Abstract

In this paper a theoretical model of the full field swept source (FF SS) OCT signal is presented based on the angular spectrum wave propagation approach which accounts for the defocus error with imaging depth. It is shown that using the same theoretical model of the signal, numerical defocus correction methods based on a simple forward model (FM) and inverse scattering (IS), the latter being similar to interferometric synthetic aperture microscopy (ISAM), can be derived. Both FM and IS are compared quantitatively with sub-aperture based digital adaptive optics (DAO). FM has the least numerical complexity, and is the fastest in terms of computational speed among the three. SNR improvement of more than 10 dB is shown for all the three methods over a sample depth of 1.5 mm. For a sample with non-uniform refractive index with depth, FM and IS both improved the depth of focus (DOF) by a factor of 7x for an imaging NA of 0.1. DAO performs the best in case of non-uniform refractive index with respect to DOF improvement by 11x.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. W. Drexler, “Ultrahigh-resolution optical coherence tomography,” J. Biomed. Opt.9(1), 47–74 (2004).
    [CrossRef] [PubMed]
  2. 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(4), 243–245 (2002).
    [CrossRef] [PubMed]
  3. R. A. Leitgeb, M. Villiger, A. H. Bachmann, L. Steinmann, and T. Lasser, “Extended focus depth for Fourier domain optical coherence microscopy,” Opt. Lett.31(16), 2450–2452 (2006).
    [CrossRef] [PubMed]
  4. K. S. Lee and J. P. Rolland, “Bessel beam spectral-domain high-resolution optical coherence tomography with micro-optic axicon providing extended focusing range,” Opt. Lett.33(15), 1696–1698 (2008).
    [CrossRef] [PubMed]
  5. C. Blatter, B. Grajciar, C. M. Eigenwillig, W. Wieser, B. R. Biedermann, R. Huber, and R. A. Leitgeb, “Extended focus high-speed swept source OCT with self-reconstructive illumination,” Opt. Express19(13), 12141–12155 (2011).
    [CrossRef] [PubMed]
  6. A. Zlotnik, Y. Abraham, L. Liraz, I. Abdulhalim, and Z. Zalevsky, “Improved extended depth of focus full field spectral domain Optical Coherence Tomography,” Opt. Commun.283(24), 4963–4968 (2010).
    [CrossRef]
  7. J. Mo, M. de Groot, and J. F. de Boer, “Focus-extension by depth-encoded synthetic aperture in Optical Coherence Tomography,” Opt. Express21(8), 10048–10061 (2013).
    [CrossRef] [PubMed]
  8. K. Sasaki, K. Kurokawa, S. Makita, and Y. Yasuno, “Extended depth of focus adaptive optics spectral domain optical coherence tomography,” Biomed. Opt. Express3(10), 2353–2370 (2012).
    [CrossRef] [PubMed]
  9. P. Hariharan, Optical Interferometry (Academic, 2003).
  10. Y. Yasuno, J. Sugisaka, Y. Sando, Y. Nakamura, S. Makita, M. Itoh, and T. Yatagai, “Non-iterative numerical method for laterally superresolving Fourier domain optical coherence tomography,” Opt. Express14(3), 1006–1020 (2006).
    [CrossRef] [PubMed]
  11. L. Yu, B. Rao, J. Zhang, J. Su, Q. Wang, S. Guo, and Z. Chen, “Improved lateral resolution in optical coherence tomography by digital focusing using two-dimensional numerical diffraction method,” Opt. Express15(12), 7634–7641 (2007).
