Abstract

This Letter presents a means of measuring the dipole orientation of a fluorescent, orientationally fixed single molecule, which uses a specially designed phase mask, termed a “quadrated pupil,” conjugate to the back focal plane of a conventional wide-field microscope. The method leverages the spatial anisotropy of the far-field emission pattern of a dipole emitter and makes this anisotropy amenable to quantitative analysis at the image plane. In comparison to older image-fitting techniques that infer orientation by matching simulations to defocused or excessively magnified images, the quadrated pupil approach is more robust to minor modeling discrepancies and optical aberrations. Precision of 1°–5° is achieved in proof-of-concept experiments for both azimuthal (φ) and polar (θ) angles without defocusing. Since the phase mask is implemented on a liquid-crystal spatial light modulator that may be deactivated without any mechanical perturbation of the sample or imaging system, the technique may be readily integrated into clear aperture imaging studies.

© 2013 Optical Society of America

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2012 (2)

M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, G. Grover, A. Agrawal, R. Piestun, and W. E. Moerner, Proc. Natl. Acad. Sci. USA 109, 19087 (2012).
[CrossRef]

S. Stallinga and B. Rieger, Opt. Express 20, 6 (2012).

2011 (1)

J. Engelhardt, J. Keller, P. Hoyer, M. Reuss, T. Staudt, and S. W. Hell, Nano Lett. 11, 209 (2011).
[CrossRef]

2010 (1)

K. I. Mortensen, L. S. Churchman, J. A. Spudich, and H. Flyvbjerg, Nat. Methods 7, 377 (2010).
[CrossRef]

2009 (1)

2006 (1)

E. Toprak, J. Enderlein, S. Syed, S. A. McKinney, R. G. Petschek, T. Ha, Y. E. Goldman, and P. R. Selvin, Proc. Natl. Acad. Sci. USA 103, 6495 (2006).
[CrossRef]

2005 (2)

J. N. Forkey, M. E. Quinlan, and Y. E. Goldman, Biophys. J. 89, 1261 (2005).
[CrossRef]

S. A. Rosenberg, M. E. Quinlan, J. N. Forkey, and Y. E. Goldman, Acc. Chem. Res. 38, 583 (2005).
[CrossRef]

2004 (2)

2003 (1)

2001 (1)

1996 (1)

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

1989 (1)

D. Axelrod, Methods Cell Biol. 30, 333 (1989).
[CrossRef]

1987 (1)

Agrawal, A.

M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, G. Grover, A. Agrawal, R. Piestun, and W. E. Moerner, Proc. Natl. Acad. Sci. USA 109, 19087 (2012).
[CrossRef]

Aguet, F.

Axelrod, D.

Backer, A. S.

M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, G. Grover, A. Agrawal, R. Piestun, and W. E. Moerner, Proc. Natl. Acad. Sci. USA 109, 19087 (2012).
[CrossRef]

Backlund, M. P.

M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, G. Grover, A. Agrawal, R. Piestun, and W. E. Moerner, Proc. Natl. Acad. Sci. USA 109, 19087 (2012).
[CrossRef]

Böhmer, M.

Chemla, D. S.

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

Churchman, L. S.

K. I. Mortensen, L. S. Churchman, J. A. Spudich, and H. Flyvbjerg, Nat. Methods 7, 377 (2010).
[CrossRef]

Enderle, T.

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

Enderlein, J.

E. Toprak, J. Enderlein, S. Syed, S. A. McKinney, R. G. Petschek, T. Ha, Y. E. Goldman, and P. R. Selvin, Proc. Natl. Acad. Sci. USA 103, 6495 (2006).
[CrossRef]

M. Böhmer and J. Enderlein, J. Opt. Soc. Am. B 20, 554 (2003).
[CrossRef]

Engelhardt, J.

J. Engelhardt, J. Keller, P. Hoyer, M. Reuss, T. Staudt, and S. W. Hell, Nano Lett. 11, 209 (2011).
[CrossRef]

Flyvbjerg, H.

K. I. Mortensen, L. S. Churchman, J. A. Spudich, and H. Flyvbjerg, Nat. Methods 7, 377 (2010).
[CrossRef]

Forkey, J. N.

S. A. Rosenberg, M. E. Quinlan, J. N. Forkey, and Y. E. Goldman, Acc. Chem. Res. 38, 583 (2005).
[CrossRef]

J. N. Forkey, M. E. Quinlan, and Y. E. Goldman, Biophys. J. 89, 1261 (2005).
[CrossRef]

Fourkas, J. T.

Geissbühler, S.

Goldman, Y. E.

