Abstract

The Single Particle Orientation and Rotational Tracking (SPORT) technique, which utilizes anisotropic plasmonic gold nanorods and differential interference contrast (DIC) microscopy, has shown potential as an effective alternative to fluorescence-based techniques to decipher rotational motions on the cellular and molecular levels. However, localizing gold nanorods from their DIC images with high accuracy and precision is more challenging than the procedures applied in fluorescence or scattering microscopy techniques due to the asymmetric DIC point spread function with bright and dark parts superimposed over a grey background. In this paper, localization accuracy and inherited uncertainties from unique DIC image patterns are elucidated with the assistance of computer simulation. These discussions provide guidance for researchers to properly evaluate their data and avoid making claims beyond the technical limits. The understanding of the intrinsic localization errors and the principle of DIC microscopy leads us to propose a new localization strategy that utilizes the experimentally-measured shear distance of the DIC microscope to improve the localization accuracy.

© 2017 Optical Society of America

Full Article  |  PDF Article
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References

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2016 (1)

L. Wei, J. Xu, Z. Ye, X. Zhu, M. Zhong, W. Luo, B. Chen, H. Duan, Q. Liu, and L. Xiao, “Orientational imaging of a single gold nanorod at the liquid/solid interface with polarized evanescent field illumination,” Anal. Chem. 88(4), 1995–1999 (2016).
[Crossref] [PubMed]

2013 (5)

K. Marchuk, J. W. Ha, and N. Fang, “Three-dimensional high-resolution rotational tracking with superlocalization reveals conformations of surface-bound anisotropic nanoparticles,” Nano Lett. 13(3), 1245–1250 (2013).
[Crossref] [PubMed]

M. D. Lew, M. P. Backlund, and W. E. Moerner, “Rotational mobility of single molecules affects localization accuracy in super-resolution fluorescence microscopy,” Nano Lett. 13(9), 3967–3972 (2013).
[Crossref] [PubMed]

E. J. Titus and K. A. Willets, “Superlocalization surface-enhanced Raman scattering microscopy: comparing point spread function models in the ensemble and single-molecule limits,” ACS Nano 7(9), 8284–8294 (2013).
[Crossref] [PubMed]

Y. Gu, G. Wang, and N. Fang, “Simultaneous single-particle superlocalization and rotational tracking,” ACS Nano 7(2), 1658–1665 (2013).
[Crossref] [PubMed]

M. Shribak, “Quantitative orientation-independent DIC microscope with fast switching shear direction and bias modulation,” J. Opt. Soc. Am. A 30, 769–782 (2013).
[Crossref]

2012 (4)

L. Xiao, J. W. Ha, L. Wei, G. Wang, and N. Fang, “Determining the full three-dimensional orientation of single anisotropic nanoparticles by differential interference contrast microscopy,” Angew. Chem. Int. Ed. Engl. 51(31), 7734–7738 (2012).
[Crossref] [PubMed]

Y. Gu, X. Di, W. Sun, G. Wang, and N. Fang, “Three-dimensional super-localization and tracking of single gold nanoparticles in cells,” Anal. Chem. 84(9), 4111–4117 (2012).
[Crossref] [PubMed]

J. W. Ha, K. Marchuk, and N. Fang, “Focused orientation and position imaging (FOPI) of single anisotropic plasmonic nanoparticles by total internal reflection scattering microscopy,” Nano Lett. 12(8), 4282–4288 (2012).
[Crossref] [PubMed]

Y. Gu, W. Sun, G. Wang, K. Jeftinija, S. Jeftinija, and N. Fang, “Rotational dynamics of cargos at pauses during axonal transport,” Nat. Commun. 3, 1030 (2012).
[Crossref] [PubMed]

2011 (3)

Y. Gu, W. Sun, G. Wang, and N. Fang, “Single particle orientation and rotation tracking discloses distinctive rotational dynamics of drug delivery vectors on live cell membranes,” J. Am. Chem. Soc. 133(15), 5720–5723 (2011).
[Crossref] [PubMed]

L. Xiao, Y. Qiao, Y. He, and E. S. Yeung, “Imaging translational and rotational diffusion of single anisotropic nanoparticles with planar illumination microscopy,” J. Am. Chem. Soc. 133(27), 10638–10645 (2011).
[Crossref] [PubMed]

J. W. Ha, W. Sun, G. Wang, and N. Fang, “Differential interference contrast polarization anisotropy for tracking rotational dynamics of gold nanorods,” Chem. Commun. (Camb.) 47(27), 7743–7745 (2011).
[Crossref] [PubMed]

2010 (5)

L. Xiao, Y. Qiao, Y. He, and E. S. Yeung, “Three dimensional orientational imaging of nanoparticles with darkfield microscopy,” Anal. Chem. 82(12), 5268–5274 (2010).
[Crossref] [PubMed]

G. Wang, W. Sun, Y. Luo, and N. Fang, “Resolving rotational motions of nano-objects in engineered environments and live cells with gold nanorods and differential interference contrast microscopy,” J. Am. Chem. Soc. 132(46), 16417–16422 (2010).
[Crossref] [PubMed]

A. S. Stender, G. Wang, W. Sun, and N. Fang, “Influence of gold nanorod geometry on optical response,” ACS Nano 4(12), 7667–7675 (2010).
[Crossref] [PubMed]

K. I. Mortensen, L. S. Churchman, J. A. Spudich, and H. Flyvbjerg, “Optimized localization analysis for single-molecule tracking and super-resolution microscopy,” Nat. Methods 7(5), 377–381 (2010).
[Crossref] [PubMed]

S. B. Mehta and C. J. R. Sheppard, “Sample-less calibration of the differential interference contrast microscope,” Appl. Opt. 49(15), 2954–2968 (2010).
[Crossref] [PubMed]

2006 (4)

M. Shribak and S. Inoué, “Orientation-independent differential interference contrast microscopy,” Appl. Opt. 45(3), 460–469 (2006).
[Crossref] [PubMed]

J. Enderlein, E. Toprak, and P. R. Selvin, “Polarization effect on position accuracy of fluorophore localization,” Opt. Express 14(18), 8111–8120 (2006).
[Crossref] [PubMed]

E. Toprak, J. Enderlein, S. Syed, S. A. McKinney, R. G. Petschek, T. Ha, Y. E. Goldman, and P. R. Selvin, “Defocused orientation and position imaging (DOPI) of myosin V,” Proc. Natl. Acad. Sci. U.S.A. 103(17), 6495–6499 (2006).
[Crossref] [PubMed]

