Abstract

The resolution of stimulated emission depletion (STED) microscopes is ultimately limited by the quality of the doughnut-shaped illumination profile of the STED erase beam. We show here that in the focal plane this illumination profile is well approximated by an analytical expression - a difference of Gaussian functions, which tends towards a first order Laguerre-Gaussian profile in the case of a well aligned beam with a true zero-intensity central minimum. We further show that along the optical axis the maximum intensity profile is reasonably approximated by a Gaussian decay away from the focal plane. The result is a fully Gaussian analytical approximation of the three-dimensional point-spread function of STED erase beams. This allows the derivation of an analytical form for the autocorrelation function of the fluorescence generated by fluorophore diffusion through the STED depletion volume. We verified this form to be correct by performing fluorescence correlation spectroscopy (FCS) experiments in solutions of the dye Alexa Fluor 532. Since the quality of the illumination profile is reflected in the shape of the autocorrelation function, we propose that fluctuation analysis can be used as a tool to assess the quality of STED erase beams.

© 2014 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  3. A. Rittweger, K. Y. Han, S. E. Irvine, C. Eggeling, and S. W. Hell, “STED microscopy reveals crystal colour centres with nanometric resolution,” Nat. Photonics 3, 144–147 (2009).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  6. D. Wildanger, E. Rittweger, L. Kastrup, and S. W. Hell, “STED microscopy with a supercontinuum laser source,” Opt. Express 16(13), 9614–9621 (2008).
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  7. G. Moneron, R. Medda, B. Hein, A. Giske, V. Westphal, and S. W. Hell, “Fast STED microscopy with continuous wave fiber lasers,” Opt. Express 18(2), 1302–1309 (2010).
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
  25. S. T. Hess and W. W. Webb, “Focal volume optics and experimental artifacts in confocal fluorescence correlation spectroscopy,” Biophys. J. 83(4), 2300–2317 (2002).
    [Crossref] [PubMed]
  26. N. L. Thompson, “Fluorescence correlation spectroscopy,” in Topics in Fluorescence Spectroscopy, (Springer, 1999), 337–378.

2013 (2)

D. McBride, C. Su, J. Kameoka, and S. Vitha, “A low cost and versatile STED superresolution fluorescent microscope,” Mod. Inst. 2, 41–48 (2013).

H. Xie, Y. Liu, D. Jin, P. J. Santangelo, and P. Xi, “Analytical description of high-aperture STED resolution with 0–2π vortex phase modulation,” J. Opt. Soc. Am. A 30(8), 1640–1645 (2013).
[Crossref]

2012 (1)

2011 (1)

R. W. Cole, T. Jinadasa, and C. M. Brown, “Measuring and interpreting point spread functions to determine confocal microscope resolution and ensure quality control,” Nat. Protoc. 6(12), 1929–1941 (2011).
[Crossref] [PubMed]

2010 (3)

2009 (2)

C. Eggeling, C. Ringemann, R. Medda, G. Schwarzmann, K. Sandhoff, S. Polyakova, V. N. Belov, B. Hein, C. von Middendorff, A. Schonle, and S. W. Hell, “Direct observation of the nanoscale dynamics of membrane lipids in a living cell,” Nature 457(7233), 1159–1162 (2009).
[Crossref]

A. Rittweger, K. Y. Han, S. E. Irvine, C. Eggeling, and S. W. Hell, “STED microscopy reveals crystal colour centres with nanometric resolution,” Nat. Photonics 3, 144–147 (2009).
[Crossref]

2008 (3)

2007 (2)

G. Donnert, J. Keller, C. A. Wurm, S. O. Rizzoli, V. Westphal, A. Schonle, R. Jahn, S. Jakobs, C. Eggeling, and S. W. Hell, “Two-color far-field fluorescence nanoscopy,” Biophys. J. 92(8), L67–L69 (2007).
[Crossref] [PubMed]

B. Zhang, J. Zerubia, and J. C. Olivo-Marin, “Gaussian approximations of fluorescence microscope point-spread function models,” Appl. Opt. 46(10), 1819–1829 (2007).
[Crossref] [PubMed]

2005 (3)

N. Bokor, Y. Iketaki, T. Watanabe, and M. Fujii, “Investigation of polarization effects for high-numerical-aperture first-order laguerre-gaussian beams by 2d scanning with a single fluorescent microbead,” Opt. Express 13(26), 10440–10447 (2005).
[Crossref] [PubMed]

L. Kastrup, H. Blom, C. Eggeling, and S. W. Hell, “Fluorescence fluctuation spectroscopy in subdiffraction focal volumes,” Phys. Rev. Lett. 94(17), 178104 (2005).
[Crossref] [PubMed]

V. Westphal and S. W. Hell, “Nanoscale resolution in the focal plane of an optical microscope,” Phys. Rev. Lett. 94(14), 143903 (2005).
[Crossref] [PubMed]

2004 (1)

2003 (1)

2002 (1)

S. T. Hess and W. W. Webb, “Focal volume optics and experimental artifacts in confocal fluorescence correlation spectroscopy,” Biophys. J. 83(4), 2300–2317 (2002).
[Crossref] [PubMed]

1994 (1)

1993 (1)

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

1974 (1)

D. Koppel, “Statistical accuracy in fluorescence correlation spectroscopy,” Phys. Rev. A 10, 1938–1945 (1974).
[Crossref]

1959 (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. Roy. Soc. London. Series A, Mathematical and Physical Sciences 253, 358–379 (1959).
[Crossref]

Belov, V. N.

C. Eggeling, C. Ringemann, R. Medda, G. Schwarzmann, K. Sandhoff, S. Polyakova, V. N. Belov, B. Hein, C. von Middendorff, A. Schonle, and S. W. Hell, “Direct observation of the nanoscale dynamics of membrane lipids in a living cell,” Nature 457(7233), 1159–1162 (2009).
[Crossref]

Bewersdorf, J.

Blom, H.

L. Kastrup, H. Blom, C. Eggeling, and S. W. Hell, “Fluorescence fluctuation spectroscopy in subdiffraction focal volumes,” Phys. Rev. Lett. 94(17), 178104 (2005).
[Crossref] [PubMed]

Bokor, N.

Brown, C. M.

R. W. Cole, T. Jinadasa, and C. M. Brown, “Measuring and interpreting point spread functions to determine confocal microscope resolution and ensure quality control,” Nat. Protoc. 6(12), 1929–1941 (2011).
[Crossref] [PubMed]

Cole, R. W.

R. W. Cole, T. Jinadasa, and C. M. Brown, “Measuring and interpreting point spread functions to determine confocal microscope resolution and ensure quality control,” Nat. Protoc. 6(12), 1929–1941 (2011).
[Crossref] [PubMed]

Cremer, C.

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

Donnert, G.

G. Donnert, J. Keller, C. A. Wurm, S. O. Rizzoli, V. Westphal, A. Schonle, R. Jahn, S. Jakobs, C. Eggeling, and S. W. Hell, “Two-color far-field fluorescence nanoscopy,” Biophys. J. 92(8), L67–L69 (2007).
[Crossref] [PubMed]

Eggeling, C.

A. Rittweger, K. Y. Han, S. E. Irvine, C. Eggeling, and S. W. Hell, “STED microscopy reveals crystal colour centres with nanometric resolution,” Nat. Photonics 3, 144–147 (2009).
[Crossref]

C. Eggeling, C. Ringemann, R. Medda, G. Schwarzmann, K. Sandhoff, S. Polyakova, V. N. Belov, B. Hein, C. von Middendorff, A. Schonle, and S. W. Hell, “Direct observation of the nanoscale dynamics of membrane lipids in a living cell,” Nature 457(7233), 1159–1162 (2009).
[Crossref]

G. Donnert, J. Keller, C. A. Wurm, S. O. Rizzoli, V. Westphal, A. Schonle, R. Jahn, S. Jakobs, C. Eggeling, and S. W. Hell, “Two-color far-field fluorescence nanoscopy,” Biophys. J. 92(8), L67–L69 (2007).
[Crossref] [PubMed]

L. Kastrup, H. Blom, C. Eggeling, and S. W. Hell, “Fluorescence fluctuation spectroscopy in subdiffraction focal volumes,” Phys. Rev. Lett. 94(17), 178104 (2005).
[Crossref] [PubMed]

Fujii, M.

Gan, X.

Ganic, D.

Giske, A.

Gould, T. J.

Gu, M.

Han, K. Y.

A. Rittweger, K. Y. Han, S. E. Irvine, C. Eggeling, and S. W. Hell, “STED microscopy reveals crystal colour centres with nanometric resolution,” Nat. Photonics 3, 144–147 (2009).
[Crossref]

Hao, X. A.

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

Harke, B.

Hein, B.

G. Moneron, R. Medda, B. Hein, A. Giske, V. Westphal, and S. W. Hell, “Fast STED microscopy with continuous wave fiber lasers,” Opt. Express 18(2), 1302–1309 (2010).
[Crossref] [PubMed]

C. Eggeling, C. Ringemann, R. Medda, G. Schwarzmann, K. Sandhoff, S. Polyakova, V. N. Belov, B. Hein, C. von Middendorff, A. Schonle, and S. W. Hell, “Direct observation of the nanoscale dynamics of membrane lipids in a living cell,” Nature 457(7233), 1159–1162 (2009).
[Crossref]

Hell, S. W.

G. Moneron, R. Medda, B. Hein, A. Giske, V. Westphal, and S. W. Hell, “Fast STED microscopy with continuous wave fiber lasers,” Opt. Express 18(2), 1302–1309 (2010).
[Crossref] [PubMed]

A. Rittweger, K. Y. Han, S. E. Irvine, C. Eggeling, and S. W. Hell, “STED microscopy reveals crystal colour centres with nanometric resolution,” Nat. Photonics 3, 144–147 (2009).
[Crossref]

C. Eggeling, C. Ringemann, R. Medda, G. Schwarzmann, K. Sandhoff, S. Polyakova, V. N. Belov, B. Hein, C. von Middendorff, A. Schonle, and S. W. Hell, “Direct observation of the nanoscale dynamics of membrane lipids in a living cell,” Nature 457(7233), 1159–1162 (2009).
[Crossref]

D. Wildanger, E. Rittweger, L. Kastrup, and S. W. Hell, “STED microscopy with a supercontinuum laser source,” Opt. Express 16(13), 9614–9621 (2008).
[Crossref] [PubMed]

B. Harke, J. Keller, C. K. Ullal, V. Westphal, and S. W. Hell, “Resolution scaling in STED microscopy,” Opt. Express 16(6), 4154–4162 (2008).
[Crossref] [PubMed]

G. Donnert, J. Keller, C. A. Wurm, S. O. Rizzoli, V. Westphal, A. Schonle, R. Jahn, S. Jakobs, C. Eggeling, and S. W. Hell, “Two-color far-field fluorescence nanoscopy,” Biophys. J. 92(8), L67–L69 (2007).
[Crossref] [PubMed]

L. Kastrup, H. Blom, C. Eggeling, and S. W. Hell, “Fluorescence fluctuation spectroscopy in subdiffraction focal volumes,” Phys. Rev. Lett. 94(17), 178104 (2005).
[Crossref] [PubMed]

V. Westphal and S. W. Hell, “Nanoscale resolution in the focal plane of an optical microscope,” Phys. Rev. Lett. 94(14), 143903 (2005).
[Crossref] [PubMed]

S. W. Hell and J. Wichmann, “Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy,” Opt. Lett. 19(11), 780–782 (1994).
[Crossref] [PubMed]

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

L. Kastrup, D. Wildanger, B. Rankin, and S. W. Hell, “STED microscopy with compact light sources,” in Nanoscopy and Multidimensional Optical Fluorescence Microscopy, (CRC Press, 2010), 1.1–1.13.

Hess, S. T.

S. T. Hess and W. W. Webb, “Focal volume optics and experimental artifacts in confocal fluorescence correlation spectroscopy,” Biophys. J. 83(4), 2300–2317 (2002).
[Crossref] [PubMed]

Iketaki, Y.

Irvine, S. E.

A. Rittweger, K. Y. Han, S. E. Irvine, C. Eggeling, and S. W. Hell, “STED microscopy reveals crystal colour centres with nanometric resolution,” Nat. Photonics 3, 144–147 (2009).
[Crossref]

Jahn, R.

G. Donnert, J. Keller, C. A. Wurm, S. O. Rizzoli, V. Westphal, A. Schonle, R. Jahn, S. Jakobs, C. Eggeling, and S. W. Hell, “Two-color far-field fluorescence nanoscopy,” Biophys. J. 92(8), L67–L69 (2007).
[Crossref] [PubMed]

Jakobs, S.

G. Donnert, J. Keller, C. A. Wurm, S. O. Rizzoli, V. Westphal, A. Schonle, R. Jahn, S. Jakobs, C. Eggeling, and S. W. Hell, “Two-color far-field fluorescence nanoscopy,” Biophys. J. 92(8), L67–L69 (2007).
[Crossref] [PubMed]

Jin, D.

Jinadasa, T.

R. W. Cole, T. Jinadasa, and C. M. Brown, “Measuring and interpreting point spread functions to determine confocal microscope resolution and ensure quality control,” Nat. Protoc. 6(12), 1929–1941 (2011).
[Crossref] [PubMed]

Juette, M. F.

Kameoka, J.

D. McBride, C. Su, J. Kameoka, and S. Vitha, “A low cost and versatile STED superresolution fluorescent microscope,” Mod. Inst. 2, 41–48 (2013).

Kastrup, L.

D. Wildanger, E. Rittweger, L. Kastrup, and S. W. Hell, “STED microscopy with a supercontinuum laser source,” Opt. Express 16(13), 9614–9621 (2008).
[Crossref] [PubMed]

L. Kastrup, H. Blom, C. Eggeling, and S. W. Hell, “Fluorescence fluctuation spectroscopy in subdiffraction focal volumes,” Phys. Rev. Lett. 94(17), 178104 (2005).
[Crossref] [PubMed]

L. Kastrup, D. Wildanger, B. Rankin, and S. W. Hell, “STED microscopy with compact light sources,” in Nanoscopy and Multidimensional Optical Fluorescence Microscopy, (CRC Press, 2010), 1.1–1.13.

Keller, J.

B. Harke, J. Keller, C. K. Ullal, V. Westphal, and S. W. Hell, “Resolution scaling in STED microscopy,” Opt. Express 16(6), 4154–4162 (2008).
[Crossref] [PubMed]

G. Donnert, J. Keller, C. A. Wurm, S. O. Rizzoli, V. Westphal, A. Schonle, R. Jahn, S. Jakobs, C. Eggeling, and S. W. Hell, “Two-color far-field fluorescence nanoscopy,” Biophys. J. 92(8), L67–L69 (2007).
[Crossref] [PubMed]

Koppel, D.

D. Koppel, “Statistical accuracy in fluorescence correlation spectroscopy,” Phys. Rev. A 10, 1938–1945 (1974).
[Crossref]

Kromann, E. B.

Kuang, C. F.

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

Liu, X.

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

Liu, Y.

McBride, D.

D. McBride, C. Su, J. Kameoka, and S. Vitha, “A low cost and versatile STED superresolution fluorescent microscope,” Mod. Inst. 2, 41–48 (2013).

Medda, R.

G. Moneron, R. Medda, B. Hein, A. Giske, V. Westphal, and S. W. Hell, “Fast STED microscopy with continuous wave fiber lasers,” Opt. Express 18(2), 1302–1309 (2010).
[Crossref] [PubMed]

C. Eggeling, C. Ringemann, R. Medda, G. Schwarzmann, K. Sandhoff, S. Polyakova, V. N. Belov, B. Hein, C. von Middendorff, A. Schonle, and S. W. Hell, “Direct observation of the nanoscale dynamics of membrane lipids in a living cell,” Nature 457(7233), 1159–1162 (2009).
[Crossref]

Moneron, G.

Munro, P

Nasse, M. J.

Olivo-Marin, J. C.

Petrášek, Z.

Z. Petrášek and P. Schwille, “Precise measurement of diffusion coefficients using scanning fluorescence correlation spectroscopy,” Biophys. J. 94(4), 1437–1448 (2008).
[Crossref]

Polyakova, S.

