Abstract

We present an approach for point spread function (PSF) engineering that allows one to shape the optical wavefront independently in both polarisation directions, with two adjacent phase masks displayed on a single liquid-crystal spatial light modulator (LC-SLM). The set-up employs a polarising beam splitter and a geometric image rotator to rectify and process both polarisation directions detected by the camera. We shape a single-lobe (“corkscrew”) PSF that rotates upon defocus for each polarisation channel and combine the two polarisation channels with a relative 180° phase-shift on the computer, merging them into a single PSF that exhibits two lobes whose orientation contains information about the axial position. A major advantage lies in the possibility to measure and eliminate the aberrations in the two polarisation channels independently. We demonstrate axial super-localisation of isotropically emitting fluorescent nanoparticles. Our implementation of the single-lobe PSFs follows the method proposed by Prasad [Opt. Lett.38, 585 (2013)], and thus is to the best of our knowledge the first experimental realisation of this suggestion. For comparison we also study an approach with a rotating double-helix PSFs (in only one polarisation channel) and ascertain the trade-off between localisation precision and axial working range.

© 2014 Optical Society of America

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  1. M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples,” Nat. Meth. 5, 527–529 (2008).
    [CrossRef]
  2. B. Huang, W. Wang, M. Bates, X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319(5864):810–813 (2008).
    [CrossRef] [PubMed]
  3. S. Pavani, R. Piestun, “Three dimensional tracking of fluorescent microparticles using a photon-limited double-helix response system,” Opt. Express 16, 22048–22057 (2008).
    [CrossRef] [PubMed]
  4. S. Pavani, J. DeLuca, R. Piestun, “Polarization sensitive, three-dimensional, single-molecule imaging of cells with a double-helix system,” Opt. Express 17, 19644–19655 (2009).
    [CrossRef] [PubMed]
  5. G. Grover, S. Quirin, C. Fiedler, R. Piestun, “Photon efficient double-helix PSF microscopy with application to 3D photo-activation localization imaging,” Biomed. Opt. Express 2, 3010–3020 (2011).
    [CrossRef] [PubMed]
  6. M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, G. Grover, A. Agrawal, R. Piestun, W. E. Moerner, “Simultaneous, accurate measurement of the 3D position and orientation of single molecules,” Proc. Natl. Acad. Sci. USA 109, 19087 (2012).
    [CrossRef] [PubMed]
  7. A. Backer, M. Backlund, M. Lew, W. Moerner, “Single-molecule orientation measurements with a quadrated pupil,” Opt. Lett. 38, 1521–1523 (2013).
    [CrossRef] [PubMed]
  8. A. Kress, X. Wang, H. Ranchon, J. Savatier, H. Rigneault, P. Ferrand, S. Brasselet, “Mapping the local organization of cell membranes using excitation-polarization-resolved confocal fluorescence microscopy,” Biophys. J. 105(1), 127–136 (2013).
    [CrossRef] [PubMed]
  9. S. Prasad, “Rotating point spread function via pupil-phase engineering,” Opt. Lett. 38, 585–587 (2013).
    [CrossRef] [PubMed]
  10. M. Neil, M. Booth, T. Wilson, “New modal wave-front sensor: a theoretical analysis,” J. Opt. Soc. Am. A 17, 1098–1107 (2000).
    [CrossRef]
  11. J. Enderlein, “Theoretical study of detecting a dipole emitter through an objective with high numerical aperture,” Opt. Lett. 25, 634–636 (2000).
    [CrossRef]
  12. B. Richards, E. Wolf, “The airy pattern in systems of high angular aperture,” Proc. Phys. Soc. B 69, 854 (1956).
    [CrossRef]
  13. C. J. R. Sheppard, P. Torok, “Electromagnetic field in the focal region of an electric dipole wave,” Optik 104175–177 (1997).

2013

A. Kress, X. Wang, H. Ranchon, J. Savatier, H. Rigneault, P. Ferrand, S. Brasselet, “Mapping the local organization of cell membranes using excitation-polarization-resolved confocal fluorescence microscopy,” Biophys. J. 105(1), 127–136 (2013).
[CrossRef] [PubMed]

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

A. Backer, M. Backlund, M. Lew, W. Moerner, “Single-molecule orientation measurements with a quadrated pupil,” Opt. Lett. 38, 1521–1523 (2013).
[CrossRef] [PubMed]

2012

M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, G. Grover, A. Agrawal, R. Piestun, W. E. Moerner, “Simultaneous, accurate measurement of the 3D position and orientation of single molecules,” Proc. Natl. Acad. Sci. USA 109, 19087 (2012).
[CrossRef] [PubMed]

2011

2009

2008

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

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

B. Huang, W. Wang, M. Bates, X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319(5864):810–813 (2008).
[CrossRef] [PubMed]

2000

1997

C. J. R. Sheppard, P. Torok, “Electromagnetic field in the focal region of an electric dipole wave,” Optik 104175–177 (1997).

1956

B. Richards, E. Wolf, “The airy pattern in systems of high angular aperture,” Proc. Phys. Soc. B 69, 854 (1956).
[CrossRef]

Agrawal, A.

M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, G. Grover, A. Agrawal, R. Piestun, W. E. Moerner, “Simultaneous, accurate measurement of the 3D position and orientation of single molecules,” Proc. Natl. Acad. Sci. USA 109, 19087 (2012).
[CrossRef] [PubMed]

Backer, A.

Backer, A. S.

M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, G. Grover, A. Agrawal, R. Piestun, W. E. Moerner, “Simultaneous, accurate measurement of the 3D position and orientation of single molecules,” Proc. Natl. Acad. Sci. USA 109, 19087 (2012).
[CrossRef] [PubMed]

Backlund, M.

Backlund, M. P.

M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, G. Grover, A. Agrawal, R. Piestun, W. E. Moerner, “Simultaneous, accurate measurement of the 3D position and orientation of single molecules,” Proc. Natl. Acad. Sci. USA 109, 19087 (2012).
[CrossRef] [PubMed]

Bates, M.

B. Huang, W. Wang, M. Bates, X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319(5864):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, J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples,” Nat. Meth. 5, 527–529 (2008).
[CrossRef]

Bewersdorf, J.

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

Booth, M.

Brasselet, S.

A. Kress, X. Wang, H. Ranchon, J. Savatier, H. Rigneault, P. Ferrand, S. Brasselet, “Mapping the local organization of cell membranes using excitation-polarization-resolved confocal fluorescence microscopy,” Biophys. J. 105(1), 127–136 (2013).
[CrossRef] [PubMed]

DeLuca, J.

Enderlein, J.

Ferrand, P.

A. Kress, X. Wang, H. Ranchon, J. Savatier, H. Rigneault, P. Ferrand, S. Brasselet, “Mapping the local organization of cell membranes using excitation-polarization-resolved confocal fluorescence microscopy,” Biophys. J. 105(1), 127–136 (2013).
[CrossRef] [PubMed]

Fiedler, C.

Gould, T. J.

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

Grover, G.

M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, G. Grover, A. Agrawal, R. Piestun, W. E. Moerner, “Simultaneous, accurate measurement of the 3D position and orientation of single molecules,” Proc. Natl. Acad. Sci. USA 109, 19087 (2012).
[CrossRef] [PubMed]

G. Grover, S. Quirin, C. Fiedler, R. Piestun, “Photon efficient double-helix PSF microscopy with application to 3D photo-activation localization imaging,” Biomed. Opt. Express 2, 3010–3020 (2011).
[CrossRef] [PubMed]

Hess, S. T.

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

Huang, B.

B. Huang, W. Wang, M. Bates, X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319(5864):810–813 (2008).
[CrossRef] [PubMed]

Juette, M. F.