H. Uji-i, S. M. Melnikov, A. Deres, G. Bergamini, F. De Schryver, A. Herrmann, K. Mullen, J. Enderlein, and J. Hofkens, “Visualizing spatial and temporal heterogeneity of single molecule rotational diffusion in a glassy polymer by defocused wide-field imaging,” Polymer (Guildf.) 47(7), 2511–2518 (2006).
[Crossref]

2005 (3)

C. Sönnichsen and A. P. Alivisatos, “Gold nanorods as novel nonbleaching plasmon-based orientation sensors for polarized single-particle microscopy,” Nano Lett. 5(2), 301–304 (2005).
[Crossref] [PubMed]

D. Patra, I. Gregor, J. Enderlein, and M. Sauer, “Defocused imaging of quantum-dot angular distribution of radiation,” Appl. Phys. Lett. 87(10), 101103 (2005).
[Crossref]

A. Yildiz and P. R. Selvin, “Fluorescence imaging with one nanometer accuracy: application to molecular motors,” Acc. Chem. Res. 38(7), 574–582 (2005).
[Crossref] [PubMed]

2004 (1)

A. Yildiz, M. Tomishige, R. D. Vale, and P. R. Selvin, “Kinesin walks hand-over-hand,” Science 303(5658), 676–678 (2004).
[Crossref] [PubMed]

2003 (2)

M. Böhmer and J. Enderlein, “Orientation imaging of single molecules by wide-field epifluorescence microscopy,” J. Opt. Soc. Am. B 20(3), 554–559 (2003).
[Crossref]

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, “Myosin V walks hand-over-hand: single fluorophore imaging with 1.5-nm localization,” Science 300(5628), 2061–2065 (2003).
[Crossref] [PubMed]

2001 (1)

Z. Salamon and G. Tollin, “Optical anisotropy in lipid bilayer membranes: Coupled plasmon-waveguide resonance measurements of molecular orientation, polarizability, and shape,” Biophys. J. 80(3), 1557–1567 (2001).
[Crossref] [PubMed]

1999 (2)

1997 (2)

E. B. van Munster, L. J. van Vliet, and J. A. Aten, “Reconstruction of optical pathlength distributions from images obtained by a wide-field differential interference contrast microscope,” J. Microsc. 188(2), 149–157 (1997).
[Crossref] [PubMed]

R. Swaminathan, C. P. Hoang, and A. S. Verkman, “Photobleaching recovery and anisotropy decay of green fluorescent protein GFP-S65T in solution and cells: Cytoplasmic viscosity probed by green fluorescent protein translational and rotational diffusion,” Biophys. J. 72(4), 1900–1907 (1997).
[Crossref] [PubMed]

1988 (1)

J. Gelles, B. J. Schnapp, and M. P. Sheetz, “Tracking kinesin-driven movements with nanometre-scale precision,” Nature 331(6155), 450–453 (1988).
[Crossref] [PubMed]

Alivisatos, A. P.

C. Sönnichsen and A. P. Alivisatos, “Gold nanorods as novel nonbleaching plasmon-based orientation sensors for polarized single-particle microscopy,” Nano Lett. 5(2), 301–304 (2005).
[Crossref] [PubMed]

Aten, J. A.

E. B. van Munster, L. J. van Vliet, and J. A. Aten, “Reconstruction of optical pathlength distributions from images obtained by a wide-field differential interference contrast microscope,” J. Microsc. 188(2), 149–157 (1997).
[Crossref] [PubMed]

Backlund, M. P.

M. D. Lew, M. P. Backlund, and W. E. Moerner, “Rotational mobility of single molecules affects localization accuracy in super-resolution fluorescence microscopy,” Nano Lett. 13(9), 3967–3972 (2013).
[Crossref] [PubMed]

Bergamini, G.

H. Uji-i, S. M. Melnikov, A. Deres, G. Bergamini, F. De Schryver, A. Herrmann, K. Mullen, J. Enderlein, and J. Hofkens, “Visualizing spatial and temporal heterogeneity of single molecule rotational diffusion in a glassy polymer by defocused wide-field imaging,” Polymer (Guildf.) 47(7), 2511–2518 (2006).
[Crossref]

Böhmer, M.

Chemla, D. S.

T. Ha, T. A. Laurence, D. S. Chemla, and S. Weiss, “Polarization spectroscopy of single fluorescent molecules,” J. Phys. Chem. B 103(33), 6839–6850 (1999).
[Crossref]

Chen, B.

L. Wei, J. Xu, Z. Ye, X. Zhu, M. Zhong, W. Luo, B. Chen, H. Duan, Q. Liu, and L. Xiao, “Orientational imaging of a single gold nanorod at the liquid/solid interface with polarized evanescent field illumination,” Anal. Chem. 88(4), 1995–1999 (2016).
[Crossref] [PubMed]

Churchman, L. S.

K. I. Mortensen, L. S. Churchman, J. A. Spudich, and H. Flyvbjerg, “Optimized localization analysis for single-molecule tracking and super-resolution microscopy,” Nat. Methods 7(5), 377–381 (2010).
[Crossref] [PubMed]

Conchello, J. A.

De Schryver, F.

H. Uji-i, S. M. Melnikov, A. Deres, G. Bergamini, F. De Schryver, A. Herrmann, K. Mullen, J. Enderlein, and J. Hofkens, “Visualizing spatial and temporal heterogeneity of single molecule rotational diffusion in a glassy polymer by defocused wide-field imaging,” Polymer (Guildf.) 47(7), 2511–2518 (2006).
[Crossref]

Deres, A.

H. Uji-i, S. M. Melnikov, A. Deres, G. Bergamini, F. De Schryver, A. Herrmann, K. Mullen, J. Enderlein, and J. Hofkens, “Visualizing spatial and temporal heterogeneity of single molecule rotational diffusion in a glassy polymer by defocused wide-field imaging,” Polymer (Guildf.) 47(7), 2511–2518 (2006).
[Crossref]

Di, X.

Y. Gu, X. Di, W. Sun, G. Wang, and N. Fang, “Three-dimensional super-localization and tracking of single gold nanoparticles in cells,” Anal. Chem. 84(9), 4111–4117 (2012).
[Crossref] [PubMed]

Duan, H.

L. Wei, J. Xu, Z. Ye, X. Zhu, M. Zhong, W. Luo, B. Chen, H. Duan, Q. Liu, and L. Xiao, “Orientational imaging of a single gold nanorod at the liquid/solid interface with polarized evanescent field illumination,” Anal. Chem. 88(4), 1995–1999 (2016).
[Crossref] [PubMed]

Enderlein, J.

H. Uji-i, S. M. Melnikov, A. Deres, G. Bergamini, F. De Schryver, A. Herrmann, K. Mullen, J. Enderlein, and J. Hofkens, “Visualizing spatial and temporal heterogeneity of single molecule rotational diffusion in a glassy polymer by defocused wide-field imaging,” Polymer (Guildf.) 47(7), 2511–2518 (2006).
[Crossref]

E. Toprak, J. Enderlein, S. Syed, S. A. McKinney, R. G. Petschek, T. Ha, Y. E. Goldman, and P. R. Selvin, “Defocused orientation and position imaging (DOPI) of myosin V,” Proc. Natl. Acad. Sci. U.S.A. 103(17), 6495–6499 (2006).
[Crossref] [PubMed]

J. Enderlein, E. Toprak, and P. R. Selvin, “Polarization effect on position accuracy of fluorophore localization,” Opt. Express 14(18), 8111–8120 (2006).
[Crossref] [PubMed]

D. Patra, I. Gregor, J. Enderlein, and M. Sauer, “Defocused imaging of quantum-dot angular distribution of radiation,” Appl. Phys. Lett. 87(10), 101103 (2005).
[Crossref]

M. Böhmer and J. Enderlein, “Orientation imaging of single molecules by wide-field epifluorescence microscopy,” J. Opt. Soc. Am. B 20(3), 554–559 (2003).
[Crossref]

Fang, N.

Y. Gu, G. Wang, and N. Fang, “Simultaneous single-particle superlocalization and rotational tracking,” ACS Nano 7(2), 1658–1665 (2013).
[Crossref] [PubMed]

K. Marchuk, J. W. Ha, and N. Fang, “Three-dimensional high-resolution rotational tracking with superlocalization reveals conformations of surface-bound anisotropic nanoparticles,” Nano Lett. 13(3), 1245–1250 (2013).
[Crossref] [PubMed]

J. W. Ha, K. Marchuk, and N. Fang, “Focused orientation and position imaging (FOPI) of single anisotropic plasmonic nanoparticles by total internal reflection scattering microscopy,” Nano Lett. 12(8), 4282–4288 (2012).
[Crossref] [PubMed]

Y. Gu, W. Sun, G. Wang, K. Jeftinija, S. Jeftinija, and N. Fang, “Rotational dynamics of cargos at pauses during axonal transport,” Nat. Commun. 3, 1030 (2012).
[Crossref] [PubMed]

Y. Gu, X. Di, W. Sun, G. Wang, and N. Fang, “Three-dimensional super-localization and tracking of single gold nanoparticles in cells,” Anal. Chem. 84(9), 4111–4117 (2012).
[Crossref] [PubMed]

L. Xiao, J. W. Ha, L. Wei, G. Wang, and N. Fang, “Determining the full three-dimensional orientation of single anisotropic nanoparticles by differential interference contrast microscopy,” Angew. Chem. Int. Ed. Engl. 51(31), 7734–7738 (2012).
[Crossref] [PubMed]

Y. Gu, W. Sun, G. Wang, and N. Fang, “Single particle orientation and rotation tracking discloses distinctive rotational dynamics of drug delivery vectors on live cell membranes,” J. Am. Chem. Soc. 133(15), 5720–5723 (2011).
[Crossref] [PubMed]

J. W. Ha, W. Sun, G. Wang, and N. Fang, “Differential interference contrast polarization anisotropy for tracking rotational dynamics of gold nanorods,” Chem. Commun. (Camb.) 47(27), 7743–7745 (2011).
[Crossref] [PubMed]

A. S. Stender, G. Wang, W. Sun, and N. Fang, “Influence of gold nanorod geometry on optical response,” ACS Nano 4(12), 7667–7675 (2010).
[Crossref] [PubMed]

G. Wang, W. Sun, Y. Luo, and N. Fang, “Resolving rotational motions of nano-objects in engineered environments and live cells with gold nanorods and differential interference contrast microscopy,” J. Am. Chem. Soc. 132(46), 16417–16422 (2010).
[Crossref] [PubMed]

Flyvbjerg, H.

K. I. Mortensen, L. S. Churchman, J. A. Spudich, and H. Flyvbjerg, “Optimized localization analysis for single-molecule tracking and super-resolution microscopy,” Nat. Methods 7(5), 377–381 (2010).
[Crossref] [PubMed]

Forkey, J. N.

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, “Myosin V walks hand-over-hand: single fluorophore imaging with 1.5-nm localization,” Science 300(5628), 2061–2065 (2003).
[Crossref] [PubMed]

Gelles, J.

J. Gelles, B. J. Schnapp, and M. P. Sheetz, “Tracking kinesin-driven movements with nanometre-scale precision,” Nature 331(6155), 450–453 (1988).
[Crossref] [PubMed]

Goldman, Y. E.

E. Toprak, J. Enderlein, S. Syed, S. A. McKinney, R. G. Petschek, T. Ha, Y. E. Goldman, and P. R. Selvin, “Defocused orientation and position imaging (DOPI) of myosin V,” Proc. Natl. Acad. Sci. U.S.A. 103(17), 6495–6499 (2006).
[Crossref] [PubMed]

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, “Myosin V walks hand-over-hand: single fluorophore imaging with 1.5-nm localization,” Science 300(5628), 2061–2065 (2003).
[Crossref] [PubMed]

Gregor, I.

D. Patra, I. Gregor, J. Enderlein, and M. Sauer, “Defocused imaging of quantum-dot angular distribution of radiation,” Appl. Phys. Lett. 87(10), 101103 (2005).
[Crossref]

Gu, Y.

Y. Gu, G. Wang, and N. Fang, “Simultaneous single-particle superlocalization and rotational tracking,” ACS Nano 7(2), 1658–1665 (2013).
[Crossref] [PubMed]

Y. Gu, X. Di, W. Sun, G. Wang, and N. Fang, “Three-dimensional super-localization and tracking of single gold nanoparticles in cells,” Anal. Chem. 84(9), 4111–4117 (2012).
[Crossref] [PubMed]

Y. Gu, W. Sun, G. Wang, K. Jeftinija, S. Jeftinija, and N. Fang, “Rotational dynamics of cargos at pauses during axonal transport,” Nat. Commun. 3, 1030 (2012).
[Crossref] [PubMed]

Y. Gu, W. Sun, G. Wang, and N. Fang, “Single particle orientation and rotation tracking discloses distinctive rotational dynamics of drug delivery vectors on live cell membranes,” J. Am. Chem. Soc. 133(15), 5720–5723 (2011).
[Crossref] [PubMed]

Ha, J. W.