C. Eggeling, C. Ringemann, R. Medda, G. Schwarzmann, K. Sandhoff, S. Polyakova, V. N. Belov, B. Hein, C. von Middendorff, A. Schonle, and S. W. Hell, “Direct observation of the nanoscale dynamics of membrane lipids in a living cell,” Nature 457(7233), 1159–1162 (2009).
[Crossref]

Rankin, B.

L. Kastrup, D. Wildanger, B. Rankin, and S. W. Hell, “STED microscopy with compact light sources,” in Nanoscopy and Multidimensional Optical Fluorescence Microscopy, (CRC Press, 2010), 1.1–1.13.

Reiner, G.

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

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. Roy. Soc. London. Series A, Mathematical and Physical Sciences 253, 358–379 (1959).
[Crossref]

Ringemann, C.

C. Eggeling, C. Ringemann, R. Medda, G. Schwarzmann, K. Sandhoff, S. Polyakova, V. N. Belov, B. Hein, C. von Middendorff, A. Schonle, and S. W. Hell, “Direct observation of the nanoscale dynamics of membrane lipids in a living cell,” Nature 457(7233), 1159–1162 (2009).
[Crossref]

Rittweger, A.

A. Rittweger, K. Y. Han, S. E. Irvine, C. Eggeling, and S. W. Hell, “STED microscopy reveals crystal colour centres with nanometric resolution,” Nat. Photonics 3, 144–147 (2009).
[Crossref]

Rittweger, E.

Rizzoli, S. O.

G. Donnert, J. Keller, C. A. Wurm, S. O. Rizzoli, V. Westphal, A. Schonle, R. Jahn, S. Jakobs, C. Eggeling, and S. W. Hell, “Two-color far-field fluorescence nanoscopy,” Biophys. J. 92(8), L67–L69 (2007).
[Crossref] [PubMed]

Sandhoff, K.

C. Eggeling, C. Ringemann, R. Medda, G. Schwarzmann, K. Sandhoff, S. Polyakova, V. N. Belov, B. Hein, C. von Middendorff, A. Schonle, and S. W. Hell, “Direct observation of the nanoscale dynamics of membrane lipids in a living cell,” Nature 457(7233), 1159–1162 (2009).
[Crossref]

Santangelo, P. J.

Schonle, A.

C. Eggeling, C. Ringemann, R. Medda, G. Schwarzmann, K. Sandhoff, S. Polyakova, V. N. Belov, B. Hein, C. von Middendorff, A. Schonle, and S. W. Hell, “Direct observation of the nanoscale dynamics of membrane lipids in a living cell,” Nature 457(7233), 1159–1162 (2009).
[Crossref]

G. Donnert, J. Keller, C. A. Wurm, S. O. Rizzoli, V. Westphal, A. Schonle, R. Jahn, S. Jakobs, C. Eggeling, and S. W. Hell, “Two-color far-field fluorescence nanoscopy,” Biophys. J. 92(8), L67–L69 (2007).
[Crossref] [PubMed]

Schwarzmann, G.

C. Eggeling, C. Ringemann, R. Medda, G. Schwarzmann, K. Sandhoff, S. Polyakova, V. N. Belov, B. Hein, C. von Middendorff, A. Schonle, and S. W. Hell, “Direct observation of the nanoscale dynamics of membrane lipids in a living cell,” Nature 457(7233), 1159–1162 (2009).
[Crossref]

Schwille, P.

Z. Petrášek and P. Schwille, “Precise measurement of diffusion coefficients using scanning fluorescence correlation spectroscopy,” Biophys. J. 94(4), 1437–1448 (2008).
[Crossref]

Stelzer, E. H. K.

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

Su, C.

D. McBride, C. Su, J. Kameoka, and S. Vitha, “A low cost and versatile STED superresolution fluorescent microscope,” Mod. Inst. 2, 41–48 (2013).

Thompson, N. L.

N. L. Thompson, “Fluorescence correlation spectroscopy,” in Topics in Fluorescence Spectroscopy, (Springer, 1999), 337–378.

Török, P

Ullal, C. K.