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

Kress, A.

A. Kress, X. Wang, H. Ranchon, J. Savatier, H. Rigneault, P. Ferrand, S. Brasselet, “Mapping the local organization of cell membranes using excitation-polarization-resolved confocal fluorescence microscopy,” Biophys. J. 105(1), 127–136 (2013).
[CrossRef] [PubMed]

Lessard, M. D.

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

Lew, M.

Lew, M. D.

M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, G. Grover, A. Agrawal, R. Piestun, W. E. Moerner, “Simultaneous, accurate measurement of the 3D position and orientation of single molecules,” Proc. Natl. Acad. Sci. USA 109, 19087 (2012).
[CrossRef] [PubMed]

Mlodzianoski, M. J.

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

Moerner, W.

Moerner, W. E.

M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, G. Grover, A. Agrawal, R. Piestun, W. E. Moerner, “Simultaneous, accurate measurement of the 3D position and orientation of single molecules,” Proc. Natl. Acad. Sci. USA 109, 19087 (2012).
[CrossRef] [PubMed]

Nagpure, B. S.

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

Neil, M.

Pavani, S.

Piestun, R.

Prasad, S.

Quirin, S.

Ranchon, H.

A. Kress, X. Wang, H. Ranchon, J. Savatier, H. Rigneault, P. Ferrand, S. Brasselet, “Mapping the local organization of cell membranes using excitation-polarization-resolved confocal fluorescence microscopy,” Biophys. J. 105(1), 127–136 (2013).
[CrossRef] [PubMed]

Richards, B.

B. Richards, E. Wolf, “The airy pattern in systems of high angular aperture,” Proc. Phys. Soc. B 69, 854 (1956).
[CrossRef]

Rigneault, H.

A. Kress, X. Wang, H. Ranchon, J. Savatier, H. Rigneault, P. Ferrand, S. Brasselet, “Mapping the local organization of cell membranes using excitation-polarization-resolved confocal fluorescence microscopy,” Biophys. J. 105(1), 127–136 (2013).
[CrossRef] [PubMed]

Sahl, S. J.

M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, G. Grover, A. Agrawal, R. Piestun, W. E. Moerner, “Simultaneous, accurate measurement of the 3D position and orientation of single molecules,” Proc. Natl. Acad. Sci. USA 109, 19087 (2012).
[CrossRef] [PubMed]

Savatier, J.

A. Kress, X. Wang, H. Ranchon, J. Savatier, H. Rigneault, P. Ferrand, S. Brasselet, “Mapping the local organization of cell membranes using excitation-polarization-resolved confocal fluorescence microscopy,” Biophys. J. 105(1), 127–136 (2013).
[CrossRef] [PubMed]

Sheppard, C. J. R.

C. J. R. Sheppard, P. Torok, “Electromagnetic field in the focal region of an electric dipole wave,” Optik 104175–177 (1997).

Torok, P.

C. J. R. Sheppard, P. Torok, “Electromagnetic field in the focal region of an electric dipole wave,” Optik 104175–177 (1997).

Wang, W.

B. Huang, W. Wang, M. Bates, X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319(5864):810–813 (2008).
[CrossRef] [PubMed]

Wang, X.

A. Kress, X. Wang, H. Ranchon, J. Savatier, H. Rigneault, P. Ferrand, S. Brasselet, “Mapping the local organization of cell membranes using excitation-polarization-resolved confocal fluorescence microscopy,” Biophys. J. 105(1), 127–136 (2013).
[CrossRef] [PubMed]

Wilson, T.

Wolf, E.

B. Richards, E. Wolf, “The airy pattern in systems of high angular aperture,” Proc. Phys. Soc. B 69, 854 (1956).
[CrossRef]

Zhuang, X.

B. Huang, W. Wang, M. Bates, X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319(5864):810–813 (2008).
[CrossRef] [PubMed]

Biomed. Opt. Express

Biophys. J.

