Abstract

The vortex self-imaging (SI) implemented in optical imaging systems and its usage for a robust axial localization of point-like objects are presented. The vortex SI is used to generate a double-helix point spread function (DH PSF) maintaining its shape and size unchanged in a large working area. The robustness of the axial localization is demonstrated by a resistance against the spherical aberration. Using a thorough analysis, the experiments are optimized to achieve the highest localization sensitivity and to find a trade-off between the aberration stability of the DH PSF, the length of the localization range and the energy efficiency. The benefits of the method are achieved by applying the SI of nondiffracting vortices prepared by a spatial light modulator (SLM). The feasibility of the proposed technique is demonstrated by a defocusing induced rotation of the fixed and moving 1μm polystyrene beads, carried out in the transmitted light illumination.

© 2015 Optical Society of America

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References

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  1. B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy, ” Science 319, 810–813 (2008).
    [Crossref] [PubMed]
  2. M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, and J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples, ” Nature Methods 5, 527–529 (2008).
    [Crossref] [PubMed]
  3. A. Vaziri, J. Tang, H. Shroff, and C.V. Shank, “Multilayer three-dimensional super resolution imaging of thick biological samples,” Proc. Nat. Acad. Sci. USA 105, 20221–20226 (2008).
    [PubMed]
  4. Y. Y. Schechner, R. Piestun, and J. Shamir, “Wave propagation with rotating intensity distributions,” Phys. Rev. E 54, R50–R53 (1996).
  5. V. V. Kotlyar, V. A. Soifer, and S. N. Khonina, “An algorithm for the generation of laser beams with longitudinal periodicity: rotating images”, J. Mod. Opt. 44, 1409–1416 (1997).
  6. A. Greengard, Y. Y. Schechner, and R. Piestun, “Depth from diffracted rotation,” Opt. Lett. 31, 181–183 (2006).
    [PubMed]
  7. S. R. P. Pavani and R. Piestun, “High-efficiency rotating point spread functions,” Opt. Express 16, 3484–3489 (2008).
    [PubMed]
  8. S. Furhapter, A. Jesacher, S. Bernet, and M. R. Marte, “Spiral phase contrast imaging in microscopy,” Opt. Express 13, 689–694 (2005).
    [PubMed]
  9. J. Rosen and G. Brooker, “Digital spatially incoherent Fresnel holography,” Opt. Lett. 32, 912–914 (2007).
    [PubMed]
  10. P. Bouchal, J. Kapitán, Radim Chmelík, and Z. Bouchal, “Point spread function and two-point resolution in Fresnel incoherent correlation holography,” Opt. Express 19, 15603–15620 (2011).
    [PubMed]
  11. P. Bouchal and Z. Bouchal, “Selective edge enhancement in three-dimensional vortex imaging with incoherent light,” Opt. Lett. 37, 2949–2951 (2012).
    [Crossref] [PubMed]
  12. M. Baranek and Z. Bouchal, “Rotating vortex imaging implemented by a quantized spiral phase modulation,” J. Europ. Opt. Soc. Rap. Public. 8, 13017 (2013).
    [Crossref]
  13. S. Prasad, “Rotating point spread function via pupil-phase engineering,” Opt. Lett. 38, 585–587 (2013).
    [Crossref] [PubMed]
  14. C. Roider, A. Jesacher, S. Bernet, and M. R. Marte, “Axial super-localisation using rotating point spread functions shaped by polarisation-dependent phase modulation,” Opt. Express 22, 4029–4037 (2014).
    [Crossref] [PubMed]
  15. P. Bouchal and Z. Bouchal, “Non-iterative holographic axial localization using complex amplitude of diffraction-free vortices,” Opt. Express 22, 30200–30216 (2014).
    [Crossref]
  16. S. R. P. Pavani and R. Piestun, “Three dimensional tracking of fluorescent microparticles using a photon-limited double-helix response system,” Opt. Express 16, 22048–22057 (2008).
    [Crossref] [PubMed]
  17. M. D. Lew, S. F. Lee, M. Badieirostami, and W. E. Moerner, “Corkscrew point spread function for far-field three-dimensional nanoscale localization of pointlike objects,” Opt. Lett. 36, 202–204 (2011).
    [Crossref] [PubMed]
  18. H. L. D. Lee, S. J. Sahl, M. D. Lew, and W. E. Moerner, “The double-helix microscope super-resolves extended biological structures by localizing single blinking molecules in three dimensions with nanoscale precision,” Appl. Phys. Lett. 100153701 (2012).
    [Crossref] [PubMed]
  19. S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Nat. Acad. Sci. USA 106, 2995–2999 (2009).
    [Crossref] [PubMed]
  20. S. Ghosh and Ch. Preza, “Characterization of a three-dimensional double-helix point-spread function for fluorescence microscopy in the presence of spherical aberration,” J. Biomed. Opt. 18, 036010 (2013).
    [Crossref] [PubMed]
  21. W. D. Montgomery, “Self-imaging objects of infinite aperture,” J. Opt. Soc. Am. 57, 772–778 (1967).
    [Crossref]
  22. K. Patorski, “The self-imaging phenomenon and its applications,” in Progress in Optics, Vol. XXVII, E. Wolf, ed. (Elsevier, Amsterdam, 1989).
  23. Z. Bouchal and J. Kyvalský, “Controllable 3D spatial localization of light fields synthesized by non-diffracting modes,” J. Mod. Opt. 51, 157–176 (2004).
    [Crossref]
  24. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).
  25. I. S. Gradstein and I. M. Ryzhik, Tables of Integrals, Sums, Series, and Products (Academic Press, 1965).
  26. J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am A 4, 651–654 (1987).
    [Crossref]
  27. Z. Bouchal, “Nondiffracting optical beams: physical properties, experiments and applications,” Czech. J. Phys. 53, 537–624 (2003).
    [Crossref]
  28. Z. Bouchal, “Physical principle of experiments with pseudo-nondiffracting beams,” Czech. J. Phys. 55, 1223–1236 (2005).
    [Crossref]

