Abstract

Employing interference patterns for illumination has been shown to reduce the focal volume in fluorescence microscopy. For example, the 4Pi technique employs two interfering laser beams and significantly decreases the focal volume, as compared to conventional microscopy. We study theoretically the effect of using multiple interfering laser beams on the focal volume. In realistic setups with three or four beams, the focal volume is about half of that from the 4Pi case. This improvement reaches a limit quickly as more beams are added, and for the idealized case of an infinite number of beams the focal volume is rather close to the three- or four-beam cases. Thus, our study suggests a limit for the possible reduction of the focal volume in a purely optical far-field setup.

© 2009 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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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]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2008 (1)

M. C. Lang, T. Staudt, J. Engelhardt, and S. W. Hell, "4Pi microscopy with negligible sidelobes," New J. Phys. 10, 043041 (2008).
[CrossRef]

2007 (2)

A. Arkhipov, J. Hüve, M. Kahms, R. Peters, and K. Schulten, "Continuous fluorescence microphotolysis and correlation spectroscopy using 4Pi microscopy," Biophys. J. 93, 4006-4017 (2007).
[CrossRef] [PubMed]

S. W. Hell, "Far-Field Optical Nanoscopy," Science 316, 1153-1158 (2007).
[CrossRef] [PubMed]

2006 (4)

J. Ryu, S. S. Hong, B. K. P. Horn, D. M. Freeman, and M. S. Mermelstein, "Multibeam interferometric illumination as the primary source of resolution in optical microscopy," Appl. Phys. Lett. 88, 171,112 (2006).
[CrossRef]

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, "Ultra-High Resolution Imaging by Fluorescence Photoactivation Localization Microscopy," Biophys. J. 91, 4258-4272 (2006).
[CrossRef] [PubMed]

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, "Imaging Intracellular Fluorescent Proteins at Nanometer Resolution," Science 313, 1642-1645 (2006).
[CrossRef] [PubMed]

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

2005 (2)

L. Kastrup, H. Blom, C. Eggeling, and S. W. Hell, "Fluorescence Fluctuation Spectroscopy in Subdiffraction Focal Volumes," Phys. Rev. Lett. 94, 178104 (2005).
[CrossRef] [PubMed]

M. G. L. Gustafsson, "Nonlinear structured-illumination microscopy: Wide-field fluorescence imaging with theoretically unlimited resolution," Proc. Natl. Acad. Sci. USA 102, 13,081-13,086 (2005).
[CrossRef]

2003 (1)

2001 (2)

2000 (3)

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

J. T. Frohn, H. F. Knapp, and A. Stemmer, "True optical resolution beyond the Rayleigh limit achieved by standing wave illumination," Proc. Natl. Acad. Sci. USA 97, 7232-7235 (2000).
[CrossRef] [PubMed]

G. E. Cragg and P. T. C. So, "Lateral resolution enhancement with standing evanescent waves," Opt. Lett. 25, 46-48 (2000).
[CrossRef]

1999 (2)

R. Heintzmann and C. G. Cremer, "Laterally modulated excitation microscopy: improvement of resolution by using a diffraction grating," Proc. SPIE 3568, 185-196 (1999).
[CrossRef]

M. G. L. Gustafsson, D. A. Agard, and J. W. Sedat, "I5M: 3D widefield light microscopy with better than 100 nm axial resolution," J. Microsc. 195, 10-16 (1999).
[CrossRef] [PubMed]

1997 (1)

1996 (2)

V. Krishnamurthi, B. Bailey, and F. Lanni, "Image processing in 3D standing-wave fluorescence microscopy," Proc. SPIE 2655, 18-25 (1996).
[CrossRef]

W. Humphrey, A. Dalke, and K. Schulten, "VMD - Visual Molecular Dynamics," J. Mol. Graphics 14, 33-38 (1996).
[CrossRef]

1995 (1)

M. G. L. Gustafsson, D. A. Agard, and J.W. Sedat, "Sevenfold improvement of axial resolution in 3D wide-field microscopy using two objective lenses," Proc. SPIE 2412, 147-156 (1995).
[CrossRef]

1994 (2)

S. Lindek, R. Pick, and E. H. K. Stelzer, "Confocal Theta Microscope with Three Objective Lenses," Rev. Sci. Instrum. 65, 3367-3372 (1994).
[CrossRef]

S. W. Hell and J. Wichmann, "Breaking the diffraction resolution limit by stimulated emission," Opt. Lett. 19, 780-782 (1994).
[CrossRef] [PubMed]

1993 (1)

B. Bailey, D. L. Farkas, D. L. Taylor, and F. Lanni, "Enhancement of axial resolution in fluorescence microscopy by standing-wave excitation," Nature 366, 44-48 (1993).
[CrossRef] [PubMed]

1992 (1)

S. Hell and E. H. K. Stelzer, "Fundamental improvement of resolution with a 4Pi-confocal fluorescence microscope using two-photon excitation," Opt. Commun. 93, 277-282 (1992).
[CrossRef]

1959 (1)

B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system," Proc. R. Soc. Lond. A. (Math. Phys. Sci.) 253, 358-379 (1959).
[CrossRef]

Agard, D. A.

M. G. L. Gustafsson, D. A. Agard, and J. W. Sedat, "I5M: 3D widefield light microscopy with better than 100 nm axial resolution," J. Microsc. 195, 10-16 (1999).
[CrossRef] [PubMed]

M. G. L. Gustafsson, D. A. Agard, and J.W. Sedat, "Sevenfold improvement of axial resolution in 3D wide-field microscopy using two objective lenses," Proc. SPIE 2412, 147-156 (1995).
[CrossRef]

Arkhipov, A.

A. Arkhipov, J. Hüve, M. Kahms, R. Peters, and K. Schulten, "Continuous fluorescence microphotolysis and correlation spectroscopy using 4Pi microscopy," Biophys. J. 93, 4006-4017 (2007).
[CrossRef] [PubMed]

Bailey, B.

V. Krishnamurthi, B. Bailey, and F. Lanni, "Image processing in 3D standing-wave fluorescence microscopy," Proc. SPIE 2655, 18-25 (1996).
[CrossRef]

B. Bailey, D. L. Farkas, D. L. Taylor, and F. Lanni, "Enhancement of axial resolution in fluorescence microscopy by standing-wave excitation," Nature 366, 44-48 (1993).
[CrossRef] [PubMed]

Bates, M.

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

Betzig, E.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, "Imaging Intracellular Fluorescent Proteins at Nanometer Resolution," Science 313, 1642-1645 (2006).
[CrossRef] [PubMed]

Blom, H.

L. Kastrup, H. Blom, C. Eggeling, and S. W. Hell, "Fluorescence Fluctuation Spectroscopy in Subdiffraction Focal Volumes," Phys. Rev. Lett. 94, 178104 (2005).
[CrossRef] [PubMed]

Bonifacino, J. S.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, "Imaging Intracellular Fluorescent Proteins at Nanometer Resolution," Science 313, 1642-1645 (2006).
[CrossRef] [PubMed]

Cragg, G. E.

Cremer, C. G.

R. Heintzmann and C. G. Cremer, "Laterally modulated excitation microscopy: improvement of resolution by using a diffraction grating," Proc. SPIE 3568, 185-196 (1999).
[CrossRef]

Dalke, A.

W. Humphrey, A. Dalke, and K. Schulten, "VMD - Visual Molecular Dynamics," J. Mol. Graphics 14, 33-38 (1996).
[CrossRef]

Davidson, M. W.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, "Imaging Intracellular Fluorescent Proteins at Nanometer Resolution," Science 313, 1642-1645 (2006).
[CrossRef] [PubMed]

Dieterlen, A.

Dong, C. Y.

Eggeling, C.

L. Kastrup, H. Blom, C. Eggeling, and S. W. Hell, "Fluorescence Fluctuation Spectroscopy in Subdiffraction Focal Volumes," Phys. Rev. Lett. 94, 178104 (2005).
[CrossRef] [PubMed]

Engelhardt, J.

M. C. Lang, T. Staudt, J. Engelhardt, and S. W. Hell, "4Pi microscopy with negligible sidelobes," New J. Phys. 10, 043041 (2008).
[CrossRef]

Farkas, D. L.

B. Bailey, D. L. Farkas, D. L. Taylor, and F. Lanni, "Enhancement of axial resolution in fluorescence microscopy by standing-wave excitation," Nature 366, 44-48 (1993).
[CrossRef] [PubMed]

Freeman, D. M.

J. Ryu, S. S. Hong, B. K. P. Horn, D. M. Freeman, and M. S. Mermelstein, "Multibeam interferometric illumination as the primary source of resolution in optical microscopy," Appl. Phys. Lett. 88, 171,112 (2006).
[CrossRef]

Frohn, J. T.

J. T. Frohn, H. F. Knapp, and A. Stemmer, "True optical resolution beyond the Rayleigh limit achieved by standing wave illumination," Proc. Natl. Acad. Sci. USA 97, 7232-7235 (2000).
[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, 4258-4272 (2006).
[CrossRef] [PubMed]

Gustafsson, M. G. L.

M. G. L. Gustafsson, "Nonlinear structured-illumination microscopy: Wide-field fluorescence imaging with theoretically unlimited resolution," Proc. Natl. Acad. Sci. USA 102, 13,081-13,086 (2005).
[CrossRef]

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

M. G. L. Gustafsson, D. A. Agard, and J. W. Sedat, "I5M: 3D widefield light microscopy with better than 100 nm axial resolution," J. Microsc. 195, 10-16 (1999).
[CrossRef] [PubMed]

M. G. L. Gustafsson, D. A. Agard, and J.W. Sedat, "Sevenfold improvement of axial resolution in 3D wide-field microscopy using two objective lenses," Proc. SPIE 2412, 147-156 (1995).
[CrossRef]

Haeberle, O.

Heintzmann, R.

R. Heintzmann and C. G. Cremer, "Laterally modulated excitation microscopy: improvement of resolution by using a diffraction grating," Proc. SPIE 3568, 185-196 (1999).
[CrossRef]

Hell, S.

S. Hell and E. H. K. Stelzer, "Fundamental improvement of resolution with a 4Pi-confocal fluorescence microscope using two-photon excitation," Opt. Commun. 93, 277-282 (1992).
[CrossRef]

Hell, S. W.

M. C. Lang, T. Staudt, J. Engelhardt, and S. W. Hell, "4Pi microscopy with negligible sidelobes," New J. Phys. 10, 043041 (2008).
[CrossRef]

S. W. Hell, "Far-Field Optical Nanoscopy," Science 316, 1153-1158 (2007).
[CrossRef] [PubMed]

L. Kastrup, H. Blom, C. Eggeling, and S. W. Hell, "Fluorescence Fluctuation Spectroscopy in Subdiffraction Focal Volumes," Phys. Rev. Lett. 94, 178104 (2005).
[CrossRef] [PubMed]

S. W. Hell and J. Wichmann, "Breaking the diffraction resolution limit by stimulated emission," Opt. Lett. 19, 780-782 (1994).
[CrossRef] [PubMed]

Hess, H. F.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, "Imaging Intracellular Fluorescent Proteins at Nanometer Resolution," Science 313, 1642-1645 (2006).
[CrossRef] [PubMed]

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, 4258-4272 (2006).
[CrossRef] [PubMed]

Hong, S. S.

J. Ryu, S. S. Hong, B. K. P. Horn, D. M. Freeman, and M. S. Mermelstein, "Multibeam interferometric illumination as the primary source of resolution in optical microscopy," Appl. Phys. Lett. 88, 171,112 (2006).
[CrossRef]

Horn, B. K. P.

J. Ryu, S. S. Hong, B. K. P. Horn, D. M. Freeman, and M. S. Mermelstein, "Multibeam interferometric illumination as the primary source of resolution in optical microscopy," Appl. Phys. Lett. 88, 171,112 (2006).
[CrossRef]

Huisken, J.

Humphrey, W.

W. Humphrey, A. Dalke, and K. Schulten, "VMD - Visual Molecular Dynamics," J. Mol. Graphics 14, 33-38 (1996).
[CrossRef]

Hüve, J.

