Abstract

Two-photon fluorescence microscopy has become an indispensable tool for imaging scattering biological samples by detecting scattered fluorescence photons generated from a spatially confined excitation volume. However, this optical sectioning capability breaks down eventually when imaging much deeper, as the out-of-focus fluorescence gradually overwhelms the in-focal signal in the scattering samples. The resulting loss of image contrast defines a fundamental imaging-depth limit, which cannot be overcome by increasing excitation efficiency. Herein we propose to extend this depth limit by performing stimulated emission reduced fluorescence (SERF) microscopy in which the two-photon excited fluorescence at the focus is preferentially switched on and off by a modulated and focused laser beam that is capable of inducing stimulated emission of the fluorophores from the excited states. The resulting image, constructed from the reduced fluorescence signal, is found to exhibit a significantly improved signal-to-background contrast owing to its overall higher-order nonlinear dependence on the incident laser intensity. We demonstrate this new concept by both analytical theory and numerical simulations. For brain tissues, SERF is expected to extend the imaging depth limit of two-photon fluorescence microscopy by a factor of more than 1.8.

© 2012 OSA

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2012 (1)

P. Bianchini, B. Harke, S. Galiani, G. Vicidomini, and A. Diaspro, “Single-wavelength two-photon excitation-stimulated emission depletion (SW2PE-STED) superresolution imaging,” Proc. Natl. Acad. Sci. U.S.A.109(17), 6390–6393 (2012).
[CrossRef] [PubMed]

2011 (3)

W. Min, “Label-free optical imaging of nonfluorescent molecules by stimulated radiation,” Curr. Opin. Chem. Biol.15(6), 831–837 (2011).
[CrossRef] [PubMed]

D. Kobat, N. G. Horton, and C. Xu, “In vivo two-photon microscopy to 1.6-mm depth in mouse cortex,” J. Biomed. Opt.16(10), 106014 (2011).
[CrossRef] [PubMed]

N. J. Durr, C. T. Weisspfennig, B. A. Holfeld, and A. Ben-Yakar, “Maximum imaging depth of two-photon autofluorescence microscopy in epithelial tissues,” J. Biomed. Opt.16(2), 026008 (2011).
[CrossRef] [PubMed]

2010 (3)

N. Ji, D. E. Milkie, and E. Betzig, “Adaptive optics via pupil segmentation for high-resolution imaging in biological tissues,” Nat. Methods7(2), 141–147 (2010).
[CrossRef] [PubMed]

B. Huang, H. Babcock, and X. Zhuang, “Breaking the diffraction barrier: super-resolution imaging of cells,” Cell143(7), 1047–1058 (2010).
[CrossRef] [PubMed]

K. Isobe, A. Suda, H. Hashimoto, F. Kannari, H. Kawano, H. Mizuno, A. Miyawaki, and K. Midorikawa, “High-resolution fluorescence microscopy based on a cyclic sequential multiphoton process,” Biomed. Opt. Express1(3), 791–797 (2010).
[CrossRef] [PubMed]

2009 (3)

J. B. Ding, K. T. Takasaki, and B. L. Sabatini, “Supraresolution imaging in brain slices using stimulated-emission depletion two-photon laser scanning microscopy,” Neuron63(4), 429–437 (2009).
[CrossRef] [PubMed]

W. Min, S. Lu, S. Chong, R. Roy, G. R. Holtom, and X. S. Xie, “Imaging chromophores with undetectable fluorescence by stimulated emission microscopy,” Nature461(7267), 1105–1109 (2009).
[CrossRef] [PubMed]

S. W. Hell, “Microscopy and its focal switch,” Nat. Methods6(1), 24–32 (2009).
[CrossRef] [PubMed]

2008 (3)

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Photonics2(2), 110–115 (2008).
[CrossRef] [PubMed]

A. Leray, K. Lillis, and J. Mertz, “Enhanced background rejection in thick tissue with differential-aberration two-photon microscopy,” Biophys. J.94(4), 1449–1458 (2008).
[CrossRef] [PubMed]

N. Chen, C. H. Wong, and C. J. Sheppard, “Focal modulation microscopy,” Opt. Express16(23), 18764–18769 (2008).
[CrossRef] [PubMed]

