Abstract

Here we recount the standard two-level model that describes saturated excitation (SAX) in multiphoton microscopy (MPM), a new technique for super-resolution fluorescence microscopy in scattering tissue, which requires no special chemistry and only simple modifications to a commercial MPM microscope. We use the model to study conditions required for improvements in MPM SAX resolution and experimental implementation strategies. Simulation results find zeros, or nodes, in the frequency response, which generate highly irregular point-spread functions (PSFs), such as rings and ripples, that contain spatial frequency content >3× larger than allowed by diffraction. These PSFs are a direct result of zeros in the frequency response of saturated fluorophores under specific excitation conditions. The impact on image quality is discussed using simulations of targets imaged with SAX PSFs. Further, we explore engineering sets of irregular PSFs by varying the excitation power and reconstructing super-resolution images from the set of captured images.

© 2017 Optical Society of America

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2016 (1)

2015 (3)

A. D. Nguyen, F. Duport, A. Bouwens, F. Vanholsbeeck, D. Egrise, G. Van Simaeys, P. Emplit, S. Goldman, and S.-P. Gorza, “3D super-resolved in vitro multiphoton microscopy by saturation of excitation,” Opt. Express 23, 22667–22675 (2015).
[Crossref]

S. W. Hell, S. J. Sahl, M. Bates, X. Zhuang, R. Heintzmann, M. J. Booth, J. Bewersdorf, G. Shtengel, H. Hess, P. Tinnefeld, A. Honigmann, S. Jakobs, I. Testa, L. Cognet, B. Lounis, H. Ewers, S. J. Davis, C. Eggeling, D. Klenerman, K. I. Willig, G. Vicidomini, M. Castello, A. Diaspro, and T. Cordes, “The 2015 super-resolution microscopy roadmap,” J. Phys. D 48, 443001 (2015).
[Crossref]

M. Yamanaka, S. Kawano, K. Fujita, N. I. Smith, and S. Kawata, “Beyond the diffraction-limit biological imaging by saturated excitation microscopy,” J. Biomed. Opt. 13, 050507 (2015).
[Crossref]

2014 (2)

2013 (1)

N. G. Horton, K. Wang, D. Kobat, C. G. Clark, F. W. Wise, C. B. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7, 205–209 (2013).
[Crossref]

2012 (2)

V. Andresen, K. Pollok, J.-L. Rinnenthal, L. Oehme, R. Günther, H. Spiecker, H. Radbruch, J. Gerhard, A. Sporbert, Z. Cseresnyes, A. E. Hauser, and R. Niesner, “High-resolution intravital microscopy,” PLoS One 101, 1435–1439 (2012).
[Crossref]

S. S. Howard, A. Straub, N. G. Horton, D. Kobat, and C. Xu, “Frequency-multiplexed in vivo multiphoton phosphorescence lifetime microscopy,” Nat. Photon. Lett. 7, 33–37 (2012).
[Crossref]

2011 (1)

2010 (1)

B. Huang, M. Bates, and X. Zhuang, “Super resolution fluorescence microscopy,” Annu. Rev. Biochem. 78, 993–1016 (2010).
[Crossref]

2009 (4)

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. USA 106, 2995–2999 (2009).
[Crossref]

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

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

D. Kobat, M. E. Durst, N. Nishimura, A. W. Wong, C. B. Schaffer, and C. Xu, “Deep tissue multiphoton microscopy using longer wavelength excitation,” Opt. Express 17, 13354–13364 (2009).
[Crossref]

2008 (2)

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

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

2007 (1)

K. Fujita, M. Kobayashi, S. Kawano, M. Yamanaka, and S. Kawata, “High-resolution confocal microscopy by saturated excitation of fluorescence,” Phys. Rev. Lett. 99, 1–4 (2007).
[Crossref]

2006 (2)

P. Theer and W. Denk, “On the fundamental imaging-depth limit in two-photon microscopy,” J. Opt. Soc. Am. A 23, 3139–3149 (2006).
[Crossref]

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]

2004 (1)

G. C. Cianci, J. Wu, and K. M. Berland, “Saturation modified point spread functions in two-photon microscopy,” Microsc. Res. Tech. 64, 135–141 (2004).
[Crossref]

1995 (1)

1994 (2)

Agard, D. A.

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

Andresen, V.

V. Andresen, K. Pollok, J.-L. Rinnenthal, L. Oehme, R. Günther, H. Spiecker, H. Radbruch, J. Gerhard, A. Sporbert, Z. Cseresnyes, A. E. Hauser, and R. Niesner, “High-resolution intravital microscopy,” PLoS One 101, 1435–1439 (2012).
[Crossref]

Bates, M.

S. W. Hell, S. J. Sahl, M. Bates, X. Zhuang, R. Heintzmann, M. J. Booth, J. Bewersdorf, G. Shtengel, H. Hess, P. Tinnefeld, A. Honigmann, S. Jakobs, I. Testa, L. Cognet, B. Lounis, H. Ewers, S. J. Davis, C. Eggeling, D. Klenerman, K. I. Willig, G. Vicidomini, M. Castello, A. Diaspro, and T. Cordes, “The 2015 super-resolution microscopy roadmap,” J. Phys. D 48, 443001 (2015).
[Crossref]

B. Huang, M. Bates, and X. Zhuang, “Super resolution fluorescence microscopy,” Annu. Rev. Biochem. 78, 993–1016 (2010).
[Crossref]

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

Berland, K. M.

G. C. Cianci, J. Wu, and K. M. Berland, “Saturation modified point spread functions in two-photon microscopy,” Microsc. Res. Tech. 64, 135–141 (2004).
[Crossref]

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]

E. Betzig, “Proposed method for molecular optical imaging,” Opt. Lett. 20, 237–239 (1995).
[Crossref]

E. Betzig, S. W. Hell, and W. E. Moerner, “How the optical microscope became a nanoscope” (2014), pp. 1–7.

Bewersdorf, J.

S. W. Hell, S. J. Sahl, M. Bates, X. Zhuang, R. Heintzmann, M. J. Booth, J. Bewersdorf, G. Shtengel, H. Hess, P. Tinnefeld, A. Honigmann, S. Jakobs, I. Testa, L. Cognet, B. Lounis, H. Ewers, S. J. Davis, C. Eggeling, D. Klenerman, K. I. Willig, G. Vicidomini, M. Castello, A. Diaspro, and T. Cordes, “The 2015 super-resolution microscopy roadmap,” J. Phys. D 48, 443001 (2015).
[Crossref]

Biteen, J. S.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. USA 106, 2995–2999 (2009).
[Crossref]

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]

Booth, M. J.

S. W. Hell, S. J. Sahl, M. Bates, X. Zhuang, R. Heintzmann, M. J. Booth, J. Bewersdorf, G. Shtengel, H. Hess, P. Tinnefeld, A. Honigmann, S. Jakobs, I. Testa, L. Cognet, B. Lounis, H. Ewers, S. J. Davis, C. Eggeling, D. Klenerman, K. I. Willig, G. Vicidomini, M. Castello, A. Diaspro, and T. Cordes, “The 2015 super-resolution microscopy roadmap,” J. Phys. D 48, 443001 (2015).
[Crossref]

Bouwens, A.

Cande, W. Z.

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

Carlton, P. M.

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

Castello, M.

S. W. Hell, S. J. Sahl, M. Bates, X. Zhuang, R. Heintzmann, M. J. Booth, J. Bewersdorf, G. Shtengel, H. Hess, P. Tinnefeld, A. Honigmann, S. Jakobs, I. Testa, L. Cognet, B. Lounis, H. Ewers, S. J. Davis, C. Eggeling, D. Klenerman, K. I. Willig, G. Vicidomini, M. Castello, A. Diaspro, and T. Cordes, “The 2015 super-resolution microscopy roadmap,” J. Phys. D 48, 443001 (2015).
[Crossref]

Caulfield, H. J.

Chitnis, A.

Chou, K. C.

Christensen, R.

Chu, S.-W.

Cianci, G. C.

G. C. Cianci, J. Wu, and K. M. Berland, “Saturation modified point spread functions in two-photon microscopy,” Microsc. Res. Tech. 64, 135–141 (2004).
[Crossref]

Clark, C. G.

N. G. Horton, K. Wang, D. Kobat, C. G. Clark, F. W. Wise, C. B. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7, 205–209 (2013).
[Crossref]

Cognet, L.

S. W. Hell, S. J. Sahl, M. Bates, X. Zhuang, R. Heintzmann, M. J. Booth, J. Bewersdorf, G. Shtengel, H. Hess, P. Tinnefeld, A. Honigmann, S. Jakobs, I. Testa, L. Cognet, B. Lounis, H. Ewers, S. J. Davis, C. Eggeling, D. Klenerman, K. I. Willig, G. Vicidomini, M. Castello, A. Diaspro, and T. Cordes, “The 2015 super-resolution microscopy roadmap,” J. Phys. D 48, 443001 (2015).
[Crossref]

Cordes, T.