A. Arkhipov, J. Hüve, M. Kahms, R. Peters, and K. Schulten, "Continuous fluorescence microphotolysis and correlation spectroscopy using 4Pi microscopy," Biophys. J. 93, 4006-4017 (2007).
[CrossRef] [PubMed]

Jacquey, S.

Juskaitis, R.

Kahms, M.

A. Arkhipov, J. Hüve, M. Kahms, R. Peters, and K. Schulten, "Continuous fluorescence microphotolysis and correlation spectroscopy using 4Pi microscopy," Biophys. J. 93, 4006-4017 (2007).
[CrossRef] [PubMed]

Kastrup, L.

L. Kastrup, H. Blom, C. Eggeling, and S. W. Hell, "Fluorescence Fluctuation Spectroscopy in Subdiffraction Focal Volumes," Phys. Rev. Lett. 94, 178104 (2005).
[CrossRef] [PubMed]

Knapp, H. F.

J. T. Frohn, H. F. Knapp, and A. Stemmer, "True optical resolution beyond the Rayleigh limit achieved by standing wave illumination," Proc. Natl. Acad. Sci. USA 97, 7232-7235 (2000).
[CrossRef] [PubMed]

Krishnamurthi, V.

V. Krishnamurthi, B. Bailey, and F. Lanni, "Image processing in 3D standing-wave fluorescence microscopy," Proc. SPIE 2655, 18-25 (1996).
[CrossRef]

Kwon, H.-S.

Lang, M. C.

M. C. Lang, T. Staudt, J. Engelhardt, and S. W. Hell, "4Pi microscopy with negligible sidelobes," New J. Phys. 10, 043041 (2008).
[CrossRef]

Lanni, F.

V. Krishnamurthi, B. Bailey, and F. Lanni, "Image processing in 3D standing-wave fluorescence microscopy," Proc. SPIE 2655, 18-25 (1996).
[CrossRef]

B. Bailey, D. L. Farkas, D. L. Taylor, and F. Lanni, "Enhancement of axial resolution in fluorescence microscopy by standing-wave excitation," Nature 366, 44-48 (1993).
[CrossRef] [PubMed]

Lindek, S.

S. Lindek, R. Pick, and E. H. K. Stelzer, "Confocal Theta Microscope with Three Objective Lenses," Rev. Sci. Instrum. 65, 3367-3372 (1994).
[CrossRef]

Lindwasser, O. W.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, "Imaging Intracellular Fluorescent Proteins at Nanometer Resolution," Science 313, 1642-1645 (2006).
[CrossRef] [PubMed]

Lippincott-Schwartz, J.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, "Imaging Intracellular Fluorescent Proteins at Nanometer Resolution," Science 313, 1642-1645 (2006).
[CrossRef] [PubMed]

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, 4258-4272 (2006).
[CrossRef] [PubMed]

Mermelstein, M. S.

J. Ryu, S. S. Hong, B. K. P. Horn, D. M. Freeman, and M. S. Mermelstein, "Multibeam interferometric illumination as the primary source of resolution in optical microscopy," Appl. Phys. Lett. 88, 171,112 (2006).
[CrossRef]

Neil, M. A. A.

Olenych, S.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, "Imaging Intracellular Fluorescent Proteins at Nanometer Resolution," Science 313, 1642-1645 (2006).
[CrossRef] [PubMed]

Patterson, G. H.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, "Imaging Intracellular Fluorescent Proteins at Nanometer Resolution," Science 313, 1642-1645 (2006).
[CrossRef] [PubMed]

Peters, R.

A. Arkhipov, J. Hüve, M. Kahms, R. Peters, and K. Schulten, "Continuous fluorescence microphotolysis and correlation spectroscopy using 4Pi microscopy," Biophys. J. 93, 4006-4017 (2007).
[CrossRef] [PubMed]

Pick, R.

S. Lindek, R. Pick, and E. H. K. Stelzer, "Confocal Theta Microscope with Three Objective Lenses," Rev. Sci. Instrum. 65, 3367-3372 (1994).
[CrossRef]

Richards, B.

