OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 27 — Dec. 19, 2011
  • pp: 26891–26904

Selection of convolution kernel in non-uniform fast Fourier transform for Fourier domain optical coherence tomography

Kenny K.H. Chan and Shuo Tang  »View Author Affiliations

Optics Express, Vol. 19, Issue 27, pp. 26891-26904 (2011)

View Full Text Article

Enhanced HTML    Acrobat PDF (3524 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Gridding based non-uniform fast Fourier transform (NUFFT) has recently been shown as an efficient method of processing non-linearly sampled data from Fourier-domain optical coherence tomography (FD-OCT). This method requires selecting design parameters, such as kernel function type, oversampling ratio and kernel width, to balance between computational complexity and accuracy. The Kaiser-Bessel (KB) and Gaussian kernels have been used independently on the NUFFT algorithm for FD-OCT. This paper compares the reconstruction error and speed for the optimization of these design parameters and justifies particular kernel choice for FD-OCT applications. It is found that for on-the-fly computation of the kernel function, the simpler Gaussian function offers a better accuracy-speed tradeoff. The KB kernel, however, is a better choice in the pre-computed kernel mode of NUFFT, in which the processing speed is no longer dependent on the kernel function type. Finally, the algorithm is used to reconstruct in-vivo images of a human finger at a camera limited 50k A-line/s.

© 2011 OSA

OCIS Codes
(170.4500) Medical optics and biotechnology : Optical coherence tomography
(070.2025) Fourier optics and signal processing : Discrete optical signal processing
(110.3010) Imaging systems : Image reconstruction techniques

ToC Category:
Medical Optics and Biotechnology

Original Manuscript: October 14, 2011
Revised Manuscript: December 3, 2011
Manuscript Accepted: December 5, 2011
Published: December 16, 2011

