Abstract

This paper proposes a non-iterative, two-dimensional numerical method to alleviate the compromise between the lateral resolution and wide depth measurement range in optical coherence tomography (OCT). A two-dimensional scalar diffraction model was developed to simulate the wave propagation process from out-of-focus scatterers within the short coherence gate of the OCT system. High-resolution details can be recovered from outside the depth-of-field region with minimum loss of lateral resolution. Experiments were performed to demonstrate the effectiveness of the proposed method.

© 2007 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, C. A. Puliafito, and J. G. Fujimoto, "Optical Coherence Tomography," Science 254, 1178-1181 (1991).
    [CrossRef] [PubMed]
  2. A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. Elzaiat, "Measurement of intraocular distances by backscattering spectral interferometry," Opt. Commun. 117, 43-48 (1995).
    [CrossRef]
  3. G. Hausler and M. W. Linduer, "Coherence radar and spectral radar-new tools for dermatological diagnosis," J. Biomed. Opt. 3, 21-31 (1998).
    [CrossRef]
  4. M. Wojtkowski, V. J. Srinivasan, T. H. Ko, J. G. Fujimoto, A. Kowalczyk, and J. S. Duker, "Ultrahigh resolution, high-speed, Fourier domain optical coherence tomography and methods for dispersion compensation," Opt. Express 12, 2404-2422 (2004).
    [CrossRef] [PubMed]
  5. B. Cense, N. A. Nassif, T. C. Chen, M. C. Pierce, S. Yun, B. H. Park, B. E. Bouma, G. J. Tearney, and J. F. de Boer, "Ultrahigh-resolution high-speed retinal imaging using spectral-domain optical coherence tomography," Opt. Express 12, 2435-2447 (2004).
    [CrossRef] [PubMed]
  6. S. Jiao, R. Knighton, X. Huang, G. Gregori, and C. A. Puliafito, "Simultaneous acquisition of sectional and fundus ophthalmic images with spectral-domain optical coherence tomography," Opt. Express 13, 444- 452 (2005).
    [CrossRef] [PubMed]
  7. S. H. Yun, G. J. Tearney, J. F. de Boer, N. Iftimia, and B. E. Bouma, "High-speed optical frequency domain imaging," Opt. Express 11, 2953-2963 (2003).
    [CrossRef] [PubMed]
  8. S. R. Chinn, E. A. Swanson, and J. G. Fujimoto, "Optical coherence tomography using a frequency-tunable optical source," Opt. Lett. 22, 340-342 (1997).
    [CrossRef] [PubMed]
  9. S. H. Yun, C. Boudoux, G. J. Tearney, and B. E. Bouma, "High-speed wavelength-swept semiconductor laser with a polygon-scanner-based wavelength filter," Opt. Lett. 28, 1981-1983 (2003).
    [CrossRef] [PubMed]
  10. R. Huber, M. Wojtkowski, K. Taira, J. G. Fujimoto, and K. Hsu, "Amplified, frequency swept lasers for frequency domain reflectometry and OCT imaging: design and scaling principles," Opt. Express 13, 3513- 3528 (2005).
    [CrossRef] [PubMed]
  11. R. Huber, D. C. Adler, and J. G. Fujimoto, "Buffered Fourier domain mode locking: unidirectional swept laser sources for optical coherence tomography imaging at 370,000 lines/s," Opt. Lett. 31, 2975-2977 (2006).
    [CrossRef] [PubMed]
  12. 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]
