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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 21 — Oct. 21, 2013
  • pp: 24431–24451

Image filtering in structured illumination microscopy using the Lukosz bound

Christiaan H. Righolt, Johan A. Slotman, Ian T. Young, Sabine Mai, Lucas J. van Vliet, and Sjoerd Stallinga  »View Author Affiliations

Optics Express, Vol. 21, Issue 21, pp. 24431-24451 (2013)

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Various aspects of image filtering affect the final image quality in Structured Illumination Microscopy, in particular the regularization parameter and type of regularization function, the relative height of the side bands, and the shape of the apodization function. We propose an apodization filter without adjustable parameters based on the application of the Lukosz bound in order to guarantee a non-negative point spread function. Simulations of digital resolution charts and experimental data of chromatin structures and of actin filaments show artefact free reconstructions for a wide range of filter parameters. In general, a trade-off is observed between sharpness and noise suppression.

© 2013 Optical Society of America

OCIS Codes
(100.1830) Image processing : Deconvolution
(100.6640) Image processing : Superresolution
(110.4280) Imaging systems : Noise in imaging systems
(180.2520) Microscopy : Fluorescence microscopy
(070.2615) Fourier optics and signal processing : Frequency filtering

ToC Category:
Image Processing

Original Manuscript: July 10, 2013
Revised Manuscript: September 6, 2013
Manuscript Accepted: September 12, 2013
Published: October 7, 2013

Christiaan H. Righolt, Johan A. Slotman, Ian T. Young, Sabine Mai, Lucas J. van Vliet, and Sjoerd Stallinga, "Image filtering in structured illumination microscopy using the Lukosz bound," Opt. Express 21, 24431-24451 (2013)

