Abstract

Practical clinical optical coherence tomography (OCT) systems require automatic tools for identifying and correcting flaws in OCT images. One type of flaw is the loss of image detail owing to the dispersion of the medium, which in most cases is unknown. We present an autofocus algorithm for estimating the delay line and material dispersion from OCT reflectance data, integrating a previously presented dispersion compensation algorithm to correct the data. The algorithm is based on minimizing the Renyi entropy of the corrected axial-scan image, which is a contrast-enhancement criterion. This autofocus algorithm can be used in conjunction with a high-speed, digital-signal-processor-based OCT acquisition system for rapid image correction.

© 2003 Optical Society of America

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References

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    [CrossRef]
  3. W. Drexler, U. Morgner, F. X. Kartner, C. Pitris, S. A. Boppart, X. Li, E. P. Ippen, J. G. Fujimoto, “In vivo ultrahigh resolution optical coherence tomography,” Opt. Lett. 24, 1221–1223 (1999).
    [CrossRef]
  4. K. M. Yung, S. L. Lee, J. M. Schmitt, “Phase-domain processing of optical coherence tomography images,” J. Biomed. Opt. 4, 125–136 (1999).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  7. A. Renyi, Probability Theory (North-Holland, Amsterdam, Netherlands, 1970).
  8. E. Kenneth, I. Hild, D. Erdogmus, J. C. Principe, “Blind source separation using Renyi’s Mutual Information,” IEEE Signal Proc. Lett. 8, 174–176 (2001).
    [CrossRef]
  9. J. J. Knab, “Interpolation of band-limited functions using the approximate prolate series,” IEEE Trans. Inf. Theory IT-25, 717–720 (1979).
    [CrossRef]
  10. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C (Cambridge University Press, Cambridge, U.K., 1988).
  11. J. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
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    [CrossRef]

2003 (1)

2002 (1)

2001 (2)

1999 (2)

1998 (1)

J. M. Schmitt, “Restoration of optical coherence images of living tissue using the clean algorithm,” J. Biomed. Opt. 3, 66–75 (1998).
[CrossRef] [PubMed]

1979 (1)

J. J. Knab, “Interpolation of band-limited functions using the approximate prolate series,” IEEE Trans. Inf. Theory IT-25, 717–720 (1979).
[CrossRef]

Boppart, S. A.

Cover, T. M.

T. M. Cover, J. A. Thomas, Elements of Information Theory (Wiley, New York, 1991).
[CrossRef]

Drexler, W.

Erdogmus, D.

E. Kenneth, I. Hild, D. Erdogmus, J. C. Principe, “Blind source separation using Renyi’s Mutual Information,” IEEE Signal Proc. Lett. 8, 174–176 (2001).
[CrossRef]

Fercher, A. F.

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C (Cambridge University Press, Cambridge, U.K., 1988).

Fujimoto, J. G.

Goodman, J.

J. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Hild, I.

E. Kenneth, I. Hild, D. Erdogmus, J. C. Principe, “Blind source separation using Renyi’s Mutual Information,” IEEE Signal Proc. Lett. 8, 174–176 (2001).
[CrossRef]

Hitzenberger, C. K.

Ippen, E. P.

Karamata, B.

Kartner, F. X.

Kenneth, E.

E. Kenneth, I. Hild, D. Erdogmus, J. C. Principe, “Blind source separation using Renyi’s Mutual Information,” IEEE Signal Proc. Lett. 8, 174–176 (2001).
[CrossRef]

Knab, J. J.

J. J. Knab, “Interpolation of band-limited functions using the approximate prolate series,” IEEE Trans. Inf. Theory IT-25, 717–720 (1979).
[CrossRef]

Lasser, T.

Lee, S. L.

K. M. Yung, S. L. Lee, J. M. Schmitt, “Phase-domain processing of optical coherence tomography images,” J. Biomed. Opt. 4, 125–136 (1999).
[CrossRef] [PubMed]

Li, X.

Marks, D. L.

Morgner, U.

Oldenburg, A. L.

Pitris, C.

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C (Cambridge University Press, Cambridge, U.K., 1988).

Principe, J. C.

E. Kenneth, I. Hild, D. Erdogmus, J. C. Principe, “Blind source separation using Renyi’s Mutual Information,” IEEE Signal Proc. Lett. 8, 174–176 (2001).
[CrossRef]

Renyi, A.

