Abstract

Sinusoidally patterned illumination has been used to obtain lateral superresolution and axial sectioning in images. In both of these techniques multiple images are taken with the object illuminated by a sinusoidal pattern, the phase of the sinusoidal illumination being shifted differently in each image. The knowledge of these phase shifts is critical for image reconstruction. We discuss a method to estimate this phase shift with no prior knowledge of the shifts. In postprocessing we estimate randomly introduced, unknown phase shifts and process the images to obtain a superresolved image. Results of computer simulations are shown.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Gustaffson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198, 82-87 (2000).
    [CrossRef]
  2. M. Gustafsson, “Extended-resolution reconstruction of structured illumination microscopy data,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings (on CD-ROM), OSA Technical Digest (Optical Society of America, 2005), paper JMA2.
    [PubMed]
  3. M. Gustafsson, L. Shao, D. A. Agard, and J. W. Sedat, “Fluorescence microscopy without resolution limit,” in Biophotonics/Optical Interconnects and VLSI Photonics/WBM Microcavities, 2004 Digest of the LEOS Summer Topical Meetings (IEEE, 2004), Vol. 2, pp. 28-30.
  4. R. Heintzmann and C. Cremer, “Laterally modulated excitation microscopy: Improvement of resolution by using a diffraction grating,” Proc. SPIE 3568, 185-196 (1999).
    [CrossRef]
  5. M. Gustafsson, “Extended resolution fluorescence microscopy,” Curr. Opin. Struct. Biol. 9, 627-634 (1999).
    [CrossRef] [PubMed]
  6. W. Lukosz, “Optical systems with resolving powers exceeding the classical limits II,” J. Opt. Soc. Am. 57, 932-941 (1967).
    [CrossRef]
  7. D. Mendlovic, A. W. Lohmann, N. Konforti, I. Kiryuschev, and Z. Zalevsky, “One-dimensional superresolution optical system for temporally restricted objects,” Appl. Opt. 36, 2353-2359 (1997).
    [CrossRef] [PubMed]
  8. E. Sabo, Z. Zalevsky, D. Mendlovic, N. Konforti, and I. Kiryuschev, “Superresolution optical system using three fixed generalized gratings: experimental results,” J. Opt. Soc. Am. A 18, 514-520 (2001).
    [CrossRef]
  9. A. Shemer, Z. Zalevsky, D. Mendlovic, N. Konforti, and E. Marom, “Time multiplexing superresolution based on interference grating projection,” Appl. Opt. 41, 7397-7404 (2002).
    [CrossRef] [PubMed]
  10. S. W. Hell and J. Wichmann, “Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy,” Opt. Lett. 19, 780 (1994).
    [CrossRef] [PubMed]
  11. X. Chen and S. R. J. Brueck, “Imaging interferometric lithography: approaching the resolution limits of optics,” Opt. Lett. 24, 124-126 (1999).
    [CrossRef]
  12. C. J. Schwarz, Y. Kuznetsova, and S. R. J. Brueck, “Imaging interferometric microscopy,” Opt. Lett. 28, 1424-1426 (2003).
    [CrossRef] [PubMed]
  13. V. Mico, Z. Zalevsky, and J. García, “Superresolution optical system by common-path interferometry,” Opt. Express 14, 5168-5177 (2006).
    [CrossRef] [PubMed]
  14. G. E. Cragg and P. T. C. So, “Lateral resolution enhancement with standing evanescent waves,” Opt. Lett. 25, 46-48 (2000).
    [CrossRef]
