Abstract

Exact knowledge of the numerical aperture is crucial in many applications using high-aperture objectives such as confocal microscopy, optical trapping, or advanced sub-wavelength imaging methods. We propose and apply a precise and straightforward method for measuring this fundamental parameter of microscope objectives with numerical apertures above unity. Our method exploits the peculiarities of the fluorescence emission of molecules at a glass/air interface.

© 2005 Optical Society of America

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  1. P.M. Goodwin , W.P. Ambrose , and R.A. Keller “ Single-molecule detection in liquids by laser-induced fluorescence ,” Acc. Chem. Res.   29 , 607 – 613 ( 1996 ).
    [Crossref]
  2. J. Enderlein and M. Böhmer “ Fluorescence spectroscopy of single molecules under ambient conditions: Methodology and technology ,” Chem. Phys. Chem.   4 , 792 – 808 ( 2003 ).
    [Crossref]
  3. R. Rigler and J. Widengren “ Ultrasensitive Detection of single molecules by fluorescence correlation spectroscopy ,” Bioscience   3 , 180 – 183 ( 1990 ).
  4. P. Schwille “ Fluorescene correlation spectroscopy and its potential for intracellular applications ,” Cell Biochem. Biophys.   34 , 383 – 408 ( 2001 ).
    [Crossref]
  5. A. Ashkin “ Optical Trapping And Manipulation Of Neutral Particles Using Lasers ,” Proc. Nat. Acad. Sci.   94 , 4853 – 4860 ( 1997 ).
    [Crossref] [PubMed]
  6. K.C. Neuman and S.M. Block “ Optical Trapping ,” Rev. Sci. Instrum.   75 , 2787 – 809 ( 2004 ).
    [Crossref]
  7. D.R. Sandison , D.W. Piston , R.M. Williams , and W.W. Webb “ Quantitative comparison of background rejection, signal-to-noise ratio, and resolution in confocal and full-field laser scanning microscopes ,” Appl. Opt.   34 , 3576 – 3588 ( 1995 ).
    [Crossref] [PubMed]
  8. D.W. Piston “ Choosing objective lenses; The importance of numerical aperture and magnification ,” Biol. Bull.   195 , 1 – 4 ( 1998 ).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  12. Neto P.A. Maia and H.M. Nussenzveig “ Theory of optical tweezers ” Europhys. Lett.   50 , 702 – 708 ( 2000 ).
    [Crossref]
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    [Crossref]
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    [Crossref]
  15. J. Enderlein , I. Gregor , D. Patra , T. Dertinger , and B. Kaupp “ Performance of fluorescence correlation spectroscopy for measuring diffusion and concentration ,” Chem. Phys. Chem. ( 2005 ) in press.
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    [Crossref] [PubMed]
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    [Crossref]
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  20. J. Enderlein , T. Ruckstuhl , and S. Seeger “ Highly Efficient Optical Detection of Surface-Generated Fluorescence ,” Appl. Opt.   38 , 724 – 732 ( 1999 ).
    [Crossref]
  21. W. Schroeyers , R. Vallee , D. Patra , J. Hofkens , S. Habuchi , T. Vosch , M. Cotlet , K. Müllen , J. Enderlein , and F.C. De Schryver “ Fluorescence Lifetimes and Emission Patterns Probe the 3D Orientation of the Emitting Chromophore in a Multichromophoric System ,” J. Am. Chem. Soc.   126 , 14310 – 14311 ( 2004 ).
    [Crossref] [PubMed]
  22. D. Patra , I. Gregor , and J. Enderlein “ Image Analysis of Defocused Single-Molecule Images for Three-Dimensional Molecule Orientation Studies ,” J. Phys. Chem. A   108 , 6836 – 6841 ( 2004 ).
    [Crossref]

2004 (3)

K.C. Neuman and S.M. Block “ Optical Trapping ,” Rev. Sci. Instrum.   75 , 2787 – 809 ( 2004 ).
[Crossref]