Vitha, S.

D. McBride, C. Su, J. Kameoka, and S. Vitha, “A low cost and versatile STED superresolution fluorescent microscope,” Mod. Inst. 2, 41–48 (2013).

von Middendorff, C.

C. Eggeling, C. Ringemann, R. Medda, G. Schwarzmann, K. Sandhoff, S. Polyakova, V. N. Belov, B. Hein, C. von Middendorff, A. Schonle, and S. W. Hell, “Direct observation of the nanoscale dynamics of membrane lipids in a living cell,” Nature 457(7233), 1159–1162 (2009).
[Crossref]

Wang, T. T.

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

Watanabe, T.

Webb, W. W.

S. T. Hess and W. W. Webb, “Focal volume optics and experimental artifacts in confocal fluorescence correlation spectroscopy,” Biophys. J. 83(4), 2300–2317 (2002).
[Crossref] [PubMed]

Westphal, V.

G. Moneron, R. Medda, B. Hein, A. Giske, V. Westphal, and S. W. Hell, “Fast STED microscopy with continuous wave fiber lasers,” Opt. Express 18(2), 1302–1309 (2010).
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B. Harke, J. Keller, C. K. Ullal, V. Westphal, and S. W. Hell, “Resolution scaling in STED microscopy,” Opt. Express 16(6), 4154–4162 (2008).
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G. Donnert, J. Keller, C. A. Wurm, S. O. Rizzoli, V. Westphal, A. Schonle, R. Jahn, S. Jakobs, C. Eggeling, and S. W. Hell, “Two-color far-field fluorescence nanoscopy,” Biophys. J. 92(8), L67–L69 (2007).
[Crossref] [PubMed]

V. Westphal and S. W. Hell, “Nanoscale resolution in the focal plane of an optical microscope,” Phys. Rev. Lett. 94(14), 143903 (2005).
[Crossref] [PubMed]

Wichmann, J.

Wildanger, D.

D. Wildanger, E. Rittweger, L. Kastrup, and S. W. Hell, “STED microscopy with a supercontinuum laser source,” Opt. Express 16(13), 9614–9621 (2008).
[Crossref] [PubMed]

L. Kastrup, D. Wildanger, B. Rankin, and S. W. Hell, “STED microscopy with compact light sources,” in Nanoscopy and Multidimensional Optical Fluorescence Microscopy, (CRC Press, 2010), 1.1–1.13.

Wilhjelm, J. E.

Woehl, J. C.

Wolf, E.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. Roy. Soc. London. Series A, Mathematical and Physical Sciences 253, 358–379 (1959).
[Crossref]

Wurm, C. A.

G. Donnert, J. Keller, C. A. Wurm, S. O. Rizzoli, V. Westphal, A. Schonle, R. Jahn, S. Jakobs, C. Eggeling, and S. W. Hell, “Two-color far-field fluorescence nanoscopy,” Biophys. J. 92(8), L67–L69 (2007).
[Crossref] [PubMed]

Xi, P.

Xie, H.

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Zhang, B.

Appl. Opt. (1)

Biophys. J. (3)

S. T. Hess and W. W. Webb, “Focal volume optics and experimental artifacts in confocal fluorescence correlation spectroscopy,” Biophys. J. 83(4), 2300–2317 (2002).
[Crossref] [PubMed]

G. Donnert, J. Keller, C. A. Wurm, S. O. Rizzoli, V. Westphal, A. Schonle, R. Jahn, S. Jakobs, C. Eggeling, and S. W. Hell, “Two-color far-field fluorescence nanoscopy,” Biophys. J. 92(8), L67–L69 (2007).
[Crossref] [PubMed]

Z. Petrášek and P. Schwille, “Precise measurement of diffusion coefficients using scanning fluorescence correlation spectroscopy,” Biophys. J. 94(4), 1437–1448 (2008).
[Crossref]

J. Microsc.-Oxford (1)

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

J. Opt. (1)

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

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

Mod. Inst. (1)

D. McBride, C. Su, J. Kameoka, and S. Vitha, “A low cost and versatile STED superresolution fluorescent microscope,” Mod. Inst. 2, 41–48 (2013).

