Abstract

Super-resolution techniques that localize single molecules in three dimensions through point spread function (PSF) engineering are very sensitive to aberrations and optical alignment. Here we show how double-helix point spread function is affected by such mis-alignment and aberration. Specifically, we demonstrate through simulation and experiment how misplacement of phase masks in infinity corrected systems is a common source of significant loss of accuracy. We also describe an optimal alignment and calibration procedure to correct for these errors. In combination, these optimizations allow for a maximal field of view with high accuracy and precision. Though discussed with reference to double-helix point spread function (DHPSF), the optimization techniques are equally applicable to other engineered PSFs.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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  1. 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, 1642–1645 (2006).
    [Crossref] [PubMed]
  2. M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3, 793–796 (2006).
    [Crossref] [PubMed]
  3. B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319, 810–813 (2008).
    [Crossref] [PubMed]
  4. S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. 106, 2995–2999 (2009).
    [Crossref] [PubMed]
  5. A. von Diezmann, Y. Shechtman, and W. Moerner, “Three-dimensional localization of single molecules for super-resolution imaging and single-particle tracking,” Chem. Rev. 117(11), 7244–7275 (2017).
    [Crossref] [PubMed]
  6. S. R. P. Pavani and R. Piestun, “Three dimensional tracking of fluorescent microparticles using a photon-limited double-helix response system,” Opt. Express 16, 22048–22057 (2008).
    [Crossref] [PubMed]
  7. M. Badieirostami, M. D. Lew, M. A. Thompson, and W. Moerner, “Three-dimensional localization precision of the double-helix point spread function versus astigmatism and biplane,” Appl. Phys. Lett. 97, 161103 (2010).
    [Crossref] [PubMed]
  8. M. D. Lew, M. A. Thompson, M. Badieirostami, and W. Moerner, “In vivo three-dimensional superresolution fluorescence tracking using a double-helix point spread function,” Proc. SPIE 7571, 75710Z (2010).
    [Crossref]
  9. A. von Diezmann, M. Y. Lee, M. D. Lew, and W. Moerner, “Correcting field-dependent aberrations with nanoscale accuracy in three-dimensional single-molecule localization microscopy,” Optica 2, 985–993 (2015).
    [Crossref]
  10. B. Shuang, W. Wang, H. Shen, L. J. Tauzin, C. Flatebo, J. Chen, N. A. Moringo, L. D. Bishop, K. F. Kelly, and C. F. Landes, “Generalized recovery algorithm for 3d super-resolution microscopy using rotating point spread functions,” Sci. Rep. 6, 30826 (2016).
    [Crossref] [PubMed]
  11. A. R. Carr, A. Ponjavic, S. Basu, J. McColl, A. M. Santos, S. Davis, E. D. Laue, D. Klenerman, and S. F. Lee, “Three-dimensional super-resolution in eukaryotic cells using the double-helix point spread function,” Biophysical J. 112, 1444–1454 (2017).
    [Crossref]
  12. S. R. P. Pavani and R. Piestun, “High-efficiency rotating point spread functions,” Opt. Express 16, 3484–3489 (2008).
    [Crossref] [PubMed]
  13. M. D. Lew, A. R. von Diezmann, and W. Moerner, “Easy-DHPSF open-source software for three-dimensional localization of single molecules with precision beyond the optical diffraction limit,” Protocol Exchange 2013, 26 (2013).

