Abstract

We present a simple processing technique that uses the concept of minimum-phase functions to improve frequency-domain optical coherence tomography systems. Our approach removes the autocorrelation noise and therefore increases both the accessible depth range and the recovery accuracy. To our knowledge, this is the first time that the concept of minimum-phase functions has been applied to improve optical coherence tomography.

© 2006 Optical Society of America

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  1. T. Asakura, International Trends in Optics and Photonics ICO IV,(Springer-Verlag, 1999), pp. 359-389.
  2. 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, 1178-1181 (1991).
    [CrossRef] [PubMed]
  3. J. G. Fujimoto, M. E. Brezinski, G. J. Tearney, S. A. Boppart, B. Bouma, M. R. Hee, J. F. Southern, and E. A. Swanson, 'Optical biopsy and imaging using optical coherence tomography,' Nat. Med. (N.Y.) 1, 970-972 (1995).
  4. A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, 'Measurement of intraocular distances by backscattering spectral interferometry,' Opt. Commun. 117, 43-48 (1995).
    [CrossRef]
  5. M. W. Lindner, P. Andretzky, F. Kiesewetter, and G. Hausler, 'Spectral radar: optical coherence tomography in the Fourier domain,' in Handbook of Optical Coherence Tomography, B.E.Bouma and G.T.Tearney, eds. (Marcel Dekker, 2001), Chap. 12.
  6. M. Wojtkowski, R. A. 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 (2003).
    [CrossRef]
  7. R. A. 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. 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]
  9. R. A. Leitgeb, C. K. Hitzenberger, A. F. Fercher, and T. Bajraszewski, 'Phase-shifting algorithm to achieve high-speed long-depth-range probing by frequency domain optical coherence tomography,' Opt. Lett. 28, 2201-2203 (2003).
    [CrossRef] [PubMed]
  10. R. A. Leitgeb, W. Drexler, A. Unterhuber, B. Hermann, T. Bajraszewski, T. Le, A. Stingl, and A. F. Fercher, 'Ultrahigh resolution Fourier domain optical coherence tomography,' Opt. Express 12, 2156-2165 (2004).
    [CrossRef] [PubMed]
  11. A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, 'Optical coherence tomography--principles and applications,' Rep. Prog. Phys. 66, 293-303 (2003).
  12. V. Oppenheim and R. W. Schafer, Digital Signal Processing (Prentice Hall, 2002), Chap. 7.
  13. T. F. Quatieri, Jr. and A. V. Oppenheim, 'Iterative techniques for minimum phase signal reconstruction from phase or magnitude,' IEEE Trans. Acoust., Speech, Signal Process. 29, 1187-1193 (1981).
    [CrossRef]
  14. M. Hayes, J. S. Lim, and A. V. Oppenheim, 'Signal reconstruction from phase or magnitude,' IEEE Trans. Acoust., Speech, Signal Process. 28, 672-680 (1980).
    [CrossRef]
  15. J. R. Fienup, 'Reconstruction of an object from the modulus of its Fourier transform,' Opt. Lett. 3, 27-29 (1978).
    [CrossRef] [PubMed]
  16. R. W. Gerchberg and W. O. Saxton, 'Practical algorithm for the determination of phase from image and diffraction plane pictures,' Optik (Stuttgart) 35, 237-246 (1972).
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    [CrossRef] [PubMed]
  18. A. Ozcan, M. J. F. Digonnet, and G. S. Kino, 'Group delay recovery using iterative processing of amplitude of transmission spectra of fibre Bragg gratings,' Electron. Lett. 40, 1104-1106 (2004).
    [CrossRef]
  19. J. M. Schmitt, S. H. Xiang, and K. M. Yung, 'Speckle in optical coherence tomography,' J. Biomed. Opt. 4, 95-105 (1999).
    [CrossRef]
  20. J. M. Schmitt, 'Optical coherence tomography: a review,' IEEE J. Quantum Electron. 5, 1205-1215 (1999).
    [CrossRef]
  21. N. Nakajima, 'Improvement in evaluating the logarithmic Hilbert transform in phase retrieval,' Opt. Lett. 11, 600-602 (1986).
    [CrossRef] [PubMed]
  22. M. A. Muriel and A. Carballar, 'Phase reconstruction from reflectivity in uniform fiber Bragg gratings,' Opt. Lett. 22, 93-95 (1997).
    [CrossRef] [PubMed]
  23. Digital Signal Processing Committee, Programs for Digital Signal Processing (IEEE, 1979).
  24. A. Ozcan, M. J. F. Digonnet, and G. S. Kino, 'Characterization of fiber Bragg gratings using spectral interferometry based on minimum-phase functions,' J. Lightwave Technol. 24, 1739-1757 (2006).
    [CrossRef]
  25. A. Ozcan, M. J. F. Digonnet, and G. S. Kino, 'A new iterative technique to characterize and design transmission fiber Bragg gratings,' J. Lightwave Technol. 24, 1913-1921 (2006).
    [CrossRef]