W. Schroeyers , R. Vallee , D. Patra , J. Hofkens , S. Habuchi , T. Vosch , M. Cotlet , K. Müllen , J. Enderlein , and F.C. De Schryver “ Fluorescence Lifetimes and Emission Patterns Probe the 3D Orientation of the Emitting Chromophore in a Multichromophoric System ,” J. Am. Chem. Soc.   126 , 14310 – 14311 ( 2004 ).
[Crossref] [PubMed]

D. Patra , I. Gregor , and J. Enderlein “ Image Analysis of Defocused Single-Molecule Images for Three-Dimensional Molecule Orientation Studies ,” J. Phys. Chem. A   108 , 6836 – 6841 ( 2004 ).
[Crossref]

2003 (2)

J. Enderlein and M. Böhmer “ Fluorescence spectroscopy of single molecules under ambient conditions: Methodology and technology ,” Chem. Phys. Chem.   4 , 792 – 808 ( 2003 ).
[Crossref]

M. Böhmer and J. Enderlein “ Orientation imaging of single molecules by wide-field epi-fluorescence microscopy ,” J. Opt. Soc. Am. B   20 , 554 – 559 ( 2003 ).
[Crossref]

2002 (1)

2001 (1)

P. Schwille “ Fluorescene correlation spectroscopy and its potential for intracellular applications ,” Cell Biochem. Biophys.   34 , 383 – 408 ( 2001 ).
[Crossref]

2000 (1)

Neto P.A. Maia and H.M. Nussenzveig “ Theory of optical tweezers ” Europhys. Lett.   50 , 702 – 708 ( 2000 ).
[Crossref]

1999 (2)

1998 (1)

D.W. Piston “ Choosing objective lenses; The importance of numerical aperture and magnification ,” Biol. Bull.   195 , 1 – 4 ( 1998 ).
[Crossref] [PubMed]

1997 (1)

A. Ashkin “ Optical Trapping And Manipulation Of Neutral Particles Using Lasers ,” Proc. Nat. Acad. Sci.   94 , 4853 – 4860 ( 1997 ).
[Crossref] [PubMed]

1996 (1)

P.M. Goodwin , W.P. Ambrose , and R.A. Keller “ Single-molecule detection in liquids by laser-induced fluorescence ,” Acc. Chem. Res.   29 , 607 – 613 ( 1996 ).
[Crossref]

1995 (2)

1994 (1)

1993 (1)

W. Lehmann and A. Wachtel “ Numerical apertures of light microscope objectives ,” J. Microsc.   169 , 89 – 90 ( 1993 ).
[Crossref]

1992 (1)

1990 (1)

R. Rigler and J. Widengren “ Ultrasensitive Detection of single molecules by fluorescence correlation spectroscopy ,” Bioscience   3 , 180 – 183 ( 1990 ).

1981 (1)

Ambrose, W.P.

P.M. Goodwin , W.P. Ambrose , and R.A. Keller “ Single-molecule detection in liquids by laser-induced fluorescence ,” Acc. Chem. Res.   29 , 607 – 613 ( 1996 ).
[Crossref]

Ashkin, A.

A. Ashkin “ Optical Trapping And Manipulation Of Neutral Particles Using Lasers ,” Proc. Nat. Acad. Sci.   94 , 4853 – 4860 ( 1997 ).
[Crossref] [PubMed]

Block, S.M.

K.C. Neuman and S.M. Block “ Optical Trapping ,” Rev. Sci. Instrum.   75 , 2787 – 809 ( 2004 ).
[Crossref]

Böhmer, M.

J. Enderlein and M. Böhmer “ Fluorescence spectroscopy of single molecules under ambient conditions: Methodology and technology ,” Chem. Phys. Chem.   4 , 792 – 808 ( 2003 ).
[Crossref]

M. Böhmer and J. Enderlein “ Orientation imaging of single molecules by wide-field epi-fluorescence microscopy ,” J. Opt. Soc. Am. B   20 , 554 – 559 ( 2003 ).
[Crossref]

Brakenhoff, G.J.

