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

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. L. M. Smith, C. C. Dobson, "Absolute Displacement Measurements using Modulation of the Spectrum of White Light in a Michelson Interferometer," Appl. Opt. 28, 3339-42, (1981).
    [CrossRef]
  2. J. Schwider and L. Zhou, "Dispersive interferometric profilometer," Opt. Lett. 19, 995-997, 1994).
    [CrossRef] [PubMed]
  3. K. -N. Joo and S. -W. Kim, "Absolute distance measurement by dispersive interferometry using a femtosecond pulse laser," Opt. Express 14, 5954-5960 (2006)
    [CrossRef] [PubMed]
  4. S. Taplin, A. Gh. PodoleanuD. J. Webb, D. A. Jackson, "Displacement Sensor Using Channeled Spectrum Dispersed on a Linear CCD Array," Electron. Lett. 29,896-897, (1993).
    [CrossRef]
  5. A. Gh. PodoleanuS. Taplin,D. J. Webb, D. A. Jackson, "Channelled Spectrum Liquid Refractometer," Rev. Sci. Instr. 64,3028-9, (1993).
    [CrossRef]
  6. G. Hausler, M. W. Lindner, ""Coherence radar" and "spectral radar" - new tools for dermatological diagnosis," J. Biomed. Opt. 3,21-31 (1998).
    [CrossRef]
  7. R. Leitgeb, C. K. Hitzenberger, and A. F. Fercher, "Performance of Fourier domain vs. time domain optical coherence tomography", Opt. Express 11, 889-894, (2003).
    [CrossRef] [PubMed]
  8. 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. 28,2067-2069 (2003).
    [CrossRef] [PubMed]
  9. T. Endo, Y. Yasuno, S. Makita, M. Itoh, and T. Yatagai, "Profilometry with line-field Fourier-domain interferometry," Opt. Express 13, 695-701 (2005).
    [CrossRef] [PubMed]
  10. B. Park, M. C. Pierce, B. Cense, S. -H. Yun, M. Mujat, G. Tearney, B. Bouma, and J. de Boer, "Real-time fiber-based multi-functional spectral-domain optical coherence tomography at 1.3 µm," Opt. Express 13, 3931-3944 (2005)
    [CrossRef] [PubMed]
  11. A. Gh. Podoleanu, S. TaplinD. J. Webb, D. A. Jackson, "Channeled Spectrum Display using a CCD Array for Student Laboratory Demonstrations," European J. Phys. 15,266-271, (1994).
    [CrossRef]
  12. F. A. Jenkins, H. E. White, in Fundamentals of Optics, (McGraw-Hill, 1957), 284;
  13. M. Wojtkowski, R. Leitgeb, A. Kowalczyk, T. Bajraszewski, A. F. Fercher, "In vivo human retinal imaging by Fourier domain optical coherence tomography," J. Biomed. Opt. 7, 457-463 (2002).
    [CrossRef] [PubMed]
  14. A. Bachmann, R. Leitgeb, and T. Lasser, "Heterodyne Fourier domain optical coherence tomography for full range probing with high axial resolution," Opt. Express 14, 1487-1496 (2006)
    [CrossRef] [PubMed]
  15. M. A. Choma, M. V. Sarunic, C. Yang and J. A. Izatt, "Sensitivity advantage of swept source and Fourier domain optical coherence tomography," Opt. Express 11, 2183-2189, (2003).
    [CrossRef] [PubMed]
  16. A. B. Vakhtin, K. A. Peterson, and D. J. Kane, "Resolving the complex conjugate ambiguity in Fourier-domain OCT by harmonic lock-in detection of the spectral interferogram," Opt. Lett. 31, 1271-1273 (2006).
    [CrossRef] [PubMed]
  17. M. Sarunic, M. A. Choma, C. Yang, and J. A. Izatt, "Instantaneous complex conjugate resolved spectral domain and swept-source OCT using 3x3 fiber couplers," Opt. Express 13, 957-967 (2005).
    [CrossRef] [PubMed]
  18. F. Talbot, "An experiment on the interference of light," Philos. Mag. 10, 364, (1837).
  19. 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]
  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, 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.
  23. M. Warengham, C. P. Grover, "Dispersion curve measurement using Talbot bands," Revue Phys. Appl. 23, 1169-1178 (1998).
    [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, 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, C. P. Grover, "Dispersion curve measurement using Talbot bands," Revue Phys. Appl. 23, 1169-1178 (1998).
[CrossRef]