  15. E. Chung, D. Kim, and P. T. So, “Extended resolution wide-field optical imaging: objective-launched standing-wave total internal reflection fluorescence microscopy,” Opt. Lett. 31, 945-947 (2006).
    [CrossRef] [PubMed]
  16. T. Wilson and C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, 1983).
  17. 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]
  18. M. A. A. Neil, R. Juškaitis, and T. Wilson, “Real time 3D fluorescence microscopy by two beam interference illumination,” Opt. Commun. 153, 1-4 (1998).
    [CrossRef]
  19. L. H. Schaefer, D. Schuster, and J. Schaffer, “Structured illumination microscopy: artefact analysis and reduction utilizing a parameter optimization approach,” J. Microsc. 216, 165-174 (2004).
    [CrossRef] [PubMed]
  20. G. Strang, Linear Algebra and Its Applications (Thomson Learning, Inc., 1998).
  21. L. P. Yaroslavsky and H. J. Caulfield, “Deconvolution of multiple images of the same object,” Appl. Opt. 33, 2157-2162 (1994).
    [CrossRef] [PubMed]
  22. D. J. Tolhurst, Y. Tadmore, and T. Chao, “Amplitude spectra of natural images,” Ophthalmic Physiol. Opt. 12, 229-232 (1992).
    [CrossRef] [PubMed]
  23. A. van der Schaaf and J. H. van Hateren, “Modelling the power spectra of natural images: statistics and information,” Vision Res. 36, 2759-2770 (1996).
    [CrossRef] [PubMed]
  24. D. R. Gerwe, M. Jain, B. Calef, and C. Luna, “Regularization for nonlinear image restoration using a prior on the object power spectrum,” Proc. SPIE 5896, 1-15 (2005).
  25. J. R. Fienup, D. Griffith, L. Harrington, A. M. Kowalczyk, J. J. Miller, and J. A. Mooney, “Comparison of reconstruction algorithms for images from sparse-aperture systems,” Proc. SPIE 4792, 1-8 (2002).
    [CrossRef]
  26. C. W. Helstrom, “Image restoration by the method of least squares,” J. Opt. Soc. Am. 57, 297-303 (1967).
    [CrossRef]
  27. S. A. Shroff, J. R. Fienup, and D. R. Williams, “OTF compensation in structured illumination superresolution images,” Proc. SPIE 7094, 709402 (2008).
    [CrossRef]
  28. S. A. Shroff, J. R. Fienup, and D. R. Williams, “Phase shift estimation in structured illumination imaging for lateral resolution enhancement,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings (on CD-ROM), OSA Technical Digest (Optical Society of America, 2007), paper SMA2.
    [PubMed]
  29. S. A. Shroff, J. R. Fienup, and D. R. Williams, “Estimation of phase shifts in structured illumination for high resolution imaging,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2007), paper FMH4.
  30. P. Artal, S. Marcos, R. Navarro, and D. R. Williams, “Odd aberrations and double-pass measurements of retinal image quality,” J. Opt. Soc. Am. A 12, 195-201 (1995).
    [CrossRef]
  31. M. Guizar-Sicairos, S. T. Thurman, and J. R. Fienup, “Efficient image registration algorithms for computation of invariant error metrics,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings (on CD-ROM), OSA Technical Digest (Optical Society of America, 2007), paper SMC3.
    [PubMed]
  32. M. Guizar-Sicairos, S. T. Thurman, and J. R. Fienup, “Efficient subpixel image registration algorithms,” Opt. Lett. 33, 156-158 (2008).
    [CrossRef] [PubMed]

2008

S. A. Shroff, J. R. Fienup, and D. R. Williams, “OTF compensation in structured illumination superresolution images,” Proc. SPIE 7094, 709402 (2008).
[CrossRef]

M. Guizar-Sicairos, S. T. Thurman, and J. R. Fienup, “Efficient subpixel image registration algorithms,” Opt. Lett. 33, 156-158 (2008).
[CrossRef] [PubMed]

2006

2005

D. R. Gerwe, M. Jain, B. Calef, and C. Luna, “Regularization for nonlinear image restoration using a prior on the object power spectrum,” Proc. SPIE 5896, 1-15 (2005).

2004

L. H. Schaefer, D. Schuster, and J. Schaffer, “Structured illumination microscopy: artefact analysis and reduction utilizing a parameter optimization approach,” J. Microsc. 216, 165-174 (2004).
[CrossRef] [PubMed]

2003

2002

A. Shemer, Z. Zalevsky, D. Mendlovic, N. Konforti, and E. Marom, “Time multiplexing superresolution based on interference grating projection,” Appl. Opt. 41, 7397-7404 (2002).
[CrossRef] [PubMed]

J. R. Fienup, D. Griffith, L. Harrington, A. M. Kowalczyk, J. J. Miller, and J. A. Mooney, “Comparison of reconstruction algorithms for images from sparse-aperture systems,” Proc. SPIE 4792, 1-8 (2002).
[CrossRef]

2001

2000

M. Gustaffson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198, 82-87 (2000).
[CrossRef]

G. E. Cragg and P. T. C. So, “Lateral resolution enhancement with standing evanescent waves,” Opt. Lett. 25, 46-48 (2000).
[CrossRef]

1999

1998

M. A. A. Neil, R. Juškaitis, and T. Wilson, “Real time 3D fluorescence microscopy by two beam interference illumination,” Opt. Commun. 153, 1-4 (1998).
[CrossRef]

1997

1996

A. van der Schaaf and J. H. van Hateren, “Modelling the power spectra of natural images: statistics and information,” Vision Res. 36, 2759-2770 (1996).
[CrossRef] [PubMed]

1995

1994

1992

D. J. Tolhurst, Y. Tadmore, and T. Chao, “Amplitude spectra of natural images,” Ophthalmic Physiol. Opt. 12, 229-232 (1992).
[CrossRef] [PubMed]

1967

Agard, D. A.

M. Gustafsson, L. Shao, D. A. Agard, and J. W. Sedat, “Fluorescence microscopy without resolution limit,” in Biophotonics/Optical Interconnects and VLSI Photonics/WBM Microcavities, 2004 Digest of the LEOS Summer Topical Meetings (IEEE, 2004), Vol. 2, pp. 28-30.

Artal, P.

Brueck, S. R. J.

Calef, B.

D. R. Gerwe, M. Jain, B. Calef, and C. Luna, “Regularization for nonlinear image restoration using a prior on the object power spectrum,” Proc. SPIE 5896, 1-15 (2005).

Caulfield, H. J.

Chao, T.

D. J. Tolhurst, Y. Tadmore, and T. Chao, “Amplitude spectra of natural images,” Ophthalmic Physiol. Opt. 12, 229-232 (1992).
[CrossRef] [PubMed]

Chen, X.

Chung, E.

Cragg, G. E.

Cremer, C.

R. Heintzmann and C. Cremer, “Laterally modulated excitation microscopy: Improvement of resolution by using a diffraction grating,” Proc. SPIE 3568, 185-196 (1999).
[CrossRef]

Fienup, J. R.

S. A. Shroff, J. R. Fienup, and D. R. Williams, “OTF compensation in structured illumination superresolution images,” Proc. SPIE 7094, 709402 (2008).
[CrossRef]

M. Guizar-Sicairos, S. T. Thurman, and J. R. Fienup, “Efficient subpixel image registration algorithms,” Opt. Lett. 33, 156-158 (2008).
[CrossRef] [PubMed]

J. R. Fienup, D. Griffith, L. Harrington, A. M. Kowalczyk, J. J. Miller, and J. A. Mooney, “Comparison of reconstruction algorithms for images from sparse-aperture systems,” Proc. SPIE 4792, 1-8 (2002).
[CrossRef]

S. A. Shroff, J. R. Fienup, and D. R. Williams, “Phase shift estimation in structured illumination imaging for lateral resolution enhancement,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings (on CD-ROM), OSA Technical Digest (Optical Society of America, 2007), paper SMA2.
[PubMed]

S. A. Shroff, J. R. Fienup, and D. R. Williams, “Estimation of phase shifts in structured illumination for high resolution imaging,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2007), paper FMH4.

M. Guizar-Sicairos, S. T. Thurman, and J. R. Fienup, “Efficient image registration algorithms for computation of invariant error metrics,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings (on CD-ROM), OSA Technical Digest (Optical Society of America, 2007), paper SMC3.
[PubMed]

García, J.