S. W. Hell, S. J. Sahl, M. Bates, X. Zhuang, R. Heintzmann, M. J. Booth, J. Bewersdorf, G. Shtengel, H. Hess, P. Tinnefeld, A. Honigmann, S. Jakobs, I. Testa, L. Cognet, B. Lounis, H. Ewers, S. J. Davis, C. Eggeling, D. Klenerman, K. I. Willig, G. Vicidomini, M. Castello, A. Diaspro, and T. Cordes, “The 2015 super-resolution microscopy roadmap,” J. Phys. D 48, 443001 (2015).
[Crossref]

Cseresnyes, Z.

V. Andresen, K. Pollok, J.-L. Rinnenthal, L. Oehme, R. Günther, H. Spiecker, H. Radbruch, J. Gerhard, A. Sporbert, Z. Cseresnyes, A. E. Hauser, and R. Niesner, “High-resolution intravital microscopy,” PLoS One 101, 1435–1439 (2012).
[Crossref]

Davidson, M. W.

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

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]

Davis, S. J.

S. W. Hell, S. J. Sahl, M. Bates, X. Zhuang, R. Heintzmann, M. J. Booth, J. Bewersdorf, G. Shtengel, H. Hess, P. Tinnefeld, A. Honigmann, S. Jakobs, I. Testa, L. Cognet, B. Lounis, H. Ewers, S. J. Davis, C. Eggeling, D. Klenerman, K. I. Willig, G. Vicidomini, M. Castello, A. Diaspro, and T. Cordes, “The 2015 super-resolution microscopy roadmap,” J. Phys. D 48, 443001 (2015).
[Crossref]

Denk, W.

Diaspro, A.

S. W. Hell, S. J. Sahl, M. Bates, X. Zhuang, R. Heintzmann, M. J. Booth, J. Bewersdorf, G. Shtengel, H. Hess, P. Tinnefeld, A. Honigmann, S. Jakobs, I. Testa, L. Cognet, B. Lounis, H. Ewers, S. J. Davis, C. Eggeling, D. Klenerman, K. I. Willig, G. Vicidomini, M. Castello, A. Diaspro, and T. Cordes, “The 2015 super-resolution microscopy roadmap,” J. Phys. D 48, 443001 (2015).
[Crossref]

Duport, F.

Durst, M. E.

Eggeling, C.

S. W. Hell, S. J. Sahl, M. Bates, X. Zhuang, R. Heintzmann, M. J. Booth, J. Bewersdorf, G. Shtengel, H. Hess, P. Tinnefeld, A. Honigmann, S. Jakobs, I. Testa, L. Cognet, B. Lounis, H. Ewers, S. J. Davis, C. Eggeling, D. Klenerman, K. I. Willig, G. Vicidomini, M. Castello, A. Diaspro, and T. Cordes, “The 2015 super-resolution microscopy roadmap,” J. Phys. D 48, 443001 (2015).
[Crossref]

Egrise, D.

Emplit, P.

Ewers, H.

S. W. Hell, S. J. Sahl, M. Bates, X. Zhuang, R. Heintzmann, M. J. Booth, J. Bewersdorf, G. Shtengel, H. Hess, P. Tinnefeld, A. Honigmann, S. Jakobs, I. Testa, L. Cognet, B. Lounis, H. Ewers, S. J. Davis, C. Eggeling, D. Klenerman, K. I. Willig, G. Vicidomini, M. Castello, A. Diaspro, and T. Cordes, “The 2015 super-resolution microscopy roadmap,” J. Phys. D 48, 443001 (2015).
[Crossref]

Fetter, R. D.

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

Fujita, K.

M. Yamanaka, S. Kawano, K. Fujita, N. I. Smith, and S. Kawata, “Beyond the diffraction-limit biological imaging by saturated excitation microscopy,” J. Biomed. Opt. 13, 050507 (2015).
[Crossref]

H. Lee, R. Oketani, Y.-T. Huang, K.-Y. Li, Y. Yonemaru, M. Yamanaka, S. Kawata, K. Fujita, and S.-W. Chu, “Point spread function analysis with saturable and reverse saturable scattering,” Opt. Express 22, 26016–26022 (2014).
[Crossref]

K. Fujita, M. Kobayashi, S. Kawano, M. Yamanaka, and S. Kawata, “High-resolution confocal microscopy by saturated excitation of fluorescence,” Phys. Rev. Lett. 99, 1–4 (2007).
[Crossref]

Galbraith, C. G.