Nat. Photonics (1)

A. Rittweger, K. Y. Han, S. E. Irvine, C. Eggeling, and S. W. Hell, “STED microscopy reveals crystal colour centres with nanometric resolution,” Nat. Photonics 3, 144–147 (2009).
[Crossref]

Nat. Protoc. (1)

R. W. Cole, T. Jinadasa, and C. M. Brown, “Measuring and interpreting point spread functions to determine confocal microscope resolution and ensure quality control,” Nat. Protoc. 6(12), 1929–1941 (2011).
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Nature (1)

C. Eggeling, C. Ringemann, R. Medda, G. Schwarzmann, K. Sandhoff, S. Polyakova, V. N. Belov, B. Hein, C. von Middendorff, A. Schonle, and S. W. Hell, “Direct observation of the nanoscale dynamics of membrane lipids in a living cell,” Nature 457(7233), 1159–1162 (2009).
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Opt. Express (6)

Opt. Lett. (2)

Phys. Rev. A (1)

D. Koppel, “Statistical accuracy in fluorescence correlation spectroscopy,” Phys. Rev. A 10, 1938–1945 (1974).
[Crossref]

Phys. Rev. Lett. (2)

V. Westphal and S. W. Hell, “Nanoscale resolution in the focal plane of an optical microscope,” Phys. Rev. Lett. 94(14), 143903 (2005).
[Crossref] [PubMed]

L. Kastrup, H. Blom, C. Eggeling, and S. W. Hell, “Fluorescence fluctuation spectroscopy in subdiffraction focal volumes,” Phys. Rev. Lett. 94(17), 178104 (2005).
[Crossref] [PubMed]

Proc. Roy. Soc. London. Series A, Mathematical and Physical Sciences (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. Roy. Soc. London. Series A, Mathematical and Physical Sciences 253, 358–379 (1959).
[Crossref]

Other (2)

L. Kastrup, D. Wildanger, B. Rankin, and S. W. Hell, “STED microscopy with compact light sources,” in Nanoscopy and Multidimensional Optical Fluorescence Microscopy, (CRC Press, 2010), 1.1–1.13.

N. L. Thompson, “Fluorescence correlation spectroscopy,” in Topics in Fluorescence Spectroscopy, (Springer, 1999), 337–378.

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Figures (5)

Fig. 1
Fig. 1

Calculated illumination profiles in the focal plane, in the absence (a) or in the presence (b) of 2π phase modulation. All profiles were obtained for λ = 532 nm, n = 1.3, NA = 1.27, θmax = 78° and w/ρmax = 1. The 2D illumination profiles are shown above the radial profiles (scale bar: 0.5λ). Ideal profiles (expected when imaging infinitely small objects with R = 0 nm) calculated directly according to Eq. (1) (dark symbols) are compared to profiles convoluted with the shape of a ball with radius R = 50 nm (light symbols). Note that the radial profiles have all been normalized to the height of the ideal profile in the absence of phase modulation, and that the vertical scale is different in (a) and (b). The 2D illumination profiles, on the other hand, have all been normalized by the highest intensity point in the image. Solid lines are Gaussian fits, using Eq. (2) in (a) and either Eq. (4) (for R = 0 nm) or Eq. (3) with σ = 0.99 (for R = 50 nm) in (b). Residuals are shown in the lower panels. (c) Height of the central minimum relative to maximum height as a function of bead size, for profiles obtained in the presence of phase modulation. (d) Characteristic profile size (obtained from the Gaussian fits) as a function of bead size.

Fig. 2
Fig. 2

Representative PSFs measured by imaging single fluorescent beads in the focal plane, without (a) or with (b) phase modulation. The left panels show images obtained with a 50 μm-diameter pinhole (scale bars: 400 nm). The right panels show the normalized average radial intensity computed from images acquired with or without a confocal pinhole. Solid lines are fits of the profiles with simple Gaussian approximations (Eq. (2) in (a) and Eq. (3) with the value of σ fixed to 0.99 in (b) - in both cases a constant background term was added).

