Abstract

The combination of two opposing objective lenses in 4Pi fluorescence microscopy significantly improves the axial resolution and increases the collection efficiency. Combining 4Pi microscopy with other super-resolution techniques has resulted in the highest three-dimensional (3D) resolution in fluorescence microscopy to date. It has previously been shown that the performance of 4Pi microscopy is significantly affected by aberrations. However, a comprehensive description of 4Pi microscope aberrations has been missing. In this paper, we introduce an approach to describe aberrations in a 4Pi cavity through a new functional representation. We discuss the focusing properties of 4Pi systems affected by aberrations and discuss the implications for adaptive optics schemes for 4Pi microscopes based on this new insight.

© 2017 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Polarization effects in 4Pi confocal microscopy studied with water-immersion lenses

Karsten Bahlmann and Stefan W. Hell
Appl. Opt. 39(10) 1652-1658 (2000)

Adaptive optics enables 3D STED microscopy in aberrating specimens

Travis J. Gould, Daniel Burke, Joerg Bewersdorf, and Martin J. Booth
Opt. Express 20(19) 20998-21009 (2012)

4Pi confocal microscopy with alternate interference

Stefan W. Hell and Matthias Nagorni
Opt. Lett. 23(20) 1567-1569 (1998)

References

  • View by:
  • |
  • |
  • |

  1. S. W. Hell, “Double-confocal scanning microscope,” Euro Patent EP0491289 B1 (1996).
  2. H. Gugel, J. Bewersdorf, S. Jakobs, J. Engelhardt, R. Storz, and S. W. Hell, “Cooperative 4Pi excitation and detection yields sevenfold sharper optical sections in live-cell microscopy,” Biophys. J. 87(6), 4146–4152 (2004).
    [Crossref] [PubMed]
  3. J. Bewersdorf, R. Schmidt, and S. W. Hell, “Comparison of I5M and 4Pi-microscopy,” J. Microsc. 222(2), 105–117 (2006).
    [Crossref] [PubMed]
  4. M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J. 94(12), 4957–4970 (2008).
    [Crossref] [PubMed]
  5. S. W. Hell, S. Lindek, C. Cremer, and E. H. K. Stelzer, “Measurement of the 4Pi‐confocal point spread function proves 75 nm axial resolution,” Appl. Phys. Lett. 64(11), 1335–1337 (1994).
    [Crossref]
  6. R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, “Spherical nanosized focal spot unravels the interior of cells,” Nat. Methods 5(6), 539–544 (2008).
    [Crossref] [PubMed]
  7. M. Dyba and S. W. Hell, “Focal spots of size λ/23 open up far-field fluorescence microscopy at 33 nm axial resolution,” Phys. Rev. Lett. 88(16), 163901 (2002).
    [Crossref] [PubMed]
  8. 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(9), 3125–3130 (2009).
    [Crossref] [PubMed]
  9. D. Aquino, A. Schönle, C. Geisler, C. V. Middendorff, C. A. Wurm, Y. Okamura, T. Lang, S. W. Hell, and A. Egner, “Two-color nanoscopy of three-dimensional volumes by 4Pi detection of stochastically switched fluorophores,” Nat. Methods 8(4), 353–359 (2011).
    [Crossref] [PubMed]
  10. F. Huang, G. Sirinakis, E. S. Allgeyer, L. K. Schroeder, W. C. Duim, E. B. Kromann, T. Phan, F. E. Rivera-Molina, J. R. Myers, I. Irnov, M. Lessard, Y. Zhang, M. A. Handel, C. Jacobs-Wagner, C. P. Lusk, J. E. Rothman, D. Toomre, M. J. Booth, and J. Bewersdorf, “Ultra-high resolution 3D imaging of whole cells,” Cell 166, 1–13 (2016).
    [PubMed]
  11. U. Böhm, S. W. Hell, and R. Schmidt, “4Pi-RESOLFT nanoscopy,” Nat. Commun. 7, 10504 (2016).
    [Crossref] [PubMed]
  12. X. Hao, E. S. Allgeyer, M. J. Booth, and J. Bewersdorf, “Point-spread function optimization in isoSTED nanoscopy,” Opt. Lett. 40(15), 3627–3630 (2015).
    [Crossref] [PubMed]
  13. F. Zernike, “Beugungstheorie des Schneidenverfahrens und seiner verbesserten Form, der Phasenkontrastmethode,” Physica 1(7-12), 689–704 (1934).
    [Crossref]
  14. M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999).
  15. S. W. Hell, R. Schmidt, and A. Egner, “Diffraction-unlimited three-dimensional optical nanoscopy with opposing lenses,” Nat. Photonics 3(7), 381–387 (2009).
    [Crossref]
  16. R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66(3), 207–211 (1976).
    [Crossref]
  17. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” P. Roy. Soc. A-Math. Phys. 253, 358–379 (1959).
  18. X. Hao, C. Kuang, T. Wang, and X. Liu, “Effects of polarization on the de-excitation dark focal spot in STED microscopy,” J. Opt. 12(11), 115707 (2010).
    [Crossref]
  19. K. Bahlmann and S. W. Hell, “Polarization effects in 4Pi confocal microscopy studied with water-immersion lenses,” Appl. Opt. 39(10), 1652–1658 (2000).
    [Crossref] [PubMed]
  20. F. Curdt, S. J. Herr, T. Lutz, R. Schmidt, J. Engelhardt, S. J. Sahl, and S. W. Hell, “isoSTED nanoscopy with intrinsic beam alignment,” Opt. Express 23(24), 30891–30903 (2015).
    [Crossref] [PubMed]
  21. M. J. Booth, “Adaptive optical microscopy: the ongoing quest for a perfect image,” Light Sci. Appl. 3(4), e165 (2014).
    [Crossref]
  22. S. Liu, E. B. Kromann, W. D. Krueger, J. Bewersdorf, and K. A. Lidke, “Three dimensional single molecule localization using a phase retrieved pupil function,” Opt. Express 21(24), 29462–29487 (2013).
    [Crossref] [PubMed]
  23. 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(11), 1805–1807 (2012).
    [Crossref] [PubMed]

2016 (2)

F. Huang, G. Sirinakis, E. S. Allgeyer, L. K. Schroeder, W. C. Duim, E. B. Kromann, T. Phan, F. E. Rivera-Molina, J. R. Myers, I. Irnov, M. Lessard, Y. Zhang, M. A. Handel, C. Jacobs-Wagner, C. P. Lusk, J. E. Rothman, D. Toomre, M. J. Booth, and J. Bewersdorf, “Ultra-high resolution 3D imaging of whole cells,” Cell 166, 1–13 (2016).
[PubMed]

U. Böhm, S. W. Hell, and R. Schmidt, “4Pi-RESOLFT nanoscopy,” Nat. Commun. 7, 10504 (2016).
[Crossref] [PubMed]

2015 (2)

2014 (1)

M. J. Booth, “Adaptive optical microscopy: the ongoing quest for a perfect image,” Light Sci. Appl. 3(4), e165 (2014).
[Crossref]

2013 (1)

2012 (1)

2011 (1)

D. Aquino, A. Schönle, C. Geisler, C. V. Middendorff, C. A. Wurm, Y. Okamura, T. Lang, S. W. Hell, and A. Egner, “Two-color nanoscopy of three-dimensional volumes by 4Pi detection of stochastically switched fluorophores,” Nat. Methods 8(4), 353–359 (2011).
[Crossref] [PubMed]

2010 (1)

X. Hao, C. Kuang, T. Wang, and X. Liu, “Effects of polarization on the de-excitation dark focal spot in STED microscopy,” J. Opt. 12(11), 115707 (2010).
[Crossref]

2009 (2)

S. W. Hell, R. Schmidt, and A. Egner, “Diffraction-unlimited three-dimensional optical nanoscopy with opposing lenses,” Nat. Photonics 3(7), 381–387 (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(9), 3125–3130 (2009).
[Crossref] [PubMed]

2008 (2)

R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, “Spherical nanosized focal spot unravels the interior of cells,” Nat. Methods 5(6), 539–544 (2008).
[Crossref] [PubMed]

M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J. 94(12), 4957–4970 (2008).
[Crossref] [PubMed]

2006 (1)

J. Bewersdorf, R. Schmidt, and S. W. Hell, “Comparison of I5M and 4Pi-microscopy,” J. Microsc. 222(2), 105–117 (2006).
[Crossref] [PubMed]

2004 (1)

H. Gugel, J. Bewersdorf, S. Jakobs, J. Engelhardt, R. Storz, and S. W. Hell, “Cooperative 4Pi excitation and detection yields sevenfold sharper optical sections in live-cell microscopy,” Biophys. J. 87(6), 4146–4152 (2004).
[Crossref] [PubMed]

2002 (1)

M. Dyba and S. W. Hell, “Focal spots of size λ/23 open up far-field fluorescence microscopy at 33 nm axial resolution,” Phys. Rev. Lett. 88(16), 163901 (2002).
[Crossref] [PubMed]

2000 (1)

1994 (1)

S. W. Hell, S. Lindek, C. Cremer, and E. H. K. Stelzer, “Measurement of the 4Pi‐confocal point spread function proves 75 nm axial resolution,” Appl. Phys. Lett. 64(11), 1335–1337 (1994).
[Crossref]

1976 (1)

1959 (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” P. Roy. Soc. A-Math. Phys. 253, 358–379 (1959).

1934 (1)

F. Zernike, “Beugungstheorie des Schneidenverfahrens und seiner verbesserten Form, der Phasenkontrastmethode,” Physica 1(7-12), 689–704 (1934).
[Crossref]

Agard, D. A.

M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J. 94(12), 4957–4970 (2008).
[Crossref] [PubMed]

Allgeyer, E. S.

F. Huang, G. Sirinakis, E. S. Allgeyer, L. K. Schroeder, W. C. Duim, E. B. Kromann, T. Phan, F. E. Rivera-Molina, J. R. Myers, I. Irnov, M. Lessard, Y. Zhang, M. A. Handel, C. Jacobs-Wagner, C. P. Lusk, J. E. Rothman, D. Toomre, M. J. Booth, and J. Bewersdorf, “Ultra-high resolution 3D imaging of whole cells,” Cell 166, 1–13 (2016).
[PubMed]

X. Hao, E. S. Allgeyer, M. J. Booth, and J. Bewersdorf, “Point-spread function optimization in isoSTED nanoscopy,” Opt. Lett. 40(15), 3627–3630 (2015).
[Crossref] [PubMed]

Aquino, D.

D. Aquino, A. Schönle, C. Geisler, C. V. Middendorff, C. A. Wurm, Y. Okamura, T. Lang, S. W. Hell, and A. Egner, “Two-color nanoscopy of three-dimensional volumes by 4Pi detection of stochastically switched fluorophores,” Nat. Methods 8(4), 353–359 (2011).
[Crossref] [PubMed]

Bahlmann, K.

Bewersdorf, J.