  13. 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]
  14. M. A. Choma, M. V. Sarunic, C. H. Yang, and J. A. Izatt, "Sensitivity advantage of swept source and Fourier domain optical coherence tomography," Opt. Express 11, 2183-2189 (2003).
    [CrossRef] [PubMed]
  15. B. Hermann, E. J. Fernandez, A. Unterhuber, H. Sattmann, A. F. Fercher, W. Drexler, P. M. Prieto, and P. Artal, "Adaptive-optics ultrahigh-resolution optical coherence tomography," Opt. Lett. 29, 2142-2144 (2004).
    [CrossRef] [PubMed]
  16. Z. Ding, H. Ren, Y. Zhao, J. S. Nelson, and Z. Chen, "High-resolution optical coherence tomography over a large depth range with an axicon lens," Opt. Lett. 27, 243-245 (2002).
    [CrossRef]
  17. Y. Wang, Y. Zhao, J. S. Nelson, and Z. Chen, "Ultrahighresolution optical coherence tomography by broadband continuum generation from a photonic crystal fiber," Opt. Lett. 28, 182-184 (2003).
    [CrossRef] [PubMed]
  18. M. J. Cobb, X. Liu, and X. Li, "Continuous focus tracking for real-time optical coherence tomography," Opt. Lett. 30, 1680-1682 (2005).
    [CrossRef] [PubMed]
  19. T. S. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, "Inverse scattering for optical coherence tomography," J. Opt. Soc. Am. A 23, 1027-1037 (2006).
    [CrossRef]
  20. M. D. Kulkarni, C. W. Thomas, and J. A. Izatt, "Image enhancement in optical coherence tomography using deconvolution," Electron. Lett. 331365-1367 (1997).
    [CrossRef]
  21. J. M. Schmitt, "Restoration of optical coherence images of living tissue using the clean algorithm," J. Biomed. Opt. 3, 66-75 (1998).
    [CrossRef]
  22. D. Piao, Q. Zhu, N. Dutta, S. Yan, and L. Otis, "Cancellation of coherent artifacts in optical coherence tomography imaging," Appl. Opt. 40, 5124-5131 (2001).
    [CrossRef]
  23. J. Hsu, C.W. Sun, C.W. Lu, C. C. Yang, C. P. Chiang, and C.W. Lin, "Resolution improvement with dispersion manipulation and a retrieval algorithm in optical coherence tomography," Appl. Opt. 42, 227-234 (2003).
    [CrossRef] [PubMed]
  24. Y. Yasuno, J. -i. Sugisaka, Y. Sando, Y. Nakamura, S. Makita, M. Itoh, and T. Yatagai, "Non-iterative numerical method for laterally super resolving Fourier domain optical coherence tomography," Opt. Express 14, 1006-1020 (2006).
    [CrossRef] [PubMed]
  25. T. S. Ralston, D. L. Marks, S. A. Boppart, and P. S. Carney, "Inverse scattering for high-resolution interferometric microscopy," Opt. Lett. 31, 3585-3587 (2006).
    [CrossRef] [PubMed]
  26. T. S. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart. "Interferometric Synthetic Aperture Microscopy," Nat. Phys. 3, 129-134, (2007).
    [CrossRef]
  27. R. M. Lewis, "Physical optics inverse diffraction," IEEE Trans. Antennas Propag. AP-17, 308-314 (1969).
    [CrossRef]
  28. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
  29. L. Yu and M. K. Kim, "Wavelength-scanning digital interference holography for tomographic three-dimensional imaging by use of the angular spectrum method," Opt. Lett. 30, 2092-2094 (2005).
    [CrossRef] [PubMed]