Gerwe, D. R.

D. R. Gerwe, M. Jain, B. Calef, and C. Luna, “Regularization for nonlinear image restoration using a prior on the object power spectrum,” Proc. SPIE 5896, 1-15 (2005).

Griffith, D.

J. R. Fienup, D. Griffith, L. Harrington, A. M. Kowalczyk, J. J. Miller, and J. A. Mooney, “Comparison of reconstruction algorithms for images from sparse-aperture systems,” Proc. SPIE 4792, 1-8 (2002).
[CrossRef]

Guizar-Sicairos, M.

M. Guizar-Sicairos, S. T. Thurman, and J. R. Fienup, “Efficient subpixel image registration algorithms,” Opt. Lett. 33, 156-158 (2008).
[CrossRef] [PubMed]

M. Guizar-Sicairos, S. T. Thurman, and J. R. Fienup, “Efficient image registration algorithms for computation of invariant error metrics,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings (on CD-ROM), OSA Technical Digest (Optical Society of America, 2007), paper SMC3.
[PubMed]

Gustaffson, M.

M. Gustaffson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198, 82-87 (2000).
[CrossRef]

Gustafsson, M.

M. Gustafsson, “Extended resolution fluorescence microscopy,” Curr. Opin. Struct. Biol. 9, 627-634 (1999).
[CrossRef] [PubMed]

M. Gustafsson, “Extended-resolution reconstruction of structured illumination microscopy data,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings (on CD-ROM), OSA Technical Digest (Optical Society of America, 2005), paper JMA2.
[PubMed]

M. Gustafsson, L. Shao, D. A. Agard, and J. W. Sedat, “Fluorescence microscopy without resolution limit,” in Biophotonics/Optical Interconnects and VLSI Photonics/WBM Microcavities, 2004 Digest of the LEOS Summer Topical Meetings (IEEE, 2004), Vol. 2, pp. 28-30.

Harrington, L.

J. R. Fienup, D. Griffith, L. Harrington, A. M. Kowalczyk, J. J. Miller, and J. A. Mooney, “Comparison of reconstruction algorithms for images from sparse-aperture systems,” Proc. SPIE 4792, 1-8 (2002).
[CrossRef]

Heintzmann, R.

R. Heintzmann and C. Cremer, “Laterally modulated excitation microscopy: Improvement of resolution by using a diffraction grating,” Proc. SPIE 3568, 185-196 (1999).
[CrossRef]

Hell, S. W.

Helstrom, C. W.

Jain, M.

D. R. Gerwe, M. Jain, B. Calef, and C. Luna, “Regularization for nonlinear image restoration using a prior on the object power spectrum,” Proc. SPIE 5896, 1-15 (2005).

Juskaitis, R.

Juškaitis, R.

M. A. A. Neil, R. Juškaitis, and T. Wilson, “Real time 3D fluorescence microscopy by two beam interference illumination,” Opt. Commun. 153, 1-4 (1998).
[CrossRef]

Kim, D.

Kiryuschev, I.

Konforti, N.

Kowalczyk, A. M.

J. R. Fienup, D. Griffith, L. Harrington, A. M. Kowalczyk, J. J. Miller, and J. A. Mooney, “Comparison of reconstruction algorithms for images from sparse-aperture systems,” Proc. SPIE 4792, 1-8 (2002).
[CrossRef]

Kuznetsova, Y.

Lohmann, A. W.

Lukosz, W.

Luna, C.

D. R. Gerwe, M. Jain, B. Calef, and C. Luna, “Regularization for nonlinear image restoration using a prior on the object power spectrum,” Proc. SPIE 5896, 1-15 (2005).

Marcos, S.

Marom, E.

Mendlovic, D.

Mico, V.

Miller, J. J.

J. R. Fienup, D. Griffith, L. Harrington, A. M. Kowalczyk, J. J. Miller, and J. A. Mooney, “Comparison of reconstruction algorithms for images from sparse-aperture systems,” Proc. SPIE 4792, 1-8 (2002).
[CrossRef]

Mooney, J. A.

J. R. Fienup, D. Griffith, L. Harrington, A. M. Kowalczyk, J. J. Miller, and J. A. Mooney, “Comparison of reconstruction algorithms for images from sparse-aperture systems,” Proc. SPIE 4792, 1-8 (2002).
[CrossRef]

Navarro, R.

Neil, M. A. A.

M. A. A. Neil, R. Juškaitis, and T. Wilson, “Real time 3D fluorescence microscopy by two beam interference illumination,” Opt. Commun. 153, 1-4 (1998).
[CrossRef]

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]

Sabo, E.

Schaefer, L. H.

L. H. Schaefer, D. Schuster, and J. Schaffer, “Structured illumination microscopy: artefact analysis and reduction utilizing a parameter optimization approach,” J. Microsc. 216, 165-174 (2004).
[CrossRef] [PubMed]

Schaffer, J.

L. H. Schaefer, D. Schuster, and J. Schaffer, “Structured illumination microscopy: artefact analysis and reduction utilizing a parameter optimization approach,” J. Microsc. 216, 165-174 (2004).
[CrossRef] [PubMed]

Schuster, D.

L. H. Schaefer, D. Schuster, and J. Schaffer, “Structured illumination microscopy: artefact analysis and reduction utilizing a parameter optimization approach,” J. Microsc. 216, 165-174 (2004).
[CrossRef] [PubMed]

Schwarz, C. J.

Sedat, J. W.

M. Gustafsson, L. Shao, D. A. Agard, and J. W. Sedat, “Fluorescence microscopy without resolution limit,” in Biophotonics/Optical Interconnects and VLSI Photonics/WBM Microcavities, 2004 Digest of the LEOS Summer Topical Meetings (IEEE, 2004), Vol. 2, pp. 28-30.

Shao, L.

M. Gustafsson, L. Shao, D. A. Agard, and J. W. Sedat, “Fluorescence microscopy without resolution limit,” in Biophotonics/Optical Interconnects and VLSI Photonics/WBM Microcavities, 2004 Digest of the LEOS Summer Topical Meetings (IEEE, 2004), Vol. 2, pp. 28-30.

Shemer, A.

Sheppard, C. J. R.

T. Wilson and C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, 1983).

Shroff, S. A.

S. A. Shroff, J. R. Fienup, and D. R. Williams, “OTF compensation in structured illumination superresolution images,” Proc. SPIE 7094, 709402 (2008).
[CrossRef]

S. A. Shroff, J. R. Fienup, and D. R. Williams, “Phase shift estimation in structured illumination imaging for lateral resolution enhancement,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings (on CD-ROM), OSA Technical Digest (Optical Society of America, 2007), paper SMA2.
[PubMed]

S. A. Shroff, J. R. Fienup, and D. R. Williams, “Estimation of phase shifts in structured illumination for high resolution imaging,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2007), paper FMH4.

So, P. T.

So, P. T. C.

Strang, G.

G. Strang, Linear Algebra and Its Applications (Thomson Learning, Inc., 1998).

Tadmore, Y.

D. J. Tolhurst, Y. Tadmore, and T. Chao, “Amplitude spectra of natural images,” Ophthalmic Physiol. Opt. 12, 229-232 (1992).
[CrossRef] [PubMed]

Thurman, S. T.

M. Guizar-Sicairos, S. T. Thurman, and J. R. Fienup, “Efficient subpixel image registration algorithms,” Opt. Lett. 33, 156-158 (2008).
[CrossRef] [PubMed]

M. Guizar-Sicairos, S. T. Thurman, and J. R. Fienup, “Efficient image registration algorithms for computation of invariant error metrics,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings (on CD-ROM), OSA Technical Digest (Optical Society of America, 2007), paper SMC3.
[PubMed]

Tolhurst, D. J.

