Abstract

Nonlinear structured illumination microscopy (SIM) in theory has unlimited resolution over a full field of view. However under a realistic signal-to-noise ratio and a limited photon budget, the performance of nonlinear SIM strongly depends on the behavior of the nonlinear effect. Saturated SIM (SSIM) is not ideal in biological applications due to its strong photobleaching. Stimulated emission depletion (STED) SIM will have high sensitivity, higher resolution and less photo toxicity than SSIM. However, the laser power necessary to support a strong full-field STED effect is not attainable with current laser technology. We experimentally proved that surface plasmon resonance enhances (SPR) near surface STED effect by a factor of 8, and therefore STED-SIM is feasible in the total internal reflection microscopy mode with SPR enhancement. Simulation analysis predicts that SPR enhanced 2D STED is strong enough for nonlinear SIM to achieve high-speed imaging at 30-nm resolution and single molecule sensitivity. The STED-SIM superresolution microscopy method would provide a solution for observing single molecule processes in vitro or on the basal membrane of live cells.

© 2011 OSA

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2010 (4)

B. Huang, H. Babcock, and X. Zhuang, “Breaking the diffraction barrier: super-resolution imaging of cells,” Cell 143(7), 1047–1058 (2010).
[CrossRef] [PubMed]

M. Wagner, P. Weber, T. Bruns, W. S. Strauss, R. Wittig, and H. Schneckenburger, “Light dose is a limiting factor to maintain cell viability in fluorescence microscopy and single molecule detection,” Int. J. Mol. Sci. 11(3), 956–966 (2010).
[CrossRef] [PubMed]

R. Kasper, B. Harke, C. Forthmann, P. Tinnefeld, S. W. Hell, and M. Sauer, “Single-molecule STED microscopy with photostable organic fluorophores,” Small 6(13), 1379–1384 (2010).
[CrossRef] [PubMed]

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photon. Rev. 4(6), 795–808 (2010).
[CrossRef]

2009 (7)

R.-Y. He, Y.-D. Su, K.-C. Cho, C.-Y. Lin, N.-S. Chang, C.-H. Chang, and S. J. Chen, “Surface plasmon-enhanced two-photon fluorescence microscopy for live cell membrane imaging,” Opt. Express 17(8), 5987–5997 (2009).
[CrossRef] [PubMed]

E. Chung, Y.-H. Kim, W. T. Tang, C. J. R. Sheppard, and P. T. C. So, “Wide-field extended-resolution fluorescence microscopy with standing surface-plasmon-resonance waves,” Opt. Lett. 34(15), 2366–2368 (2009).
[CrossRef] [PubMed]

P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. L. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nat. Methods 6(5), 339–342 (2009).
[CrossRef] [PubMed]

E. 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(3), 144–147 (2009).
[CrossRef]

B. Huang, M. Bates, and X. Zhuang, “Super-resolution fluorescence microscopy,” Annu. Rev. Biochem. 78(1), 993–1016 (2009).
[CrossRef] [PubMed]

R. Heintzmann and M. G. L. Gustafsson, “Subdiffraction resolution in continuous samples,” Nat. Photonics 3(7), 362–364 (2009).
[CrossRef]

S. W. Hell, “Microscopy and its focal switch,” Nat. Methods 6(1), 24–32 (2009).
[PubMed]

2008 (6)

B. Hein, K. I. Willig, and S. W. Hell, “Stimulated emission depletion (STED) nanoscopy of a fluorescent protein-labeled organelle inside a living cell,” Proc. Natl. Acad. Sci. U.S.A. 105(38), 14271–14276 (2008).
[CrossRef] [PubMed]

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

U. V. Naegerl, K. I. Willig, B. Hein, S. W. Hell, and T. Bonhoeffer, “Live-cell imaging of dendritic spines by STED microscopy,” Proc. Natl. Acad. Sci. U.S.A. 105(48), 18982–18987 (2008).
[CrossRef] [PubMed]

V. Westphal, S. O. Rizzoli, M. A. Lauterbach, D. Kamin, R. Jahn, and S. W. Hell, “Video-rate far-field optical nanoscopy dissects synaptic vesicle movement,” Science 320(5873), 246–249 (2008).
[CrossRef] [PubMed]

J. Fölling, M. Bossi, H. Bock, R. Medda, C. A. Wurm, B. Hein, S. Jakobs, C. Eggeling, and S. W. Hell, “Fluorescence nanoscopy by ground-state depletion and single-molecule return,” Nat. Methods 5(11), 943–945 (2008).
[CrossRef] [PubMed]

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

2007 (2)

K. I. Willig, B. Harke, R. Medda, and S. W. Hell, “STED microscopy with continuous wave beams,” Nat. Methods 4(11), 915–918 (2007).
[CrossRef] [PubMed]

S. W. Hell, “Far-field optical nanoscopy,” Science 316(5828), 1153–1158 (2007).
[CrossRef] [PubMed]

2006 (5)

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91(11), 4258–4272 (2006).
[CrossRef] [PubMed]

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006).
[CrossRef] [PubMed]

R.-Y. He, G.-L. Chang, H.-L. Wu, C.-H. Lin, K.-C. Chiu, Y.-D. Su, and S. J. Chen, “Enhanced live cell membrane imaging using surface plasmon-enhanced total internal reflection fluorescence microscopy,” Opt. Express 14(20), 9307–9316 (2006).
[CrossRef] [PubMed]

J. Homola, “Electromagnetic Theory of Surface Plasmons,” Springer Ser Chem Sens Biosens 4, 3–44 (2006).
[CrossRef]

K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, “STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis,” Nature 440(7086), 935–939 (2006).
[CrossRef] [PubMed]

2005 (3)

S. Ekgasit, F. Yu, and W. Knoll, “Fluorescence intensity in surface-plasmon field-enhanced fluorescence spectroscopy,” Sens. Actuators B Chem. 104(2), 294–301 (2005).
[CrossRef]

M. Hofmann, C. Eggeling, S. Jakobs, and S. W. Hell, “Breaking the diffraction barrier in fluorescence microscopy at low light intensities by using reversibly photoswitchable proteins,” Proc. Natl. Acad. Sci. U.S.A. 102(49), 17565–17569 (2005).
[CrossRef] [PubMed]

M. G. Gustafsson, “Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution,” Proc. Natl. Acad. Sci. U.S.A. 102(37), 13081–13086 (2005).
[CrossRef] [PubMed]

2003 (1)

R. Heintzmann, “Saturated patterned excitation microscopy with two-dimensional excitation patterns,” Micron 34(6-7), 283–291 (2003).
[CrossRef] [PubMed]

2002 (1)

2001 (1)

2000 (2)

T. Liebermann and W. Knoll, “Surface-plasmon field-enhanced fluorescence spectroscopy,” Colloids Surf., A 171(1-3), 115–130 (2000).
[CrossRef]

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198(2), 82–87 (2000).
[CrossRef] [PubMed]

1997 (1)

K. Kneipp, Y. Wang, H. Kneipp, L. Perelman, I. Itzkan, R. Dasari, and M. Feld, “Single Molecule Detection Using Surface-Enhanced Raman Scattering (SERS),” Phys. Rev. Lett. 78(9), 1667–1670 (1997).
[CrossRef]

1994 (1)

Babcock, H.

B. Huang, H. Babcock, and X. Zhuang, “Breaking the diffraction barrier: super-resolution imaging of cells,” Cell 143(7), 1047–1058 (2010).
[CrossRef] [PubMed]

Bates, M.

B. Huang, M. Bates, and X. Zhuang, “Super-resolution fluorescence microscopy,” Annu. Rev. Biochem. 78(1), 993–1016 (2009).
[CrossRef] [PubMed]

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

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006).
[CrossRef] [PubMed]

Bock, H.

J. Fölling, M. Bossi, H. Bock, R. Medda, C. A. Wurm, B. Hein, S. Jakobs, C. Eggeling, and S. W. Hell, “Fluorescence nanoscopy by ground-state depletion and single-molecule return,” Nat. Methods 5(11), 943–945 (2008).
[CrossRef] [PubMed]

Boltasseva, A.

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photon. Rev. 4(6), 795–808 (2010).
[CrossRef]

Bonhoeffer, T.

U. V. Naegerl, K. I. Willig, B. Hein, S. W. Hell, and T. Bonhoeffer, “Live-cell imaging of dendritic spines by STED microscopy,” Proc. Natl. Acad. Sci. U.S.A. 105(48), 18982–18987 (2008).
[CrossRef] [PubMed]

Bossi, M.

J. Fölling, M. Bossi, H. Bock, R. Medda, C. A. Wurm, B. Hein, S. Jakobs, C. Eggeling, and S. W. Hell, “Fluorescence nanoscopy by ground-state depletion and single-molecule return,” Nat. Methods 5(11), 943–945 (2008).
[CrossRef] [PubMed]

Bruns, T.

M. Wagner, P. Weber, T. Bruns, W. S. Strauss, R. Wittig, and H. Schneckenburger, “Light dose is a limiting factor to maintain cell viability in fluorescence microscopy and single molecule detection,” Int. J. Mol. Sci. 11(3), 956–966 (2010).
[CrossRef] [PubMed]

Chang, C.-H.

Chang, G.-L.

Chang, N.-S.

Chen, S. J.

Chhun, B. B.

P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. L. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nat. Methods 6(5), 339–342 (2009).
[CrossRef] [PubMed]

Chiu, K.-C.

Cho, K.-C.

Chung, E.

Cremer, C.

Dasari, R.

K. Kneipp, Y. Wang, H. Kneipp, L. Perelman, I. Itzkan, R. Dasari, and M. Feld, “Single Molecule Detection Using Surface-Enhanced Raman Scattering (SERS),” Phys. Rev. Lett. 78(9), 1667–1670 (1997).
[CrossRef]

Dong, C. Y.

Eggeling, C.

E. 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(3), 144–147 (2009).
[CrossRef]

J. Fölling, M. Bossi, H. Bock, R. Medda, C. A. Wurm, B. Hein, S. Jakobs, C. Eggeling, and S. W. Hell, “Fluorescence nanoscopy by ground-state depletion and single-molecule return,” Nat. Methods 5(11), 943–945 (2008).
[CrossRef] [PubMed]

M. Hofmann, C. Eggeling, S. Jakobs, and S. W. Hell, “Breaking the diffraction barrier in fluorescence microscopy at low light intensities by using reversibly photoswitchable proteins,” Proc. Natl. Acad. Sci. U.S.A. 102(49), 17565–17569 (2005).
[CrossRef] [PubMed]

Ekgasit, S.

S. Ekgasit, F. Yu, and W. Knoll, “Fluorescence intensity in surface-plasmon field-enhanced fluorescence spectroscopy,” Sens. Actuators B Chem. 104(2), 294–301 (2005).
[CrossRef]

Emani, N. K.

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photon. Rev. 4(6), 795–808 (2010).
[CrossRef]

Feld, M.

K. Kneipp, Y. Wang, H. Kneipp, L. Perelman, I. Itzkan, R. Dasari, and M. Feld, “Single Molecule Detection Using Surface-Enhanced Raman Scattering (SERS),” Phys. Rev. Lett. 78(9), 1667–1670 (1997).
[CrossRef]

Fölling, J.

J. Fölling, M. Bossi, H. Bock, R. Medda, C. A. Wurm, B. Hein, S. Jakobs, C. Eggeling, and S. W. Hell, “Fluorescence nanoscopy by ground-state depletion and single-molecule return,” Nat. Methods 5(11), 943–945 (2008).
[CrossRef] [PubMed]

Forthmann, C.

R. Kasper, B. Harke, C. Forthmann, P. Tinnefeld, S. W. Hell, and M. Sauer, “Single-molecule STED microscopy with photostable organic fluorophores,” Small 6(13), 1379–1384 (2010).
[CrossRef] [PubMed]

Girirajan, T. P. K.

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91(11), 4258–4272 (2006).
[CrossRef] [PubMed]

Griffis, E. R.

P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. L. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nat. Methods 6(5), 339–342 (2009).
[CrossRef] [PubMed]

Gustafsson, M. G.

M. G. Gustafsson, “Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution,” Proc. Natl. Acad. Sci. U.S.A. 102(37), 13081–13086 (2005).
[CrossRef] [PubMed]

Gustafsson, M. G. L.

P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. L. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nat. Methods 6(5), 339–342 (2009).
[CrossRef] [PubMed]

R. Heintzmann and M. G. L. Gustafsson, “Subdiffraction resolution in continuous samples,” Nat. Photonics 3(7), 362–364 (2009).
[CrossRef]

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198(2), 82–87 (2000).
[CrossRef] [PubMed]

Han, K. Y.

E. 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(3), 144–147 (2009).
[CrossRef]

Harke, B.

R. Kasper, B. Harke, C. Forthmann, P. Tinnefeld, S. W. Hell, and M. Sauer, “Single-molecule STED microscopy with photostable organic fluorophores,” Small 6(13), 1379–1384 (2010).
[CrossRef] [PubMed]

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

K. I. Willig, B. Harke, R. Medda, and S. W. Hell, “STED microscopy with continuous wave beams,” Nat. Methods 4(11), 915–918 (2007).
[CrossRef] [PubMed]

He, R.-Y.

Hein, B.

U. V. Naegerl, K. I. Willig, B. Hein, S. W. Hell, and T. Bonhoeffer, “Live-cell imaging of dendritic spines by STED microscopy,” Proc. Natl. Acad. Sci. U.S.A. 105(48), 18982–18987 (2008).
[CrossRef] [PubMed]

B. Hein, K. I. Willig, and S. W. Hell, “Stimulated emission depletion (STED) nanoscopy of a fluorescent protein-labeled organelle inside a living cell,” Proc. Natl. Acad. Sci. U.S.A. 105(38), 14271–14276 (2008).
[CrossRef] [PubMed]

J. Fölling, M. Bossi, H. Bock, R. Medda, C. A. Wurm, B. Hein, S. Jakobs, C. Eggeling, and S. W. Hell, “Fluorescence nanoscopy by ground-state depletion and single-molecule return,” Nat. Methods 5(11), 943–945 (2008).
[CrossRef] [PubMed]

Heintzmann, R.

R. Heintzmann and M. G. L. Gustafsson, “Subdiffraction resolution in continuous samples,” Nat. Photonics 3(7), 362–364 (2009).
[CrossRef]

R. Heintzmann, “Saturated patterned excitation microscopy with two-dimensional excitation patterns,” Micron 34(6-7), 283–291 (2003).
[CrossRef] [PubMed]

R. Heintzmann, T. M. Jovin, and C. Cremer, “Saturated patterned excitation microscopy--a concept for optical resolution improvement,” J. Opt. Soc. Am. A 19(8), 1599–1609 (2002).
[CrossRef] [PubMed]

Hell, S. W.

