Abstract

We demonstrate three-dimensional tracking of fluorescent microparticles, with a computational optical system whose point spread function (PSF) has been engineered to have two twisting lobes along the optical axis, generating a three-dimensional (3D) double-helix (DH) PSF. An information theoretical comparison in photon limited systems shows that the DH-PSF delivers higher Fisher information for 3D localization than the standard PSF. Hence, DH-PSF systems provide better position estimation accuracy. Experiments demonstrate average position estimation accuracies under 14nm and 37nm in the transverse and axial dimensions respectively. The system determines the 3D position of multiple particles with a single image and tracks them over time while providing their velocities.

© 2008 Optical Society of America

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  1. J. A. Steyer and W. Almers, "Tracking single secretory granules in live chromaffin cells by evanescent-field fluorescence microscopy," Biophys. J. 76, 2262-2271 (1999).
    [CrossRef] [PubMed]
  2. D. Li, J. Xiong, A. Qu, and T. Xu, "Three-dimensional tracking of single secretory granules in live pc12 cells," Biophys. J. 87, 1991-2001 (2004).
    [CrossRef] [PubMed]
  3. R. M. Dickson, A. B. Cubitt, R. Y. Tsien, and W. E. Moerner, "On/off blinking and switching behaviour of single molecules of green fluorescent protein," Nature 388, 355 (1997)
    [CrossRef] [PubMed]
  4. G. J. Schütz, M. Axmann, and H. Schindler, "Imaging single molecules in three dimensions," Sing. Mol. 2,69-74 (2001).
    [CrossRef]
  5. J. A. Steinkamp, J. S. Wilson, G. C. Saunders, and C. C. Stewart, "Phagocytosis: flow cytometric quantitation with fluorescent microspheres," Science 215, 64-66 (1982).
    [CrossRef] [PubMed]
  6. R. E. Thompson, D. R. Larson, and W. W. Webb, "Precise nanometer localization analysis for individual fluorescent probes," Biophys. J. 82,2775-2783 (2002).
    [CrossRef] [PubMed]
  7. M. Speidel, A. Jonas, and E.-L. Florin, "Three-dimensional tracking of fluorescent nanoparticles with subnanometer precision by use of off-focus imaging," Opt. Lett. 28, 69 (2003).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  10. B. Huang, W. Wang, M. Bates, and X. Zhuang, "Three-Dimensional Super-Resolution Imaging by Stochastic Optical Reconstruction Microscopy," Science 319, 5864, 810-813 (2008).
    [CrossRef] [PubMed]
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    [CrossRef]
  14. S. R. P. Pavani, A. Greengard, and R. Piestun, "Three-dimensional localization with nanometer accuracy using a double-helix point spread function system," (submitted).
  15. S. R. P. Pavani and R. Piestun, "High-efficiency rotating point spread functions," Opt. Express 16, 3484-3489 (2008).
    [CrossRef] [PubMed]
  16. A. Greengard, Y. Y. Schechner, and R. Piestun, "Depth from diffracted rotation," Opt. Lett. 31, 181-183 (2006).
    [CrossRef] [PubMed]
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    [CrossRef]
  18. R. Piestun, Y. Y. Schechner, and J. Shamir, "Propagation-invariant wave fields with finite energy," J. Opt. Soc. Am. A 17, 294-303 (2000).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]

2008

J. Rosen and G. Brooker, "Non-scanning motionless fluorescence three-dimensional holographic microscopy," Nature Photon. 2, 190-195 (2008).
[CrossRef]

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

B. Huang, W. Wang, M. Bates, and X. Zhuang, "Three-Dimensional Super-Resolution Imaging by Stochastic Optical Reconstruction Microscopy," Science 319, 5864, 810-813 (2008).
[CrossRef] [PubMed]

2007

2006

2004

D. Li, J. Xiong, A. Qu, and T. Xu, "Three-dimensional tracking of single secretory granules in live pc12 cells," Biophys. J. 87, 1991-2001 (2004).
[CrossRef] [PubMed]

R. J. Ober, S. Ram, and S.E. Ward, "Localization accuracy in single-molecule microscopy," Biophys. J. 86, 1185-1200 (2004).
[CrossRef] [PubMed]

2003

2002

R. E. Thompson, D. R. Larson, and W. W. Webb, "Precise nanometer localization analysis for individual fluorescent probes," Biophys. J. 82,2775-2783 (2002).
[CrossRef] [PubMed]

