Abstract

In this paper, we propose a new and simple method based on two-photon excitation fluorescence (TPEF) microscopy to measure the scattering coefficient µs of thick turbid media. We show, from Monte Carlo simulations, that µs can be derived from the axial profile of the ratio of the TPEF signals epi-collected by the confocal and the non-descanned ports of a scanning microscope, independently of the anisotropy factor g and of the absorption coefficient µa of the medium. The method is validated experimentally on tissue-mimicking optical phantoms, and is shown to have potential for imaging the scattering coefficient of heterogeneous media.

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  1. V. V. Tuchin, “Light scattering study of tissues,” Phys.- Usp.40(5), 495–515 (1997).
    [CrossRef]
  2. V. V. Tuchin, Handbook of Biomedical Diagnostics, PM107 (SPIE Press, 2002).
  3. L.-V. Wang and H. Wu, Biomedical Optics, Principles and Imaging (Wiley Inter-Science 2007).
  4. S. L. Jacques, B. Wang, and R. Samatham, “Reflectance confocal microscopy of optical phantoms,” Biomed. Opt. Express3(6), 1162–1172 (2012).
    [CrossRef] [PubMed]
  5. W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science248(4951), 73–76 (1990).
    [CrossRef] [PubMed]
  6. A. Leray, C. Odin, E. Huguet, F. Amblard, and Y. Le Grand, “Spatially distributed two-photon excitation fluorescence in scattering media: Experiments and time-resolved Monte Carlo simulations,” Opt. Commun.272(1), 269–278 (2007).
    [CrossRef]
  7. Y. Le Grand, A. Leray, T. Guilbert, and C. Odin, “Non-descanned versus descanned epifluorescence collection in two-photon microscopy: Experiments and Monte Carlo simulations,” Opt. Commun.281(21), 5480–5486 (2008).
    [CrossRef]
  8. E. Beaurepaire and J. Mertz, “Epifluorescence collection in two-photon microscopy,” Appl. Opt.41(25), 5376–5382 (2002).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  10. A. Leray, C. Odin, and Y. Le Grand, “Out-of-focus fluorescence collection in two-photon microscopy of scattering media,” Opt. Commun.281(24), 6139–6144 (2008).
    [CrossRef]
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    [CrossRef] [PubMed]
  12. W. R. Zipfel, R. M. Williams, and W. W. Webb, “Nonlinear magic: multiphoton microscopy in the biosciences,” Nat. Biotechnol.21(11), 1369–1377 (2003).
    [CrossRef] [PubMed]
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    [CrossRef]
  14. N. Ghosh, H. S. Patel, and P. K. Gupta, “Depolarization of light in tissue phantoms - effect of a distribution in the size of scatterers,” Opt. Express11(18), 2198–2205 (2003).
    [CrossRef] [PubMed]
  15. L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J.93, 70–83 (1941).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  20. W.-F. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron.26(12), 2166–2185 (1990).
    [CrossRef]

2012

2008

Y. Le Grand, A. Leray, T. Guilbert, and C. Odin, “Non-descanned versus descanned epifluorescence collection in two-photon microscopy: Experiments and Monte Carlo simulations,” Opt. Commun.281(21), 5480–5486 (2008).
[CrossRef]

A. Leray, C. Odin, and Y. Le Grand, “Out-of-focus fluorescence collection in two-photon microscopy of scattering media,” Opt. Commun.281(24), 6139–6144 (2008).
[CrossRef]

2007

A. Leray, C. Odin, E. Huguet, F. Amblard, and Y. Le Grand, “Spatially distributed two-photon excitation fluorescence in scattering media: Experiments and time-resolved Monte Carlo simulations,” Opt. Commun.272(1), 269–278 (2007).
[CrossRef]

S. N. Kasarova, N. G. Sultanova, C. D. Ivanov, and I. D. Nikolov, “Analysis of the dispersion of optical plastic materials,” Opt. Mater.29(11), 1481–1490 (2007).
[CrossRef]

M. Daimon and A. Masumura, “Measurement of the refractive index of distilled water from the near-infrared region to the ultraviolet region,” Appl. Opt.46(18), 3811–3820 (2007).
[CrossRef] [PubMed]

2003

W. R. Zipfel, R. M. Williams, and W. W. Webb, “Nonlinear magic: multiphoton microscopy in the biosciences,” Nat. Biotechnol.21(11), 1369–1377 (2003).
[CrossRef] [PubMed]

N. Ghosh, H. S. Patel, and P. K. Gupta, “Depolarization of light in tissue phantoms - effect of a distribution in the size of scatterers,” Opt. Express11(18), 2198–2205 (2003).
[CrossRef] [PubMed]

2002

1998

H. Szmacinski, I. Gryczynski, and J. R. Lakowicz, “Spatially localized ballistic two-photon excitation in scattering media,” Biospectroscopy4(5), 303–310 (1998).
[CrossRef] [PubMed]

S. L. Jacques, “Light distributions from point, line and plane sources for photochemical reactions and fluorescence in turbid biological tissues,” Photochem. Photobiol.67(1), 23–32 (1998).
[CrossRef] [PubMed]

1997

V. V. Tuchin, “Light scattering study of tissues,” Phys.- Usp.40(5), 495–515 (1997).
[CrossRef]

1996

C. Xu, R. M. Williams, W. Zipfel, and W. W. Webb, “Multiphoton excitation cross-sections of molecular fluorophores,” Bioimaging4(3), 198–207 (1996).
[CrossRef]

1990

W.-F. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron.26(12), 2166–2185 (1990).
[CrossRef]

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

1964

G. Marsaglia and T. A. Bray, “A Convenient Method for Generating Normal Variables,” SIAM Rev.6(3), 260–264 (1964).
[CrossRef]

1941

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

Amblard, F.

A. Leray, C. Odin, E. Huguet, F. Amblard, and Y. Le Grand, “Spatially distributed two-photon excitation fluorescence in scattering media: Experiments and time-resolved Monte Carlo simulations,” Opt. Commun.272(1), 269–278 (2007).
[CrossRef]

Beaurepaire, E.

Bray, T. A.

G. Marsaglia and T. A. Bray, “A Convenient Method for Generating Normal Variables,” SIAM Rev.6(3), 260–264 (1964).
[CrossRef]

Cheong, W.-F.

W.-F. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron.26(12), 2166–2185 (1990).
[CrossRef]

Daimon, M.

Denk, W.

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

Erickson, D.

Ghosh, N.

Greenstein, J. L.

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

Gryczynski, I.

H. Szmacinski, I. Gryczynski, and J. R. Lakowicz, “Spatially localized ballistic two-photon excitation in scattering media,” Biospectroscopy4(5), 303–310 (1998).
[CrossRef] [PubMed]

Guilbert, T.

Y. Le Grand, A. Leray, T. Guilbert, and C. Odin, “Non-descanned versus descanned epifluorescence collection in two-photon microscopy: Experiments and Monte Carlo simulations,” Opt. Commun.281(21), 5480–5486 (2008).
[CrossRef]

Gupta, P. K.

Henyey, L. G.

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

Huguet, E.

A. Leray, C. Odin, E. Huguet, F. Amblard, and Y. Le Grand, “Spatially distributed two-photon excitation fluorescence in scattering media: Experiments and time-resolved Monte Carlo simulations,” Opt. Commun.272(1), 269–278 (2007).
[CrossRef]

Ivanov, C. D.

S. N. Kasarova, N. G. Sultanova, C. D. Ivanov, and I. D. Nikolov, “Analysis of the dispersion of optical plastic materials,” Opt. Mater.29(11), 1481–1490 (2007).
[CrossRef]

Jacques, S. L.

S. L. Jacques, B. Wang, and R. Samatham, “Reflectance confocal microscopy of optical phantoms,” Biomed. Opt. Express3(6), 1162–1172 (2012).
[CrossRef] [PubMed]

S. L. Jacques, “Light distributions from point, line and plane sources for photochemical reactions and fluorescence in turbid biological tissues,” Photochem. Photobiol.67(1), 23–32 (1998).
[CrossRef] [PubMed]

Jain, A.

Kasarova, S. N.

S. N. Kasarova, N. G. Sultanova, C. D. Ivanov, and I. D. Nikolov, “Analysis of the dispersion of optical plastic materials,” Opt. Mater.29(11), 1481–1490 (2007).
[CrossRef]

Lakowicz, J. R.

H. Szmacinski, I. Gryczynski, and J. R. Lakowicz, “Spatially localized ballistic two-photon excitation in scattering media,” Biospectroscopy4(5), 303–310 (1998).
[CrossRef] [PubMed]

Le Grand, Y.

A. Leray, C. Odin, and Y. Le Grand, “Out-of-focus fluorescence collection in two-photon microscopy of scattering media,” Opt. Commun.281(24), 6139–6144 (2008).
[CrossRef]

Y. Le Grand, A. Leray, T. Guilbert, and C. Odin, “Non-descanned versus descanned epifluorescence collection in two-photon microscopy: Experiments and Monte Carlo simulations,” Opt. Commun.281(21), 5480–5486 (2008).
[CrossRef]

A. Leray, C. Odin, E. Huguet, F. Amblard, and Y. Le Grand, “Spatially distributed two-photon excitation fluorescence in scattering media: Experiments and time-resolved Monte Carlo simulations,” Opt. Commun.272(1), 269–278 (2007).
[CrossRef]

Leray, A.

Y. Le Grand, A. Leray, T. Guilbert, and C. Odin, “Non-descanned versus descanned epifluorescence collection in two-photon microscopy: Experiments and Monte Carlo simulations,” Opt. Commun.281(21), 5480–5486 (2008).
[CrossRef]

A. Leray, C. Odin, and Y. Le Grand, “Out-of-focus fluorescence collection in two-photon microscopy of scattering media,” Opt. Commun.281(24), 6139–6144 (2008).
[CrossRef]

A. Leray, C. Odin, E. Huguet, F. Amblard, and Y. Le Grand, “Spatially distributed two-photon excitation fluorescence in scattering media: Experiments and time-resolved Monte Carlo simulations,” Opt. Commun.272(1), 269–278 (2007).
[CrossRef]

Marsaglia, G.