D. J. Tolhurst, Y. Tadmore, and T. Chao, “Amplitude spectra of natural images,” Ophthalmic Physiol. Opt. 12, 229-232 (1992).
[CrossRef] [PubMed]

van der Schaaf, A.

A. van der Schaaf and J. H. van Hateren, “Modelling the power spectra of natural images: statistics and information,” Vision Res. 36, 2759-2770 (1996).
[CrossRef] [PubMed]

van Hateren, J. H.

A. van der Schaaf and J. H. van Hateren, “Modelling the power spectra of natural images: statistics and information,” Vision Res. 36, 2759-2770 (1996).
[CrossRef] [PubMed]

Wichmann, J.

Williams, D. R.

S. A. Shroff, J. R. Fienup, and D. R. Williams, “OTF compensation in structured illumination superresolution images,” Proc. SPIE 7094, 709402 (2008).
[CrossRef]

P. Artal, S. Marcos, R. Navarro, and D. R. Williams, “Odd aberrations and double-pass measurements of retinal image quality,” J. Opt. Soc. Am. A 12, 195-201 (1995).
[CrossRef]

S. A. Shroff, J. R. Fienup, and D. R. Williams, “Estimation of phase shifts in structured illumination for high resolution imaging,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2007), paper FMH4.

S. A. Shroff, J. R. Fienup, and D. R. Williams, “Phase shift estimation in structured illumination imaging for lateral resolution enhancement,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings (on CD-ROM), OSA Technical Digest (Optical Society of America, 2007), paper SMA2.
[PubMed]

Wilson, T.

M. A. A. Neil, R. Juškaitis, and T. Wilson, “Real time 3D fluorescence microscopy by two beam interference illumination,” Opt. Commun. 153, 1-4 (1998).
[CrossRef]

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]

T. Wilson and C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, 1983).

Yaroslavsky, L. P.

Zalevsky, Z.

Appl. Opt.

Curr. Opin. Struct. Biol.

M. Gustafsson, “Extended resolution fluorescence microscopy,” Curr. Opin. Struct. Biol. 9, 627-634 (1999).
[CrossRef] [PubMed]

J. Microsc.

M. Gustaffson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198, 82-87 (2000).
[CrossRef]

L. H. Schaefer, D. Schuster, and J. Schaffer, “Structured illumination microscopy: artefact analysis and reduction utilizing a parameter optimization approach,” J. Microsc. 216, 165-174 (2004).
[CrossRef] [PubMed]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Ophthalmic Physiol. Opt.

D. J. Tolhurst, Y. Tadmore, and T. Chao, “Amplitude spectra of natural images,” Ophthalmic Physiol. Opt. 12, 229-232 (1992).
[CrossRef] [PubMed]

Opt. Commun.

M. A. A. Neil, R. Juškaitis, and T. Wilson, “Real time 3D fluorescence microscopy by two beam interference illumination,” Opt. Commun. 153, 1-4 (1998).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. SPIE

S. A. Shroff, J. R. Fienup, and D. R. Williams, “OTF compensation in structured illumination superresolution images,” Proc. SPIE 7094, 709402 (2008).
[CrossRef]

D. R. Gerwe, M. Jain, B. Calef, and C. Luna, “Regularization for nonlinear image restoration using a prior on the object power spectrum,” Proc. SPIE 5896, 1-15 (2005).

J. R. Fienup, D. Griffith, L. Harrington, A. M. Kowalczyk, J. J. Miller, and J. A. Mooney, “Comparison of reconstruction algorithms for images from sparse-aperture systems,” Proc. SPIE 4792, 1-8 (2002).
[CrossRef]

Vision Res.