F. Huang, G. Sirinakis, E. S. Allgeyer, L. K. Schroeder, W. C. Duim, E. B. Kromann, T. Phan, F. E. Rivera-Molina, J. R. Myers, I. Irnov, M. Lessard, Y. Zhang, M. A. Handel, C. Jacobs-Wagner, C. P. Lusk, J. E. Rothman, D. Toomre, M. J. Booth, and J. Bewersdorf, “Ultra-high resolution 3D imaging of whole cells,” Cell 166, 1–13 (2016).
[PubMed]

X. Hao, E. S. Allgeyer, M. J. Booth, and J. Bewersdorf, “Point-spread function optimization in isoSTED nanoscopy,” Opt. Lett. 40(15), 3627–3630 (2015).
[Crossref] [PubMed]

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

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(11), 1805–1807 (2012).
[Crossref] [PubMed]

J. Bewersdorf, R. Schmidt, and S. W. Hell, “Comparison of I5M and 4Pi-microscopy,” J. Microsc. 222(2), 105–117 (2006).
[Crossref] [PubMed]

H. Gugel, J. Bewersdorf, S. Jakobs, J. Engelhardt, R. Storz, and S. W. Hell, “Cooperative 4Pi excitation and detection yields sevenfold sharper optical sections in live-cell microscopy,” Biophys. J. 87(6), 4146–4152 (2004).
[Crossref] [PubMed]

Böhm, U.

U. Böhm, S. W. Hell, and R. Schmidt, “4Pi-RESOLFT nanoscopy,” Nat. Commun. 7, 10504 (2016).
[Crossref] [PubMed]

Booth, M. J.

F. Huang, G. Sirinakis, E. S. Allgeyer, L. K. Schroeder, W. C. Duim, E. B. Kromann, T. Phan, F. E. Rivera-Molina, J. R. Myers, I. Irnov, M. Lessard, Y. Zhang, M. A. Handel, C. Jacobs-Wagner, C. P. Lusk, J. E. Rothman, D. Toomre, M. J. Booth, and J. Bewersdorf, “Ultra-high resolution 3D imaging of whole cells,” Cell 166, 1–13 (2016).
[PubMed]

X. Hao, E. S. Allgeyer, M. J. Booth, and J. Bewersdorf, “Point-spread function optimization in isoSTED nanoscopy,” Opt. Lett. 40(15), 3627–3630 (2015).
[Crossref] [PubMed]

M. J. Booth, “Adaptive optical microscopy: the ongoing quest for a perfect image,” Light Sci. Appl. 3(4), e165 (2014).
[Crossref]

Cande, W. Z.

M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J. 94(12), 4957–4970 (2008).
[Crossref] [PubMed]

Carlton, P. M.

M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J. 94(12), 4957–4970 (2008).
[Crossref] [PubMed]

Cremer, C.

S. W. Hell, S. Lindek, C. Cremer, and E. H. K. Stelzer, “Measurement of the 4Pi‐confocal point spread function proves 75 nm axial resolution,” Appl. Phys. Lett. 64(11), 1335–1337 (1994).
[Crossref]

Curdt, F.

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(9), 3125–3130 (2009).
[Crossref] [PubMed]

Duim, W. C.

F. Huang, G. Sirinakis, E. S. Allgeyer, L. K. Schroeder, W. C. Duim, E. B. Kromann, T. Phan, F. E. Rivera-Molina, J. R. Myers, I. Irnov, M. Lessard, Y. Zhang, M. A. Handel, C. Jacobs-Wagner, C. P. Lusk, J. E. Rothman, D. Toomre, M. J. Booth, and J. Bewersdorf, “Ultra-high resolution 3D imaging of whole cells,” Cell 166, 1–13 (2016).
[PubMed]

Dyba, M.

M. Dyba and S. W. Hell, “Focal spots of size λ/23 open up far-field fluorescence microscopy at 33 nm axial resolution,” Phys. Rev. Lett. 88(16), 163901 (2002).
[Crossref] [PubMed]

Egner, A.

D. Aquino, A. Schönle, C. Geisler, C. V. Middendorff, C. A. Wurm, Y. Okamura, T. Lang, S. W. Hell, and A. Egner, “Two-color nanoscopy of three-dimensional volumes by 4Pi detection of stochastically switched fluorophores,” Nat. Methods 8(4), 353–359 (2011).
[Crossref] [PubMed]

S. W. Hell, R. Schmidt, and A. Egner, “Diffraction-unlimited three-dimensional optical nanoscopy with opposing lenses,” Nat. Photonics 3(7), 381–387 (2009).
[Crossref]

R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, “Spherical nanosized focal spot unravels the interior of cells,” Nat. Methods 5(6), 539–544 (2008).
[Crossref] [PubMed]

Engelhardt, J.

F. Curdt, S. J. Herr, T. Lutz, R. Schmidt, J. Engelhardt, S. J. Sahl, and S. W. Hell, “isoSTED nanoscopy with intrinsic beam alignment,” Opt. Express 23(24), 30891–30903 (2015).
[Crossref] [PubMed]

R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, “Spherical nanosized focal spot unravels the interior of cells,” Nat. Methods 5(6), 539–544 (2008).
[Crossref] [PubMed]

H. Gugel, J. Bewersdorf, S. Jakobs, J. Engelhardt, R. Storz, and S. W. Hell, “Cooperative 4Pi excitation and detection yields sevenfold sharper optical sections in live-cell microscopy,” Biophys. J. 87(6), 4146–4152 (2004).
[Crossref] [PubMed]

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(9), 3125–3130 (2009).
[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(9), 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(9), 3125–3130 (2009).
[Crossref] [PubMed]

Geisler, C.