2006 (2)

2004 (3)

2003 (5)

1999 (2)

J. M. Schmitt, S. H. Xiang, and K. M. Yung, 'Speckle in optical coherence tomography,' J. Biomed. Opt. 4, 95-105 (1999).
[CrossRef]

J. M. Schmitt, 'Optical coherence tomography: a review,' IEEE J. Quantum Electron. 5, 1205-1215 (1999).
[CrossRef]

1997 (1)

1995 (2)

J. G. Fujimoto, M. E. Brezinski, G. J. Tearney, S. A. Boppart, B. Bouma, M. R. Hee, J. F. Southern, and E. A. Swanson, 'Optical biopsy and imaging using optical coherence tomography,' Nat. Med. (N.Y.) 1, 970-972 (1995).

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, 'Measurement of intraocular distances by backscattering spectral interferometry,' Opt. Commun. 117, 43-48 (1995).
[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, 1178-1181 (1991).
[CrossRef] [PubMed]

1986 (1)

1981 (1)

T. F. Quatieri, Jr. and A. V. Oppenheim, 'Iterative techniques for minimum phase signal reconstruction from phase or magnitude,' IEEE Trans. Acoust., Speech, Signal Process. 29, 1187-1193 (1981).
[CrossRef]

1980 (1)

M. Hayes, J. S. Lim, and A. V. Oppenheim, 'Signal reconstruction from phase or magnitude,' IEEE Trans. Acoust., Speech, Signal Process. 28, 672-680 (1980).
[CrossRef]

1978 (1)

1972 (1)

R. W. Gerchberg and W. O. Saxton, 'Practical algorithm for the determination of phase from image and diffraction plane pictures,' Optik (Stuttgart) 35, 237-246 (1972).

Andretzky, P.

M. W. Lindner, P. Andretzky, F. Kiesewetter, and G. Hausler, 'Spectral radar: optical coherence tomography in the Fourier domain,' in Handbook of Optical Coherence Tomography, B.E.Bouma and G.T.Tearney, eds. (Marcel Dekker, 2001), Chap. 12.

Asakura, T.

T. Asakura, International Trends in Optics and Photonics ICO IV,(Springer-Verlag, 1999), pp. 359-389.

Bajraszewski, T.

Boppart, S. A.

J. G. Fujimoto, M. E. Brezinski, G. J. Tearney, S. A. Boppart, B. Bouma, M. R. Hee, J. F. Southern, and E. A. Swanson, 'Optical biopsy and imaging using optical coherence tomography,' Nat. Med. (N.Y.) 1, 970-972 (1995).

Bouma, B.

J. G. Fujimoto, M. E. Brezinski, G. J. Tearney, S. A. Boppart, B. Bouma, M. R. Hee, J. F. Southern, and E. A. Swanson, 'Optical biopsy and imaging using optical coherence tomography,' Nat. Med. (N.Y.) 1, 970-972 (1995).

Brezinski, M. E.