2007

T. S. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart. "Interferometric Synthetic Aperture Microscopy," Nat. Phys. 3, 129-134, (2007).
[CrossRef]

2006

2005

2004

2003

2002

2001

1998

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

G. Hausler and M. W. Linduer, "Coherence radar and spectral radar-new tools for dermatological diagnosis," J. Biomed. Opt. 3, 21-31 (1998).
[CrossRef]

1997

S. R. Chinn, E. A. Swanson, and J. G. Fujimoto, "Optical coherence tomography using a frequency-tunable optical source," Opt. Lett. 22, 340-342 (1997).
[CrossRef] [PubMed]

M. D. Kulkarni, C. W. Thomas, and J. A. Izatt, "Image enhancement in optical coherence tomography using deconvolution," Electron. Lett. 331365-1367 (1997).
[CrossRef]

1995

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. Elzaiat, "Measurement of intraocular distances by backscattering spectral interferometry," Opt. Commun. 117, 43-48 (1995).
[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, C. A. Puliafito, and J. G. Fujimoto, "Optical Coherence Tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

1969

R. M. Lewis, "Physical optics inverse diffraction," IEEE Trans. Antennas Propag. AP-17, 308-314 (1969).
[CrossRef]

Adler, D. C.

Artal, P.

Boppart, S. A.

Boudoux, C.

Bouma, B. E.

Carney, P. S.

Cense, B.

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]

Chen, T. C.

Chen, Z.

Chiang, C. P.

Chinn, S. R.

Choma, M. A.

Cobb, M. J.

de Boer, J. F.

Ding, Z.

Drexler, W.

Duker, J. S.

Dutta, N.

Elzaiat, S. Y.

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

Fercher, A. F.

Fernandez, E. J.

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.

Gregori, 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, C. A. Puliafito, and J. G. Fujimoto, "Optical Coherence Tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Hausler, G.

G. Hausler and M. W. Linduer, "Coherence radar and spectral radar-new tools for dermatological diagnosis," J. Biomed. Opt. 3, 21-31 (1998).
[CrossRef]

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, 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, 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. Elzaiat, "Measurement of intraocular distances by backscattering spectral interferometry," Opt. Commun. 117, 43-48 (1995).
[CrossRef]

Hsu, J.

Hsu, K.

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]

Huang, X.

Huber, R.

Iftimia, N.

Itoh, M.

Izatt, J. A.

M. A. Choma, M. V. Sarunic, C. H. Yang, and J. A. Izatt, "Sensitivity advantage of swept source and Fourier domain optical coherence tomography," Opt. Express 11, 2183-2189 (2003).
[CrossRef] [PubMed]

M. D. Kulkarni, C. W. Thomas, and J. A. Izatt, "Image enhancement in optical coherence tomography using deconvolution," Electron. Lett. 331365-1367 (1997).
[CrossRef]

Jiao, S.

Kamp, G.

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

Kim, M. K.

Knighton, R.

Ko, T. H.

Kowalczyk, A.

Kulkarni, M. D.

M. D. Kulkarni, C. W. Thomas, and J. A. Izatt, "Image enhancement in optical coherence tomography using deconvolution," Electron. Lett. 331365-1367 (1997).
[CrossRef]

Leitgeb, R. A.

Lewis, R. M.

R. M. Lewis, "Physical optics inverse diffraction," IEEE Trans. Antennas Propag. AP-17, 308-314 (1969).
[CrossRef]

Li, X.

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]

Lin, C.W.

Linduer, M. W.

G. Hausler and M. W. Linduer, "Coherence radar and spectral radar-new tools for dermatological diagnosis," J. Biomed. Opt. 3, 21-31 (1998).
[CrossRef]

Liu, X.

Lu, C.W.

Makita, S.

Marks, D. L.

Nakamura, Y.

Nassif, N. A.

Nelson, J. S.

Otis, L.

Park, B. H.

Piao, D.

Pierce, M. C.

Prieto, P. M.

Puliafito, C. A.

S. Jiao, R. Knighton, X. Huang, G. Gregori, and C. A. Puliafito, "Simultaneous acquisition of sectional and fundus ophthalmic images with spectral-domain optical coherence tomography," Opt. Express 13, 444- 452 (2005).
[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, C. A. Puliafito, and J. G. Fujimoto, "Optical Coherence Tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Ralston, T. S.

Ren, H.

Sando, Y.

Sarunic, M. V.

Sattmann, H.

Schmitt, J. M.

J. M. Schmitt, "Restoration of optical coherence images of living tissue using the clean algorithm," J. Biomed. Opt. 3, 66-75 (1998).
[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]

Srinivasan, V. J.

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]

Sugisaka, J. -i.

Sun, C.W.

Swanson, E. A.

S. R. Chinn, E. A. Swanson, and J. G. Fujimoto, "Optical coherence tomography using a frequency-tunable optical source," Opt. Lett. 22, 340-342 (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, C. A. Puliafito, and J. G. Fujimoto, "Optical Coherence Tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Taira, K.

Tearney, G. J.

Thomas, C. W.

M. D. Kulkarni, C. W. Thomas, and J. A. Izatt, "Image enhancement in optical coherence tomography using deconvolution," Electron. Lett. 331365-1367 (1997).
[CrossRef]

Unterhuber, A.

Wang, Y.

Wojtkowski, M.

Yan, S.

Yang, C. C.

Yang, C. H.

Yasuno, Y.

Yatagai, T.

Yu, L.

Yun, S.

Yun, S. H.

Zhao, Y.

Zhu, Q.

Appl. Opt.

Electron. Lett.

M. D. Kulkarni, C. W. Thomas, and J. A. Izatt, "Image enhancement in optical coherence tomography using deconvolution," Electron. Lett. 331365-1367 (1997).
[CrossRef]

IEEE Trans. Antennas Propag.

R. M. Lewis, "Physical optics inverse diffraction," IEEE Trans. Antennas Propag. AP-17, 308-314 (1969).
[CrossRef]

J. Biomed. Opt.

G. Hausler and M. W. Linduer, "Coherence radar and spectral radar-new tools for dermatological diagnosis," J. Biomed. Opt. 3, 21-31 (1998).
[CrossRef]

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

J. Opt. Soc. Am. A

Nat. Phys.

T. S. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart. "Interferometric Synthetic Aperture Microscopy," Nat. Phys. 3, 129-134, (2007).
[CrossRef]

Opt. Commun.

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

Opt. Express

S. H. Yun, G. J. Tearney, J. F. de Boer, N. Iftimia, and B. E. Bouma, "High-speed optical frequency domain imaging," Opt. Express 11, 2953-2963 (2003).
[CrossRef] [PubMed]

M. A. Choma, M. V. Sarunic, C. H. Yang, and J. A. Izatt, "Sensitivity advantage of swept source and Fourier domain optical coherence tomography," Opt. Express 11, 2183-2189 (2003).
[CrossRef] [PubMed]

M. Wojtkowski, V. J. Srinivasan, T. H. Ko, J. G. Fujimoto, A. Kowalczyk, and J. S. Duker, "Ultrahigh resolution, high-speed, Fourier domain optical coherence tomography and methods for dispersion compensation," Opt. Express 12, 2404-2422 (2004).
[CrossRef] [PubMed]

B. Cense, N. A. Nassif, T. C. Chen, M. C. Pierce, S. Yun, B. H. Park, B. E. Bouma, G. J. Tearney, and J. F. de Boer, "Ultrahigh-resolution high-speed retinal imaging using spectral-domain optical coherence tomography," Opt. Express 12, 2435-2447 (2004).
[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]

S. Jiao, R. Knighton, X. Huang, G. Gregori, and C. A. Puliafito, "Simultaneous acquisition of sectional and fundus ophthalmic images with spectral-domain optical coherence tomography," Opt. Express 13, 444- 452 (2005).
[CrossRef] [PubMed]

R. Huber, M. Wojtkowski, K. Taira, J. G. Fujimoto, and K. Hsu, "Amplified, frequency swept lasers for frequency domain reflectometry and OCT imaging: design and scaling principles," Opt. Express 13, 3513- 3528 (2005).
[CrossRef] [PubMed]

Y. Yasuno, J. -i. Sugisaka, Y. Sando, Y. Nakamura, S. Makita, M. Itoh, and T. Yatagai, "Non-iterative numerical method for laterally super resolving Fourier domain optical coherence tomography," Opt. Express 14, 1006-1020 (2006).
[CrossRef] [PubMed]

Opt. Lett.