    [CrossRef] [PubMed]
  12. Y. Nakamura, J. Sugisaka, Y. Sando, T. Endo, M. Itoh, T. Yatagai, and Y. Yasuno, “Complex numerical processing for in-focus line-field spectral-domain optical coherence tomography,” Jpn. J. Appl. Phys.46(4A), 1774–1778 (2007).
    [CrossRef]
  13. T. S. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy,” Nat. Phys.3(2), 129–134 (2007).
    [CrossRef]
  14. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, 1988).
  15. T. S. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, “Real-time interferometric synthetic aperture microscopy,” Opt. Express16(4), 2555–2569 (2008).
    [CrossRef] [PubMed]
  16. T. S. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, “Phase stability technique for inverse scattering in optical coherence tomography,” 3rd IEEE International Symposium on Biomedical Imaging: Nano to Macro, 578–581 (2006).
    [CrossRef]
  17. S. Labiau, G. David, S. Gigan, and A. C. Boccara, “Defocus test and defocus correction in full-field optical coherence tomography,” Opt. Lett.34(10), 1576–1578 (2009).
    [CrossRef] [PubMed]
  18. G. Min, W. J. Choi, J. W. Kim, and B. H. Lee, “Refractive index measurements of multiple layers using numerical refocusing in FF-OCT,” Opt. Express21(24), 29955–29967 (2013).
    [CrossRef] [PubMed]
  19. D. L. Marks, T. S. Ralston, S. A. Boppart, and P. S. Carney, “Inverse scattering for frequency-scanned full-field optical coherence tomography,” J. Opt. Soc. Am. A24(4), 1034–1041 (2007).
    [CrossRef] [PubMed]
  20. A. Kumar, W. Drexler, and R. A. Leitgeb, “Subaperture correlation based digital adaptive optics for full field optical coherence tomography,” Opt. Express21(9), 10850–10866 (2013).
    [CrossRef] [PubMed]
  21. D. Hillmann, G. Franke, C. Lührs, P. Koch, and G. Hüttmann, “Efficient holoscopy image reconstruction,” Opt. Express20(19), 21247–21263 (2012).
    [CrossRef] [PubMed]
  22. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes 3rd Edition: The Art of Scientific Computing (Cambridge University, 2007).
  23. W. G. Carrara, R. S. Goodman, and R. M. Majewski, Spotlight Synthetic Aperture Radar (Artech House, 1995), Chap. 6.
  24. M. Guizar-Sicairos, S. T. Thurman, and J. R. Fienup, “Efficient subpixel image registration algorithms,” Opt. Lett.33(2), 156–158 (2008).
    [CrossRef] [PubMed]
  25. S. G. Adie, B. W. Graf, A. Ahmad, P. S. Carney, and S. A. Boppart, “Computational adaptive optics for broadband optical interferometric tomography of biological tissue,” Proc. Natl. Acad. Sci. U.S.A.109(19), 7175–7180 (2012).
    [CrossRef] [PubMed]
  26. A. E. Tippie, A. Kumar, and J. R. Fienup, “High-resolution synthetic-aperture digital holography with digital phase and pupil correction,” Opt. Express19(13), 12027–12038 (2011).
    [CrossRef] [PubMed]
  27. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 2004).
  28. A. Ahmad, N. D. Shemonski, S. G. Adie, H. S. Kim, W. M. W. Hwu, P. S. Carney, and S. A. Boppart, “Real-time in vivo computed optical interferometric tomography,” Nat. Photonics7(6), 444–448 (2013).
    [CrossRef] [PubMed]

2013 (4)

2012 (3)

2011 (2)

2010 (1)

A. Zlotnik, Y. Abraham, L. Liraz, I. Abdulhalim, and Z. Zalevsky, “Improved extended depth of focus full field spectral domain Optical Coherence Tomography,” Opt. Commun.283(24), 4963–4968 (2010).
[CrossRef]

2009 (1)

2008 (3)

2007 (4)

D. L. Marks, T. S. Ralston, S. A. Boppart, and P. S. Carney, “Inverse scattering for frequency-scanned full-field optical coherence tomography,” J. Opt. Soc. Am. A24(4), 1034–1041 (2007).
[CrossRef] [PubMed]

L. Yu, B. Rao, J. Zhang, J. Su, Q. Wang, S. Guo, and Z. Chen, “Improved lateral resolution in optical coherence tomography by digital focusing using two-dimensional numerical diffraction method,” Opt. Express15(12), 7634–7641 (2007).
[CrossRef] [PubMed]

Y. Nakamura, J. Sugisaka, Y. Sando, T. Endo, M. Itoh, T. Yatagai, and Y. Yasuno, “Complex numerical processing for in-focus line-field spectral-domain optical coherence tomography,” Jpn. J. Appl. Phys.46(4A), 1774–1778 (2007).
[CrossRef]

T. S. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy,” Nat. Phys.3(2), 129–134 (2007).
[CrossRef]

2006 (2)

2004 (1)

W. Drexler, “Ultrahigh-resolution optical coherence tomography,” J. Biomed. Opt.9(1), 47–74 (2004).
[CrossRef] [PubMed]

2002 (1)

Abdulhalim, I.

A. Zlotnik, Y. Abraham, L. Liraz, I. Abdulhalim, and Z. Zalevsky, “Improved extended depth of focus full field spectral domain Optical Coherence Tomography,” Opt. Commun.283(24), 4963–4968 (2010).
[CrossRef]

Abraham, Y.

A. Zlotnik, Y. Abraham, L. Liraz, I. Abdulhalim, and Z. Zalevsky, “Improved extended depth of focus full field spectral domain Optical Coherence Tomography,” Opt. Commun.283(24), 4963–4968 (2010).
[CrossRef]

Adie, S. G.

A. Ahmad, N. D. Shemonski, S. G. Adie, H. S. Kim, W. M. W. Hwu, P. S. Carney, and S. A. Boppart, “Real-time in vivo computed optical interferometric tomography,” Nat. Photonics7(6), 444–448 (2013).
[CrossRef] [PubMed]

S. G. Adie, B. W. Graf, A. Ahmad, P. S. Carney, and S. A. Boppart, “Computational adaptive optics for broadband optical interferometric tomography of biological tissue,” Proc. Natl. Acad. Sci. U.S.A.109(19), 7175–7180 (2012).
[CrossRef] [PubMed]

Ahmad, A.

A. Ahmad, N. D. Shemonski, S. G. Adie, H. S. Kim, W. M. W. Hwu, P. S. Carney, and S. A. Boppart, “Real-time in vivo computed optical interferometric tomography,” Nat. Photonics7(6), 444–448 (2013).
[CrossRef] [PubMed]

S. G. Adie, B. W. Graf, A. Ahmad, P. S. Carney, and S. A. Boppart, “Computational adaptive optics for broadband optical interferometric tomography of biological tissue,” Proc. Natl. Acad. Sci. U.S.A.109(19), 7175–7180 (2012).
[CrossRef] [PubMed]

Bachmann, A. H.

Biedermann, B. R.

Blatter, C.

Boccara, A. C.

Boppart, S. A.

A. Ahmad, N. D. Shemonski, S. G. Adie, H. S. Kim, W. M. W. Hwu, P. S. Carney, and S. A. Boppart, “Real-time in vivo computed optical interferometric tomography,” Nat. Photonics7(6), 444–448 (2013).
[CrossRef] [PubMed]

S. G. Adie, B. W. Graf, A. Ahmad, P. S. Carney, and S. A. Boppart, “Computational adaptive optics for broadband optical interferometric tomography of biological tissue,” Proc. Natl. Acad. Sci. U.S.A.109(19), 7175–7180 (2012).
[CrossRef] [PubMed]

T. S. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, “Real-time interferometric synthetic aperture microscopy,” Opt. Express16(4), 2555–2569 (2008).
[CrossRef] [PubMed]

T. S. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy,” Nat. Phys.3(2), 129–134 (2007).
[CrossRef]

D. L. Marks, T. S. Ralston, S. A. Boppart, and P. S. Carney, “Inverse scattering for frequency-scanned full-field optical coherence tomography,” J. Opt. Soc. Am. A24(4), 1034–1041 (2007).
[CrossRef] [PubMed]

Carney, P. S.

