Abstract

Point spread function (PSF) engineering is used in single emitter localization to measure the emitter position in 3D and possibly other parameters such as the emission color or dipole orientation as well. Advanced PSF models such as spline fits to experimental PSFs or the vectorial PSF model can be used in the corresponding localization algorithms in order to model the intricate spot shape and deformations correctly. The complexity of the optical architecture and fit model makes PSF engineering approaches particularly sensitive to optical aberrations. Here, we present a calibration and alignment protocol for fluorescence microscopes equipped with a spatial light modulator (SLM) with the goal of establishing a wavefront error well below the diffraction limit for optimum application of complex engineered PSFs. We achieve high-precision wavefront control, to a level below 20 mλ wavefront aberration over a 30 minute time window after the calibration procedure, using a separate light path for calibrating the pixel-to-pixel variations of the SLM, and alignment of the SLM with respect to the optical axis and Fourier plane within 3 μm (x/y) and 100 μm (z) error. Aberrations are retrieved from a fit of the vectorial PSF model to a bead z-stack and compensated with a residual wavefront error comparable to the error of the SLM calibration step. This well-calibrated and corrected setup makes it possible to create complex ‘3D+λ’ PSFs that fit very well to the vectorial PSF model. Proof-of-principle bead experiments show precisions below 10 nm in x, y, and λ, and below 20 nm in z over an axial range of 1 μm with 2000 signal photons and 12 background photons.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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)

Simultaneous measurement of emission color and 3D position of single molecules

Carlas Smith, Max Huisman, Marijn Siemons, David Grünwald, and Sjoerd Stallinga
Opt. Express 24(5) 4996-5013 (2016)

Multicolor localization microscopy and point-spread-function engineering by deep learning

Eran Hershko, Lucien E. Weiss, Tomer Michaeli, and Yoav Shechtman
Opt. Express 27(5) 6158-6183 (2019)

References

  • View by:
  • |
  • |
  • |

  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, 1643–1645 (2006).
    [Crossref]
  2. M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3, 793–795 (2006).
    [Crossref] [PubMed]
  3. S. T. Hess, T. P. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91, 4258–4272 (2006).
    [Crossref] [PubMed]
  4. S. W. Hell, “Far-field optical nanoscopy,” Science 316, 1153–1158 (2007).
    [Crossref] [PubMed]
  5. R. P. J. Nieuwenhuizen, K. A. Lidke, M. Bates, D. Leyton Puig, D. Grünwald, S. Stallinga, and B. Rieger, “Measuring image resolution in optical nanoscopy,” Nat. Methods 10, 557–562 (2013).
    [Crossref] [PubMed]
  6. H. P. Kao and A. S. Verkman, “Tracking of single fluorescent particles in three dimensions: use of cylindrical optics to encode particle position,” Biophys. J. 67, 1291–1300 (1994).
    [Crossref] [PubMed]
  7. L. Holtzer, T. Meckel, and T. Schmidt, “Nanometric three-dimensional tracking of individual quantum dots in cells,” Appl. Phys. Lett. 90, 053902 (2007).
    [Crossref]
  8. 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]
  9. E. Toprak, H. Balci, B. Blehm, H. Benjamin, and P.R. Selvin, “Three-dimensional particle tracking via bifocal imaging,” Nano Lett. 7, 2043–2045 (2007).
    [Crossref] [PubMed]
  10. S. Ram, P. Prabhat, J. Chao, E. S. Ward, and R. J. Ober, “High accuracy 3D quantum dot tracking with multifocal plane microscopy for the study of fast intracellular dynamics in live cells,” Biophys. J. 95, 6025–6043 (2008).
    [Crossref] [PubMed]
  11. M. F. Juette, T. J. D Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, and J. Bewersdorf, “Three-dimensional sub–100 nm resolution fluorescence microscopy of thick samples,” Nat. Methods 5, 527–529 (2008).
    [Crossref] [PubMed]
  12. Y. Shechtman, S. J. Sahl, A. S. Backer, and W. E. Moerner, “Optimal point spread function design for 3D imaging,” Phys. Rev. Lett. 113, 133902 (2014).
    [Crossref] [PubMed]
  13. 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, 202–204 (2011).
    [Crossref] [PubMed]
  14. S. R. P. Pavani and R. Piestun, “High-efficiency rotating point spread functions,” Opt. Express 16, 3484–3489 (2009).
    [Crossref]
  15. 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. 116, 2995–2999 (2009).
    [Crossref]
  16. G. Grover, S. R. P. Pavani, and R. Piestun, “Performance limits on three-dimensional particle localization in photon-limited microscopy,” Opt. Lett. 35, 3306–3308 (2010).
    [Crossref] [PubMed]
  17. S. Prasad, “Rotating point spread function via pupil-phase engineering,” Opt. Lett. 38, 585–587 (2013).
    [Crossref] [PubMed]
  18. C. Roider, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “Axial super-localisation using rotating point spread functions shaped by polarisation-dependent phase modulation,” Opt. Express 22, 4029–4037 (2014).
    [Crossref] [PubMed]
  19. 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]
  20. D. Baddeley, M. B. Cannell, and C. Soeller, “Three-dimensional sub-100 nm super-resolution imaging of biological samples using a phase ramp in the objective pupil,” Nano Research 4, 589–598 (2011).
    [Crossref]
  21. S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic three-dimensional super-resolution imaging with a self-bending point spread function,” Nat. Photonics 8, 302–306, (2014).
    [Crossref]
  22. G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H.F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. 106, 3125–3130 (2009).
    [Crossref] [PubMed]
  23. M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, and W. E. Moerner, “The role of molecular dipole orientation in single-molecule fluorescence microscopy and implications for super-resolution imaging,” Chem. Phys. Chem. 15, 587–599 (2014).
    [Crossref] [PubMed]
  24. J. Broeken, B. Rieger, and S. Stallinga, “Simultaneous measurement of position and color of single fluorescent emitters using diffractive optics,” Opt. Lett. 39, 3352–3355 (2014).
    [Crossref] [PubMed]
  25. C. Smith, M. Huisman, M. Siemons, D. Grünwald, and S. Stallinga, “Simultaneous measurement of emission color and 3D position of single molecules,” Opt. Express 24, 4996–5013 (2016).
    [Crossref] [PubMed]
  26. Y. Shechtman, L. E. Weiss, A. S. Backer, M. Y. Lee, and W. E. Moerner, “Multicolour localization microscopy by point-spread-function engineering,” Nat. Photonics 10, 590–594 (2016).
    [Crossref] [PubMed]
  27. S. Stallinga and B. Rieger, “Accuracy of the Gaussian point spread function model in 2D localization microscopy,” Opt. Express 18, 24461–24476 (2010).
    [Crossref] [PubMed]
  28. S. F. Gibson and F. Lanni, “Experimental test of an analytical model of aberration in an oil-immersion objective lens used in three-dimensional light microscopy,” J. Opt. Soc. Am. A 9, 154–166 (1992).
    [Crossref] [PubMed]
  29. S. Stallinga and B. Rieger, “Position and orientation estimation of fixed dipole emitters using an effective Hermite point spread function model,” Opt. Express 20, 5896–5921 (2012).
    [Crossref] [PubMed]
  30. H. Kirshner, C. Vonesch, and M. Unser, “Can localization microscopy benefit from approximation theory?” 10th International Symposium on Biomedical Imaging, 588–591 (2013).
  31. A. Tahmasbi, E. S. Ward, and R. J. Ober, “Determination of localization accuracy based on experimentally acquired image sets: applications to single molecule microscopy,” Opt. Express 23, 7630–7652 (2015).
    [Crossref] [PubMed]
  32. H. P. Babcock and X. Zhuang, “Analyzing single molecule localization microscopy data using cubic splines,” Sci. Rep. 7, 552 (2017).
    [Crossref] [PubMed]
  33. Y. Li, M. Mund, P. Hoess, U. Matti, B. Nijmeijer, V. J. Sabinina, J. Ellenberg, I. Schoen, and J. Ries, “Fast, robust and precise 3D localization for arbitrary point spread functions,” bioRxiv 172643; doi: https://doi.org/10.1101/172643 .
  34. A. 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, 985–993 (2015).
    [Crossref]
  35. D. Débarre, M. J. Booth, and T. Wilson, “Image based adaptive optics through optimisation of low spatial frequencies,” Opt. Express,  15, 8176–8190 (2007).
    [Crossref] [PubMed]
  36. M. J. Booth, D. Andrade, D. Burke, B. Patton, and M. Zurauskas, “Aberrations and adaptive optics in super-resolution microscopy,” Microscopy 64, 251–261 (2015).
    [Crossref] [PubMed]
  37. D. Burke, B. Patton, F. Huang, J. Bewersdorf, and M. J. Booth, “Adaptive optics correction of specimen-induced aberrations in single-molecule switching microscopy,” Optica 2, 177–185 (2015).
    [Crossref]
  38. B. M. Hanser, M. G. L. Gustafsson, D. A. Agard, and J. W. Sedat, “Phase retrieval for high-numerical-aperture optical systems,” Opt. Lett. 28, 801–803 (2003).
    [Crossref] [PubMed]
  39. 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, 29462–29487 (2013).
    [Crossref]
  40. E. B. Kromann, T. J. Gould, M. F. Juette, J. E. Wilhjelm, and J. Bewersdorf, “Quantitative pupil analysis in stimulated emission depletion microscopy using phase retrieval,” Opt. Lett. 37, 1805–1807 (2012).
    [Crossref] [PubMed]
  41. P. N. Petrov, Y. Shechtman, and W. E. Moerner, “Measurement-based estimation of global pupil functions in 3D localization microscopy,” Opt. Express 25, 7945–7959 (2017).
    [Crossref] [PubMed]
  42. 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, 377–381 (2010).
    [Crossref] [PubMed]
  43. S. Stallinga, “Effect of rotational diffusion in an orientational potential well on the point spread function of electric dipole emitters,” J. Opt. Soc. Am. A 32, 213–223 (2015).
    [Crossref]
  44. E. Ronzitti, M. Guillon, V. de Sars, and V. Emiliani, “LCoS nematic SLM characterization and modeling for diffraction efficiency optimization, zero and ghost orders suppression,” Opt. Express 20, 17843–17855 (2012).
    [Crossref] [PubMed]
  45. M. Persson, D. Engström, and M. Goksör, “Reducing the effect of pixel crosstalk in phase only spatial light modulators,” Opt. Express 20, 22334–22343 (2012).
    [Crossref] [PubMed]
  46. C. Lingel, T. Haist, and W. Osten, “Optimizing the diffraction efficiency of SLM-based holography with respect to the fringing field effect,” Appl. Opt. 52, 6877–6883 (2013).
    [Crossref] [PubMed]
  47. H. Akaike, “A new look at the statistical model identification,” IEEE Trans. Automatic Control 19, 716–723 (1974).
    [Crossref]
  48. C. S. Smith, S. Stallinga, K. A. Lidke, B. Rieger, and D. Grünwald, “Probability-based particle detection that enables threshold-free and robust in vivo single molecule tracking,” Mol. Biol. Cell 26, 4057–4062 (2015).
    [Crossref]
  49. J. Mertz, H. Paudel, and T. G. Bifano, “Field of view advantage of conjugate adaptive optics in microscopy applications,” Appl. Opt. 54, 3498–3506 (2015).
    [Crossref] [PubMed]
  50. S. Stallinga, ftp://qiftp.tudelft.nl/stallinga/wavefrontcontrolPSFengineeringSMLM.zip.

2017 (2)

2016 (2)

C. Smith, M. Huisman, M. Siemons, D. Grünwald, and S. Stallinga, “Simultaneous measurement of emission color and 3D position of single molecules,” Opt. Express 24, 4996–5013 (2016).
[Crossref] [PubMed]

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

2015 (8)

C. S. Smith, S. Stallinga, K. A. Lidke, B. Rieger, and D. Grünwald, “Probability-based particle detection that enables threshold-free and robust in vivo single molecule tracking,” Mol. Biol. Cell 26, 4057–4062 (2015).
[Crossref]

M. J. Booth, D. Andrade, D. Burke, B. Patton, and M. Zurauskas, “Aberrations and adaptive optics in super-resolution microscopy,” Microscopy 64, 251–261 (2015).
[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]

S. Stallinga, “Effect of rotational diffusion in an orientational potential well on the point spread function of electric dipole emitters,” J. Opt. Soc. Am. A 32, 213–223 (2015).
[Crossref]

D. Burke, B. Patton, F. Huang, J. Bewersdorf, and M. J. Booth, “Adaptive optics correction of specimen-induced aberrations in single-molecule switching microscopy,” Optica 2, 177–185 (2015).
[Crossref]

A. Tahmasbi, E. S. Ward, and R. J. Ober, “Determination of localization accuracy based on experimentally acquired image sets: applications to single molecule microscopy,” Opt. Express 23, 7630–7652 (2015).
[Crossref] [PubMed]

J. Mertz, H. Paudel, and T. G. Bifano, “Field of view advantage of conjugate adaptive optics in microscopy applications,” Appl. Opt. 54, 3498–3506 (2015).
[Crossref] [PubMed]

A. 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, 985–993 (2015).
[Crossref]

2014 (5)

C. Roider, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “Axial super-localisation using rotating point spread functions shaped by polarisation-dependent phase modulation,” Opt. Express 22, 4029–4037 (2014).
[Crossref] [PubMed]

J. Broeken, B. Rieger, and S. Stallinga, “Simultaneous measurement of position and color of single fluorescent emitters using diffractive optics,” Opt. Lett. 39, 3352–3355 (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, 302–306, (2014).
[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, 133902 (2014).
[Crossref] [PubMed]

M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, and W. E. Moerner, “The role of molecular dipole orientation in single-molecule fluorescence microscopy and implications for super-resolution imaging,” Chem. Phys. Chem. 15, 587–599 (2014).
[Crossref] [PubMed]

2013 (4)

2012 (4)

2011 (2)

D. Baddeley, M. B. Cannell, and C. Soeller, “Three-dimensional sub-100 nm super-resolution imaging of biological samples using a phase ramp in the objective pupil,” Nano Research 4, 589–598 (2011).
[Crossref]

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, 202–204 (2011).
[Crossref] [PubMed]

2010 (3)

2009 (3)

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H.F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. 106, 3125–3130 (2009).
[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. 116, 2995–2999 (2009).
[Crossref]

S. R. P. Pavani and R. Piestun, “High-efficiency rotating point spread functions,” Opt. Express 16, 3484–3489 (2009).
[Crossref]

2008 (3)

S. Ram, P. Prabhat, J. Chao, E. S. Ward, and R. J. Ober, “High accuracy 3D quantum dot tracking with multifocal plane microscopy for the study of fast intracellular dynamics in live cells,” Biophys. J. 95, 6025–6043 (2008).
[Crossref] [PubMed]

M. F. Juette, T. J. D Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, and J. Bewersdorf, “Three-dimensional sub–100 nm resolution fluorescence microscopy of thick samples,” Nat. Methods 5, 527–529 (2008).
[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]

2007 (4)

E. Toprak, H. Balci, B. Blehm, H. Benjamin, and P.R. Selvin, “Three-dimensional particle tracking via bifocal imaging,” Nano Lett. 7, 2043–2045 (2007).
[Crossref] [PubMed]

S. W. Hell, “Far-field optical nanoscopy,” Science 316, 1153–1158 (2007).
[Crossref] [PubMed]

L. Holtzer, T. Meckel, and T. Schmidt, “Nanometric three-dimensional tracking of individual quantum dots in cells,” Appl. Phys. Lett. 90, 053902 (2007).
[Crossref]

D. Débarre, M. J. Booth, and T. Wilson, “Image based adaptive optics through optimisation of low spatial frequencies,” Opt. Express,  15, 8176–8190 (2007).
[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, 1643–1645 (2006).
[Crossref]

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

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

2003 (1)

1994 (1)

H. P. Kao and A. S. Verkman, “Tracking of single fluorescent particles in three dimensions: use of cylindrical optics to encode particle position,” Biophys. J. 67, 1291–1300 (1994).
[Crossref] [PubMed]

1992 (1)

1974 (1)

H. Akaike, “A new look at the statistical model identification,” IEEE Trans. Automatic Control 19, 716–723 (1974).
[Crossref]

Agard, D. A.

Akaike, H.

H. Akaike, “A new look at the statistical model identification,” IEEE Trans. Automatic Control 19, 716–723 (1974).
[Crossref]

Andrade, D.

M. J. Booth, D. Andrade, D. Burke, B. Patton, and M. Zurauskas, “Aberrations and adaptive optics in super-resolution microscopy,” Microscopy 64, 251–261 (2015).
[Crossref] [PubMed]

Babcock, H. P.

H. P. Babcock and X. Zhuang, “Analyzing single molecule localization microscopy data using cubic splines,” Sci. Rep. 7, 552 (2017).
[Crossref] [PubMed]

Backer, A. S.

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

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

M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, and W. E. Moerner, “The role of molecular dipole orientation in single-molecule fluorescence microscopy and implications for super-resolution imaging,” Chem. Phys. Chem. 15, 587–599 (2014).
[Crossref] [PubMed]

Backlund, M. P.

M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, and W. E. Moerner, “The role of molecular dipole orientation in single-molecule fluorescence microscopy and implications for super-resolution imaging,” Chem. Phys. Chem. 15, 587–599 (2014).
[Crossref] [PubMed]

Baddeley, D.

D. Baddeley, M. B. Cannell, and C. Soeller, “Three-dimensional sub-100 nm super-resolution imaging of biological samples using a phase ramp in the objective pupil,” Nano Research 4, 589–598 (2011).
[Crossref]

Badieirostami, M.

Balci, H.

E. Toprak, H. Balci, B. Blehm, H. Benjamin, and P.R. Selvin, “Three-dimensional particle tracking via bifocal imaging,” Nano Lett. 7, 2043–2045 (2007).
[Crossref] [PubMed]

Bates, M.

R. P. J. Nieuwenhuizen, K. A. Lidke, M. Bates, D. Leyton Puig, D. Grünwald, S. Stallinga, and B. Rieger, “Measuring image resolution in optical nanoscopy,” Nat. Methods 10, 557–562 (2013).
[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]

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

Benjamin, H.

E. Toprak, H. Balci, B. Blehm, H. Benjamin, and P.R. Selvin, “Three-dimensional particle tracking via bifocal imaging,” Nano Lett. 7, 2043–2045 (2007).
[Crossref] [PubMed]

Bennett, B. T.

M. F. Juette, T. J. D Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, and J. Bewersdorf, “Three-dimensional sub–100 nm resolution fluorescence microscopy of thick samples,” Nat. Methods 5, 527–529 (2008).
[Crossref] [PubMed]

Bernet, S.

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, 1643–1645 (2006).
[Crossref]

Bewersdorf, J.

Bifano, T. G.

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. 116, 2995–2999 (2009).
[Crossref]

Blehm, B.

E. Toprak, H. Balci, B. Blehm, H. Benjamin, and P.R. Selvin, “Three-dimensional particle tracking via bifocal imaging,” Nano Lett. 7, 2043–2045 (2007).
[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, 1643–1645 (2006).
[Crossref]

Booth, M. J.

Broeken, J.

Burke, D.

D. Burke, B. Patton, F. Huang, J. Bewersdorf, and M. J. Booth, “Adaptive optics correction of specimen-induced aberrations in single-molecule switching microscopy,” Optica 2, 177–185 (2015).
[Crossref]

M. J. Booth, D. Andrade, D. Burke, B. Patton, and M. Zurauskas, “Aberrations and adaptive optics in super-resolution microscopy,” Microscopy 64, 251–261 (2015).
[Crossref] [PubMed]

Cannell, M. B.

D. Baddeley, M. B. Cannell, and C. Soeller, “Three-dimensional sub-100 nm super-resolution imaging of biological samples using a phase ramp in the objective pupil,” Nano Research 4, 589–598 (2011).
[Crossref]

Chao, J.

S. Ram, P. Prabhat, J. Chao, E. S. Ward, and R. J. Ober, “High accuracy 3D quantum dot tracking with multifocal plane microscopy for the study of fast intracellular dynamics in live cells,” Biophys. J. 95, 6025–6043 (2008).
[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, 377–381 (2010).
[Crossref] [PubMed]

Davidson, M. W.

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H.F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. 106, 3125–3130 (2009).
[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, 1643–1645 (2006).
[Crossref]

de Sars, V.

Débarre, D.

Diezmann, A.

Emiliani, V.

Engström, D.

Fetter, R. D.

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H.F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. 106, 3125–3130 (2009).
[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, 377–381 (2010).
[Crossref] [PubMed]

Galbraith, C. G.

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H.F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. 106, 3125–3130 (2009).
[Crossref] [PubMed]

Galbraith, J. A.

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H.F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. 106, 3125–3130 (2009).
[Crossref] [PubMed]

Gibson, S. F.

Gillette, J. M.

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H.F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. 106, 3125–3130 (2009).
[Crossref] [PubMed]

Girirajan, T. P.

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

Goksör, M.

Gould, T. J.

Gould, T. J. D

M. F. Juette, T. J. D Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, and J. Bewersdorf, “Three-dimensional sub–100 nm resolution fluorescence microscopy of thick samples,” Nat. Methods 5, 527–529 (2008).
[Crossref] [PubMed]

Grover, G.

Grünwald, D.

C. Smith, M. Huisman, M. Siemons, D. Grünwald, and S. Stallinga, “Simultaneous measurement of emission color and 3D position of single molecules,” Opt. Express 24, 4996–5013 (2016).
[Crossref] [PubMed]

C. S. Smith, S. Stallinga, K. A. Lidke, B. Rieger, and D. Grünwald, “Probability-based particle detection that enables threshold-free and robust in vivo single molecule tracking,” Mol. Biol. Cell 26, 4057–4062 (2015).
[Crossref]

R. P. J. Nieuwenhuizen, K. A. Lidke, M. Bates, D. Leyton Puig, D. Grünwald, S. Stallinga, and B. Rieger, “Measuring image resolution in optical nanoscopy,” Nat. Methods 10, 557–562 (2013).
[Crossref] [PubMed]

Guillon, M.

Gustafsson, M. G. L.

Haist, T.

Hanser, B. M.

Hell, S. W.

S. W. Hell, “Far-field optical nanoscopy,” Science 316, 1153–1158 (2007).
[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, 1643–1645 (2006).
[Crossref]

Hess, H.F.

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H.F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. 106, 3125–3130 (2009).
[Crossref] [PubMed]

Hess, S. T.

M. F. Juette, T. J. D Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, and J. Bewersdorf, “Three-dimensional sub–100 nm resolution fluorescence microscopy of thick samples,” Nat. Methods 5, 527–529 (2008).
[Crossref] [PubMed]

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

Holtzer, L.

L. Holtzer, T. Meckel, and T. Schmidt, “Nanometric three-dimensional tracking of individual quantum dots in cells,” Appl. Phys. Lett. 90, 053902 (2007).
[Crossref]

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]

Huang, F.

Huisman, M.

Jesacher, A.

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, 302–306, (2014).
[Crossref]

Juette, M. F.

E. B. Kromann, T. J. Gould, M. F. Juette, J. E. Wilhjelm, and J. Bewersdorf, “Quantitative pupil analysis in stimulated emission depletion microscopy using phase retrieval,” Opt. Lett. 37, 1805–1807 (2012).
[Crossref] [PubMed]

M. F. Juette, T. J. D Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, and J. Bewersdorf, “Three-dimensional sub–100 nm resolution fluorescence microscopy of thick samples,” Nat. Methods 5, 527–529 (2008).
[Crossref] [PubMed]

Kanchanawong, P.

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H.F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. 106, 3125–3130 (2009).
[Crossref] [PubMed]

Kao, H. P.

H. P. Kao and A. S. Verkman, “Tracking of single fluorescent particles in three dimensions: use of cylindrical optics to encode particle position,” Biophys. J. 67, 1291–1300 (1994).
[Crossref] [PubMed]

Kirshner, H.

H. Kirshner, C. Vonesch, and M. Unser, “Can localization microscopy benefit from approximation theory?” 10th International Symposium on Biomedical Imaging, 588–591 (2013).

Kromann, E. B.

Krueger, W. D.

Lanni, F.

Lee, M. Y.

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

A. 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, 985–993 (2015).
[Crossref]

Lee, S. F.

Lessard, M. D.

M. F. Juette, T. J. D Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, and J. Bewersdorf, “Three-dimensional sub–100 nm resolution fluorescence microscopy of thick samples,” Nat. Methods 5, 527–529 (2008).
[Crossref] [PubMed]

Lew, M. D.

Leyton Puig, D.

R. P. J. Nieuwenhuizen, K. A. Lidke, M. Bates, D. Leyton Puig, D. Grünwald, S. Stallinga, and B. Rieger, “Measuring image resolution in optical nanoscopy,” Nat. Methods 10, 557–562 (2013).
[Crossref] [PubMed]

Lidke, K. A.

C. S. Smith, S. Stallinga, K. A. Lidke, B. Rieger, and D. Grünwald, “Probability-based particle detection that enables threshold-free and robust in vivo single molecule tracking,” Mol. Biol. Cell 26, 4057–4062 (2015).
[Crossref]

R. P. J. Nieuwenhuizen, K. A. Lidke, M. Bates, D. Leyton Puig, D. Grünwald, S. Stallinga, and B. Rieger, “Measuring image resolution in optical nanoscopy,” Nat. Methods 10, 557–562 (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, 29462–29487 (2013).
[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, 1643–1645 (2006).
[Crossref]

Lingel, C.

Lippincott-Schwartz, J.

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H.F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. 106, 3125–3130 (2009).
[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, 1643–1645 (2006).
[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. 116, 2995–2999 (2009).
[Crossref]

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. 116, 2995–2999 (2009).
[Crossref]

Manley, S.

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H.F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. 106, 3125–3130 (2009).
[Crossref] [PubMed]

Mason, M. D.

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

Meckel, T.

L. Holtzer, T. Meckel, and T. Schmidt, “Nanometric three-dimensional tracking of individual quantum dots in cells,” Appl. Phys. Lett. 90, 053902 (2007).
[Crossref]

Mertz, J.

Mlodzianoski, M. J.

M. F. Juette, T. J. D Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, and J. Bewersdorf, “Three-dimensional sub–100 nm resolution fluorescence microscopy of thick samples,” Nat. Methods 5, 527–529 (2008).
[Crossref] [PubMed]

Moerner, W. E.

P. N. Petrov, Y. Shechtman, and W. E. Moerner, “Measurement-based estimation of global pupil functions in 3D localization microscopy,” Opt. Express 25, 7945–7959 (2017).
[Crossref] [PubMed]

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

A. 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, 985–993 (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, 133902 (2014).
[Crossref] [PubMed]

M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, and W. E. Moerner, “The role of molecular dipole orientation in single-molecule fluorescence microscopy and implications for super-resolution imaging,” Chem. Phys. Chem. 15, 587–599 (2014).
[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, 202–204 (2011).
[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. 116, 2995–2999 (2009).
[Crossref]

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, 377–381 (2010).
[Crossref] [PubMed]

Nagpure, B. S.

M. F. Juette, T. J. D Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, and J. Bewersdorf, “Three-dimensional sub–100 nm resolution fluorescence microscopy of thick samples,” Nat. Methods 5, 527–529 (2008).
[Crossref] [PubMed]

Nieuwenhuizen, R. P. J.

R. P. J. Nieuwenhuizen, K. A. Lidke, M. Bates, D. Leyton Puig, D. Grünwald, S. Stallinga, and B. Rieger, “Measuring image resolution in optical nanoscopy,” Nat. Methods 10, 557–562 (2013).
[Crossref] [PubMed]

Ober, R. J.

A. Tahmasbi, E. S. Ward, and R. J. Ober, “Determination of localization accuracy based on experimentally acquired image sets: applications to single molecule microscopy,” Opt. Express 23, 7630–7652 (2015).
[Crossref] [PubMed]

S. Ram, P. Prabhat, J. Chao, E. S. Ward, and R. J. Ober, “High accuracy 3D quantum dot tracking with multifocal plane microscopy for the study of fast intracellular dynamics in live cells,” Biophys. J. 95, 6025–6043 (2008).
[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, 1643–1645 (2006).
[Crossref]

Osten, W.

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, 1643–1645 (2006).
[Crossref]

Patton, B.

M. J. Booth, D. Andrade, D. Burke, B. Patton, and M. Zurauskas, “Aberrations and adaptive optics in super-resolution microscopy,” Microscopy 64, 251–261 (2015).
[Crossref] [PubMed]

D. Burke, B. Patton, F. Huang, J. Bewersdorf, and M. J. Booth, “Adaptive optics correction of specimen-induced aberrations in single-molecule switching microscopy,” Optica 2, 177–185 (2015).
[Crossref]

Paudel, H.

Pavani, S. R. P.

G. Grover, S. R. P. Pavani, and R. Piestun, “Performance limits on three-dimensional particle localization in photon-limited microscopy,” Opt. Lett. 35, 3306–3308 (2010).
[Crossref] [PubMed]

S. R. P. Pavani and R. Piestun, “High-efficiency rotating point spread functions,” Opt. Express 16, 3484–3489 (2009).
[Crossref]

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. 116, 2995–2999 (2009).
[Crossref]

Persson, M.

Petrov, P. N.

Piestun, R.

G. Grover, S. R. P. Pavani, and R. Piestun, “Performance limits on three-dimensional particle localization in photon-limited microscopy,” Opt. Lett. 35, 3306–3308 (2010).
[Crossref] [PubMed]

S. R. P. Pavani and R. Piestun, “High-efficiency rotating point spread functions,” Opt. Express 16, 3484–3489 (2009).
[Crossref]

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. 116, 2995–2999 (2009).
[Crossref]

Prabhat, P.

S. Ram, P. Prabhat, J. Chao, E. S. Ward, and R. J. Ober, “High accuracy 3D quantum dot tracking with multifocal plane microscopy for the study of fast intracellular dynamics in live cells,” Biophys. J. 95, 6025–6043 (2008).
[Crossref] [PubMed]

Prasad, S.

Ram, S.

S. Ram, P. Prabhat, J. Chao, E. S. Ward, and R. J. Ober, “High accuracy 3D quantum dot tracking with multifocal plane microscopy for the study of fast intracellular dynamics in live cells,” Biophys. J. 95, 6025–6043 (2008).
[Crossref] [PubMed]

Rieger, B.

C. S. Smith, S. Stallinga, K. A. Lidke, B. Rieger, and D. Grünwald, “Probability-based particle detection that enables threshold-free and robust in vivo single molecule tracking,” Mol. Biol. Cell 26, 4057–4062 (2015).
[Crossref]

J. Broeken, B. Rieger, and S. Stallinga, “Simultaneous measurement of position and color of single fluorescent emitters using diffractive optics,” Opt. Lett. 39, 3352–3355 (2014).
[Crossref] [PubMed]

R. P. J. Nieuwenhuizen, K. A. Lidke, M. Bates, D. Leyton Puig, D. Grünwald, S. Stallinga, and B. Rieger, “Measuring image resolution in optical nanoscopy,” Nat. Methods 10, 557–562 (2013).
[Crossref] [PubMed]

S. Stallinga and B. Rieger, “Position and orientation estimation of fixed dipole emitters using an effective Hermite point spread function model,” Opt. Express 20, 5896–5921 (2012).
[Crossref] [PubMed]

S. Stallinga and B. Rieger, “Accuracy of the Gaussian point spread function model in 2D localization microscopy,” Opt. Express 18, 24461–24476 (2010).
[Crossref] [PubMed]

Ritsch-Marte, M.

Roider, C.

Ronzitti, E.

Rust, M. J.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3, 793–795 (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, 133902 (2014).
[Crossref] [PubMed]

M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, and W. E. Moerner, “The role of molecular dipole orientation in single-molecule fluorescence microscopy and implications for super-resolution imaging,” Chem. Phys. Chem. 15, 587–599 (2014).
[Crossref] [PubMed]

Schmidt, T.

L. Holtzer, T. Meckel, and T. Schmidt, “Nanometric three-dimensional tracking of individual quantum dots in cells,” Appl. Phys. Lett. 90, 053902 (2007).
[Crossref]

Sedat, J. W.

Selvin, P.R.

E. Toprak, H. Balci, B. Blehm, H. Benjamin, and P.R. Selvin, “Three-dimensional particle tracking via bifocal imaging,” Nano Lett. 7, 2043–2045 (2007).
[Crossref] [PubMed]

Shechtman, Y.

P. N. Petrov, Y. Shechtman, and W. E. Moerner, “Measurement-based estimation of global pupil functions in 3D localization microscopy,” Opt. Express 25, 7945–7959 (2017).
[Crossref] [PubMed]

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

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

Shtengel, G.

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H.F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. 106, 3125–3130 (2009).
[Crossref] [PubMed]

Siemons, M.

Smith, C.

Smith, C. S.

C. S. Smith, S. Stallinga, K. A. Lidke, B. Rieger, and D. Grünwald, “Probability-based particle detection that enables threshold-free and robust in vivo single molecule tracking,” Mol. Biol. Cell 26, 4057–4062 (2015).
[Crossref]

Soeller, C.

D. Baddeley, M. B. Cannell, and C. Soeller, “Three-dimensional sub-100 nm super-resolution imaging of biological samples using a phase ramp in the objective pupil,” Nano Research 4, 589–598 (2011).
[Crossref]

Sougrat, R.

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H.F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. 106, 3125–3130 (2009).
[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, 1643–1645 (2006).
[Crossref]

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, 377–381 (2010).
[Crossref] [PubMed]

Stallinga, S.

Tahmasbi, A.

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. 116, 2995–2999 (2009).
[Crossref]

Toprak, E.

E. Toprak, H. Balci, B. Blehm, H. Benjamin, and P.R. Selvin, “Three-dimensional particle tracking via bifocal imaging,” Nano Lett. 7, 2043–2045 (2007).
[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. 116, 2995–2999 (2009).
[Crossref]

Unser, M.

H. Kirshner, C. Vonesch, and M. Unser, “Can localization microscopy benefit from approximation theory?” 10th International Symposium on Biomedical Imaging, 588–591 (2013).

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, 302–306, (2014).
[Crossref]

Verkman, A. S.

H. P. Kao and A. S. Verkman, “Tracking of single fluorescent particles in three dimensions: use of cylindrical optics to encode particle position,” Biophys. J. 67, 1291–1300 (1994).
[Crossref] [PubMed]

Vonesch, C.

H. Kirshner, C. Vonesch, and M. Unser, “Can localization microscopy benefit from approximation theory?” 10th International Symposium on Biomedical Imaging, 588–591 (2013).

Wang, W.

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]

Ward, E. S.

A. Tahmasbi, E. S. Ward, and R. J. Ober, “Determination of localization accuracy based on experimentally acquired image sets: applications to single molecule microscopy,” Opt. Express 23, 7630–7652 (2015).
[Crossref] [PubMed]

S. Ram, P. Prabhat, J. Chao, E. S. Ward, and R. J. Ober, “High accuracy 3D quantum dot tracking with multifocal plane microscopy for the study of fast intracellular dynamics in live cells,” Biophys. J. 95, 6025–6043 (2008).
[Crossref] [PubMed]

Waterman, C. M.

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H.F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. 106, 3125–3130 (2009).
[Crossref] [PubMed]

Weiss, L. E.

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

Wilhjelm, J. E.

Wilson, T.

Zhuang, X.

H. P. Babcock and X. Zhuang, “Analyzing single molecule localization microscopy data using cubic splines,” Sci. Rep. 7, 552 (2017).
[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, 302–306, (2014).
[Crossref]

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, 793–795 (2006).
[Crossref] [PubMed]

Zurauskas, M.

M. J. Booth, D. Andrade, D. Burke, B. Patton, and M. Zurauskas, “Aberrations and adaptive optics in super-resolution microscopy,” Microscopy 64, 251–261 (2015).
[Crossref] [PubMed]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

L. Holtzer, T. Meckel, and T. Schmidt, “Nanometric three-dimensional tracking of individual quantum dots in cells,” Appl. Phys. Lett. 90, 053902 (2007).
[Crossref]

Biophys. J. (3)

H. P. Kao and A. S. Verkman, “Tracking of single fluorescent particles in three dimensions: use of cylindrical optics to encode particle position,” Biophys. J. 67, 1291–1300 (1994).
[Crossref] [PubMed]

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

S. Ram, P. Prabhat, J. Chao, E. S. Ward, and R. J. Ober, “High accuracy 3D quantum dot tracking with multifocal plane microscopy for the study of fast intracellular dynamics in live cells,” Biophys. J. 95, 6025–6043 (2008).
[Crossref] [PubMed]

Chem. Phys. Chem. (1)

M. P. Backlund, M. D. Lew, A. S. Backer, S. J. Sahl, and W. E. Moerner, “The role of molecular dipole orientation in single-molecule fluorescence microscopy and implications for super-resolution imaging,” Chem. Phys. Chem. 15, 587–599 (2014).
[Crossref] [PubMed]

IEEE Trans. Automatic Control (1)

H. Akaike, “A new look at the statistical model identification,” IEEE Trans. Automatic Control 19, 716–723 (1974).
[Crossref]

J. Opt. Soc. Am. A (2)

Microscopy (1)

M. J. Booth, D. Andrade, D. Burke, B. Patton, and M. Zurauskas, “Aberrations and adaptive optics in super-resolution microscopy,” Microscopy 64, 251–261 (2015).
[Crossref] [PubMed]

Mol. Biol. Cell (1)

C. S. Smith, S. Stallinga, K. A. Lidke, B. Rieger, and D. Grünwald, “Probability-based particle detection that enables threshold-free and robust in vivo single molecule tracking,” Mol. Biol. Cell 26, 4057–4062 (2015).
[Crossref]

Nano Lett. (2)

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]

E. Toprak, H. Balci, B. Blehm, H. Benjamin, and P.R. Selvin, “Three-dimensional particle tracking via bifocal imaging,” Nano Lett. 7, 2043–2045 (2007).
[Crossref] [PubMed]

Nano Research (1)

D. Baddeley, M. B. Cannell, and C. Soeller, “Three-dimensional sub-100 nm super-resolution imaging of biological samples using a phase ramp in the objective pupil,” Nano Research 4, 589–598 (2011).
[Crossref]

Nat. Methods (4)

M. F. Juette, T. J. D Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, and J. Bewersdorf, “Three-dimensional sub–100 nm resolution fluorescence microscopy of thick samples,” Nat. Methods 5, 527–529 (2008).
[Crossref] [PubMed]

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

R. P. J. Nieuwenhuizen, K. A. Lidke, M. Bates, D. Leyton Puig, D. Grünwald, S. Stallinga, and B. Rieger, “Measuring image resolution in optical nanoscopy,” Nat. Methods 10, 557–562 (2013).
[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, 377–381 (2010).
[Crossref] [PubMed]

Nat. Photonics (2)

Y. Shechtman, L. E. Weiss, A. S. Backer, M. Y. Lee, and W. E. Moerner, “Multicolour localization microscopy by point-spread-function engineering,” Nat. Photonics 10, 590–594 (2016).
[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, 302–306, (2014).
[Crossref]

Opt. Express (11)

D. Débarre, M. J. Booth, and T. Wilson, “Image based adaptive optics through optimisation of low spatial frequencies,” Opt. Express,  15, 8176–8190 (2007).
[Crossref] [PubMed]