2017 (2)

A. R. Carr, A. Ponjavic, S. Basu, J. McColl, A. M. Santos, S. Davis, E. D. Laue, D. Klenerman, and S. F. Lee, “Three-dimensional super-resolution in eukaryotic cells using the double-helix point spread function,” Biophysical J. 112, 1444–1454 (2017).
[Crossref]

A. von Diezmann, Y. Shechtman, and W. Moerner, “Three-dimensional localization of single molecules for super-resolution imaging and single-particle tracking,” Chem. Rev. 117(11), 7244–7275 (2017).
[Crossref] [PubMed]

2016 (1)

B. Shuang, W. Wang, H. Shen, L. J. Tauzin, C. Flatebo, J. Chen, N. A. Moringo, L. D. Bishop, K. F. Kelly, and C. F. Landes, “Generalized recovery algorithm for 3d super-resolution microscopy using rotating point spread functions,” Sci. Rep. 6, 30826 (2016).
[Crossref] [PubMed]

2015 (1)

2013 (1)

M. D. Lew, A. R. von Diezmann, and W. Moerner, “Easy-DHPSF open-source software for three-dimensional localization of single molecules with precision beyond the optical diffraction limit,” Protocol Exchange 2013, 26 (2013).

2010 (2)

M. Badieirostami, M. D. Lew, M. A. Thompson, and W. Moerner, “Three-dimensional localization precision of the double-helix point spread function versus astigmatism and biplane,” Appl. Phys. Lett. 97, 161103 (2010).
[Crossref] [PubMed]

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

2009 (1)

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

2008 (3)

2006 (2)

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, 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, 793–796 (2006).
[Crossref] [PubMed]

Badieirostami, M.

M. Badieirostami, M. D. Lew, M. A. Thompson, and W. Moerner, “Three-dimensional localization precision of the double-helix point spread function versus astigmatism and biplane,” Appl. Phys. Lett. 97, 161103 (2010).
[Crossref] [PubMed]

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

Basu, S.

A. R. Carr, A. Ponjavic, S. Basu, J. McColl, A. M. Santos, S. Davis, E. D. Laue, D. Klenerman, and S. F. Lee, “Three-dimensional super-resolution in eukaryotic cells using the double-helix point spread function,” Biophysical J. 112, 1444–1454 (2017).
[Crossref]

Bates, M.

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319, 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, 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, 1642–1645 (2006).
[Crossref] [PubMed]

Bishop, L. D.

B. Shuang, W. Wang, H. Shen, L. J. Tauzin, C. Flatebo, J. Chen, N. A. Moringo, L. D. Bishop, K. F. Kelly, and C. F. Landes, “Generalized recovery algorithm for 3d super-resolution microscopy using rotating point spread functions,” Sci. Rep. 6, 30826 (2016).
[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. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. 106, 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, 1642–1645 (2006).
[Crossref] [PubMed]

Carr, A. R.

A. R. Carr, A. Ponjavic, S. Basu, J. McColl, A. M. Santos, S. Davis, E. D. Laue, D. Klenerman, and S. F. Lee, “Three-dimensional super-resolution in eukaryotic cells using the double-helix point spread function,” Biophysical J. 112, 1444–1454 (2017).
[Crossref]

Chen, J.

B. Shuang, W. Wang, H. Shen, L. J. Tauzin, C. Flatebo, J. Chen, N. A. Moringo, L. D. Bishop, K. F. Kelly, and C. F. Landes, “Generalized recovery algorithm for 3d super-resolution microscopy using rotating point spread functions,” Sci. Rep. 6, 30826 (2016).
[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, 1642–1645 (2006).
[Crossref] [PubMed]

Davis, S.

A. R. Carr, A. Ponjavic, S. Basu, J. McColl, A. M. Santos, S. Davis, E. D. Laue, D. Klenerman, and S. F. Lee, “Three-dimensional super-resolution in eukaryotic cells using the double-helix point spread function,” Biophysical J. 112, 1444–1454 (2017).
[Crossref]

Flatebo, C.

B. Shuang, W. Wang, H. Shen, L. J. Tauzin, C. Flatebo, J. Chen, N. A. Moringo, L. D. Bishop, K. F. Kelly, and C. F. Landes, “Generalized recovery algorithm for 3d super-resolution microscopy using rotating point spread functions,” Sci. Rep. 6, 30826 (2016).
[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, 1642–1645 (2006).
[Crossref] [PubMed]

Huang, B.

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

Kelly, K. F.