A. Ahmad, N. D. Shemonski, S. G. Adie, H. S. Kim, W. M. W. Hwu, P. S. Carney, and S. A. Boppart, “Real-time in vivo computed optical interferometric tomography,” Nat. Photonics7(6), 444–448 (2013).
[CrossRef] [PubMed]

S. G. Adie, B. W. Graf, A. Ahmad, P. S. Carney, and S. A. Boppart, “Computational adaptive optics for broadband optical interferometric tomography of biological tissue,” Proc. Natl. Acad. Sci. U.S.A.109(19), 7175–7180 (2012).
[CrossRef] [PubMed]

T. S. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, “Real-time interferometric synthetic aperture microscopy,” Opt. Express16(4), 2555–2569 (2008).
[CrossRef] [PubMed]

T. S. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy,” Nat. Phys.3(2), 129–134 (2007).
[CrossRef]

D. L. Marks, T. S. Ralston, S. A. Boppart, and P. S. Carney, “Inverse scattering for frequency-scanned full-field optical coherence tomography,” J. Opt. Soc. Am. A24(4), 1034–1041 (2007).
[CrossRef] [PubMed]

Chen, Z.

Choi, W. J.

David, G.

de Boer, J. F.

de Groot, M.

Ding, Z.

Drexler, W.

Eigenwillig, C. M.

Endo, T.

Y. Nakamura, J. Sugisaka, Y. Sando, T. Endo, M. Itoh, T. Yatagai, and Y. Yasuno, “Complex numerical processing for in-focus line-field spectral-domain optical coherence tomography,” Jpn. J. Appl. Phys.46(4A), 1774–1778 (2007).
[CrossRef]

Fienup, J. R.

Franke, G.

Gigan, S.

Graf, B. W.

S. G. Adie, B. W. Graf, A. Ahmad, P. S. Carney, and S. A. Boppart, “Computational adaptive optics for broadband optical interferometric tomography of biological tissue,” Proc. Natl. Acad. Sci. U.S.A.109(19), 7175–7180 (2012).
[CrossRef] [PubMed]

Grajciar, B.

Guizar-Sicairos, M.

Guo, S.

Hillmann, D.

Huber, R.

Hüttmann, G.

Hwu, W. M. W.

A. Ahmad, N. D. Shemonski, S. G. Adie, H. S. Kim, W. M. W. Hwu, P. S. Carney, and S. A. Boppart, “Real-time in vivo computed optical interferometric tomography,” Nat. Photonics7(6), 444–448 (2013).
[CrossRef] [PubMed]

Itoh, M.

Y. Nakamura, J. Sugisaka, Y. Sando, T. Endo, M. Itoh, T. Yatagai, and Y. Yasuno, “Complex numerical processing for in-focus line-field spectral-domain optical coherence tomography,” Jpn. J. Appl. Phys.46(4A), 1774–1778 (2007).
[CrossRef]

Y. Yasuno, J. Sugisaka, Y. Sando, Y. Nakamura, S. Makita, M. Itoh, and T. Yatagai, “Non-iterative numerical method for laterally superresolving Fourier domain optical coherence tomography,” Opt. Express14(3), 1006–1020 (2006).
[CrossRef] [PubMed]

Kim, H. S.

A. Ahmad, N. D. Shemonski, S. G. Adie, H. S. Kim, W. M. W. Hwu, P. S. Carney, and S. A. Boppart, “Real-time in vivo computed optical interferometric tomography,” Nat. Photonics7(6), 444–448 (2013).
[CrossRef] [PubMed]

Kim, J. W.

Koch, P.

Kumar, A.

Kurokawa, K.

Labiau, S.

Lasser, T.

Lee, B. H.

Lee, K. S.

Leitgeb, R. A.

Liraz, L.

A. Zlotnik, Y. Abraham, L. Liraz, I. Abdulhalim, and Z. Zalevsky, “Improved extended depth of focus full field spectral domain Optical Coherence Tomography,” Opt. Commun.283(24), 4963–4968 (2010).
[CrossRef]

Lührs, C.

Makita, S.

Marks, D. L.

Min, G.

Mo, J.

Nakamura, Y.

Y. Nakamura, J. Sugisaka, Y. Sando, T. Endo, M. Itoh, T. Yatagai, and Y. Yasuno, “Complex numerical processing for in-focus line-field spectral-domain optical coherence tomography,” Jpn. J. Appl. Phys.46(4A), 1774–1778 (2007).
[CrossRef]

Y. Yasuno, J. Sugisaka, Y. Sando, Y. Nakamura, S. Makita, M. Itoh, and T. Yatagai, “Non-iterative numerical method for laterally superresolving Fourier domain optical coherence tomography,” Opt. Express14(3), 1006–1020 (2006).
[CrossRef] [PubMed]

Nelson, J. S.

Ralston, T. S.

Rao, B.

Ren, H.

Rolland, J. P.

Sando, Y.

Y. Nakamura, J. Sugisaka, Y. Sando, T. Endo, M. Itoh, T. Yatagai, and Y. Yasuno, “Complex numerical processing for in-focus line-field spectral-domain optical coherence tomography,” Jpn. J. Appl. Phys.46(4A), 1774–1778 (2007).
[CrossRef]

Y. Yasuno, J. Sugisaka, Y. Sando, Y. Nakamura, S. Makita, M. Itoh, and T. Yatagai, “Non-iterative numerical method for laterally superresolving Fourier domain optical coherence tomography,” Opt. Express14(3), 1006–1020 (2006).
[CrossRef] [PubMed]

Sasaki, K.

Shemonski, N. D.

A. Ahmad, N. D. Shemonski, S. G. Adie, H. S. Kim, W. M. W. Hwu, P. S. Carney, and S. A. Boppart, “Real-time in vivo computed optical interferometric tomography,” Nat. Photonics7(6), 444–448 (2013).
[CrossRef] [PubMed]

Steinmann, L.

Su, J.

Sugisaka, J.

Y. Nakamura, J. Sugisaka, Y. Sando, T. Endo, M. Itoh, T. Yatagai, and Y. Yasuno, “Complex numerical processing for in-focus line-field spectral-domain optical coherence tomography,” Jpn. J. Appl. Phys.46(4A), 1774–1778 (2007).
[CrossRef]

Y. Yasuno, J. Sugisaka, Y. Sando, Y. Nakamura, S. Makita, M. Itoh, and T. Yatagai, “Non-iterative numerical method for laterally superresolving Fourier domain optical coherence tomography,” Opt. Express14(3), 1006–1020 (2006).
[CrossRef] [PubMed]

Thurman, S. T.

Tippie, A. E.

Villiger, M.

Wang, Q.

Wieser, W.

Yasuno, Y.

Yatagai, T.

Y. Nakamura, J. Sugisaka, Y. Sando, T. Endo, M. Itoh, T. Yatagai, and Y. Yasuno, “Complex numerical processing for in-focus line-field spectral-domain optical coherence tomography,” Jpn. J. Appl. Phys.46(4A), 1774–1778 (2007).
[CrossRef]

Y. Yasuno, J. Sugisaka, Y. Sando, Y. Nakamura, S. Makita, M. Itoh, and T. Yatagai, “Non-iterative numerical method for laterally superresolving Fourier domain optical coherence tomography,” Opt. Express14(3), 1006–1020 (2006).
[CrossRef] [PubMed]

Yu, L.

Zalevsky, Z.

A. Zlotnik, Y. Abraham, L. Liraz, I. Abdulhalim, and Z. Zalevsky, “Improved extended depth of focus full field spectral domain Optical Coherence Tomography,” Opt. Commun.283(24), 4963–4968 (2010).
[CrossRef]

Zhang, J.