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

Galbraith, J. A.

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

Gerhard, J.

V. Andresen, K. Pollok, J.-L. Rinnenthal, L. Oehme, R. Günther, H. Spiecker, H. Radbruch, J. Gerhard, A. Sporbert, Z. Cseresnyes, A. E. Hauser, and R. Niesner, “High-resolution intravital microscopy,” PLoS One 101, 1435–1439 (2012).
[Crossref]

Gillette, J. M.

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N. G. Horton, K. Wang, D. Kobat, C. G. Clark, F. W. Wise, C. B. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7, 205–209 (2013).
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D. Kobat, M. E. Durst, N. Nishimura, A. W. Wong, C. B. Schaffer, and C. Xu, “Deep tissue multiphoton microscopy using longer wavelength excitation,” Opt. Express 17, 13354–13364 (2009).
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M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J. 94, 4957–4970 (2008).
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M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J. 94, 4957–4970 (2008).
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Shtengel, G.

S. W. Hell, S. J. Sahl, M. Bates, X. Zhuang, R. Heintzmann, M. J. Booth, J. Bewersdorf, G. Shtengel, H. Hess, P. Tinnefeld, A. Honigmann, S. Jakobs, I. Testa, L. Cognet, B. Lounis, H. Ewers, S. J. Davis, C. Eggeling, D. Klenerman, K. I. Willig, G. Vicidomini, M. Castello, A. Diaspro, and T. Cordes, “The 2015 super-resolution microscopy roadmap,” J. Phys. D 48, 443001 (2015).
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M. Yamanaka, S. Kawano, K. Fujita, N. I. Smith, and S. Kawata, “Beyond the diffraction-limit biological imaging by saturated excitation microscopy,” J. Biomed. Opt. 13, 050507 (2015).
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G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. USA 106, 3125–3130 (2009).
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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).
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V. Andresen, K. Pollok, J.-L. Rinnenthal, L. Oehme, R. Günther, H. Spiecker, H. Radbruch, J. Gerhard, A. Sporbert, Z. Cseresnyes, A. E. Hauser, and R. Niesner, “High-resolution intravital microscopy,” PLoS One 101, 1435–1439 (2012).
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Sporbert, A.

V. Andresen, K. Pollok, J.-L. Rinnenthal, L. Oehme, R. Günther, H. Spiecker, H. Radbruch, J. Gerhard, A. Sporbert, Z. Cseresnyes, A. E. Hauser, and R. Niesner, “High-resolution intravital microscopy,” PLoS One 101, 1435–1439 (2012).
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S. S. Howard, A. Straub, N. G. Horton, D. Kobat, and C. Xu, “Frequency-multiplexed in vivo multiphoton phosphorescence lifetime microscopy,” Nat. Photon. Lett. 7, 33–37 (2012).
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S. W. Hell, S. J. Sahl, M. Bates, X. Zhuang, R. Heintzmann, M. J. Booth, J. Bewersdorf, G. Shtengel, H. Hess, P. Tinnefeld, A. Honigmann, S. Jakobs, I. Testa, L. Cognet, B. Lounis, H. Ewers, S. J. Davis, C. Eggeling, D. Klenerman, K. I. Willig, G. Vicidomini, M. Castello, A. Diaspro, and T. Cordes, “The 2015 super-resolution microscopy roadmap,” J. Phys. D 48, 443001 (2015).
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Theer, P.

Thompson, M. A.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. USA 106, 2995–2999 (2009).
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S. W. Hell, S. J. Sahl, M. Bates, X. Zhuang, R. Heintzmann, M. J. Booth, J. Bewersdorf, G. Shtengel, H. Hess, P. Tinnefeld, A. Honigmann, S. Jakobs, I. Testa, L. Cognet, B. Lounis, H. Ewers, S. J. Davis, C. Eggeling, D. Klenerman, K. I. Willig, G. Vicidomini, M. Castello, A. Diaspro, and T. Cordes, “The 2015 super-resolution microscopy roadmap,” J. Phys. D 48, 443001 (2015).
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Twieg, R. J.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. USA 106, 2995–2999 (2009).
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Vanholsbeeck, F.