D. Aquino, A. Schönle, C. Geisler, C. V. Middendorff, C. A. Wurm, Y. Okamura, T. Lang, S. W. Hell, and A. Egner, “Two-color nanoscopy of three-dimensional volumes by 4Pi detection of stochastically switched fluorophores,” Nat. Methods 8(4), 353–359 (2011).
[Crossref] [PubMed]

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(9), 3125–3130 (2009).
[Crossref] [PubMed]

Golubovskaya, I. N.

M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J. 94(12), 4957–4970 (2008).
[Crossref] [PubMed]

Gould, T. J.

Gugel, H.

H. Gugel, J. Bewersdorf, S. Jakobs, J. Engelhardt, R. Storz, and S. W. Hell, “Cooperative 4Pi excitation and detection yields sevenfold sharper optical sections in live-cell microscopy,” Biophys. J. 87(6), 4146–4152 (2004).
[Crossref] [PubMed]

Gustafsson, M. G. L.

M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J. 94(12), 4957–4970 (2008).
[Crossref] [PubMed]

Handel, M. A.

F. Huang, G. Sirinakis, E. S. Allgeyer, L. K. Schroeder, W. C. Duim, E. B. Kromann, T. Phan, F. E. Rivera-Molina, J. R. Myers, I. Irnov, M. Lessard, Y. Zhang, M. A. Handel, C. Jacobs-Wagner, C. P. Lusk, J. E. Rothman, D. Toomre, M. J. Booth, and J. Bewersdorf, “Ultra-high resolution 3D imaging of whole cells,” Cell 166, 1–13 (2016).
[PubMed]

Hao, X.

X. Hao, E. S. Allgeyer, M. J. Booth, and J. Bewersdorf, “Point-spread function optimization in isoSTED nanoscopy,” Opt. Lett. 40(15), 3627–3630 (2015).
[Crossref] [PubMed]

X. Hao, C. Kuang, T. Wang, and X. Liu, “Effects of polarization on the de-excitation dark focal spot in STED microscopy,” J. Opt. 12(11), 115707 (2010).
[Crossref]

Hell, S. W.

U. Böhm, S. W. Hell, and R. Schmidt, “4Pi-RESOLFT nanoscopy,” Nat. Commun. 7, 10504 (2016).
[Crossref] [PubMed]

F. Curdt, S. J. Herr, T. Lutz, R. Schmidt, J. Engelhardt, S. J. Sahl, and S. W. Hell, “isoSTED nanoscopy with intrinsic beam alignment,” Opt. Express 23(24), 30891–30903 (2015).
[Crossref] [PubMed]

D. Aquino, A. Schönle, C. Geisler, C. V. Middendorff, C. A. Wurm, Y. Okamura, T. Lang, S. W. Hell, and A. Egner, “Two-color nanoscopy of three-dimensional volumes by 4Pi detection of stochastically switched fluorophores,” Nat. Methods 8(4), 353–359 (2011).
[Crossref] [PubMed]

S. W. Hell, R. Schmidt, and A. Egner, “Diffraction-unlimited three-dimensional optical nanoscopy with opposing lenses,” Nat. Photonics 3(7), 381–387 (2009).
[Crossref]

R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, “Spherical nanosized focal spot unravels the interior of cells,” Nat. Methods 5(6), 539–544 (2008).
[Crossref] [PubMed]

J. Bewersdorf, R. Schmidt, and S. W. Hell, “Comparison of I5M and 4Pi-microscopy,” J. Microsc. 222(2), 105–117 (2006).
[Crossref] [PubMed]

H. Gugel, J. Bewersdorf, S. Jakobs, J. Engelhardt, R. Storz, and S. W. Hell, “Cooperative 4Pi excitation and detection yields sevenfold sharper optical sections in live-cell microscopy,” Biophys. J. 87(6), 4146–4152 (2004).
[Crossref] [PubMed]

M. Dyba and S. W. Hell, “Focal spots of size λ/23 open up far-field fluorescence microscopy at 33 nm axial resolution,” Phys. Rev. Lett. 88(16), 163901 (2002).
[Crossref] [PubMed]

K. Bahlmann and S. W. Hell, “Polarization effects in 4Pi confocal microscopy studied with water-immersion lenses,” Appl. Opt. 39(10), 1652–1658 (2000).
[Crossref] [PubMed]

S. W. Hell, S. Lindek, C. Cremer, and E. H. K. Stelzer, “Measurement of the 4Pi‐confocal point spread function proves 75 nm axial resolution,” Appl. Phys. Lett. 64(11), 1335–1337 (1994).
[Crossref]

Herr, S. J.

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(9), 3125–3130 (2009).
[Crossref] [PubMed]

Huang, F.

F. Huang, G. Sirinakis, E. S. Allgeyer, L. K. Schroeder, W. C. Duim, E. B. Kromann, T. Phan, F. E. Rivera-Molina, J. R. Myers, I. Irnov, M. Lessard, Y. Zhang, M. A. Handel, C. Jacobs-Wagner, C. P. Lusk, J. E. Rothman, D. Toomre, M. J. Booth, and J. Bewersdorf, “Ultra-high resolution 3D imaging of whole cells,” Cell 166, 1–13 (2016).
[PubMed]

Irnov, I.