Fig. 3
Fig. 3

Representative three-dimensional PSFs obtained (a–c) in the absence and (d–f) in the presence of phase modulation. (a,d) Image stack showing the enlarging and dimming of the PSF away from the focal plane (at z ≈ 0nm). (b,e) Examples of radial intensity profiles at different distances from he focal plane (solid circles). Solid lines are fits of the data with Eq. (2) (b) or Eq. (4) (e). In (a,d) and (b,e), the confocal pinhole diameter was 50μm. (c,f) Maximum intensity profile (left panel) and characteristic size of the PSF (right panel) as a function of distance from the focal plane. Data is shown for three different pinhole sizes. The continuous lines are fits of the data with the expected dependence for a propagating Gaussian beam (Eq. (5) in the left panel and Eq. (6) in the right panel). The dashed lines in the left panel show an alternate fit with a Gaussian function.

Fig. 4
Fig. 4

(a) Normalized illumination profiles generated using the difference of Gaussian model (Eq. (3)) with σ = 0.99 and f varying from 0 (ring-shaped profile) to 1 (Gaussian profile). (b) Depth of the central minimum as a function of f. The transition between ring-shaped and peak-shaped PSFs occurs at f = 1 − σ2 = 0.02. (c) ACFs calculated for the profiles shown in a). (d) Amplitude and (e) half-time of the ACFs as a function of f. (f) ACFs (same as in c)), normalized with respect to both G(0) and τ1/2. (f) Shape factor of the ACFs as a function of f. Inset shows the shape factor as a function of the depth of the central minimum.

Fig. 5
Fig. 5

Experimentally determined ACFs without (orange symbols) and with (blue symbols) phase modulation. The measurement time in this case was 5 min. The ACFs half-times, τ1/2 = 42μs and τ1/2 = 82μs, are indicated by arrows. Fits with Eq. (7) (orange line) and Eq. (9) (blue line), respectively, are shown. The inset shows the same ACFs after normalization by τ1/2. The two arrows in the inset highlight the sameness of the curves at τ1/2, and their dissimilarity around τ1/2/5.

Tables (1)

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Table 1 Characteristic dimensions of the PSFs

Equations (10)

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I ( r ) = I 0 | 0 θ max d θ cos θ sin θ 0 2 π d ϕ P ( ρ , θ ) , ϕ ) e i k r sin θ cos ϕ | 2 .
I G ( r , z ) = 2 P π ω G 2 e 2 r 2 ω G 2 e 2 z 2 S G 2 ω G 2 ,
I D σ , f ( r , z ) = 2 P / ( π ω D 2 ) ( 1 / σ 2 1 + f ) [ e 2 r 2 ω D 2 ( 1 f ) e 2 r 2 σ 2 ω D 2 ] e 2 z 2 S D 2 ω D 2 .
I D ( r , z ) = 2 P π ω D 2 2 r 2 ω D 2 e 2 r 2 ω D 2 e 2 z 2 S D 2 ω D 2 ,
I max , G / D ( z ) = 2 P π ω G / D 2 ( 1 + ( z / z G / D ) 2 ) ,
ω G / D ( z ) = ω G / D 1 + ( z / z G / D ) 2 .
G G ( τ ) = γ G N G 1 ( 1 + τ / τ G ) 1 + τ / ( S G 2 τ G ) .
G D σ , f = γ D σ , f N D σ , f 1 + ( A σ , f / D σ , f ) τ τ D + ( B σ , f / D σ , f ) ( τ τ D ) 2 [ 1 + τ τ D ] [ 1 + σ 2 τ τ D ] [ 1 + 2 τ ( 1 + 1 / σ 2 ) τ D ] 1 + τ S 2 τ D ,
A σ , f = σ 2 ( 1 1 σ 2 f ) [ 1 1 σ 4 f ( 1 + 3 σ 2 ) ] , B σ , f = 2 σ 2 ( 1 1 σ 2 f ) 2 , D σ , f = 1 σ 2 + 1 σ 4 + ( 1 f ) [ 1 3 σ 2 f ( 1 + 1 σ 2 ) ] .
G D ( τ ) = γ D N D 1 + 2 τ τ D + 2 ( τ τ D ) 2 [ 1 + τ τ D ] 3 1 + τ S 2 τ D .

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