2007 (1)

S. W. Hell, “Far-field optical nanoscopy,” Science316(5828), 1153–1158 (2007).
[CrossRef] [PubMed]

2006 (3)

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,” Science313(5793), 1642–1645 (2006).
[CrossRef] [PubMed]

M. Rueckel, J. A. Mack-Bucher, and W. Denk, “Adaptive wavefront correction in two-photon microscopy using coherence-gated wavefront sensing,” Proc. Natl. Acad. Sci. U.S.A.103(46), 17137–17142 (2006).
[CrossRef] [PubMed]

P. Theer and W. Denk, “On the fundamental imaging-depth limit in two-photon microscopy,” J. Opt. Soc. Am. A23(12), 3139–3149 (2006).
[CrossRef] [PubMed]

2005 (1)

F. Helmchen and W. Denk, “Deep tissue two-photon microscopy,” Nat. Methods2(12), 932–940 (2005).
[CrossRef] [PubMed]

2003 (1)

1999 (1)

1997 (1)

1990 (1)

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science248(4951), 73–76 (1990).
[CrossRef] [PubMed]

Alfano, R. R.

Babcock, H.

B. Huang, H. Babcock, and X. Zhuang, “Breaking the diffraction barrier: super-resolution imaging of cells,” Cell143(7), 1047–1058 (2010).
[CrossRef] [PubMed]

Ben-Yakar, A.

N. J. Durr, C. T. Weisspfennig, B. A. Holfeld, and A. Ben-Yakar, “Maximum imaging depth of two-photon autofluorescence microscopy in epithelial tissues,” J. Biomed. Opt.16(2), 026008 (2011).
[CrossRef] [PubMed]

Betzig, E.

N. Ji, D. E. Milkie, and E. Betzig, “Adaptive optics via pupil segmentation for high-resolution imaging in biological tissues,” Nat. Methods7(2), 141–147 (2010).
[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,” Science313(5793), 1642–1645 (2006).
[CrossRef] [PubMed]

Bianchini, P.

P. Bianchini, B. Harke, S. Galiani, G. Vicidomini, and A. Diaspro, “Single-wavelength two-photon excitation-stimulated emission depletion (SW2PE-STED) superresolution imaging,” Proc. Natl. Acad. Sci. U.S.A.109(17), 6390–6393 (2012).
[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,” Science313(5793), 1642–1645 (2006).
[CrossRef] [PubMed]

Chen, N.

Chong, S.

W. Min, S. Lu, S. Chong, R. Roy, G. R. Holtom, and X. S. Xie, “Imaging chromophores with undetectable fluorescence by stimulated emission microscopy,” Nature461(7267), 1105–1109 (2009).
[CrossRef] [PubMed]

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,” Science313(5793), 1642–1645 (2006).
[CrossRef] [PubMed]

Denk, W.

P. Theer and W. Denk, “On the fundamental imaging-depth limit in two-photon microscopy,” J. Opt. Soc. Am. A23(12), 3139–3149 (2006).
[CrossRef] [PubMed]

M. Rueckel, J. A. Mack-Bucher, and W. Denk, “Adaptive wavefront correction in two-photon microscopy using coherence-gated wavefront sensing,” Proc. Natl. Acad. Sci. U.S.A.103(46), 17137–17142 (2006).
[CrossRef] [PubMed]

F. Helmchen and W. Denk, “Deep tissue two-photon microscopy,” Nat. Methods2(12), 932–940 (2005).
[CrossRef] [PubMed]

P. Theer, M. T. Hasan, and W. Denk, “Two-photon imaging to a depth of 1000 μm in living brains by use of a Ti:Al2O3 regenerative amplifier,” Opt. Lett.28(12), 1022–1024 (2003).
[CrossRef] [PubMed]

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science248(4951), 73–76 (1990).
[CrossRef] [PubMed]

Diaspro, A.

P. Bianchini, B. Harke, S. Galiani, G. Vicidomini, and A. Diaspro, “Single-wavelength two-photon excitation-stimulated emission depletion (SW2PE-STED) superresolution imaging,” Proc. Natl. Acad. Sci. U.S.A.109(17), 6390–6393 (2012).
[CrossRef] [PubMed]

Ding, J. B.

J. B. Ding, K. T. Takasaki, and B. L. Sabatini, “Supraresolution imaging in brain slices using stimulated-emission depletion two-photon laser scanning microscopy,” Neuron63(4), 429–437 (2009).
[CrossRef] [PubMed]

Durr, N. J.

N. J. Durr, C. T. Weisspfennig, B. A. Holfeld, and A. Ben-Yakar, “Maximum imaging depth of two-photon autofluorescence microscopy in epithelial tissues,” J. Biomed. Opt.16(2), 026008 (2011).
[CrossRef] [PubMed]

Feld, M. S.

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Photonics2(2), 110–115 (2008).
[CrossRef] [PubMed]

Galiani, S.

P. Bianchini, B. Harke, S. Galiani, G. Vicidomini, and A. Diaspro, “Single-wavelength two-photon excitation-stimulated emission depletion (SW2PE-STED) superresolution imaging,” Proc. Natl. Acad. Sci. U.S.A.109(17), 6390–6393 (2012).
[CrossRef] [PubMed]

Harke, B.

P. Bianchini, B. Harke, S. Galiani, G. Vicidomini, and A. Diaspro, “Single-wavelength two-photon excitation-stimulated emission depletion (SW2PE-STED) superresolution imaging,” Proc. Natl. Acad. Sci. U.S.A.109(17), 6390–6393 (2012).
[CrossRef] [PubMed]

Hasan, M. T.

Hashimoto, H.

Hell, S. W.

S. W. Hell, “Microscopy and its focal switch,” Nat. Methods6(1), 24–32 (2009).
[CrossRef] [PubMed]

S. W. Hell, “Far-field optical nanoscopy,” Science316(5828), 1153–1158 (2007).
[CrossRef] [PubMed]

Helmchen, F.

F. Helmchen and W. Denk, “Deep tissue two-photon microscopy,” Nat. Methods2(12), 932–940 (2005).
[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,” Science313(5793), 1642–1645 (2006).
[CrossRef] [PubMed]

Holfeld, B. A.

N. J. Durr, C. T. Weisspfennig, B. A. Holfeld, and A. Ben-Yakar, “Maximum imaging depth of two-photon autofluorescence microscopy in epithelial tissues,” J. Biomed. Opt.16(2), 026008 (2011).
[CrossRef] [PubMed]

Holtom, G. R.

W. Min, S. Lu, S. Chong, R. Roy, G. R. Holtom, and X. S. Xie, “Imaging chromophores with undetectable fluorescence by stimulated emission microscopy,” Nature461(7267), 1105–1109 (2009).
[CrossRef] [PubMed]

Horton, N. G.

D. Kobat, N. G. Horton, and C. Xu, “In vivo two-photon microscopy to 1.6-mm depth in mouse cortex,” J. Biomed. Opt.16(10), 106014 (2011).
[CrossRef] [PubMed]

Huang, B.

B. Huang, H. Babcock, and X. Zhuang, “Breaking the diffraction barrier: super-resolution imaging of cells,” Cell143(7), 1047–1058 (2010).
[CrossRef] [PubMed]

Isobe, K.

Ji, N.

N. Ji, D. E. Milkie, and E. Betzig, “Adaptive optics via pupil segmentation for high-resolution imaging in biological tissues,” Nat. Methods7(2), 141–147 (2010).
[CrossRef] [PubMed]

Juskaitis, R.

Kannari, F.

Kawano, H.

Kobat, D.

D. Kobat, N. G. Horton, and C. Xu, “In vivo two-photon microscopy to 1.6-mm depth in mouse cortex,” J. Biomed. Opt.16(10), 106014 (2011).
[CrossRef] [PubMed]

Leray, A.

A. Leray, K. Lillis, and J. Mertz, “Enhanced background rejection in thick tissue with differential-aberration two-photon microscopy,” Biophys. J.94(4), 1449–1458 (2008).
[CrossRef] [PubMed]

Lillis, K.