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  1. S. W. Hell, “Microscopy and its focal switch,” Nat. Methods6, 24–32 (2009). [CrossRef] [PubMed]
  2. L. Schermelleh, R. Heintzmann, and H. Leonhardt, “A guide to super-resolution fluorescence microscopy,” J. Cell Biol.190, 165–175 (2012). [CrossRef]
  3. W. Lukosz, “Optical systems with resolving powers exceeding the classical limit,” J. Opt. Soc. Am.56, 1463–1471 (1966). [CrossRef]
  4. M. A. A. Neil, R. Juskaitis, and T. Wilson, “Method of obtaining optical sectioning by using structured light in a conventional microscope,” Opt. Lett.22, 1905–1907 (1997). [CrossRef]
  5. M. A. A. Neil, A. Squire, R. Juskaitis, P. I. H. Bastiaens, and T. Wilson, “Wide-field optically sectioning fluorescence microscopy with laser illumination,” J. Microsc.197, 1–4 (2000). [CrossRef] [PubMed]
  6. R. Heintzmann and C. Cremer, “Laterally modulated excitation microscopy: improvement of resolution by using a diffraction grating,” Proc. SPIE3568, 185–196 (1999). [CrossRef]
  7. G. E. Cragg and P. T. C. So, “Lateral resolution enhancement with standing evanescent waves,” Opt. Lett.25, 46–48 (2000). [CrossRef]
  8. M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc.198, 82–87 (2000). [CrossRef] [PubMed]
  9. J. T. Frohn, H. F. Knapp, and A. Stemmer, “True optical resolution beyond the Rayleigh limit achieved by standing wave illumination,” Proc. Natl. Acad. Sci. U.S.A.97, 7232–7236 (2000). [CrossRef] [PubMed]
  10. R. Heintzmann, T. Jovin, and C. Cremer, “Saturated patterned excitation microscopy - a concept for optical resolution improvement,” J. Opt. Soc. Am. B19, 1599–1609 (2002). [CrossRef]
  11. M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy: Wide-field fluorescence imaging with theoretically unlimited resolution,” Proc. Natl. Acad. Sci. U.S.A.102, 13081–13086 (2005). [CrossRef] [PubMed]
  12. L. Wang, M. C. Pitter, and M. G. Somekh, “Wide-field high-resolution structured illumination solid immersion fluorescence microscopy,” Opt. Lett.36, 2794–2796 (2011). [CrossRef] [PubMed]
  13. M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J.94, 4957–4970 (2008). [CrossRef] [PubMed]
  14. P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. L. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nat. Methods6, 339–342 (2009). [CrossRef] [PubMed]
  15. L. Shao, P. Kner, E. H. Rego, and M. G. L. Gustafsson, “Super-resolution 3d microscopy of live whole cells using structured illumination,” Nat. Methods12, 1044–1046 (2011). [CrossRef]
  16. R. Fiolka, M. Beck, and A. Stemmer, “Structured illumination in total internal reflection fluorescence microscopy using a spatial light modulator,” Opt. Lett.33, 1629–1631 (2008). [CrossRef] [PubMed]
  17. O. Mandula, M. Kielhorn, K. Wicker, G. Krampert, I. Kleppe, and R. Heintzmann, “Line scan - structured illumination microscopy super-resolution imaging in thick fluorescent samples,” Opt. Express20, 24167–24174 (2012). [CrossRef] [PubMed]
  18. G. M. P. van Kempen, L. J. van Vliet, P. Verveer, and H. van der Voort, “A quantitative comparison of image restoration methods for confocal microscopy,” J. Microsc.185, 354–365 (1997). [CrossRef]
  19. P. Pankajakshan, B. Zhang, L. Blanc-Feraud, Z. Kam, J. C. Olivo-Marin, and J. Zerubia, “Parametric blind deconvolution for confocal laser scanning microscopy,” Conf. Proc. IEEE Eng. Med. Biol. Soc.2007, 6532–6535 (2007).
  20. G. M. P. van Kempen and L. J. van Vliet, “Background estimation in nonlinear image restoration,” J. Opt. Soc. Am. A17, 425–434 (2000). [CrossRef]
  21. N. Dey, L. Blanc-Feraud, C. Zimmer, P. Roux, Z. Kam, J. C. Olivo-Marin, and J. Zerubia, “Richardson-Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution,” Microsc. Res. Tech.69, 260–266 (2006). [CrossRef] [PubMed]
  22. C. Berenstein and E. Patrick, “Exact deconvolution for multiple convolution operators–an overview, plus performance characterizations for imaging sensors,” Proc. IEEE78, 723–734 (1990). [CrossRef]
  23. L. P. Yaroslavsky and H. J. Caulfield, “Deconvolution of multiple images of the same object,” Appl. Opt.33, 2157–2162 (1994). [CrossRef] [PubMed]
  24. S. A. Shroff, J. R. Fienup, and D. R. Williams, “Phase-shift estimation in sinusoidally illuminated images for lateral superresolution,” J. Opt. Soc. Am. A26, 413–424 (2009). [CrossRef]
  25. W. Lukosz, “Übertragung nicht-negativer signale durch lineare filter,” J. Mod. Opt.9, 335–364 (1962).
  26. W. Lukosz, “Properties of linear low-pass filters for nonnegative signals,” J. Opt. Soc. Am.52, 827–829 (1962). [CrossRef]
  27. P. T. C. So, H.-S. Kwon, and C. Y. Dong, “Resolution enhancement in standing-wave total internal reflection microscopy: a point-spread-function engineering approach,” J. Opt. Soc. Am. A25, 1319–1329 (2008).
  28. M. G. Somekh, K. Hsu, and M. C. Pitter, “Resolution in structured illumination microscopy: a probabilistic approach,” J. Opt. Soc. Am. A25, 1319–1329 (2008). [CrossRef]
  29. A. N. Tikhonov and V. A. Arsenin, Solution of Ill-posed Problems (Winston-Wiley, 1977).
  30. N. Wiener, Extrapolation, Interpolation, and Smoothing of Stationary Time Series (Wiley, 1949).
  31. K. Wicker, O. Mandula, G. Best, R. Fiolka, and R. Heintzmann, “Phase optimization for structured illumination microscopy,” Opt. Express21, 2032–2049 (2013). [CrossRef] [PubMed]
  32. C. Luengo Hendriks, B. Rieger, M. van Ginkel, G. M. P. van Kempen, and L. J. van Vliet, “DIP-image: a scientific image processing toolbox for MATLAB,” (1999-). Delft University of Technology, http://www.diplib.org/ .
  33. H. G. Drexler, G. Gaedicke, M. S. Lok, V. Diehl, and J. Minowada, “Hodgkin’s disease derived cell lines HDLM-2 and L-428: comparison of morphology, immunological and isoenzyme profiles,” Leuk. Res.10, 487–500 (1986). [CrossRef]
  34. K. Wicker, PhD thesis, King’s College London, (2010).
  35. G. M. P. van Kempen and L. J. van Vliet, “The influence of the regularization parameter and the first estimate on the performance of Tikhonov regularized non-linear image restoration algorithms,” J. Microsc.198, 63–75 (2000). [CrossRef] [PubMed]
  36. N. P. Galatsanos and A. K. Katsaggelos, “Methods for choosing the regularization parameter and estimating the noise variance in image restoration and their relation,” IEEE Trans. Image Process.1, 322–336 (1992). [CrossRef] [PubMed]

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