F. Huang, G. Sirinakis, E. S. Allgeyer, L. K. Schroeder, W. C. Duim, E. B. Kromann, T. Phan, F. E. Rivera-Molina, J. R. Myers, I. Irnov, M. Lessard, Y. Zhang, M. A. Handel, C. Jacobs-Wagner, C. P. Lusk, J. E. Rothman, D. Toomre, M. J. Booth, and J. Bewersdorf, “Ultra-high resolution 3D imaging of whole cells,” Cell 166, 1–13 (2016).
[PubMed]

Jacobs-Wagner, C.

F. Huang, G. Sirinakis, E. S. Allgeyer, L. K. Schroeder, W. C. Duim, E. B. Kromann, T. Phan, F. E. Rivera-Molina, J. R. Myers, I. Irnov, M. Lessard, Y. Zhang, M. A. Handel, C. Jacobs-Wagner, C. P. Lusk, J. E. Rothman, D. Toomre, M. J. Booth, and J. Bewersdorf, “Ultra-high resolution 3D imaging of whole cells,” Cell 166, 1–13 (2016).
[PubMed]

Jakobs, S.

R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, “Spherical nanosized focal spot unravels the interior of cells,” Nat. Methods 5(6), 539–544 (2008).
[Crossref] [PubMed]

H. Gugel, J. Bewersdorf, S. Jakobs, J. Engelhardt, R. Storz, and S. W. Hell, “Cooperative 4Pi excitation and detection yields sevenfold sharper optical sections in live-cell microscopy,” Biophys. J. 87(6), 4146–4152 (2004).
[Crossref] [PubMed]

Juette, M. F.

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(9), 3125–3130 (2009).
[Crossref] [PubMed]

Kromann, E. B.

F. Huang, G. Sirinakis, E. S. Allgeyer, L. K. Schroeder, W. C. Duim, E. B. Kromann, T. Phan, F. E. Rivera-Molina, J. R. Myers, I. Irnov, M. Lessard, Y. Zhang, M. A. Handel, C. Jacobs-Wagner, C. P. Lusk, J. E. Rothman, D. Toomre, M. J. Booth, and J. Bewersdorf, “Ultra-high resolution 3D imaging of whole cells,” Cell 166, 1–13 (2016).
[PubMed]

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

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(11), 1805–1807 (2012).
[Crossref] [PubMed]

Krueger, W. D.

Kuang, C.

X. Hao, C. Kuang, T. Wang, and X. Liu, “Effects of polarization on the de-excitation dark focal spot in STED microscopy,” J. Opt. 12(11), 115707 (2010).
[Crossref]

Lang, T.

D. Aquino, A. Schönle, C. Geisler, C. V. Middendorff, C. A. Wurm, Y. Okamura, T. Lang, S. W. Hell, and A. Egner, “Two-color nanoscopy of three-dimensional volumes by 4Pi detection of stochastically switched fluorophores,” Nat. Methods 8(4), 353–359 (2011).
[Crossref] [PubMed]

Lessard, M.

F. Huang, G. Sirinakis, E. S. Allgeyer, L. K. Schroeder, W. C. Duim, E. B. Kromann, T. Phan, F. E. Rivera-Molina, J. R. Myers, I. Irnov, M. Lessard, Y. Zhang, M. A. Handel, C. Jacobs-Wagner, C. P. Lusk, J. E. Rothman, D. Toomre, M. J. Booth, and J. Bewersdorf, “Ultra-high resolution 3D imaging of whole cells,” Cell 166, 1–13 (2016).
[PubMed]

Lidke, K. A.

Lindek, S.

S. W. Hell, S. Lindek, C. Cremer, and E. H. K. Stelzer, “Measurement of the 4Pi‐confocal point spread function proves 75 nm axial resolution,” Appl. Phys. Lett. 64(11), 1335–1337 (1994).
[Crossref]

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(9), 3125–3130 (2009).
[Crossref] [PubMed]

Liu, S.

Liu, X.

X. Hao, C. Kuang, T. Wang, and X. Liu, “Effects of polarization on the de-excitation dark focal spot in STED microscopy,” J. Opt. 12(11), 115707 (2010).
[Crossref]

Lusk, C. P.

F. Huang, G. Sirinakis, E. S. Allgeyer, L. K. Schroeder, W. C. Duim, E. B. Kromann, T. Phan, F. E. Rivera-Molina, J. R. Myers, I. Irnov, M. Lessard, Y. Zhang, M. A. Handel, C. Jacobs-Wagner, C. P. Lusk, J. E. Rothman, D. Toomre, M. J. Booth, and J. Bewersdorf, “Ultra-high resolution 3D imaging of whole cells,” Cell 166, 1–13 (2016).
[PubMed]

Lutz, T.

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(9), 3125–3130 (2009).
[Crossref] [PubMed]

Middendorff, C. V.

D. Aquino, A. Schönle, C. Geisler, C. V. Middendorff, C. A. Wurm, Y. Okamura, T. Lang, S. W. Hell, and A. Egner, “Two-color nanoscopy of three-dimensional volumes by 4Pi detection of stochastically switched fluorophores,” Nat. Methods 8(4), 353–359 (2011).
[Crossref] [PubMed]

Myers, J. R.

F. Huang, G. Sirinakis, E. S. Allgeyer, L. K. Schroeder, W. C. Duim, E. B. Kromann, T. Phan, F. E. Rivera-Molina, J. R. Myers, I. Irnov, M. Lessard, Y. Zhang, M. A. Handel, C. Jacobs-Wagner, C. P. Lusk, J. E. Rothman, D. Toomre, M. J. Booth, and J. Bewersdorf, “Ultra-high resolution 3D imaging of whole cells,” Cell 166, 1–13 (2016).
[PubMed]

Noll, R. J.

Okamura, Y.

D. Aquino, A. Schönle, C. Geisler, C. V. Middendorff, C. A. Wurm, Y. Okamura, T. Lang, S. W. Hell, and A. Egner, “Two-color nanoscopy of three-dimensional volumes by 4Pi detection of stochastically switched fluorophores,” Nat. Methods 8(4), 353–359 (2011).
[Crossref] [PubMed]

Phan, T.

F. Huang, G. Sirinakis, E. S. Allgeyer, L. K. Schroeder, W. C. Duim, E. B. Kromann, T. Phan, F. E. Rivera-Molina, J. R. Myers, I. Irnov, M. Lessard, Y. Zhang, M. A. Handel, C. Jacobs-Wagner, C. P. Lusk, J. E. Rothman, D. Toomre, M. J. Booth, and J. Bewersdorf, “Ultra-high resolution 3D imaging of whole cells,” Cell 166, 1–13 (2016).
[PubMed]

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” P. Roy. Soc. A-Math. Phys. 253, 358–379 (1959).

Rivera-Molina, F. E.

F. Huang, G. Sirinakis, E. S. Allgeyer, L. K. Schroeder, W. C. Duim, E. B. Kromann, T. Phan, F. E. Rivera-Molina, J. R. Myers, I. Irnov, M. Lessard, Y. Zhang, M. A. Handel, C. Jacobs-Wagner, C. P. Lusk, J. E. Rothman, D. Toomre, M. J. Booth, and J. Bewersdorf, “Ultra-high resolution 3D imaging of whole cells,” Cell 166, 1–13 (2016).
[PubMed]

Rothman, J. E.

F. Huang, G. Sirinakis, E. S. Allgeyer, L. K. Schroeder, W. C. Duim, E. B. Kromann, T. Phan, F. E. Rivera-Molina, J. R. Myers, I. Irnov, M. Lessard, Y. Zhang, M. A. Handel, C. Jacobs-Wagner, C. P. Lusk, J. E. Rothman, D. Toomre, M. J. Booth, and J. Bewersdorf, “Ultra-high resolution 3D imaging of whole cells,” Cell 166, 1–13 (2016).
[PubMed]

Sahl, S. J.

Schmidt, R.

U. Böhm, S. W. Hell, and R. Schmidt, “4Pi-RESOLFT nanoscopy,” Nat. Commun. 7, 10504 (2016).
[Crossref] [PubMed]

F. Curdt, S. J. Herr, T. Lutz, R. Schmidt, J. Engelhardt, S. J. Sahl, and S. W. Hell, “isoSTED nanoscopy with intrinsic beam alignment,” Opt. Express 23(24), 30891–30903 (2015).
[Crossref] [PubMed]

S. W. Hell, R. Schmidt, and A. Egner, “Diffraction-unlimited three-dimensional optical nanoscopy with opposing lenses,” Nat. Photonics 3(7), 381–387 (2009).
[Crossref]

R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, “Spherical nanosized focal spot unravels the interior of cells,” Nat. Methods 5(6), 539–544 (2008).
[Crossref] [PubMed]

J. Bewersdorf, R. Schmidt, and S. W. Hell, “Comparison of I5M and 4Pi-microscopy,” J. Microsc. 222(2), 105–117 (2006).
[Crossref] [PubMed]

Schönle, A.

D. Aquino, A. Schönle, C. Geisler, C. V. Middendorff, C. A. Wurm, Y. Okamura, T. Lang, S. W. Hell, and A. Egner, “Two-color nanoscopy of three-dimensional volumes by 4Pi detection of stochastically switched fluorophores,” Nat. Methods 8(4), 353–359 (2011).
[Crossref] [PubMed]

Schroeder, L. K.

F. Huang, G. Sirinakis, E. S. Allgeyer, L. K. Schroeder, W. C. Duim, E. B. Kromann, T. Phan, F. E. Rivera-Molina, J. R. Myers, I. Irnov, M. Lessard, Y. Zhang, M. A. Handel, C. Jacobs-Wagner, C. P. Lusk, J. E. Rothman, D. Toomre, M. J. Booth, and J. Bewersdorf, “Ultra-high resolution 3D imaging of whole cells,” Cell 166, 1–13 (2016).
[PubMed]

Sedat, J. W.

M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J. 94(12), 4957–4970 (2008).
[Crossref] [PubMed]

Shao, L.

M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J. 94(12), 4957–4970 (2008).
[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(9), 3125–3130 (2009).
[Crossref] [PubMed]

Sirinakis, G.

F. Huang, G. Sirinakis, E. S. Allgeyer, L. K. Schroeder, W. C. Duim, E. B. Kromann, T. Phan, F. E. Rivera-Molina, J. R. Myers, I. Irnov, M. Lessard, Y. Zhang, M. A. Handel, C. Jacobs-Wagner, C. P. Lusk, J. E. Rothman, D. Toomre, M. J. Booth, and J. Bewersdorf, “Ultra-high resolution 3D imaging of whole cells,” Cell 166, 1–13 (2016).
[PubMed]

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(9), 3125–3130 (2009).
[Crossref] [PubMed]

Stelzer, E. H. K.

S. W. Hell, S. Lindek, C. Cremer, and E. H. K. Stelzer, “Measurement of the 4Pi‐confocal point spread function proves 75 nm axial resolution,” Appl. Phys. Lett. 64(11), 1335–1337 (1994).
[Crossref]

Storz, R.

H. Gugel, J. Bewersdorf, S. Jakobs, J. Engelhardt, R. Storz, and S. W. Hell, “Cooperative 4Pi excitation and detection yields sevenfold sharper optical sections in live-cell microscopy,” Biophys. J. 87(6), 4146–4152 (2004).
[Crossref] [PubMed]

Toomre, D.

F. Huang, G. Sirinakis, E. S. Allgeyer, L. K. Schroeder, W. C. Duim, E. B. Kromann, T. Phan, F. E. Rivera-Molina, J. R. Myers, I. Irnov, M. Lessard, Y. Zhang, M. A. Handel, C. Jacobs-Wagner, C. P. Lusk, J. E. Rothman, D. Toomre, M. J. Booth, and J. Bewersdorf, “Ultra-high resolution 3D imaging of whole cells,” Cell 166, 1–13 (2016).
[PubMed]

Wang, C. J. R.

M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J. 94(12), 4957–4970 (2008).
[Crossref] [PubMed]

Wang, T.

X. Hao, C. Kuang, T. Wang, and X. Liu, “Effects of polarization on the de-excitation dark focal spot in STED microscopy,” J. Opt. 12(11), 115707 (2010).
[Crossref]

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(9), 3125–3130 (2009).
[Crossref] [PubMed]

Wilhjelm, J. E.

Wolf, E.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” P. Roy. Soc. A-Math. Phys. 253, 358–379 (1959).

Wurm, C. A.

D. Aquino, A. Schönle, C. Geisler, C. V. Middendorff, C. A. Wurm, Y. Okamura, T. Lang, S. W. Hell, and A. Egner, “Two-color nanoscopy of three-dimensional volumes by 4Pi detection of stochastically switched fluorophores,” Nat. Methods 8(4), 353–359 (2011).
[Crossref] [PubMed]

R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, “Spherical nanosized focal spot unravels the interior of cells,” Nat. Methods 5(6), 539–544 (2008).
[Crossref] [PubMed]

Zernike, F.

F. Zernike, “Beugungstheorie des Schneidenverfahrens und seiner verbesserten Form, der Phasenkontrastmethode,” Physica 1(7-12), 689–704 (1934).
[Crossref]

Zhang, Y.

F. Huang, G. Sirinakis, E. S. Allgeyer, L. K. Schroeder, W. C. Duim, E. B. Kromann, T. Phan, F. E. Rivera-Molina, J. R. Myers, I. Irnov, M. Lessard, Y. Zhang, M. A. Handel, C. Jacobs-Wagner, C. P. Lusk, J. E. Rothman, D. Toomre, M. J. Booth, and J. Bewersdorf, “Ultra-high resolution 3D imaging of whole cells,” Cell 166, 1–13 (2016).
[PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

S. W. Hell, S. Lindek, C. Cremer, and E. H. K. Stelzer, “Measurement of the 4Pi‐confocal point spread function proves 75 nm axial resolution,” Appl. Phys. Lett. 64(11), 1335–1337 (1994).
[Crossref]

Biophys. J. (2)

H. Gugel, J. Bewersdorf, S. Jakobs, J. Engelhardt, R. Storz, and S. W. Hell, “Cooperative 4Pi excitation and detection yields sevenfold sharper optical sections in live-cell microscopy,” Biophys. J. 87(6), 4146–4152 (2004).
[Crossref] [PubMed]

M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J. 94(12), 4957–4970 (2008).
[Crossref] [PubMed]

Cell (1)

F. Huang, G. Sirinakis, E. S. Allgeyer, L. K. Schroeder, W. C. Duim, E. B. Kromann, T. Phan, F. E. Rivera-Molina, J. R. Myers, I. Irnov, M. Lessard, Y. Zhang, M. A. Handel, C. Jacobs-Wagner, C. P. Lusk, J. E. Rothman, D. Toomre, M. J. Booth, and J. Bewersdorf, “Ultra-high resolution 3D imaging of whole cells,” Cell 166, 1–13 (2016).
[PubMed]

J. Microsc. (1)

J. Bewersdorf, R. Schmidt, and S. W. Hell, “Comparison of I5M and 4Pi-microscopy,” J. Microsc. 222(2), 105–117 (2006).
[Crossref] [PubMed]

J. Opt. (1)

X. Hao, C. Kuang, T. Wang, and X. Liu, “Effects of polarization on the de-excitation dark focal spot in STED microscopy,” J. Opt. 12(11), 115707 (2010).
[Crossref]

J. Opt. Soc. Am. (1)

Light Sci. Appl. (1)

M. J. Booth, “Adaptive optical microscopy: the ongoing quest for a perfect image,” Light Sci. Appl. 3(4), e165 (2014).
[Crossref]

Nat. Commun. (1)

U. Böhm, S. W. Hell, and R. Schmidt, “4Pi-RESOLFT nanoscopy,” Nat. Commun. 7, 10504 (2016).
[Crossref] [PubMed]

Nat. Methods (2)

R. Schmidt, C. A. Wurm, S. Jakobs, J. Engelhardt, A. Egner, and S. W. Hell, “Spherical nanosized focal spot unravels the interior of cells,” Nat. Methods 5(6), 539–544 (2008).
[Crossref] [PubMed]

D. Aquino, A. Schönle, C. Geisler, C. V. Middendorff, C. A. Wurm, Y. Okamura, T. Lang, S. W. Hell, and A. Egner, “Two-color nanoscopy of three-dimensional volumes by 4Pi detection of stochastically switched fluorophores,” Nat. Methods 8(4), 353–359 (2011).
[Crossref] [PubMed]

Nat. Photonics (1)

S. W. Hell, R. Schmidt, and A. Egner, “Diffraction-unlimited three-dimensional optical nanoscopy with opposing lenses,” Nat. Photonics 3(7), 381–387 (2009).
[Crossref]

Opt. Express (2)

Opt. Lett. (2)

P. Roy. Soc. A-Math. Phys. (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” P. Roy. Soc. A-Math. Phys. 253, 358–379 (1959).