Vicidomini, G.

S. W. Hell, S. J. Sahl, M. Bates, X. Zhuang, R. Heintzmann, M. J. Booth, J. Bewersdorf, G. Shtengel, H. Hess, P. Tinnefeld, A. Honigmann, S. Jakobs, I. Testa, L. Cognet, B. Lounis, H. Ewers, S. J. Davis, C. Eggeling, D. Klenerman, K. I. Willig, G. Vicidomini, M. Castello, A. Diaspro, and T. Cordes, “The 2015 super-resolution microscopy roadmap,” J. Phys. D 48, 443001 (2015).
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Vigil, G. D.

Wang, C. J. R.

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

N. G. Horton, K. Wang, D. Kobat, C. G. Clark, F. W. Wise, C. B. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7, 205–209 (2013).
[Crossref]

Wang, W.

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319, 810–813 (2008).
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Supplementary Material (2)

NameDescription
» Visualization 1: AVI (11550 KB)      Demodulation PSF as excitation power increases.
» Visualization 2: AVI (7504 KB)      Resolution target imaged with SAM MPM PSFs at different excitation conditions.

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Figures (5)

Fig. 1.
Fig. 1.

Examples of [(a)–(f)] SAX PSFs and [(g)–(l)] OTFs using excitation powers of 2 × the onset of saturation. The (a, g) diffraction-limited, (b, h) DC, (c, i) 1 ω , (d, j) 2 ω , (e, k) 3 ω , (f, l) and 4 ω cases are shown. Notice the saturation broadened DC (b) and 1 ω (c) PSFs. Sub-diffraction PSFs are found in the (e)  3 ω and (f)  4 ω . High-spatial-frequency components can be seen in (j) the 2 ω and (l) the 4 ω case. OTFs are shown on a log scale color map.

Fig. 2.
Fig. 2.

Simulated harmonic magnitude at a single point in the excitation PSF with increasing saturation depth (top) and preliminary measured fluorescence experimental results (bottom). Node existence is predicted and confirmed in single point measurement.

Fig. 3.
Fig. 3.

Spatial frequency content of SAX generated PSFs in inverse radial (left) and axial (right) space across saturation depth. Diffraction limited results are equivalent to the DC spectrum at low (near 0) saturation depths. Shown on a log scale color map.

Fig. 4.
Fig. 4.

FWHM of SAX PSFs with saturation depth. Harmonic PSFs can improve image resolution by a factor of > 2 × over the diffraction limited case in both (a) the axial and (b) the radial direction.

Fig. 5.
Fig. 5.

Example of resolution targets imaged by simulated SAX PSFs. PSFs correspond to those shown in Fig. 1. Notice that finer details are available in the 3 ω and 4 ω cases compared to the diffraction limited case uniformly across the target of varying spatial frequency. In contrast, the blurring in the 2 ω case is highly non-uniform, achieving super-resolution imaging only for specific spatial frequencies.

Equations (10)

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d Δ N ( ρ , z , t ) d t + ( 2 W ( ρ , z , t ) + γ ) Δ N ( ρ , z , t ) = γ ,
Δ N ( ρ , z , t ) = exp ( 2 W ( ρ , z , t ) + γ d t ) d t γ exp ( 2 W ( ρ , z , t ) + γ d t ) ,
Δ N ( ρ , z , t ) = γ exp [ 2 σ S ( ρ , z ) 2 × A ( t ) 2 d t ] exp [ γ t ] exp [ γ t ] d t ,
Δ N ( ρ , z , t ) = exp [ 2 σ S ( ρ , z ) 2 A ( t ) 2 d t ] .
N 1 ( ρ , z , t ) = 1 2 ( 1 Δ N ( ρ , z , t ) ) .
N 1 ( ρ , z , t ) = 1 2 ( 1 exp [ 2 σ S ( ρ ) 2 A ( t ) 2 d t F m ( t ) 2 ] ) .
F m ( t ) = 1 2 ( cos ( ω m t ) + 1 ) ,
S ( ρ , z ) = 2 π w ( z ) 2 e 2 ρ 2 w ( z ) 2 ,
A ( t ) = 2 P h ν ln 2 π 1 f p α e ln 2 ( 2 ( t t 0 ) α ) 2 ,
N 1 = 1 2 ( 1 e ( 1 2 cos ( ω t ) + 1 2 ) 2 2 σ S ( ρ , z ) 2 β ) ,

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