R. Kasper, B. Harke, C. Forthmann, P. Tinnefeld, S. W. Hell, and M. Sauer, “Single-molecule STED microscopy with photostable organic fluorophores,” Small 6(13), 1379–1384 (2010).
[CrossRef] [PubMed]

S. W. Hell, “Microscopy and its focal switch,” Nat. Methods 6(1), 24–32 (2009).
[PubMed]

E. 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(3), 144–147 (2009).
[CrossRef]

U. V. Naegerl, K. I. Willig, B. Hein, S. W. Hell, and T. Bonhoeffer, “Live-cell imaging of dendritic spines by STED microscopy,” Proc. Natl. Acad. Sci. U.S.A. 105(48), 18982–18987 (2008).
[CrossRef] [PubMed]

V. Westphal, S. O. Rizzoli, M. A. Lauterbach, D. Kamin, R. Jahn, and S. W. Hell, “Video-rate far-field optical nanoscopy dissects synaptic vesicle movement,” Science 320(5873), 246–249 (2008).
[CrossRef] [PubMed]

J. Fölling, M. Bossi, H. Bock, R. Medda, C. A. Wurm, B. Hein, S. Jakobs, C. Eggeling, and S. W. Hell, “Fluorescence nanoscopy by ground-state depletion and single-molecule return,” Nat. Methods 5(11), 943–945 (2008).
[CrossRef] [PubMed]

B. Hein, K. I. Willig, and S. W. Hell, “Stimulated emission depletion (STED) nanoscopy of a fluorescent protein-labeled organelle inside a living cell,” Proc. Natl. Acad. Sci. U.S.A. 105(38), 14271–14276 (2008).
[CrossRef] [PubMed]

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

K. I. Willig, B. Harke, R. Medda, and S. W. Hell, “STED microscopy with continuous wave beams,” Nat. Methods 4(11), 915–918 (2007).
[CrossRef] [PubMed]

S. W. Hell, “Far-field optical nanoscopy,” Science 316(5828), 1153–1158 (2007).
[CrossRef] [PubMed]

K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, “STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis,” Nature 440(7086), 935–939 (2006).
[CrossRef] [PubMed]

M. Hofmann, C. Eggeling, S. Jakobs, and S. W. Hell, “Breaking the diffraction barrier in fluorescence microscopy at low light intensities by using reversibly photoswitchable proteins,” Proc. Natl. Acad. Sci. U.S.A. 102(49), 17565–17569 (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]

Hess, S. T.

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91(11), 4258–4272 (2006).
[CrossRef] [PubMed]

Hofmann, M.

M. Hofmann, C. Eggeling, S. Jakobs, and S. W. Hell, “Breaking the diffraction barrier in fluorescence microscopy at low light intensities by using reversibly photoswitchable proteins,” Proc. Natl. Acad. Sci. U.S.A. 102(49), 17565–17569 (2005).
[CrossRef] [PubMed]

Homola, J.

J. Homola, “Electromagnetic Theory of Surface Plasmons,” Springer Ser Chem Sens Biosens 4, 3–44 (2006).
[CrossRef]

Huang, B.

B. Huang, H. Babcock, and X. Zhuang, “Breaking the diffraction barrier: super-resolution imaging of cells,” Cell 143(7), 1047–1058 (2010).
[CrossRef] [PubMed]

B. Huang, M. Bates, and X. Zhuang, “Super-resolution fluorescence microscopy,” Annu. Rev. Biochem. 78(1), 993–1016 (2009).
[CrossRef] [PubMed]

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

Irvine, S. E.

E. 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(3), 144–147 (2009).
[CrossRef]

Ishii, S.

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photon. Rev. 4(6), 795–808 (2010).
[CrossRef]

Itzkan, I.

K. Kneipp, Y. Wang, H. Kneipp, L. Perelman, I. Itzkan, R. Dasari, and M. Feld, “Single Molecule Detection Using Surface-Enhanced Raman Scattering (SERS),” Phys. Rev. Lett. 78(9), 1667–1670 (1997).
[CrossRef]

Jahn, R.

V. Westphal, S. O. Rizzoli, M. A. Lauterbach, D. Kamin, R. Jahn, and S. W. Hell, “Video-rate far-field optical nanoscopy dissects synaptic vesicle movement,” Science 320(5873), 246–249 (2008).
[CrossRef] [PubMed]

K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, “STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis,” Nature 440(7086), 935–939 (2006).
[CrossRef] [PubMed]

Jakobs, S.

J. Fölling, M. Bossi, H. Bock, R. Medda, C. A. Wurm, B. Hein, S. Jakobs, C. Eggeling, and S. W. Hell, “Fluorescence nanoscopy by ground-state depletion and single-molecule return,” Nat. Methods 5(11), 943–945 (2008).
[CrossRef] [PubMed]

M. Hofmann, C. Eggeling, S. Jakobs, and S. W. Hell, “Breaking the diffraction barrier in fluorescence microscopy at low light intensities by using reversibly photoswitchable proteins,” Proc. Natl. Acad. Sci. U.S.A. 102(49), 17565–17569 (2005).
[CrossRef] [PubMed]

Jovin, T. M.

Kamin, D.

V. Westphal, S. O. Rizzoli, M. A. Lauterbach, D. Kamin, R. Jahn, and S. W. Hell, “Video-rate far-field optical nanoscopy dissects synaptic vesicle movement,” Science 320(5873), 246–249 (2008).
[CrossRef] [PubMed]

Kasper, R.