K. Marchuk, J. W. Ha, and N. Fang, “Three-dimensional high-resolution rotational tracking with superlocalization reveals conformations of surface-bound anisotropic nanoparticles,” Nano Lett. 13(3), 1245–1250 (2013).
[Crossref] [PubMed]

J. W. Ha, K. Marchuk, and N. Fang, “Focused orientation and position imaging (FOPI) of single anisotropic plasmonic nanoparticles by total internal reflection scattering microscopy,” Nano Lett. 12(8), 4282–4288 (2012).
[Crossref] [PubMed]

L. Xiao, J. W. Ha, L. Wei, G. Wang, and N. Fang, “Determining the full three-dimensional orientation of single anisotropic nanoparticles by differential interference contrast microscopy,” Angew. Chem. Int. Ed. Engl. 51(31), 7734–7738 (2012).
[Crossref] [PubMed]

J. W. Ha, W. Sun, G. Wang, and N. Fang, “Differential interference contrast polarization anisotropy for tracking rotational dynamics of gold nanorods,” Chem. Commun. (Camb.) 47(27), 7743–7745 (2011).
[Crossref] [PubMed]

Ha, T.

E. Toprak, J. Enderlein, S. Syed, S. A. McKinney, R. G. Petschek, T. Ha, Y. E. Goldman, and P. R. Selvin, “Defocused orientation and position imaging (DOPI) of myosin V,” Proc. Natl. Acad. Sci. U.S.A. 103(17), 6495–6499 (2006).
[Crossref] [PubMed]

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, “Myosin V walks hand-over-hand: single fluorophore imaging with 1.5-nm localization,” Science 300(5628), 2061–2065 (2003).
[Crossref] [PubMed]

T. Ha, T. A. Laurence, D. S. Chemla, and S. Weiss, “Polarization spectroscopy of single fluorescent molecules,” J. Phys. Chem. B 103(33), 6839–6850 (1999).
[Crossref]

He, Y.

L. Xiao, Y. Qiao, Y. He, and E. S. Yeung, “Imaging translational and rotational diffusion of single anisotropic nanoparticles with planar illumination microscopy,” J. Am. Chem. Soc. 133(27), 10638–10645 (2011).
[Crossref] [PubMed]

L. Xiao, Y. Qiao, Y. He, and E. S. Yeung, “Three dimensional orientational imaging of nanoparticles with darkfield microscopy,” Anal. Chem. 82(12), 5268–5274 (2010).
[Crossref] [PubMed]

Herrmann, A.

H. Uji-i, S. M. Melnikov, A. Deres, G. Bergamini, F. De Schryver, A. Herrmann, K. Mullen, J. Enderlein, and J. Hofkens, “Visualizing spatial and temporal heterogeneity of single molecule rotational diffusion in a glassy polymer by defocused wide-field imaging,” Polymer (Guildf.) 47(7), 2511–2518 (2006).
[Crossref]

Hoang, C. P.

R. Swaminathan, C. P. Hoang, and A. S. Verkman, “Photobleaching recovery and anisotropy decay of green fluorescent protein GFP-S65T in solution and cells: Cytoplasmic viscosity probed by green fluorescent protein translational and rotational diffusion,” Biophys. J. 72(4), 1900–1907 (1997).
[Crossref] [PubMed]

Hofkens, J.

H. Uji-i, S. M. Melnikov, A. Deres, G. Bergamini, F. De Schryver, A. Herrmann, K. Mullen, J. Enderlein, and J. Hofkens, “Visualizing spatial and temporal heterogeneity of single molecule rotational diffusion in a glassy polymer by defocused wide-field imaging,” Polymer (Guildf.) 47(7), 2511–2518 (2006).
[Crossref]

Inoué, S.

Jeftinija, K.

Y. Gu, W. Sun, G. Wang, K. Jeftinija, S. Jeftinija, and N. Fang, “Rotational dynamics of cargos at pauses during axonal transport,” Nat. Commun. 3, 1030 (2012).
[Crossref] [PubMed]

Jeftinija, S.

Y. Gu, W. Sun, G. Wang, K. Jeftinija, S. Jeftinija, and N. Fang, “Rotational dynamics of cargos at pauses during axonal transport,” Nat. Commun. 3, 1030 (2012).
[Crossref] [PubMed]

Laurence, T. A.

T. Ha, T. A. Laurence, D. S. Chemla, and S. Weiss, “Polarization spectroscopy of single fluorescent molecules,” J. Phys. Chem. B 103(33), 6839–6850 (1999).
[Crossref]

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M. D. Lew, M. P. Backlund, and W. E. Moerner, “Rotational mobility of single molecules affects localization accuracy in super-resolution fluorescence microscopy,” Nano Lett. 13(9), 3967–3972 (2013).
[Crossref] [PubMed]

Liu, Q.

L. Wei, J. Xu, Z. Ye, X. Zhu, M. Zhong, W. Luo, B. Chen, H. Duan, Q. Liu, and L. Xiao, “Orientational imaging of a single gold nanorod at the liquid/solid interface with polarized evanescent field illumination,” Anal. Chem. 88(4), 1995–1999 (2016).
[Crossref] [PubMed]

Luo, W.

L. Wei, J. Xu, Z. Ye, X. Zhu, M. Zhong, W. Luo, B. Chen, H. Duan, Q. Liu, and L. Xiao, “Orientational imaging of a single gold nanorod at the liquid/solid interface with polarized evanescent field illumination,” Anal. Chem. 88(4), 1995–1999 (2016).
[Crossref] [PubMed]

Luo, Y.

G. Wang, W. Sun, Y. Luo, and N. Fang, “Resolving rotational motions of nano-objects in engineered environments and live cells with gold nanorods and differential interference contrast microscopy,” J. Am. Chem. Soc. 132(46), 16417–16422 (2010).
[Crossref] [PubMed]

Marchuk, K.

K. Marchuk, J. W. Ha, and N. Fang, “Three-dimensional high-resolution rotational tracking with superlocalization reveals conformations of surface-bound anisotropic nanoparticles,” Nano Lett. 13(3), 1245–1250 (2013).
[Crossref] [PubMed]

J. W. Ha, K. Marchuk, and N. Fang, “Focused orientation and position imaging (FOPI) of single anisotropic plasmonic nanoparticles by total internal reflection scattering microscopy,” Nano Lett. 12(8), 4282–4288 (2012).
[Crossref] [PubMed]

McKinney, S. A.