Cotlet, M.

W. Schroeyers , R. Vallee , D. Patra , J. Hofkens , S. Habuchi , T. Vosch , M. Cotlet , K. Müllen , J. Enderlein , and F.C. De Schryver “ Fluorescence Lifetimes and Emission Patterns Probe the 3D Orientation of the Emitting Chromophore in a Multichromophoric System ,” J. Am. Chem. Soc.   126 , 14310 – 14311 ( 2004 ).
[Crossref] [PubMed]

De Schryver, F.C.

W. Schroeyers , R. Vallee , D. Patra , J. Hofkens , S. Habuchi , T. Vosch , M. Cotlet , K. Müllen , J. Enderlein , and F.C. De Schryver “ Fluorescence Lifetimes and Emission Patterns Probe the 3D Orientation of the Emitting Chromophore in a Multichromophoric System ,” J. Am. Chem. Soc.   126 , 14310 – 14311 ( 2004 ).
[Crossref] [PubMed]

Dertinger, T.

J. Enderlein , I. Gregor , D. Patra , T. Dertinger , and B. Kaupp “ Performance of fluorescence correlation spectroscopy for measuring diffusion and concentration ,” Chem. Phys. Chem. ( 2005 ) in press.

Enderlein, J.

W. Schroeyers , R. Vallee , D. Patra , J. Hofkens , S. Habuchi , T. Vosch , M. Cotlet , K. Müllen , J. Enderlein , and F.C. De Schryver “ Fluorescence Lifetimes and Emission Patterns Probe the 3D Orientation of the Emitting Chromophore in a Multichromophoric System ,” J. Am. Chem. Soc.   126 , 14310 – 14311 ( 2004 ).
[Crossref] [PubMed]

D. Patra , I. Gregor , and J. Enderlein “ Image Analysis of Defocused Single-Molecule Images for Three-Dimensional Molecule Orientation Studies ,” J. Phys. Chem. A   108 , 6836 – 6841 ( 2004 ).
[Crossref]

M. Böhmer and J. Enderlein “ Orientation imaging of single molecules by wide-field epi-fluorescence microscopy ,” J. Opt. Soc. Am. B   20 , 554 – 559 ( 2003 ).
[Crossref]

J. Enderlein and M. Böhmer “ Fluorescence spectroscopy of single molecules under ambient conditions: Methodology and technology ,” Chem. Phys. Chem.   4 , 792 – 808 ( 2003 ).
[Crossref]

J. Enderlein , T. Ruckstuhl , and S. Seeger “ Highly Efficient Optical Detection of Surface-Generated Fluorescence ,” Appl. Opt.   38 , 724 – 732 ( 1999 ).
[Crossref]

J. Enderlein , I. Gregor , D. Patra , T. Dertinger , and B. Kaupp “ Performance of fluorescence correlation spectroscopy for measuring diffusion and concentration ,” Chem. Phys. Chem. ( 2005 ) in press.

Goodwin, P.M.

P.M. Goodwin , W.P. Ambrose , and R.A. Keller “ Single-molecule detection in liquids by laser-induced fluorescence ,” Acc. Chem. Res.   29 , 607 – 613 ( 1996 ).
[Crossref]

Gregor, I.

D. Patra , I. Gregor , and J. Enderlein “ Image Analysis of Defocused Single-Molecule Images for Three-Dimensional Molecule Orientation Studies ,” J. Phys. Chem. A   108 , 6836 – 6841 ( 2004 ).
[Crossref]

J. Enderlein , I. Gregor , D. Patra , T. Dertinger , and B. Kaupp “ Performance of fluorescence correlation spectroscopy for measuring diffusion and concentration ,” Chem. Phys. Chem. ( 2005 ) in press.

