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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 21 — Oct. 8, 2012
  • pp: 23398–23413

Dispersion compensation in Fourier domain optical coherence tomography using the fractional Fourier transform

Norman Lippok, Stéphane Coen, Poul Nielsen, and Frédérique Vanholsbeeck  »View Author Affiliations

Optics Express, Vol. 20, Issue 21, pp. 23398-23413 (2012)

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We address numerical dispersion compensation based on the use of the fractional Fourier transform (FrFT). The FrFT provides a new fundamental perspective on the nature and role of group-velocity dispersion in Fourier domain OCT. The dispersion induced by a 26 mm long water cell was compensated for a spectral bandwidth of 110 nm, allowing the theoretical axial resolution in air of 3.6 μm to be recovered from the dispersion degraded point spread function. Additionally, we present a new approach for depth dependent dispersion compensation based on numerical simulations. Finally, we show how the optimized fractional Fourier transform order parameter can be used to extract the group velocity dispersion coefficient of a material.

© 2012 OSA

OCIS Codes
(110.4500) Imaging systems : Optical coherence tomography
(170.3890) Medical optics and biotechnology : Medical optics instrumentation
(070.2575) Fourier optics and signal processing : Fractional Fourier transforms

ToC Category:
Imaging Systems

Original Manuscript: July 3, 2012
Revised Manuscript: September 6, 2012
Manuscript Accepted: September 14, 2012
Published: September 26, 2012

Norman Lippok, Stéphane Coen, Poul Nielsen, and Frédérique Vanholsbeeck, "Dispersion compensation in Fourier domain optical coherence tomography using the fractional Fourier transform," Opt. Express 20, 23398-23413 (2012)