E. Toprak, J. Enderlein, S. Syed, S. A. McKinney, R. G. Petschek, T. Ha, Y. E. Goldman, and P. R. Selvin, “Defocused orientation and position imaging (DOPI) of myosin V,” Proc. Natl. Acad. Sci. U.S.A. 103(17), 6495–6499 (2006).
[Crossref] [PubMed]

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, “Myosin V walks hand-over-hand: single fluorophore imaging with 1.5-nm localization,” Science 300(5628), 2061–2065 (2003).
[Crossref] [PubMed]

Mehta, S. B.

Melnikov, S. M.

H. Uji-i, S. M. Melnikov, A. Deres, G. Bergamini, F. De Schryver, A. Herrmann, K. Mullen, J. Enderlein, and J. Hofkens, “Visualizing spatial and temporal heterogeneity of single molecule rotational diffusion in a glassy polymer by defocused wide-field imaging,” Polymer (Guildf.) 47(7), 2511–2518 (2006).
[Crossref]

Moerner, W. E.

M. D. Lew, M. P. Backlund, and W. E. Moerner, “Rotational mobility of single molecules affects localization accuracy in super-resolution fluorescence microscopy,” Nano Lett. 13(9), 3967–3972 (2013).
[Crossref] [PubMed]

Mortensen, K. I.

K. I. Mortensen, L. S. Churchman, J. A. Spudich, and H. Flyvbjerg, “Optimized localization analysis for single-molecule tracking and super-resolution microscopy,” Nat. Methods 7(5), 377–381 (2010).
[Crossref] [PubMed]

Mullen, K.

H. Uji-i, S. M. Melnikov, A. Deres, G. Bergamini, F. De Schryver, A. Herrmann, K. Mullen, J. Enderlein, and J. Hofkens, “Visualizing spatial and temporal heterogeneity of single molecule rotational diffusion in a glassy polymer by defocused wide-field imaging,” Polymer (Guildf.) 47(7), 2511–2518 (2006).
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Patra, D.

D. Patra, I. Gregor, J. Enderlein, and M. Sauer, “Defocused imaging of quantum-dot angular distribution of radiation,” Appl. Phys. Lett. 87(10), 101103 (2005).
[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, “Defocused orientation and position imaging (DOPI) of myosin V,” Proc. Natl. Acad. Sci. U.S.A. 103(17), 6495–6499 (2006).
[Crossref] [PubMed]

Preza, C.

Qiao, Y.

L. Xiao, Y. Qiao, Y. He, and E. S. Yeung, “Imaging translational and rotational diffusion of single anisotropic nanoparticles with planar illumination microscopy,” J. Am. Chem. Soc. 133(27), 10638–10645 (2011).
[Crossref] [PubMed]

L. Xiao, Y. Qiao, Y. He, and E. S. Yeung, “Three dimensional orientational imaging of nanoparticles with darkfield microscopy,” Anal. Chem. 82(12), 5268–5274 (2010).
[Crossref] [PubMed]

Salamon, Z.

Z. Salamon and G. Tollin, “Optical anisotropy in lipid bilayer membranes: Coupled plasmon-waveguide resonance measurements of molecular orientation, polarizability, and shape,” Biophys. J. 80(3), 1557–1567 (2001).
[Crossref] [PubMed]

Sauer, M.

D. Patra, I. Gregor, J. Enderlein, and M. Sauer, “Defocused imaging of quantum-dot angular distribution of radiation,” Appl. Phys. Lett. 87(10), 101103 (2005).
[Crossref]

Schnapp, B. J.

J. Gelles, B. J. Schnapp, and M. P. Sheetz, “Tracking kinesin-driven movements with nanometre-scale precision,” Nature 331(6155), 450–453 (1988).
[Crossref] [PubMed]

Selvin, P. R.

J. Enderlein, E. Toprak, and P. R. Selvin, “Polarization effect on position accuracy of fluorophore localization,” Opt. Express 14(18), 8111–8120 (2006).
[Crossref] [PubMed]

E. Toprak, J. Enderlein, S. Syed, S. A. McKinney, R. G. Petschek, T. Ha, Y. E. Goldman, and P. R. Selvin, “Defocused orientation and position imaging (DOPI) of myosin V,” Proc. Natl. Acad. Sci. U.S.A. 103(17), 6495–6499 (2006).
[Crossref] [PubMed]

A. Yildiz and P. R. Selvin, “Fluorescence imaging with one nanometer accuracy: application to molecular motors,” Acc. Chem. Res. 38(7), 574–582 (2005).
[Crossref] [PubMed]

A. Yildiz, M. Tomishige, R. D. Vale, and P. R. Selvin, “Kinesin walks hand-over-hand,” Science 303(5658), 676–678 (2004).
[Crossref] [PubMed]

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, “Myosin V walks hand-over-hand: single fluorophore imaging with 1.5-nm localization,” Science 300(5628), 2061–2065 (2003).
[Crossref] [PubMed]

Sheetz, M. P.

J. Gelles, B. J. Schnapp, and M. P. Sheetz, “Tracking kinesin-driven movements with nanometre-scale precision,” Nature 331(6155), 450–453 (1988).
[Crossref] [PubMed]

Sheppard, C. J. R.

Shribak, M.

Snyder, D. L.

Sönnichsen, C.

C. Sönnichsen and A. P. Alivisatos, “Gold nanorods as novel nonbleaching plasmon-based orientation sensors for polarized single-particle microscopy,” Nano Lett. 5(2), 301–304 (2005).
[Crossref] [PubMed]

Spudich, J. A.

K. I. Mortensen, L. S. Churchman, J. A. Spudich, and H. Flyvbjerg, “Optimized localization analysis for single-molecule tracking and super-resolution microscopy,” Nat. Methods 7(5), 377–381 (2010).
[Crossref] [PubMed]

Stender, A. S.

A. S. Stender, G. Wang, W. Sun, and N. Fang, “Influence of gold nanorod geometry on optical response,” ACS Nano 4(12), 7667–7675 (2010).
[Crossref] [PubMed]

Sun, W.

Y. Gu, W. Sun, G. Wang, K. Jeftinija, S. Jeftinija, and N. Fang, “Rotational dynamics of cargos at pauses during axonal transport,” Nat. Commun. 3, 1030 (2012).
[Crossref] [PubMed]

Y. Gu, X. Di, W. Sun, G. Wang, and N. Fang, “Three-dimensional super-localization and tracking of single gold nanoparticles in cells,” Anal. Chem. 84(9), 4111–4117 (2012).
[Crossref] [PubMed]

J. W. Ha, W. Sun, G. Wang, and N. Fang, “Differential interference contrast polarization anisotropy for tracking rotational dynamics of gold nanorods,” Chem. Commun. (Camb.) 47(27), 7743–7745 (2011).
[Crossref] [PubMed]

Y. Gu, W. Sun, G. Wang, and N. Fang, “Single particle orientation and rotation tracking discloses distinctive rotational dynamics of drug delivery vectors on live cell membranes,” J. Am. Chem. Soc. 133(15), 5720–5723 (2011).
[Crossref] [PubMed]

A. S. Stender, G. Wang, W. Sun, and N. Fang, “Influence of gold nanorod geometry on optical response,” ACS Nano 4(12), 7667–7675 (2010).
[Crossref] [PubMed]

G. Wang, W. Sun, Y. Luo, and N. Fang, “Resolving rotational motions of nano-objects in engineered environments and live cells with gold nanorods and differential interference contrast microscopy,” J. Am. Chem. Soc. 132(46), 16417–16422 (2010).
[Crossref] [PubMed]

Swaminathan, R.

R. Swaminathan, C. P. Hoang, and A. S. Verkman, “Photobleaching recovery and anisotropy decay of green fluorescent protein GFP-S65T in solution and cells: Cytoplasmic viscosity probed by green fluorescent protein translational and rotational diffusion,” Biophys. J. 72(4), 1900–1907 (1997).
[Crossref] [PubMed]

Syed, S.

E. Toprak, J. Enderlein, S. Syed, S. A. McKinney, R. G. Petschek, T. Ha, Y. E. Goldman, and P. R. Selvin, “Defocused orientation and position imaging (DOPI) of myosin V,” Proc. Natl. Acad. Sci. U.S.A. 103(17), 6495–6499 (2006).
[Crossref] [PubMed]

Titus, E. J.

E. J. Titus and K. A. Willets, “Superlocalization surface-enhanced Raman scattering microscopy: comparing point spread function models in the ensemble and single-molecule limits,” ACS Nano 7(9), 8284–8294 (2013).
[Crossref] [PubMed]

Tollin, G.

Z. Salamon and G. Tollin, “Optical anisotropy in lipid bilayer membranes: Coupled plasmon-waveguide resonance measurements of molecular orientation, polarizability, and shape,” Biophys. J. 80(3), 1557–1567 (2001).
[Crossref] [PubMed]

Tomishige, M.

A. Yildiz, M. Tomishige, R. D. Vale, and P. R. Selvin, “Kinesin walks hand-over-hand,” Science 303(5658), 676–678 (2004).
[Crossref] [PubMed]

Toprak, E.

J. Enderlein, E. Toprak, and P. R. Selvin, “Polarization effect on position accuracy of fluorophore localization,” Opt. Express 14(18), 8111–8120 (2006).
[Crossref] [PubMed]

E. Toprak, J. Enderlein, S. Syed, S. A. McKinney, R. G. Petschek, T. Ha, Y. E. Goldman, and P. R. Selvin, “Defocused orientation and position imaging (DOPI) of myosin V,” Proc. Natl. Acad. Sci. U.S.A. 103(17), 6495–6499 (2006).
[Crossref] [PubMed]

Uji-i, H.

H. Uji-i, S. M. Melnikov, A. Deres, G. Bergamini, F. De Schryver, A. Herrmann, K. Mullen, J. Enderlein, and J. Hofkens, “Visualizing spatial and temporal heterogeneity of single molecule rotational diffusion in a glassy polymer by defocused wide-field imaging,” Polymer (Guildf.) 47(7), 2511–2518 (2006).
[Crossref]

Vale, R. D.

A. Yildiz, M. Tomishige, R. D. Vale, and P. R. Selvin, “Kinesin walks hand-over-hand,” Science 303(5658), 676–678 (2004).
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van Munster, E. B.

E. B. van Munster, L. J. van Vliet, and J. A. Aten, “Reconstruction of optical pathlength distributions from images obtained by a wide-field differential interference contrast microscope,” J. Microsc. 188(2), 149–157 (1997).
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van Vliet, L. J.

E. B. van Munster, L. J. van Vliet, and J. A. Aten, “Reconstruction of optical pathlength distributions from images obtained by a wide-field differential interference contrast microscope,” J. Microsc. 188(2), 149–157 (1997).
[Crossref] [PubMed]

Verkman, A. S.

R. Swaminathan, C. P. Hoang, and A. S. Verkman, “Photobleaching recovery and anisotropy decay of green fluorescent protein GFP-S65T in solution and cells: Cytoplasmic viscosity probed by green fluorescent protein translational and rotational diffusion,” Biophys. J. 72(4), 1900–1907 (1997).
[Crossref] [PubMed]

Wang, G.

Y. Gu, G. Wang, and N. Fang, “Simultaneous single-particle superlocalization and rotational tracking,” ACS Nano 7(2), 1658–1665 (2013).
[Crossref] [PubMed]

Y. Gu, X. Di, W. Sun, G. Wang, and N. Fang, “Three-dimensional super-localization and tracking of single gold nanoparticles in cells,” Anal. Chem. 84(9), 4111–4117 (2012).
[Crossref] [PubMed]

L. Xiao, J. W. Ha, L. Wei, G. Wang, and N. Fang, “Determining the full three-dimensional orientation of single anisotropic nanoparticles by differential interference contrast microscopy,” Angew. Chem. Int. Ed. Engl. 51(31), 7734–7738 (2012).
[Crossref] [PubMed]

Y. Gu, W. Sun, G. Wang, K. Jeftinija, S. Jeftinija, and N. Fang, “Rotational dynamics of cargos at pauses during axonal transport,” Nat. Commun. 3, 1030 (2012).
[Crossref] [PubMed]

J. W. Ha, W. Sun, G. Wang, and N. Fang, “Differential interference contrast polarization anisotropy for tracking rotational dynamics of gold nanorods,” Chem. Commun. (Camb.) 47(27), 7743–7745 (2011).
[Crossref] [PubMed]

Y. Gu, W. Sun, G. Wang, and N. Fang, “Single particle orientation and rotation tracking discloses distinctive rotational dynamics of drug delivery vectors on live cell membranes,” J. Am. Chem. Soc. 133(15), 5720–5723 (2011).
[Crossref] [PubMed]

G. Wang, W. Sun, Y. Luo, and N. Fang, “Resolving rotational motions of nano-objects in engineered environments and live cells with gold nanorods and differential interference contrast microscopy,” J. Am. Chem. Soc. 132(46), 16417–16422 (2010).
[Crossref] [PubMed]

A. S. Stender, G. Wang, W. Sun, and N. Fang, “Influence of gold nanorod geometry on optical response,” ACS Nano 4(12), 7667–7675 (2010).
[Crossref] [PubMed]

Wei, L.

L. Wei, J. Xu, Z. Ye, X. Zhu, M. Zhong, W. Luo, B. Chen, H. Duan, Q. Liu, and L. Xiao, “Orientational imaging of a single gold nanorod at the liquid/solid interface with polarized evanescent field illumination,” Anal. Chem. 88(4), 1995–1999 (2016).
[Crossref] [PubMed]

L. Xiao, J. W. Ha, L. Wei, G. Wang, and N. Fang, “Determining the full three-dimensional orientation of single anisotropic nanoparticles by differential interference contrast microscopy,” Angew. Chem. Int. Ed. Engl. 51(31), 7734–7738 (2012).
[Crossref] [PubMed]

Weiss, S.

T. Ha, T. A. Laurence, D. S. Chemla, and S. Weiss, “Polarization spectroscopy of single fluorescent molecules,” J. Phys. Chem. B 103(33), 6839–6850 (1999).
[Crossref]

Willets, K. A.

E. J. Titus and K. A. Willets, “Superlocalization surface-enhanced Raman scattering microscopy: comparing point spread function models in the ensemble and single-molecule limits,” ACS Nano 7(9), 8284–8294 (2013).
[Crossref] [PubMed]

Xiao, L.

L. Wei, J. Xu, Z. Ye, X. Zhu, M. Zhong, W. Luo, B. Chen, H. Duan, Q. Liu, and L. Xiao, “Orientational imaging of a single gold nanorod at the liquid/solid interface with polarized evanescent field illumination,” Anal. Chem. 88(4), 1995–1999 (2016).
[Crossref] [PubMed]

L. Xiao, J. W. Ha, L. Wei, G. Wang, and N. Fang, “Determining the full three-dimensional orientation of single anisotropic nanoparticles by differential interference contrast microscopy,” Angew. Chem. Int. Ed. Engl. 51(31), 7734–7738 (2012).
[Crossref] [PubMed]

L. Xiao, Y. Qiao, Y. He, and E. S. Yeung, “Imaging translational and rotational diffusion of single anisotropic nanoparticles with planar illumination microscopy,” J. Am. Chem. Soc. 133(27), 10638–10645 (2011).
[Crossref] [PubMed]

L. Xiao, Y. Qiao, Y. He, and E. S. Yeung, “Three dimensional orientational imaging of nanoparticles with darkfield microscopy,” Anal. Chem. 82(12), 5268–5274 (2010).
[Crossref] [PubMed]

Xu, J.

L. Wei, J. Xu, Z. Ye, X. Zhu, M. Zhong, W. Luo, B. Chen, H. Duan, Q. Liu, and L. Xiao, “Orientational imaging of a single gold nanorod at the liquid/solid interface with polarized evanescent field illumination,” Anal. Chem. 88(4), 1995–1999 (2016).
[Crossref] [PubMed]

Ye, Z.

L. Wei, J. Xu, Z. Ye, X. Zhu, M. Zhong, W. Luo, B. Chen, H. Duan, Q. Liu, and L. Xiao, “Orientational imaging of a single gold nanorod at the liquid/solid interface with polarized evanescent field illumination,” Anal. Chem. 88(4), 1995–1999 (2016).
[Crossref] [PubMed]

Yeung, E. S.

L. Xiao, Y. Qiao, Y. He, and E. S. Yeung, “Imaging translational and rotational diffusion of single anisotropic nanoparticles with planar illumination microscopy,” J. Am. Chem. Soc. 133(27), 10638–10645 (2011).
[Crossref] [PubMed]

L. Xiao, Y. Qiao, Y. He, and E. S. Yeung, “Three dimensional orientational imaging of nanoparticles with darkfield microscopy,” Anal. Chem. 82(12), 5268–5274 (2010).
[Crossref] [PubMed]

Yildiz, A.

A. Yildiz and P. R. Selvin, “Fluorescence imaging with one nanometer accuracy: application to molecular motors,” Acc. Chem. Res. 38(7), 574–582 (2005).
[Crossref] [PubMed]

A. Yildiz, M. Tomishige, R. D. Vale, and P. R. Selvin, “Kinesin walks hand-over-hand,” Science 303(5658), 676–678 (2004).
[Crossref] [PubMed]

A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, “Myosin V walks hand-over-hand: single fluorophore imaging with 1.5-nm localization,” Science 300(5628), 2061–2065 (2003).
[Crossref] [PubMed]

Zhong, M.

L. Wei, J. Xu, Z. Ye, X. Zhu, M. Zhong, W. Luo, B. Chen, H. Duan, Q. Liu, and L. Xiao, “Orientational imaging of a single gold nanorod at the liquid/solid interface with polarized evanescent field illumination,” Anal. Chem. 88(4), 1995–1999 (2016).
[Crossref] [PubMed]

Zhu, X.

L. Wei, J. Xu, Z. Ye, X. Zhu, M. Zhong, W. Luo, B. Chen, H. Duan, Q. Liu, and L. Xiao, “Orientational imaging of a single gold nanorod at the liquid/solid interface with polarized evanescent field illumination,” Anal. Chem. 88(4), 1995–1999 (2016).
[Crossref] [PubMed]

Acc. Chem. Res. (1)

A. Yildiz and P. R. Selvin, “Fluorescence imaging with one nanometer accuracy: application to molecular motors,” Acc. Chem. Res. 38(7), 574–582 (2005).
[Crossref] [PubMed]

ACS Nano (3)

Y. Gu, G. Wang, and N. Fang, “Simultaneous single-particle superlocalization and rotational tracking,” ACS Nano 7(2), 1658–1665 (2013).
[Crossref] [PubMed]

E. J. Titus and K. A. Willets, “Superlocalization surface-enhanced Raman scattering microscopy: comparing point spread function models in the ensemble and single-molecule limits,” ACS Nano 7(9), 8284–8294 (2013).
[Crossref] [PubMed]

A. S. Stender, G. Wang, W. Sun, and N. Fang, “Influence of gold nanorod geometry on optical response,” ACS Nano 4(12), 7667–7675 (2010).
[Crossref] [PubMed]

Anal. Chem. (3)

L. Wei, J. Xu, Z. Ye, X. Zhu, M. Zhong, W. Luo, B. Chen, H. Duan, Q. Liu, and L. Xiao, “Orientational imaging of a single gold nanorod at the liquid/solid interface with polarized evanescent field illumination,” Anal. Chem. 88(4), 1995–1999 (2016).
[Crossref] [PubMed]

L. Xiao, Y. Qiao, Y. He, and E. S. Yeung, “Three dimensional orientational imaging of nanoparticles with darkfield microscopy,” Anal. Chem. 82(12), 5268–5274 (2010).
[Crossref] [PubMed]

Y. Gu, X. Di, W. Sun, G. Wang, and N. Fang, “Three-dimensional super-localization and tracking of single gold nanoparticles in cells,” Anal. Chem. 84(9), 4111–4117 (2012).
[Crossref] [PubMed]

Angew. Chem. Int. Ed. Engl. (1)

L. Xiao, J. W. Ha, L. Wei, G. Wang, and N. Fang, “Determining the full three-dimensional orientation of single anisotropic nanoparticles by differential interference contrast microscopy,” Angew. Chem. Int. Ed. Engl. 51(31), 7734–7738 (2012).
[Crossref] [PubMed]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

D. Patra, I. Gregor, J. Enderlein, and M. Sauer, “Defocused imaging of quantum-dot angular distribution of radiation,” Appl. Phys. Lett. 87(10), 101103 (2005).
[Crossref]

Biophys. J. (2)

R. Swaminathan, C. P. Hoang, and A. S. Verkman, “Photobleaching recovery and anisotropy decay of green fluorescent protein GFP-S65T in solution and cells: Cytoplasmic viscosity probed by green fluorescent protein translational and rotational diffusion,” Biophys. J. 72(4), 1900–1907 (1997).
[Crossref] [PubMed]

Z. Salamon and G. Tollin, “Optical anisotropy in lipid bilayer membranes: Coupled plasmon-waveguide resonance measurements of molecular orientation, polarizability, and shape,” Biophys. J. 80(3), 1557–1567 (2001).
[Crossref] [PubMed]

Chem. Commun. (Camb.) (1)

J. W. Ha, W. Sun, G. Wang, and N. Fang, “Differential interference contrast polarization anisotropy for tracking rotational dynamics of gold nanorods,” Chem. Commun. (Camb.) 47(27), 7743–7745 (2011).
[Crossref] [PubMed]

J. Am. Chem. Soc. (3)

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Figures (6)

Fig. 1
Fig. 1

(a) Schematic illustration of a fixed dipole with polar angle ψ and azimuthal angle θ. One of the polarization direction (x-axis) may be referred to as the dark optical axis because a gold nanorod would generate a nearly all dark image when its long axis is aligned with this polarization direction; similarly, the other orthogonal polarization direction (y-axis) may be called the bright optical axis in accordance to the presentation of nearly all bright DIC image. These definitions of optical axes are used consistently in all the experimental and simulated images of gold nanorods in this study. (b) Experimental DIC images of a gold nanorod with the azimuthal angles from 0° to 180° in 15° steps. Note that 0° and 180° are equivalent due to the symmetry. (c) The corresponding bright-part intensity (blue) and dark-part intensity (red) traces for the experimental DIC images in b. (d) Computer simulated DIC images of a gold nanorod with a polar angle of 90° and azimuthal angles from 0° to 180° in 15° steps. (e) The corresponding bright-part intensity (blue) and dark-part intensity (red) traces for the simulated DIC images in d.

Fig. 2
Fig. 2

Two intermediate bright-field images of an 80-nm gold nanosphere obtained when the angle between the first and second polarizer is (a) 45° and (b) −45°. (c) The merged image. The two crosses are the centers of the two intermediate bright-field images (a) and (b) by fitting with 2D Gaussian functions. The distance between the two centers is the shear distance. The shear direction is from northwest to southeast, which is indicated by the relative positions of the two centers.

Fig. 3
Fig. 3

Experimental and simulated DIC images of (a) a 40 nm × 118 nm gold nanorod (90° polar angle and 45° azimuthal angle) and (b) an 80-nm gold nanosphere under 540 or 700 nm incident light with either Nikon standard/high-contrast (100XI) or high-resolution (100XI-R) prisms. It is worth noting that the measured shear distance is not affected by the size and shape of the nanoparticle when other configurations are the same.

Fig. 4
Fig. 4

(a) Localization of the simulated gold nanorod images with a constant polar angle of 90° and various azimuthal angles. Red and blue: the x and y coordinates of the weighed centers of the bright part. Black and green: the x and y coordinates of the weighed centers of the dark part. Cyan and magenta: the x and y coordinates of the midpoint between the weighed centers of the bright part and dark part. Grey and yellow: the x and y centroid coordinates of the gold nanorod when either bright or dark part dominates. Yellow squares are hardly visible in the figure because they are closely overlapped with grey squares. (b) Standard deviations of the localized x (black) and y (red) coordinates of gold nanorods at four polar angles: 45°, 60°, 75°and 90°. Each data point is calculated from the simulated images with various azimuthal angles from 0 to 180°, in 5° step size. The localization is determined from the weighed centers of the bright part and the dark part of the images.

Fig. 5
Fig. 5

Localization of the simulated gold nanorod images with constant polar angles at 75° (a), 60° (b) and 45° (c) and with various azimuthal angles. Red and blue: the x and y coordinates of the weighed center of the bright part. Black and green: the x and y coordinates of the weighed center of the dark part. Cyan and magenta: the x and y coordinates of the midpoint between the weighed centers of the bright part and dark part. Grey and yellow: the x and y centroid coordinates of the gold nanorod when either the bright or dark part dominates; they are calculated as the weighed bright center minus half of the shear distance or the weighed dark center plus half of the shear distance.

Fig. 6
Fig. 6

(a). The DIC images of two neighboring gold nanorods (labeled with 1 and 2) during 360° in-plane rotation. The scale bar represents 2 μm. (b) The bright (blue) and dark (red) DIC intensity traces of particle 1 (solid square) and 2 (hollow square) during the 360° in-plane rotation. (c) Localization of particle 2 relative to the position of particle 1. The radius of the green circle indicates the average distance between these two particles.

Tables (1)

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Table 1 Shear distances for different configurations.

Equations (2)

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h( x,y ) = ( 1R ) exp ( jΔθ )p( x+ Δx,y+ Δy ) Rexp ( jΔθ )p( x Δx,y Δy )
x= i j ( x i | I i,j Threshold| ) i j | I i,j Threshold| y= i j ( y i | I i,j Threshold| ) i j | I i,j Threshold|

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