Gu, M.

Habuchi, S.

W. Schroeyers , R. Vallee , D. Patra , J. Hofkens , S. Habuchi , T. Vosch , M. Cotlet , K. Müllen , J. Enderlein , and F.C. De Schryver “ Fluorescence Lifetimes and Emission Patterns Probe the 3D Orientation of the Emitting Chromophore in a Multichromophoric System ,” J. Am. Chem. Soc.   126 , 14310 – 14311 ( 2004 ).
[Crossref] [PubMed]

Hell, S.W.

Hofkens, J.

W. Schroeyers , R. Vallee , D. Patra , J. Hofkens , S. Habuchi , T. Vosch , M. Cotlet , K. Müllen , J. Enderlein , and F.C. De Schryver “ Fluorescence Lifetimes and Emission Patterns Probe the 3D Orientation of the Emitting Chromophore in a Multichromophoric System ,” J. Am. Chem. Soc.   126 , 14310 – 14311 ( 2004 ).
[Crossref] [PubMed]

Juškaitis, R.

R. Juškaitis “ Characterizing High Numerical Aperture Microscope Objective Lenses ” in: Optical Imaging and Microscopy , Eds.: P. Török and F.-J. Kao ( Springer , 2003 ) pp. 21 – 43 .

Kaupp, B.

J. Enderlein , I. Gregor , D. Patra , T. Dertinger , and B. Kaupp “ Performance of fluorescence correlation spectroscopy for measuring diffusion and concentration ,” Chem. Phys. Chem. ( 2005 ) in press.

Kawata, S.

Kawata, Y.

Keller, R.A.

P.M. Goodwin , W.P. Ambrose , and R.A. Keller “ Single-molecule detection in liquids by laser-induced fluorescence ,” Acc. Chem. Res.   29 , 607 – 613 ( 1996 ).
[Crossref]

Klar, T.A.

Lehmann, W.

W. Lehmann and A. Wachtel “ Numerical apertures of light microscope objectives ,” J. Microsc.   169 , 89 – 90 ( 1993 ).
[Crossref]

Lukosz, W.

Maia, Neto P.A.

Neto P.A. Maia and H.M. Nussenzveig “ Theory of optical tweezers ” Europhys. Lett.   50 , 702 – 708 ( 2000 ).
[Crossref]

Müllen, K.

W. Schroeyers , R. Vallee , D. Patra , J. Hofkens , S. Habuchi , T. Vosch , M. Cotlet , K. Müllen , J. Enderlein , and F.C. De Schryver “ Fluorescence Lifetimes and Emission Patterns Probe the 3D Orientation of the Emitting Chromophore in a Multichromophoric System ,” J. Am. Chem. Soc.   126 , 14310 – 14311 ( 2004 ).
[Crossref] [PubMed]

Müller, M.

Neuman, K.C.

K.C. Neuman and S.M. Block “ Optical Trapping ,” Rev. Sci. Instrum.   75 , 2787 – 809 ( 2004 ).
[Crossref]

Nussenzveig, H.M.

Neto P.A. Maia and H.M. Nussenzveig “ Theory of optical tweezers ” Europhys. Lett.   50 , 702 – 708 ( 2000 ).
[Crossref]

Patra, D.

W. Schroeyers , R. Vallee , D. Patra , J. Hofkens , S. Habuchi , T. Vosch , M. Cotlet , K. Müllen , J. Enderlein , and F.C. De Schryver “ Fluorescence Lifetimes and Emission Patterns Probe the 3D Orientation of the Emitting Chromophore in a Multichromophoric System ,” J. Am. Chem. Soc.   126 , 14310 – 14311 ( 2004 ).
[Crossref] [PubMed]

D. Patra , I. Gregor , and J. Enderlein “ Image Analysis of Defocused Single-Molecule Images for Three-Dimensional Molecule Orientation Studies ,” J. Phys. Chem. A   108 , 6836 – 6841 ( 2004 ).
[Crossref]

J. Enderlein , I. Gregor , D. Patra , T. Dertinger , and B. Kaupp “ Performance of fluorescence correlation spectroscopy for measuring diffusion and concentration ,” Chem. Phys. Chem. ( 2005 ) in press.

