Abstract

The ability to localize precisely a single optical emitter is important for particle tracking applications and super resolution microscopy. It is known that for a traditional microscope the ability to localize such an emitter is limited by the photon count. Here we analyze the ability to improve such localization by imposing interference fringes. We show here that a simple grating interferometer can introduce such improvement in certain circumstances and analyze what is required to increase the localization precision further.

© 2017 Optical Society of America

Full Article  |  PDF Article
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  1. R. E. Thompson, D. R. Larson, and W. W. Webb, “Precise nanometer localization analysis for individual fluorescent probes,” Biophys. J. 82(5), 2775–2783 (2002).
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  2. 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]
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  8. M. Lindner, G. Nir, S. Medalion, H. R. Dietrich, Y. Rabin, and Y. Garini, “Force-free measurements of the conformations of DNA molecules tethered to a wall,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(1), 011916 (2011).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  10. X. Nan, P. A. Sims, and X. S. Xie, “Organelle tracking in a living cell with microsecond time resolution and nanometer spatial precision,” ChemPhysChem 9(5), 707–712 (2008).
    [Crossref] [PubMed]
  11. E. C. Arnspang, J. R. Brewer, and B. C. Lagerholm, “Multi-color single particle tracking with quantum dots,” PLoS One 7(11), e48521 (2012).
    [Crossref] [PubMed]
  12. L. M. Browning, T. Huang, and X. N. Xu, “Far-field photostable optical nanoscopy (PHOTON) for real-time super-resolution single-molecular imaging of signaling pathways of single live cells,” Nanoscale 4, 2797–2812 (2012).
  13. R. J. Ober, S. Ram, and E. S. Ward, “Localization accuracy in single-molecule microscopy,” Biophys. J. 86(2), 1185–1200 (2004).
    [Crossref] [PubMed]
  14. 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]
  15. E. A. Mukamel and M. J. Schnitzer, “Unified resolution bounds for conventional and stochastic localization fluorescence microscopy,” Phys. Rev. Lett. 109(16), 168102 (2012).
    [Crossref] [PubMed]
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    [Crossref]
  17. C. S. Smith, N. Joseph, B. Rieger, and K. A. Lidke, “Fast, single-molecule localization that achieves theoretically minimum uncertainty,” Nat. Methods 7(5), 373–375 (2010).
    [Crossref] [PubMed]
  18. R. Parthasarathy, “Rapid, accurate particle tracking by calculation of radial symmetry centers,” Nat. Methods 9(7), 724–726 (2012).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  20. S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 2995–2999 (2009).
    [Crossref] [PubMed]
  21. Y. Shechtman, S. J. Sahl, A. S. Backer, and W. E. Moerner, “Optimal point spread function design for 3D imaging,” Phys. Rev. Lett. 113(13), 133902 (2014).
    [Crossref] [PubMed]
  22. Y. Shechtman, L. E. Weiss, A. S. Backer, S. J. Sahl, and W. E. Moerner, “Precise 3D scan-free multiple-particle tracking over large axial ranges with Tetrapod point spread functions,” Nano Lett. 15, 4194–4199 (2015).
    [Crossref]
  23. C. G. Ebeling, A. Meiri, J. Martineau, Z. Zalevsky, J. M. Gerton, and R. Menon, “Increased localization precision by interference fringe analysis,” Nanoscale 7(23), 10430–10437 (2015).
    [Crossref] [PubMed]
  24. B. J. Thompson and E. Wolf, “Two-beam interference with partially coherent light,” JOSA 47(10), 895–902 (1957).
    [Crossref]
  25. J. Martineau, R. Menon, A. Meiri, Z. Zalevsky, and J. M. Gerton, “Increasing theoretical localization precision using multi-peaked point spread functions,” Submitted.
  26. E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
    [Crossref] [PubMed]
  27. M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006).
    [Crossref] [PubMed]
  28. S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91(11), 4258–4272 (2006).
    [Crossref] [PubMed]
  29. A. Tamada, S. Kawase, F. Murakami, and H. Kamiguchi, “Autonomous right-screw rotation of growth cone filopodia drives neurite turning,” J. Cell Biol. 188(3), 429–441 (2010).
    [Crossref] [PubMed]
  30. D. Tian, M. Diao, Y. Jiang, L. Sun, Y. Zhang, Z. Chen, S. Huang, and G. Ou, “Anillin regulates neuronal migration and neurite growth by linking RhoG to the actin cytoskeleton,” Curr. Biol. 25(9), 1135–1145 (2015).
    [Crossref] [PubMed]

2015 (3)

Y. Shechtman, L. E. Weiss, A. S. Backer, S. J. Sahl, and W. E. Moerner, “Precise 3D scan-free multiple-particle tracking over large axial ranges with Tetrapod point spread functions,” Nano Lett. 15, 4194–4199 (2015).
[Crossref]

C. G. Ebeling, A. Meiri, J. Martineau, Z. Zalevsky, J. M. Gerton, and R. Menon, “Increased localization precision by interference fringe analysis,” Nanoscale 7(23), 10430–10437 (2015).
[Crossref] [PubMed]

D. Tian, M. Diao, Y. Jiang, L. Sun, Y. Zhang, Z. Chen, S. Huang, and G. Ou, “Anillin regulates neuronal migration and neurite growth by linking RhoG to the actin cytoskeleton,” Curr. Biol. 25(9), 1135–1145 (2015).
[Crossref] [PubMed]

2014 (2)

Y. Shechtman, S. J. Sahl, A. S. Backer, and W. E. Moerner, “Optimal point spread function design for 3D imaging,” Phys. Rev. Lett. 113(13), 133902 (2014).
[Crossref] [PubMed]

P. Lebel, A. Basu, F. C. Oberstrass, E. M. Tretter, and Z. Bryant, “Gold rotor bead tracking for high-speed measurements of DNA twist, torque and extension,” Nat. Methods 11(4), 456–462 (2014).
[Crossref] [PubMed]

2012 (4)

E. C. Arnspang, J. R. Brewer, and B. C. Lagerholm, “Multi-color single particle tracking with quantum dots,” PLoS One 7(11), e48521 (2012).
[Crossref] [PubMed]

L. M. Browning, T. Huang, and X. N. Xu, “Far-field photostable optical nanoscopy (PHOTON) for real-time super-resolution single-molecular imaging of signaling pathways of single live cells,” Nanoscale 4, 2797–2812 (2012).

E. A. Mukamel and M. J. Schnitzer, “Unified resolution bounds for conventional and stochastic localization fluorescence microscopy,” Phys. Rev. Lett. 109(16), 168102 (2012).
[Crossref] [PubMed]

R. Parthasarathy, “Rapid, accurate particle tracking by calculation of radial symmetry centers,” Nat. Methods 9(7), 724–726 (2012).
[Crossref] [PubMed]

2011 (1)

M. Lindner, G. Nir, S. Medalion, H. R. Dietrich, Y. Rabin, and Y. Garini, “Force-free measurements of the conformations of DNA molecules tethered to a wall,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(1), 011916 (2011).
[Crossref] [PubMed]

2010 (3)

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]

A. Tamada, S. Kawase, F. Murakami, and H. Kamiguchi, “Autonomous right-screw rotation of growth cone filopodia drives neurite turning,” J. Cell Biol. 188(3), 429–441 (2010).
[Crossref] [PubMed]

C. S. Smith, N. Joseph, B. Rieger, and K. A. Lidke, “Fast, single-molecule localization that achieves theoretically minimum uncertainty,” Nat. Methods 7(5), 373–375 (2010).
[Crossref] [PubMed]

2009 (1)

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 2995–2999 (2009).
[Crossref] [PubMed]

2008 (2)

S. R. P. Pavani and R. Piestun, “Three dimensional tracking of fluorescent microparticles using a photon-limited double-helix response system,” Opt. Express 16(26), 22048–22057 (2008).
[Crossref] [PubMed]

X. Nan, P. A. Sims, and X. S. Xie, “Organelle tracking in a living cell with microsecond time resolution and nanometer spatial precision,” ChemPhysChem 9(5), 707–712 (2008).
[Crossref] [PubMed]

2006 (3)

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006).
[Crossref] [PubMed]

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91(11), 4258–4272 (2006).
[Crossref] [PubMed]

2004 (2)

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

R. J. Ober, S. Ram, and E. S. Ward, “Localization accuracy in single-molecule microscopy,” Biophys. J. 86(2), 1185–1200 (2004).
[Crossref] [PubMed]

2003 (1)

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]

2002 (1)

R. E. Thompson, D. R. Larson, and W. W. Webb, “Precise nanometer localization analysis for individual fluorescent probes,” Biophys. J. 82(5), 2775–2783 (2002).
[Crossref] [PubMed]

2001 (1)

D. Mendlovic, G. Shabtay, Z. Zalevsky, and S. G. Lipson, “The optimal system for sub-wavelength point source localization,” Opt. Commun. 198(4-6), 311–315 (2001).
[Crossref]

2000 (1)

J. Enderlein, “Tracking of fluorescent molecules diffusing within membranes,” Appl. Phys. B 71(5), 773–777 (2000).
[Crossref]

1997 (1)

G. J. Schütz, H. Schindler, and T. Schmidt, “Single-molecule microscopy on model membranes reveals anomalous diffusion,” Biophys. J. 73(2), 1073–1080 (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]

1957 (1)

B. J. Thompson and E. Wolf, “Two-beam interference with partially coherent light,” JOSA 47(10), 895–902 (1957).
[Crossref]

Arnspang, E. C.

E. C. Arnspang, J. R. Brewer, and B. C. Lagerholm, “Multi-color single particle tracking with quantum dots,” PLoS One 7(11), e48521 (2012).
[Crossref] [PubMed]

Backer, A. S.

Y. Shechtman, L. E. Weiss, A. S. Backer, S. J. Sahl, and W. E. Moerner, “Precise 3D scan-free multiple-particle tracking over large axial ranges with Tetrapod point spread functions,” Nano Lett. 15, 4194–4199 (2015).
[Crossref]

Y. Shechtman, S. J. Sahl, A. S. Backer, and W. E. Moerner, “Optimal point spread function design for 3D imaging,” Phys. Rev. Lett. 113(13), 133902 (2014).
[Crossref] [PubMed]

Basu, A.

P. Lebel, A. Basu, F. C. Oberstrass, E. M. Tretter, and Z. Bryant, “Gold rotor bead tracking for high-speed measurements of DNA twist, torque and extension,” Nat. Methods 11(4), 456–462 (2014).
[Crossref] [PubMed]

Bates, M.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006).
[Crossref] [PubMed]

Betzig, E.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Biteen, J. S.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 2995–2999 (2009).
[Crossref] [PubMed]

Bonifacino, J. S.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Brewer, J. R.

E. C. Arnspang, J. R. Brewer, and B. C. Lagerholm, “Multi-color single particle tracking with quantum dots,” PLoS One 7(11), e48521 (2012).
[Crossref] [PubMed]

Browning, L. M.

L. M. Browning, T. Huang, and X. N. Xu, “Far-field photostable optical nanoscopy (PHOTON) for real-time super-resolution single-molecular imaging of signaling pathways of single live cells,” Nanoscale 4, 2797–2812 (2012).

Bryant, Z.

P. Lebel, A. Basu, F. C. Oberstrass, E. M. Tretter, and Z. Bryant, “Gold rotor bead tracking for high-speed measurements of DNA twist, torque and extension,” Nat. Methods 11(4), 456–462 (2014).
[Crossref] [PubMed]

Chen, Z.

D. Tian, M. Diao, Y. Jiang, L. Sun, Y. Zhang, Z. Chen, S. Huang, and G. Ou, “Anillin regulates neuronal migration and neurite growth by linking RhoG to the actin cytoskeleton,” Curr. Biol. 25(9), 1135–1145 (2015).
[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]

Davidson, M. W.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Diao, M.

D. Tian, M. Diao, Y. Jiang, L. Sun, Y. Zhang, Z. Chen, S. Huang, and G. Ou, “Anillin regulates neuronal migration and neurite growth by linking RhoG to the actin cytoskeleton,” Curr. Biol. 25(9), 1135–1145 (2015).
[Crossref] [PubMed]

Dietrich, H. R.

M. Lindner, G. Nir, S. Medalion, H. R. Dietrich, Y. Rabin, and Y. Garini, “Force-free measurements of the conformations of DNA molecules tethered to a wall,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(1), 011916 (2011).
[Crossref] [PubMed]

Ebeling, C. G.

C. G. Ebeling, A. Meiri, J. Martineau, Z. Zalevsky, J. M. Gerton, and R. Menon, “Increased localization precision by interference fringe analysis,” Nanoscale 7(23), 10430–10437 (2015).
[Crossref] [PubMed]

Enderlein, J.

J. Enderlein, “Tracking of fluorescent molecules diffusing within membranes,” Appl. Phys. B 71(5), 773–777 (2000).
[Crossref]

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]

Garini, Y.

M. Lindner, G. Nir, S. Medalion, H. R. Dietrich, Y. Rabin, and Y. Garini, “Force-free measurements of the conformations of DNA molecules tethered to a wall,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(1), 011916 (2011).
[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]

Gerton, J. M.

C. G. Ebeling, A. Meiri, J. Martineau, Z. Zalevsky, J. M. Gerton, and R. Menon, “Increased localization precision by interference fringe analysis,” Nanoscale 7(23), 10430–10437 (2015).
[Crossref] [PubMed]

J. Martineau, R. Menon, A. Meiri, Z. Zalevsky, and J. M. Gerton, “Increasing theoretical localization precision using multi-peaked point spread functions,” Submitted.

Girirajan, T. P. K.

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91(11), 4258–4272 (2006).
[Crossref] [PubMed]

Goldman, Y. E.

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]

Ha, T.

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]

Hess, H. F.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Hess, S. T.

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91(11), 4258–4272 (2006).
[Crossref] [PubMed]

Huang, S.

D. Tian, M. Diao, Y. Jiang, L. Sun, Y. Zhang, Z. Chen, S. Huang, and G. Ou, “Anillin regulates neuronal migration and neurite growth by linking RhoG to the actin cytoskeleton,” Curr. Biol. 25(9), 1135–1145 (2015).
[Crossref] [PubMed]

Huang, T.

L. M. Browning, T. Huang, and X. N. Xu, “Far-field photostable optical nanoscopy (PHOTON) for real-time super-resolution single-molecular imaging of signaling pathways of single live cells,” Nanoscale 4, 2797–2812 (2012).

Jiang, Y.

D. Tian, M. Diao, Y. Jiang, L. Sun, Y. Zhang, Z. Chen, S. Huang, and G. Ou, “Anillin regulates neuronal migration and neurite growth by linking RhoG to the actin cytoskeleton,” Curr. Biol. 25(9), 1135–1145 (2015).
[Crossref] [PubMed]

Joseph, N.

C. S. Smith, N. Joseph, B. Rieger, and K. A. Lidke, “Fast, single-molecule localization that achieves theoretically minimum uncertainty,” Nat. Methods 7(5), 373–375 (2010).
[Crossref] [PubMed]

Kamiguchi, H.

A. Tamada, S. Kawase, F. Murakami, and H. Kamiguchi, “Autonomous right-screw rotation of growth cone filopodia drives neurite turning,” J. Cell Biol. 188(3), 429–441 (2010).
[Crossref] [PubMed]

Kawase, S.

A. Tamada, S. Kawase, F. Murakami, and H. Kamiguchi, “Autonomous right-screw rotation of growth cone filopodia drives neurite turning,” J. Cell Biol. 188(3), 429–441 (2010).
[Crossref] [PubMed]

Lagerholm, B. C.

E. C. Arnspang, J. R. Brewer, and B. C. Lagerholm, “Multi-color single particle tracking with quantum dots,” PLoS One 7(11), e48521 (2012).
[Crossref] [PubMed]

Larson, D. R.

R. E. Thompson, D. R. Larson, and W. W. Webb, “Precise nanometer localization analysis for individual fluorescent probes,” Biophys. J. 82(5), 2775–2783 (2002).
[Crossref] [PubMed]

Lebel, P.

P. Lebel, A. Basu, F. C. Oberstrass, E. M. Tretter, and Z. Bryant, “Gold rotor bead tracking for high-speed measurements of DNA twist, torque and extension,” Nat. Methods 11(4), 456–462 (2014).
[Crossref] [PubMed]

Lidke, K. A.

C. S. Smith, N. Joseph, B. Rieger, and K. A. Lidke, “Fast, single-molecule localization that achieves theoretically minimum uncertainty,” Nat. Methods 7(5), 373–375 (2010).
[Crossref] [PubMed]

Lindner, M.

M. Lindner, G. Nir, S. Medalion, H. R. Dietrich, Y. Rabin, and Y. Garini, “Force-free measurements of the conformations of DNA molecules tethered to a wall,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(1), 011916 (2011).
[Crossref] [PubMed]

Lindwasser, O. W.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Lippincott-Schwartz, J.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Lipson, S. G.

D. Mendlovic, G. Shabtay, Z. Zalevsky, and S. G. Lipson, “The optimal system for sub-wavelength point source localization,” Opt. Commun. 198(4-6), 311–315 (2001).
[Crossref]

Liu, N.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 2995–2999 (2009).
[Crossref] [PubMed]

Lord, S. J.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 2995–2999 (2009).
[Crossref] [PubMed]

Martineau, J.

C. G. Ebeling, A. Meiri, J. Martineau, Z. Zalevsky, J. M. Gerton, and R. Menon, “Increased localization precision by interference fringe analysis,” Nanoscale 7(23), 10430–10437 (2015).
[Crossref] [PubMed]

J. Martineau, R. Menon, A. Meiri, Z. Zalevsky, and J. M. Gerton, “Increasing theoretical localization precision using multi-peaked point spread functions,” Submitted.

Mason, M. D.

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91(11), 4258–4272 (2006).
[Crossref] [PubMed]

McKinney, S. A.

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]

Medalion, S.

M. Lindner, G. Nir, S. Medalion, H. R. Dietrich, Y. Rabin, and Y. Garini, “Force-free measurements of the conformations of DNA molecules tethered to a wall,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(1), 011916 (2011).
[Crossref] [PubMed]

Meiri, A.

C. G. Ebeling, A. Meiri, J. Martineau, Z. Zalevsky, J. M. Gerton, and R. Menon, “Increased localization precision by interference fringe analysis,” Nanoscale 7(23), 10430–10437 (2015).
[Crossref] [PubMed]

J. Martineau, R. Menon, A. Meiri, Z. Zalevsky, and J. M. Gerton, “Increasing theoretical localization precision using multi-peaked point spread functions,” Submitted.

Mendlovic, D.

D. Mendlovic, G. Shabtay, Z. Zalevsky, and S. G. Lipson, “The optimal system for sub-wavelength point source localization,” Opt. Commun. 198(4-6), 311–315 (2001).
[Crossref]

Menon, R.

C. G. Ebeling, A. Meiri, J. Martineau, Z. Zalevsky, J. M. Gerton, and R. Menon, “Increased localization precision by interference fringe analysis,” Nanoscale 7(23), 10430–10437 (2015).
[Crossref] [PubMed]

J. Martineau, R. Menon, A. Meiri, Z. Zalevsky, and J. M. Gerton, “Increasing theoretical localization precision using multi-peaked point spread functions,” Submitted.

Moerner, W. E.

Y. Shechtman, L. E. Weiss, A. S. Backer, S. J. Sahl, and W. E. Moerner, “Precise 3D scan-free multiple-particle tracking over large axial ranges with Tetrapod point spread functions,” Nano Lett. 15, 4194–4199 (2015).
[Crossref]

Y. Shechtman, S. J. Sahl, A. S. Backer, and W. E. Moerner, “Optimal point spread function design for 3D imaging,” Phys. Rev. Lett. 113(13), 133902 (2014).
[Crossref] [PubMed]

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 2995–2999 (2009).
[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]

Mukamel, E. A.

E. A. Mukamel and M. J. Schnitzer, “Unified resolution bounds for conventional and stochastic localization fluorescence microscopy,” Phys. Rev. Lett. 109(16), 168102 (2012).
[Crossref] [PubMed]

Murakami, F.

A. Tamada, S. Kawase, F. Murakami, and H. Kamiguchi, “Autonomous right-screw rotation of growth cone filopodia drives neurite turning,” J. Cell Biol. 188(3), 429–441 (2010).
[Crossref] [PubMed]

Nan, X.

X. Nan, P. A. Sims, and X. S. Xie, “Organelle tracking in a living cell with microsecond time resolution and nanometer spatial precision,” ChemPhysChem 9(5), 707–712 (2008).
[Crossref] [PubMed]

Nir, G.

M. Lindner, G. Nir, S. Medalion, H. R. Dietrich, Y. Rabin, and Y. Garini, “Force-free measurements of the conformations of DNA molecules tethered to a wall,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(1), 011916 (2011).
[Crossref] [PubMed]

Ober, R. J.

R. J. Ober, S. Ram, and E. S. Ward, “Localization accuracy in single-molecule microscopy,” Biophys. J. 86(2), 1185–1200 (2004).
[Crossref] [PubMed]

Oberstrass, F. C.

P. Lebel, A. Basu, F. C. Oberstrass, E. M. Tretter, and Z. Bryant, “Gold rotor bead tracking for high-speed measurements of DNA twist, torque and extension,” Nat. Methods 11(4), 456–462 (2014).
[Crossref] [PubMed]

Olenych, S.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Ou, G.

D. Tian, M. Diao, Y. Jiang, L. Sun, Y. Zhang, Z. Chen, S. Huang, and G. Ou, “Anillin regulates neuronal migration and neurite growth by linking RhoG to the actin cytoskeleton,” Curr. Biol. 25(9), 1135–1145 (2015).
[Crossref] [PubMed]

Parthasarathy, R.

R. Parthasarathy, “Rapid, accurate particle tracking by calculation of radial symmetry centers,” Nat. Methods 9(7), 724–726 (2012).
[Crossref] [PubMed]

Patterson, G. H.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Pavani, S. R. P.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 2995–2999 (2009).
[Crossref] [PubMed]

S. R. P. Pavani and R. Piestun, “Three dimensional tracking of fluorescent microparticles using a photon-limited double-helix response system,” Opt. Express 16(26), 22048–22057 (2008).
[Crossref] [PubMed]

Piestun, R.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 2995–2999 (2009).
[Crossref] [PubMed]

S. R. P. Pavani and R. Piestun, “Three dimensional tracking of fluorescent microparticles using a photon-limited double-helix response system,” Opt. Express 16(26), 22048–22057 (2008).
[Crossref] [PubMed]

Rabin, Y.

M. Lindner, G. Nir, S. Medalion, H. R. Dietrich, Y. Rabin, and Y. Garini, “Force-free measurements of the conformations of DNA molecules tethered to a wall,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(1), 011916 (2011).
[Crossref] [PubMed]

Ram, S.

R. J. Ober, S. Ram, and E. S. Ward, “Localization accuracy in single-molecule microscopy,” Biophys. J. 86(2), 1185–1200 (2004).
[Crossref] [PubMed]

Rieger, B.

C. S. Smith, N. Joseph, B. Rieger, and K. A. Lidke, “Fast, single-molecule localization that achieves theoretically minimum uncertainty,” Nat. Methods 7(5), 373–375 (2010).
[Crossref] [PubMed]

Rust, M. J.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006).
[Crossref] [PubMed]

Sahl, S. J.

Y. Shechtman, L. E. Weiss, A. S. Backer, S. J. Sahl, and W. E. Moerner, “Precise 3D scan-free multiple-particle tracking over large axial ranges with Tetrapod point spread functions,” Nano Lett. 15, 4194–4199 (2015).
[Crossref]

Y. Shechtman, S. J. Sahl, A. S. Backer, and W. E. Moerner, “Optimal point spread function design for 3D imaging,” Phys. Rev. Lett. 113(13), 133902 (2014).
[Crossref] [PubMed]

Schindler, H.

G. J. Schütz, H. Schindler, and T. Schmidt, “Single-molecule microscopy on model membranes reveals anomalous diffusion,” Biophys. J. 73(2), 1073–1080 (1997).
[Crossref] [PubMed]

Schmidt, T.

G. J. Schütz, H. Schindler, and T. Schmidt, “Single-molecule microscopy on model membranes reveals anomalous diffusion,” Biophys. J. 73(2), 1073–1080 (1997).
[Crossref] [PubMed]

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]

Schnitzer, M. J.

E. A. Mukamel and M. J. Schnitzer, “Unified resolution bounds for conventional and stochastic localization fluorescence microscopy,” Phys. Rev. Lett. 109(16), 168102 (2012).
[Crossref] [PubMed]

Schütz, G. J.

G. J. Schütz, H. Schindler, and T. Schmidt, “Single-molecule microscopy on model membranes reveals anomalous diffusion,” Biophys. J. 73(2), 1073–1080 (1997).
[Crossref] [PubMed]

Selvin, P. R.

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]

Shabtay, G.

D. Mendlovic, G. Shabtay, Z. Zalevsky, and S. G. Lipson, “The optimal system for sub-wavelength point source localization,” Opt. Commun. 198(4-6), 311–315 (2001).
[Crossref]

Shechtman, Y.

Y. Shechtman, L. E. Weiss, A. S. Backer, S. J. Sahl, and W. E. Moerner, “Precise 3D scan-free multiple-particle tracking over large axial ranges with Tetrapod point spread functions,” Nano Lett. 15, 4194–4199 (2015).
[Crossref]

Y. Shechtman, S. J. Sahl, A. S. Backer, and W. E. Moerner, “Optimal point spread function design for 3D imaging,” Phys. Rev. Lett. 113(13), 133902 (2014).
[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]

Sims, P. A.

X. Nan, P. A. Sims, and X. S. Xie, “Organelle tracking in a living cell with microsecond time resolution and nanometer spatial precision,” ChemPhysChem 9(5), 707–712 (2008).
[Crossref] [PubMed]

Smith, C. S.

C. S. Smith, N. Joseph, B. Rieger, and K. A. Lidke, “Fast, single-molecule localization that achieves theoretically minimum uncertainty,” Nat. Methods 7(5), 373–375 (2010).
[Crossref] [PubMed]

Sougrat, R.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[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]

Sun, L.

D. Tian, M. Diao, Y. Jiang, L. Sun, Y. Zhang, Z. Chen, S. Huang, and G. Ou, “Anillin regulates neuronal migration and neurite growth by linking RhoG to the actin cytoskeleton,” Curr. Biol. 25(9), 1135–1145 (2015).
[Crossref] [PubMed]

Tamada, A.

A. Tamada, S. Kawase, F. Murakami, and H. Kamiguchi, “Autonomous right-screw rotation of growth cone filopodia drives neurite turning,” J. Cell Biol. 188(3), 429–441 (2010).
[Crossref] [PubMed]

Thompson, B. J.

B. J. Thompson and E. Wolf, “Two-beam interference with partially coherent light,” JOSA 47(10), 895–902 (1957).
[Crossref]

Thompson, M. A.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 2995–2999 (2009).
[Crossref] [PubMed]

Thompson, R. E.

R. E. Thompson, D. R. Larson, and W. W. Webb, “Precise nanometer localization analysis for individual fluorescent probes,” Biophys. J. 82(5), 2775–2783 (2002).
[Crossref] [PubMed]

Tian, D.

D. Tian, M. Diao, Y. Jiang, L. Sun, Y. Zhang, Z. Chen, S. Huang, and G. Ou, “Anillin regulates neuronal migration and neurite growth by linking RhoG to the actin cytoskeleton,” Curr. Biol. 25(9), 1135–1145 (2015).
[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]

Tretter, E. M.

P. Lebel, A. Basu, F. C. Oberstrass, E. M. Tretter, and Z. Bryant, “Gold rotor bead tracking for high-speed measurements of DNA twist, torque and extension,” Nat. Methods 11(4), 456–462 (2014).
[Crossref] [PubMed]

Twieg, R. J.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 2995–2999 (2009).
[Crossref] [PubMed]

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).
[Crossref] [PubMed]

Ward, E. S.

R. J. Ober, S. Ram, and E. S. Ward, “Localization accuracy in single-molecule microscopy,” Biophys. J. 86(2), 1185–1200 (2004).
[Crossref] [PubMed]

Webb, W. W.

R. E. Thompson, D. R. Larson, and W. W. Webb, “Precise nanometer localization analysis for individual fluorescent probes,” Biophys. J. 82(5), 2775–2783 (2002).
[Crossref] [PubMed]

Weiss, L. E.

Y. Shechtman, L. E. Weiss, A. S. Backer, S. J. Sahl, and W. E. Moerner, “Precise 3D scan-free multiple-particle tracking over large axial ranges with Tetrapod point spread functions,” Nano Lett. 15, 4194–4199 (2015).
[Crossref]

Wolf, E.

B. J. Thompson and E. Wolf, “Two-beam interference with partially coherent light,” JOSA 47(10), 895–902 (1957).
[Crossref]

Xie, X. S.

X. Nan, P. A. Sims, and X. S. Xie, “Organelle tracking in a living cell with microsecond time resolution and nanometer spatial precision,” ChemPhysChem 9(5), 707–712 (2008).
[Crossref] [PubMed]

Xu, X. N.

L. M. Browning, T. Huang, and X. N. Xu, “Far-field photostable optical nanoscopy (PHOTON) for real-time super-resolution single-molecular imaging of signaling pathways of single live cells,” Nanoscale 4, 2797–2812 (2012).

Yildiz, A.

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]

Zalevsky, Z.

C. G. Ebeling, A. Meiri, J. Martineau, Z. Zalevsky, J. M. Gerton, and R. Menon, “Increased localization precision by interference fringe analysis,” Nanoscale 7(23), 10430–10437 (2015).
[Crossref] [PubMed]

D. Mendlovic, G. Shabtay, Z. Zalevsky, and S. G. Lipson, “The optimal system for sub-wavelength point source localization,” Opt. Commun. 198(4-6), 311–315 (2001).
[Crossref]

J. Martineau, R. Menon, A. Meiri, Z. Zalevsky, and J. M. Gerton, “Increasing theoretical localization precision using multi-peaked point spread functions,” Submitted.

Zhang, Y.

D. Tian, M. Diao, Y. Jiang, L. Sun, Y. Zhang, Z. Chen, S. Huang, and G. Ou, “Anillin regulates neuronal migration and neurite growth by linking RhoG to the actin cytoskeleton,” Curr. Biol. 25(9), 1135–1145 (2015).
[Crossref] [PubMed]

Zhuang, X.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006).
[Crossref] [PubMed]

Appl. Phys. B (1)

J. Enderlein, “Tracking of fluorescent molecules diffusing within membranes,” Appl. Phys. B 71(5), 773–777 (2000).
[Crossref]

Biophys. J. (4)

R. E. Thompson, D. R. Larson, and W. W. Webb, “Precise nanometer localization analysis for individual fluorescent probes,” Biophys. J. 82(5), 2775–2783 (2002).
[Crossref] [PubMed]

G. J. Schütz, H. Schindler, and T. Schmidt, “Single-molecule microscopy on model membranes reveals anomalous diffusion,” Biophys. J. 73(2), 1073–1080 (1997).
[Crossref] [PubMed]

R. J. Ober, S. Ram, and E. S. Ward, “Localization accuracy in single-molecule microscopy,” Biophys. J. 86(2), 1185–1200 (2004).
[Crossref] [PubMed]

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91(11), 4258–4272 (2006).
[Crossref] [PubMed]

ChemPhysChem (1)

X. Nan, P. A. Sims, and X. S. Xie, “Organelle tracking in a living cell with microsecond time resolution and nanometer spatial precision,” ChemPhysChem 9(5), 707–712 (2008).
[Crossref] [PubMed]

Curr. Biol. (1)

D. Tian, M. Diao, Y. Jiang, L. Sun, Y. Zhang, Z. Chen, S. Huang, and G. Ou, “Anillin regulates neuronal migration and neurite growth by linking RhoG to the actin cytoskeleton,” Curr. Biol. 25(9), 1135–1145 (2015).
[Crossref] [PubMed]

J. Cell Biol. (1)

A. Tamada, S. Kawase, F. Murakami, and H. Kamiguchi, “Autonomous right-screw rotation of growth cone filopodia drives neurite turning,” J. Cell Biol. 188(3), 429–441 (2010).
[Crossref] [PubMed]

JOSA (1)

B. J. Thompson and E. Wolf, “Two-beam interference with partially coherent light,” JOSA 47(10), 895–902 (1957).
[Crossref]

Nano Lett. (1)

Y. Shechtman, L. E. Weiss, A. S. Backer, S. J. Sahl, and W. E. Moerner, “Precise 3D scan-free multiple-particle tracking over large axial ranges with Tetrapod point spread functions,” Nano Lett. 15, 4194–4199 (2015).
[Crossref]

Nanoscale (2)

C. G. Ebeling, A. Meiri, J. Martineau, Z. Zalevsky, J. M. Gerton, and R. Menon, “Increased localization precision by interference fringe analysis,” Nanoscale 7(23), 10430–10437 (2015).
[Crossref] [PubMed]

L. M. Browning, T. Huang, and X. N. Xu, “Far-field photostable optical nanoscopy (PHOTON) for real-time super-resolution single-molecular imaging of signaling pathways of single live cells,” Nanoscale 4, 2797–2812 (2012).

Nat. Methods (5)

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006).
[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]

C. S. Smith, N. Joseph, B. Rieger, and K. A. Lidke, “Fast, single-molecule localization that achieves theoretically minimum uncertainty,” Nat. Methods 7(5), 373–375 (2010).
[Crossref] [PubMed]

R. Parthasarathy, “Rapid, accurate particle tracking by calculation of radial symmetry centers,” Nat. Methods 9(7), 724–726 (2012).
[Crossref] [PubMed]

P. Lebel, A. Basu, F. C. Oberstrass, E. M. Tretter, and Z. Bryant, “Gold rotor bead tracking for high-speed measurements of DNA twist, torque and extension,” Nat. Methods 11(4), 456–462 (2014).
[Crossref] [PubMed]

Nature (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]

Opt. Commun. (1)

D. Mendlovic, G. Shabtay, Z. Zalevsky, and S. G. Lipson, “The optimal system for sub-wavelength point source localization,” Opt. Commun. 198(4-6), 311–315 (2001).
[Crossref]

Opt. Express (1)

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

M. Lindner, G. Nir, S. Medalion, H. R. Dietrich, Y. Rabin, and Y. Garini, “Force-free measurements of the conformations of DNA molecules tethered to a wall,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(1), 011916 (2011).
[Crossref] [PubMed]

Phys. Rev. Lett. (2)

E. A. Mukamel and M. J. Schnitzer, “Unified resolution bounds for conventional and stochastic localization fluorescence microscopy,” Phys. Rev. Lett. 109(16), 168102 (2012).
[Crossref] [PubMed]

Y. Shechtman, S. J. Sahl, A. S. Backer, and W. E. Moerner, “Optimal point spread function design for 3D imaging,” Phys. Rev. Lett. 113(13), 133902 (2014).
[Crossref] [PubMed]

PLoS One (1)

E. C. Arnspang, J. R. Brewer, and B. C. Lagerholm, “Multi-color single particle tracking with quantum dots,” PLoS One 7(11), e48521 (2012).
[Crossref] [PubMed]

Proc. Natl. Acad. Sci. U.S.A. (1)

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 2995–2999 (2009).
[Crossref] [PubMed]

Science (3)

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]

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

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Other (2)

J. Martineau, R. Menon, A. Meiri, Z. Zalevsky, and J. M. Gerton, “Increasing theoretical localization precision using multi-peaked point spread functions,” Submitted.

A. Kusumi, H. Ike, C. Nakada, K. Murase, and T. Fujiwara, “Single-molecule tracking of membrane molecules: plasma membrane compartmentalization and dynamic assembly of raft-philic signaling molecules,” in Seminars in Immunology (Elsevier, 2005), Vol. 17, pp. 3–21.

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Figures (13)

Fig. 1
Fig. 1

Examples of PSFs modified by interference fringes. (a) Constant phase of 0. Inset: cross section of one of the PSFs (b) Constant phase of π. Inset: cross section of one of the PSFs. (c) A mixed case of linear phase in x ( M=ω) and constant phase of 0 in y. The linear phase in x results in fringe peaks which are at the same spatial locations regardless of PSF center position. For a constant phase, the fringe peaks are determined by the position of the PSF.

Fig. 2
Fig. 2

Interference Scheme. The signal is coming from the left, and split by the grating (red). The two mirrors (yellow) redirect the signal towards the center, where the interference pattern is captured by the camera (green). The incoming signal on the left, is the output of a microscope and can contain a widefield image with one or more imaged point objects (PSFs), or a confocal microscope image with a single PSF.

Fig. 3
Fig. 3

Simulation Results. (a),(b) Localization error as a function of the number of detected photons for a (a) constant, known phase ( + , + for φ = 0, π/2) and (b) unknown (estimated) phase (∆, ∆ for φ = 0, π/2) .● - Gaussian PSF. (c) Localization error as a function of the linear phase slope (M) for different fringe spatial frequency (ω). O, O, Ο - ωis 40/µm, 60/µm and 80/µm, respectively. ● - Gaussian PSF.

Fig. 4
Fig. 4

(a) Localization error as a function of fringe spatial frequency. + , + , + - pixel sizes of 25 nm, 50 nm, 100nm, respectively. ● - Gaussian PSF. (b) Localization error as a function of fringe visibility. + , + - pixel sizes of 25 nm,50 nm respectively. ● - Gaussian PSF. (c) Localization error as a function of mean background photons count. ∆, + - cases of estimated and known phase, respectively. ● - Gaussian PSF. (d) Localization error as a function of background photons per pixel for different linear phase slopes of , , , :20/µm, 40/µm, 60/µm and 80/µm respectively. ● - Gaussian PSF. (e) CRLB for interfering and non-interfering background. ●, - - Gaussian PSF and modulated PSF with interfering background, respectively. Dashed orange - Modulated PSF with non-interfering background.

Fig. 5
Fig. 5

(a) Experimental Setup (b) Experimental PSF. Insets: y (blue) and x (red) projections of the PSF. In this experiment γ>0.9 (c) Tracking experiment. Red circles: the predetermined pattern, Blue crosses: the localized positions. (d) Phase Vs Position . Blue dots – experimental data, Red Curve – linear fit, Green curve –phase vs position curve extracted from numerical propagation simulations. (e) Widefield image showing interference fringes on two PSFs. Scalebar is 500nm.

Fig. 6
Fig. 6

Resolution target simulations. (a) The binary target. (b) Gaussian PSF. (c) Constant Phase. (d) Estimated Phase. (e) Linear Phase, ω=M=40/μm . (f) Linear Phase, ω=40/μm,M=80/μm. Red lines show the cross section in the middle of the target. (g) Contrast of the different cases for background photon count of 0 (blue), 3 (cyan), 5 (yellow), 10 (red). See Appendix A for the ring target simulations for all background photon values.

Fig. 7
Fig. 7

Localization standard deviation ratio between modulated PSF and Gaussian PSF for different background values, computed from CRLB for 1000 signal photons,. R= σ Gaussian / σ modulated , for constant, known phase ( + ), Non-interfering background (orange dashed line) and interfering background (red solid line). The ratio increases with background, which indicates that modulated PSF localization improves compared to Gaussian PSF when the noise level is higher. The ratio equals 1 for the interfering background for all background values indicating that this case achieves the same localization error as Gaussian PSF, as we have seen earlier.

Fig. 8
Fig. 8

2D grating system.

Fig. 9
Fig. 9

The experimental setup. The confocal microscope is constructed in a scan\de-scan configuration. An optional widefield lens is placed in a way that the excitation beam is focused on the back focal plane of the microscope objective, generating a widefield image on the EMCCD camera. In our experiments, the sample contained nanoparticles on top of a glass slide.

Fig. 10
Fig. 10

CRLB for the case of known (Ο) and unknown phase (*) compared to Gaussian PSF (solid line). The need to find the phase changes the localization precision dramatically and the fringes do not contribute to the localization precision in this case.

Fig. 11
Fig. 11

CRLB of the modulated PSF as a function of fringe spatial frequency (Ο), compared with the Gaussian case (solid line). The localization precision increases with fringe spatial frequency.

Fig. 12
Fig. 12

Resolution target simulations. First column - Gaussian PSF. Second column - Constant Phase. Third column - Estimated Phase. Fourth column - Linear Phase, ω=M=0.04n m 1 . Fifth Column - Linear Phase, ω=0.04n m 1 ,M=0.08n m 1 . (a)-(e) background photon count is 0. (f)-(j) background is 3 photons/pixels. (k)-(o) 5 photons/pixel. (p)-(t) 10 photons/pixel. Red lines show the cross section in the middle of the target.

Fig. 13
Fig. 13

(a) The Analyzed optical system. (b) A reference 4F system. The plane p1 is located just after the second lens.

Equations (23)

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f(x, x 0 )=g( x x 0 )[ 1+γcos( ω( x x 0 )+C ) ]
f(x, x 0 )=g( x x 0 )[ 1+γcos( ω( x x 0 )+ϕ ) ].
f(x, x 0 )=g( x x 0 )[ 1+γcos( ω( x x 0 )+M x 0 ) ],
Δ x 2 = s a 2 N ( 1+ 0 1 lnt 1+N a 2 t/2π s a 2 b 2 dt ) 1 , s a 2 = s 2 + a 2 12
f(x, x 0 )=[ g( x x 0 ) ][ 1+γcos( ω( x x 0 )+ϕ ) ]+b,
f(x, x 0 )=[ g( x x 0 )+b ][ 1+γcos( ω( x x 0 )+ϕ ) ].
I=2[ 1+cos( 2πxν ) ] I ˜ ,
C= r s R( r,s )| O( r,s )=1 r s R( r,s )| O( r,s )=0
p(x,z= p 2 ) | x 0 =0 = P( f x ,z= p 2 ) e 2πi f x x d f x ,
U( f x ,z)=U( f x ,0) e i k z z ,
p(x,z= p 2 )= P( f x ,z= p 2 ) e 2πi f x x e 2πi f x x 0 d f x
p(x,z= p 1 )= P( f x ,z= p 2 ) e 2πi f x x e 2πi f x x 0 e 2π λ i(2 z 0 +Δz) 1 λ 2 f x 2 d f x
g( x )= m A m e 2πim ν 1 x
p(x,z= p 1 + )= m A m P( f x , p 2 ) e 2πix( f x +m ν 1 ) e 2πi f x x 0 e 2π λ i(2 z 0 +Δz) 1 λ 2 f x 2 d f x
p(x,z= p 1 + z 0 )= m A m [ P( f x ,z= p 2 ) e 2πix( f x +m ν 1 ) e 2πi f x x 0 × e 2π λ i(2 z 0 +Δz) 1 λ 2 f x 2 e 2π λ i z 0 1 λ 2 ( f x +m ν 1 ) 2 ]d f x
p(x,z= p 1 + z 0 + )= m A m [ P( f x ,z= p 2 ) e 2πix( f x +m ν 1 ν 2 ) e 2πi f x x 0 × e 2π λ i(2 z 0 +Δz) 1 λ 2 f x 2 e 2π λ i z 0 1 λ 2 ( f x +m ν 1 ) 2 ]d f x
p (x,z= p 1 +2 z 0 ) + = m A m [ P( f x ,z= p 2 ) e 2πix( f x +m ν 1 ν 2 ) e 2πi f x x 0 × e 2π λ i(2 z 0 +Δz) 1 λ 2 f x 2 e 2π λ i z 0 1 λ 2 ( f x +m ν 1 ) 2 e 2π λ i z 0 1 λ 2 ( f x +m ν 1 ν 2 ) 2 ]d f x
p (x,z= p 1 +2 z 0 ) + = m A m [ P( f x ,z= p 2 ) e 2πix( f x ν) e 2πi f x x 0 × e 2π λ i(2 z 0 +Δz) 1 λ 2 f x 2 e 2π λ i z 0 1 λ 2 ( f x +ν ) 2 e 2π λ i z 0 1 λ 2 ( f x ν ) 2 ]d f x
p (x,z= p 1 +2 z 0 ) = m A m [ P( f x ,z= p 2 ) e 2πix( f x +ν) e 2πi f x x 0 × e 2π λ i(2 z 0 +Δz) 1 λ 2 f x 2 e 2π λ i z 0 1 λ 2 ( f x ν ) 2 e 2π λ i z 0 1 λ 2 ( f x +ν ) 2 ]d f x
p(x,z= p 1 +2 z 0 )=p (x,z= p 1 +2 z 0 ) + +p (x,z= p 1 +2 z 0 ) = ( e 2πixν + e 2πixν )× P( f x ,z= p 2 ) e 2πix f x e 2πi f x x 0 e 2π λ i 1 λ 2 f x 2 ( Δz+2 z 0 ) e 2π λ i z 0 [ 1 λ 2 ( f x ν ) 2 + 1 λ 2 ( f x +ν ) 2 ] d f x
I= | p(x,z= p 1 +2 z 0 ) | 2 =( e 2πixν + e 2πixν )× P( f x ,z= p 2 ) e 2πix f x e 2πi f x x 0 e 2π λ i 1 λ 2 f x 2 ( Δz+2 z 0 ) e 2π λ i z 0 [ 1 λ 2 ( f x ν ) 2 + 1 λ 2 ( f x +ν ) 2 ] d f x × ( e 2πixν + e 2πixν )× ( P( f x ,z= p 2 ) e 2πix f x e 2πi f x x 0 e 2π λ i 1 λ 2 f x 2 ( Δz+2 z 0 ) e 2π λ i z 0 [ 1 λ 2 ( f x ν ) 2 + 1 λ 2 ( f x +ν ) 2 ] d f x ) *
I=2[ 1+cos( 2πxν ) ] I ˜ ,
I ˜ = | P( f x ,z= p 2 ) e 2πix f x e 2πi f x x 0 e 2π λ i 1 λ 2 f x 2 ( Δz+2 z 0 ) e 2π λ i z 0 [ 1 λ 2 ( f x ν ) 2 + 1 λ 2 ( f x +ν ) 2 ] d f x | 2