R. Kasper, B. Harke, C. Forthmann, P. Tinnefeld, S. W. Hell, and M. Sauer, “Single-molecule STED microscopy with photostable organic fluorophores,” Small 6(13), 1379–1384 (2010).
[CrossRef] [PubMed]

Keller, J.

Kim, Y.-H.

Kneipp, H.

K. Kneipp, Y. Wang, H. Kneipp, L. Perelman, I. Itzkan, R. Dasari, and M. Feld, “Single Molecule Detection Using Surface-Enhanced Raman Scattering (SERS),” Phys. Rev. Lett. 78(9), 1667–1670 (1997).
[CrossRef]

Kneipp, K.

K. Kneipp, Y. Wang, H. Kneipp, L. Perelman, I. Itzkan, R. Dasari, and M. Feld, “Single Molecule Detection Using Surface-Enhanced Raman Scattering (SERS),” Phys. Rev. Lett. 78(9), 1667–1670 (1997).
[CrossRef]

Kner, P.

P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. L. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nat. Methods 6(5), 339–342 (2009).
[CrossRef] [PubMed]

Knoll, W.

S. Ekgasit, F. Yu, and W. Knoll, “Fluorescence intensity in surface-plasmon field-enhanced fluorescence spectroscopy,” Sens. Actuators B Chem. 104(2), 294–301 (2005).
[CrossRef]

T. Liebermann and W. Knoll, “Surface-plasmon field-enhanced fluorescence spectroscopy,” Colloids Surf., A 171(1-3), 115–130 (2000).
[CrossRef]

Kwon, H.-S.

Lauterbach, M. A.

V. Westphal, S. O. Rizzoli, M. A. Lauterbach, D. Kamin, R. Jahn, and S. W. Hell, “Video-rate far-field optical nanoscopy dissects synaptic vesicle movement,” Science 320(5873), 246–249 (2008).
[CrossRef] [PubMed]

Liebermann, T.

T. Liebermann and W. Knoll, “Surface-plasmon field-enhanced fluorescence spectroscopy,” Colloids Surf., A 171(1-3), 115–130 (2000).
[CrossRef]

Lin, C.-H.

Lin, C.-Y.

Mason, M. D.

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91(11), 4258–4272 (2006).
[CrossRef] [PubMed]

Medda, R.

J. Fölling, M. Bossi, H. Bock, R. Medda, C. A. Wurm, B. Hein, S. Jakobs, C. Eggeling, and S. W. Hell, “Fluorescence nanoscopy by ground-state depletion and single-molecule return,” Nat. Methods 5(11), 943–945 (2008).
[CrossRef] [PubMed]

K. I. Willig, B. Harke, R. Medda, and S. W. Hell, “STED microscopy with continuous wave beams,” Nat. Methods 4(11), 915–918 (2007).
[CrossRef] [PubMed]

Naegerl, U. V.

U. V. Naegerl, K. I. Willig, B. Hein, S. W. Hell, and T. Bonhoeffer, “Live-cell imaging of dendritic spines by STED microscopy,” Proc. Natl. Acad. Sci. U.S.A. 105(48), 18982–18987 (2008).
[CrossRef] [PubMed]

Naik, G. V.

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photon. Rev. 4(6), 795–808 (2010).
[CrossRef]

Perelman, L.

K. Kneipp, Y. Wang, H. Kneipp, L. Perelman, I. Itzkan, R. Dasari, and M. Feld, “Single Molecule Detection Using Surface-Enhanced Raman Scattering (SERS),” Phys. Rev. Lett. 78(9), 1667–1670 (1997).
[CrossRef]

Rittweger, E.

E. 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(3), 144–147 (2009).
[CrossRef]

Rizzoli, S. O.

V. Westphal, S. O. Rizzoli, M. A. Lauterbach, D. Kamin, R. Jahn, and S. W. Hell, “Video-rate far-field optical nanoscopy dissects synaptic vesicle movement,” Science 320(5873), 246–249 (2008).
[CrossRef] [PubMed]

K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, “STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis,” Nature 440(7086), 935–939 (2006).
[CrossRef] [PubMed]

Rust, M. J.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006).
[CrossRef] [PubMed]

Sauer, M.

R. Kasper, B. Harke, C. Forthmann, P. Tinnefeld, S. W. Hell, and M. Sauer, “Single-molecule STED microscopy with photostable organic fluorophores,” Small 6(13), 1379–1384 (2010).
[CrossRef] [PubMed]

Schneckenburger, H.

M. Wagner, P. Weber, T. Bruns, W. S. Strauss, R. Wittig, and H. Schneckenburger, “Light dose is a limiting factor to maintain cell viability in fluorescence microscopy and single molecule detection,” Int. J. Mol. Sci. 11(3), 956–966 (2010).
[CrossRef] [PubMed]

Schönle, A.

Shalaev, V. M.

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photon. Rev. 4(6), 795–808 (2010).
[CrossRef]

Sheppard, C. J. R.

So, P. T. C.

Strauss, W. S.

M. Wagner, P. Weber, T. Bruns, W. S. Strauss, R. Wittig, and H. Schneckenburger, “Light dose is a limiting factor to maintain cell viability in fluorescence microscopy and single molecule detection,” Int. J. Mol. Sci. 11(3), 956–966 (2010).
[CrossRef] [PubMed]

Su, Y.-D.

