Abstract

We present a simple model to describe epifluorescence collection in two-photon microscopy when one images in a turbid slab with an objective. Bulk and surface scattering determine the spatial and angular distributions of the outgoing fluorescence photons at the slab surface, and geometrical optics determines how efficiently the photons are collected. The collection optics are parameterized by the objective’s numerical aperture and working distance and by an effective collection field of view. We identify the roles of each of these parameters and provide simple rules of thumb for the optimization of the epifluorescence collection efficiency. Analytical results are corroborated by Monte Carlo simulation.

© 2002 Optical Society of America

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References

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    [CrossRef] [PubMed]
  2. W. Denk, K. Delaney, A. Gelperin, D. Kleinfeld, B. Strowbridge, D. Tank, R. Yuste, “Anatomical and functional imaging of neurons using two-photon laser scanning microscopy,” J. Neurosci. Methods 54, 151–162 (1994).
    [CrossRef] [PubMed]
  3. E. Beaurepaire, M. Oheim, J. Mertz, “Ultra-deep two-photon fluorescence excitation in turbid media,” Opt. Commun. 188, 25–29 (2001).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  7. M. Oheim, E. Beaurepaire, E. Chaigneau, J. Mertz, S. Charpak, “Two-photon microscopy in brain tissue: parameters influencing the imaging depth,” J. Neurosci. Methods 112, 205 (2001).
    [CrossRef]
  8. V. Tuchin, Tissue Optics (SPIE, Bellingham, Washington, 2000).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  14. S. A. Prahl, M. Keijzer, S. L. Jacques, A. J. Welch, “A Monte Carlo model of light propagation in tissue,” in SPIE Proceedings of Dosimetry of Laser Radiation in Medicine and Biology, G. J. Mueller, D. H. Sliney, eds., Vol. IS05 of SPIE Institute Series (SPIE, Bellingham, Wash., 1989), pp. 102–111.

2001 (2)

E. Beaurepaire, M. Oheim, J. Mertz, “Ultra-deep two-photon fluorescence excitation in turbid media,” Opt. Commun. 188, 25–29 (2001).
[CrossRef]

M. Oheim, E. Beaurepaire, E. Chaigneau, J. Mertz, S. Charpak, “Two-photon microscopy in brain tissue: parameters influencing the imaging depth,” J. Neurosci. Methods 112, 205 (2001).
[CrossRef]

2000 (2)

1998 (1)

1994 (2)

W. Denk, K. Delaney, A. Gelperin, D. Kleinfeld, B. Strowbridge, D. Tank, R. Yuste, “Anatomical and functional imaging of neurons using two-photon laser scanning microscopy,” J. Neurosci. Methods 54, 151–162 (1994).
[CrossRef] [PubMed]

R. C. Haskell, L. O. Svaasand, T.-T. Tsay, T.-C. Feng, M. S. McAdams, B. J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. A 11, 2727–2741 (1994).
[CrossRef]

1990 (1)

W. Denk, J. H. Strickler, W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[CrossRef] [PubMed]

1989 (1)

1941 (1)

L. Henyey, J. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Alfano, R. R.

Beaurepaire, E.

M. Oheim, E. Beaurepaire, E. Chaigneau, J. Mertz, S. Charpak, “Two-photon microscopy in brain tissue: parameters influencing the imaging depth,” J. Neurosci. Methods 112, 205 (2001).
[CrossRef]

E. Beaurepaire, M. Oheim, J. Mertz, “Ultra-deep two-photon fluorescence excitation in turbid media,” Opt. Commun. 188, 25–29 (2001).
[CrossRef]

Berns, M. W.

Blanca, C. M.

Carslaw, H. S.

H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids, 2nd ed. (Oxford Science, Oxford, 1996).

Case, K. M.

K. M. Case, P. F. Zweifel, Linear Transport Theory (Addison-Wesley, Reading, Mass., 1967).

Chaigneau, E.

M. Oheim, E. Beaurepaire, E. Chaigneau, J. Mertz, S. Charpak, “Two-photon microscopy in brain tissue: parameters influencing the imaging depth,” J. Neurosci. Methods 112, 205 (2001).
[CrossRef]

Chance, B.