E. Toprak, J. Enderlein, S. Syed, S. A. McKinney, R. G. Petschek, T. Ha, Y. E. Goldman, and P. R. Selvin, Proc. Natl. Acad. Sci. USA 103, 6495 (2006).
[CrossRef]

S. A. Rosenberg, M. E. Quinlan, J. N. Forkey, and Y. E. Goldman, Acc. Chem. Res. 38, 583 (2005).
[CrossRef]

J. N. Forkey, M. E. Quinlan, and Y. E. Goldman, Biophys. J. 89, 1261 (2005).
[CrossRef]

Grover, G.

M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, G. Grover, A. Agrawal, R. Piestun, and W. E. Moerner, Proc. Natl. Acad. Sci. USA 109, 19087 (2012).
[CrossRef]

Ha, T.

E. Toprak, J. Enderlein, S. Syed, S. A. McKinney, R. G. Petschek, T. Ha, Y. E. Goldman, and P. R. Selvin, Proc. Natl. Acad. Sci. USA 103, 6495 (2006).
[CrossRef]

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

Hell, S. W.

J. Engelhardt, J. Keller, P. Hoyer, M. Reuss, T. Staudt, and S. W. Hell, Nano Lett. 11, 209 (2011).
[CrossRef]

Hellen, E. H.

Hoyer, P.

J. Engelhardt, J. Keller, P. Hoyer, M. Reuss, T. Staudt, and S. W. Hell, Nano Lett. 11, 209 (2011).
[CrossRef]

Keller, J.

J. Engelhardt, J. Keller, P. Hoyer, M. Reuss, T. Staudt, and S. W. Hell, Nano Lett. 11, 209 (2011).
[CrossRef]

Lasser, T.

Lew, M. D.

M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, G. Grover, A. Agrawal, R. Piestun, and W. E. Moerner, Proc. Natl. Acad. Sci. USA 109, 19087 (2012).
[CrossRef]

Lieb, M. A.

Märki, I.

McKinney, S. A.

E. Toprak, J. Enderlein, S. Syed, S. A. McKinney, R. G. Petschek, T. Ha, Y. E. Goldman, and P. R. Selvin, Proc. Natl. Acad. Sci. USA 103, 6495 (2006).
[CrossRef]

Moerner, W. E.

M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, G. Grover, A. Agrawal, R. Piestun, and W. E. Moerner, Proc. Natl. Acad. Sci. USA 109, 19087 (2012).
[CrossRef]

Mortensen, K. I.

K. I. Mortensen, L. S. Churchman, J. A. Spudich, and H. Flyvbjerg, Nat. Methods 7, 377 (2010).
[CrossRef]

Novotny, L.

Ober, R. J.

R. J. Ober, S. Ram, and E. S. Ward, Biophys. J. 86, 1185 (2004).
[CrossRef]

Petschek, R. G.

E. Toprak, J. Enderlein, S. Syed, S. A. McKinney, R. G. Petschek, T. Ha, Y. E. Goldman, and P. R. Selvin, Proc. Natl. Acad. Sci. USA 103, 6495 (2006).
[CrossRef]

Piestun, R.

M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, G. Grover, A. Agrawal, R. Piestun, and W. E. Moerner, Proc. Natl. Acad. Sci. USA 109, 19087 (2012).
[CrossRef]

Quinlan, M. E.

J. N. Forkey, M. E. Quinlan, and Y. E. Goldman, Biophys. J. 89, 1261 (2005).
[CrossRef]

S. A. Rosenberg, M. E. Quinlan, J. N. Forkey, and Y. E. Goldman, Acc. Chem. Res. 38, 583 (2005).
[CrossRef]

Ram, S.

R. J. Ober, S. Ram, and E. S. Ward, Biophys. J. 86, 1185 (2004).
[CrossRef]

Reuss, M.

J. Engelhardt, J. Keller, P. Hoyer, M. Reuss, T. Staudt, and S. W. Hell, Nano Lett. 11, 209 (2011).
[CrossRef]

Rieger, B.

S. Stallinga and B. Rieger, Opt. Express 20, 6 (2012).

Rosenberg, S. A.

S. A. Rosenberg, M. E. Quinlan, J. N. Forkey, and Y. E. Goldman, Acc. Chem. Res. 38, 583 (2005).
[CrossRef]

Sahl, S. J.

M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, G. Grover, A. Agrawal, R. Piestun, and W. E. Moerner, Proc. Natl. Acad. Sci. USA 109, 19087 (2012).
[CrossRef]

Selvin, P. R.

E. Toprak, J. Enderlein, S. Syed, S. A. McKinney, R. G. Petschek, T. Ha, Y. E. Goldman, and P. R. Selvin, Proc. Natl. Acad. Sci. USA 103, 6495 (2006).
[CrossRef]

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

Spudich, J. A.

K. I. Mortensen, L. S. Churchman, J. A. Spudich, and H. Flyvbjerg, Nat. Methods 7, 377 (2010).
[CrossRef]

Stallinga, S.

S. Stallinga and B. Rieger, Opt. Express 20, 6 (2012).

Staudt, T.

J. Engelhardt, J. Keller, P. Hoyer, M. Reuss, T. Staudt, and S. W. Hell, Nano Lett. 11, 209 (2011).
[CrossRef]

Syed, S.

E. Toprak, J. Enderlein, S. Syed, S. A. McKinney, R. G. Petschek, T. Ha, Y. E. Goldman, and P. R. Selvin, Proc. Natl. Acad. Sci. USA 103, 6495 (2006).
[CrossRef]

Toprak, E.

E. Toprak, J. Enderlein, S. Syed, S. A. McKinney, R. G. Petschek, T. Ha, Y. E. Goldman, and P. R. Selvin, Proc. Natl. Acad. Sci. USA 103, 6495 (2006).
[CrossRef]

Unser, M.

Ward, E. S.

R. J. Ober, S. Ram, and E. S. Ward, Biophys. J. 86, 1185 (2004).
[CrossRef]

Weiss, S.

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

Zavislan, J. M.

Acc. Chem. Res. (1)

S. A. Rosenberg, M. E. Quinlan, J. N. Forkey, and Y. E. Goldman, Acc. Chem. Res. 38, 583 (2005).
[CrossRef]

Biophys. J. (2)

J. N. Forkey, M. E. Quinlan, and Y. E. Goldman, Biophys. J. 89, 1261 (2005).
[CrossRef]

R. J. Ober, S. Ram, and E. S. Ward, Biophys. J. 86, 1185 (2004).
[CrossRef]

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

Methods Cell Biol. (1)

D. Axelrod, Methods Cell Biol. 30, 333 (1989).
[CrossRef]

Nano Lett. (1)

J. Engelhardt, J. Keller, P. Hoyer, M. Reuss, T. Staudt, and S. W. Hell, Nano Lett. 11, 209 (2011).
[CrossRef]

Nat. Methods (1)

K. I. Mortensen, L. S. Churchman, J. A. Spudich, and H. Flyvbjerg, Nat. Methods 7, 377 (2010).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. Lett. (1)

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

Proc. Natl. Acad. Sci. USA (2)

E. Toprak, J. Enderlein, S. Syed, S. A. McKinney, R. G. Petschek, T. Ha, Y. E. Goldman, and P. R. Selvin, Proc. Natl. Acad. Sci. USA 103, 6495 (2006).
[CrossRef]

M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, G. Grover, A. Agrawal, R. Piestun, and W. E. Moerner, Proc. Natl. Acad. Sci. USA 109, 19087 (2012).
[CrossRef]

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Figures (2)

Fig. 1.
Fig. 1.

(a) Quadrated phase mask. (b) Simulated emission patterns at the back focal plane. Dotted red lines indicate quadrant boundaries of phase mask. (c) Wide-field image of the R and T polarization channels. Inset: parameterization of dipole orientation P. (d) R and T images used to infer SM orientation (simulated).

Fig. 2.
Fig. 2.

Orientation measurements for two representative SMs. (a) and (b) (top row) Data collected for Mol. 1 and Mol. 2, respectively, and (bottom row) simulated images generated using orientation estimates inferred from this data (scale bar is 1 μm). (c) and (d) Plots of objective-function evaluations throughout the unit hemisphere. Overlaid on these plots are the results of repeated orientation measurements of the same molecule (black dots). The 2σ ellipse predicted by the CRLB and the data-covariance matrix are plotted in red and green, respectively. (e) and (f) Enlarged regions of interest in (c) and (d), respectively. Black lines represent 5° angular increments. (g) Orientation measurements as a function of depth (black dots) for the molecule Mol. 3. Standard deviations at each depth are denoted by blue lines. (h) Images of Mol. 3 with different amounts of defocus.

Tables (1)

Tables Icon

Table 1. Fitting Statistics for Representative Molecules

Equations (4)

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

EDETR(x,y)=R{FT{eiψ(ξ,η)FT{EIPS(x,y)}}}EDETT(x,y)=FT{eiψ(ξ,η)FT{EIPS(x,y)}},
ψ(ξ,η)=C0C(|ξ|+|η|).
O(θ,φ)=i=18xiln(yi+Nb)(yi+Nb).
P={Px,Py,Pz}={sin(θ)cos(φ),sin(θ)sin(φ),cos(θ)}.

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