2001

G. J. Schütz, M. Axmann, and H. Schindler, "Imaging single molecules in three dimensions," Sing. Mol. 2,69-74 (2001).
[CrossRef]

2000

1999

J. A. Steyer and W. Almers, "Tracking single secretory granules in live chromaffin cells by evanescent-field fluorescence microscopy," Biophys. J. 76, 2262-2271 (1999).
[CrossRef] [PubMed]

1997

R. M. Dickson, A. B. Cubitt, R. Y. Tsien, and W. E. Moerner, "On/off blinking and switching behaviour of single molecules of green fluorescent protein," Nature 388, 355 (1997)
[CrossRef] [PubMed]

1996

Y. Y. Schechner, R. Piestun, and J. Shamir, "Wave propagation with rotating intensity distributions," Phys. Rev. E 54, R50-R53 (1996).
[CrossRef]

1994

H. P. Kao and A. S. Verkman, "Tracking of single fluorescent particles in three dimensions: use of cylindrical optics to encode particle position," Biophys. J. 67, 1291-1300 (1994).
[CrossRef] [PubMed]

1982

J. A. Steinkamp, J. S. Wilson, G. C. Saunders, and C. C. Stewart, "Phagocytosis: flow cytometric quantitation with fluorescent microspheres," Science 215, 64-66 (1982).
[CrossRef] [PubMed]

Almers, W.

J. A. Steyer and W. Almers, "Tracking single secretory granules in live chromaffin cells by evanescent-field fluorescence microscopy," Biophys. J. 76, 2262-2271 (1999).
[CrossRef] [PubMed]

Axmann, M.

G. J. Schütz, M. Axmann, and H. Schindler, "Imaging single molecules in three dimensions," Sing. Mol. 2,69-74 (2001).
[CrossRef]

Bates, M.

B. Huang, W. Wang, M. Bates, and X. Zhuang, "Three-Dimensional Super-Resolution Imaging by Stochastic Optical Reconstruction Microscopy," Science 319, 5864, 810-813 (2008).
[CrossRef] [PubMed]

Brooker, G.

J. Rosen and G. Brooker, "Non-scanning motionless fluorescence three-dimensional holographic microscopy," Nature Photon. 2, 190-195 (2008).
[CrossRef]

Cubitt, A. B.

R. M. Dickson, A. B. Cubitt, R. Y. Tsien, and W. E. Moerner, "On/off blinking and switching behaviour of single molecules of green fluorescent protein," Nature 388, 355 (1997)
[CrossRef] [PubMed]

Dickson, R. M.

R. M. Dickson, A. B. Cubitt, R. Y. Tsien, and W. E. Moerner, "On/off blinking and switching behaviour of single molecules of green fluorescent protein," Nature 388, 355 (1997)
[CrossRef] [PubMed]

Florin, E.-L.

Greengard, A.

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

S. R. P. Pavani, A. Greengard, and R. Piestun, "Three-dimensional localization with nanometer accuracy using a double-helix point spread function system," (submitted).

Grier, D. G.

Holtzer, L.

L. Holtzer, T. Meckel, and T. Schmidt, "Nanometric three-dimensional tracking of individual quantum dots in cells," Appl. Phys. Lett. 90, 053902 (2007).
[CrossRef]

Huang, B.

B. Huang, W. Wang, M. Bates, and X. Zhuang, "Three-Dimensional Super-Resolution Imaging by Stochastic Optical Reconstruction Microscopy," Science 319, 5864, 810-813 (2008).
[CrossRef] [PubMed]

Jonas, A.

Kao, H. P.

H. P. Kao and A. S. Verkman, "Tracking of single fluorescent particles in three dimensions: use of cylindrical optics to encode particle position," Biophys. J. 67, 1291-1300 (1994).
[CrossRef] [PubMed]

Kim, S. -H.

Larson, D. R.

R. E. Thompson, D. R. Larson, and W. W. Webb, "Precise nanometer localization analysis for individual fluorescent probes," Biophys. J. 82,2775-2783 (2002).
[CrossRef] [PubMed]

Lee, S. -H.

Li, D.

D. Li, J. Xiong, A. Qu, and T. Xu, "Three-dimensional tracking of single secretory granules in live pc12 cells," Biophys. J. 87, 1991-2001 (2004).
[CrossRef] [PubMed]

Meckel, T.

