Abstract

A simple method for real-time determination of the full three-dimensional orientation of the emission dipole of single molecules is presented. Introduction of a π phase step in the back focal plane of the collector lens breaks the inherent symmetry, allowing the longitudinal dipole component to be measured. Experimental tolerances and the consequence of a nonzero bandwidth emission spectrum are also discussed. The scheme also allows for the longitudinal component of an electric field to be found experimentally.

© 2008 Optical Society of America

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References

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  1. W. E. Moerner and D. P. Fromm, Rev. Sci. Instrum. 74, 3597 (2003).
    [CrossRef]
  2. S. Weiss, Nat. Struct. Biol. 7, 724 (2000).
    [CrossRef] [PubMed]
  3. T. Ha, T. Enderle, D. F. Ogletree, D. S. Chemla, P. R. Selvin, and S. Weiss, Proc. Natl. Acad. Sci. USA 93, 6264 (1996).
    [CrossRef] [PubMed]
  4. L. A. Deschenes and D. A. Van den Bout, Science 292, 233 (2001).
    [CrossRef]
  5. T. Ha, T. Enderle, D. S. Chemla, P. R. Selvin, and S. Weiss, Phys. Rev. Lett. 77, 3979 (1996).
    [CrossRef] [PubMed]
  6. T. M. Jovin, M. Bartholdi, W. L. C. Vaz, and R. H. Austin, Ann. N.Y. Acad. Sci. 366, 176 (1981).
    [CrossRef] [PubMed]
  7. B. Sick, B. Hecht, and L. Novotny, Phys. Rev. Lett. 85, 4482 (2000).
    [CrossRef] [PubMed]
  8. R. M. Dickson, D. J. Norris, and W. E. Moerner, Phys. Rev. Lett. 81, 5322 (1998).
    [CrossRef]
  9. D. Patra, I. Gregor, and J. Enderlein, J. Phys. Chem. A 108, 6836 (2004).
    [CrossRef]
  10. P. Török, Opt. Lett. 25, 1463 (2000).
    [CrossRef]
  11. P. Török, P. D. Higdon, and T. Wilson, J. Mod. Opt. 45, 1681 (1998).
    [CrossRef]
  12. D. J. Innes and A. L. Bloom, Spectra-Phys. Laser Tech. Bull. 5, 1 (1966).
  13. B. Richards and E. Wolf, Proc. R. Soc. London, Ser. A 253, 358 (1959).
    [CrossRef]
  14. M. R. Foreman, S. S. Sherif, and P. Török, Opt. Express 15, 13597 (2007).
    [CrossRef] [PubMed]
  15. H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).
  16. P. Török, P. D. Higdon, and T. Wilson, Opt. Commun. 148, 300 (1998).
    [CrossRef]

2007 (1)

2004 (1)

D. Patra, I. Gregor, and J. Enderlein, J. Phys. Chem. A 108, 6836 (2004).
[CrossRef]

2003 (1)

W. E. Moerner and D. P. Fromm, Rev. Sci. Instrum. 74, 3597 (2003).
[CrossRef]

2001 (1)

L. A. Deschenes and D. A. Van den Bout, Science 292, 233 (2001).
[CrossRef]

2000 (3)

S. Weiss, Nat. Struct. Biol. 7, 724 (2000).
[CrossRef] [PubMed]

B. Sick, B. Hecht, and L. Novotny, Phys. Rev. Lett. 85, 4482 (2000).
[CrossRef] [PubMed]

P. Török, Opt. Lett. 25, 1463 (2000).
[CrossRef]

1998 (3)

P. Török, P. D. Higdon, and T. Wilson, Opt. Commun. 148, 300 (1998).
[CrossRef]

R. M. Dickson, D. J. Norris, and W. E. Moerner, Phys. Rev. Lett. 81, 5322 (1998).
[CrossRef]

P. Török, P. D. Higdon, and T. Wilson, J. Mod. Opt. 45, 1681 (1998).
[CrossRef]

1996 (2)

T. Ha, T. Enderle, D. F. Ogletree, D. S. Chemla, P. R. Selvin, and S. Weiss, Proc. Natl. Acad. Sci. USA 93, 6264 (1996).
[CrossRef] [PubMed]

T. Ha, T. Enderle, D. S. Chemla, P. R. Selvin, and S. Weiss, Phys. Rev. Lett. 77, 3979 (1996).
[CrossRef] [PubMed]

1981 (1)

T. M. Jovin, M. Bartholdi, W. L. C. Vaz, and R. H. Austin, Ann. N.Y. Acad. Sci. 366, 176 (1981).
[CrossRef] [PubMed]

1966 (1)

D. J. Innes and A. L. Bloom, Spectra-Phys. Laser Tech. Bull. 5, 1 (1966).

1959 (1)

B. Richards and E. Wolf, Proc. R. Soc. London, Ser. A 253, 358 (1959).
[CrossRef]

Austin, R. H.

T. M. Jovin, M. Bartholdi, W. L. C. Vaz, and R. H. Austin, Ann. N.Y. Acad. Sci. 366, 176 (1981).
[CrossRef] [PubMed]

Bartholdi, M.

T. M. Jovin, M. Bartholdi, W. L. C. Vaz, and R. H. Austin, Ann. N.Y. Acad. Sci. 366, 176 (1981).
[CrossRef] [PubMed]

Bloom, A. L.

D. J. Innes and A. L. Bloom, Spectra-Phys. Laser Tech. Bull. 5, 1 (1966).

Chemla, D. S.

T. Ha, T. Enderle, D. S. Chemla, P. R. Selvin, and S. Weiss, Phys. Rev. Lett. 77, 3979 (1996).
[CrossRef] [PubMed]

T. Ha, T. Enderle, D. F. Ogletree, D. S. Chemla, P. R. Selvin, and S. Weiss, Proc. Natl. Acad. Sci. USA 93, 6264 (1996).
[CrossRef] [PubMed]

Deschenes, L. A.

L. A. Deschenes and D. A. Van den Bout, Science 292, 233 (2001).
[CrossRef]

Dickson, R. M.

R. M. Dickson, D. J. Norris, and W. E. Moerner, Phys. Rev. Lett. 81, 5322 (1998).
[CrossRef]

Enderle, T.

T. Ha, T. Enderle, D. S. Chemla, P. R. Selvin, and S. Weiss, Phys. Rev. Lett. 77, 3979 (1996).
[CrossRef] [PubMed]

T. Ha, T. Enderle, D. F. Ogletree, D. S. Chemla, P. R. Selvin, and S. Weiss, Proc. Natl. Acad. Sci. USA 93, 6264 (1996).
[CrossRef] [PubMed]

Enderlein, J.

D. Patra, I. Gregor, and J. Enderlein, J. Phys. Chem. A 108, 6836 (2004).
[CrossRef]

Foreman, M. R.

Fromm, D. P.

W. E. Moerner and D. P. Fromm, Rev. Sci. Instrum. 74, 3597 (2003).
[CrossRef]

Gregor, I.

D. Patra, I. Gregor, and J. Enderlein, J. Phys. Chem. A 108, 6836 (2004).
[CrossRef]

Ha, T.

T. Ha, T. Enderle, D. S. Chemla, P. R. Selvin, and S. Weiss, Phys. Rev. Lett. 77, 3979 (1996).
[CrossRef] [PubMed]

T. Ha, T. Enderle, D. F. Ogletree, D. S. Chemla, P. R. Selvin, and S. Weiss, Proc. Natl. Acad. Sci. USA 93, 6264 (1996).
[CrossRef] [PubMed]

Hecht, B.

B. Sick, B. Hecht, and L. Novotny, Phys. Rev. Lett. 85, 4482 (2000).
[CrossRef] [PubMed]

Higdon, P. D.

P. Török, P. D. Higdon, and T. Wilson, J. Mod. Opt. 45, 1681 (1998).
[CrossRef]

P. Török, P. D. Higdon, and T. Wilson, Opt. Commun. 148, 300 (1998).
[CrossRef]

Innes, D. J.

D. J. Innes and A. L. Bloom, Spectra-Phys. Laser Tech. Bull. 5, 1 (1966).

Jovin, T. M.

T. M. Jovin, M. Bartholdi, W. L. C. Vaz, and R. H. Austin, Ann. N.Y. Acad. Sci. 366, 176 (1981).
[CrossRef] [PubMed]

Moerner, W. E.

W. E. Moerner and D. P. Fromm, Rev. Sci. Instrum. 74, 3597 (2003).
[CrossRef]

R. M. Dickson, D. J. Norris, and W. E. Moerner, Phys. Rev. Lett. 81, 5322 (1998).
[CrossRef]

Norris, D. J.

R. M. Dickson, D. J. Norris, and W. E. Moerner, Phys. Rev. Lett. 81, 5322 (1998).
[CrossRef]

Novotny, L.

B. Sick, B. Hecht, and L. Novotny, Phys. Rev. Lett. 85, 4482 (2000).
[CrossRef] [PubMed]

Ogletree, D. F.

T. Ha, T. Enderle, D. F. Ogletree, D. S. Chemla, P. R. Selvin, and S. Weiss, Proc. Natl. Acad. Sci. USA 93, 6264 (1996).
[CrossRef] [PubMed]

Patra, D.

D. Patra, I. Gregor, and J. Enderlein, J. Phys. Chem. A 108, 6836 (2004).
[CrossRef]

Richards, B.

B. Richards and E. Wolf, Proc. R. Soc. London, Ser. A 253, 358 (1959).
[CrossRef]

Selvin, P. R.

T. Ha, T. Enderle, D. F. Ogletree, D. S. Chemla, P. R. Selvin, and S. Weiss, Proc. Natl. Acad. Sci. USA 93, 6264 (1996).
[CrossRef] [PubMed]

T. Ha, T. Enderle, D. S. Chemla, P. R. Selvin, and S. Weiss, Phys. Rev. Lett. 77, 3979 (1996).
[CrossRef] [PubMed]

Sherif, S. S.

Sick, B.

B. Sick, B. Hecht, and L. Novotny, Phys. Rev. Lett. 85, 4482 (2000).
[CrossRef] [PubMed]

Török, P.

M. R. Foreman, S. S. Sherif, and P. Török, Opt. Express 15, 13597 (2007).
[CrossRef] [PubMed]

P. Török, Opt. Lett. 25, 1463 (2000).
[CrossRef]

P. Török, P. D. Higdon, and T. Wilson, J. Mod. Opt. 45, 1681 (1998).
[CrossRef]

P. Török, P. D. Higdon, and T. Wilson, Opt. Commun. 148, 300 (1998).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).

Van den Bout, D. A.

L. A. Deschenes and D. A. Van den Bout, Science 292, 233 (2001).
[CrossRef]

Vaz, W. L. C.

T. M. Jovin, M. Bartholdi, W. L. C. Vaz, and R. H. Austin, Ann. N.Y. Acad. Sci. 366, 176 (1981).
[CrossRef] [PubMed]

Weiss, S.

S. Weiss, Nat. Struct. Biol. 7, 724 (2000).
[CrossRef] [PubMed]

T. Ha, T. Enderle, D. F. Ogletree, D. S. Chemla, P. R. Selvin, and S. Weiss, Proc. Natl. Acad. Sci. USA 93, 6264 (1996).
[CrossRef] [PubMed]

T. Ha, T. Enderle, D. S. Chemla, P. R. Selvin, and S. Weiss, Phys. Rev. Lett. 77, 3979 (1996).
[CrossRef] [PubMed]

Wilson, T.

P. Török, P. D. Higdon, and T. Wilson, Opt. Commun. 148, 300 (1998).
[CrossRef]

P. Török, P. D. Higdon, and T. Wilson, J. Mod. Opt. 45, 1681 (1998).
[CrossRef]

Wolf, E.

B. Richards and E. Wolf, Proc. R. Soc. London, Ser. A 253, 358 (1959).
[CrossRef]

Ann. N.Y. Acad. Sci. (1)

T. M. Jovin, M. Bartholdi, W. L. C. Vaz, and R. H. Austin, Ann. N.Y. Acad. Sci. 366, 176 (1981).
[CrossRef] [PubMed]

J. Mod. Opt. (1)

P. Török, P. D. Higdon, and T. Wilson, J. Mod. Opt. 45, 1681 (1998).
[CrossRef]

J. Phys. Chem. A (1)

D. Patra, I. Gregor, and J. Enderlein, J. Phys. Chem. A 108, 6836 (2004).
[CrossRef]

Nat. Struct. Biol. (1)

S. Weiss, Nat. Struct. Biol. 7, 724 (2000).
[CrossRef] [PubMed]

Opt. Commun. (1)

P. Török, P. D. Higdon, and T. Wilson, Opt. Commun. 148, 300 (1998).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. Lett. (3)

T. Ha, T. Enderle, D. S. Chemla, P. R. Selvin, and S. Weiss, Phys. Rev. Lett. 77, 3979 (1996).
[CrossRef] [PubMed]

B. Sick, B. Hecht, and L. Novotny, Phys. Rev. Lett. 85, 4482 (2000).
[CrossRef] [PubMed]

R. M. Dickson, D. J. Norris, and W. E. Moerner, Phys. Rev. Lett. 81, 5322 (1998).
[CrossRef]

Proc. Natl. Acad. Sci. USA (1)

T. Ha, T. Enderle, D. F. Ogletree, D. S. Chemla, P. R. Selvin, and S. Weiss, Proc. Natl. Acad. Sci. USA 93, 6264 (1996).
[CrossRef] [PubMed]

Proc. R. Soc. London, Ser. A (1)

B. Richards and E. Wolf, Proc. R. Soc. London, Ser. A 253, 358 (1959).
[CrossRef]

Rev. Sci. Instrum. (1)

W. E. Moerner and D. P. Fromm, Rev. Sci. Instrum. 74, 3597 (2003).
[CrossRef]

Science (1)

L. A. Deschenes and D. A. Van den Bout, Science 292, 233 (2001).
[CrossRef]

Spectra-Phys. Laser Tech. Bull. (1)

D. J. Innes and A. L. Bloom, Spectra-Phys. Laser Tech. Bull. 5, 1 (1966).

Other (1)

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).

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Figures (4)

Fig. 1
Fig. 1

Field distributions for E x (top) and E y (bottom) in the back focal plane of a collecting lens ( NA = 0.966 ) arising from orthogonal electric dipoles orientated along the x, y, and z coordinate axes (left to right).

Fig. 2
Fig. 2

Proposed optical setup for determination of the full 3D orientation of an electric dipole.

Fig. 3
Fig. 3

(a) Proposed phase mask. (b) Rotational misalignment. (c) Translational misalignment.

Fig. 4
Fig. 4

(a) Extinction ratios as a function of mask misalignment (bottom-left axes) and spectral bandwidth (top-right axes). (b) SNR for finite detector sizes.

Equations (9)

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

E b f = 1 2 cos θ ( p x a 1 x p y a y 2 p z a 1 z p y a 2 x p x a y 2 p z a 2 z 0 ) ,
a 1 x = ( 1 + cos θ ) ( 1 cos θ ) cos 2 ϕ ,
a 2 x = ( 1 + cos θ ) + ( 1 cos θ ) cos 2 ϕ ,
a y = ( 1 cos θ ) sin 2 ϕ ,
a 1 z = 2 sin θ cos ϕ ,
a 2 z = 2 sin θ sin ϕ .
T ( x , y ) = { 1 for x 0 + 1 for x < 0 .
T ( x , y ) = { 1 for x Δ x + 1 for x < Δ x ,
D ν tot = λ min λ min + Δ λ S ( λ ) D ν ( λ ) d λ ν = 1 , 2 , 3 ,

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