Tang, W. T.

Tinnefeld, P.

R. Kasper, B. Harke, C. Forthmann, P. Tinnefeld, S. W. Hell, and M. Sauer, “Single-molecule STED microscopy with photostable organic fluorophores,” Small 6(13), 1379–1384 (2010).
[CrossRef] [PubMed]

Ullal, C. K.

Wagner, M.

M. Wagner, P. Weber, T. Bruns, W. S. Strauss, R. Wittig, and H. Schneckenburger, “Light dose is a limiting factor to maintain cell viability in fluorescence microscopy and single molecule detection,” Int. J. Mol. Sci. 11(3), 956–966 (2010).
[CrossRef] [PubMed]

Wang, W.

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

Wang, Y.

K. Kneipp, Y. Wang, H. Kneipp, L. Perelman, I. Itzkan, R. Dasari, and M. Feld, “Single Molecule Detection Using Surface-Enhanced Raman Scattering (SERS),” Phys. Rev. Lett. 78(9), 1667–1670 (1997).
[CrossRef]

Weber, P.

M. Wagner, P. Weber, T. Bruns, W. S. Strauss, R. Wittig, and H. Schneckenburger, “Light dose is a limiting factor to maintain cell viability in fluorescence microscopy and single molecule detection,” Int. J. Mol. Sci. 11(3), 956–966 (2010).
[CrossRef] [PubMed]

West, P. R.

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photon. Rev. 4(6), 795–808 (2010).
[CrossRef]

Westphal, V.

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

V. Westphal, S. O. Rizzoli, M. A. Lauterbach, D. Kamin, R. Jahn, and S. W. Hell, “Video-rate far-field optical nanoscopy dissects synaptic vesicle movement,” Science 320(5873), 246–249 (2008).
[CrossRef] [PubMed]

K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, “STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis,” Nature 440(7086), 935–939 (2006).
[CrossRef] [PubMed]

Wichmann, J.

Willig, K. I.

B. Hein, K. I. Willig, and S. W. Hell, “Stimulated emission depletion (STED) nanoscopy of a fluorescent protein-labeled organelle inside a living cell,” Proc. Natl. Acad. Sci. U.S.A. 105(38), 14271–14276 (2008).
[CrossRef] [PubMed]

U. V. Naegerl, K. I. Willig, B. Hein, S. W. Hell, and T. Bonhoeffer, “Live-cell imaging of dendritic spines by STED microscopy,” Proc. Natl. Acad. Sci. U.S.A. 105(48), 18982–18987 (2008).
[CrossRef] [PubMed]

K. I. Willig, B. Harke, R. Medda, and S. W. Hell, “STED microscopy with continuous wave beams,” Nat. Methods 4(11), 915–918 (2007).
[CrossRef] [PubMed]

K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, “STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis,” Nature 440(7086), 935–939 (2006).
[CrossRef] [PubMed]

Winoto, L.

P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. L. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nat. Methods 6(5), 339–342 (2009).
[CrossRef] [PubMed]

Wittig, R.

M. Wagner, P. Weber, T. Bruns, W. S. Strauss, R. Wittig, and H. Schneckenburger, “Light dose is a limiting factor to maintain cell viability in fluorescence microscopy and single molecule detection,” Int. J. Mol. Sci. 11(3), 956–966 (2010).
[CrossRef] [PubMed]

Wu, H.-L.

Wurm, C. A.

J. Fölling, M. Bossi, H. Bock, R. Medda, C. A. Wurm, B. Hein, S. Jakobs, C. Eggeling, and S. W. Hell, “Fluorescence nanoscopy by ground-state depletion and single-molecule return,” Nat. Methods 5(11), 943–945 (2008).
[CrossRef] [PubMed]

Yu, F.

S. Ekgasit, F. Yu, and W. Knoll, “Fluorescence intensity in surface-plasmon field-enhanced fluorescence spectroscopy,” Sens. Actuators B Chem. 104(2), 294–301 (2005).
[CrossRef]

Zhuang, X.

B. Huang, H. Babcock, and X. Zhuang, “Breaking the diffraction barrier: super-resolution imaging of cells,” Cell 143(7), 1047–1058 (2010).
[CrossRef] [PubMed]

B. Huang, M. Bates, and X. Zhuang, “Super-resolution fluorescence microscopy,” Annu. Rev. Biochem. 78(1), 993–1016 (2009).
[CrossRef] [PubMed]

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

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006).
[CrossRef] [PubMed]

Annu. Rev. Biochem. (1)

B. Huang, M. Bates, and X. Zhuang, “Super-resolution fluorescence microscopy,” Annu. Rev. Biochem. 78(1), 993–1016 (2009).
[CrossRef] [PubMed]

Biophys. J. (1)

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91(11), 4258–4272 (2006).
[CrossRef] [PubMed]

Cell (1)

B. Huang, H. Babcock, and X. Zhuang, “Breaking the diffraction barrier: super-resolution imaging of cells,” Cell 143(7), 1047–1058 (2010).
[CrossRef] [PubMed]