A. van der Schaaf and J. H. van Hateren, “Modelling the power spectra of natural images: statistics and information,” Vision Res. 36, 2759-2770 (1996).
[CrossRef] [PubMed]

Other

G. Strang, Linear Algebra and Its Applications (Thomson Learning, Inc., 1998).

S. A. Shroff, J. R. Fienup, and D. R. Williams, “Phase shift estimation in structured illumination imaging for lateral resolution enhancement,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings (on CD-ROM), OSA Technical Digest (Optical Society of America, 2007), paper SMA2.
[PubMed]

S. A. Shroff, J. R. Fienup, and D. R. Williams, “Estimation of phase shifts in structured illumination for high resolution imaging,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2007), paper FMH4.

M. Guizar-Sicairos, S. T. Thurman, and J. R. Fienup, “Efficient image registration algorithms for computation of invariant error metrics,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings (on CD-ROM), OSA Technical Digest (Optical Society of America, 2007), paper SMC3.
[PubMed]

T. Wilson and C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, 1983).

M. Gustafsson, “Extended-resolution reconstruction of structured illumination microscopy data,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings (on CD-ROM), OSA Technical Digest (Optical Society of America, 2005), paper JMA2.
[PubMed]

M. Gustafsson, L. Shao, D. A. Agard, and J. W. Sedat, “Fluorescence microscopy without resolution limit,” in Biophotonics/Optical Interconnects and VLSI Photonics/WBM Microcavities, 2004 Digest of the LEOS Summer Topical Meetings (IEEE, 2004), Vol. 2, pp. 28-30.

R. Heintzmann and C. Cremer, “Laterally modulated excitation microscopy: Improvement of resolution by using a diffraction grating,” Proc. SPIE 3568, 185-196 (1999).
[CrossRef]

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 (14)

Fig. 1
Fig. 1

Visualization of structured illumination image in Fourier domain.

Fig. 2
Fig. 2

(a) Pristine object; (b) Fourier transform of pristine object.

Fig. 3
Fig. 3

RMS error in phase-shift estimate versus spatial frequency of sinusoidal illumination, f o f c with no noise [28].

Fig. 4
Fig. 4

RMS error in phase-shift estimate versus SNR for sinusoidal illumination with f o = 50 % f c [28].

Fig. 5
Fig. 5

RMS error in phase-shift estimate versus SNR for sinusoidal illumination with f o = 91 % f c [28].

Fig. 6
Fig. 6

(a) Reconstructed image with fringe artifacts due to a large error in the phase-shift estimate in one orientation of sinusoidal illumination; (b) Fourier transform of reconstructed image with residual peak artifacts (indicated by white arrows) due to a large error in the phase-shift estimate in one orientation of sinusoidal illumination.

Fig. 7
Fig. 7

RMS error in phase-shift estimate versus upsampling factor, f o = 50 % f c , SNR = 15.5 .

Fig. 8
Fig. 8

(a) Conventional image; (b) Fourier transform of conventional image.

Fig. 9
Fig. 9

(a) Conventional image with OTF compensation; (b) Fourier transform of OTF compensated conventional image.

Fig. 10
Fig. 10

(a) Image with 75% superresolution, using estimated phase shifts (RMS error less than 4 × 10 3 rad ); (b) Fourier transform of image with 75% superresolution, using estimated phase shifts. White arrows indicate locations of potential residual peaks.

Fig. 11
Fig. 11

(a) Image with 86% superresolution, estimated phase shifts (RMS error less than 7 × 10 3 rad ); (b) Fourier transform of image with 86% superresolution, estimated phase shifts. White arrows indicate locations of dim residual peaks.

Fig. 12
Fig. 12

(a) Image with 91% superresolution, estimated phase shifts (RMS error less than 2 × 10 2 rad ); (b) Fourier transform of image with 91% superresolution, estimated phase shifts. White arrows indicate locations of residual peaks.

Fig. 13
Fig. 13

(a) Single image reconstruction with 75% superresolution from noisy structured illumination images having an SNR of 124, using estimated phase shifts (RMS error less than 0.3 rad ); (b) Fourier transform of noisy reconstruction with 75% superresolution.