Charpak, S.

M. Oheim, E. Beaurepaire, E. Chaigneau, J. Mertz, S. Charpak, “Two-photon microscopy in brain tissue: parameters influencing the imaging depth,” J. Neurosci. Methods 112, 205 (2001).
[CrossRef]

Coleno, M.

Delaney, K.

W. Denk, K. Delaney, A. Gelperin, D. Kleinfeld, B. Strowbridge, D. Tank, R. Yuste, “Anatomical and functional imaging of neurons using two-photon laser scanning microscopy,” J. Neurosci. Methods 54, 151–162 (1994).
[CrossRef] [PubMed]

Denk, W.

W. Denk, K. Delaney, A. Gelperin, D. Kleinfeld, B. Strowbridge, D. Tank, R. Yuste, “Anatomical and functional imaging of neurons using two-photon laser scanning microscopy,” J. Neurosci. Methods 54, 151–162 (1994).
[CrossRef] [PubMed]

W. Denk, J. H. Strickler, W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[CrossRef] [PubMed]

Dunn, A. K.

Feng, T.-C.

R. C. Haskell, L. O. Svaasand, T.-T. Tsay, T.-C. Feng, M. S. McAdams, B. J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. A 11, 2727–2741 (1994).
[CrossRef]

Gelperin, A.

W. Denk, K. Delaney, A. Gelperin, D. Kleinfeld, B. Strowbridge, D. Tank, R. Yuste, “Anatomical and functional imaging of neurons using two-photon laser scanning microscopy,” J. Neurosci. Methods 54, 151–162 (1994).
[CrossRef] [PubMed]

Greenstein, J.

L. Henyey, J. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Haskell, R. C.

R. C. Haskell, L. O. Svaasand, T.-T. Tsay, T.-C. Feng, M. S. McAdams, B. J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. A 11, 2727–2741 (1994).
[CrossRef]

Henyey, L.

L. Henyey, J. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Jacques, S. L.

S. A. Prahl, M. Keijzer, S. L. Jacques, A. J. Welch, “A Monte Carlo model of light propagation in tissue,” in SPIE Proceedings of Dosimetry of Laser Radiation in Medicine and Biology, G. J. Mueller, D. H. Sliney, eds., Vol. IS05 of SPIE Institute Series (SPIE, Bellingham, Wash., 1989), pp. 102–111.

Jaeger, J. C.

H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids, 2nd ed. (Oxford Science, Oxford, 1996).

Keijzer, M.

S. A. Prahl, M. Keijzer, S. L. Jacques, A. J. Welch, “A Monte Carlo model of light propagation in tissue,” in SPIE Proceedings of Dosimetry of Laser Radiation in Medicine and Biology, G. J. Mueller, D. H. Sliney, eds., Vol. IS05 of SPIE Institute Series (SPIE, Bellingham, Wash., 1989), pp. 102–111.

Kleinfeld, D.

W. Denk, K. Delaney, A. Gelperin, D. Kleinfeld, B. Strowbridge, D. Tank, R. Yuste, “Anatomical and functional imaging of neurons using two-photon laser scanning microscopy,” J. Neurosci. Methods 54, 151–162 (1994).
[CrossRef] [PubMed]

Liu, F.

McAdams, M. S.

R. C. Haskell, L. O. Svaasand, T.-T. Tsay, T.-C. Feng, M. S. McAdams, B. J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. A 11, 2727–2741 (1994).
[CrossRef]

Mertz, J.

M. Oheim, E. Beaurepaire, E. Chaigneau, J. Mertz, S. Charpak, “Two-photon microscopy in brain tissue: parameters influencing the imaging depth,” J. Neurosci. Methods 112, 205 (2001).
[CrossRef]

E. Beaurepaire, M. Oheim, J. Mertz, “Ultra-deep two-photon fluorescence excitation in turbid media,” Opt. Commun. 188, 25–29 (2001).
[CrossRef]

Oheim, M.