2014 (2)

2013 (3)

M. Baranek and Z. Bouchal, “Rotating vortex imaging implemented by a quantized spiral phase modulation,” J. Europ. Opt. Soc. Rap. Public. 8, 13017 (2013).
[Crossref]

S. Prasad, “Rotating point spread function via pupil-phase engineering,” Opt. Lett. 38, 585–587 (2013).
[Crossref] [PubMed]

S. Ghosh and Ch. Preza, “Characterization of a three-dimensional double-helix point-spread function for fluorescence microscopy in the presence of spherical aberration,” J. Biomed. Opt. 18, 036010 (2013).
[Crossref] [PubMed]

2012 (2)

H. L. D. Lee, S. J. Sahl, M. D. Lew, and W. E. Moerner, “The double-helix microscope super-resolves extended biological structures by localizing single blinking molecules in three dimensions with nanoscale precision,” Appl. Phys. Lett. 100153701 (2012).
[Crossref] [PubMed]

P. Bouchal and Z. Bouchal, “Selective edge enhancement in three-dimensional vortex imaging with incoherent light,” Opt. Lett. 37, 2949–2951 (2012).
[Crossref] [PubMed]

2011 (2)

2009 (1)

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Nat. Acad. Sci. USA 106, 2995–2999 (2009).
[Crossref] [PubMed]

2008 (5)

S. R. P. Pavani and R. Piestun, “Three dimensional tracking of fluorescent microparticles using a photon-limited double-helix response system,” Opt. Express 16, 22048–22057 (2008).
[Crossref] [PubMed]

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy, ” Science 319, 810–813 (2008).
[Crossref] [PubMed]

M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, and J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples, ” Nature Methods 5, 527–529 (2008).
[Crossref] [PubMed]

A. Vaziri, J. Tang, H. Shroff, and C.V. Shank, “Multilayer three-dimensional super resolution imaging of thick biological samples,” Proc. Nat. Acad. Sci. USA 105, 20221–20226 (2008).
[PubMed]

S. R. P. Pavani and R. Piestun, “High-efficiency rotating point spread functions,” Opt. Express 16, 3484–3489 (2008).
[PubMed]

2007 (1)

2006 (1)

2005 (2)