M. J. Cobb, X. Liu, and X. Li, "Continuous focus tracking for real-time optical coherence tomography," Opt. Lett. 30, 1680-1682 (2005).
[CrossRef] [PubMed]

L. Yu and M. K. Kim, "Wavelength-scanning digital interference holography for tomographic three-dimensional imaging by use of the angular spectrum method," Opt. Lett. 30, 2092-2094 (2005).
[CrossRef] [PubMed]

S. H. Yun, C. Boudoux, G. J. Tearney, and B. E. Bouma, "High-speed wavelength-swept semiconductor laser with a polygon-scanner-based wavelength filter," Opt. Lett. 28, 1981-1983 (2003).
[CrossRef] [PubMed]

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]

R. Huber, D. C. Adler, and J. G. Fujimoto, "Buffered Fourier domain mode locking: unidirectional swept laser sources for optical coherence tomography imaging at 370,000 lines/s," Opt. Lett. 31, 2975-2977 (2006).
[CrossRef] [PubMed]

T. S. Ralston, D. L. Marks, S. A. Boppart, and P. S. Carney, "Inverse scattering for high-resolution interferometric microscopy," Opt. Lett. 31, 3585-3587 (2006).
[CrossRef] [PubMed]

B. Hermann, E. J. Fernandez, A. Unterhuber, H. Sattmann, A. F. Fercher, W. Drexler, P. M. Prieto, and P. Artal, "Adaptive-optics ultrahigh-resolution optical coherence tomography," Opt. Lett. 29, 2142-2144 (2004).
[CrossRef] [PubMed]

Y. Wang, Y. Zhao, J. S. Nelson, and Z. Chen, "Ultrahighresolution optical coherence tomography by broadband continuum generation from a photonic crystal fiber," Opt. Lett. 28, 182-184 (2003).
[CrossRef] [PubMed]

Z. Ding, H. Ren, Y. Zhao, J. S. Nelson, and Z. Chen, "High-resolution optical coherence tomography over a large depth range with an axicon lens," Opt. Lett. 27, 243-245 (2002).
[CrossRef]

S. R. Chinn, E. A. Swanson, and J. G. Fujimoto, "Optical coherence tomography using a frequency-tunable optical source," Opt. Lett. 22, 340-342 (1997).
[CrossRef] [PubMed]

Science

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

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

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Figures (5)

Fig. 1.
Fig. 1.

Illumination and detection in OCT system. (a) A Gaussian probe beam illuminates an out-of-focus sample. (b) OCT detects the diffracted and scattered light from the sample.

Fig. 2.
Fig. 2.

Flow diagram of the numerical focusing process (FL, focusing lens; DG, diffraction grating; CM, collimator; LSC, line-scan camera; LCL, low coherent laser).

Fig. 3.
Fig. 3.

(a). Evenly k-spaced spectral interferogram; (b) inverse Fourier transform of (a) to get positive, negative and low frequency terms in z space; (c) extraction of a single layer; (d) Fourier transformed from (c) to get an absolute spectral distribution of the single layer in (c). (All the vertical scales are normalized.)

Fig. 4.
Fig. 4.

B-scan and en-face images of an onion: (a) B-scan x-z images and (b) en-face x-y image of a focused onion; (c) B-scan x-z images and (d) en-face amplitude image of a defocused onion. Figure (e) shows the B-scan images after digital focusing, obtained at the same cross section position as (c). Figure (f) shows the digitally focused en-face image from (d). The scale bar represents 0.5 mm.

Fig. 5.
Fig. 5.

En-face (x-y) images of a defocused onion. (a) Onion cells under microscope; (b) a defocused onion layer ∼240μm away from the focal plane. Figures (c) and (d) show the reconstructed images with different focusing distances. The scale bar represents 100 μm.

Equations (3)

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S ( k x , k y ; 0 ) = E ( x , y ; 0 ) exp [ i ( k x x + k y y ) ] dxdy ,
E ( x , y ; 0 ) = S ( k x , k y ; 0 ) exp [ i ( k x x + k y y ) ] d k x d k y .
E ( x , y ; z ) = S ( k x , k y ; z ) exp [ i ( k x x + k y y ) ] d k x d k y .

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