E. Beaurepaire, M. Oheim, J. Mertz, “Ultra-deep two-photon fluorescence excitation in turbid media,” Opt. Commun. 188, 25–29 (2001).
[CrossRef]

M. Oheim, E. Beaurepaire, E. Chaigneau, J. Mertz, S. Charpak, “Two-photon microscopy in brain tissue: parameters influencing the imaging depth,” J. Neurosci. Methods 112, 205 (2001).
[CrossRef]

Patterson, M. S.

Prahl, S. A.

S. A. Prahl, M. Keijzer, S. L. Jacques, A. J. Welch, “A Monte Carlo model of light propagation in tissue,” in SPIE Proceedings of Dosimetry of Laser Radiation in Medicine and Biology, G. J. Mueller, D. H. Sliney, eds., Vol. IS05 of SPIE Institute Series (SPIE, Bellingham, Wash., 1989), pp. 102–111.

Saloma, C.

Strickler, J. H.

W. Denk, J. H. Strickler, W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[CrossRef] [PubMed]

Strowbridge, B.

W. Denk, K. Delaney, A. Gelperin, D. Kleinfeld, B. Strowbridge, D. Tank, R. Yuste, “Anatomical and functional imaging of neurons using two-photon laser scanning microscopy,” J. Neurosci. Methods 54, 151–162 (1994).
[CrossRef] [PubMed]

Svaasand, L. O.

R. C. Haskell, L. O. Svaasand, T.-T. Tsay, T.-C. Feng, M. S. McAdams, B. J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. A 11, 2727–2741 (1994).
[CrossRef]

Tank, D.

W. Denk, K. Delaney, A. Gelperin, D. Kleinfeld, B. Strowbridge, D. Tank, R. Yuste, “Anatomical and functional imaging of neurons using two-photon laser scanning microscopy,” J. Neurosci. Methods 54, 151–162 (1994).
[CrossRef] [PubMed]

Tromberg, B. J.

A. K. Dunn, V. P. Wallace, M. Coleno, M. W. Berns, B. J. Tromberg, “Influence of optical properties on two-photon fluorescence imaging in turbid samples,” Appl. Opt. 39, 1194–1201 (2000).
[CrossRef]

R. C. Haskell, L. O. Svaasand, T.-T. Tsay, T.-C. Feng, M. S. McAdams, B. J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. A 11, 2727–2741 (1994).
[CrossRef]

Tsay, T.-T.

R. C. Haskell, L. O. Svaasand, T.-T. Tsay, T.-C. Feng, M. S. McAdams, B. J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. A 11, 2727–2741 (1994).
[CrossRef]

Tuchin, V.

V. Tuchin, Tissue Optics (SPIE, Bellingham, Washington, 2000).

Wallace, V. P.

Webb, W. W.

W. Denk, J. H. Strickler, W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[CrossRef] [PubMed]

Welch, A. J.

S. A. Prahl, M. Keijzer, S. L. Jacques, A. J. Welch, “A Monte Carlo model of light propagation in tissue,” in SPIE Proceedings of Dosimetry of Laser Radiation in Medicine and Biology, G. J. Mueller, D. H. Sliney, eds., Vol. IS05 of SPIE Institute Series (SPIE, Bellingham, Wash., 1989), pp. 102–111.

Wilson, B. C.

Ying, J.

Yuste, R.

W. Denk, K. Delaney, A. Gelperin, D. Kleinfeld, B. Strowbridge, D. Tank, R. Yuste, “Anatomical and functional imaging of neurons using two-photon laser scanning microscopy,” J. Neurosci. Methods 54, 151–162 (1994).
[CrossRef] [PubMed]

Zweifel, P. F.