A. Renyi, Probability Theory (North-Holland, Amsterdam, Netherlands, 1970).

Reynolds, J. J.

Schmitt, J. M.

K. M. Yung, S. L. Lee, J. M. Schmitt, “Phase-domain processing of optical coherence tomography images,” J. Biomed. Opt. 4, 125–136 (1999).
[CrossRef] [PubMed]

J. M. Schmitt, “Restoration of optical coherence images of living tissue using the clean algorithm,” J. Biomed. Opt. 3, 66–75 (1998).
[CrossRef] [PubMed]

Sticker, M.

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C (Cambridge University Press, Cambridge, U.K., 1988).

Thomas, J. A.

T. M. Cover, J. A. Thomas, Elements of Information Theory (Wiley, New York, 1991).
[CrossRef]

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C (Cambridge University Press, Cambridge, U.K., 1988).

Yung, K. M.

K. M. Yung, S. L. Lee, J. M. Schmitt, “Phase-domain processing of optical coherence tomography images,” J. Biomed. Opt. 4, 125–136 (1999).
[CrossRef] [PubMed]

Zawadzki, R.

Appl. Opt. (1)

IEEE Signal Proc. Lett. (1)

E. Kenneth, I. Hild, D. Erdogmus, J. C. Principe, “Blind source separation using Renyi’s Mutual Information,” IEEE Signal Proc. Lett. 8, 174–176 (2001).
[CrossRef]

IEEE Trans. Inf. Theory (1)

J. J. Knab, “Interpolation of band-limited functions using the approximate prolate series,” IEEE Trans. Inf. Theory IT-25, 717–720 (1979).
[CrossRef]

J. Biomed. Opt. (2)

K. M. Yung, S. L. Lee, J. M. Schmitt, “Phase-domain processing of optical coherence tomography images,” J. Biomed. Opt. 4, 125–136 (1999).
[CrossRef] [PubMed]

J. M. Schmitt, “Restoration of optical coherence images of living tissue using the clean algorithm,” J. Biomed. Opt. 3, 66–75 (1998).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (2)

Other (4)

T. M. Cover, J. A. Thomas, Elements of Information Theory (Wiley, New York, 1991).
[CrossRef]

A. Renyi, Probability Theory (North-Holland, Amsterdam, Netherlands, 1970).

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C (Cambridge University Press, Cambridge, U.K., 1988).

J. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

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Figures (6)

Fig. 1
Fig. 1

Low-resolution OCT image of the PDMS microfluidic structure with a schematic of the cross section of the microfluidic channel.

Fig. 2
Fig. 2

Source spectrum and digitally modified spectrum.

Fig. 3
Fig. 3

Autofocus digitally corrected reflections off of interfaces of microfluidic structure. Plots (a), (c), (e), and (g) correspond to the uncorrected reflectance functions, whereas (b), (d), (f), and (h) are the corrected point-spread functions.

Fig. 4
Fig. 4

Image of a tadpole: (a) before automatic dispersion correction and (b) after automatic dispersion correction. The boxes to the right of each image show an expanded version of each image.

Fig. 5
Fig. 5

Four sections of pointlike objects (cell nuclei) from the tadpole images, taken at different depths in the image, and their corrected versions.

Fig. 6
Fig. 6

Dependence of Renyi quadratic entropy (γ = 1) on the chirp parameters α2 and β2.

Equations (12)

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Λ=-0 |gz|21+γdz.
dΛdγγ=0=-0 |gz|2log|gz|2dz.
F˜n=j=0N-1 fj expπijnN.
G˜n=F˜n maxS˜n-N0, 0maxS˜n-N0, 02+N02.
ωctr=n=0N-1 n maxS˜n-N0, 0n=0N-1 N maxS˜n-N0, 0.
G˜n=G˜n expiπα2nN-ωctr2+iπα3nN-ωctr3.
in=n+β2nN-ωctr2+β3nN-ωctr3.
G˜n=in+1-inj=0N-1 G˜j sinπj-inπj-in.
gn=1Nj=0N-1 G˜j exp-πijnN.
gn=gn+m, for n<N-m, gn=0, otherwise, hn=gn+m, for n<m-m.
Λh=-n=0m-m-1 |hn|21+γ.
α2new=α2old-β2d/N, α3new=α3old-β3d/N.

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