Zhao, Y.

Zlotnik, A.

A. Zlotnik, Y. Abraham, L. Liraz, I. Abdulhalim, and Z. Zalevsky, “Improved extended depth of focus full field spectral domain Optical Coherence Tomography,” Opt. Commun.283(24), 4963–4968 (2010).
[CrossRef]

Biomed. Opt. Express (1)

J. Biomed. Opt. (1)

W. Drexler, “Ultrahigh-resolution optical coherence tomography,” J. Biomed. Opt.9(1), 47–74 (2004).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (1)

Jpn. J. Appl. Phys. (1)

Y. Nakamura, J. Sugisaka, Y. Sando, T. Endo, M. Itoh, T. Yatagai, and Y. Yasuno, “Complex numerical processing for in-focus line-field spectral-domain optical coherence tomography,” Jpn. J. Appl. Phys.46(4A), 1774–1778 (2007).
[CrossRef]

Nat. Photonics (1)

A. Ahmad, N. D. Shemonski, S. G. Adie, H. S. Kim, W. M. W. Hwu, P. S. Carney, and S. A. Boppart, “Real-time in vivo computed optical interferometric tomography,” Nat. Photonics7(6), 444–448 (2013).
[CrossRef] [PubMed]

Nat. Phys. (1)

T. S. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy,” Nat. Phys.3(2), 129–134 (2007).
[CrossRef]

Opt. Commun. (1)

A. Zlotnik, Y. Abraham, L. Liraz, I. Abdulhalim, and Z. Zalevsky, “Improved extended depth of focus full field spectral domain Optical Coherence Tomography,” Opt. Commun.283(24), 4963–4968 (2010).
[CrossRef]

Opt. Express (9)

J. Mo, M. de Groot, and J. F. de Boer, “Focus-extension by depth-encoded synthetic aperture in Optical Coherence Tomography,” Opt. Express21(8), 10048–10061 (2013).
[CrossRef] [PubMed]

Y. Yasuno, J. Sugisaka, Y. Sando, Y. Nakamura, S. Makita, M. Itoh, and T. Yatagai, “Non-iterative numerical method for laterally superresolving Fourier domain optical coherence tomography,” Opt. Express14(3), 1006–1020 (2006).
[CrossRef] [PubMed]

L. Yu, B. Rao, J. Zhang, J. Su, Q. Wang, S. Guo, and Z. Chen, “Improved lateral resolution in optical coherence tomography by digital focusing using two-dimensional numerical diffraction method,” Opt. Express15(12), 7634–7641 (2007).
[CrossRef] [PubMed]

T. S. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, “Real-time interferometric synthetic aperture microscopy,” Opt. Express16(4), 2555–2569 (2008).
[CrossRef] [PubMed]

C. Blatter, B. Grajciar, C. M. Eigenwillig, W. Wieser, B. R. Biedermann, R. Huber, and R. A. Leitgeb, “Extended focus high-speed swept source OCT with self-reconstructive illumination,” Opt. Express19(13), 12141–12155 (2011).
[CrossRef] [PubMed]

G. Min, W. J. Choi, J. W. Kim, and B. H. Lee, “Refractive index measurements of multiple layers using numerical refocusing in FF-OCT,” Opt. Express21(24), 29955–29967 (2013).
[CrossRef] [PubMed]

A. Kumar, W. Drexler, and R. A. Leitgeb, “Subaperture correlation based digital adaptive optics for full field optical coherence tomography,” Opt. Express21(9), 10850–10866 (2013).
[CrossRef] [PubMed]

D. Hillmann, G. Franke, C. Lührs, P. Koch, and G. Hüttmann, “Efficient holoscopy image reconstruction,” Opt. Express20(19), 21247–21263 (2012).
[CrossRef] [PubMed]