A. Leray, K. Lillis, and J. Mertz, “Enhanced background rejection in thick tissue with differential-aberration two-photon microscopy,” Biophys. J.94(4), 1449–1458 (2008).
[CrossRef] [PubMed]

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,” Science313(5793), 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,” Science313(5793), 1642–1645 (2006).
[CrossRef] [PubMed]

Liu, F.

Lu, S.

W. Min, S. Lu, S. Chong, R. Roy, G. R. Holtom, and X. S. Xie, “Imaging chromophores with undetectable fluorescence by stimulated emission microscopy,” Nature461(7267), 1105–1109 (2009).
[CrossRef] [PubMed]

Mack-Bucher, J. A.

M. Rueckel, J. A. Mack-Bucher, and W. Denk, “Adaptive wavefront correction in two-photon microscopy using coherence-gated wavefront sensing,” Proc. Natl. Acad. Sci. U.S.A.103(46), 17137–17142 (2006).
[CrossRef] [PubMed]

Mertz, J.

A. Leray, K. Lillis, and J. Mertz, “Enhanced background rejection in thick tissue with differential-aberration two-photon microscopy,” Biophys. J.94(4), 1449–1458 (2008).
[CrossRef] [PubMed]

Midorikawa, K.

Milkie, D. E.

N. Ji, D. E. Milkie, and E. Betzig, “Adaptive optics via pupil segmentation for high-resolution imaging in biological tissues,” Nat. Methods7(2), 141–147 (2010).
[CrossRef] [PubMed]

Min, W.

W. Min, “Label-free optical imaging of nonfluorescent molecules by stimulated radiation,” Curr. Opin. Chem. Biol.15(6), 831–837 (2011).
[CrossRef] [PubMed]

W. Min, S. Lu, S. Chong, R. Roy, G. R. Holtom, and X. S. Xie, “Imaging chromophores with undetectable fluorescence by stimulated emission microscopy,” Nature461(7267), 1105–1109 (2009).
[CrossRef] [PubMed]

Miyawaki, A.

Mizuno, H.

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,” Science313(5793), 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,” Science313(5793), 1642–1645 (2006).
[CrossRef] [PubMed]

Psaltis, D.

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Photonics2(2), 110–115 (2008).
[CrossRef] [PubMed]

Roy, R.

W. Min, S. Lu, S. Chong, R. Roy, G. R. Holtom, and X. S. Xie, “Imaging chromophores with undetectable fluorescence by stimulated emission microscopy,” Nature461(7267), 1105–1109 (2009).
[CrossRef] [PubMed]

Rueckel, M.

M. Rueckel, J. A. Mack-Bucher, and W. Denk, “Adaptive wavefront correction in two-photon microscopy using coherence-gated wavefront sensing,” Proc. Natl. Acad. Sci. U.S.A.103(46), 17137–17142 (2006).
[CrossRef] [PubMed]

Sabatini, B. L.

J. B. Ding, K. T. Takasaki, and B. L. Sabatini, “Supraresolution imaging in brain slices using stimulated-emission depletion two-photon laser scanning microscopy,” Neuron63(4), 429–437 (2009).
[CrossRef] [PubMed]

Sheppard, C. J.

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,” Science313(5793), 1642–1645 (2006).
[CrossRef] [PubMed]

Strickler, J. H.

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science248(4951), 73–76 (1990).
[CrossRef] [PubMed]

Suda, A.

Takasaki, K. T.

J. B. Ding, K. T. Takasaki, and B. L. Sabatini, “Supraresolution imaging in brain slices using stimulated-emission depletion two-photon laser scanning microscopy,” Neuron63(4), 429–437 (2009).
[CrossRef] [PubMed]

Theer, P.

Vicidomini, G.

P. Bianchini, B. Harke, S. Galiani, G. Vicidomini, and A. Diaspro, “Single-wavelength two-photon excitation-stimulated emission depletion (SW2PE-STED) superresolution imaging,” Proc. Natl. Acad. Sci. U.S.A.109(17), 6390–6393 (2012).
[CrossRef] [PubMed]

Webb, W. W.

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science248(4951), 73–76 (1990).
[CrossRef] [PubMed]

Weisspfennig, C. T.

N. J. Durr, C. T. Weisspfennig, B. A. Holfeld, and A. Ben-Yakar, “Maximum imaging depth of two-photon autofluorescence microscopy in epithelial tissues,” J. Biomed. Opt.16(2), 026008 (2011).
[CrossRef] [PubMed]

Wilson, T.

Wong, C. H.

Xie, X. S.

W. Min, S. Lu, S. Chong, R. Roy, G. R. Holtom, and X. S. Xie, “Imaging chromophores with undetectable fluorescence by stimulated emission microscopy,” Nature461(7267), 1105–1109 (2009).
[CrossRef] [PubMed]

Xu, C.

D. Kobat, N. G. Horton, and C. Xu, “In vivo two-photon microscopy to 1.6-mm depth in mouse cortex,” J. Biomed. Opt.16(10), 106014 (2011).
[CrossRef] [PubMed]

Yang, C.

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Photonics2(2), 110–115 (2008).
[CrossRef] [PubMed]

Yaqoob, Z.

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Photonics2(2), 110–115 (2008).
[CrossRef] [PubMed]

Ying, J.

Zhuang, X.

B. Huang, H. Babcock, and X. Zhuang, “Breaking the diffraction barrier: super-resolution imaging of cells,” Cell143(7), 1047–1058 (2010).
[CrossRef] [PubMed]

Appl. Opt. (1)

Biomed. Opt. Express (1)

Biophys. J. (1)

A. Leray, K. Lillis, and J. Mertz, “Enhanced background rejection in thick tissue with differential-aberration two-photon microscopy,” Biophys. J.94(4), 1449–1458 (2008).
[CrossRef] [PubMed]

Cell (1)

B. Huang, H. Babcock, and X. Zhuang, “Breaking the diffraction barrier: super-resolution imaging of cells,” Cell143(7), 1047–1058 (2010).
[CrossRef] [PubMed]

Curr. Opin. Chem. Biol. (1)

W. Min, “Label-free optical imaging of nonfluorescent molecules by stimulated radiation,” Curr. Opin. Chem. Biol.15(6), 831–837 (2011).
[CrossRef] [PubMed]

J. Biomed. Opt. (2)

D. Kobat, N. G. Horton, and C. Xu, “In vivo two-photon microscopy to 1.6-mm depth in mouse cortex,” J. Biomed. Opt.16(10), 106014 (2011).
[CrossRef] [PubMed]

N. J. Durr, C. T. Weisspfennig, B. A. Holfeld, and A. Ben-Yakar, “Maximum imaging depth of two-photon autofluorescence microscopy in epithelial tissues,” J. Biomed. Opt.16(2), 026008 (2011).
[CrossRef] [PubMed]

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

Nat. Methods (3)

N. Ji, D. E. Milkie, and E. Betzig, “Adaptive optics via pupil segmentation for high-resolution imaging in biological tissues,” Nat. Methods7(2), 141–147 (2010).
[CrossRef] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

Demonstration of the fundamental imaging-depth limit of two-photon microscopy. (a) Under constant two-photon excitation power, volume images of a turbid gel sample doped with fluorescent beads exhibit a decreasing fluorescence signal over depth. (b) Deeper images can be acquired for the same sample when using compensating higher laser power in deeper layers. However, increasingly reduced signal-to-background ratio was observed. (c) The reduced image contrast when imaging deep inside the sample is due to the inevitable excitation of out-of-focus fluorophores. A formal definition of fundamental imaging-depth limit of two-photon microscopy is where fluorescence signal generated from in-focus and from out-of-focus are comparable.

Fig. 2
Fig. 2

(a) A simplified Jablonski diagram of a typical fluorophore under two-photon excitation and one-photon stimulated emission. (b) The intensity dependence of reduced fluorescence and residual fluorescence on the S.E. beam. τfl = 10 ns, λS.E. = 750 nm, σS.E. = =10–17 cm2.

Fig. 3
Fig. 3

Cartoon representation of the principle of SERF. Stimulated emission beam preferentially reduces the in-focus fluorescence signal over out-of-focus background fluorescence due to its intensity distribution disparity. The resulting differential signal would be mainly generated from the laser focus. Consequently, images reconstructed with the differential signal are expected to exhibit a higher contrast when comparing with original two-photon fluorescence image.

