Abstract

In recent years, new optical systems have been developed with the ability to collect light at very high angles of emission, exceeding the critical angle of total internal reflection. Prominent examples are solid-immersion lenses and paraboloid collectors. These systems achieve high efficiencies in fluorescence detection which is an important issue for sensitive applications in analytical chemistry and biochemical assays. The exclusive collection of supercritical angle fluorescence (SAF) allows for the detection of evanescent modes and thus to confine the detection volume within one wavelength to an interface. For conventional optical systems with high numerical aperture a precise wave-optical theory of imaging was developed by Richards and Wolf in the fifties of the last century. However, their theory is not directly applicable to non-imaging, strongly aberratic light collection systems systems that collect a significant part of light above the critical angle. Here, we extend the theory to describe the optical properties of such systems.

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  17. T. Ruckstuhl and D. Verdes, “Supercritical angle fluorescence (SAF) microscopy,” Opt. Express 12, 4246–4254 (2004).
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  19. M. Bhmer and J. Enderlein, “Orientation imaging of single molecules by wide-field epifluorescence microscopy,” J. Opt. Soc. Am. B 20, 554–559 (2003).
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2008

2006

2005

2004

2003

2000

T. Ruckstuhl, J. Enderlein, S. Jung, and S. Seeger, “Forbidden light detection from single molecules,” Anal. Chem. 72, 2117–2123 (2000).
[CrossRef] [PubMed]

1998

P. Török, P. D. Higdon, and T. Wilson, “On the general properties of polarised light conventional and confocal microscopes,” Opt. Commun. 148, 300–315 (1998).
[CrossRef]

1990

S. M. Mansfield and G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. 57, 2615–2616 (1990).
[CrossRef]

1979

1977

1959

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. Roy. Soc. London A 253, 358–379 (1959).
[CrossRef]

E. Wolf, “Electromagnetic diffraction in optical systems I. An integral representation of the image field,” Proc. Roy. Soc. London A 253349–357 (1959).
[CrossRef]

1947

F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Physik 436, 333–346 (1947).
[CrossRef]

Bhmer, M.

Born, M.

M. Born and E. Wolf, Principles of Optics , 6th ed. (Pergamon Press, 1987).

Enderlein, J.

Foreman, M.

Goos, F.

F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Physik 436, 333–346 (1947).
[CrossRef]

Hänchen, H.

F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Physik 436, 333–346 (1947).
[CrossRef]

Higdon, P. D.

P. Török, P. D. Higdon, and T. Wilson, “On the general properties of polarised light conventional and confocal microscopes,” Opt. Commun. 148, 300–315 (1998).
[CrossRef]

Jung, S.

T. Ruckstuhl, J. Enderlein, S. Jung, and S. Seeger, “Forbidden light detection from single molecules,” Anal. Chem. 72, 2117–2123 (2000).
[CrossRef] [PubMed]

Kino, G. S.

S. M. Mansfield and G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. 57, 2615–2616 (1990).
[CrossRef]

Kriezis, E. E.

Kunz, R. E.

Landau, L. D.

E. M. Lifshitz, L. D. Landau, and L. P. Pitaevskii, Electrodynamics of Continuous Media: 8 (Course of Theoretical Physics) (Butterworth Heinemann, 1984), Chap. X.

Lasser, T.

Leitgeb, R.

Leutenegger, M.

Lifshitz, E. M.

E. M. Lifshitz, L. D. Landau, and L. P. Pitaevskii, Electrodynamics of Continuous Media: 8 (Course of Theoretical Physics) (Butterworth Heinemann, 1984), Chap. X.

Lukosz, W.

Mansfield, S. M.

S. M. Mansfield and G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. 57, 2615–2616 (1990).
[CrossRef]

Matthew, R.

Munro, P. R.

Munro, P. R. T.

Pitaevskii, L. P.

E. M. Lifshitz, L. D. Landau, and L. P. Pitaevskii, Electrodynamics of Continuous Media: 8 (Course of Theoretical Physics) (Butterworth Heinemann, 1984), Chap. X.

Rao, R.

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. Roy. Soc. London A 253, 358–379 (1959).
[CrossRef]

Ries, J.

J. Ries, T. Ruckstuhl, D. Verdes, and P. Schwille, “Supercritical angle fluorescence correlation spectroscopy,” Biophys. J. 94, 221–229 (2008).
[CrossRef]

Ruckstuhl, T.

Schwille, P.

J. Ries, T. Ruckstuhl, D. Verdes, and P. Schwille, “Supercritical angle fluorescence correlation spectroscopy,” Biophys. J. 94, 221–229 (2008).
[CrossRef]

Seeger, S.

T. Ruckstuhl and S. Seeger, “Confocal total-internal-reflection fluorescence microscopy with a high-aperture parabolic mirror lens,” Appl. Opt. 42, 3277–3283 (2003).
[CrossRef] [PubMed]

T. Ruckstuhl, J. Enderlein, S. Jung, and S. Seeger, “Forbidden light detection from single molecules,” Anal. Chem. 72, 2117–2123 (2000).
[CrossRef] [PubMed]

Sherif, S.

Török, P.

Verdes, D.

J. Ries, T. Ruckstuhl, D. Verdes, and P. Schwille, “Supercritical angle fluorescence correlation spectroscopy,” Biophys. J. 94, 221–229 (2008).
[CrossRef]

T. Ruckstuhl and D. Verdes, “Supercritical angle fluorescence (SAF) microscopy,” Opt. Express 12, 4246–4254 (2004).
[CrossRef] [PubMed]

Wilson, T.