B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system," Proc. R. Soc. Lond. A. (Math. Phys. Sci.) 253, 358-379 (1959).
[CrossRef]

Rust, M. J.

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

Ryu, J.

J. Ryu, S. S. Hong, B. K. P. Horn, D. M. Freeman, and M. S. Mermelstein, "Multibeam interferometric illumination as the primary source of resolution in optical microscopy," Appl. Phys. Lett. 88, 171,112 (2006).
[CrossRef]

Schulten, K.

A. Arkhipov, J. Hüve, M. Kahms, R. Peters, and K. Schulten, "Continuous fluorescence microphotolysis and correlation spectroscopy using 4Pi microscopy," Biophys. J. 93, 4006-4017 (2007).
[CrossRef] [PubMed]

W. Humphrey, A. Dalke, and K. Schulten, "VMD - Visual Molecular Dynamics," J. Mol. Graphics 14, 33-38 (1996).
[CrossRef]

Sedat, J. W.

M. G. L. Gustafsson, D. A. Agard, and J. W. Sedat, "I5M: 3D widefield light microscopy with better than 100 nm axial resolution," J. Microsc. 195, 10-16 (1999).
[CrossRef] [PubMed]

Sedat, J.W.

M. G. L. Gustafsson, D. A. Agard, and J.W. Sedat, "Sevenfold improvement of axial resolution in 3D wide-field microscopy using two objective lenses," Proc. SPIE 2412, 147-156 (1995).
[CrossRef]

So, P. T. C.

Sougrat, R.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, "Imaging Intracellular Fluorescent Proteins at Nanometer Resolution," Science 313, 1642-1645 (2006).
[CrossRef] [PubMed]

Staudt, T.

M. C. Lang, T. Staudt, J. Engelhardt, and S. W. Hell, "4Pi microscopy with negligible sidelobes," New J. Phys. 10, 043041 (2008).
[CrossRef]

Stelzer, E. H. K.

J. Swoger, J. Huisken, and E. H. K. Stelzer, "Multiple imaging axis microscopy improves resolution for thicksample applications," Opt. Lett. 28, 1654-1656 (2003).
[CrossRef] [PubMed]

S. Lindek, R. Pick, and E. H. K. Stelzer, "Confocal Theta Microscope with Three Objective Lenses," Rev. Sci. Instrum. 65, 3367-3372 (1994).
[CrossRef]

S. Hell and E. H. K. Stelzer, "Fundamental improvement of resolution with a 4Pi-confocal fluorescence microscope using two-photon excitation," Opt. Commun. 93, 277-282 (1992).
[CrossRef]

Stemmer, A.

J. T. Frohn, H. F. Knapp, and A. Stemmer, "True optical resolution beyond the Rayleigh limit achieved by standing wave illumination," Proc. Natl. Acad. Sci. USA 97, 7232-7235 (2000).
[CrossRef] [PubMed]

Swoger, J.

Taylor, D. L.

B. Bailey, D. L. Farkas, D. L. Taylor, and F. Lanni, "Enhancement of axial resolution in fluorescence microscopy by standing-wave excitation," Nature 366, 44-48 (1993).
[CrossRef] [PubMed]

Wichmann, J.

Wilson, T.

Wolf, E.

B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system," Proc. R. Soc. Lond. A. (Math. Phys. Sci.) 253, 358-379 (1959).
[CrossRef]

Xu, C.

Zhuang, X.

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

Appl. Phys. Lett. (1)

J. Ryu, S. S. Hong, B. K. P. Horn, D. M. Freeman, and M. S. Mermelstein, "Multibeam interferometric illumination as the primary source of resolution in optical microscopy," Appl. Phys. Lett. 88, 171,112 (2006).
[CrossRef]

Biophys. J. (2)

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, "Ultra-High Resolution Imaging by Fluorescence Photoactivation Localization Microscopy," Biophys. J. 91, 4258-4272 (2006).
[CrossRef] [PubMed]

A. Arkhipov, J. Hüve, M. Kahms, R. Peters, and K. Schulten, "Continuous fluorescence microphotolysis and correlation spectroscopy using 4Pi microscopy," Biophys. J. 93, 4006-4017 (2007).
[CrossRef] [PubMed]

