Abstract

Many single-particle tracking and localization-based superresolution imaging techniques use the width of a single lateral fluorescence image to estimate a molecule’s axial position. This determination is often done by use of a calibration data set derived from a source adhered to a glass–water interface. However, for sources deeper in solution, aberrations will change the relationship between the image width and the axial position. We analyzed the depth-varying point spread function of a high numerical aperture objective near an index of refraction mismatch at the water–glass interface using an optical trap. In addition to the well-known focal shift, spherical aberrations cause up to 30% relative systematic error in axial position estimation. This effect is nonuniform in depth, and we find that, although molecules below the focal plane are correctly localized, molecules deeper than the focal plane are found to be lower than their actual positions.

© 2009 Optical Society of America

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[CrossRef] [PubMed]

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J. Bewersdorf, A. Egner, and S. W. Hell, “Multifocal multiphoton microscopy” in Handbook of Biological Confocal Microscopy, J. B. Pawley, ed., 3rd ed. (Springer, 2006), Chap. 29.

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91, 4258-4272 (2006).
[CrossRef] [PubMed]

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642-1645(2006).
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M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3, 793-795 (2006).
[CrossRef] [PubMed]

2005

2003

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, “Myosin V walks hand-over-hand: single fluorophore imaging with 1.5 nm localization,” Science 300, 2061-2065 (2003).
[CrossRef] [PubMed]

2002

1999

M. G. Gustafsson, D. A. Agard, and J. W. Sedat, “15 m:3D widefield light microscopy with better than 100 nm axial resolution,” J. Microsc. 195, 10-16 (1999).
[CrossRef] [PubMed]

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C. J. R. Sheppard and P. Torok, “Effects of specimen refractive index on confocal imaging,” J. Microsc. 185, 366-374 (1997).
[CrossRef]

1994

1992

1990

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73-76 (1990).
[CrossRef] [PubMed]

1987

J. G. White, W. B. Amos, and M. Fordham, “An evaluation of confocal versus conventional imaging of biological structures by fluorescence light microscopy,” J. Cell Biol. 105, 41-48(1987).
[CrossRef] [PubMed]

Abbondanzieri, E. A.

Agard, D. A.

M. G. Gustafsson, D. A. Agard, and J. W. Sedat, “15 m:3D widefield light microscopy with better than 100 nm axial resolution,” J. Microsc. 195, 10-16 (1999).
[CrossRef] [PubMed]

Aguet, F.

Amos, W. B.

J. G. White, W. B. Amos, and M. Fordham, “An evaluation of confocal versus conventional imaging of biological structures by fluorescence light microscopy,” J. Cell Biol. 105, 41-48(1987).
[CrossRef] [PubMed]

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]

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3, 793-795 (2006).
[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,” Nat. Methods 5, 527-529 (2008).
[CrossRef] [PubMed]

Betzig, E.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642-1645(2006).
[CrossRef] [PubMed]

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,” Nat. Methods 5, 527-529 (2008).
[CrossRef] [PubMed]

J. Bewersdorf, A. Egner, and S. W. Hell, “Multifocal multiphoton microscopy” in Handbook of Biological Confocal Microscopy, J. B. Pawley, ed., 3rd ed. (Springer, 2006), Chap. 29.

Block, S. M.

Bonifacino, J. S.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642-1645(2006).
[CrossRef] [PubMed]

Conchello, J. A.

Davidson, M. W.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642-1645(2006).
[CrossRef] [PubMed]

Denk, W.

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73-76 (1990).
[CrossRef] [PubMed]

Diaspro, A.

Egner, A.

R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, “Spherical nanosized focal spot unravels the interior of cells,” Nat. Methods 5, 539-544 (2008).
[CrossRef] [PubMed]

J. Bewersdorf, A. Egner, and S. W. Hell, “Multifocal multiphoton microscopy” in Handbook of Biological Confocal Microscopy, J. B. Pawley, ed., 3rd ed. (Springer, 2006), Chap. 29.

Engelhardt, J.

R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, “Spherical nanosized focal spot unravels the interior of cells,” Nat. Methods 5, 539-544 (2008).
[CrossRef] [PubMed]

Federici, F.

Fletcher, D. A.

Fordham, M.