Colloids Surf., A (1)

T. Liebermann and W. Knoll, “Surface-plasmon field-enhanced fluorescence spectroscopy,” Colloids Surf., A 171(1-3), 115–130 (2000).
[CrossRef]

Int. J. Mol. Sci. (1)

M. Wagner, P. Weber, T. Bruns, W. S. Strauss, R. Wittig, and H. Schneckenburger, “Light dose is a limiting factor to maintain cell viability in fluorescence microscopy and single molecule detection,” Int. J. Mol. Sci. 11(3), 956–966 (2010).
[CrossRef] [PubMed]

J. Microsc. (1)

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198(2), 82–87 (2000).
[CrossRef] [PubMed]

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

Laser Photon. Rev. (1)

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photon. Rev. 4(6), 795–808 (2010).
[CrossRef]

Micron (1)

R. Heintzmann, “Saturated patterned excitation microscopy with two-dimensional excitation patterns,” Micron 34(6-7), 283–291 (2003).
[CrossRef] [PubMed]

Nat. Methods (5)

P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. L. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nat. Methods 6(5), 339–342 (2009).
[CrossRef] [PubMed]

K. I. Willig, B. Harke, R. Medda, and S. W. Hell, “STED microscopy with continuous wave beams,” Nat. Methods 4(11), 915–918 (2007).
[CrossRef] [PubMed]

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006).
[CrossRef] [PubMed]

J. Fölling, M. Bossi, H. Bock, R. Medda, C. A. Wurm, B. Hein, S. Jakobs, C. Eggeling, and S. W. Hell, “Fluorescence nanoscopy by ground-state depletion and single-molecule return,” Nat. Methods 5(11), 943–945 (2008).
[CrossRef] [PubMed]

S. W. Hell, “Microscopy and its focal switch,” Nat. Methods 6(1), 24–32 (2009).
[PubMed]

Nat. Photonics (2)

R. Heintzmann and M. G. L. Gustafsson, “Subdiffraction resolution in continuous samples,” Nat. Photonics 3(7), 362–364 (2009).
[CrossRef]

E. 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(3), 144–147 (2009).
[CrossRef]

Nature (1)

K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, “STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis,” Nature 440(7086), 935–939 (2006).
[CrossRef] [PubMed]

Opt. Express (3)

Opt. Lett. (2)

Phys. Rev. Lett. (1)

K. Kneipp, Y. Wang, H. Kneipp, L. Perelman, I. Itzkan, R. Dasari, and M. Feld, “Single Molecule Detection Using Surface-Enhanced Raman Scattering (SERS),” Phys. Rev. Lett. 78(9), 1667–1670 (1997).
[CrossRef]

Proc. Natl. Acad. Sci. U.S.A. (4)

B. Hein, K. I. Willig, and S. W. Hell, “Stimulated emission depletion (STED) nanoscopy of a fluorescent protein-labeled organelle inside a living cell,” Proc. Natl. Acad. Sci. U.S.A. 105(38), 14271–14276 (2008).
[CrossRef] [PubMed]

M. Hofmann, C. Eggeling, S. Jakobs, and S. W. Hell, “Breaking the diffraction barrier in fluorescence microscopy at low light intensities by using reversibly photoswitchable proteins,” Proc. Natl. Acad. Sci. U.S.A. 102(49), 17565–17569 (2005).
[CrossRef] [PubMed]

U. V. Naegerl, K. I. Willig, B. Hein, S. W. Hell, and T. Bonhoeffer, “Live-cell imaging of dendritic spines by STED microscopy,” Proc. Natl. Acad. Sci. U.S.A. 105(48), 18982–18987 (2008).
[CrossRef] [PubMed]

M. G. Gustafsson, “Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution,” Proc. Natl. Acad. Sci. U.S.A. 102(37), 13081–13086 (2005).
[CrossRef] [PubMed]

Science (3)

V. Westphal, S. O. Rizzoli, M. A. Lauterbach, D. Kamin, R. Jahn, and S. W. Hell, “Video-rate far-field optical nanoscopy dissects synaptic vesicle movement,” Science 320(5873), 246–249 (2008).
[CrossRef] [PubMed]

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

S. W. Hell, “Far-field optical nanoscopy,” Science 316(5828), 1153–1158 (2007).
[CrossRef] [PubMed]

Sens. Actuators B Chem. (1)

S. Ekgasit, F. Yu, and W. Knoll, “Fluorescence intensity in surface-plasmon field-enhanced fluorescence spectroscopy,” Sens. Actuators B Chem. 104(2), 294–301 (2005).
[CrossRef]

Small (1)

R. Kasper, B. Harke, C. Forthmann, P. Tinnefeld, S. W. Hell, and M. Sauer, “Single-molecule STED microscopy with photostable organic fluorophores,” Small 6(13), 1379–1384 (2010).
[CrossRef] [PubMed]

Springer Ser Chem Sens Biosens (1)

J. Homola, “Electromagnetic Theory of Surface Plasmons,” Springer Ser Chem Sens Biosens 4, 3–44 (2006).
[CrossRef]

Other (2)

L. Hirvonen, O. Mandula, K. Wicker, and R. Heintzmann, “Structured illumination microscopy using photoswitchable fluorescent proteins,” in Proceedings of SPIE, (SPIE, 2008), p. 68610L.

T. Klar, S. Jakobs, M. Dyba, A. Egner, and S. W. Hell, “Fluorescence microscopy with diffraction resolution barrier broken by stimulated emission,” in PNAS, (2000), p. 8206.

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Figures (6)

Fig. 1
Fig. 1

Harmonic strengths of nonlinear effects caused by an interference illumination pattern with an increasing intensity. (a) Saturation (b) STED. The resolution increases when higher harmonic orders of the illumination pattern are detected.

Fig. 2
Fig. 2

TIRF-STED setup for measuring SPR enhanced STED. PBS: Polarized beam splitter.

Fig. 3
Fig. 3

Calculated SPR field enhancement at the SiO2-water interface of a glass-silver-SiO2-water structure. The optical field incidents from the glass side. Two conditions were calculated: collimated incident beam at a single wavelength of 705 nm, and a focused Gaussian beam with a 50 nm bandwidth, 10 μm focal size and a 2° focusing angle, which matched the experimental condition. (a) SPR field enhancement factor vs. silver thickness. The SiO2 layer thickness is 15 nm. The incident angle was optimized to maximal enhancement at each thickness. (b) SPR Field enhancement factor vs. incident angle. The SiO2 layer thickness is 15 nm. The silver layer thickness is 40 nm.

Fig. 4
Fig. 4

SPR enhanced STED. Top: spontaneous emission patterns from Atto 633 water solution on a glass-silver-SiO2 substrate under an increasing STED power. The pattern frame size is 30 × 30 μm2. The STED power was increased from 0 to 2.5, 10, and 50 mW respectively. The STED beam had an FWHM size of 18 × 11 μm2. Considering the objective lens caused a 40% transmission loss, the estimated instantaneous STED intensities on the sample were approximately 0, 3, 13, and 65 MW/cm2 at the beam center. Bottom: Quenching of spontaneous emission at the center of the STED beam on SPR substrate and glass. The SPR substrate was a glass coverslip coated with 40 nm silver followed by 15 nm SiO2. Due to the long excitation pulse and large temporal overlapping between the excitation and the STED pulse, the STED quenching effect follows ( 1+ P STED / P SAT ) 1 , which is the same as the quenching behavior under CW STED [33]. PSAT values are listed in Table 1.

Fig. 5
Fig. 5

(a) Proposed 2D STED-SIM setup. The excitation beam will be merged with one of the four STED beam through a dichroic mirror. (b) Simulating raw frame formation of 2D STED-SIM. The simulation used an object that contains 10-nm wide features inducing a circle, three pairs of thin bars separated by 20, 30, and 40 nm respectively, and a single dot. The STED quenching grid was simulated as { 1+0.25 I STED [ 2+cos( k 0 x+ ϕ x )+cos( k 0 y+ ϕ y ) ] } 1 , where ISTED was a uniform field at 40 ISAT. The fringe spacing of the STED grid was 250 nm. The grid was phase-shifted in 13 × 13 steps along the two dimensions. A set of 169 raw frames was simulated. Raw frame was binned down to a Nyquist sampling of 125 nm/pixel. Poisson shot noise and a 2 e- camera readout noise was added.

Fig. 6
Fig. 6

Image reconstruction of 2D STED-SIM. Raw data was simulated as in Fig. 5(b). To remove ringing, a Hann window filter was applied to the Fourier image before IFFT.

Tables (1)

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Table 1 Full-field STED on Different Substrates

Equations (8)

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F( x,y,p,q )= O( x,y ) 1+0.25 I STED ( x,y )[ 2+cos( k 0 x+ 2pπ N )+cos( k 0 y+ 2qπ N ) ] A( x,y )
1 1+0.25 I STED ( x,y )[ 2+cos( k 0 x+ 2pπ N )+cos( k 0 y+ 2qπ N ) ] = m=0,n=0 N α mn ( x,y )exp( im k 0 x+i 2mpπ N )exp( in k 0 y+i 2npπ N )
α mn ( x,y )= m+n [ 1+0.5 I STED ( x,y )+0.25ΔI ] 1 Δ I m+n [ I STED ( x,y ) ] m+n = ( 1 4 ) m+n [ I STED ( x,y ) ] m+n [ 1+0.5 I STED ( x,y ) ] 1mn
α mn ( x,y ) β m+n [ 1+0.5 I STED ( x,y ) ] 1
β= 1 2A (x,y)A I STED ( x,y ) 1+0.5 I STED ( x,y ) dxdy
F ˜ ( k x , k y ,p,q )= m=1,n=1 N exp( 2impπ N + 2inqπ N ) β m+n O ˜ ( k x m k 0 , k y n k 0 ) A ˜ ( k x ,ky )
O ˜ ( k x , k y )=FT[ O( x,y ) 1+0.5 I STED ( x,y ) ] FT[ O( x,y ) ], when I STED ( x,y ) is slow varying
O ˜ ( k x m k 0 , k y n k 0 )= M 1 F ˜ ( k x , k y ,p,q ) β m+n A ˜ ( k x , k y )

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