Abstract

A theoretical model is developed to interpret the output of the diffraction grating spectrometer used to analyze the channelled spectrum produced by a low coherence interferometer set-up. This model leads to an unique interpretation which covers both cases (i) of Talbot bands and (ii) of a Michelson interferometer used in most spectral interferometry set-ups for sensing as well as for Fourier domain optical coherence tomography (FDOCT). Explanation of Talbot bands visibility as well as the decay of sensitivity with depth, characteristic for FDOCT, is explained by considering the extension of the two wavetrains diffracted by the diffraction grating in the spectrometer.

© 2007 Optical Society of America

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  20. A. L. King and R. Davis, “The Curious Bands of Talbot,” Am. J. Phys. 39, 1195–1198, (1971).
    [Crossref]
  21. A. Gh. Podoleanu, S. Taplin, D. J. Webb, and D. A. Jackson, “Talbot-like Bands for Laser Diode Below Threshold,” J. Opt. A, Pure Appl. Opt. 6, 413–424, (1997).
  22. A. Gh. Podoleanu, S. Taplin, D. J. Webb, and D. A. Jackson, “Theoretical Study of Talbot-like Bands Observed Using a Laser Diode Below Threshold,” J. Opt. A, Pure Appl. Opt. Vol. 7, (1998), 517–536.
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    [Crossref]
  24. M. Wojtkowski, A. Kowalczyk, R. Leitgeb, and A. F. Fercher, “Full range complex spectral optical coherence tomography technique in eye imaging,” Opt. Lett. 27, 1415–1417 (2002).
    [Crossref]

2006 (3)

2005 (3)

2003 (3)

2002 (2)

M. Wojtkowski, R. Leitgeb, A. Kowalczyk, T. Bajraszewski, and A. F. Fercher, “In vivo human retinal imaging by Fourier domain optical coherence tomography,” J. Biomed. Opt. 7, 457–463 (2002).
[Crossref] [PubMed]

M. Wojtkowski, A. Kowalczyk, R. Leitgeb, and A. F. Fercher, “Full range complex spectral optical coherence tomography technique in eye imaging,” Opt. Lett. 27, 1415–1417 (2002).
[Crossref]

1998 (3)

A. Gh. Podoleanu, S. Taplin, D. J. Webb, and D. A. Jackson, “Theoretical Study of Talbot-like Bands Observed Using a Laser Diode Below Threshold,” J. Opt. A, Pure Appl. Opt. Vol. 7, (1998), 517–536.

M. Warengham and C. P. Grover, “Dispersion curve measurement using Talbot bands,” Revue Phys. Appl. 23, 1169–1178 (1998).
[Crossref]

G. Hausler and M. W. Lindner, ““Coherence radar” and “spectral radar” - new tools for dermatological diagnosis,” J. Biomed. Opt. 3, 21–31 (1998).
[Crossref]

1997 (1)

A. Gh. Podoleanu, S. Taplin, D. J. Webb, and D. A. Jackson, “Talbot-like Bands for Laser Diode Below Threshold,” J. Opt. A, Pure Appl. Opt. 6, 413–424, (1997).

1994 (2)

A. Gh. Podoleanu, S. Taplin, D. J. Webb, and D. A. Jackson, “Channeled Spectrum Display using a CCD Array for Student Laboratory Demonstrations,” European J. Phys. 15, 266–271, (1994).
[Crossref]

J. Schwider and Liang Zhou, “Dispersive interferometric profilometer,”  19, Opt. Lett.995–997, 1994).
[Crossref] [PubMed]

1993 (2)

S. Taplin, A. Gh. Podoleanu, D. J. Webb, and D. A. Jackson, “Displacement Sensor Using Channeled Spectrum Dispersed on a Linear CCD Array,” Electron. Lett. 29, 896–897, (1993).
[Crossref]