B. Shuang, W. Wang, H. Shen, L. J. Tauzin, C. Flatebo, J. Chen, N. A. Moringo, L. D. Bishop, K. F. Kelly, and C. F. Landes, “Generalized recovery algorithm for 3d super-resolution microscopy using rotating point spread functions,” Sci. Rep. 6, 30826 (2016).
[Crossref] [PubMed]

Klenerman, D.

A. R. Carr, A. Ponjavic, S. Basu, J. McColl, A. M. Santos, S. Davis, E. D. Laue, D. Klenerman, and S. F. Lee, “Three-dimensional super-resolution in eukaryotic cells using the double-helix point spread function,” Biophysical J. 112, 1444–1454 (2017).
[Crossref]

Landes, C. F.

B. Shuang, W. Wang, H. Shen, L. J. Tauzin, C. Flatebo, J. Chen, N. A. Moringo, L. D. Bishop, K. F. Kelly, and C. F. Landes, “Generalized recovery algorithm for 3d super-resolution microscopy using rotating point spread functions,” Sci. Rep. 6, 30826 (2016).
[Crossref] [PubMed]

Laue, E. D.

A. R. Carr, A. Ponjavic, S. Basu, J. McColl, A. M. Santos, S. Davis, E. D. Laue, D. Klenerman, and S. F. Lee, “Three-dimensional super-resolution in eukaryotic cells using the double-helix point spread function,” Biophysical J. 112, 1444–1454 (2017).
[Crossref]

Lee, M. Y.

Lee, S. F.

A. R. Carr, A. Ponjavic, S. Basu, J. McColl, A. M. Santos, S. Davis, E. D. Laue, D. Klenerman, and S. F. Lee, “Three-dimensional super-resolution in eukaryotic cells using the double-helix point spread function,” Biophysical J. 112, 1444–1454 (2017).
[Crossref]

Lew, M. D.

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

M. D. Lew, A. R. von Diezmann, and W. Moerner, “Easy-DHPSF open-source software for three-dimensional localization of single molecules with precision beyond the optical diffraction limit,” Protocol Exchange 2013, 26 (2013).

M. Badieirostami, M. D. Lew, M. A. Thompson, and W. Moerner, “Three-dimensional localization precision of the double-helix point spread function versus astigmatism and biplane,” Appl. Phys. Lett. 97, 161103 (2010).
[Crossref] [PubMed]

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

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, 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, 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. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. 106, 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. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. 106, 2995–2999 (2009).
[Crossref] [PubMed]

McColl, J.

A. R. Carr, A. Ponjavic, S. Basu, J. McColl, A. M. Santos, S. Davis, E. D. Laue, D. Klenerman, and S. F. Lee, “Three-dimensional super-resolution in eukaryotic cells using the double-helix point spread function,” Biophysical J. 112, 1444–1454 (2017).
[Crossref]

Moerner, W.

A. von Diezmann, Y. Shechtman, and W. Moerner, “Three-dimensional localization of single molecules for super-resolution imaging and single-particle tracking,” Chem. Rev. 117(11), 7244–7275 (2017).
[Crossref] [PubMed]

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

M. D. Lew, A. R. von Diezmann, and W. Moerner, “Easy-DHPSF open-source software for three-dimensional localization of single molecules with precision beyond the optical diffraction limit,” Protocol Exchange 2013, 26 (2013).

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

M. Badieirostami, M. D. Lew, M. A. Thompson, and W. Moerner, “Three-dimensional localization precision of the double-helix point spread function versus astigmatism and biplane,” Appl. Phys. Lett. 97, 161103 (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. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. 106, 2995–2999 (2009).
[Crossref] [PubMed]

Moringo, N. A.