J. G. White, W. B. Amos, and M. Fordham, “An evaluation of confocal versus conventional imaging of biological structures by fluorescence light microscopy,” J. Cell Biol. 105, 41-48(1987).
[CrossRef] [PubMed]

Forkey, J. N.

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, “Myosin V walks hand-over-hand: single fluorophore imaging with 1.5 nm localization,” Science 300, 2061-2065 (2003).
[CrossRef] [PubMed]

Girirajan, T. P. K.

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91, 4258-4272 (2006).
[CrossRef] [PubMed]

Goldman, Y. E.

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, “Myosin V walks hand-over-hand: single fluorophore imaging with 1.5 nm localization,” Science 300, 2061-2065 (2003).
[CrossRef] [PubMed]

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,” Nat. Methods 5, 527-529 (2008).
[CrossRef] [PubMed]

Gustafsson, M. G.

M. G. Gustafsson, D. A. Agard, and J. W. Sedat, “15 m:3D widefield light microscopy with better than 100 nm axial resolution,” J. Microsc. 195, 10-16 (1999).
[CrossRef] [PubMed]

Gustafsson, M. G. L.

M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution,” Proc. Natl. Acad. Sci. USA 102, 13081-13086 (2005).
[CrossRef] [PubMed]

Ha, T.

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, “Myosin V walks hand-over-hand: single fluorophore imaging with 1.5 nm localization,” Science 300, 2061-2065 (2003).
[CrossRef] [PubMed]

Hell, S. W.

R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, “Spherical nanosized focal spot unravels the interior of cells,” Nat. Methods 5, 539-544 (2008).
[CrossRef] [PubMed]

J. Bewersdorf, A. Egner, and S. W. Hell, “Multifocal multiphoton microscopy” in Handbook of Biological Confocal Microscopy, J. B. Pawley, ed., 3rd ed. (Springer, 2006), Chap. 29.

S. W. Hell and J. Wichmann, “Breaking the diffraction resolution limit by stimulated-emission: stimulated-emission-depletion fluorescence microscopy,” Opt. Lett. 19, 780-782(1994).
[CrossRef] [PubMed]

S. W. Hell and E. Stelzer, “Properties of a 4Pi confocal fluorescence microscope,” J. Opt. Soc. Am. A 9, 2159-2166 (1992).
[CrossRef]

Hess, H. F.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642-1645(2006).
[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, and J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples,” Nat. Methods 5, 527-529 (2008).
[CrossRef] [PubMed]

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91, 4258-4272 (2006).
[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]

Jakobs, S.

R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, “Spherical nanosized focal spot unravels the interior of cells,” Nat. Methods 5, 539-544 (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, and J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples,” Nat. Methods 5, 527-529 (2008).
[CrossRef] [PubMed]

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]

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,” Nat. Methods 5, 527-529 (2008).
[CrossRef] [PubMed]

Lindwasser, O. W.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642-1645(2006).
[CrossRef] [PubMed]

Lippincott-Schwartz, J.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642-1645(2006).
[CrossRef] [PubMed]

Mason, M. D.

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91, 4258-4272 (2006).
[CrossRef] [PubMed]

McKinney, S. A.

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, “Myosin V walks hand-over-hand: single fluorophore imaging with 1.5 nm localization,” Science 300, 2061-2065 (2003).
[CrossRef] [PubMed]

McNally, J. G.

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,” Nat. Methods 5, 527-529 (2008).
[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, and J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples,” Nat. Methods 5, 527-529 (2008).
[CrossRef] [PubMed]

Neuman, K. C.

Olenych, S.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642-1645(2006).
[CrossRef] [PubMed]

Patterson, G. H.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642-1645(2006).
[CrossRef] [PubMed]

Preza, C.

Robello, M.

Rust, M. J.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3, 793-795 (2006).
[CrossRef] [PubMed]

Schmidt, R.

R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, “Spherical nanosized focal spot unravels the interior of cells,” Nat. Methods 5, 539-544 (2008).
[CrossRef] [PubMed]

Sedat, J. W.

M. G. Gustafsson, D. A. Agard, and J. W. Sedat, “15 m:3D widefield light microscopy with better than 100 nm axial resolution,” J. Microsc. 195, 10-16 (1999).
[CrossRef] [PubMed]

Selvin, P. R.

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, “Myosin V walks hand-over-hand: single fluorophore imaging with 1.5 nm localization,” Science 300, 2061-2065 (2003).
[CrossRef] [PubMed]

Shaevitz, J. W.