S. Furhapter, A. Jesacher, S. Bernet, and M. R. Marte, “Spiral phase contrast imaging in microscopy,” Opt. Express 13, 689–694 (2005).
[PubMed]

Z. Bouchal, “Physical principle of experiments with pseudo-nondiffracting beams,” Czech. J. Phys. 55, 1223–1236 (2005).
[Crossref]

2004 (1)

Z. Bouchal and J. Kyvalský, “Controllable 3D spatial localization of light fields synthesized by non-diffracting modes,” J. Mod. Opt. 51, 157–176 (2004).
[Crossref]

2003 (1)

Z. Bouchal, “Nondiffracting optical beams: physical properties, experiments and applications,” Czech. J. Phys. 53, 537–624 (2003).
[Crossref]

1997 (1)

V. V. Kotlyar, V. A. Soifer, and S. N. Khonina, “An algorithm for the generation of laser beams with longitudinal periodicity: rotating images”, J. Mod. Opt. 44, 1409–1416 (1997).

1996 (1)

Y. Y. Schechner, R. Piestun, and J. Shamir, “Wave propagation with rotating intensity distributions,” Phys. Rev. E 54, R50–R53 (1996).

1987 (1)

J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am A 4, 651–654 (1987).
[Crossref]

1967 (1)

Badieirostami, M.

Baranek, M.

M. Baranek and Z. Bouchal, “Rotating vortex imaging implemented by a quantized spiral phase modulation,” J. Europ. Opt. Soc. Rap. Public. 8, 13017 (2013).
[Crossref]

Bates, M.

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy, ” Science 319, 810–813 (2008).
[Crossref] [PubMed]

Bennett, B. T.

M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, and J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples, ” Nature Methods 5, 527–529 (2008).
[Crossref] [PubMed]

Bernet, S.

Bewersdorf, J.

M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, and J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples, ” Nature Methods 5, 527–529 (2008).
[Crossref] [PubMed]

Biteen, J. S.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Nat. Acad. Sci. USA 106, 2995–2999 (2009).
[Crossref] [PubMed]

Bouchal, P.

Bouchal, Z.

P. Bouchal and Z. Bouchal, “Non-iterative holographic axial localization using complex amplitude of diffraction-free vortices,” Opt. Express 22, 30200–30216 (2014).
[Crossref]

M. Baranek and Z. Bouchal, “Rotating vortex imaging implemented by a quantized spiral phase modulation,” J. Europ. Opt. Soc. Rap. Public. 8, 13017 (2013).
[Crossref]

P. Bouchal and Z. Bouchal, “Selective edge enhancement in three-dimensional vortex imaging with incoherent light,” Opt. Lett. 37, 2949–2951 (2012).
[Crossref] [PubMed]

P. Bouchal, J. Kapitán, Radim Chmelík, and Z. Bouchal, “Point spread function and two-point resolution in Fresnel incoherent correlation holography,” Opt. Express 19, 15603–15620 (2011).
[PubMed]

Z. Bouchal, “Physical principle of experiments with pseudo-nondiffracting beams,” Czech. J. Phys. 55, 1223–1236 (2005).
[Crossref]

Z. Bouchal and J. Kyvalský, “Controllable 3D spatial localization of light fields synthesized by non-diffracting modes,” J. Mod. Opt. 51, 157–176 (2004).
[Crossref]

Z. Bouchal, “Nondiffracting optical beams: physical properties, experiments and applications,” Czech. J. Phys. 53, 537–624 (2003).
[Crossref]

Brooker, G.

Chmelík, Radim

Durnin, J.

J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am A 4, 651–654 (1987).
[Crossref]

Furhapter, S.

Ghosh, S.

S. Ghosh and Ch. Preza, “Characterization of a three-dimensional double-helix point-spread function for fluorescence microscopy in the presence of spherical aberration,” J. Biomed. Opt. 18, 036010 (2013).
[Crossref] [PubMed]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

Gould, T. J.

M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, and J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples, ” Nature Methods 5, 527–529 (2008).
[Crossref] [PubMed]

Gradstein, I. S.

I. S. Gradstein and I. M. Ryzhik, Tables of Integrals, Sums, Series, and Products (Academic Press, 1965).

Greengard, A.

Hess, S. T.

M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, and J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples, ” Nature Methods 5, 527–529 (2008).
[Crossref] [PubMed]

Huang, B.

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy, ” Science 319, 810–813 (2008).
[Crossref] [PubMed]

Jesacher, A.

Juette, M. F.

M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, and J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples, ” Nature Methods 5, 527–529 (2008).
[Crossref] [PubMed]

Kapitán, J.

Khonina, S. N.

V. V. Kotlyar, V. A. Soifer, and S. N. Khonina, “An algorithm for the generation of laser beams with longitudinal periodicity: rotating images”, J. Mod. Opt. 44, 1409–1416 (1997).

Kotlyar, V. V.

V. V. Kotlyar, V. A. Soifer, and S. N. Khonina, “An algorithm for the generation of laser beams with longitudinal periodicity: rotating images”, J. Mod. Opt. 44, 1409–1416 (1997).

Kyvalský, J.

Z. Bouchal and J. Kyvalský, “Controllable 3D spatial localization of light fields synthesized by non-diffracting modes,” J. Mod. Opt. 51, 157–176 (2004).
[Crossref]

Lee, H. L. D.

H. L. D. Lee, S. J. Sahl, M. D. Lew, and W. E. Moerner, “The double-helix microscope super-resolves extended biological structures by localizing single blinking molecules in three dimensions with nanoscale precision,” Appl. Phys. Lett. 100153701 (2012).
[Crossref] [PubMed]

Lee, S. F.

Lessard, M. D.

M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, and J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples, ” Nature Methods 5, 527–529 (2008).
[Crossref] [PubMed]

Lew, M. D.

H. L. D. Lee, S. J. Sahl, M. D. Lew, and W. E. Moerner, “The double-helix microscope super-resolves extended biological structures by localizing single blinking molecules in three dimensions with nanoscale precision,” Appl. Phys. Lett. 100153701 (2012).
[Crossref] [PubMed]

M. D. Lew, S. F. Lee, M. Badieirostami, and W. E. Moerner, “Corkscrew point spread function for far-field three-dimensional nanoscale localization of pointlike objects,” Opt. Lett. 36, 202–204 (2011).
[Crossref] [PubMed]

Liu, N.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Nat. Acad. Sci. USA 106, 2995–2999 (2009).
[Crossref] [PubMed]

Lord, S. J.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Nat. Acad. Sci. USA 106, 2995–2999 (2009).
[Crossref] [PubMed]

Marte, M. R.

Mlodzianoski, M. J.

M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, and J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples, ” Nature Methods 5, 527–529 (2008).
[Crossref] [PubMed]

Moerner, W. E.

H. L. D. Lee, S. J. Sahl, M. D. Lew, and W. E. Moerner, “The double-helix microscope super-resolves extended biological structures by localizing single blinking molecules in three dimensions with nanoscale precision,” Appl. Phys. Lett. 100153701 (2012).
[Crossref] [PubMed]

M. D. Lew, S. F. Lee, M. Badieirostami, and W. E. Moerner, “Corkscrew point spread function for far-field three-dimensional nanoscale localization of pointlike objects,” Opt. Lett. 36, 202–204 (2011).
[Crossref] [PubMed]

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Nat. Acad. Sci. USA 106, 2995–2999 (2009).
[Crossref] [PubMed]

Montgomery, W. D.

Nagpure, B. S.

M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, and J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples, ” Nature Methods 5, 527–529 (2008).
[Crossref] [PubMed]

Patorski, K.

K. Patorski, “The self-imaging phenomenon and its applications,” in Progress in Optics, Vol. XXVII, E. Wolf, ed. (Elsevier, Amsterdam, 1989).

Pavani, S. R. P.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Nat. Acad. Sci. USA 106, 2995–2999 (2009).
[Crossref] [PubMed]

S. R. P. Pavani and R. Piestun, “Three dimensional tracking of fluorescent microparticles using a photon-limited double-helix response system,” Opt. Express 16, 22048–22057 (2008).
[Crossref] [PubMed]

S. R. P. Pavani and R. Piestun, “High-efficiency rotating point spread functions,” Opt. Express 16, 3484–3489 (2008).
[PubMed]

Piestun, R.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Nat. Acad. Sci. USA 106, 2995–2999 (2009).
[Crossref] [PubMed]

S. R. P. Pavani and R. Piestun, “High-efficiency rotating point spread functions,” Opt. Express 16, 3484–3489 (2008).
[PubMed]

S. R. P. Pavani and R. Piestun, “Three dimensional tracking of fluorescent microparticles using a photon-limited double-helix response system,” Opt. Express 16, 22048–22057 (2008).
[Crossref] [PubMed]

A. Greengard, Y. Y. Schechner, and R. Piestun, “Depth from diffracted rotation,” Opt. Lett. 31, 181–183 (2006).
[PubMed]

Y. Y. Schechner, R. Piestun, and J. Shamir, “Wave propagation with rotating intensity distributions,” Phys. Rev. E 54, R50–R53 (1996).

Prasad, S.

Preza, Ch.

S. Ghosh and Ch. Preza, “Characterization of a three-dimensional double-helix point-spread function for fluorescence microscopy in the presence of spherical aberration,” J. Biomed. Opt. 18, 036010 (2013).
[Crossref] [PubMed]

Roider, C.

Rosen, J.

Ryzhik, I. M.

I. S. Gradstein and I. M. Ryzhik, Tables of Integrals, Sums, Series, and Products (Academic Press, 1965).

Sahl, S. J.

H. L. D. Lee, S. J. Sahl, M. D. Lew, and W. E. Moerner, “The double-helix microscope super-resolves extended biological structures by localizing single blinking molecules in three dimensions with nanoscale precision,” Appl. Phys. Lett. 100153701 (2012).
[Crossref] [PubMed]

Schechner, Y. Y.

A. Greengard, Y. Y. Schechner, and R. Piestun, “Depth from diffracted rotation,” Opt. Lett. 31, 181–183 (2006).
[PubMed]

Y. Y. Schechner, R. Piestun, and J. Shamir, “Wave propagation with rotating intensity distributions,” Phys. Rev. E 54, R50–R53 (1996).

Shamir, J.

Y. Y. Schechner, R. Piestun, and J. Shamir, “Wave propagation with rotating intensity distributions,” Phys. Rev. E 54, R50–R53 (1996).

Shank, C.V.

A. Vaziri, J. Tang, H. Shroff, and C.V. Shank, “Multilayer three-dimensional super resolution imaging of thick biological samples,” Proc. Nat. Acad. Sci. USA 105, 20221–20226 (2008).
[PubMed]

Shroff, H.

A. Vaziri, J. Tang, H. Shroff, and C.V. Shank, “Multilayer three-dimensional super resolution imaging of thick biological samples,” Proc. Nat. Acad. Sci. USA 105, 20221–20226 (2008).
[PubMed]

Soifer, V. A.

V. V. Kotlyar, V. A. Soifer, and S. N. Khonina, “An algorithm for the generation of laser beams with longitudinal periodicity: rotating images”, J. Mod. Opt. 44, 1409–1416 (1997).

Tang, J.

A. Vaziri, J. Tang, H. Shroff, and C.V. Shank, “Multilayer three-dimensional super resolution imaging of thick biological samples,” Proc. Nat. Acad. Sci. USA 105, 20221–20226 (2008).
[PubMed]

Thompson, M. A.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Nat. Acad. Sci. USA 106, 2995–2999 (2009).
[Crossref] [PubMed]

Twieg, R. J.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Nat. Acad. Sci. USA 106, 2995–2999 (2009).
[Crossref] [PubMed]

Vaziri, A.

A. Vaziri, J. Tang, H. Shroff, and C.V. Shank, “Multilayer three-dimensional super resolution imaging of thick biological samples,” Proc. Nat. Acad. Sci. USA 105, 20221–20226 (2008).
[PubMed]

Wang, W.

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy, ” Science 319, 810–813 (2008).
[Crossref] [PubMed]

Zhuang, X.

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy, ” Science 319, 810–813 (2008).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

H. L. D. Lee, S. J. Sahl, M. D. Lew, and W. E. Moerner, “The double-helix microscope super-resolves extended biological structures by localizing single blinking molecules in three dimensions with nanoscale precision,” Appl. Phys. Lett. 100153701 (2012).
[Crossref] [PubMed]

Czech. J. Phys. (2)

Z. Bouchal, “Nondiffracting optical beams: physical properties, experiments and applications,” Czech. J. Phys. 53, 537–624 (2003).
[Crossref]

Z. Bouchal, “Physical principle of experiments with pseudo-nondiffracting beams,” Czech. J. Phys. 55, 1223–1236 (2005).
[Crossref]

J. Biomed. Opt. (1)

S. Ghosh and Ch. Preza, “Characterization of a three-dimensional double-helix point-spread function for fluorescence microscopy in the presence of spherical aberration,” J. Biomed. Opt. 18, 036010 (2013).
[Crossref] [PubMed]

J. Europ. Opt. Soc. Rap. Public. (1)

M. Baranek and Z. Bouchal, “Rotating vortex imaging implemented by a quantized spiral phase modulation,” J. Europ. Opt. Soc. Rap. Public. 8, 13017 (2013).
[Crossref]

J. Mod. Opt. (2)

V. V. Kotlyar, V. A. Soifer, and S. N. Khonina, “An algorithm for the generation of laser beams with longitudinal periodicity: rotating images”, J. Mod. Opt. 44, 1409–1416 (1997).

Z. Bouchal and J. Kyvalský, “Controllable 3D spatial localization of light fields synthesized by non-diffracting modes,” J. Mod. Opt. 51, 157–176 (2004).
[Crossref]

J. Opt. Soc. Am A (1)

J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am A 4, 651–654 (1987).
[Crossref]

J. Opt. Soc. Am. (1)

Nature Methods (1)

M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, and J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples, ” Nature Methods 5, 527–529 (2008).
[Crossref] [PubMed]

Opt. Express (6)

Opt. Lett. (5)

Phys. Rev. E (1)

Y. Y. Schechner, R. Piestun, and J. Shamir, “Wave propagation with rotating intensity distributions,” Phys. Rev. E 54, R50–R53 (1996).

Proc. Nat. Acad. Sci. USA (2)

A. Vaziri, J. Tang, H. Shroff, and C.V. Shank, “Multilayer three-dimensional super resolution imaging of thick biological samples,” Proc. Nat. Acad. Sci. USA 105, 20221–20226 (2008).
[PubMed]

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Nat. Acad. Sci. USA 106, 2995–2999 (2009).
[Crossref] [PubMed]

Science (1)

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy, ” Science 319, 810–813 (2008).
[Crossref] [PubMed]

Other (3)

K. Patorski, “The self-imaging phenomenon and its applications,” in Progress in Optics, Vol. XXVII, E. Wolf, ed. (Elsevier, Amsterdam, 1989).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

I. S. Gradstein and I. M. Ryzhik, Tables of Integrals, Sums, Series, and Products (Academic Press, 1965).

Supplementary Material (2)

» Media 1: AVI (291 KB)     
» Media 2: AVI (257 KB)     

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Figures (8)

Fig. 1
Fig. 1

Axial localization by the rotating PSF based on the SI of vortices implemented by the spiral mask SM. (a) SM is placed in the Fourier plane of the 4-f system so that the nondiffracting vortices are created by interference of plane waves behind the lens FL2. (b) SM is placed in the exit pupil of the lens L and the divergent vortices are created by interference of spherical waves.

Fig. 2
Fig. 2

Graphical illustration of the rotating image (10) demonstrating two mode vortex SI (M = 2) with difference of the topological charges Δl = 2 and Δl = 3. The image rotation occurs due to an azimuthal displacement of the interference maxima during defocusing.

Fig. 3
Fig. 3

Experimental setup for aberration resistant axial localization by the vortex SI (SF -spatial filter, MO - microscope objective, C - capillary tube with a suspension of polystyrene beads, AM - amplitude mask, BS1, BS2 - beam splitters, TL - tube lens, FL1, FL2 – Fourier lenses, P - polarizer, SLM - spatial light modulator): (a) optical path for calibration and testing of the axial localization, (b) optical path for tracking of polystyrene beads.