B. Shuang, W. Wang, H. Shen, L. J. Tauzin, C. Flatebo, J. Chen, N. A. Moringo, L. D. Bishop, K. F. Kelly, and C. F. Landes, “Generalized recovery algorithm for 3d super-resolution microscopy using rotating point spread functions,” Sci. Rep. 6, 30826 (2016).
[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, 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, 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. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. 106, 2995–2999 (2009).
[Crossref] [PubMed]

S. R. P. Pavani and R. Piestun, “High-efficiency rotating point spread functions,” Opt. Express 16, 3484–3489 (2008).
[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, 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. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. 106, 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, 22048–22057 (2008).
[Crossref] [PubMed]

S. R. P. Pavani and R. Piestun, “High-efficiency rotating point spread functions,” Opt. Express 16, 3484–3489 (2008).
[Crossref] [PubMed]

Ponjavic, A.

A. R. Carr, A. Ponjavic, S. Basu, J. McColl, A. M. Santos, S. Davis, E. D. Laue, D. Klenerman, and S. F. Lee, “Three-dimensional super-resolution in eukaryotic cells using the double-helix point spread function,” Biophysical J. 112, 1444–1454 (2017).
[Crossref]

Rust, M. J.

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

Santos, A. M.

A. R. Carr, A. Ponjavic, S. Basu, J. McColl, A. M. Santos, S. Davis, E. D. Laue, D. Klenerman, and S. F. Lee, “Three-dimensional super-resolution in eukaryotic cells using the double-helix point spread function,” Biophysical J. 112, 1444–1454 (2017).
[Crossref]

Shechtman, Y.

A. von Diezmann, Y. Shechtman, and W. Moerner, “Three-dimensional localization of single molecules for super-resolution imaging and single-particle tracking,” Chem. Rev. 117(11), 7244–7275 (2017).
[Crossref] [PubMed]

Shen, H.

B. Shuang, W. Wang, H. Shen, L. J. Tauzin, C. Flatebo, J. Chen, N. A. Moringo, L. D. Bishop, K. F. Kelly, and C. F. Landes, “Generalized recovery algorithm for 3d super-resolution microscopy using rotating point spread functions,” Sci. Rep. 6, 30826 (2016).
[Crossref] [PubMed]

Shuang, B.

B. Shuang, W. Wang, H. Shen, L. J. Tauzin, C. Flatebo, J. Chen, N. A. Moringo, L. D. Bishop, K. F. Kelly, and C. F. Landes, “Generalized recovery algorithm for 3d super-resolution microscopy using rotating point spread functions,” Sci. Rep. 6, 30826 (2016).
[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, 1642–1645 (2006).
[Crossref] [PubMed]

Tauzin, L. J.

B. Shuang, W. Wang, H. Shen, L. J. Tauzin, C. Flatebo, J. Chen, N. A. Moringo, L. D. Bishop, K. F. Kelly, and C. F. Landes, “Generalized recovery algorithm for 3d super-resolution microscopy using rotating point spread functions,” Sci. Rep. 6, 30826 (2016).
[Crossref] [PubMed]

Thompson, M. A.

M. Badieirostami, M. D. Lew, M. A. Thompson, and W. Moerner, “Three-dimensional localization precision of the double-helix point spread function versus astigmatism and biplane,” Appl. Phys. Lett. 97, 161103 (2010).
[Crossref] [PubMed]

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

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

von Diezmann, A.

A. von Diezmann, Y. Shechtman, and W. Moerner, “Three-dimensional localization of single molecules for super-resolution imaging and single-particle tracking,” Chem. Rev. 117(11), 7244–7275 (2017).
[Crossref] [PubMed]

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

von Diezmann, A. R.

M. D. Lew, A. R. von Diezmann, and W. Moerner, “Easy-DHPSF open-source software for three-dimensional localization of single molecules with precision beyond the optical diffraction limit,” Protocol Exchange 2013, 26 (2013).

Wang, W.

B. Shuang, W. Wang, H. Shen, L. J. Tauzin, C. Flatebo, J. Chen, N. A. Moringo, L. D. Bishop, K. F. Kelly, and C. F. Landes, “Generalized recovery algorithm for 3d super-resolution microscopy using rotating point spread functions,” Sci. Rep. 6, 30826 (2016).
[Crossref] [PubMed]

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

Zhuang, X.