L. Holtzer, T. Meckel, and T. Schmidt, "Nanometric three-dimensional tracking of individual quantum dots in cells," Appl. Phys. Lett. 90, 053902 (2007).
[CrossRef]

Moerner, W. E.

R. M. Dickson, A. B. Cubitt, R. Y. Tsien, and W. E. Moerner, "On/off blinking and switching behaviour of single molecules of green fluorescent protein," Nature 388, 355 (1997)
[CrossRef] [PubMed]

Ober, R. J.

R. J. Ober, S. Ram, and S.E. Ward, "Localization accuracy in single-molecule microscopy," Biophys. J. 86, 1185-1200 (2004).
[CrossRef] [PubMed]

Pavani, S. R. P.

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

S. R. P. Pavani, A. Greengard, and R. Piestun, "Three-dimensional localization with nanometer accuracy using a double-helix point spread function system," (submitted).

Piestun, R.

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

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

R. Piestun, Y. Y. Schechner, and J. Shamir, "Propagation-invariant wave fields with finite energy," J. Opt. Soc. Am. A 17, 294-303 (2000).
[CrossRef]

Y. Y. Schechner, R. Piestun, and J. Shamir, "Wave propagation with rotating intensity distributions," Phys. Rev. E 54, R50-R53 (1996).
[CrossRef]

S. R. P. Pavani, A. Greengard, and R. Piestun, "Three-dimensional localization with nanometer accuracy using a double-helix point spread function system," (submitted).

Qu, A.

D. Li, J. Xiong, A. Qu, and T. Xu, "Three-dimensional tracking of single secretory granules in live pc12 cells," Biophys. J. 87, 1991-2001 (2004).
[CrossRef] [PubMed]

Ram, S.

R. J. Ober, S. Ram, and S.E. Ward, "Localization accuracy in single-molecule microscopy," Biophys. J. 86, 1185-1200 (2004).
[CrossRef] [PubMed]

Roichman, Y.

Rosen, J.

J. Rosen and G. Brooker, "Non-scanning motionless fluorescence three-dimensional holographic microscopy," Nature Photon. 2, 190-195 (2008).
[CrossRef]

Saunders, G. C.

J. A. Steinkamp, J. S. Wilson, G. C. Saunders, and C. C. Stewart, "Phagocytosis: flow cytometric quantitation with fluorescent microspheres," Science 215, 64-66 (1982).
[CrossRef] [PubMed]

Schechner, Y. Y.

Schindler, H.

G. J. Schütz, M. Axmann, and H. Schindler, "Imaging single molecules in three dimensions," Sing. Mol. 2,69-74 (2001).
[CrossRef]

Schmidt, T.

L. Holtzer, T. Meckel, and T. Schmidt, "Nanometric three-dimensional tracking of individual quantum dots in cells," Appl. Phys. Lett. 90, 053902 (2007).
[CrossRef]

Schütz, G. J.

G. J. Schütz, M. Axmann, and H. Schindler, "Imaging single molecules in three dimensions," Sing. Mol. 2,69-74 (2001).
[CrossRef]

Shamir, J.

R. Piestun, Y. Y. Schechner, and J. Shamir, "Propagation-invariant wave fields with finite energy," J. Opt. Soc. Am. A 17, 294-303 (2000).
[CrossRef]

Y. Y. Schechner, R. Piestun, and J. Shamir, "Wave propagation with rotating intensity distributions," Phys. Rev. E 54, R50-R53 (1996).
[CrossRef]

Speidel, M.

Steinkamp, J. A.

J. A. Steinkamp, J. S. Wilson, G. C. Saunders, and C. C. Stewart, "Phagocytosis: flow cytometric quantitation with fluorescent microspheres," Science 215, 64-66 (1982).
[CrossRef] [PubMed]

Stewart, C. C.

J. A. Steinkamp, J. S. Wilson, G. C. Saunders, and C. C. Stewart, "Phagocytosis: flow cytometric quantitation with fluorescent microspheres," Science 215, 64-66 (1982).
[CrossRef] [PubMed]

Steyer, J. A.

J. A. Steyer and W. Almers, "Tracking single secretory granules in live chromaffin cells by evanescent-field fluorescence microscopy," Biophys. J. 76, 2262-2271 (1999).
[CrossRef] [PubMed]

Thompson, R. E.

R. E. Thompson, D. R. Larson, and W. W. Webb, "Precise nanometer localization analysis for individual fluorescent probes," Biophys. J. 82,2775-2783 (2002).
[CrossRef] [PubMed]

Tsien, R. Y.

R. M. Dickson, A. B. Cubitt, R. Y. Tsien, and W. E. Moerner, "On/off blinking and switching behaviour of single molecules of green fluorescent protein," Nature 388, 355 (1997)
[CrossRef] [PubMed]

van Blaaderen, A.

van Oostrum, P.

Verkman, A. S.

H. P. Kao and A. S. Verkman, "Tracking of single fluorescent particles in three dimensions: use of cylindrical optics to encode particle position," Biophys. J. 67, 1291-1300 (1994).
[CrossRef] [PubMed]

Wang, W.

B. Huang, W. Wang, M. Bates, and X. Zhuang, "Three-Dimensional Super-Resolution Imaging by Stochastic Optical Reconstruction Microscopy," Science 319, 5864, 810-813 (2008).
[CrossRef] [PubMed]

Ward, S.E.

R. J. Ober, S. Ram, and S.E. Ward, "Localization accuracy in single-molecule microscopy," Biophys. J. 86, 1185-1200 (2004).
[CrossRef] [PubMed]

Webb, W. W.

R. E. Thompson, D. R. Larson, and W. W. Webb, "Precise nanometer localization analysis for individual fluorescent probes," Biophys. J. 82,2775-2783 (2002).
[CrossRef] [PubMed]

Wilson, J. S.

J. A. Steinkamp, J. S. Wilson, G. C. Saunders, and C. C. Stewart, "Phagocytosis: flow cytometric quantitation with fluorescent microspheres," Science 215, 64-66 (1982).
[CrossRef] [PubMed]

Xiong, J.

D. Li, J. Xiong, A. Qu, and T. Xu, "Three-dimensional tracking of single secretory granules in live pc12 cells," Biophys. J. 87, 1991-2001 (2004).
[CrossRef] [PubMed]

Xu, T.

D. Li, J. Xiong, A. Qu, and T. Xu, "Three-dimensional tracking of single secretory granules in live pc12 cells," Biophys. J. 87, 1991-2001 (2004).
[CrossRef] [PubMed]

Yang, S. -M.

Yi, G. -R.

Zhuang, X.

B. Huang, W. Wang, M. Bates, and X. Zhuang, "Three-Dimensional Super-Resolution Imaging by Stochastic Optical Reconstruction Microscopy," Science 319, 5864, 810-813 (2008).
[CrossRef] [PubMed]

Appl. Phys. Lett.

L. Holtzer, T. Meckel, and T. Schmidt, "Nanometric three-dimensional tracking of individual quantum dots in cells," Appl. Phys. Lett. 90, 053902 (2007).
[CrossRef]

Biophys. J.

J. A. Steyer and W. Almers, "Tracking single secretory granules in live chromaffin cells by evanescent-field fluorescence microscopy," Biophys. J. 76, 2262-2271 (1999).
[CrossRef] [PubMed]

D. Li, J. Xiong, A. Qu, and T. Xu, "Three-dimensional tracking of single secretory granules in live pc12 cells," Biophys. J. 87, 1991-2001 (2004).
[CrossRef] [PubMed]

R. E. Thompson, D. R. Larson, and W. W. Webb, "Precise nanometer localization analysis for individual fluorescent probes," Biophys. J. 82,2775-2783 (2002).
[CrossRef] [PubMed]

H. P. Kao and A. S. Verkman, "Tracking of single fluorescent particles in three dimensions: use of cylindrical optics to encode particle position," Biophys. J. 67, 1291-1300 (1994).
[CrossRef] [PubMed]

R. J. Ober, S. Ram, and S.E. Ward, "Localization accuracy in single-molecule microscopy," Biophys. J. 86, 1185-1200 (2004).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A

Nature

R. M. Dickson, A. B. Cubitt, R. Y. Tsien, and W. E. Moerner, "On/off blinking and switching behaviour of single molecules of green fluorescent protein," Nature 388, 355 (1997)
[CrossRef] [PubMed]

Nature Photon.

J. Rosen and G. Brooker, "Non-scanning motionless fluorescence three-dimensional holographic microscopy," Nature Photon. 2, 190-195 (2008).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. E

Y. Y. Schechner, R. Piestun, and J. Shamir, "Wave propagation with rotating intensity distributions," Phys. Rev. E 54, R50-R53 (1996).
[CrossRef]

Science

B. Huang, W. Wang, M. Bates, and X. Zhuang, "Three-Dimensional Super-Resolution Imaging by Stochastic Optical Reconstruction Microscopy," Science 319, 5864, 810-813 (2008).
[CrossRef] [PubMed]

J. A. Steinkamp, J. S. Wilson, G. C. Saunders, and C. C. Stewart, "Phagocytosis: flow cytometric quantitation with fluorescent microspheres," Science 215, 64-66 (1982).
[CrossRef] [PubMed]

Sing. Mol.

G. J. Schütz, M. Axmann, and H. Schindler, "Imaging single molecules in three dimensions," Sing. Mol. 2,69-74 (2001).
[CrossRef]

Other

S. R. P. Pavani, A. Greengard, and R. Piestun, "Three-dimensional localization with nanometer accuracy using a double-helix point spread function system," (submitted).

S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice-Hall, 1993).

T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley-Interscience, 1991).
[CrossRef]

Supplementary Material (2)

» Media 1: MOV (3077 KB)     
» Media 2: MOV (3439 KB)     

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Figures (6)

Fig. 1.
Fig. 1.

Comparison of the (a) DH-PSF and the (b) standard PSF at different axial planes for a system with 0.45 numerical aperture (NA) and 633nm wavelength.

Fig. 2.
Fig. 2.

Information theoretical comparison of DH and standard PSFs for a photon-limited system with Poisson noise. The system has 0.45NA, 40x magnification, 6.3µm pixel width, and 633nm wavelength. See text for explanation of SNR. (a–c) compare the CRBs of the DH and standard PSFs as a function of axial distance for the (a) Z, (b) X, and (c) Y dimensions. (d) compares CRB3D of the DH and standard PSFs. DH-PSF has lower CRB3D than the standard PSF in regions A (focal region) and C, while the standard PSF has lower CRB3D in region B. CRBAVG is lower for the DH-PSF than the standard PSF. DH-PSF, therefore, on an average, carries more information about the position of a particle than the standard PSF.

Fig. 3.
Fig. 3.

Experimental setup for three dimensional tracking of moving fluorescent particles: A horizontally polarized beam with 488nm wavelength excites 1µm wide yellow-green (Excitation peak: 505nm, Emission peak: 515nm) fluorescent microspheres. The microspheres are imaged by a 1.3NA oil-immersion infinity corrected objective and a tube lens. In the infinity space of the objective, a 515nm interference filter with 10nm bandwidth blocks out the excitation wavelength, and a polarizer passes only horizontally polarized emitted light. Finally, a phase-only spatial light modulator encoding the DH-PSF mask (top-right inset) engineers the system’s PSF to have two rotating lobes. Unlike the standard PSF image which blurs the particles outside the focal region, the DH-PSF image encodes the particle’s axial location in the angular orientation of its PSF lobes (bottom insets). The scale bar in the images represents 1µm.

Fig. 4.
Fig. 4.

Movies of fluorescent microsphere tracking in three dimensions. (Media 1) (a–c) shows (a) the DH-PSF image, (b) the standard PSF image, and (c) the 3D locations of four microspheres. (Media 2) (d–f) displays X-Y, X-Z, and Y-Z projections of the microspheres’ 3D locations

Fig. 5.
Fig. 5.

Time-varying velocities in all three dimensions for (a) particle 1, (b) particle 2, and (c) particle 3.

Fig. 6.
Fig. 6.

(a) Calibration plot that maps rotation angle to axial distance. Correction factors for (b) X and (c) Y dimensions that are used in transverse position estimation.

Tables (1)

Tables Icon

Table 1: Positions and standard deviations of the four fluorescent microspheres shown in Fig. 3.

Equations (2)

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

I θ [ m , n ] = i , j E [ ln P i , j ( k θ ) θ [ m ] ln P i , j ( k θ ) θ [ n ] ] = i , j E [ 2 ln p i , j ( k θ ) θ [ m ] θ [ n ] ] ,
CRB AVG = 1 ΔZ ΔZ CRB 3 D ( Z ) d Z ,

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