Virtual Issues
Vol. 7, Iss. 2 Virtual Journal for Biomedical Optics

Kenny K.H. Chan and Shuo Tang, "Selection of convolution kernel in non-uniform fast Fourier transform for Fourier domain optical coherence tomography," Opt. Express 19, 26891-26904 (2011)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. Z. Hu and A. M. Rollins, “Fourier domain optical coherence tomography with a linear-in-wavenumber spectrometer,” Opt. Lett. 32(24), 3525–3527 (2007). [CrossRef] [PubMed]
  2. C. M. Eigenwillig, B. R. Biedermann, G. Palte, and R. Huber, “K-space linear Fourier domain mode locked laser and applications for optical coherence tomography,” Opt. Express 16(12), 8916–8937 (2008). [CrossRef] [PubMed]
  3. D. C. Adler, Y. Chen, R. Huber, J. Schmitt, J. Connolly, and J. G. Fujimoto, “Three-dimensional endomicroscopy using optical coherence tomography,” Nat. Photonics 1(12), 709–716 (2007). [CrossRef]
  4. J. Xi, L. Huo, J. Li, and X. Li, “Generic real-time uniform K-space sampling method for high-speed swept-source optical coherence tomography,” Opt. Express 18(9), 9511–9517 (2010). [CrossRef] [PubMed]
  5. G. Liu, J. Zhang, L. Yu, T. Xie, and Z. Chen, “Real-time polarization-sensitive optical coherence tomography data processing with parallel computing,” Appl. Opt. 48(32), 6365–6370 (2009). [CrossRef] [PubMed]
  6. 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(18), 2183–2189 (2003). [CrossRef] [PubMed]
  7. 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(11), 2404–2422 (2004). [CrossRef] [PubMed]
  8. D. Hillmann, G. Huttmann, and P. Koch, “Using nonequispaced fast Fourier transformation to process optical coherence tomography signals,” Proc. SPIE 7372, 73720R (2009). [CrossRef]
  9. K. K. H. Chan and S. Tang, “High-speed spectral domain optical coherence tomography using non-uniform fast Fourier transform,” Biomed. Opt. Express 1(5), 1309–1319 (2010). [CrossRef] [PubMed]
  10. K. Zhang and J. U. Kang, “Graphics processing unit accelerated non-uniform fast Fourier transform for ultrahigh-speed, real-time Fourier-domain OCT,” Opt. Express 18(22), 23472–23487 (2010). [CrossRef] [PubMed]
  11. S. Vergnole, D. Lévesque, and G. Lamouche, “Experimental validation of an optimized signal processing method to handle non-linearity in swept-source optical coherence tomography,” Opt. Express 18(10), 10446–10461 (2010). [CrossRef] [PubMed]
  12. K. Wang, Z. Ding, T. Wu, C. Wang, J. Meng, M. Chen, and L. Xu, “Development of a non-uniform discrete Fourier transform based high speed spectral domain optical coherence tomography system,” Opt. Express 17(14), 12121–12131 (2009). [CrossRef] [PubMed]
  13. K. Zhang and J. U. Kang, “Real-time intraoperative 4D full-range FD-OCT based on the dual graphics processing units architecture for microsurgery guidance,” Biomed. Opt. Express 2(4), 764–770 (2011). [CrossRef] [PubMed]
  14. A. Dutt and V. Rokhlin, “Fast Fourier transforms for nonequispaced data,” SIAM J. Sci. Comput. 14(6), 1368–1393 (1993). [CrossRef]
  15. L. Greengard and J. Lee, “Accelerating the nonuniform Fast Fourier Transform,” SIAM Rev. 46(3), 443–454 (2004). [CrossRef]
  16. J. I. Jackson, C. H. Meyer, D. G. Nishimura, and A. Macovski, “Selection of a convolution function for Fourier inversion using gridding [computerised tomography application],” IEEE Trans. Med. Imaging 10(3), 473–478 (1991). [CrossRef] [PubMed]
  17. P. J. Beatty, D. G. Nishimura, and J. M. Pauly, “Rapid gridding reconstruction with a minimal oversampling ratio,” IEEE Trans. Med. Imaging 24(6), 799–808 (2005). [CrossRef] [PubMed]
  18. G. E. Sarty, R. Bennett, and R. W. Cox, “Direct reconstruction of non-Cartesian k-space data using a nonuniform fast Fourier transform,” Magn. Reson. Med. 45(5), 908–915 (2001). [CrossRef] [PubMed]
  19. A. J. W. Duijndam and M. A. Schonewille, “Nonuniform fast Fourier transform,” Geophysics 64(2), 539–551 (1999). [CrossRef]
  20. J. A. Fessler and B. P. Sutton, “Nonuniform fast Fourier transforms using min-max interpolation,” IEEE Trans. Signal Process. 51(2), 560–574 (2003). [CrossRef]
  21. J. D. O’Sullivan, “A fast sinc function gridding algorithm for fourier inversion in computer tomography,” IEEE Trans. Med. Imaging 4(4), 200–207 (1985). [CrossRef] [PubMed]
  22. D. Potts, G. Steidl, and M. Tasche, “Fast Fourier transforms for nonequispaced data: a tutorial,” in Modern Sampling Theory: Mathematics and Applications, J. J. Benedetto and P. Ferreira, eds. (Springer, 2001), Chap. 12, 249–274.
  23. M. Frigo and S. G. Johnson, “The design and implementation of FFTW3,” Proc. IEEE 93(2), 216–231 (2005). [CrossRef]
  24. B. Liu, E. Azimi, and M. E. Brezinski, “True logarithmic amplification of frequency clock in SS-OCT for calibration,” Biomed. Opt. Express 2(6), 1769–1777 (2011). [CrossRef] [PubMed]
  25. T. E. Ustun, N. V. Iftimia, R. D. Ferguson, and D. X. Hammer, “Real-time processing for Fourier domain optical coherence tomography using a field programmable gate array,” Rev. Sci. Instrum. 79(11), 114301 (2008). [CrossRef] [PubMed]
  26. A. W. Schaefer, J. J. Reynolds, D. L. Marks, and S. A. Boppart, “Real-time digital signal processing-based optical coherence tomography and Doppler optical coherence tomography,” IEEE Trans. Biomed. Eng. 51(1), 186–190 (2004). [CrossRef] [PubMed]
  27. OpenMP Architecture Review Board, “The OpenMP API specification for parallel programming,” http://www.openmp.org/ .
  28. T. S. Sorensen, T. Schaeffter, K. O. Noe, and M. S. Hansen, “Accelerating the nonequispaced fast Fourier transform on commodity graphics hardware,” IEEE Trans. Med. Imaging 27(4), 538–547 (2008). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited