Abstract

We report the use of a phase retrieval procedure based on maximum likelihood estimation (MLE) to produce an improved, experimentally calibrated model of a point spread function (PSF) for use in three-dimensional (3D) localization microscopy experiments. The method estimates a global pupil phase function (which includes both the PSF and system aberrations) over the full axial range from a simple calibration scan. The pupil function is used to refine the PSF model and hence enable superior localizations from experimental data. To demonstrate the utility of the procedure, we apply it to experimental data acquired with a microscope employing a tetrapod PSF with a 6 µm axial range. The phase-retrieved model demonstrates significant improvements in both accuracy and precision of 3D localizations relative to the model based on scalar diffraction theory. The localization precision of the phase-retrieved model is shown to be near the limits imposed by estimation theory, and the reproducibility of the procedure is characterized and discussed. Code which performs the phase retrieval algorithm is provided.

© 2017 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Computational correction of spatially variant optical aberrations in 3D single-molecule localization microscopy

T. Yan, C. J. Richardson, M. Zhang, and A. Gahlmann
Opt. Express 27(9) 12582-12599 (2019)

Three dimensional single molecule localization using a phase retrieved pupil function

Sheng Liu, Emil B. Kromann, Wesley D. Krueger, Joerg Bewersdorf, and Keith A. Lidke
Opt. Express 21(24) 29462-29487 (2013)

High precision wavefront control in point spread function engineering for single emitter localization

M. Siemons, C. N. Hulleman, R. Ø. Thorsen, C. S. Smith, and S. Stallinga
Opt. Express 26(7) 8397-8416 (2018)

References

  • View by:
  • |
  • |
  • |

  1. H. Qian, M. P. Sheetz, and E. L. Elson, “Single particle tracking. Analysis of diffusion and flow in two-dimensional systems,” Biophys. J. 60(4), 910–921 (1991).
    [Crossref] [PubMed]
  2. M. J. Saxton, “Single-particle tracking: the distribution of diffusion coefficients,” Biophys. J. 72(4), 1744–1753 (1997).
    [Crossref] [PubMed]
  3. A. Dupont and D. C. Lamb, “Nanoscale three-dimensional single particle tracking,” Nanoscale 3(11), 4532–4541 (2011).
    [Crossref] [PubMed]
  4. 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]
  5. 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]
  6. M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–795 (2006).
    [Crossref] [PubMed]
  7. W. E. Moerner, “Microscopy beyond the diffraction limit using actively controlled single molecules,” J. Microsc. 246(3), 213–220 (2012).
    [Crossref] [PubMed]
  8. A. Small and S. Stahlheber, “Fluorophore localization algorithms for super-resolution microscopy,” Nat. Methods 11(3), 267–279 (2014).
    [Crossref] [PubMed]
  9. B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319(5864), 810–813 (2008).
    [Crossref] [PubMed]
  10. 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]
  11. A. Gahlmann, J. L. Ptacin, G. Grover, S. Quirin, A. R. S. von Diezmann, M. K. Lee, M. P. Backlund, L. Shapiro, R. Piestun, and W. E. Moerner, “Quantitative multicolor subdiffraction imaging of bacterial protein ultrastructures in three dimensions,” Nano Lett. 13(3), 987–993 (2013).
    [Crossref] [PubMed]
  12. M. D. Lew, S. F. Lee, M. Badieirostami, and W. E. Moerner, “Corkscrew point spread function for far-field three-dimensional nanoscale localization of pointlike objects,” Opt. Lett. 36(2), 202–204 (2011).
    [Crossref] [PubMed]
  13. S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic three-dimensional super-resolution imaging with a self-bending point spread function,” Nat. Photonics 8(4), 302–306 (2014).
    [Crossref] [PubMed]
  14. 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]
  15. 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] [PubMed]
  16. Y. Shechtman, L. E. Weiss, A. S. Backer, M. L. Lee, and W. E. Moerner, “Multicolor localization microscopy by point-spread-function engineering,” Nat. Photonics 10(9), 590–594 (2016).
    [Crossref]
  17. S. Quirin, S. R. P. Pavani, and R. Piestun, “Optimal 3D single-molecule localization for superresolution microscopy with aberrations and engineered point spread functions,” Proc. Natl. Acad. Sci. U.S.A. 109(3), 675–679 (2012).
    [Crossref] [PubMed]
  18. I. Izeddin, M. El Beheiry, J. Andilla, D. Ciepielewski, X. Darzacq, and M. Dahan, “PSF shaping using adaptive optics for three-dimensional single-molecule super-resolution imaging and tracking,” Opt. Express 20(5), 4957–4967 (2012).
    [Crossref] [PubMed]
  19. S. Liu, E. B. Kromann, W. D. Krueger, J. Bewersdorf, and K. A. Lidke, “Three dimensional single molecule localization using a phase retrieved pupil function,” Opt. Express 21(24), 29462–29487 (2013).
    [Crossref] [PubMed]
  20. R. McGorty, J. Schnitzbauer, W. Zhang, and B. Huang, “Correction of depth-dependent aberrations in 3D single-molecule localization and super-resolution microscopy,” Opt. Lett. 39(2), 275–278 (2014).
    [Crossref] [PubMed]
  21. B. M. Hanser, M. G. Gustafsson, D. A. Agard, and J. W. Sedat, “Phase-retrieved pupil functions in wide-field fluorescence microscopy,” J. Microsc. 216(1), 32–48 (2004).
    [Crossref] [PubMed]
  22. J. A. Sakamoto and H. H. Barrett, “Maximum-likelihood estimation of parameterized wavefronts from multifocal data,” Opt. Express 20(14), 15928–15944 (2012).
    [Crossref] [PubMed]
  23. R. J. Ober, S. Ram, and E. S. Ward, “Localization accuracy in single-molecule microscopy,” Biophys. J. 86(2), 1185–1200 (2004).
    [Crossref] [PubMed]
  24. 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]
  25. 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]
  26. J. W. Goodman, Introduction to Fourier Optics (Roberts & Company Publishers, 2005).
  27. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
    [Crossref]
  28. S. W. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169(3), 391–405 (1993).
    [Crossref]
  29. M. A. Lieb, J. M. Zavislan, and L. Novotny, “Single-molecule orientations determined by direct emission pattern imaging,” J. Opt. Soc. Am. B 21(6), 1210–1215 (2004).
    [Crossref]
  30. M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
  31. J. C. Wyant and K. Creath, “Basic wavefront aberration theory for optical metrology,” in R. R. Shannon and J. C. Wyant, (eds. 1992), pp. 1–53.
  32. R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66(3), 207–211 (1976).
    [Crossref]
  33. S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice-Hall PTR, 1993).
  34. B. Moomaw, “Camera Technologies for Low Light Imaging: Overview and Relative Advantages,” in Methods in Cell Biology, G. Sluder and D. E. Wolf, eds. (Elsevier, 2013), pp. 243–283.
  35. M. Hirsch, R. J. Wareham, M. L. Martin-Fernandez, M. P. Hobson, and D. J. Rolfe, “A stochastic model for electron multiplication charge-coupled devices--from theory to practice,” PLoS One 8(1), e53671 (2013).
    [Crossref] [PubMed]
  36. A. von Diezmann, M. Y. Lee, M. D. Lew, and W. E. Moerner, “Correcting field-dependent aberrations with nanoscale accuracy in three-dimensional single-molecule localization microscopy,” Optica 2(11), 985–993 (2015).
    [Crossref] [PubMed]
  37. L. Carlini, S. J. Holden, K. M. Douglass, and S. Manley, “Correction of a depth-dependent lateral distortion in 3D super-resolution imaging,” PLoS One 10(11), e0142949 (2015).
    [Crossref] [PubMed]
  38. M. D. Lew, M. A. Thompson, M. Badieirostami, and W. E. Moerner, “In vivo three-dimensional superresolution fluorescence tracking using a double-helix point spread function,” Proc SPIE Int Soc Opt Eng 7571, 75710Z (2010).
    [Crossref] [PubMed]
  39. P. N. Petrov and W. E. Moerner, “Easy Pupil Finder,” SourceForge (2017) [retrieved 17 January 2017], http://sourceforge.net/p/easy-pupil-finder .

2016 (1)

Y. Shechtman, L. E. Weiss, A. S. Backer, M. L. Lee, and W. E. Moerner, “Multicolor localization microscopy by point-spread-function engineering,” Nat. Photonics 10(9), 590–594 (2016).
[Crossref]

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] [PubMed]

L. Carlini, S. J. Holden, K. M. Douglass, and S. Manley, “Correction of a depth-dependent lateral distortion in 3D super-resolution imaging,” PLoS One 10(11), e0142949 (2015).
[Crossref] [PubMed]

A. von Diezmann, M. Y. Lee, M. D. Lew, and W. E. Moerner, “Correcting field-dependent aberrations with nanoscale accuracy in three-dimensional single-molecule localization microscopy,” Optica 2(11), 985–993 (2015).
[Crossref] [PubMed]

2014 (4)

R. McGorty, J. Schnitzbauer, W. Zhang, and B. Huang, “Correction of depth-dependent aberrations in 3D single-molecule localization and super-resolution microscopy,” Opt. Lett. 39(2), 275–278 (2014).
[Crossref] [PubMed]

S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic three-dimensional super-resolution imaging with a self-bending point spread function,” Nat. Photonics 8(4), 302–306 (2014).
[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]

A. Small and S. Stahlheber, “Fluorophore localization algorithms for super-resolution microscopy,” Nat. Methods 11(3), 267–279 (2014).
[Crossref] [PubMed]

2013 (3)

A. Gahlmann, J. L. Ptacin, G. Grover, S. Quirin, A. R. S. von Diezmann, M. K. Lee, M. P. Backlund, L. Shapiro, R. Piestun, and W. E. Moerner, “Quantitative multicolor subdiffraction imaging of bacterial protein ultrastructures in three dimensions,” Nano Lett. 13(3), 987–993 (2013).
[Crossref] [PubMed]

S. Liu, E. B. Kromann, W. D. Krueger, J. Bewersdorf, and K. A. Lidke, “Three dimensional single molecule localization using a phase retrieved pupil function,” Opt. Express 21(24), 29462–29487 (2013).
[Crossref] [PubMed]

M. Hirsch, R. J. Wareham, M. L. Martin-Fernandez, M. P. Hobson, and D. J. Rolfe, “A stochastic model for electron multiplication charge-coupled devices--from theory to practice,” PLoS One 8(1), e53671 (2013).
[Crossref] [PubMed]

2012 (4)

I. Izeddin, M. El Beheiry, J. Andilla, D. Ciepielewski, X. Darzacq, and M. Dahan, “PSF shaping using adaptive optics for three-dimensional single-molecule super-resolution imaging and tracking,” Opt. Express 20(5), 4957–4967 (2012).
[Crossref] [PubMed]

J. A. Sakamoto and H. H. Barrett, “Maximum-likelihood estimation of parameterized wavefronts from multifocal data,” Opt. Express 20(14), 15928–15944 (2012).
[Crossref] [PubMed]

S. Quirin, S. R. P. Pavani, and R. Piestun, “Optimal 3D single-molecule localization for superresolution microscopy with aberrations and engineered point spread functions,” Proc. Natl. Acad. Sci. U.S.A. 109(3), 675–679 (2012).
[Crossref] [PubMed]

W. E. Moerner, “Microscopy beyond the diffraction limit using actively controlled single molecules,” J. Microsc. 246(3), 213–220 (2012).
[Crossref] [PubMed]

2011 (2)

2010 (3)

M. D. Lew, M. A. Thompson, M. Badieirostami, and W. E. Moerner, “In vivo three-dimensional superresolution fluorescence tracking using a double-helix point spread function,” Proc SPIE Int Soc Opt Eng 7571, 75710Z (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]

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]

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 (1)

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319(5864), 810–813 (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]

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]

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–795 (2006).
[Crossref] [PubMed]

2004 (3)

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

B. M. Hanser, M. G. Gustafsson, D. A. Agard, and J. W. Sedat, “Phase-retrieved pupil functions in wide-field fluorescence microscopy,” J. Microsc. 216(1), 32–48 (2004).
[Crossref] [PubMed]

M. A. Lieb, J. M. Zavislan, and L. Novotny, “Single-molecule orientations determined by direct emission pattern imaging,” J. Opt. Soc. Am. B 21(6), 1210–1215 (2004).
[Crossref]

1997 (1)

M. J. Saxton, “Single-particle tracking: the distribution of diffusion coefficients,” Biophys. J. 72(4), 1744–1753 (1997).
[Crossref] [PubMed]

1993 (1)

S. W. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169(3), 391–405 (1993).
[Crossref]

1991 (1)

H. Qian, M. P. Sheetz, and E. L. Elson, “Single particle tracking. Analysis of diffusion and flow in two-dimensional systems,” Biophys. J. 60(4), 910–921 (1991).
[Crossref] [PubMed]

1976 (1)

1959 (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

Agard, D. A.

B. M. Hanser, M. G. Gustafsson, D. A. Agard, and J. W. Sedat, “Phase-retrieved pupil functions in wide-field fluorescence microscopy,” J. Microsc. 216(1), 32–48 (2004).
[Crossref] [PubMed]

Andilla, J.

Backer, A. S.

Y. Shechtman, L. E. Weiss, A. S. Backer, M. L. Lee, and W. E. Moerner, “Multicolor localization microscopy by point-spread-function engineering,” Nat. Photonics 10(9), 590–594 (2016).
[Crossref]

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] [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]

Backlund, M. P.

A. Gahlmann, J. L. Ptacin, G. Grover, S. Quirin, A. R. S. von Diezmann, M. K. Lee, M. P. Backlund, L. Shapiro, R. Piestun, and W. E. Moerner, “Quantitative multicolor subdiffraction imaging of bacterial protein ultrastructures in three dimensions,” Nano Lett. 13(3), 987–993 (2013).
[Crossref] [PubMed]

Badieirostami, M.

M. D. Lew, S. F. Lee, M. Badieirostami, and W. E. Moerner, “Corkscrew point spread function for far-field three-dimensional nanoscale localization of pointlike objects,” Opt. Lett. 36(2), 202–204 (2011).
[Crossref] [PubMed]

M. D. Lew, M. A. Thompson, M. Badieirostami, and W. E. Moerner, “In vivo three-dimensional superresolution fluorescence tracking using a double-helix point spread function,” Proc SPIE Int Soc Opt Eng 7571, 75710Z (2010).
[Crossref] [PubMed]

Barrett, H. H.

Bates, M.

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319(5864), 810–813 (2008).
[Crossref] [PubMed]

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–795 (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]

Bewersdorf, J.

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]

Carlini, L.

L. Carlini, S. J. Holden, K. M. Douglass, and S. Manley, “Correction of a depth-dependent lateral distortion in 3D super-resolution imaging,” PLoS One 10(11), e0142949 (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]

Ciepielewski, D.

Cremer, C.

S. W. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169(3), 391–405 (1993).
[Crossref]

Dahan, M.

Darzacq, X.

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]

Douglass, K. M.

L. Carlini, S. J. Holden, K. M. Douglass, and S. Manley, “Correction of a depth-dependent lateral distortion in 3D super-resolution imaging,” PLoS One 10(11), e0142949 (2015).
[Crossref] [PubMed]

Dupont, A.

A. Dupont and D. C. Lamb, “Nanoscale three-dimensional single particle tracking,” Nanoscale 3(11), 4532–4541 (2011).
[Crossref] [PubMed]

El Beheiry, M.

Elson, E. L.

H. Qian, M. P. Sheetz, and E. L. Elson, “Single particle tracking. Analysis of diffusion and flow in two-dimensional systems,” Biophys. J. 60(4), 910–921 (1991).
[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]

Gahlmann, A.

A. Gahlmann, J. L. Ptacin, G. Grover, S. Quirin, A. R. S. von Diezmann, M. K. Lee, M. P. Backlund, L. Shapiro, R. Piestun, and W. E. Moerner, “Quantitative multicolor subdiffraction imaging of bacterial protein ultrastructures in three dimensions,” Nano Lett. 13(3), 987–993 (2013).
[Crossref] [PubMed]

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]

Grover, G.

A. Gahlmann, J. L. Ptacin, G. Grover, S. Quirin, A. R. S. von Diezmann, M. K. Lee, M. P. Backlund, L. Shapiro, R. Piestun, and W. E. Moerner, “Quantitative multicolor subdiffraction imaging of bacterial protein ultrastructures in three dimensions,” Nano Lett. 13(3), 987–993 (2013).
[Crossref] [PubMed]

Gustafsson, M. G.

B. M. Hanser, M. G. Gustafsson, D. A. Agard, and J. W. Sedat, “Phase-retrieved pupil functions in wide-field fluorescence microscopy,” J. Microsc. 216(1), 32–48 (2004).
[Crossref] [PubMed]

Hanser, B. M.

B. M. Hanser, M. G. Gustafsson, D. A. Agard, and J. W. Sedat, “Phase-retrieved pupil functions in wide-field fluorescence microscopy,” J. Microsc. 216(1), 32–48 (2004).
[Crossref] [PubMed]

Hell, S. W.

S. W. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169(3), 391–405 (1993).
[Crossref]

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]

Hirsch, M.

M. Hirsch, R. J. Wareham, M. L. Martin-Fernandez, M. P. Hobson, and D. J. Rolfe, “A stochastic model for electron multiplication charge-coupled devices--from theory to practice,” PLoS One 8(1), e53671 (2013).
[Crossref] [PubMed]

Hobson, M. P.

M. Hirsch, R. J. Wareham, M. L. Martin-Fernandez, M. P. Hobson, and D. J. Rolfe, “A stochastic model for electron multiplication charge-coupled devices--from theory to practice,” PLoS One 8(1), e53671 (2013).
[Crossref] [PubMed]

Holden, S. J.

L. Carlini, S. J. Holden, K. M. Douglass, and S. Manley, “Correction of a depth-dependent lateral distortion in 3D super-resolution imaging,” PLoS One 10(11), e0142949 (2015).
[Crossref] [PubMed]

Huang, B.

R. McGorty, J. Schnitzbauer, W. Zhang, and B. Huang, “Correction of depth-dependent aberrations in 3D single-molecule localization and super-resolution microscopy,” Opt. Lett. 39(2), 275–278 (2014).
[Crossref] [PubMed]

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319(5864), 810–813 (2008).
[Crossref] [PubMed]

Izeddin, I.

Jia, S.

S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic three-dimensional super-resolution imaging with a self-bending point spread function,” Nat. Photonics 8(4), 302–306 (2014).
[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]

Kromann, E. B.

Krueger, W. D.

Lamb, D. C.

A. Dupont and D. C. Lamb, “Nanoscale three-dimensional single particle tracking,” Nanoscale 3(11), 4532–4541 (2011).
[Crossref] [PubMed]

Lee, M. K.

A. Gahlmann, J. L. Ptacin, G. Grover, S. Quirin, A. R. S. von Diezmann, M. K. Lee, M. P. Backlund, L. Shapiro, R. Piestun, and W. E. Moerner, “Quantitative multicolor subdiffraction imaging of bacterial protein ultrastructures in three dimensions,” Nano Lett. 13(3), 987–993 (2013).
[Crossref] [PubMed]

Lee, M. L.

Y. Shechtman, L. E. Weiss, A. S. Backer, M. L. Lee, and W. E. Moerner, “Multicolor localization microscopy by point-spread-function engineering,” Nat. Photonics 10(9), 590–594 (2016).
[Crossref]

Lee, M. Y.

Lee, S. F.

Lew, M. D.

Lidke, K. A.

S. Liu, E. B. Kromann, W. D. Krueger, J. Bewersdorf, and K. A. Lidke, “Three dimensional single molecule localization using a phase retrieved pupil function,” Opt. Express 21(24), 29462–29487 (2013).
[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]

Lieb, M. A.

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]

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]

Liu, S.

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]

Manley, S.

L. Carlini, S. J. Holden, K. M. Douglass, and S. Manley, “Correction of a depth-dependent lateral distortion in 3D super-resolution imaging,” PLoS One 10(11), e0142949 (2015).
[Crossref] [PubMed]

Martin-Fernandez, M. L.

M. Hirsch, R. J. Wareham, M. L. Martin-Fernandez, M. P. Hobson, and D. J. Rolfe, “A stochastic model for electron multiplication charge-coupled devices--from theory to practice,” PLoS One 8(1), e53671 (2013).
[Crossref] [PubMed]

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]

McGorty, R.

Moerner, W. E.

Y. Shechtman, L. E. Weiss, A. S. Backer, M. L. Lee, and W. E. Moerner, “Multicolor localization microscopy by point-spread-function engineering,” Nat. Photonics 10(9), 590–594 (2016).
[Crossref]

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] [PubMed]

A. von Diezmann, M. Y. Lee, M. D. Lew, and W. E. Moerner, “Correcting field-dependent aberrations with nanoscale accuracy in three-dimensional single-molecule localization microscopy,” Optica 2(11), 985–993 (2015).
[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]

A. Gahlmann, J. L. Ptacin, G. Grover, S. Quirin, A. R. S. von Diezmann, M. K. Lee, M. P. Backlund, L. Shapiro, R. Piestun, and W. E. Moerner, “Quantitative multicolor subdiffraction imaging of bacterial protein ultrastructures in three dimensions,” Nano Lett. 13(3), 987–993 (2013).
[Crossref] [PubMed]

W. E. Moerner, “Microscopy beyond the diffraction limit using actively controlled single molecules,” J. Microsc. 246(3), 213–220 (2012).
[Crossref] [PubMed]

M. D. Lew, S. F. Lee, M. Badieirostami, and W. E. Moerner, “Corkscrew point spread function for far-field three-dimensional nanoscale localization of pointlike objects,” Opt. Lett. 36(2), 202–204 (2011).
[Crossref] [PubMed]

M. D. Lew, M. A. Thompson, M. Badieirostami, and W. E. Moerner, “In vivo three-dimensional superresolution fluorescence tracking using a double-helix point spread function,” Proc SPIE Int Soc Opt Eng 7571, 75710Z (2010).
[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]

Noll, R. J.

Novotny, L.

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]

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]

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. Quirin, S. R. P. Pavani, and R. Piestun, “Optimal 3D single-molecule localization for superresolution microscopy with aberrations and engineered point spread functions,” Proc. Natl. Acad. Sci. U.S.A. 109(3), 675–679 (2012).
[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]

Piestun, R.

A. Gahlmann, J. L. Ptacin, G. Grover, S. Quirin, A. R. S. von Diezmann, M. K. Lee, M. P. Backlund, L. Shapiro, R. Piestun, and W. E. Moerner, “Quantitative multicolor subdiffraction imaging of bacterial protein ultrastructures in three dimensions,” Nano Lett. 13(3), 987–993 (2013).
[Crossref] [PubMed]

S. Quirin, S. R. P. Pavani, and R. Piestun, “Optimal 3D single-molecule localization for superresolution microscopy with aberrations and engineered point spread functions,” Proc. Natl. Acad. Sci. U.S.A. 109(3), 675–679 (2012).
[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]

Ptacin, J. L.

A. Gahlmann, J. L. Ptacin, G. Grover, S. Quirin, A. R. S. von Diezmann, M. K. Lee, M. P. Backlund, L. Shapiro, R. Piestun, and W. E. Moerner, “Quantitative multicolor subdiffraction imaging of bacterial protein ultrastructures in three dimensions,” Nano Lett. 13(3), 987–993 (2013).
[Crossref] [PubMed]

Qian, H.

H. Qian, M. P. Sheetz, and E. L. Elson, “Single particle tracking. Analysis of diffusion and flow in two-dimensional systems,” Biophys. J. 60(4), 910–921 (1991).
[Crossref] [PubMed]

Quirin, S.

A. Gahlmann, J. L. Ptacin, G. Grover, S. Quirin, A. R. S. von Diezmann, M. K. Lee, M. P. Backlund, L. Shapiro, R. Piestun, and W. E. Moerner, “Quantitative multicolor subdiffraction imaging of bacterial protein ultrastructures in three dimensions,” Nano Lett. 13(3), 987–993 (2013).
[Crossref] [PubMed]

S. Quirin, S. R. P. Pavani, and R. Piestun, “Optimal 3D single-molecule localization for superresolution microscopy with aberrations and engineered point spread functions,” Proc. Natl. Acad. Sci. U.S.A. 109(3), 675–679 (2012).
[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]

Reiner, G.

S. W. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169(3), 391–405 (1993).
[Crossref]

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

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]

Rolfe, D. J.

M. Hirsch, R. J. Wareham, M. L. Martin-Fernandez, M. P. Hobson, and D. J. Rolfe, “A stochastic model for electron multiplication charge-coupled devices--from theory to practice,” PLoS One 8(1), e53671 (2013).
[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), 793–795 (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] [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]

Sakamoto, J. A.

Saxton, M. J.

M. J. Saxton, “Single-particle tracking: the distribution of diffusion coefficients,” Biophys. J. 72(4), 1744–1753 (1997).
[Crossref] [PubMed]

Schnitzbauer, J.

Sedat, J. W.

B. M. Hanser, M. G. Gustafsson, D. A. Agard, and J. W. Sedat, “Phase-retrieved pupil functions in wide-field fluorescence microscopy,” J. Microsc. 216(1), 32–48 (2004).
[Crossref] [PubMed]

Shapiro, L.

A. Gahlmann, J. L. Ptacin, G. Grover, S. Quirin, A. R. S. von Diezmann, M. K. Lee, M. P. Backlund, L. Shapiro, R. Piestun, and W. E. Moerner, “Quantitative multicolor subdiffraction imaging of bacterial protein ultrastructures in three dimensions,” Nano Lett. 13(3), 987–993 (2013).
[Crossref] [PubMed]

Shechtman, Y.

Y. Shechtman, L. E. Weiss, A. S. Backer, M. L. Lee, and W. E. Moerner, “Multicolor localization microscopy by point-spread-function engineering,” Nat. Photonics 10(9), 590–594 (2016).
[Crossref]

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] [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]

Sheetz, M. P.

H. Qian, M. P. Sheetz, and E. L. Elson, “Single particle tracking. Analysis of diffusion and flow in two-dimensional systems,” Biophys. J. 60(4), 910–921 (1991).
[Crossref] [PubMed]

Small, A.

A. Small and S. Stahlheber, “Fluorophore localization algorithms for super-resolution microscopy,” Nat. Methods 11(3), 267–279 (2014).
[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]

Stahlheber, S.

A. Small and S. Stahlheber, “Fluorophore localization algorithms for super-resolution microscopy,” Nat. Methods 11(3), 267–279 (2014).
[Crossref] [PubMed]

Stelzer, E. H. K.

S. W. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169(3), 391–405 (1993).
[Crossref]

Thompson, M. A.

M. D. Lew, M. A. Thompson, M. Badieirostami, and W. E. Moerner, “In vivo three-dimensional superresolution fluorescence tracking using a double-helix point spread function,” Proc SPIE Int Soc Opt Eng 7571, 75710Z (2010).
[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]

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]

Vaughan, J. C.

S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic three-dimensional super-resolution imaging with a self-bending point spread function,” Nat. Photonics 8(4), 302–306 (2014).
[Crossref] [PubMed]

von Diezmann, A.

von Diezmann, A. R. S.

A. Gahlmann, J. L. Ptacin, G. Grover, S. Quirin, A. R. S. von Diezmann, M. K. Lee, M. P. Backlund, L. Shapiro, R. Piestun, and W. E. Moerner, “Quantitative multicolor subdiffraction imaging of bacterial protein ultrastructures in three dimensions,” Nano Lett. 13(3), 987–993 (2013).
[Crossref] [PubMed]

Wang, W.

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319(5864), 810–813 (2008).
[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]

Wareham, R. J.

M. Hirsch, R. J. Wareham, M. L. Martin-Fernandez, M. P. Hobson, and D. J. Rolfe, “A stochastic model for electron multiplication charge-coupled devices--from theory to practice,” PLoS One 8(1), e53671 (2013).
[Crossref] [PubMed]

Weiss, L. E.

Y. Shechtman, L. E. Weiss, A. S. Backer, M. L. Lee, and W. E. Moerner, “Multicolor localization microscopy by point-spread-function engineering,” Nat. Photonics 10(9), 590–594 (2016).
[Crossref]

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] [PubMed]

Wolf, E.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

Zavislan, J. M.

Zhang, W.

Zhuang, X.

S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic three-dimensional super-resolution imaging with a self-bending point spread function,” Nat. Photonics 8(4), 302–306 (2014).
[Crossref] [PubMed]

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319(5864), 810–813 (2008).
[Crossref] [PubMed]

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–795 (2006).
[Crossref] [PubMed]

Biophys. J. (4)

H. Qian, M. P. Sheetz, and E. L. Elson, “Single particle tracking. Analysis of diffusion and flow in two-dimensional systems,” Biophys. J. 60(4), 910–921 (1991).
[Crossref] [PubMed]

M. J. Saxton, “Single-particle tracking: the distribution of diffusion coefficients,” Biophys. J. 72(4), 1744–1753 (1997).
[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]

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

J. Microsc. (3)

B. M. Hanser, M. G. Gustafsson, D. A. Agard, and J. W. Sedat, “Phase-retrieved pupil functions in wide-field fluorescence microscopy,” J. Microsc. 216(1), 32–48 (2004).
[Crossref] [PubMed]

S. W. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169(3), 391–405 (1993).
[Crossref]

W. E. Moerner, “Microscopy beyond the diffraction limit using actively controlled single molecules,” J. Microsc. 246(3), 213–220 (2012).
[Crossref] [PubMed]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (1)

Nano Lett. (2)

A. Gahlmann, J. L. Ptacin, G. Grover, S. Quirin, A. R. S. von Diezmann, M. K. Lee, M. P. Backlund, L. Shapiro, R. Piestun, and W. E. Moerner, “Quantitative multicolor subdiffraction imaging of bacterial protein ultrastructures in three dimensions,” Nano Lett. 13(3), 987–993 (2013).
[Crossref] [PubMed]

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] [PubMed]

Nanoscale (1)

A. Dupont and D. C. Lamb, “Nanoscale three-dimensional single particle tracking,” Nanoscale 3(11), 4532–4541 (2011).
[Crossref] [PubMed]

Nat. Methods (4)

A. Small and S. Stahlheber, “Fluorophore localization algorithms for super-resolution microscopy,” Nat. Methods 11(3), 267–279 (2014).
[Crossref] [PubMed]

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–795 (2006).
[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]

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]

Nat. Photonics (2)

Y. Shechtman, L. E. Weiss, A. S. Backer, M. L. Lee, and W. E. Moerner, “Multicolor localization microscopy by point-spread-function engineering,” Nat. Photonics 10(9), 590–594 (2016).
[Crossref]

S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic three-dimensional super-resolution imaging with a self-bending point spread function,” Nat. Photonics 8(4), 302–306 (2014).
[Crossref] [PubMed]

Opt. Express (3)

Opt. Lett. (2)

Optica (1)

Phys. Rev. Lett. (1)

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 (2)

L. Carlini, S. J. Holden, K. M. Douglass, and S. Manley, “Correction of a depth-dependent lateral distortion in 3D super-resolution imaging,” PLoS One 10(11), e0142949 (2015).
[Crossref] [PubMed]

M. Hirsch, R. J. Wareham, M. L. Martin-Fernandez, M. P. Hobson, and D. J. Rolfe, “A stochastic model for electron multiplication charge-coupled devices--from theory to practice,” PLoS One 8(1), e53671 (2013).
[Crossref] [PubMed]

Proc SPIE Int Soc Opt Eng (1)

M. D. Lew, M. A. Thompson, M. Badieirostami, and W. E. Moerner, “In vivo three-dimensional superresolution fluorescence tracking using a double-helix point spread function,” Proc SPIE Int Soc Opt Eng 7571, 75710Z (2010).
[Crossref] [PubMed]

Proc. Natl. Acad. Sci. U.S.A. (2)

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. Quirin, S. R. P. Pavani, and R. Piestun, “Optimal 3D single-molecule localization for superresolution microscopy with aberrations and engineered point spread functions,” Proc. Natl. Acad. Sci. U.S.A. 109(3), 675–679 (2012).
[Crossref] [PubMed]

Proc. R. Soc. Lond. A Math. Phys. Sci. (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

Science (2)

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319(5864), 810–813 (2008).
[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 (6)

J. W. Goodman, Introduction to Fourier Optics (Roberts & Company Publishers, 2005).

P. N. Petrov and W. E. Moerner, “Easy Pupil Finder,” SourceForge (2017) [retrieved 17 January 2017], http://sourceforge.net/p/easy-pupil-finder .

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

J. C. Wyant and K. Creath, “Basic wavefront aberration theory for optical metrology,” in R. R. Shannon and J. C. Wyant, (eds. 1992), pp. 1–53.

S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice-Hall PTR, 1993).

B. Moomaw, “Camera Technologies for Low Light Imaging: Overview and Relative Advantages,” in Methods in Cell Biology, G. Sluder and D. E. Wolf, eds. (Elsevier, 2013), pp. 243–283.

Supplementary Material (1)

NameDescription
» Code 1       Code for pupil function determination

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1 (a) Schematic of the phase retrieval algorithm. A map of the phase mask pattern is used to produce the theoretical model, and a set of experimental images of the PSF is used to perform the MLE step. The estimation procedure returns a phase aberration term, which is added to the original phase mask pattern to produce the overall pupil function. In all cases, only the phase portion of the field is shown. (b) Schematic of the emission path of the microscope. Fluorescence collected from the sample by the objective is focused by a tube lens onto the intermediate image plane and relayed by a pair of 4f lenses onto the final image plane, where the camera is placed. The phase mask is placed in the Fourier plane, located half way between the two 4f lenses.
Fig. 2
Fig. 2 (a) Left: phase-only portion of the theoretical pupil function with the tetrapod phase mask. Right: tetrapod PSFs calculated using the phase pattern on the left. (b) Experimentally-acquired images of the tetrapod PSF. Green (purple) arrows indicate features reproduced better in the phase-retrieved (calculated theoretical) PSF model, but a more quantitative comparison is shown in Fig. 3. (c) Left: phase-only portion of the phase-retrieved pupil function. Right: tetrapod PSFs calculated using the phase pattern on the left. Side length is 6 µm in all PSF images.
Fig. 3
Fig. 3 Results of axial scan of a fluorescent bead. (a) Left: estimated axial position at each frame in the scan. Each fit is shown as a dot, and dashed lines are added at ± 3000 nm to guide the eyes. Inset shows a close-up of five steps, with localizations in each axial step connected by lines to illustrate fluctuations. Estimates of zo are arbitrarily defined to be 0 in the middle of both scans. Right: step size plotted against axial step number. The true value is indicated with a dashed line. (b) Localization precision in x (left), y (middle), and z (right) as a function of known z position for the uncorrected (theoretical) and phase-retrieved PSF. Insets show magnified views of the curves over part of the axial range, indicated by blue boxes in the main plots. Localization precision is determined from the full set of localizations at each axial position. CRLB is calculated for the phase-retrieved PSF with 95000 signal photons and 3.7 background photons per pixel, as measured for the bead.
Fig. 4
Fig. 4 Reproducibility from 35 scans (per channel). Circles show mean Zernike polynomial peak-to-valley phase difference; error bars show standard deviation. Negative peak-to-valley values correspond to negative polynomial coefficients. Mean signal photons across all scans were 54000 (green) and 46000 (red). Insets show phase aberrations calculated from mean value of each aberration.

Equations (14)

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

I( x , y | x o , y o , z o ) | { E FP (ρ,φ| x o , y o , z o ) } | 2
E 0 (ρ,φ) E FP (ρ,φ|0,0,0)= circ(ρ) [ 1 ( NA n ρ ) 2 ] 1/4 exp[ iM( ρ,φ ) ]
Φ lat (ξ,η| x o , y o )= 2π λ f 4f ( x o ξ+ y o η)
Φ lat (ρ,φ| x o , y o )= 2πNA λ M 2 N A 2 ρ( x o cosφ+ y o sinφ)
Φ ax (ρ,φ| z o )= 2πn λ z o 1 ( NA n ρ ) 2
E FP (ρ,φ| x o , y o , z o )= E 0 (ρ,φ)exp{ i[ Φ lat (ρ,φ| x o , y o )+ Φ ax (ρ,φ| z o ) ] }
Ψ(ρ,φ|c)= j=4 J c j Z j ( ρ,φ )
E FP Ψ (ρ,φ|0,0,0;c)= E FP (ρ,φ|0,0,0)exp[ iΨ(ρ,φ|c) ]
(c;{ I 1 , I 2 ,, I K })= k=1 K s=1 S ( X k,s |c) X ˜ k,s exp( X k,s |c) X ˜ k,s !
c ^ ML = argmin c { log[ (c;{ I 1 , I 2 ,, I K }) ] } = argmin c { k=1 K s=1 S ( X k,s |c) X ˜ k,s log( X k,s |c) +log( X ˜ k,s !) }
M(ξ',η')=M(ξ+Δξ,η+Δη)
I ij ( θ )=E[ 2 lnf(ξ;θ) θ i θ j ]
I ij ( θ )= s=1 S 1 μ(s|θ)+b [ μ(s|θ) θ i ][ μ(s|θ) θ j ]
σ i 2 { [ I( θ ) ] 1 } ii CRL B i

Metrics