A. Gh. Podoleanu, S. Taplin, D. J. Webb, and D. A. Jackson, “Channelled Spectrum Liquid Refractometer,” Rev. Sci. Instr. 64, 3028–9, (1993).
[Crossref]

1981 (1)

1971 (1)

A. L. King and R. Davis, “The Curious Bands of Talbot,” Am. J. Phys. 39, 1195–1198, (1971).
[Crossref]

1840 (1)

G. B. Airy, “The Bakerian Lecture - on the theoretical explanation of an apparent new polarity of light,” Phil. Trans. R. Soc. London 130, 225–244, (1840).
[Crossref]

1837 (1)

F. Talbot, “An experiment on the interference of light,” Philos. Mag. 10, 364, (1837).

Airy, G. B.

G. B. Airy, “The Bakerian Lecture - on the theoretical explanation of an apparent new polarity of light,” Phil. Trans. R. Soc. London 130, 225–244, (1840).
[Crossref]

Bachmann, A.

Bajraszewski, T.

M. Wojtkowski, R. Leitgeb, A. Kowalczyk, T. Bajraszewski, and A. F. Fercher, “In vivo human retinal imaging by Fourier domain optical coherence tomography,” J. Biomed. Opt. 7, 457–463 (2002).
[Crossref] [PubMed]

Bouma, B.

Bouma, B. E.

Cense, B.

Choma, M. A.

Davis, R.

A. L. King and R. Davis, “The Curious Bands of Talbot,” Am. J. Phys. 39, 1195–1198, (1971).
[Crossref]

de Boer, J.

de Boer, J. F.

Dobson, C. C.

Endo, T.

Fercher, A. F.

Grover, C. P.

M. Warengham and C. P. Grover, “Dispersion curve measurement using Talbot bands,” Revue Phys. Appl. 23, 1169–1178 (1998).
[Crossref]

Hausler, G.

G. Hausler and M. W. Lindner, ““Coherence radar” and “spectral radar” - new tools for dermatological diagnosis,” J. Biomed. Opt. 3, 21–31 (1998).
[Crossref]

Hitzenberger, C. K.

Itoh, M.

Izatt, J. A.

Jackson, D. A.

A. Gh. Podoleanu, S. Taplin, D. J. Webb, and D. A. Jackson, “Theoretical Study of Talbot-like Bands Observed Using a Laser Diode Below Threshold,” J. Opt. A, Pure Appl. Opt. Vol. 7, (1998), 517–536.

A. Gh. Podoleanu, S. Taplin, D. J. Webb, and D. A. Jackson, “Talbot-like Bands for Laser Diode Below Threshold,” J. Opt. A, Pure Appl. Opt. 6, 413–424, (1997).

A. Gh. Podoleanu, S. Taplin, D. J. Webb, and D. A. Jackson, “Channeled Spectrum Display using a CCD Array for Student Laboratory Demonstrations,” European J. Phys. 15, 266–271, (1994).
[Crossref]

A. Gh. Podoleanu, S. Taplin, D. J. Webb, and D. A. Jackson, “Channelled Spectrum Liquid Refractometer,” Rev. Sci. Instr. 64, 3028–9, (1993).
[Crossref]

S. Taplin, A. Gh. Podoleanu, D. J. Webb, and D. A. Jackson, “Displacement Sensor Using Channeled Spectrum Dispersed on a Linear CCD Array,” Electron. Lett. 29, 896–897, (1993).
[Crossref]

Jenkins, F. A.

F. A. Jenkins and H. E. White, in Fundamentals of Optics, (McGraw-Hill, 1957), 284;

Joo, K. -N.

Kane, D. J.

Kim, S. -W.

King, A. L.

A. L. King and R. Davis, “The Curious Bands of Talbot,” Am. J. Phys. 39, 1195–1198, (1971).
[Crossref]

Kowalczyk, A.

M. Wojtkowski, R. Leitgeb, A. Kowalczyk, T. Bajraszewski, and A. F. Fercher, “In vivo human retinal imaging by Fourier domain optical coherence tomography,” J. Biomed. Opt. 7, 457–463 (2002).
[Crossref] [PubMed]

M. Wojtkowski, A. Kowalczyk, R. Leitgeb, and A. F. Fercher, “Full range complex spectral optical coherence tomography technique in eye imaging,” Opt. Lett. 27, 1415–1417 (2002).
[Crossref]

Lasser, T.

Leitgeb, R.

Lindner, M. W.

G. Hausler and M. W. Lindner, ““Coherence radar” and “spectral radar” - new tools for dermatological diagnosis,” J. Biomed. Opt. 3, 21–31 (1998).
[Crossref]

Makita, S.

Mujat, M.

Park, B.

Park, B. H.

Peterson, K. A.

Pierce, M. C.

Podoleanu, A. Gh.

A. Gh. Podoleanu, S. Taplin, D. J. Webb, and D. A. Jackson, “Theoretical Study of Talbot-like Bands Observed Using a Laser Diode Below Threshold,” J. Opt. A, Pure Appl. Opt. Vol. 7, (1998), 517–536.

A. Gh. Podoleanu, S. Taplin, D. J. Webb, and D. A. Jackson, “Talbot-like Bands for Laser Diode Below Threshold,” J. Opt. A, Pure Appl. Opt. 6, 413–424, (1997).

A. Gh. Podoleanu, S. Taplin, D. J. Webb, and D. A. Jackson, “Channeled Spectrum Display using a CCD Array for Student Laboratory Demonstrations,” European J. Phys. 15, 266–271, (1994).
[Crossref]

S. Taplin, A. Gh. Podoleanu, D. J. Webb, and D. A. Jackson, “Displacement Sensor Using Channeled Spectrum Dispersed on a Linear CCD Array,” Electron. Lett. 29, 896–897, (1993).
[Crossref]

A. Gh. Podoleanu, S. Taplin, D. J. Webb, and D. A. Jackson, “Channelled Spectrum Liquid Refractometer,” Rev. Sci. Instr. 64, 3028–9, (1993).
[Crossref]

Sarunic, M.

Sarunic, M. V.

Schwider, J.

Smith, L. M.

Talbot, F.

F. Talbot, “An experiment on the interference of light,” Philos. Mag. 10, 364, (1837).

Taplin, S.

A. Gh. Podoleanu, S. Taplin, D. J. Webb, and D. A. Jackson, “Theoretical Study of Talbot-like Bands Observed Using a Laser Diode Below Threshold,” J. Opt. A, Pure Appl. Opt. Vol. 7, (1998), 517–536.

A. Gh. Podoleanu, S. Taplin, D. J. Webb, and D. A. Jackson, “Talbot-like Bands for Laser Diode Below Threshold,” J. Opt. A, Pure Appl. Opt. 6, 413–424, (1997).

A. Gh. Podoleanu, S. Taplin, D. J. Webb, and D. A. Jackson, “Channeled Spectrum Display using a CCD Array for Student Laboratory Demonstrations,” European J. Phys. 15, 266–271, (1994).
[Crossref]

S. Taplin, A. Gh. Podoleanu, D. J. Webb, and D. A. Jackson, “Displacement Sensor Using Channeled Spectrum Dispersed on a Linear CCD Array,” Electron. Lett. 29, 896–897, (1993).
[Crossref]

A. Gh. Podoleanu, S. Taplin, D. J. Webb, and D. A. Jackson, “Channelled Spectrum Liquid Refractometer,” Rev. Sci. Instr. 64, 3028–9, (1993).
[Crossref]

Tearney, G.

Tearney, G. J.

Vakhtin, A. B.

Warengham, M.

M. Warengham and C. P. Grover, “Dispersion curve measurement using Talbot bands,” Revue Phys. Appl. 23, 1169–1178 (1998).
[Crossref]

Webb, D. J.

A. Gh. Podoleanu, S. Taplin, D. J. Webb, and D. A. Jackson, “Theoretical Study of Talbot-like Bands Observed Using a Laser Diode Below Threshold,” J. Opt. A, Pure Appl. Opt. Vol. 7, (1998), 517–536.

A. Gh. Podoleanu, S. Taplin, D. J. Webb, and D. A. Jackson, “Talbot-like Bands for Laser Diode Below Threshold,” J. Opt. A, Pure Appl. Opt. 6, 413–424, (1997).

A. Gh. Podoleanu, S. Taplin, D. J. Webb, and D. A. Jackson, “Channeled Spectrum Display using a CCD Array for Student Laboratory Demonstrations,” European J. Phys. 15, 266–271, (1994).
[Crossref]

A. Gh. Podoleanu, S. Taplin, D. J. Webb, and D. A. Jackson, “Channelled Spectrum Liquid Refractometer,” Rev. Sci. Instr. 64, 3028–9, (1993).
[Crossref]

S. Taplin, A. Gh. Podoleanu, D. J. Webb, and D. A. Jackson, “Displacement Sensor Using Channeled Spectrum Dispersed on a Linear CCD Array,” Electron. Lett. 29, 896–897, (1993).
[Crossref]

White, H. E.

F. A. Jenkins and H. E. White, in Fundamentals of Optics, (McGraw-Hill, 1957), 284;

Wojtkowski, M.

M. Wojtkowski, R. Leitgeb, A. Kowalczyk, T. Bajraszewski, and A. F. Fercher, “In vivo human retinal imaging by Fourier domain optical coherence tomography,” J. Biomed. Opt. 7, 457–463 (2002).
[Crossref] [PubMed]

M. Wojtkowski, A. Kowalczyk, R. Leitgeb, and A. F. Fercher, “Full range complex spectral optical coherence tomography technique in eye imaging,” Opt. Lett. 27, 1415–1417 (2002).
[Crossref]

Yang, C.

Yasuno, Y.

Yatagai, T.

Yun, S. -H.

Zhou, Liang

Am. J. Phys. (1)

A. L. King and R. Davis, “The Curious Bands of Talbot,” Am. J. Phys. 39, 1195–1198, (1971).
[Crossref]

Appl. Opt. (1)

Electron. Lett. (1)

S. Taplin, A. Gh. Podoleanu, D. J. Webb, and D. A. Jackson, “Displacement Sensor Using Channeled Spectrum Dispersed on a Linear CCD Array,” Electron. Lett. 29, 896–897, (1993).
[Crossref]

European J. Phys. (1)

A. Gh. Podoleanu, S. Taplin, D. J. Webb, and D. A. Jackson, “Channeled Spectrum Display using a CCD Array for Student Laboratory Demonstrations,” European J. Phys. 15, 266–271, (1994).
[Crossref]

J. Biomed. Opt. (2)

M. Wojtkowski, R. Leitgeb, A. Kowalczyk, T. Bajraszewski, and A. F. Fercher, “In vivo human retinal imaging by Fourier domain optical coherence tomography,” J. Biomed. Opt. 7, 457–463 (2002).
[Crossref] [PubMed]

G. Hausler and M. W. Lindner, ““Coherence radar” and “spectral radar” - new tools for dermatological diagnosis,” J. Biomed. Opt. 3, 21–31 (1998).
[Crossref]

J. Opt. A, Pure Appl. Opt. (2)

A. Gh. Podoleanu, S. Taplin, D. J. Webb, and D. A. Jackson, “Talbot-like Bands for Laser Diode Below Threshold,” J. Opt. A, Pure Appl. Opt. 6, 413–424, (1997).

A. Gh. Podoleanu, S. Taplin, D. J. Webb, and D. A. Jackson, “Theoretical Study of Talbot-like Bands Observed Using a Laser Diode Below Threshold,” J. Opt. A, Pure Appl. Opt. Vol. 7, (1998), 517–536.

