2) and (b2) 0.5 m, (a3) and (b3) 1.0 m, (a4) and (b4) 1.5 m of extra fiber in the object arm of the interferometer

Fig. 6
Fig. 6

Average values of the optical thickness of the glass microscope plate vs. optical fiber length added to the sample arm obtained using the FT (a) and MSI method (b).

Equations (19)

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OPD(k)=2z+D(k)D( k 0 )
CS(k)=g(k)cos[ kOPD(k) ]
OPD(k)=pa+D(k)D( k 0 )=pa+δD(k), for z>0
a= 8ln2 Δk
M g,p =g(k)cos{ k[ pa+δD(k) ] }
M p =cos{ k[ pa+δD(k) ] }
CS(k)= r=1 P A r g(k)cos{ k[ ra+δD(k) ] }
C p (K)= r=1 P A r g(k)cos{ k[ ra+δD(k) ] } M p = r=1 P A r C rp (K)
C rp (K)=g(k)cos{ k[ ra+δD(k) ] } M p
C rp (K)= k min k max g(k)cos{ k[ ra+δD(k) ] }cos{ ( k+K )[ pa+δD( k+K ) ] }dk
C rp (0)= 1 2 k min k max g(k){ cos[ k(pr)a ]+cos[ k(p+r)2δD(k) ] }dk
C rp (0)={ 0, for pr 1 2 k min k max g(k)dk, for p=r .
C p (0)= r=1 p A r C rp (0)= A p 2 k min k max g (k)dk.
C p (K)= k min k max CS(k) M p (k+K)dk
C p (y)= n=0 U1 CS(n) M p (n+yU)
C p = y=UW y=U+W C p (y)
C p = y=UW y=U+W n=0 U1 CS(n) M p (n+yU)
S(MSI)=40+20log[ A(OP D p ,W,sample arm unblocked) A(OP D p ,W,sample arm blocked) ]
S(FT)=40+20log[ Amplitude FFT signal (OP D p ) Amplitude noise floor measured outside OP D p ]

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