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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,” Science254, 1178–1181 (1991). [CrossRef] [PubMed]
  2. 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]
  3. R. Leitgeb, C. K. Hitzenberger, and A. F. Fercher, “Performance of Fourier domain vs. time domain optical coherence tomography,” Opt. Express11, 889–894 (2003). [CrossRef] [PubMed]
  4. 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]
  5. M. A. Choma, M. V. Sarunic, C. Yang, and J. A. Izatt, “Sensitivity advantage of swept source and Fourier domain optical coherence tomography,” Opt. Express11, 2183–2189 (2003). [CrossRef] [PubMed]
  6. G. Häusler and M. W. Lindner, “Coherence radar and spectral radar — New tools for dermatological diagnosis,” J. Biomed. Opt.3, 21–31 (1998). [CrossRef]
  7. M. Wojtkowski, R. Leitgeb, A. Kowalczyk, T. Bajraszewski, and A. F. Fercher, “In vivo human retinal imaging by Fourier domain optical coherence tomography”, Journal of Biomedical Optics7, 457–463 (2002). [CrossRef] [PubMed]
  8. N. A. Nassif, B. Cense, B. H. Park, M. C. Pierce, S. H. Yun, B. E. Bouma, G. J. Tearney, T. C. Chen, and J. F. de Boer, “In vivo high-resolution video-rate spectral-domain optical coherence tomography of the human retina and optic nerve,” Opt. Express12, 367–376 (2004). [CrossRef] [PubMed]
  9. 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]
  10. B. Golubovic, B. E. Bouma, G. J. Tearney, and J. G. Fujimoto, “Optical frequency-domain reflectometry using rapid wavelength tuning of a Cr4+: forsterite laser,” Opt. Lett.22, 1704–1706 (1997). [CrossRef]
  11. S. H. Yun, G. J. Tearney, J. F. de Boer, N. Iftimia, and B. E. Bouma, “High-speed optical frequency-domain imaging,” Opt. Express11, 2953–2963 (2003). [CrossRef] [PubMed]
  12. R. Huber, M. Wojtkowski, and J. G. Fujimoto, “Fourier Domain Mode Locking (FDML): A new laser operating regime and applications for optical coherence tomography,” Opt. Express14, 3225–3237 (2006). [CrossRef] [PubMed]
  13. L. Liu, J. A. Gardecki, S. K. Nadkarni, J. D. Toussaint, Y. Yagi, B. E. Bouma, and G. J. Tearney, “Imaging the subcellular structure of human coronary atherosclerosis using microoptical coherence tomography,” Nature Med.17, 1010–1014 (2011). [CrossRef] [PubMed]
  14. 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, 2450–2452 (2006). [CrossRef] [PubMed]
  15. 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, 1696–1698 (2008). [CrossRef] [PubMed]
  16. 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, 12141–12155 (2011). [CrossRef] [PubMed]
  17. L. Liu, F. Diaz, L. Wang, B. Loiseaux, J.-P. Huignard, C. J. R. Sheppard, and N. Chen, “Superresolution along extended depth of focus with binary-phase filters for the Gaussian beam,” J. Opt. Soc. Am. A25, 2095–2101 (2008). [CrossRef]
  18. J. Holmes, S. Hattersley, N. Stone, F. Bazant-Hegemark, and H. Barr, “Multi-channel Fourier domain OCT system with superior lateral resolution for biomedical applications,” Proc. of SPIE684768470O (2008). [CrossRef]
  19. B. A. Standish, K. K. C. Lee, A. Mariampillai, N. R. Munce, M. K. K. Leung, V. X. D. Yang, and I. A. Vitkin, “In vivo endoscopic multi-beam optical coherence tomography,” Phys. Med. Biol.55, 615–622 (2010). [CrossRef] [PubMed]
  20. C. K. Hitzenberger, A. Baumgartner, W. Drexler, and A. F. Fercher, “Dispersion effects in partial coherence interferometry: implications for intraocular ranging,” J. of Biomed. Opt., 144–151 (1999). [CrossRef]
  21. A. F. Fercher, C. K. Hitzenberger, M. Sticker, R. Zawadzki, B. Karamata, and T. Lasser, “Dispersion compensation for optical coherence tomography depth-scan signals by a numerical technique,” Opt. Comm.204, 67–74 (2002). [CrossRef]
  22. A. G. Van Engen, S. A. Diddams, and T. S. Clement, “Dispersion measurements of water with white-light interferometry,” Appl. Opt.37, 5679–5686 (1998). [CrossRef]
  23. B. Bouma, G. J. Tearney, S. A. Boppart, M. R. Hee, M. E. Brezinski, and J. G. Fujimoto, “High-resolution optical coherence tomographic imaging using a mode-locked Ti:Al2O3 laser source,” Opt. Lett.20, 1486–1488 (1995). [CrossRef] [PubMed]
  24. W. Drexler, U. Morgner, F. X. Kartner, C. Pitris, S. A. Boppart, X. D. Li, E. P. Ippen, and J. G. Fujimoto, “In vivo ultrahigh-resolution optical coherence tomography,” Opt. Lett.24, 1221–1223 (1999). [CrossRef]
  25. W. Drexler, U. Morgner, R. K. Ghanta, F. X. Krtner, J. S. Schuman, and J. G. Fujimoto, “Ultrahighresolution ophthalmic optical coherence tomography,” Nature Medicine7, 502–507 (2001). [CrossRef] [PubMed]
  26. G. J. Tearney, B. E. Bouma, and J. G. Fujimoto, “High-speed phase- and group-delay scanning with a grating-based phase control delay line,” Opt. Lett.22, 1811–1813 (1997). [CrossRef]
  27. S. Iyer, S. Coen, and F. Vanholsbeeck, “Dual-fiber stretcher as a tunable dispersion compensator for an all-fiber optical coherence tomography system,” Opt. Lett.34, 2903–2905 (2009). [CrossRef] [PubMed]
  28. L. Froehly, S. Iyer, and F. Vanholsbeeck, “Dual-fibre stretcher and coma as tools for independent 2nd and 3rd order tunable dispersion compensation in a fibre-based ‘scan-free’ time domain optical coherence tomography system,” Opt. Commun.284, 4099–4106 (2011). [CrossRef]
  29. A. F. Fercher, C. K. Hitzenberger, M. Sticker, R. Zawadzki, B. Karamata, and T. Lasser, “Numerical dispersion compensation for Partial Coherence Interferometry and Optical Coherence Tomography,” Opt. Express9, 610–615 (2001). [CrossRef] [PubMed]
  30. J. F. de Boer, C. E. Saxer, and J. S. Nelson, “Stable carrier generation and phase-resolved digital data processing in optical coherence tomography,” Appl. Opt.40, 5787–5790 (2001). [CrossRef]
  31. D. L. Marks, A. L. Oldenburg, J. J. Reynolds, and S. A. Boppart, “Digital algorithm for dispersion correction in optical coherence tomography for homogeneous and stratified media,” Appl. Opt.42, 204–217 (2003). [CrossRef] [PubMed]
  32. B. Cense, N. A. Nassif, T. C. Chen, M. C. Pierce, S.-H. 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. Express12, 2435–2447 (2004). [CrossRef] [PubMed]
  33. 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. Express12, 2404–2422 (2004). [CrossRef] [PubMed]
  34. B. Liu, E. A. Macdonald, D. L. Stamper, and M. E. Brezinski, “Group velocity dispersion effects with water and lipid in 1.3 μm optical coherence tomography system,” Phys. Med. Biol.49, 923–930 (2004). [CrossRef] [PubMed]
  35. J. Liebermann, C. Brckner, B. Grajciar, J. Haueisen, and A. F. Fercher, “Dual-band refractive Low Coherence Interferometry in the spectral domain for dispersion measurements,” Proc. of SPIE7889, 788922 (2011). [CrossRef]
  36. L. Cohen, “Time-frequency distributions — A review,” Proc. of the IEEE77, 941–981 (1989). [CrossRef]
  37. V. Namias, “The fractional order Fourier transform and its application to quantum mechanics,” IMA J. Appl. Math.25, 241–265 (1980). [CrossRef]
  38. D. Mendlovic, H. M. Ozaktas, and A. W. Lohmann, “Graded-index fibers, Wigner-distribution functions, and the fractional Fourier transform,” Appl. Opt.33, 6188–6193 (1994). [CrossRef] [PubMed]
  39. L. Durak and S. Aldirmaz, “Adaptive fractional Fourier domain filtering,” Sig. Proc.90, 1188–1196 (2010). [CrossRef]
  40. H. M. Ozaktas, O. Arıkan, M. A. Kutay, and G. Bozdağı, “Digital computation of the fractional Fourier transform,” IEEE Trans. Sig. Proc.44, 2141–2150 (1996). [CrossRef]
  41. C. Dorrer, N. Belabas, J. P. Likforman, and M. Joffre, “Spectral resolution and sampling issues in Fourier-transform spectral interferometry,” J. Opt. Soc. Am. B17, 1795–1802 (2000). [CrossRef]
  42. M. Mujat, B. H. Park, B. Cense, T. C. Chen, and J. F. de Boer, “Autocalibration of spectral-domain optical coherence tomography spectrometers for in vivo quantitative retinal nerve fiber layer birefringence determination,” J. Biomed. Opt.12(4), 041205 (2007). [CrossRef] [PubMed]
  43. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, 1988).
  44. T. R. Hillman and D. D. Sampson, “The effect of water dispersion and absorption on axial resolution in ultrahigh-resolution optical coherence tomography,” Opt. Express13, 1860–1874 (2005). [CrossRef] [PubMed]

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