P. Török, P. D. Higdon, and T. Wilson, “On the general properties of polarised light conventional and confocal microscopes,” Opt. Commun. 148, 300–315 (1998).
[CrossRef]

Wolf, E.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. Roy. Soc. London A 253, 358–379 (1959).
[CrossRef]

E. Wolf, “Electromagnetic diffraction in optical systems I. An integral representation of the image field,” Proc. Roy. Soc. London A 253349–357 (1959).
[CrossRef]

M. Born and E. Wolf, Principles of Optics , 6th ed. (Pergamon Press, 1987).

Anal. Chem.

T. Ruckstuhl, J. Enderlein, S. Jung, and S. Seeger, “Forbidden light detection from single molecules,” Anal. Chem. 72, 2117–2123 (2000).
[CrossRef] [PubMed]

Ann. Physik

F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Physik 436, 333–346 (1947).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

S. M. Mansfield and G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. 57, 2615–2616 (1990).
[CrossRef]

Biophys. J.

J. Ries, T. Ruckstuhl, D. Verdes, and P. Schwille, “Supercritical angle fluorescence correlation spectroscopy,” Biophys. J. 94, 221–229 (2008).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Opt. Commun.

P. Török, P. D. Higdon, and T. Wilson, “On the general properties of polarised light conventional and confocal microscopes,” Opt. Commun. 148, 300–315 (1998).
[CrossRef]

Opt. Express

Proc. Roy. Soc. London A

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. Roy. Soc. London A 253, 358–379 (1959).
[CrossRef]

E. Wolf, “Electromagnetic diffraction in optical systems I. An integral representation of the image field,” Proc. Roy. Soc. London A 253349–357 (1959).
[CrossRef]

Other

M. Born and E. Wolf, Principles of Optics , 6th ed. (Pergamon Press, 1987).

E. M. Lifshitz, L. D. Landau, and L. P. Pitaevskii, Electrodynamics of Continuous Media: 8 (Course of Theoretical Physics) (Butterworth Heinemann, 1984), Chap. X.

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Figures (7)

Fig. 1
Fig. 1

Geometry of the emission of an electric dipole close to an interface: a single dipole emitter with an inclination angle β is placed at a distance h away from a glass surface. The angular distribution of radiation into the glass is depicted by the red solid line and is a function of angles θ and ϕ. Shown is a cross section of this function in a plane containing the optical axis (vertical) and the dipole axis. The critical TIR angle θcr between glass and air is also indicated by straight lines. It is important to realize that for plane wave modes above the TIR angle in the bottom medium, there are no corresponding propagating plane wave modes in the upper medium.

Fig. 2
Fig. 2

Function z 0(θ) for a parallel (red line) and a vertically (blue line) oriented dipole on an air/glass interface. Vertical green line indicates the position of the TIR angle, where z 0(θ) diverges towards infinity. Notice that even in the limit θ → 90°, z 0 does not approach zero: the dipole seems to hover over the surface at a finite distance. This shift is a similar effect as the virtual lateral shift of the reflection point of a light beam upon TIR, the so-called Goos-Hänchen effect [16]. It should be noted that this figure will not change when moving the dipole away from the surface: For evanescent modes, the exponents in Eqs. (2) through (4) become real-valued, and the phase Φ(θ), see Eq. (6), becomes independent on the dipole’s position above the surface.

Fig. 3
Fig. 3

Schematic of the parabolic light collection system.

Fig. 4
Fig. 4

Images of a dipole emitter on glass for SAF collection. Shown are results for three dipole orientations along the horizontal figure axis (top row), vertical figure axis (middle row), and an orientation perpendicular to the figure plane (along the optical axis, bottom row). From left to right, the images show six different lateral dipole positions, from x 0 = 0 till x 0 = 5 in steps of one. Each of the 18 images has an edge length of 300.

Fig. 5
Fig. 5

Same as Fig. 4 but for “classical” light collection below the TIR angle.

Fig. 6
Fig. 6

Same as Fig. 7 but for ”classical” light collection below the TIR angle.

Fig. 7
Fig. 7

Images of a dipole emitter on glass for SAF collection. Shown are results for two dipole orientations along the horizontal figure axis (top row), and for an orientation perpendicular to the figure plane (along the optical axis, bottom row). From left to right, the images show six different positions of the image plane away from the focal plane of the focusing lens, from z = 0 till z = −40 in steps of 8. As before, each of the 12 images has an edge length of 300.

Equations (11)

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E ( θ , ϕ ) = sin β [ t s E s ( θ ) sin ϕ + t p E p ( θ ) cos ϕ ] + t p cos β E p ( θ ) ,
E p ( θ ) = n g w g w m q n m T p exp ( i w m h ) ,
E p ( θ ) = n g w g n m T p exp ( i w m h ) ,
E s ( θ ) = n g w g w m T s exp ( i w m h ) ,
t s = κ × e z | κ × e z | , t p = t s × κ ,
ϕ ( θ ) = arctan [ | E | | E | ] ,
exp [ i k 0 n g ( z cos θ + ρ sin θ ) + i ϕ ( θ ) ] .
k 0 n g ( z sin θ + ρ cos θ ) + ϕ ( θ ) = 0 ,
z 0 ( θ ) = ϕ ( θ ) k 0 n g sin θ .
r 0 = ( z 0 tan θ cos ϕ + ρ 0 cos ϕ 0 , z 0 tan θ sin ϕ + ρ 0 sin ϕ 0 , 0 ) ,
ψ 0 = k 0 n g z 0 sin 2 θ cos θ + ϕ ( θ ) ,

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