K. M. Case, P. F. Zweifel, Linear Transport Theory (Addison-Wesley, Reading, Mass., 1967).

Appl. Opt. (4)

Astrophys. J. (1)

L. Henyey, J. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

J. Neurosci. Methods (2)

W. Denk, K. Delaney, A. Gelperin, D. Kleinfeld, B. Strowbridge, D. Tank, R. Yuste, “Anatomical and functional imaging of neurons using two-photon laser scanning microscopy,” J. Neurosci. Methods 54, 151–162 (1994).
[CrossRef] [PubMed]

M. Oheim, E. Beaurepaire, E. Chaigneau, J. Mertz, S. Charpak, “Two-photon microscopy in brain tissue: parameters influencing the imaging depth,” J. Neurosci. Methods 112, 205 (2001).
[CrossRef]

J. Opt. Soc. A (1)

R. C. Haskell, L. O. Svaasand, T.-T. Tsay, T.-C. Feng, M. S. McAdams, B. J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. A 11, 2727–2741 (1994).
[CrossRef]

Opt. Commun. (1)

E. Beaurepaire, M. Oheim, J. Mertz, “Ultra-deep two-photon fluorescence excitation in turbid media,” Opt. Commun. 188, 25–29 (2001).
[CrossRef]

Science (1)

W. Denk, J. H. Strickler, W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[CrossRef] [PubMed]

Other (4)

V. Tuchin, Tissue Optics (SPIE, Bellingham, Washington, 2000).

K. M. Case, P. F. Zweifel, Linear Transport Theory (Addison-Wesley, Reading, Mass., 1967).

H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids, 2nd ed. (Oxford Science, Oxford, 1996).

S. A. Prahl, M. Keijzer, S. L. Jacques, A. J. Welch, “A Monte Carlo model of light propagation in tissue,” in SPIE Proceedings of Dosimetry of Laser Radiation in Medicine and Biology, G. J. Mueller, D. H. Sliney, eds., Vol. IS05 of SPIE Institute Series (SPIE, Bellingham, Wash., 1989), pp. 102–111.

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Figures (5)

Fig. 1
Fig. 1

Model parameters for epifluorescence collection. Fluorescence photons are generated from a point source of depth z 0 and exit the sample surface at positions r exit and angles θexit. Collection optics is defined by NA angle θNA, effective field-of-view radius r f , and objective working distance wd.

Fig. 2
Fig. 2

Probability distribution of the fluorescence photon exit angles for a perfectly rough surface and a perfectly smooth surface.

Fig. 3
Fig. 3

Fluorescence collection efficiency as a function of imaging depth in the diffusive regime (z 0l t ). The analytical model (see text) is compared with Monte Carlo simulations for rough and smooth surfaces. Curves are normalized to collected power P 0 for a transparent medium. (a) Low NA corresponds to sin(θNA) = 0.4; (b) moderate NA corresponds to sin(θNA) = 0.67. Thick vertical bars indicate boundaries for z 0 → 0. Distances are in micrometers.

Fig. 4
Fig. 4

Normalized fluorescence collection efficiency as a function of imaging depth for anisotropic bulk scattering and a rough sample surface. Monte Carlo simulations for different scattering conditions are compared to the analytical model derived in the diffusive limit for low NA and moderate NA. Thick vertical bars indicate boundaries for z 0 → 0. Distances are in micrometers.

Fig. 5
Fig. 5

Normalized fluorescence collection efficiency as a function of imaging depth for anisotropic bulk scattering and a smooth sample surface. Monte Carlo simulations for different scattering conditions are compared to the analytical model derived in the diffusive limit. (a) Influence of the bulk scattering parameters, with results of the diffusive model simulation shown for comparison. (b) Influence of the field of view of the collection optics. Scattering enhances the collection efficiency to a depth approximately equal to the radius of the field of view. Thick vertical bars indicate boundaries for z 0 → 0. Distances are in micrometers.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

Gr, z=Q4πDm=-1r2+2mL+z0-z21/2-1r2+2mL-z0-z21/2,
Fr, z0=D z Gr, zz=0,
Frexit, z0=Q4πm=-2mL+z0rexit2+2mL+z023/2-2mL-z0rexit2+2mL-z023/2.
Frexit, z0  Qz02πrexit2+z023/2.
Ftotal=Q1-z0/L.
rmrf+z0rOFA-rf/wd.
rmθmrfθNA.
P0=½ Q1-cos θNA.
PQ1-cosα θm1-z0rm2+z02,

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