Fig. 14
Fig. 14

(a) Sum of 10 noisy images with 75% superresolution, each obtained from sinusoidally patterned images having an SNR of 124, using estimated phase shifts (RMS error less than 0.3 rad ); (b) Fourier transform of sum of 10 noisy images with 75% superresolution.

Equations (16)

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

I s ( x , y ) = 1 2 [ 1 + cos ( 4 π f o x + 2 ϕ n ) ] ,
I s ( x , y ) = 1 2 [ 1 + m cos ( 4 π f o x + 2 ϕ n ) ] .
G n ( f x , f y ) = 1 2 H 1 ( 0 , 0 ) H 2 ( f x , f y ) G g ( f x , f y ) + m 4 H 1 ( 2 f o , 0 ) e i 2 ϕ n H 2 ( f x , f y ) G g ( f x 2 f o , f y ) + m 4 H 1 ( 2 f o , 0 ) e i 2 ϕ n H 2 ( f x , f y ) G g ( f x + 2 f o , f y ) ,
A X = B ,
A = [ 1 2 H 1 ( 0 , 0 ) m 4 H 1 ( 2 f o , 0 ) e i 2 ϕ 1 m 4 H 1 ( 2 f o , 0 ) e i 2 ϕ 1 1 2 H 1 ( 0 , 0 ) m 4 H 1 ( 2 f o , 0 ) e i 2 ϕ 2 m 4 H 1 ( 2 f o , 0 ) e i 2 ϕ 2 1 2 H 1 ( 0 , 0 ) m 4 H 1 ( 2 f o , 0 ) e i 2 ϕ N m 4 H 1 ( 2 f o , 0 ) e i 2 ϕ N ] N × 3 ,
X = [ H 2 ( f x , f y ) G g ( f x , f y ) H 2 ( f x , f y ) G g ( f x 2 f o , f y ) H 2 ( f x , f y ) G g ( f x + 2 f o , f y ) ] 3 × 1 ,
B = [ G 1 ( f x , f y ) G 2 ( f x , f y ) G N ( f x , f y ) ] N × 1 .
I c 1 ( f x , f y ) = H 2 ( f x , f y ) G g ( f x , f y ) ,
otf 1 ( f x , f y ) = H 2 ( f x , f y ) .
I 1 ( f x , f y ) = F T { I F T [ H 2 ( f x , f y ) G g ( f x 2 f o , f y ) ] exp [ i 2 π ( 2 f o ) x ] } = H 2 ( f x + 2 f o , f y ) G g ( f x , f y ) ,
I 1 ( f x , f y ) = F T { I F T [ H 2 ( f x , f y ) G g ( f x + 2 f o , f y ) ] exp [ + i 2 π ( 2 f o ) x ] } = H 2 ( f x 2 f o , f y ) G g ( f x , f y ) .
I c 2 ( f x , f y ) = [ H 2 ( f x + 2 f o , f y ) + H 2 ( f x 2 f o , f y ) ] G g ( f x , f y ) .
otf 2 ( f x , f y ) = [ H 2 ( f x + 2 f o , f y ) + H 2 ( f x 2 f o , f y ) ] .
I rec ( x , y ) = I F T { i = 1 M [ I ̂ c i ( f x , f y ) otf i * ( f x , f y ) × η i Φ O ( f x , f y ) Φ N i c + j = 1 M otf j ( f x , f y ) 2 × η j Φ O ( f x , f y ) Φ N j ] } ,
G n ( 2 f o , 0 ) = 1 2 H 1 ( 0 , 0 ) H 2 ( 2 f o , 0 ) G g ( 2 f o , 0 ) + e i 2 ϕ n m 4 H 1 ( 2 f o , 0 ) H 2 ( 2 f o , 0 ) G g ( 0 , 0 ) + e i 2 ϕ n m 4 H 1 ( 2 f o , 0 ) H 2 ( 2 f o , 0 ) G g ( 4 f o , 0 ) .
2 ϕ n tan 1 { imag [ G n ( 2 f o , 0 ) ] real [ G n ( 2 f o , 0 ) ] } .

Metrics