Fig. 4
Fig. 4

Proposed experimental design of SERF. (a) Absorption and fluorescence spectrum of a red emission dye candidate for SERF. Both the stimulated emission and the 2-photon excitation wavelength are in the tissue transparency window for in vivo imaging. (b) SERF setup. In addition to a standard two-photon fluorescence microscope, a modulated stimulated emission beam is combined collinearly with the two-photon excitation beam. Reduced fluorescence at each pixel is measured by a lock-in amplifier. (c) Modulation transfer scheme of SERF. The stimulated emission beam is modulated at a high frequency (>MHz), which accounts for the reduced fluorescence modulated at the same frequency after interacting with fluorophores.

Fig. 5
Fig. 5

Comparison of the fundamental imaging-depth limit between the regular two-photon imaging and SERF. (a) Using the typical parameters described in the text, the fundamental depth limit for two-photon imaging is 1023 μm at which (S/B ) 2P =1 . The yellow part beneath the curve is the integrated in-focus signal with a width of 2 μm, the red part with the z less than focus is the integrated out-of-focus background. Signal curve shown here has been normalized to the peak value of the signal. (b) The new depth limit for SERF is determined in a similar way, and is found to be 1885 μm when (S/B ) SERF =1 , extending the depth by more than 1.8 times. (c) The dependence of (S/B ) 2P as a function of the focal depth z focal between 1000 μm and 2000 μm. At the SERF extended depth limit of 1885 μm, (S/B ) 2P is only 0.001. (d) On the contrary, when at the regular 2P depth limit of 1023 μm, (S/B ) SERF is 46, which is much higher than the corresponding (S/B ) 2P =1 at this focal depth.

Equations (16)

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( S B ) 2P = V in 0 τ C S (r,z) I 2 (r,z,t)dtdV V out 0 τ C B (r,z) I 2 (r,z,t)dtdV =1
V in C S (r,z)dV V out C B (r,z)dV <<1
S 0 +2h ν exc k exc S 1 S 1 k fl S 0 +h ν fl
S 0 +2h ν exc k exc S 1 { S 1 k fl S 0 1 +h ν fl S 1 +h ν S.E. k S.E. S 0 2 +2h ν S.E.
R= f rep k exc τ exc η
R = f rep k exc τ exc η = f rep k exc τ exc η k fl k fl + k S.E.
R SERF R R = f rep k exc τ exc η k S.E. k fl + k S.E.
( S B ) SERF = V in 0 τ C S (r,z) α I S.E. (r,z) 1+α I S.E. (r,z) I exc 2 (r,z,t)dtdV V out 0 τ C B (r,z) α I S.E. (r,z) 1+α I S.E. (r,z) I exc 2 (r,z,t)dtdV
( S B ) SERF V in 0 τ C S (r,z) I S.E. (r,z) I exc 2 (r,z,t)dtdV V out 0 τ C B (r,z) I S.E. (r,z) I exc 2 (r,z,t)dtdV >1
A(z)1+ [ ( z z focal ) / z R ] 2
                P ballistic (z)= P 0 e z/ L s
( S B ) 2P z in 0 r(z) I ballistic 2 (r,z)drdz z out 0 r(z) I ballistic 2 (r,z)drdz z in [ ( P ballistic (z) A(z) ) 2 A(z)] dz z out [ ( P ballistic (z) A(z) ) 2 A(z)] dz
Q (z) 2P exp(2z/ L s ) 1+ [ ( z z focal ) / z R ] 2
( S B ) 2P z focal ε z focal +ε Q (z) 2P dz 0 z focal ε Q (z) 2P dz =1
( S B ) SERF z in 0 r(z) I ballistic 3 (r,z)drdz z out 0 r(z) I ballistic 3 (r,z)drdz z in [ ( P ballistic (z) A(z) ) 3 A(z)] dz z out [ ( P ballistic (z) A(z) ) 3 A(z)] dz
Q (z) SERF exp(3z/ L s ) ( 1+ [ (z z focal ) / z R ] 2 ) 2

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