J. G. Fujimoto, M. E. Brezinski, G. J. Tearney, S. A. Boppart, B. Bouma, M. R. Hee, J. F. Southern, and E. A. Swanson, 'Optical biopsy and imaging using optical coherence tomography,' Nat. Med. (N.Y.) 1, 970-972 (1995).

Carballar, A.

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, 1178-1181 (1991).
[CrossRef] [PubMed]

Choma, M. A.

Digonnet, M. J. F.

Drexler, W.

R. A. Leitgeb, W. Drexler, A. Unterhuber, B. Hermann, T. Bajraszewski, T. Le, A. Stingl, and A. F. Fercher, 'Ultrahigh resolution Fourier domain optical coherence tomography,' Opt. Express 12, 2156-2165 (2004).
[CrossRef] [PubMed]

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, 'Optical coherence tomography--principles and applications,' Rep. Prog. Phys. 66, 293-303 (2003).

El-Zaiat, S. Y.

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, 'Measurement of intraocular distances by backscattering spectral interferometry,' Opt. Commun. 117, 43-48 (1995).
[CrossRef]

Fercher, A. F.

R. A. Leitgeb, W. Drexler, A. Unterhuber, B. Hermann, T. Bajraszewski, T. Le, A. Stingl, and A. F. Fercher, 'Ultrahigh resolution Fourier domain optical coherence tomography,' Opt. Express 12, 2156-2165 (2004).
[CrossRef] [PubMed]

R. A. Leitgeb, C. K. Hitzenberger, A. F. Fercher, and T. Bajraszewski, 'Phase-shifting algorithm to achieve high-speed long-depth-range probing by frequency domain optical coherence tomography,' Opt. Lett. 28, 2201-2203 (2003).
[CrossRef] [PubMed]

M. Wojtkowski, R. A. 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 (2003).
[CrossRef]

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, 'Optical coherence tomography--principles and applications,' Rep. Prog. Phys. 66, 293-303 (2003).

R. A. 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]

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, 'Measurement of intraocular distances by backscattering spectral interferometry,' Opt. Commun. 117, 43-48 (1995).
[CrossRef]

Fienup, J. R.

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, 1178-1181 (1991).
[CrossRef] [PubMed]

Fujimoto, J. G.

J. G. Fujimoto, M. E. Brezinski, G. J. Tearney, S. A. Boppart, B. Bouma, M. R. Hee, J. F. Southern, and E. A. Swanson, 'Optical biopsy and imaging using optical coherence tomography,' Nat. Med. (N.Y.) 1, 970-972 (1995).

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, 1178-1181 (1991).
[CrossRef] [PubMed]

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, 'Practical algorithm for the determination of phase from image and diffraction plane pictures,' Optik (Stuttgart) 35, 237-246 (1972).

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, 1178-1181 (1991).
[CrossRef] [PubMed]

Hausler, G.

M. W. Lindner, P. Andretzky, F. Kiesewetter, and G. Hausler, 'Spectral radar: optical coherence tomography in the Fourier domain,' in Handbook of Optical Coherence Tomography, B.E.Bouma and G.T.Tearney, eds. (Marcel Dekker, 2001), Chap. 12.

Hayes, M.

M. Hayes, J. S. Lim, and A. V. Oppenheim, 'Signal reconstruction from phase or magnitude,' IEEE Trans. Acoust., Speech, Signal Process. 28, 672-680 (1980).
[CrossRef]

Hee, M. R.

J. G. Fujimoto, M. E. Brezinski, G. J. Tearney, S. A. Boppart, B. Bouma, M. R. Hee, J. F. Southern, and E. A. Swanson, 'Optical biopsy and imaging using optical coherence tomography,' Nat. Med. (N.Y.) 1, 970-972 (1995).

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, 1178-1181 (1991).
[CrossRef] [PubMed]

Hermann, B.

Hitzenberger, C. K.