Sheppard, C. J. R.

C. J. R. Sheppard and P. Torok, “Effects of specimen refractive index on confocal imaging,” J. Microsc. 185, 366-374 (1997).
[CrossRef]

Sougrat, R.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642-1645(2006).
[CrossRef] [PubMed]

Stelzer, E.

Strickler, J. H.

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73-76 (1990).
[CrossRef] [PubMed]

Thomas, L. J.

Torok, P.

C. J. R. Sheppard and P. Torok, “Effects of specimen refractive index on confocal imaging,” J. Microsc. 185, 366-374 (1997).
[CrossRef]

Unser, M.

Van De Ville, D.

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, 810-813 (2008).
[CrossRef] [PubMed]

Webb, W. W.

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73-76 (1990).
[CrossRef] [PubMed]

White, J. G.

J. G. White, W. B. Amos, and M. Fordham, “An evaluation of confocal versus conventional imaging of biological structures by fluorescence light microscopy,” J. Cell Biol. 105, 41-48(1987).
[CrossRef] [PubMed]

Wichmann, J.

Wurm, C. A.

R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, “Spherical nanosized focal spot unravels the interior of cells,” Nat. Methods 5, 539-544 (2008).
[CrossRef] [PubMed]

Yildiz, A.

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, “Myosin V walks hand-over-hand: single fluorophore imaging with 1.5 nm localization,” Science 300, 2061-2065 (2003).
[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]

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3, 793-795 (2006).
[CrossRef] [PubMed]

Appl. Opt.

Biophys. J.

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91, 4258-4272 (2006).
[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]

J. Cell Biol.

J. G. White, W. B. Amos, and M. Fordham, “An evaluation of confocal versus conventional imaging of biological structures by fluorescence light microscopy,” J. Cell Biol. 105, 41-48(1987).
[CrossRef] [PubMed]

J. Microsc.

C. J. R. Sheppard and P. Torok, “Effects of specimen refractive index on confocal imaging,” J. Microsc. 185, 366-374 (1997).
[CrossRef]

M. G. Gustafsson, D. A. Agard, and J. W. Sedat, “15 m:3D widefield light microscopy with better than 100 nm axial resolution,” J. Microsc. 195, 10-16 (1999).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A

Nat. Methods

J. W. Shaevitz, “Super-resolution for a 3D world,” Nat. Methods 5, 471-472 (2008).
[CrossRef] [PubMed]

R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, “Spherical nanosized focal spot unravels the interior of cells,” Nat. Methods 5, 539-544 (2008).
[CrossRef] [PubMed]

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3, 793-795 (2006).
[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,” Nat. Methods 5, 527-529 (2008).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Proc. Natl. Acad. Sci. USA

M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution,” Proc. Natl. Acad. Sci. USA 102, 13081-13086 (2005).
[CrossRef] [PubMed]

Science

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Figures (3)

Fig. 1
Fig. 1

Typical in-focus and defocused images of a trapped fluorescent bead and the fit width of these images with a two-dimensional Gaussian function. (a) Images of the bead 375 nm below (column 1), on (column 2), and above (column 3) the image plane. The distance between the bead and the water–glass interface is chosen as 0 (aberration-free), 900, 1800, and 2700 nm . The scale bar is 1 μm . (b) The image width is plotted as a function of the distance of the bead from the glass–water interface and from the image plane. (c) Horizontal lines scans through (b) at imaging depths of 0, 750, 1500, 2250, and 3000 nm. The dashed line in (b) and (c) indicates the location of the image plane.

Fig. 2
Fig. 2

Change in the width of a bead image with varying depth with (crosses) and without (circles) aberrations. The circles represent the widths of a source at varying depths relative to an image plane that is 375 nm above the glass–water interface. The vertical dotted line indicates the location of the image plane.

Fig. 3
Fig. 3

Apparent height of a bead calibrated with the zero-depth, aberration-free, PSF as a function of the actual depth. The glass–water interface was placed 375 nm below the image plane. A straight line of slope 1 (solid line) is drawn as a guide to the eye. The vertical dashed line indicates the location of the image plane. The top figure shows the absolute localization error.

Equations (1)

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I ( x , y ) = I 0 + A e x x 0 2 σ 2 y y 0 2 σ 2 ,

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