S. R. P. Pavani and R. Piestun, “High-efficiency rotating point spread functions,” Opt. Express 16, 3484–3489 (2009).
[Crossref]

S. Stallinga and B. Rieger, “Accuracy of the Gaussian point spread function model in 2D localization microscopy,” Opt. Express 18, 24461–24476 (2010).
[Crossref] [PubMed]

S. Stallinga and B. Rieger, “Position and orientation estimation of fixed dipole emitters using an effective Hermite point spread function model,” Opt. Express 20, 5896–5921 (2012).
[Crossref] [PubMed]

A. Tahmasbi, E. S. Ward, and R. J. Ober, “Determination of localization accuracy based on experimentally acquired image sets: applications to single molecule microscopy,” Opt. Express 23, 7630–7652 (2015).
[Crossref] [PubMed]

C. Smith, M. Huisman, M. Siemons, D. Grünwald, and S. Stallinga, “Simultaneous measurement of emission color and 3D position of single molecules,” Opt. Express 24, 4996–5013 (2016).
[Crossref] [PubMed]

P. N. Petrov, Y. Shechtman, and W. E. Moerner, “Measurement-based estimation of global pupil functions in 3D localization microscopy,” Opt. Express 25, 7945–7959 (2017).
[Crossref] [PubMed]

E. Ronzitti, M. Guillon, V. de Sars, and V. Emiliani, “LCoS nematic SLM characterization and modeling for diffraction efficiency optimization, zero and ghost orders suppression,” Opt. Express 20, 17843–17855 (2012).
[Crossref] [PubMed]

M. Persson, D. Engström, and M. Goksör, “Reducing the effect of pixel crosstalk in phase only spatial light modulators,” Opt. Express 20, 22334–22343 (2012).
[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, 29462–29487 (2013).
[Crossref]

C. Roider, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “Axial super-localisation using rotating point spread functions shaped by polarisation-dependent phase modulation,” Opt. Express 22, 4029–4037 (2014).
[Crossref] [PubMed]

Opt. Lett. (6)

Optica (2)

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, 133902 (2014).
[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. 116, 2995–2999 (2009).
[Crossref]

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H.F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U.S.A. 106, 3125–3130 (2009).
[Crossref] [PubMed]

Sci. Rep. (1)

H. P. Babcock and X. Zhuang, “Analyzing single molecule localization microscopy data using cubic splines,” Sci. Rep. 7, 552 (2017).
[Crossref] [PubMed]

Science (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]

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, 1643–1645 (2006).
[Crossref]

S. W. Hell, “Far-field optical nanoscopy,” Science 316, 1153–1158 (2007).
[Crossref] [PubMed]

Other (3)

Y. Li, M. Mund, P. Hoess, U. Matti, B. Nijmeijer, V. J. Sabinina, J. Ellenberg, I. Schoen, and J. Ries, “Fast, robust and precise 3D localization for arbitrary point spread functions,” bioRxiv 172643; doi: https://doi.org/10.1101/172643 .

H. Kirshner, C. Vonesch, and M. Unser, “Can localization microscopy benefit from approximation theory?” 10th International Symposium on Biomedical Imaging, 588–591 (2013).

S. Stallinga, ftp://qiftp.tudelft.nl/stallinga/wavefrontcontrolPSFengineeringSMLM.zip.

Supplementary Material (2)

NameDescription
» Visualization 1       Measured and fitted through-focus PSF (range: [-1, 1] micron 21 steps) before aberration correction
» Visualization 2       Measured and fitted through-focus PSF (range: [-1, 1] micron) after aberration correction

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 (9)

Fig. 1
Fig. 1 A) Schematic drawing of the SLM calibration branch and the polarization transfer through the light path. Additional linear polarization filters are not drawn as they are aligned with the polarizing beamsplitter. B) The intensity response at the camera as a function of the phase retardation of the SLM for different orientations α of λ/2-plate. C) Schematic overview of the optical setup. A relay system with SLM is added to the emission path of the microscope (red) and a separate SLM calibration path (green) is incorporated into the emission relay system. This allows for SLM calibration between experiments. BE: beam expander, DM: dichroic mirror, L: lens, LPF: linear polarizing filter, M: mirror. OL: objective lens, PBS: polarizing beam splitter, TL: Tube lens.
Fig. 2
Fig. 2 SLM calibration procedure. A) The measured intensity response for a single SLM pixel as a function of applied voltage. Every extremum corresponds to a phase change equal to an integer multiple of π and a second order polynomial is fitted to increase the precision in finding the extrema. The intensity is segmented into four parts which are scaled to [0 1]. This normalized intensity (B) is converted into phase (C) and inverted to create the LUT for that particular voltage segment and pixel (D). E) The normalized intensity response for 20 randomly selected SLM pixels, showing the pixel-to-pixel variations. F) The measured root mean square error of the wavefront as a function of the phase with calibration LUTs immediately after calibration, after 45 minutes, and the LUT provided by the manufacturer. G) The LUTs of the part of the SLM used in the imaging light path for different constant phases. Dark spots indicate pixels without 3 maxima. H) The difference between the measured average phase and the intended phase as a function of the intended phase.
Fig. 3
Fig. 3 SLM alignment principle. A) The beams collimated by the first relay lens originating from beads in the FOV (B, scalebar indicates 10 μm) will be incident on the SLM at different positions if the SLM is not aligned properly with the Fourier plane (which not necessarily coincides with the back focal plane of the relay lens). To illustrate this the SLM is temporarily replaced by a camera prior to further alignment steps. The acquired images of the beams at the correct Fourier plane or at a plane axially misaligned by approximately 5 mm are shown in C and D, respectively. The different visible circles correspond to the emission beams of the beads located at different positions in the FOV. E,F) The beads in the FOV shift laterally when a defocus aberration profile is applied by the SLM. This shift is a measure for the lateral misalignment of the aberration profile on the SLM with respect to the optical axis of the imaging system. After alignment the beads no longer shift laterally when the defocus is applied.
Fig. 4
Fig. 4 A) The emission spectra of the red and green beads are measured by applying a blazed grating to the SLM. The distance between the zeroth and first order on the camera is then a measure for the wavelength, the spread of the first order spot is a measure for the emission spectrum. The spectra for gratings applied in the x and y direction (full and dashed lines) are identical, confirming the oblique angle correction Eq. (14). B) Illustration of the blazed grating and pitch p and path length step pd. C) The phase depth is calibrated by fitting the measured intensity ratio between the zeroth and first order with Eq. (16).
Fig. 5
Fig. 5 A) Fitted Zernike aberrations coefficients (rms values) of the non aberration corrected microscope for different sets of modes taken into account. Fits have been done for modes n + |m| ≤ 2 (j + 1) with j = 1, 2, 3, 4, 5 the fit order. The coefficients found from higher order fits match reasonably well with the values found from the lower order fits. B) The retrieved aberrated wavefronts according to the fitted Zernike coefficients. C) The fit precision found in experiment (full lines) and according to the CRLB (dashed lines). D) Fit precision in simulation (data points) and CRLB of the fit (solid lines) as a function of photon count for different total rms aberration levels. E) The χ2 value of the fit as a function of fit order j, flattening off at a value about 20% higher than the expected value (dashed line). F) The rms level of the fitted Zernike coefficients as a function of fit order j converging to a value just below the diffraction limit (dashed line).
Fig. 6
Fig. 6 A–F) Measured and fitted through-focus PSF of beads emitting in the green (range: [−1, 1] μm, 21 steps) before and after aberration correction, see also Visualization 1 and Visualization 2. The left columns of A and D show measured and fitted focal slices, the right columns of A and D show the same images contrast stretched with the same scale for each exp/fit pair for visibility. Scalebar indicates 1 μm. G) Fitted Zernike coefficients (rms values) before and after aberration correction showing a reduction in the Wrms of the model PSFs that best fit the measurements from 59 ± 1 mλ to 13.4 ± 0.4 mλ.
Fig. 7
Fig. 7 A) Through-focus stacks of green emitting beads deliberately aberrated by single Zernike modes with coefficients A n m = 60 m λ and the corresponding theoretical through-focus stacks using the aberration coefficients found from the aberration fitting routine (through-focus range: [−1, 1] μm, 21 steps, estimated photon count was around 2.2×104 signal and 32 background photons). Scalebar indicates 1 μm and all exp/fit image pairs are contrast stretched with the same scale. B) The aberration retrieval appears to be mode specific, and estimates the Zernike coefficients as 67 ± 4 mλ, averaged over the 15 displayed Zernike modes.
Fig. 8
Fig. 8 PSF comparison between the measured PSF and fit with the vectorial PSF model. The phase mask of the binary astigmatic PSF (A), the blazed astigmatic PSF (B) and the Double Helix (C) alongside example acquisitions and fits for two different photon counts (D–F). G–I) The average measured PSF is compiled from the signal carried by approximately 108 photons by upsampling (3×) and overlaying all acquired spots. The scale bars indicate 1 μm.
Fig. 9
Fig. 9 A–D) Achieved localization precision for the fit parameters x/y/z/λ as a function of photon count estimated from the fit. E–H) Localization precision over the axial range for an estimated photon count around of 5 × 103 (green bead) and 3 × 103 (red bead). I) Average estimated z-position as a function of stage z-position for all acquisitions. J) Average estimated wavelength as a function of stage z-position for all acquisitions, giving values close to the weighted average emission wavelengths λ1 = 536 nm and λ2 = 693 nm. K) Histogram of estimated wavelength values for all acquisitions.

