OSA's Digital Library

Optics Letters

Optics Letters

| RAPID, SHORT PUBLICATIONS ON THE LATEST IN OPTICAL DISCOVERIES

  • Editor: Alan E. Willner
  • Vol. 38, Iss. 9 — May. 1, 2013
  • pp: 1521–1523
« Show journal navigation

Single-molecule orientation measurements with a quadrated pupil

Adam S. Backer, Mikael P. Backlund, Matthew D. Lew, and W. E. Moerner  »View Author Affiliations


Optics Letters, Vol. 38, Issue 9, pp. 1521-1523 (2013)
http://dx.doi.org/10.1364/OL.38.001521


View Full Text Article

Acrobat PDF (532 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

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

Single-molecule microscopy has long recognized the utility of measuring a fluorophore’s dipole orientation [1

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

]. A variety of methods have been employed ranging from the use of polarization optics [2

2. J. T. Fourkas, Opt. Lett. 26, 211 (2001). [CrossRef]

4

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

] to precise recording of the distorted image which occurs upon defocusing a wide-field microscope [5

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

,6

6. 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]

]. Orientation studies have shed light on numerous biological processes [3

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

,4

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

,6

6. 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]

,7

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

]. Furthermore, orientation must be taken into account when attempting to ascertain the positions of single molecules (SMs) from microscope images, so as to avoid localization errors that result when using rudimentary fitting schemes [8

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

,9

9. 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]

]. Our approach infers polar inclination without total internal reflection fluorescence (TIRF) excitation, and only one polarizer is used in the emission pathway. Precise modeling of minor defocus aberration is not required. Furthermore, in-focus SMs may be analyzed, even if the effective detector pixel size is large. Given a fixed photon budget, the technique presented in this Letter trades position information for a higher-precision orientation measurement using a single camera frame.

Our technique uses an experimental setup identical to the one presented in [9

9. 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]

], which adds Fourier plane processing to a conventional inverted epifluorescence microscope. Briefly, using a polarizing beam splitter, fluorescence exiting the microscope is separated into a reflected (R) and a transmitted (T) channel (respectively containing s- and p-polarized light, as defined relative to the surface of the beam splitter). Using a 4f optical processing configuration, the electric fields of the two polarizations are Fourier transformed and projected onto a spatial light modulator (SLM) programmed with the quadrated phase mask [Fig. 1(a)]. Modulated light from each polarization channel is Fourier transformed again, then relayed onto a separate region of an electron-multiplying charge-coupled device (EMCCD). The resulting SM emission patterns may be expressed as
EDETR(x,y)=R{FT{eiψ(ξ,η)FT{EIPS(x,y)}}}EDETT(x,y)=FT{eiψ(ξ,η)FT{EIPS(x,y)}},
(1)
EIPS,P(x,y) denote the s- or p-polarized portion of the electric field at the microscope’s image plane (prior to optical processing), and EDETR,T(x,y) represent the resulting electric fields in the R and T channels at the detector. FT{} is the Fourier transform operation, and R{} denotes a reflection operation about the y axis, which arises from the fact that the R channel incurs one additional reflection on account of the beam splitter. ψ(ξ,η) is the phase modulation imparted by the SLM. When the phase mask is in use, this term may be expressed as the following pyramid-shaped aberration consisting of four linear phase ramps:
ψ(ξ,η)=C0C(|ξ|+|η|).
(2)
The constant C0 is set by the dynamic range of the SLM (6π), and C=C0/ρmax, where ρmax, is the radius of the region in which intensity may be nonzero, as enforced by the numerical aperture, magnification, and the focal lengths of the lenses used in the 4f system.

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).

As a proof of concept, nanomolar concentrations of the fluorophore dicyanomethylenedihydrofuran-N-6 (DCDHF-N-6) in 1% polymethyl methacrylate (PMMA) were spin-coated onto microscope coverslips to form a film of orientation-fixed molecules 50nm thick [9

9. 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]

]. Samples were imaged by an Olympus IX71 microscope with a 100×/1.4NA Olympus UPlanSApo oil immersion objective. Excitation was achieved with circularly polarized 514 nm light from an Ar-ion laser. 0.1kW/cm2 peak intensity was measured at the sample. Fluorescence at 609 nm was filtered by a Chroma Z514RDC dichroic and a 590/60 bandpass filter. Optical processing was performed using a Boulder Nonlinear XY Phase Series SLM. Images were captured on an Andor iXon+EMCCD with a gain of 300 and an effective pixel size of 160 nm.

The quadrated phase mask was loaded onto the SLM, and twenty 1-s exposures were acquired. Orientation measurements were performed for the same molecule using separate images. Results for representative molecules Mol. 1 and Mol. 2 are shown in Fig. 2. Note that O(θ,φ) has few local maxima, facilitating the use of standard optimization procedures. To compute the ultimate limit of precision of our method, the Cramer–Rao lower bound (CRLB) was calculated [12

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

], and 2σ ellipses were projected onto the unit hemisphere. 2σ ellipses were also calculated using the data-covariance matrices from our measurements. To compare our technique with an established method, the SLM was deactivated, and ten 600-nm defocused images of Mol. 1 and Mol. 2 were acquired. Using template matching [6

6. 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]

,9

9. 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]

], independent orientation estimates were obtained. Since the simulated templates do not incorporate the minor optical aberrations that are present in the experimental system, results had lower precision, and may have systematic biases, thus highlighting the advantages of the quadrated pupil approach. Statistics are summarized in Table 1. Experimental precision compares favorably with similar methods [13

13. F. Aguet, S. Geissbühler, I. Märki, T. Lasser, and M. Unser, Opt. Express 17, 6829 (2009). [CrossRef]

15

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

].

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.

Table 1. Fitting Statistics for Representative Molecules

table-icon
View This Table

We demonstrated our technique to be insensitive to minor defocus errors, an advantage over alternative image-matching schemes which must gauge depth to within a few nanometers in order to generate an appropriate set of templates. The objective lens was translated in 50-nm steps, with eleven frames of data recorded at each step (Mad City Labs, C-Focus). When the focal plane is within ±150nm of the layer of SMs, the orientation measurements are largely invariant [Fig. 2(g)], since there is little change in the major features of the images acquired using the quadrated pupil over this range [Fig. 2(h)].

Minor aberrations are mitigated, since orientation is inferred from intensity summed over coarse patches of pixels. As a consequence, our precision is generally slightly worse than what is predicted by the CRLB. However, if aberrations are present (a likely possibility when imaging thick biological samples), attempts at fine-scale image matching will introduce systematic errors, negating any gain in precision. To determine two-dimensional position, our scheme may be adapted by turning the SLM on and off, and taking two separate images. Furthermore, three-dimensional position may be measured by toggling between the quadrated phase mask and an astigmatic or double-helix [9

9. 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]

] pattern.

This work was supported in part by the National Institute of General Medical Sciences grant R01GM085437. A. S. Backer acknowledges support from the National Defense Science and Engineering Graduate Fellowship. M. P. Backlund acknowledges support from a Robert and Marvel Kirby Stanford Graduate Fellowship. M. D. Lew acknowledges support from a National Science Foundation Graduate Research Fellowship and a 3Com Corporation Stanford Graduate Fellowship.

References

1.

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

2.

J. T. Fourkas, Opt. Lett. 26, 211 (2001). [CrossRef]

3.

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

4.

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

5.

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

6.

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]

7.

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

8.

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

9.

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]

10.

E. H. Hellen and D. Axelrod, J. Opt. Soc. Am. B 4, 337 (1987). [CrossRef]

11.

M. A. Lieb, J. M. Zavislan, and L. Novotny, J. Opt. Soc. Am. B 21, 1210 (2004). [CrossRef]

12.

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

13.

F. Aguet, S. Geissbühler, I. Märki, T. Lasser, and M. Unser, Opt. Express 17, 6829 (2009). [CrossRef]

14.

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

15.

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

OCIS Codes
(070.6110) Fourier optics and signal processing : Spatial filtering
(110.4850) Imaging systems : Optical transfer functions
(180.2520) Microscopy : Fluorescence microscopy
(110.1758) Imaging systems : Computational imaging

ToC Category:
Imaging Systems

History
Original Manuscript: January 7, 2013
Revised Manuscript: March 11, 2013
Manuscript Accepted: March 13, 2013
Published: April 29, 2013

Virtual Issues
Vol. 8, Iss. 6 Virtual Journal for Biomedical Optics

Citation
Adam S. Backer, Mikael P. Backlund, Matthew D. Lew, and W. E. Moerner, "Single-molecule orientation measurements with a quadrated pupil," Opt. Lett. 38, 1521-1523 (2013)
http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-38-9-1521


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. T. Ha, T. Enderle, D. S. Chemla, P. R. Selvin, and S. Weiss, Phys. Rev. Lett. 77, 3979 (1996). [CrossRef]
  2. J. T. Fourkas, Opt. Lett. 26, 211 (2001). [CrossRef]
  3. J. N. Forkey, M. E. Quinlan, and Y. E. Goldman, Biophys. J. 89, 1261 (2005). [CrossRef]
  4. S. A. Rosenberg, M. E. Quinlan, J. N. Forkey, and Y. E. Goldman, Acc. Chem. Res. 38, 583 (2005). [CrossRef]
  5. M. Böhmer and J. Enderlein, J. Opt. Soc. Am. B 20, 554 (2003). [CrossRef]
  6. 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]
  7. D. Axelrod, Methods Cell Biol. 30, 333 (1989). [CrossRef]
  8. J. Engelhardt, J. Keller, P. Hoyer, M. Reuss, T. Staudt, and S. W. Hell, Nano Lett. 11, 209 (2011). [CrossRef]
  9. 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]
  10. E. H. Hellen and D. Axelrod, J. Opt. Soc. Am. B 4, 337 (1987). [CrossRef]
  11. M. A. Lieb, J. M. Zavislan, and L. Novotny, J. Opt. Soc. Am. B 21, 1210 (2004). [CrossRef]
  12. R. J. Ober, S. Ram, and E. S. Ward, Biophys. J. 86, 1185 (2004). [CrossRef]
  13. F. Aguet, S. Geissbühler, I. Märki, T. Lasser, and M. Unser, Opt. Express 17, 6829 (2009). [CrossRef]
  14. K. I. Mortensen, L. S. Churchman, J. A. Spudich, and H. Flyvbjerg, Nat. Methods 7, 377 (2010). [CrossRef]
  15. S. Stallinga and B. Rieger, Opt. Express 20, 6 (2012).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1. Fig. 2.
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited