Abstract

We theoretically investigate the use of spatial light modulators (SLMs) for transformation of the collected fluorescence field in a high numerical aperture confocal microscope, for improved molecular orientation determination in single-molecule spectroscopy. The electric vector field in the back aperture of the microscope objective is calculated using the Weyl representation and taking into account components emitted at angles above the critical angle of the coverglass-immersion fluid interface. The coherently imaged fluorescence undergoes spatially-dependent phase and polarization transformation by the SLMs, before it passes to a polarization beamsplitter, and is subsequently focused onto two pinholes and single-photon detectors.

© 2008 Optical Society of America

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References

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  1. D. Axelrod, "Total internal reflection fluorescence microscopy," in Methods in Cell Biology (Academic Press, 1989), Vol. 30, Chap. 9.
  2. D. Axelrod and E. D. Hellen, "Emission of fluorescence at an interface," in Methods in Cell Biology (Academic Press, 1989), Vol. 30, Chap. 15.
  3. B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system," Proc. Roy. Soc. A. 253, 358-379 (1959).
    [CrossRef]
  4. K. S. Youngworth and T. G. Brown, "Focusing of high numerical aperture cylindrical-vector beams," Opt. Express 7, 77-87 (2000).
    [CrossRef] [PubMed]
  5. S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, "Focusing light to a tighter spot," Opt. Commun. 179, 1-7 (2000).
    [CrossRef]
  6. L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, "Longitudinal field modes probed by single molecules," Phys. Rev. Lett. 86, 5251-5254 (2001).
    [CrossRef] [PubMed]
  7. M. Stalder and M. Schadt, "Linearly polarized light with axial symmetry generated by liquid-crystal polarization converters," Opt. Lett. 21, 1948-1950 (1996).
    [CrossRef] [PubMed]
  8. M. Hashimoto, K. Yamada, and T. Araki, "Proposition of single molecular orientation determination using polarization controlled beam by liquid crystal spatial light modulators," Opt. Rev. 12, 37-41 (2005).
    [CrossRef]
  9. A. P. Bartko and R. M. Dickson, "Imaging three-dimensional single molecule orientations," J. Phys. Chem. B 103, 11237-11241 (1999).
    [CrossRef]
  10. M. Bohmer and J. Enderlein, "Orientation imaging of single molecules by wide-field epifluorescence microscopy,"J. Opt. Soc. Am. B 20, 554-559 (2003).
    [CrossRef]
  11. M. A. Lieb, J. M. Zavislan, and L. Novotny, "Single-molecule orientations determined by direct emission pattern imaging," J. Opt. Soc. Am. B 21, 1210-1215 (2004).
    [CrossRef]
  12. J. Enderlein, T. Ruckstuhl, and S. Seeger, "Highly efficient optical detection of surface-generated fluorescence," Appl. Opt. 38, 724-732 (1999).
    [CrossRef]
  13. E. Hecht, Optics (Addison-Wesley, Reading, MA, 1990).
  14. M. Leutenegger, R. Rao, R. A. Leitgeb, and T. Lasser, "Fast focus field calculations," Opt. Express 14, 11277-11291 (2006).
    [CrossRef] [PubMed]

2006 (1)

2005 (1)

M. Hashimoto, K. Yamada, and T. Araki, "Proposition of single molecular orientation determination using polarization controlled beam by liquid crystal spatial light modulators," Opt. Rev. 12, 37-41 (2005).
[CrossRef]

2004 (1)

2003 (1)

2001 (1)

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, "Longitudinal field modes probed by single molecules," Phys. Rev. Lett. 86, 5251-5254 (2001).
[CrossRef] [PubMed]

2000 (2)

K. S. Youngworth and T. G. Brown, "Focusing of high numerical aperture cylindrical-vector beams," Opt. Express 7, 77-87 (2000).
[CrossRef] [PubMed]

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, "Focusing light to a tighter spot," Opt. Commun. 179, 1-7 (2000).
[CrossRef]

1999 (2)

A. P. Bartko and R. M. Dickson, "Imaging three-dimensional single molecule orientations," J. Phys. Chem. B 103, 11237-11241 (1999).
[CrossRef]

J. Enderlein, T. Ruckstuhl, and S. Seeger, "Highly efficient optical detection of surface-generated fluorescence," Appl. Opt. 38, 724-732 (1999).
[CrossRef]

1996 (1)

1959 (1)

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

Araki, T.

M. Hashimoto, K. Yamada, and T. Araki, "Proposition of single molecular orientation determination using polarization controlled beam by liquid crystal spatial light modulators," Opt. Rev. 12, 37-41 (2005).
[CrossRef]

Bartko, A. P.

A. P. Bartko and R. M. Dickson, "Imaging three-dimensional single molecule orientations," J. Phys. Chem. B 103, 11237-11241 (1999).
[CrossRef]

Beversluis, M. R.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, "Longitudinal field modes probed by single molecules," Phys. Rev. Lett. 86, 5251-5254 (2001).
[CrossRef] [PubMed]

Bohmer, M.

Brown, T. G.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, "Longitudinal field modes probed by single molecules," Phys. Rev. Lett. 86, 5251-5254 (2001).
[CrossRef] [PubMed]

K. S. Youngworth and T. G. Brown, "Focusing of high numerical aperture cylindrical-vector beams," Opt. Express 7, 77-87 (2000).
[CrossRef] [PubMed]

Dickson, R. M.

A. P. Bartko and R. M. Dickson, "Imaging three-dimensional single molecule orientations," J. Phys. Chem. B 103, 11237-11241 (1999).
[CrossRef]

Dorn, R.

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, "Focusing light to a tighter spot," Opt. Commun. 179, 1-7 (2000).
[CrossRef]

Eberler, M.

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, "Focusing light to a tighter spot," Opt. Commun. 179, 1-7 (2000).
[CrossRef]

Enderlein, J.

Glockl, O.

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, "Focusing light to a tighter spot," Opt. Commun. 179, 1-7 (2000).
[CrossRef]

Hashimoto, M.

M. Hashimoto, K. Yamada, and T. Araki, "Proposition of single molecular orientation determination using polarization controlled beam by liquid crystal spatial light modulators," Opt. Rev. 12, 37-41 (2005).
[CrossRef]

Lasser, T.

Leitgeb, R. A.

Leuchs, G.

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, "Focusing light to a tighter spot," Opt. Commun. 179, 1-7 (2000).
[CrossRef]

Leutenegger, M.

Lieb, M. A.

Novotny, L.

M. A. Lieb, J. M. Zavislan, and L. Novotny, "Single-molecule orientations determined by direct emission pattern imaging," J. Opt. Soc. Am. B 21, 1210-1215 (2004).
[CrossRef]

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, "Longitudinal field modes probed by single molecules," Phys. Rev. Lett. 86, 5251-5254 (2001).
[CrossRef] [PubMed]

Quabis, S.

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, "Focusing light to a tighter spot," Opt. Commun. 179, 1-7 (2000).
[CrossRef]

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. A. 253, 358-379 (1959).
[CrossRef]

Ruckstuhl, T.

Schadt, M.

Seeger, S.

Stalder, M.

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. A. 253, 358-379 (1959).
[CrossRef]

Yamada, K.

M. Hashimoto, K. Yamada, and T. Araki, "Proposition of single molecular orientation determination using polarization controlled beam by liquid crystal spatial light modulators," Opt. Rev. 12, 37-41 (2005).
[CrossRef]

Youngworth, K. S.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, "Longitudinal field modes probed by single molecules," Phys. Rev. Lett. 86, 5251-5254 (2001).
[CrossRef] [PubMed]

K. S. Youngworth and T. G. Brown, "Focusing of high numerical aperture cylindrical-vector beams," Opt. Express 7, 77-87 (2000).
[CrossRef] [PubMed]

Zavislan, J. M.

Appl. Opt. (1)

J. Opt. Soc. Am. B (2)

J. Phys. Chem. B (1)

A. P. Bartko and R. M. Dickson, "Imaging three-dimensional single molecule orientations," J. Phys. Chem. B 103, 11237-11241 (1999).
[CrossRef]

Opt. Commun. (1)

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, "Focusing light to a tighter spot," Opt. Commun. 179, 1-7 (2000).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Opt. Rev. (1)

M. Hashimoto, K. Yamada, and T. Araki, "Proposition of single molecular orientation determination using polarization controlled beam by liquid crystal spatial light modulators," Opt. Rev. 12, 37-41 (2005).
[CrossRef]

Phys. Rev. Lett. (1)

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, "Longitudinal field modes probed by single molecules," Phys. Rev. Lett. 86, 5251-5254 (2001).
[CrossRef] [PubMed]

Proc. Roy. Soc. A. (1)

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

Other (3)

D. Axelrod, "Total internal reflection fluorescence microscopy," in Methods in Cell Biology (Academic Press, 1989), Vol. 30, Chap. 9.