A. E. Tippie, A. Kumar, and J. R. Fienup, “High-resolution synthetic-aperture digital holography with digital phase and pupil correction,” Opt. Express19(13), 12027–12038 (2011).
[CrossRef] [PubMed]

Opt. Lett. (5)

Proc. Natl. Acad. Sci. U.S.A. (1)

S. G. Adie, B. W. Graf, A. Ahmad, P. S. Carney, and S. A. Boppart, “Computational adaptive optics for broadband optical interferometric tomography of biological tissue,” Proc. Natl. Acad. Sci. U.S.A.109(19), 7175–7180 (2012).
[CrossRef] [PubMed]

Other (6)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 2004).

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes 3rd Edition: The Art of Scientific Computing (Cambridge University, 2007).

W. G. Carrara, R. S. Goodman, and R. M. Majewski, Spotlight Synthetic Aperture Radar (Artech House, 1995), Chap. 6.

P. Hariharan, Optical Interferometry (Academic, 2003).

T. S. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, “Phase stability technique for inverse scattering in optical coherence tomography,” 3rd IEEE International Symposium on Biomedical Imaging: Nano to Macro, 578–581 (2006).
[CrossRef]

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, 1988).

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 (8)

Fig. 1
Fig. 1

(a) Schematic of the FF SS OCT system based on Michelson interferometer: SSL is the swept source laser, L1-L4 are the lenses, BS is the beam-splitter, M is the mirror, RM is the reference mirror, and S is the sample. (b) Unfolded schematic of the telescopic imaging system.

Fig. 2
Fig. 2

Schematic of defocus correction of a B-scan image based on FM.

Fig. 3
Fig. 3

Schematic of the defocus correction method based on IS applied to 2-D B-scan image.

Fig. 4
Fig. 4

Visualization of the quadratic phase error in the two-equally divided subaperture in 1-D

Fig. 5
Fig. 5

Schematic of the DAO technique for defocus correction of an enface image.

Fig. 6
Fig. 6

(a) B-scan images of a uniform iron oxide nano-particle phantom showing the comparison of performance of the three defocus correction methods based on FM, IS, and DAO. Comparing enface images at depth (b) z = 1.3 mm and (d) z = 2.2 mm. (c) and (e) are the horizontal cuts through the enface images at the location shown by white arrows in the original enface images in (b) and (d) respectively. The imaging NA is 0.06 and magnification M = 2.5x.

Fig. 7
Fig. 7

(a) B-scan images of iron oxide nano-particle phantom with glass plate on top, showing the comparison of performance of the three defocus correction methods based on FM, IS, and DAO. Green dotted line shows the location of focal plane. Comparing enface images at depth (b) z = 2.4 mm. (c) the horizontal cuts through the enface images at the location shown by white arrow in the original enface image in (b). (d) Plot of SNR with depth comparing images obtained by different methods. The imaging NA is 0.1 and magnification M = 3.3x.

Fig. 8
Fig. 8

Plot of W 020 , r e s with respect to the distance from the focal plane for different magnification factors of M = 2.5x, 5x and 10x. ( λ o = 850 μ m , n o = 1.4 , Δ n = 0.1 , Δ x = 14 μ m ).

Tables (1)

Tables Icon

Table 1 Comparison of different defocus correction methods

Equations (23)