Equations (20)

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

H bead ( r ) = N 3 l = x , y j = x , y , z | w l j ( r ) | 2 ( r ) + b a 2 ,
w l j ( r ) = 1 c n | ρ | 1 d 2 ρ A ( ρ ) exp ( 2 π i W ( ρ ) λ ) q l j ( ρ ) exp ( i k ( ρ ) r ) ,
k ( ρ ) = 2 π λ ( NA ρ x , NA ρ y , n 2 NA 2 ρ 2 ) ,
μ k = D k d x d y H bead ( r r 0 ) ,
μ k θ m = 2 N 3 l = x , y j = x , y , z D k d x d y Re [ w l j ( r r 0 ) * w l j ( r r 0 ) θ m ] ( r r 0 ) .
w l j ( r r 0 ) r 0 = i c n | ρ | 1 d 2 ρ A ( ρ ) exp ( 2 π i W ( ρ ) λ ) q l j k ( ρ ) exp ( i k ( ρ ) ( r r 0 ) ) ,
w l j ( r r 0 ) λ = 2 π i c n λ 2 | ρ | 1 d 2 ρ A ( ρ ) exp ( 2 π i W ( ρ ) λ ) q l j W ( ρ ) exp ( i k ( ρ ) ( r r 0 ) ) + 1 λ ( r r 0 ) w k j ( r r 0 ) r 0 .
w l j ( r ) = 1 c n | ρ | 1 d 2 ρ A ( ρ ) exp ( 2 π i n , m A n m Z ¯ n m ( ρ ) λ ) q l j ( ρ ) exp ( i k ( ρ ) r ) ,
w l j ( r ) A k i = 2 π i c n λ | ρ | 1 d 2 ρ A ( ρ ) exp ( 2 π i λ n , m A n m Z ¯ n m ( ρ ) ) q l j Z ¯ k i ( ρ ) exp ( i k ( ρ ) r ) .
𝒥 = 𝒥 λ / 2 T 𝒥 SLM 𝒥 λ / 2 = [ cos ( 2 α ) sin ( 2 α ) sin ( 2 α ) cos ( 2 α ) ] [ exp ( i ϕ pxl ) 0 0 1 ] [ cos ( 2 α ) sin ( 2 α ) sin ( 2 α ) cos ( 2 α ) ] = [ cos 2 ( 2 α ) exp ( i ϕ pxl ) + sin 2 ( 2 α ) sin ( 2 α ) cos ( 2 α ) ( exp ( i ϕ pxl ) 1 ) sin ( 2 α ) cos ( 2 α ) ( exp ( i ϕ pxl ) 1 ) cos 2 ( 2 α ) + sin 2 ( 2 α ) exp ( i ϕ pxl ) ] ,
I pxl I 0 = | 𝒥 12 | 2 = 4 sin 2 ( ϕ pxl 2 ) cos 2 ( 2 α ) sin 2 ( 2 α ) ,
W = A 2 0 [ 2 ( ( ρ x ρ x OA ) 2 + ( ρ y ρ y OA ) 2 ) 1 ] = A 2 0 [ 2 ( ρ x 2 + ρ y 2 ) 2 1 ] 4 A 2 0 ( ρ x OA ρ x + ρ y OA ρ y ) + A 2 0 ( ρ x OA 2 + ρ y OA 2 ) ,
Δ x = 4 ρ x OA NA A 2 0 ,
W slm ( x , y ) = 1 cos θ W ( x cos θ , y ) ,
C m = 0 1 d t exp ( 2 π i p d t λ ) exp ( 2 π i m t ) = sinc ( p d λ m ) ,
I 0 I 1 = sinc ( p d / λ ) 2 sinc ( p d / λ 1 ) 2 .
W rms err = 1 N cfg N cfg n , m ( A n m true A n m est ) 2 ,
χ 2 = k = 1 K ( n k μ k ) 2 μ k ,
mean ( χ 2 ) = K ,
var ( χ 2 ) = 2 K + k = 1 K 1 μ k ,

Metrics