A. Kress, X. Wang, H. Ranchon, J. Savatier, H. Rigneault, P. Ferrand, S. Brasselet, “Mapping the local organization of cell membranes using excitation-polarization-resolved confocal fluorescence microscopy,” Biophys. J. 105(1), 127–136 (2013).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A

Nat. Meth.

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

Opt. Express

Opt. Lett.

Optik

C. J. R. Sheppard, P. Torok, “Electromagnetic field in the focal region of an electric dipole wave,” Optik 104175–177 (1997).

Proc. Natl. Acad. Sci. USA

M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, G. Grover, A. Agrawal, R. Piestun, W. E. Moerner, “Simultaneous, accurate measurement of the 3D position and orientation of single molecules,” Proc. Natl. Acad. Sci. USA 109, 19087 (2012).
[CrossRef] [PubMed]

Proc. Phys. Soc. B

B. Richards, E. Wolf, “The airy pattern in systems of high angular aperture,” Proc. Phys. Soc. B 69, 854 (1956).
[CrossRef]

Science

B. Huang, W. Wang, M. Bates, X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319(5864):810–813 (2008).
[CrossRef] [PubMed]

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Figures (6)

Fig. 1
Fig. 1

Experimental set-up: lenses TL and L1 are used to image the back focal plane of the objective onto the SLM. A polarising beamsplitter (PBS) is used to split the unpolarised light into two orthogonal polarisation directions, which are sent to different areas on the SLM. Lens L2 forms the PSF engineered image of the sample. The inset shows the actual 3D view of the non-planar polarisation rotation module, where the horizontal and vertical polarisation directions are indicated by blue and red colours, respectively. Next to the PBS two right angle prism mirrors are used for simplifying the alignment. The 2D sketch is a simplification where some components are missing.

Fig. 2
Fig. 2

(a): the mean magnitude and standard deviation of 12 aberration measurements in the set-up. (b) and (c) show images taken without and with aberration correction, respectively. Correcting aberrations improved the SNR by a factor of 1.1. (d) represents the simulation of a 500 nm fluorescent bead imaged with our set-up, which confirms the elliptical shape to be expected from linearly polarised light.

Fig. 3
Fig. 3

Shaping a double-helix PSF with a ring-segmented phase mask. In (a) a phase mask creating a double-helix PSF is shown. The red and blue lines indicate lines of constant phase 0 and π, respectively. (b) and (c) depicts simulations and experimental data of the engineered PSF of a 500 nm fluorescent bead in several planes, each 1 μm apart.

Fig. 4
Fig. 4

Tuning the properties of a rotating double-helix PSF: by changing the power for the ring diameters in the phase mask, one can achieve tighter lobes at the cost of increased rotational “spread”. Left: phase masks with seven rings, with phase values represented by gray shades. Middle: corresponding intensity PSFs at different values for defocus; the scale bar corresponds to 1μm. Right: maximum value of the PSFs plotted against defocus. The simulation assumes a NA of 1.4 and a wavelength of 550 nm.

Fig. 5
Fig. 5

z-localisation of 500 nm fluorescence particles. (a) shows the change of the rotation angle with defocus for 3, 5, and 7 rings used in the phase masks. The error bars correspond to the standard deviation of 4 measurements. (b) and (c) depict the two phase masks with 3 rings. In (d) the two engineered PSFs are encoded into different colour channels for different z-positions, each 1 μm apart.

Fig. 6
Fig. 6

SNR for different PSFs: Using only 50% of the light, i.e. a single DH-PSF, gives the lowest SNR, while the best is achieved when using a pair of corrected corkscrew-PSFs. For the corkscrews the SNR in both images is shown as they are slightly different.

Equations (3)

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P n ( ϕ ) = n ϕ ,
R out ( n ) = ( n / N ) R mask ,
α ( n ) R out ( n ) 2 n = R mask 2 N ,

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