J. Microsc. (2)

M. G. L. Gustafsson, D. A. Agard, and J. W. Sedat, "I5M: 3D widefield light microscopy with better than 100 nm axial resolution," J. Microsc. 195, 10-16 (1999).
[CrossRef] [PubMed]

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

J. Mol. Graphics (1)

W. Humphrey, A. Dalke, and K. Schulten, "VMD - Visual Molecular Dynamics," J. Mol. Graphics 14, 33-38 (1996).
[CrossRef]

J. Opt. Soc. Am. A (1)

Nat. Methods (1)

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

Nature (1)

B. Bailey, D. L. Farkas, D. L. Taylor, and F. Lanni, "Enhancement of axial resolution in fluorescence microscopy by standing-wave excitation," Nature 366, 44-48 (1993).
[CrossRef] [PubMed]

New J. Phys. (1)

M. C. Lang, T. Staudt, J. Engelhardt, and S. W. Hell, "4Pi microscopy with negligible sidelobes," New J. Phys. 10, 043041 (2008).
[CrossRef]

Opt. Commun. (1)

S. Hell and E. H. K. Stelzer, "Fundamental improvement of resolution with a 4Pi-confocal fluorescence microscope using two-photon excitation," Opt. Commun. 93, 277-282 (1992).
[CrossRef]

Opt. Lett. (5)

Phys. Rev. Lett. (1)

L. Kastrup, H. Blom, C. Eggeling, and S. W. Hell, "Fluorescence Fluctuation Spectroscopy in Subdiffraction Focal Volumes," Phys. Rev. Lett. 94, 178104 (2005).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. USA (2)

J. T. Frohn, H. F. Knapp, and A. Stemmer, "True optical resolution beyond the Rayleigh limit achieved by standing wave illumination," Proc. Natl. Acad. Sci. USA 97, 7232-7235 (2000).
[CrossRef] [PubMed]

M. G. L. Gustafsson, "Nonlinear structured-illumination microscopy: Wide-field fluorescence imaging with theoretically unlimited resolution," Proc. Natl. Acad. Sci. USA 102, 13,081-13,086 (2005).
[CrossRef]

Proc. R. Soc. Lond. A. (Math. Phys. Sci.) (1)

B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system," Proc. R. Soc. Lond. A. (Math. Phys. Sci.) 253, 358-379 (1959).
[CrossRef]

Proc. SPIE (3)

R. Heintzmann and C. G. Cremer, "Laterally modulated excitation microscopy: improvement of resolution by using a diffraction grating," Proc. SPIE 3568, 185-196 (1999).
[CrossRef]

M. G. L. Gustafsson, D. A. Agard, and J.W. Sedat, "Sevenfold improvement of axial resolution in 3D wide-field microscopy using two objective lenses," Proc. SPIE 2412, 147-156 (1995).
[CrossRef]

V. Krishnamurthi, B. Bailey, and F. Lanni, "Image processing in 3D standing-wave fluorescence microscopy," Proc. SPIE 2655, 18-25 (1996).
[CrossRef]

Rev. Sci. Instrum. (1)

S. Lindek, R. Pick, and E. H. K. Stelzer, "Confocal Theta Microscope with Three Objective Lenses," Rev. Sci. Instrum. 65, 3367-3372 (1994).
[CrossRef]

Science (2)

S. W. Hell, "Far-Field Optical Nanoscopy," Science 316, 1153-1158 (2007).
[CrossRef] [PubMed]

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, "Imaging Intracellular Fluorescent Proteins at Nanometer Resolution," Science 313, 1642-1645 (2006).
[CrossRef] [PubMed]

Other (2)

E. Wolf, "Electromagnetic diffraction in optical systems I. An integral representation of the image field," Proc. R. Soc. Lond. A. (Math. Phys. Sci.) 253, 349-357 (1959).
[CrossRef]

P. Schwille and E. Haustein, "Fluorescence Correlation Spectroscopy: A Tutorial for the Biophysics Textbook Online (BTOL)" (2002), http://www.biophysics.org/education/techniques.htm.

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Figures (4)

Fig. 1.
Fig. 1.

Schemes of multi-beam interference setups. Each beam is characterized by its wave vector k→, polarization E→, and half-aperture angle α. For 2, 3, and 4 beams, and “Inf. beams, 2D”, all k→-vectors are in the same plane and all E→-vectors are collinear. For 6 beams, the beams 1 to 4 are the same as in the case of 4 beams, k5 and k6 are perpendicular to the plane formed by k→1 to k4, and E5 and E6 are collinear with k2. “Inf. beams, 2D” assumes an infinite number of beams converging to a point uniformly from all directions in one plane. “Inf. beams, 3D” is achieved by replicating the plane with the beams from “Inf. beams, 2D”, rotating the replicas around one axis, and summing up all contributions for rotation angles from 0 to π; this results in the infinite number of beams converging to one point from all directions in 3D.

Fig. 2.
Fig. 2.

PSF isosurfaces for the geometries with various numbers of beams. The PSFs are shown as viewed in the y, z- and x,y-planes (arrangement of the beams is the same as in Fig. 1). The isosurfaces are drawn at 0.5 (red), 0.1 (blue), and 0.01 (gray) of the PSF maximum (i.e., the red isosurface corresponds to the FWHM). It is assumed that α ≈ 70° is the maximal value of a technically possible for a single beam. The maximal realistic values of a are used for 1, 2, 3, 4, and 6 beams, and α = 70° for the idealized cases of 60 and infinite number of beams. The scale bar shows λ/n, λ being the wavelength used, n the optical density. For all cases except 1-beam, two-photon excitation is assumed, while for the 1-beam case, we assume one-photon excitation and a wavelength λ/2.

Fig. 3.
Fig. 3.

Effective focal volumes V eff. The values of V eff vs. α are plotted for 1 and 2 beams, and for the limiting cases of infinite number of beams distributed in 2D or in 3D. For 3, 4, and 6 beams, Veff at the maximal realistic values of a are shown. For “60 beams” and “20 beams, 2D” (the latter denoting 20 beams uniformly distributed in a plane), α = 70° for an idealized comparison with the infinite number of beams.

Fig. 4.
Fig. 4.

PSF profiles in x-, y-, and z-directions for multi-beam microscopes. The same setups are shown as in Fig. 2. Black, 1 beam; red, 4Pi (2 beams); green, 3 beams; blue, 4 beams; cyan, 6 beams; purple, 60 beams; orange, “Inf. beams, 2D”; deep green, “Inf. beams, 3D”. The curve with circles is the theoretical approximation of the PSF for the case of “Inf. beams, 3D”, as described by Eq. (5).

Tables (1)

Tables Icon

Table 1. FWHM Δl of PSFs in x, y, and z dimension (see also Fig. 4). The setups considered are the same as in Fig. 2; Δl is measured in λ/n.

Equations (8)

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V eff = [ h ( r ) d r ] 2 h 2 ( r ) d r .
I 0,1,2 ( r ) = 0 α cos 1 / 2 θ sin θ f 0,1,2 ( θ ) J 0,1,2 ( 2 πn x 2 + y 2 sin θ λ ) exp ( i 2 πnz cos θ λ ) ,
A 0,1,2 ( r ) = ϕ r π ϕ r 0 π 0 α cos 1 / 2 θ sin f 0,1,2 ( θ ) ×
J 0,1,2 ( 2 πnr sin θ λ sin 2 θ r cos 2 φ + cos 2 χ ( sin 2 θ r sin 2 φ + cos 2 θ r ) ) ×
cos ( 2 πnr cos θ λ sin 2 θ r sin 2 + cos 2 θ r sin χ ) g ( φ ) ,
A 0,1,2 ( r ) = 2 0 π 0 α cos 1 / 2 θ sin θ f 0,1,2 ( θ ) J 0,1,2 ( 2 πnr sin θ cos χ λ ) cos ( 2 πnr cos θ sin χ λ ) .
E ( r ) [ 0 , J 0 ( 2 πnr sin α λ ) , 0 ] .
h ( r ) J 0 4 ( 0.87 2 πnr λ ) .

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