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319, 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, 793–796 (2006).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

M. Badieirostami, M. D. Lew, M. A. Thompson, and W. Moerner, “Three-dimensional localization precision of the double-helix point spread function versus astigmatism and biplane,” Appl. Phys. Lett. 97, 161103 (2010).
[Crossref] [PubMed]

Biophysical J. (1)

A. R. Carr, A. Ponjavic, S. Basu, J. McColl, A. M. Santos, S. Davis, E. D. Laue, D. Klenerman, and S. F. Lee, “Three-dimensional super-resolution in eukaryotic cells using the double-helix point spread function,” Biophysical J. 112, 1444–1454 (2017).
[Crossref]

Chem. Rev. (1)

A. von Diezmann, Y. Shechtman, and W. Moerner, “Three-dimensional localization of single molecules for super-resolution imaging and single-particle tracking,” Chem. Rev. 117(11), 7244–7275 (2017).
[Crossref] [PubMed]

Nat. Methods (1)

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

Opt. Express (2)

Optica (1)

Proc. Natl. Acad. Sci. (1)

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

Proc. SPIE (1)

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

Protocol Exchange (1)

M. D. Lew, A. R. von Diezmann, and W. Moerner, “Easy-DHPSF open-source software for three-dimensional localization of single molecules with precision beyond the optical diffraction limit,” Protocol Exchange 2013, 26 (2013).

Sci. Rep. (1)

B. Shuang, W. Wang, H. Shen, L. J. Tauzin, C. Flatebo, J. Chen, N. A. Moringo, L. D. Bishop, K. F. Kelly, and C. F. Landes, “Generalized recovery algorithm for 3d super-resolution microscopy using rotating point spread functions,” Sci. Rep. 6, 30826 (2016).
[Crossref] [PubMed]

Science (2)

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, 1642–1645 (2006).
[Crossref] [PubMed]

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

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Figures (4)

Fig. 1
Fig. 1 Emission paths for (a) idealized microscope and (b) typical infinity corrected microscope (note that the position of image plane is unchanged but conjugate BFP shifts). (c) overlap of light beams with the phase mask, from different points in the FOV, when phase mask is displaced from the conjugate BFP. The labels TL, L1, L2 and PM represent tube lens, the first and second lenses of 4f systems and the DHPSF phase mask respectively.
Fig. 2
Fig. 2 Simulation results for 35 mm displacement between the phase mask and the conjugate BFP of the objective. (a) shows radial nature of the spatially varying DHPSFs and (b) shows these lateral shifts for three distances from the center of the FOV. (c) depicts distortion in a spherical object due to the radial shifts (errors exaggerated 10 times).
Fig. 3
Fig. 3 (a) A representative image showing a distribution of fluorescent beads with three different radii marked at 7 μm, 14 μm and 21 μm. (b) and (c) show the global correction calculated from the average of bead positions assuming a shift-invariant PSF for phase mask displacements of 35 mm and 0 mm. (d), (e) and (f) show the radial shift in bead position when interpolated across the FOV for the three different phase mask displacements of 35 mm, 17 mm and 0 mm from the conjugate BFP. Curves with different colors show shifts at radial distances as shown in (a). (g) and (h) show resulting mean squared error if the global corrections shown in (b) and (c) are simply applied to a shifted phase mask (35 mm) and the correctly positioned phase mask respectively.
Fig. 4
Fig. 4 Maximum axial errors for (a) Δf = 35 mm and (b) Δf = 0 mm.

Equations (4)

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E ( k , f o ) n = 1 N [ E ( r , z ) ] 𝒪 ( k )
ϕ ( k ) = exp ( i M k r f )
Δ k = M r f Δ f .
E r ( k , z ) = exp [ i ( α ( z ) ( 2 k 2 1 ) + ϕ D H ( k Δ k ) ) ) ]

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