D. Axelrod and E. D. Hellen, "Emission of fluorescence at an interface," in Methods in Cell Biology (Academic Press, 1989), Vol. 30, Chap. 15.

E. Hecht, Optics (Addison-Wesley, Reading, MA, 1990).

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Figures (9)

Fig. 1.
Fig. 1.

(a). The field collected from a laterally-oriented dipole by a low-NA lens is linearly polarized in the direction of the dipole, (b) The field collected from a longitudinally-oriented dipole by a high-NA lens is radially polarized, (c) A plot of the field amplitude versus emission direction from a lateral or longitudinal-oriented dipole close to an interface (e.g., microscope coverglass). The amplitude of the field is greatest at angles close to the critical angle.

Fig. 2.
Fig. 2.

Implementation of polarization engineering for determining single-molecule orientation. P single-molecule dipole, COG coverglass, OBJ microscope objective with high-NA, PBS1 and PBS2 polarizing beam splitters, PBC polarizing beam combiner, MIR mirror, RET spatial light modulator phase retarder, ROT spatial light modulator linear polarization rotator.

Fig. 3.
Fig. 3.

The coordinate system used to describe emission from a dipole P located within refractive index ni just above the coverglass (COG), with refractive index n, and oriented with polar and azimuthal angles Θ, Φ. The diagram considers the optical field that is emitted into the COG substrate along a ray in a direction with polar (with respect to −z-axis) and azimuthal angles θ, ϕ. The angle θi is given by Snell’s law as sin-1((n/ni )sinθ) and will be imaginary for θ greater than the critical angle θcr = sin-1(ni /n). The field is redirected by the aplanatic objective (OBJ) to a point η,ξ in the back aperture (BA) of the objective. It is comprised of components along the unit vectors êp and ês , which are parallel and perpendicular to the plane of incidence of the ray, respectively. From here, the polarization and phase of the field may be altered before it is focused by a lens (LENS) to a detector (DET).

Fig. 4.
Fig. 4.

Theoretical predictions for the field in the back aperture of the objective from a dipole with (a) longitudinal orientation, Θ=0, (b) horizontal orientation, Θ=90°, Φ=0°: and (c) oblique orientation, Θ=30°, Φ=45°. The left column shows the electric field magnitude normalized to the peak value; the middle column shows the electric field polarization (righthanded elliptical polarization is magenta and left-handed is green); the right column shows ε, the phase difference between the η and ξ components of the electric field, modulo π.

Fig. 5.
Fig. 5.

Polarization engineered electric field in the back aperture for (a) targeted dipole orientation (TDO) and (b) and (c) other dipole orientations (right-handed elliptical polarization is magenta and left-handed is green) for the example when the TDO is Θ T = 30°, Φ T = 45°.

Fig. 6.
Fig. 6.

Dependence of the signal detected by (a) DET ξ and (b) DET η on the dipole orientation for the simple beamsplitting technique.

Fig. 7.
Fig. 7.

Dependence of the degree of polarization on the dipole orientation for the simple beamsplitting technique.

Fig. 8.
Fig. 8.

Dependence of the signal detected by (a) DET ξ and (b) DET η on the dipole orientation for the case of TDO with orientation Θ T = 30°, Φ T = 45°.

Fig. 9.
Fig. 9.

Dependence of the signed degree of polarization on the dipole orientation for the polarization engineering technique for the case of TDO with orientation Θ T = 30°, Φ T = 45°.

Equations (39)