Piston, D.W.

Rigler, R.

R. Rigler and J. Widengren “ Ultrasensitive Detection of single molecules by fluorescence correlation spectroscopy ,” Bioscience   3 , 180 – 183 ( 1990 ).

Ruckstuhl, T.

Sandison, D.R.

Schönle, A.

Schroeyers, W.

W. Schroeyers , R. Vallee , D. Patra , J. Hofkens , S. Habuchi , T. Vosch , M. Cotlet , K. Müllen , J. Enderlein , and F.C. De Schryver “ Fluorescence Lifetimes and Emission Patterns Probe the 3D Orientation of the Emitting Chromophore in a Multichromophoric System ,” J. Am. Chem. Soc.   126 , 14310 – 14311 ( 2004 ).
[Crossref] [PubMed]

Schwille, P.

P. Schwille “ Fluorescene correlation spectroscopy and its potential for intracellular applications ,” Cell Biochem. Biophys.   34 , 383 – 408 ( 2001 ).
[Crossref]

Seeger, S.

Sheppard, C.J.R.

Stelzer, H.K.

Vallee, R.

W. Schroeyers , R. Vallee , D. Patra , J. Hofkens , S. Habuchi , T. Vosch , M. Cotlet , K. Müllen , J. Enderlein , and F.C. De Schryver “ Fluorescence Lifetimes and Emission Patterns Probe the 3D Orientation of the Emitting Chromophore in a Multichromophoric System ,” J. Am. Chem. Soc.   126 , 14310 – 14311 ( 2004 ).
[Crossref] [PubMed]

Vosch, T.

W. Schroeyers , R. Vallee , D. Patra , J. Hofkens , S. Habuchi , T. Vosch , M. Cotlet , K. Müllen , J. Enderlein , and F.C. De Schryver “ Fluorescence Lifetimes and Emission Patterns Probe the 3D Orientation of the Emitting Chromophore in a Multichromophoric System ,” J. Am. Chem. Soc.   126 , 14310 – 14311 ( 2004 ).
[Crossref] [PubMed]

Wachtel, A.

W. Lehmann and A. Wachtel “ Numerical apertures of light microscope objectives ,” J. Microsc.   169 , 89 – 90 ( 1993 ).
[Crossref]

Webb, W.W.

Widengren, J.

R. Rigler and J. Widengren “ Ultrasensitive Detection of single molecules by fluorescence correlation spectroscopy ,” Bioscience   3 , 180 – 183 ( 1990 ).

Williams, R.M.

Acc. Chem. Res. (1)

P.M. Goodwin , W.P. Ambrose , and R.A. Keller “ Single-molecule detection in liquids by laser-induced fluorescence ,” Acc. Chem. Res.   29 , 607 – 613 ( 1996 ).
[Crossref]

Appl. Opt. (2)

Biol. Bull. (1)

D.W. Piston “ Choosing objective lenses; The importance of numerical aperture and magnification ,” Biol. Bull.   195 , 1 – 4 ( 1998 ).
[Crossref] [PubMed]

Bioscience (1)

R. Rigler and J. Widengren “ Ultrasensitive Detection of single molecules by fluorescence correlation spectroscopy ,” Bioscience   3 , 180 – 183 ( 1990 ).