Opt. Express (7)

Opt. Lett. (4)

Phil. Trans. R. Soc. London (1)

G. B. Airy, “The Bakerian Lecture - on the theoretical explanation of an apparent new polarity of light,” Phil. Trans. R. Soc. London 130, 225–244, (1840).
[Crossref]

Philos. Mag. (1)

F. Talbot, “An experiment on the interference of light,” Philos. Mag. 10, 364, (1837).

Rev. Sci. Instr. (1)

A. Gh. Podoleanu, S. Taplin, D. J. Webb, and D. A. Jackson, “Channelled Spectrum Liquid Refractometer,” Rev. Sci. Instr. 64, 3028–9, (1993).
[Crossref]

Revue Phys. Appl. (1)

M. Warengham and C. P. Grover, “Dispersion curve measurement using Talbot bands,” Revue Phys. Appl. 23, 1169–1178 (1998).
[Crossref]

Other (1)

F. A. Jenkins and H. E. White, in Fundamentals of Optics, (McGraw-Hill, 1957), 284;

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Figures (1)

Fig. 1.
Fig. 1.

Modified Michelson interferometer configuration [21] to reproduce Talbot bands and distinguish between positive and negative OPDs.

Tables (1)

Tables Icon

Table 1. Overlap of the two wavetrains versus OPD.

Equations (23)

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

V ( θ , λ ¯ , t ) = 1 2 { Z O ( θ , λ ¯ ) O ( λ ¯ ) X ( λ ¯ , t ) + exp [ j 2 π ( 2 q ) p ND λ ¯ ] Z R ( θ , λ ¯ ) R ( λ ¯ ) X ( λ ¯ , t ) }
D = a ( sin θ i sin θ ) =
O ( λ ¯ ) X ( λ ¯ , t ) = T O Y ( λ ¯ ) exp [ j 2 π c ( t t O ) λ ¯ ]
R ( λ ¯ ) X ( λ ¯ , t ) = T R Y ( λ ¯ ) exp [ j 2 π c ( t t R ) λ ¯ ]
Δ t = t O t R
Y ( Λ ¯ ) 2 = 1 2 πσ exp [ ( Λ ¯ λ ¯ 0 ) 2 2 σ 2 ]
σ = Δ λ 2 2 ln 2 λ 0 2
F { Y ( Λ ¯ ) 2 } = g ( x ) exp ( i 2 π λ ¯ 0 x )
g ( x ) = exp ( 2 π σ 2 x 2 )
ψ ( x ) = g ( x ) cos ( 2 π λ ¯ 0 x )
I ( D ) = η 1 2 qN ( T O 2 + T R 2 ) s = ( qN 1 ) qN 1 C s { ψ ( sD ) + 2 T O T R T O 2 + T R 2 ψ [ ( s + p ( 2 q ) N ) D c Δ t ] }
C s = qN s
qN + 1 s qN 1
c Δ t = sD + p ( 2 q ) ND
[ 2 ( 1 q ) N + 1 ] D c Δ t ( 2 N 1 ) D for p = 1
( 2 N 1 ) D c Δ t [ 2 ( 1 q ) N + 1 ] D for p = 1
( 2 N + 1 ) D c Δ t ( 2 N 1 ) D
D c Δ t ( 2 N 1 ) D for p = 1
( 2 N 1 ) D c Δ t D for p = 1
S m = Int ( c Δ t D m ) p ( 2 q ) N
V q 2 T O T R T O 2 + T R 2 s = S m r S m + r C s g [ ( s S m ) D m ] s = r r C s g ( sD m )
V q 2 T O T R T O 2 + T R 2 ( qN S m ) [ g ( 0 ) + 2 ε = 1 r g ( ε D m ) ] q Ng ( 0 ) + 2 ε = 1 r [ ( qN ε ) g ( ε D m ) ]
V q 2 T O T R T O 2 + T R 2 qN s m qN

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