G. Hausler, 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, 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. TaplinD. J. Webb, 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 L. Zhou, "Dispersive interferometric profilometer," Opt. Lett. 19, 995-997, 1994).
[CrossRef] [PubMed]

1993 (2)

S. Taplin, A. Gh. PodoleanuD. J. Webb, D. A. Jackson, "Displacement Sensor Using Channeled Spectrum Dispersed on a Linear CCD Array," Electron. Lett. 29,896-897, (1993).
[CrossRef]

A. Gh. PodoleanuS. Taplin,D. J. Webb, D. A. Jackson, "Channelled Spectrum Liquid Refractometer," Rev. Sci. Instr. 64,3028-9, (1993).
[CrossRef]

A. Gh. PodoleanuS. Taplin,D. J. Webb, 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, 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.

Gh, 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, 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. TaplinD. J. Webb, D. A. Jackson, "Channeled Spectrum Display using a CCD Array for Student Laboratory Demonstrations," European J. Phys. 15,266-271, (1994).
[CrossRef]

A. Gh. PodoleanuS. Taplin,D. J. Webb, D. A. Jackson, "Channelled Spectrum Liquid Refractometer," Rev. Sci. Instr. 64,3028-9, (1993).
[CrossRef]

S. Taplin, A. Gh. PodoleanuD. J. Webb, D. A. Jackson, "Displacement Sensor Using Channeled Spectrum Dispersed on a Linear CCD Array," Electron. Lett. 29,896-897, (1993).
[CrossRef]

Grover, C. P.

M. Warengham, C. P. Grover, "Dispersion curve measurement using Talbot bands," Revue Phys. Appl. 23, 1169-1178 (1998).
[CrossRef]

Hausler, G.

G. Hausler, 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.

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, 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]

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

Lasser, T.

Leitgeb, R.

Lindner, M. W.

G. Hausler, 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.

A. Gh. PodoleanuS. Taplin,D. J. Webb, D. A. Jackson, "Channelled Spectrum Liquid Refractometer," Rev. Sci. Instr. 64,3028-9, (1993).
[CrossRef]

S. Taplin, A. Gh. PodoleanuD. J. Webb, D. A. Jackson, "Displacement Sensor Using Channeled Spectrum Dispersed on a Linear CCD Array," Electron. Lett. 29,896-897, (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.

S. Taplin, A. Gh. PodoleanuD. J. Webb, D. A. Jackson, "Displacement Sensor Using Channeled Spectrum Dispersed on a Linear CCD Array," Electron. Lett. 29,896-897, (1993).
[CrossRef]

Tearney, G.

Tearney, G. J.

Vakhtin, A. B.

Warengham, M.

M. Warengham, C. P. Grover, "Dispersion curve measurement using Talbot bands," Revue Phys. Appl. 23, 1169-1178 (1998).
[CrossRef]

Wojtkowski, M.

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]

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

Yang, C.

Yasuno, Y.

Yatagai, T.

Yun, S. -H.

Zhou, L.

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. PodoleanuD. J. Webb, 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. TaplinD. J. Webb, 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, 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, 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, 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. PodoleanuS. Taplin,D. J. Webb, D. A. Jackson, "Channelled Spectrum Liquid Refractometer," Rev. Sci. Instr. 64,3028-9, (1993).
[CrossRef]

Revue Phys. Appl. (1)

M. Warengham, C. P. Grover, "Dispersion curve measurement using Talbot bands," Revue Phys. Appl. 23, 1169-1178 (1998).
[CrossRef]

Other (1)

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

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


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

Metrics