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E ( ξ , η ) = E p e ̂ p + E s e ̂ s .
E p = c p ( ( n n i ) cos Θ sin θ + sin Θ cos θ cos ( ϕ Φ ) ) cos θ ,
E s = c s sin Θ sin ( ϕ Φ ) cos θ ,
c p = n cos θ n i cos θ i t p Π ( θ i ) ,
c s = n cos θ n i cos θ i t s Π ( θ i ) ,
Π ( θ i ) = exp ( i k i n i cos θ i δ ) ,
t p = 2 cos θ i sin θ sin ( θ i + θ ) cos ( θ i θ ) ,
t s = 2 cos θ i sin θ sin ( θ i + θ ) .
e ̂ p = cos ϕ e ̂ ξ + sin ϕ e ̂ η ,
e ̂ s = sin ϕ e ̂ ξ + cos ϕ e ̂ η ,
cos ϕ = ξ ξ 2 + η 2 , sin ϕ = η ξ 2 + η 2 .
θ = sin 1 ( ξ 2 + η 2 f ) ,
E ( ξ , η ) = E ξ ( ξ , η ) e i φ ξ ( ξ , η ) e ̂ ξ + E η ( ξ , η ) e i φ η ( ξ , η ) e ̂ η ,
ε ( ξ , η ) = mod φ η ( ξ , η ) φ ξ ( ξ , η ) , π .
φ η TDO ( ξ , η ) = mod φ η TDO ( ξ , η ) ε ( ξ , η ) , π .
φ η ODO ( ξ , η ) = φ η ODO ( ξ , η ) + φ η TDO ( ξ , η ) φ ξ TDO ( ξ , η ) .
E ( ξ , η ) = E ξ ( ξ , η ) e i φ ξ ( ξ , η ) e ̂ ξ + E η ( ξ , η ) e i φ η ( ξ , η ) e ̂ η .
E TDO ( ξ , η ) = [ E ξ TDO E η TDO ] = R φ rot [ E ξ TDO E η TDO ] ,
R φ rot = [ cos φ rot sin φ rot sin φ rot cos φ rot ] ,
φ rot ( ξ , η ) = a tan ( E η TDO E ξ TDO ) + { 2 π cos ( φ ξ ) > 0 and cos ( φ η ) > 0 π for cos ( φ ξ ) < 0 0 cos ( φ ξ ) > 0 and cos ( φ η ) < 0 .
E ( ξ , η ) = E ξ ( ξ , η ) e i φ ξ ( ξ , η ) e ̂ ξ + E η ( ξ , η ) e i φ η ( ξ , η ) e ̂ η .
E p DET ξ ( ξ , η ) = E ξ ( ξ , η ) cos φ ps , ξ η ,
E s DET ξ ( ξ , η ) = E ξ ( ξ , η ) sin φ ps , ξ η ,
E p DET η ( ξ , η ) = E η ( ξ , η ) sin φ ps , ξ η ,
E s DET η ( ξ , η ) = E η ( ξ , η ) cos φ ps , ξ η ,
E t ξ DET ξ ( ξ , η ) = E p DET ξ ( ξ , η ) cos φ ps , ξ η cos θ t E s DET ξ ( ξ , η ) sin φ ps , ξ η ,
E DET ξ ( ξ , η ) = E p DET ξ ( ξ , η ) sin φ ps , ξ η cos θ t + E s DET ξ ( ξ , η ) cos φ ps , ξ η ,
E t ξ DET η ( ξ , η ) = E p DET η ( ξ , η ) cos φ ps , ξ η cos θ t E s DET η ( ξ , η ) sin φ ps , ξ η ,
E DET η ( ξ , η ) = E p DET η ( ξ , η ) sin φ ps , ξ η cos θ t + E s DET η ( ξ , η ) cos φ ps , ξ η .
E ( x , y ) = if λ 0 k t 2 1 cos θ t E t ( ξ , η ) exp [ i ( k x x + k y y ) ] d k x d k y ,
H ( x , y ) = if λ 0 k t 2 1 cos θ t H t ( ξ , η ) exp [ i ( k x x + k y y ) ] d k x d k y ,
S z ( x , y ) = 1 2 Re ( E x H y * E y * H x ) .
SDP ( Θ , Φ ) = P ξ P η P ξ + P η ,
P ξ ( Θ , Φ ) = 1 P n D ξ S ( x , y ; Θ , Φ Θ T , Φ T ) d σ ,
P η ( Θ , Φ ) = 1 P n D η S z η ( x , y ; Θ , Φ Θ T , Φ T ) d σ ,
P n = D ξ S z ξ ( x , y ; 0 , 0 ) d σ .
p ( Θ , Φ ) = ( P ξ ( Θ , Φ ) + B ξ ) ( P ξ ( Θ , Φ ) + P η ( Θ , Φ ) + B ξ + B η ) ,
Pr ( n ξ , n η | Θ , Φ ) = ( n ξ + n η ) ! n ξ ! n η ! p n ξ ( 1 p ) n η .
Pdf ( Θ , Φ ) sin Θ d Θ d Φ = Pr ( n ξ , n η Θ , Φ ) sin Θ d Θ d Φ Pr ( n ξ , n η Θ , Φ ) sin Θ d Θ d Φ .

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