Fig. 4
Fig. 4

Defocusing rotation of the theoretical and experimental DH PSF created in an aberration-corrected system by interference of M = 2 vortices with the topological charges l1 = −1 and l2 = 1: (a) exact SI of nondiffracting vortices generated by the mask with the narrow rings, (b) approximate SI of vortices generated by the mask with fully transparent zones.

Fig. 5
Fig. 5

The same as in Fig. 4, but for the third-order spherical aberration with the coefficient A040 = 0.4λ.

Fig. 6
Fig. 6

Experimental verification of Eq. (24) demonstrating aberration robustness of the axial localization: theoretical dependence of the rotation angle Δφ′ on the axial position Δz0 (full line), experimental evaluation of the rotation angle - the average values and the standard deviations were obtained by the processing of 40 image spots recorded in the system with different values of the spherical aberration, A040 ∈ <−0.4λ, 0.4λ> (error bars).

Fig. 7
Fig. 7

Experimental demonstration of the DH PSF obtained by the SI composed of M = 4 vortex modes with the topological charges l1 = −3, l2 = −1, l3 = 1 and l4 = 3 and the constant phase shifts κ1 = π/2, κ2 = 0, κ3 = π/2, and κ4 = 0: aberration-corrected system with A040 ≈ 0 (upper row), system with the spherical aberration given by A040 = 0.4λ (bottom row).

Fig. 8
Fig. 8

Demonstration of the two-mode SI (l1 = −1, l2 = 1) by defocusing rotation of 1μm polystyrene beads: (a) accessible field of view, (b) enlarged portion of the field of view, (c) rotation of the PSF during defocusing of fixed beads realized by a precise linear stage ( Media 1), (d) defocusing rotation of movable polystyrene beads suspended in a capillary tube ( Media 2).

Equations (24)

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U FrT z { P 2 FrT f 2 { S FrT f 1 { U 0 P 1 } } } ,
U FrT z { exp ( i Φ 2 ) FrT f 2 { S exp [ i Φ 1 ( 1 z / f 1 ) + i k W S ] } } ,
U FT f 2 { S exp [ i k ( W D + W S ) ] } ,
W D = A 020 ρ 2 ,
W S = A 040 ρ 4 ,
A 020 = R max 2 2 ( Δ z f 1 2 + Δ z f 2 2 ) ,
A 040 = R max 2 4 f 2 2 Δ z S ,
S ( R , ψ ) = m = 1 M δ ( R ρ m R max ) ρ m R max exp ( i l m ψ + i κ m ) ,
U m = 1 M J l m ( k r ρ m R max f 2 ) exp [ i l m ( φ + π 2 ) + i κ m + i k ( A 020 ρ m 2 + A 040 ρ m 4 ) ] ,
I m = 1 M J l m 2 + m = 1 M m = m + 1 M 2 J | l m | J | l m | cos Ω m , m ,
Ω m , m = ( l m l m ) φ + ( κ m κ m ) + π 2 ( | l m | | l m | ) + k A 020 ( ρ m 2 ρ m 2 ) + k A 040 ( ρ m 4 ρ m 4 ) .
d φ d A 020 = k ( ρ m 2 ρ m 2 ) l m l m = const .
ρ m = m M ,
l m = l 0 + m Δ l ,
d φ d Δ z = k N A 2 2 M Δ l ,
Λ = 2 λ M Δ l N A 2 .
Λ = 2 λ M Δ l N A 2 ,
U = FrT z { U 0 S } ,
A 020 = R max 2 2 [ Δ z z 0 ( z 0 + Δ z ) + Δ z z 0 ( z 0 + Δ z ) ] .
φ m , m = π ( m m ) Δ l [ 2 q 1 2 ( | l m | | l m | ) ] k M Δ l [ A 020 + ( m + m ) M A 040 ] .
Δ φ φ 1 , 2 = Δ φ D + Δ φ S A ,
Δ φ D = π 2 λ A 020 ,
Δ φ S A = 3 π 4 λ A 040 .
Δ z 0 = Δ z 0 meas Δ z 0 ref = 4 λ π N A 0 2 Δ φ .

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