Abstract

We describe fiber-based quadrature low-coherence interferometers that exploit the inherent phase shifts of 3×3 and higher-order fiber-optic couplers. We present a framework based on conservation of energy to account for the interferometric shifts in 3×3 interferometers, and we demonstrate that the resulting interferometers provide the entire complex interferometric signal instantaneously in homodyne and heterodyne systems. In heterodyne detection we demonstrate the capability for extraction of the magnitude and sign of Doppler shifts from the complex data. In homodyne detection we show the detection of subwavelength sample motion. N×N (N>2) low-coherence interferometer topologies will be useful in Doppler optical coherence tomography (OCT), optical coherence microscopy, Fourier-domain OCT, optical frequency domain reflectometry, and phase-referenced interferometry.

© 2003 Optical Society of America

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  1. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, and C. A. Puliafito, Science 254, 1178 (1991).
    [CrossRef] [PubMed]
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    [CrossRef]
  3. M. Wojtkowski, A. Kowalczyk, R. Leitgeb, and A. F. Fercher, Opt. Lett. 27, 1415 (2002).
    [CrossRef]
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    [CrossRef] [PubMed]
  5. J. A. Izatt, M. D. Kulkami, S. Yazdanfar, J. K. Barton, and A. J. Welch, Opt. Lett. 22, 1439 (1997).
    [CrossRef]
  6. C. Yang, A. Wax, M. S. Hahn, K. Badizadegan, R. R. Dasari, and M. S. Feld, Opt. Lett. 26, 1271 (2001).
    [CrossRef]
  7. A. M. Rollins and J. A. Izatt, Opt. Lett. 24, 1484 (1999).
    [CrossRef]
  8. Y. H. Zhao, Z. P. Chen, Z. H. Ding, H. W. Ren, and J. S. Nelson, Opt. Lett. 27, 98 (2002).
    [CrossRef]
  9. A. W. Snyder, J. Opt. Soc. Am. 62, 1267 (1972).
  10. S. K. Sheem, J. Appl. Phys. 52, 3865 (1981).
    [CrossRef]

2002

2001

1999

1997

1996

J. A. Izatt, M. D. Kulkarni, H. W. Wang, K. Kobayashi, and M. V. Sivak, IEEE J. Sel. Top. Quantum Electron. 2, 1017 (1996).
[CrossRef]

1991

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, and C. A. Puliafito, Science 254, 1178 (1991).
[CrossRef] [PubMed]

1981

S. K. Sheem, J. Appl. Phys. 52, 3865 (1981).
[CrossRef]

1972

Badizadegan, K.

Barton, J. K.

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, and C. A. Puliafito, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Chen, Z. P.

Chinn, S. R.

Dasari, R. R.

Ding, Z. H.

Feld, M. S.

Fercher, A. F.

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, and C. A. Puliafito, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Fujimoto, J. G.

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, and C. A. Puliafito, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Hahn, M. S.

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, and C. A. Puliafito, Science 254, 1178 (1991).
[CrossRef] [PubMed]

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, and C. A. Puliafito, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Izatt, J. A.

Kobayashi, K.

J. A. Izatt, M. D. Kulkarni, H. W. Wang, K. Kobayashi, and M. V. Sivak, IEEE J. Sel. Top. Quantum Electron. 2, 1017 (1996).
[CrossRef]

Kowalczyk, A.

Kulkami, M. D.

Kulkarni, M. D.

J. A. Izatt, M. D. Kulkarni, H. W. Wang, K. Kobayashi, and M. V. Sivak, IEEE J. Sel. Top. Quantum Electron. 2, 1017 (1996).
[CrossRef]

Leitgeb, R.

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, and C. A. Puliafito, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Nelson, J. S.

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, and C. A. Puliafito, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Ren, H. W.

Rollins, A. 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, and C. A. Puliafito, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Sheem, S. K.

S. K. Sheem, J. Appl. Phys. 52, 3865 (1981).
[CrossRef]

Sivak, M. V.

J. A. Izatt, M. D. Kulkarni, H. W. Wang, K. Kobayashi, and M. V. Sivak, IEEE J. Sel. Top. Quantum Electron. 2, 1017 (1996).
[CrossRef]

Snyder, A. W.

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, and C. A. Puliafito, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Swanson, E. A.

S. R. Chinn, E. A. Swanson, and J. G. Fujimoto, Opt. Lett. 22, 340 (1997).
[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, and C. A. Puliafito, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Wang, H. W.

J. A. Izatt, M. D. Kulkarni, H. W. Wang, K. Kobayashi, and M. V. Sivak, IEEE J. Sel. Top. Quantum Electron. 2, 1017 (1996).
[CrossRef]

Wax, A.

Welch, A. J.

Wojtkowski, M.

Yang, C.

Yazdanfar, S.

Zhao, Y. H.

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Figures (5)

Fig. 1
Fig. 1

(A) Conventional differential low-coherence Michelson interferometer based on 2×2 fiber couplers. I0 is the total power incident on the reference and sample arms. γ=1. D, detector; F, fiber. (B) Michelson interferometer based on a 3×3 fiber coupler. γ=1/α11+α12. A circulator may be used in place of the input couplers in both (A) and (B) for increased efficiency.7 (C) Graphic representation of Eq. (2) for the coupling ratios and intrinsic phase shifts in a 3×3 interferometer.

Fig. 2
Fig. 2

Interferometric detector outputs of a 3×3 Michelson interferometer in a heterodyne experiment.

Fig. 3
Fig. 3

(A) Three-dimensional Lissajous plots of the interferometric signal from three photodetectors in a 3×3 Michelson interferometer. Time is color coded (green–black–red). (B) Lissajous plot of i3 versus i2. (C) Real and imaginary signals calculated from i2 and i3. (D) i2 versus time plotted with color coding.

Fig. 4
Fig. 4

Magnitude, phase, and Doppler shift of complex heterodyne interferometric signal calculated from outputs of the 3×3 interferometer. The Doppler shift is calculated from the numerical derivative of the phase and is in good agreement with the predicted value of 13 kHz.

Fig. 5
Fig. 5

Magnitude and phase of the complex interferometric signal in a homodyne experiment. The reference arm was not scanned; small random motions of the reference and sample mirrors led to variations in the interferometric phase. Application of the algorithm of Eqs. (3) allowed for clean extraction of magnitude and phase from outputs D2 and D3 of a 3×3 interferometer. The magnitude was constant (mean 1.52, variance 1.96×10-4), whereas small mirror motions led to π in phase.

Equations (4)

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

In=γI0α11α1n+α12α2n+2EΔxα11α1nα12α2n1/2×cos2kΔx+ϕn.
Renα1nα2n expj2kΔxexpjϕn=0,
nα1nα2n cosϕn=nα1nα2n sinϕn=0.
iIm=in cosϕm-ϕn-βimsinϕm-ϕn,  β=α11α1nα12α2nα11α1mα12α2m1/2.

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