Phys. Rev. Lett. (1)

M. Dyba and S. W. Hell, “Focal spots of size λ/23 open up far-field fluorescence microscopy at 33 nm axial resolution,” Phys. Rev. Lett. 88(16), 163901 (2002).
[Crossref] [PubMed]

Physica (1)

F. Zernike, “Beugungstheorie des Schneidenverfahrens und seiner verbesserten Form, der Phasenkontrastmethode,” Physica 1(7-12), 689–704 (1934).
[Crossref]

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

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(9), 3125–3130 (2009).
[Crossref] [PubMed]

Other (2)

S. W. Hell, “Double-confocal scanning microscope,” Euro Patent EP0491289 B1 (1996).

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

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 (6)

Fig. 1
Fig. 1

Focal intensities with piston modes in (a) a single-objective microscope and (b~c) a 4Pi microscope. For the 4Pi microscope, the interference fringes are shifted along the optical axis when different pistons are applied to the two arms (upper and lower) in the 4Pi-cavity. Results in (b) and (c) are calculated for a mode coefficient value of 1 rad (~0.16 λ) rms.

Fig. 2
Fig. 2

The coordinate system for the 4Pi aberration modes.

Fig. 3
Fig. 3

4Pi aberration modes. For each mode, the two pupil phase functions as well as xy | z=0 (blue dot) and xz | y=0 (green dot) cross-sections through the resulting 4Pi-PSF are shown. All results are calculated for a mode coefficient value of 1 rad (~0.16 λ). All focal intensities are normalized to the maximum of the aberration-free focal intensity (equivalent to that shown for Q 1 1 ).

Fig. 4
Fig. 4

Comparison of covariant (a, c) and contra-variant (b, d) 4Pi aberration modes. (a) shows the upper and lower pupil functions of 4Pi coma mode ( Q 7 +1 ) and its effect on the focal intensity distribution, while (b-d) are for anti-coma ( Q 7 1 ), spherical aberration ( Q 11 +1 ), and anti-spherical aberration modes ( Q 11 1 ), respectively. Underneath each pupil phase function, the xy | z=0 and xz | y=0 cross-sections through the respective single-objective focal intensities are shown. To the right of the pupil phase functions, the respective cross-sections through the 4Pi-PSFs are displayed. Here all results are calculated for mode coefficient values of 1 rad (~0.16 λ) rms. Each shown focal intensity is normalized to its own peak intensity.

Fig. 5
Fig. 5

Influence of polarization on the focal intensity. (a) aberration-free focal intensities. (b) 4Pi coma mode ( Q 7 +1 ). (c) 4Pi anti-coma mode ( Q 7 1 ). (d) 4Pi spherical aberration mode ( Q 11 +1 ). (e) 4Pi anti-spherical aberration mode ( Q 11 1 ). In each figure, the xy | z=0 (the 1st row), xz | y=0 (the 2nd row), and yz | x=0 (the 3rd row) cross-sections through the respective 4Pi focal intensities are shown. For each column in the figures, from left to right, the input beams are unpolarized, x-linearly polarized, y-linearly polarized, clockwise circular polarized, and counter-clockwise circular polarized.

Fig. 6
Fig. 6

Influence of circular polarization on the total focal intensity and the focal intensity of each polarization component ( | E x | 2 , | E y | 2 and | E z | 2 ) for covariant and contra-variant 4Pi modes of odd azimuthal order (at the example of coma and anti-coma modes). In (a) and (c), the incident beam has clockwise circular polarization, while (b) and (d) show counter-clockwise circular polarization. (a) and (b) 4Pi coma mode. (c) and (d) 4Pi anti-coma mode. All figures are calculated for a mode coefficient value of 1 rad (~0.16 λ) rms. Each figure is normalized to its own peak intensity.

Equations (8)

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

x ^ u = x ^ l y ^ u = y ^ l z ^ u = z ^ l
Q i s ( r )={ Z i ( r ) for r P u s Z i ( r ) for r P l
Q i s , Q i' s' = 1 A P u P l Q i s ( r ) Q i' s' ( r ) d 2 r = 1 2π P u Z i ( r ) Z i' ( r ) d 2 r+ 1 2π P l ss' Z i ( r ) Z i' ( r ) d 2 r = ( 1+ss' ) 2π 0 1 0 2π Z i ( φ,l ) Z i' ( φ,l )ldldφ = δ s,s' Z i , Z i' 1
Φ( r )={ Φ u ( r ) for r P u Φ l ( r ) for r P l = { i=1 a i Z i ( r ) for r P u i=1 b i Z i ( r ) for r P l
R i + ( r )= 1 2 [ Q i +1 ( r )+ Q i 1 ( r ) ]={ Z i ( r ) 0 for r P u for r P l
R i ( r )= 1 2 [ Q i +1 ( r ) Q i 1 ( r ) ]={ 0 Z i ( r ) for r P u for r P l
Φ( r )= i=1 a i R i + ( r ) + i=1 b i R i ( r ) = i=1 1 2 a i [ Q i +1 ( r )+ Q i 1 ( r ) ] + i=1 1 2 b i [ Q i +1 ( r ) Q i 1 ( r ) ] = i=1 c i Q i +1 ( r )+ d i Q i 1 ( r )
I un = 1 2 ( I x + I y )

Metrics