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

I d ( x,y,k )= | E I ( x,y,k ) | 2 + | E R ( k ) | 2 + E I ( x,y,k ) E R ( k )+ E I ( x,y,k ) E R ( k )
E s ( x,y,k )= E I ( x,y,k ) E R ( k ).
E I ( x,y,k )= exp[ ik( z R + z s ) ] M E o ( ξ,η,k )P( x M ξ, y M η ) dξdη
E o ( ξ,η,k )= Z F T 1 { exp[ ik( z R +z n o )+iφ ] E ˜ o,z ( f ξ , f η ,k ) ×exp[ i2πz ( k n o / 2π ) 2 f ξ 2 f η 2 ] }dz
E R ( k )=κS( k )exp( ik z s +iφ )
E s ( x,y,k )= κS( k ) M Z F T 1 { exp[ ik( 2 z R +z n o ) ] E ˜ o,z ( f ξ , f η ,k ) ×exp[ i2πz ( k n o / 2π ) 2 f ξ 2 f η 2 ] }P( x M ξ, y M η )dξdηdz.
E ˜ s ( k x , k y ,k )=κMS( k ) P ˜ ( M k x ,M k y ) Z exp[ ik( 2 z R +z n o ) ] E ˜ o,z ( M k x ,M k y ,k ) ×exp[ iz ( k n o ) 2 ( M k x ) 2 ( M k y ) 2 ]dz
E ˜ s ( k x , k y ,k )=κMS( k ) P ˜ ( M k x ,M k y ) Z exp[ ik( 2 z R +2z n o ) ] E ˜ o,z ( M k x ,M k y ,k )dz
E ˜ o,z ( M k x ,M k y ,k )= E ˜ o,z ( M k x ,M k y ,k ) exp[ ikz n o +iz ( k n o ) 2 ( M k x ) 2 ( M k y ) 2 ].
E ˜ o,z ( M k x ,M k y ,k )= E ˜ o,z ( M k x ,M k y ,k ) exp[ i λ o z M 2 4π n o ( k x 2 + k y 2 ) ]
E s ( x,y, z )= Z E ˜ s ( k x , k y ,k )exp[ i( k x x+ k y y+k z ) ]d k x d k y dkdz κ M P( x M , y M )[ S ˜ ( z ) Z E o,z ( x M , y M ,z ) δ( z z )dz ]
E s ( k x , k y , z )= κM P ˜ ( M k x ,M k y )[ S ˜ ( z ) Z E o,z ( M k x ,M k y ,z ) δ( z z )dz ]
E ˜ o,z ( M k x ,M k y ,z )= E ˜ o,z ( M k x ,M k y ,z )exp[ i ϕ e ( k x , k y ,z ) ] = E ˜ o,z ( M k x ,M k y ,z ) exp[ i λ o z M 2 4π n o ( k x 2 + k y 2 ) ].
γ( M k x ,M k y ,z )=exp[ i ϕ e ( k x , k y ,z ) ]=exp[ +i λ o z M 2 4π n o ( k x 2 + k y 2 ) ].
z= N z λ o 2 2 n o Δλ .
E ˜ s ( k x , k y ,k )=α Z E ˜ o,z ( M k x ,M k y ,k ) exp[ ikz n o +iz ( k n o ) 2 ( M k x ) 2 ( M k y ) 2 ]dz
E s ( x,y, z )= Z E ˜ s ( k x , k y ,k )exp[ i( k x x+ k y y+k z ) ]d k x d k y dkdz Z α E ˜ o,z ( M k x ,M k y ,k ) exp[ i( k x x+ k y y+ k eff z ) ]d k x d k y dkdz
k eff = 3 2 k 1 2 n o ( k n o ) 2 ( M k x ) 2 ( M k y ) 2
k eff =k+ λ o M 2 8π n o 2 ( k x 2 + k y 2 ).
E ¯ s ( x,y, z )=  Z α E ˜ o,z ( M k x ,M k y , k eff ) exp[ i( k x x+ k y y+ k eff z ) ]d k x d k y d k eff dz κ M P( x M , y M )[ S ˜ ( z ) Z E o,z ( x M , y M ,z ) δ( z z )dz ].
k= 3 4 k eff +( 1 4 n o ) ( n o k eff ) 2 2 M 2 ( k x 2 + k y 2 ) .
ϕ e ( p , q ) = 2 π Δ n M D ( p 2 + q 2 )
W 020,res = λ o Δnz M 2 8 π 2 n o 2 ( k x 2 + k y 2 ) max = λ o Δnz M 2 8Δ x 2 n o 2

Metrics