R. A. Leitgeb, C. K. Hitzenberger, A. F. Fercher, and T. Bajraszewski, 'Phase-shifting algorithm to achieve high-speed long-depth-range probing by frequency domain optical coherence tomography,' Opt. Lett. 28, 2201-2203 (2003).
[CrossRef] [PubMed]

R. A. 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]

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, 'Optical coherence tomography--principles and applications,' Rep. Prog. Phys. 66, 293-303 (2003).

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, 'Measurement of intraocular distances by backscattering spectral interferometry,' Opt. Commun. 117, 43-48 (1995).
[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, 1178-1181 (1991).
[CrossRef] [PubMed]

Izatt, J. A.

Kamp, G.

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, 'Measurement of intraocular distances by backscattering spectral interferometry,' Opt. Commun. 117, 43-48 (1995).
[CrossRef]

Kiesewetter, F.

M. W. Lindner, P. Andretzky, F. Kiesewetter, and G. Hausler, 'Spectral radar: optical coherence tomography in the Fourier domain,' in Handbook of Optical Coherence Tomography, B.E.Bouma and G.T.Tearney, eds. (Marcel Dekker, 2001), Chap. 12.

Kino, G. S.

Kowalczyk, A.

M. Wojtkowski, R. A. 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 (2003).
[CrossRef]

Lasser, T.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, 'Optical coherence tomography--principles and applications,' Rep. Prog. Phys. 66, 293-303 (2003).

Le, T.

Leitgeb, R. A.

Lim, J. S.

M. Hayes, J. S. Lim, and A. V. Oppenheim, 'Signal reconstruction from phase or magnitude,' IEEE Trans. Acoust., Speech, Signal Process. 28, 672-680 (1980).
[CrossRef]

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, 1178-1181 (1991).
[CrossRef] [PubMed]

Lindner, M. W.

M. W. Lindner, P. Andretzky, F. Kiesewetter, and G. Hausler, 'Spectral radar: optical coherence tomography in the Fourier domain,' in Handbook of Optical Coherence Tomography, B.E.Bouma and G.T.Tearney, eds. (Marcel Dekker, 2001), Chap. 12.

Muriel, M. A.

Nakajima, N.

Oppenheim, A. V.

T. F. Quatieri, Jr. and A. V. Oppenheim, 'Iterative techniques for minimum phase signal reconstruction from phase or magnitude,' IEEE Trans. Acoust., Speech, Signal Process. 29, 1187-1193 (1981).
[CrossRef]

M. Hayes, J. S. Lim, and A. V. Oppenheim, 'Signal reconstruction from phase or magnitude,' IEEE Trans. Acoust., Speech, Signal Process. 28, 672-680 (1980).
[CrossRef]

Oppenheim, V.

V. Oppenheim and R. W. Schafer, Digital Signal Processing (Prentice Hall, 2002), Chap. 7.

Ozcan, A.

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, 1178-1181 (1991).
[CrossRef] [PubMed]

Quatieri, T. F.

T. F. Quatieri, Jr. and A. V. Oppenheim, 'Iterative techniques for minimum phase signal reconstruction from phase or magnitude,' IEEE Trans. Acoust., Speech, Signal Process. 29, 1187-1193 (1981).
[CrossRef]

Sarunic, M. V.

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, 'Practical algorithm for the determination of phase from image and diffraction plane pictures,' Optik (Stuttgart) 35, 237-246 (1972).

Schafer, R. W.

V. Oppenheim and R. W. Schafer, Digital Signal Processing (Prentice Hall, 2002), Chap. 7.

Schmitt, J. M.

J. M. Schmitt, 'Optical coherence tomography: a review,' IEEE J. Quantum Electron. 5, 1205-1215 (1999).
[CrossRef]

J. M. Schmitt, S. H. Xiang, and K. M. Yung, 'Speckle in optical coherence tomography,' J. Biomed. Opt. 4, 95-105 (1999).
[CrossRef]

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, 1178-1181 (1991).
[CrossRef] [PubMed]

Southern, J. F.

J. G. Fujimoto, M. E. Brezinski, G. J. Tearney, S. A. Boppart, B. Bouma, M. R. Hee, J. F. Southern, and E. A. Swanson, 'Optical biopsy and imaging using optical coherence tomography,' Nat. Med. (N.Y.) 1, 970-972 (1995).

Stingl, A.

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, 1178-1181 (1991).
[CrossRef] [PubMed]

Swanson, E. A.

J. G. Fujimoto, M. E. Brezinski, G. J. Tearney, S. A. Boppart, B. Bouma, M. R. Hee, J. F. Southern, and E. A. Swanson, 'Optical biopsy and imaging using optical coherence tomography,' Nat. Med. (N.Y.) 1, 970-972 (1995).

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, 1178-1181 (1991).
[CrossRef] [PubMed]

Tearney, G. J.

J. G. Fujimoto, M. E. Brezinski, G. J. Tearney, S. A. Boppart, B. Bouma, M. R. Hee, J. F. Southern, and E. A. Swanson, 'Optical biopsy and imaging using optical coherence tomography,' Nat. Med. (N.Y.) 1, 970-972 (1995).

Unterhuber, A.

Wojtkowski, M.

M. Wojtkowski, R. A. 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 (2003).
[CrossRef]

Xiang, S. H.

J. M. Schmitt, S. H. Xiang, and K. M. Yung, 'Speckle in optical coherence tomography,' J. Biomed. Opt. 4, 95-105 (1999).
[CrossRef]

Yang, C.

Yung, K. M.

J. M. Schmitt, S. H. Xiang, and K. M. Yung, 'Speckle in optical coherence tomography,' J. Biomed. Opt. 4, 95-105 (1999).
[CrossRef]

Electron. Lett. (1)

A. Ozcan, M. J. F. Digonnet, and G. S. Kino, 'Group delay recovery using iterative processing of amplitude of transmission spectra of fibre Bragg gratings,' Electron. Lett. 40, 1104-1106 (2004).
[CrossRef]

IEEE J. Quantum Electron. (1)

J. M. Schmitt, 'Optical coherence tomography: a review,' IEEE J. Quantum Electron. 5, 1205-1215 (1999).
[CrossRef]

IEEE Trans. Acoust., Speech, Signal Process. (2)

T. F. Quatieri, Jr. and A. V. Oppenheim, 'Iterative techniques for minimum phase signal reconstruction from phase or magnitude,' IEEE Trans. Acoust., Speech, Signal Process. 29, 1187-1193 (1981).
[CrossRef]

M. Hayes, J. S. Lim, and A. V. Oppenheim, 'Signal reconstruction from phase or magnitude,' IEEE Trans. Acoust., Speech, Signal Process. 28, 672-680 (1980).
[CrossRef]

J. Biomed. Opt. (2)

M. Wojtkowski, R. A. 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 (2003).
[CrossRef]

J. M. Schmitt, S. H. Xiang, and K. M. Yung, 'Speckle in optical coherence tomography,' J. Biomed. Opt. 4, 95-105 (1999).
[CrossRef]

J. Lightwave Technol. (2)

Nat. Med. (N.Y.) (1)

J. G. Fujimoto, M. E. Brezinski, G. J. Tearney, S. A. Boppart, B. Bouma, M. R. Hee, J. F. Southern, and E. A. Swanson, 'Optical biopsy and imaging using optical coherence tomography,' Nat. Med. (N.Y.) 1, 970-972 (1995).

Opt. Commun. (1)

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, 'Measurement of intraocular distances by backscattering spectral interferometry,' Opt. Commun. 117, 43-48 (1995).
[CrossRef]

Opt. Express (4)

Opt. Lett. (4)

Optik (Stuttgart) (1)

R. W. Gerchberg and W. O. Saxton, 'Practical algorithm for the determination of phase from image and diffraction plane pictures,' Optik (Stuttgart) 35, 237-246 (1972).

Rep. Prog. Phys. (1)

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, 'Optical coherence tomography--principles and applications,' Rep. Prog. Phys. 66, 293-303 (2003).

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, 1178-1181 (1991).
[CrossRef] [PubMed]

Other (4)

T. Asakura, International Trends in Optics and Photonics ICO IV,(Springer-Verlag, 1999), pp. 359-389.

M. W. Lindner, P. Andretzky, F. Kiesewetter, and G. Hausler, 'Spectral radar: optical coherence tomography in the Fourier domain,' in Handbook of Optical Coherence Tomography, B.E.Bouma and G.T.Tearney, eds. (Marcel Dekker, 2001), Chap. 12.

V. Oppenheim and R. W. Schafer, Digital Signal Processing (Prentice Hall, 2002), Chap. 7.

Digital Signal Processing Committee, Programs for Digital Signal Processing (IEEE, 1979).

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Figures (10)

Fig. 1
Fig. 1

Simplified block diagram of the measurement set up for (a) TDOCT and (b) FDOCT.

Fig. 2
Fig. 2

(a) Power spectrum I ( f ) computed numerically using the two-mirror scattering function (solid curve) of Fig. 2b. (b) Solid curve, power reflectivity of the originally assumed two-mirror scattering function; dotted-dashed curve, recovered power reflectivity by a direct IFT of Fig. 2a; dotted curve, recovered power reflectivity using the MPF-based approach. The inset shows a focused version of the first mirror peak around 0.5 mm .

Fig. 3
Fig. 3

Solid curve, arbitrarily chosen tissue-scattering function (a) amplitude, (b) phase. Dotted–dashed curve, tissue scattering function (a) amplitude, (b) phase recovered using the conventional IFT-based FDOCT processing, i.e., using Eq. (3).

Fig. 4
Fig. 4

Power spectrum I ( f ) computed numerically using the arbitrarily chosen complex tissue-scattering function (solid curves) of Fig. 3.

Fig. 5
Fig. 5

General block diagram of the iterative error-reduction algorithm to recover an MPF from its measured FT magnitude spectrum.

Fig. 6
Fig. 6

Solid curve, arbitrarily chosen tissue-scattering function (a) amplitude, (b) phase; dotted-dashed curve, tissue scattering function (a) amplitude, (b) phase recovered using our MPF-based approach (noise-free case).

Fig. 7
Fig. 7

Error improvement factor of the proposed MPF-based processing with respect to the conventional FDOCT processing as a function of the power ratio between the reference and tissue arms.

Fig. 8
Fig. 8

(a) Solid curve, arbitrarily chosen tissue-scattering function amplitude; dotted-dashed curve, its recovery achieved using the conventional IFT-based processing approach. (b) Solid curve, arbitrarily chosen tissue-scattering function amplitude; dotted-dashed curve, its recovery achieved using the MPF-based processing approach. In this example z 0 = 0.5 mm .

Fig. 9
Fig. 9

Solid curve, arbitrarily chosen tissue scattering function (a) amplitude, (b) phase. Dashed curve, tissue scattering function (a) amplitude and (b) phase recovered using our MPF-based approach for the case where the signal-to-noise ratio of the FDOCT system was degraded by random noise to 35 dB below the shot noise limit.

Fig. 10
Fig. 10

Same as Fig. 2b, except in this simulation result, the MPF-based approach was computed using the logarithmic Hilbert transform of the square root of the power spectrum of Fig. 2a.

Equations (4)

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I ( k ) = S ( k ) g ( z ) exp ( j k 2 n T z ) d z 2 ,
I ( f ) = S ( f ) G ( f ) 2 ,
IFT [ S ( f ) G ( f ) 2 ] = [ R 2 δ ( z ) + AC { t ( z ) } + R t ̃ ( z z 0 ) + R t ( z z 0 ) ] IFT { S ( f ) } ,
IFT { I ( f ) } 1 2 R [ 2 R 2 δ ( z ) + AC { t ( z ) } 2 C ( z 2 z 0 ) 4 C ̃ ( z 2 z 0 ) 4 + R t ̃ ( z z 0 ) + R t ( z z 0 ) ] IFT { S ( f ) } ,

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