Cell Biochem. Biophys. (1)

P. Schwille “ Fluorescene correlation spectroscopy and its potential for intracellular applications ,” Cell Biochem. Biophys.   34 , 383 – 408 ( 2001 ).
[Crossref]

Chem. Phys. Chem. (1)

J. Enderlein and M. Böhmer “ Fluorescence spectroscopy of single molecules under ambient conditions: Methodology and technology ,” Chem. Phys. Chem.   4 , 792 – 808 ( 2003 ).
[Crossref]

Europhys. Lett. (1)

Neto P.A. Maia and H.M. Nussenzveig “ Theory of optical tweezers ” Europhys. Lett.   50 , 702 – 708 ( 2000 ).
[Crossref]

J. Am. Chem. Soc. (1)

W. Schroeyers , R. Vallee , D. Patra , J. Hofkens , S. Habuchi , T. Vosch , M. Cotlet , K. Müllen , J. Enderlein , and F.C. De Schryver “ Fluorescence Lifetimes and Emission Patterns Probe the 3D Orientation of the Emitting Chromophore in a Multichromophoric System ,” J. Am. Chem. Soc.   126 , 14310 – 14311 ( 2004 ).
[Crossref] [PubMed]

J. Microsc. (1)

W. Lehmann and A. Wachtel “ Numerical apertures of light microscope objectives ,” J. Microsc.   169 , 89 – 90 ( 1993 ).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

J. Opt. Soc. Am. B (1)

J. Phys. Chem. A (1)

D. Patra , I. Gregor , and J. Enderlein “ Image Analysis of Defocused Single-Molecule Images for Three-Dimensional Molecule Orientation Studies ,” J. Phys. Chem. A   108 , 6836 – 6841 ( 2004 ).
[Crossref]

Opt. Lett. (2)

Proc. Nat. Acad. Sci. (1)

A. Ashkin “ Optical Trapping And Manipulation Of Neutral Particles Using Lasers ,” Proc. Nat. Acad. Sci.   94 , 4853 – 4860 ( 1997 ).
[Crossref] [PubMed]

Rev. Sci. Instrum. (1)

K.C. Neuman and S.M. Block “ Optical Trapping ,” Rev. Sci. Instrum.   75 , 2787 – 809 ( 2004 ).
[Crossref]

Other (2)

R. Juškaitis “ Characterizing High Numerical Aperture Microscope Objective Lenses ” in: Optical Imaging and Microscopy , Eds.: P. Török and F.-J. Kao ( Springer , 2003 ) pp. 21 – 43 .

J. Enderlein , I. Gregor , D. Patra , T. Dertinger , and B. Kaupp “ Performance of fluorescence correlation spectroscopy for measuring diffusion and concentration ,” Chem. Phys. Chem. ( 2005 ) in press.

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Figures (3)

Fig. 1.
Fig. 1.

(a) Angular distribution of emission into glass for isotropically oriented molecules in glass at an air/glass interface when excited by light circularly polarized within the plane of the interface. Emission maximum occurs at the angle of total internal reflection (TIR), indicated by light-red lines. (b) Intensity distribution of fluorescence within the back focal plane of an objective as a function of the distance ρ from the optical axis divided by the focal distance f of the objective. The vertical light-red lines show the position of TIR.

Fig. 2.
Fig. 2.

Principal scheme of the experimental set-up used for imaging the intensity distribution of fluorescence in the back focal plane of the objective. The imaging lens images the back focal plane of the objective onto the CCD camera. In the realized experimental set-up, this imaging was achieved by using the microscope’s tube lens (not shown) plus and additional lens.

Fig. 3.
Fig. 3.

(a) Measured intensity distribution in the back focal plane for the Olympus UApo/340 40× objective with nominal NA of 1.15. The barely visible black circle at the edge of the illuminated area is the determined out NA-determined cut-off of fluorescence collection, the cyan circle marks the position of the fluorescence discontinuity at the TIR-angle. (b) Same as Fig. 3(a), but for the Olympus PlanApo 60× objective with nominal NA of 1.4.

Equations (3)

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θ TIR = asin ( n 0 n ) ,
ρ = f n sin θ
NA = ρ max ρ TIR

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