G. Marsaglia and T. A. Bray, “A Convenient Method for Generating Normal Variables,” SIAM Rev.6(3), 260–264 (1964).
[CrossRef]

Masumura, A.

Mertz, J.

Nikolov, I. D.

S. N. Kasarova, N. G. Sultanova, C. D. Ivanov, and I. D. Nikolov, “Analysis of the dispersion of optical plastic materials,” Opt. Mater.29(11), 1481–1490 (2007).
[CrossRef]

Odin, C.

Y. Le Grand, A. Leray, T. Guilbert, and C. Odin, “Non-descanned versus descanned epifluorescence collection in two-photon microscopy: Experiments and Monte Carlo simulations,” Opt. Commun.281(21), 5480–5486 (2008).
[CrossRef]

A. Leray, C. Odin, and Y. Le Grand, “Out-of-focus fluorescence collection in two-photon microscopy of scattering media,” Opt. Commun.281(24), 6139–6144 (2008).
[CrossRef]

A. Leray, C. Odin, E. Huguet, F. Amblard, and Y. Le Grand, “Spatially distributed two-photon excitation fluorescence in scattering media: Experiments and time-resolved Monte Carlo simulations,” Opt. Commun.272(1), 269–278 (2007).
[CrossRef]

Patel, H. S.

Prahl, S. A.

W.-F. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron.26(12), 2166–2185 (1990).
[CrossRef]

Samatham, R.

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]

Sultanova, N. G.

S. N. Kasarova, N. G. Sultanova, C. D. Ivanov, and I. D. Nikolov, “Analysis of the dispersion of optical plastic materials,” Opt. Mater.29(11), 1481–1490 (2007).
[CrossRef]

Szmacinski, H.

H. Szmacinski, I. Gryczynski, and J. R. Lakowicz, “Spatially localized ballistic two-photon excitation in scattering media,” Biospectroscopy4(5), 303–310 (1998).
[CrossRef] [PubMed]

Tuchin, V. V.

V. V. Tuchin, “Light scattering study of tissues,” Phys.- Usp.40(5), 495–515 (1997).
[CrossRef]

Wang, B.

Webb, W. W.

W. R. Zipfel, R. M. Williams, and W. W. Webb, “Nonlinear magic: multiphoton microscopy in the biosciences,” Nat. Biotechnol.21(11), 1369–1377 (2003).
[CrossRef] [PubMed]

C. Xu, R. M. Williams, W. Zipfel, and W. W. Webb, “Multiphoton excitation cross-sections of molecular fluorophores,” Bioimaging4(3), 198–207 (1996).
[CrossRef]

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

Welch, A. J.

W.-F. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron.26(12), 2166–2185 (1990).
[CrossRef]

Williams, R. M.

W. R. Zipfel, R. M. Williams, and W. W. Webb, “Nonlinear magic: multiphoton microscopy in the biosciences,” Nat. Biotechnol.21(11), 1369–1377 (2003).
[CrossRef] [PubMed]

C. Xu, R. M. Williams, W. Zipfel, and W. W. Webb, “Multiphoton excitation cross-sections of molecular fluorophores,” Bioimaging4(3), 198–207 (1996).
[CrossRef]

Xu, C.

C. Xu, R. M. Williams, W. Zipfel, and W. W. Webb, “Multiphoton excitation cross-sections of molecular fluorophores,” Bioimaging4(3), 198–207 (1996).
[CrossRef]

Yang, A. H. J.

Zipfel, W.

C. Xu, R. M. Williams, W. Zipfel, and W. W. Webb, “Multiphoton excitation cross-sections of molecular fluorophores,” Bioimaging4(3), 198–207 (1996).
[CrossRef]

Zipfel, W. R.

W. R. Zipfel, R. M. Williams, and W. W. Webb, “Nonlinear magic: multiphoton microscopy in the biosciences,” Nat. Biotechnol.21(11), 1369–1377 (2003).
[CrossRef] [PubMed]

Appl. Opt.

Astrophys. J.

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

Bioimaging

C. Xu, R. M. Williams, W. Zipfel, and W. W. Webb, “Multiphoton excitation cross-sections of molecular fluorophores,” Bioimaging4(3), 198–207 (1996).
[CrossRef]

Biomed. Opt. Express

Biospectroscopy

H. Szmacinski, I. Gryczynski, and J. R. Lakowicz, “Spatially localized ballistic two-photon excitation in scattering media,” Biospectroscopy4(5), 303–310 (1998).
[CrossRef] [PubMed]

IEEE J. Quantum Electron.

W.-F. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron.26(12), 2166–2185 (1990).
[CrossRef]

Nat. Biotechnol.

W. R. Zipfel, R. M. Williams, and W. W. Webb, “Nonlinear magic: multiphoton microscopy in the biosciences,” Nat. Biotechnol.21(11), 1369–1377 (2003).
[CrossRef] [PubMed]

Opt. Commun.

A. Leray, C. Odin, E. Huguet, F. Amblard, and Y. Le Grand, “Spatially distributed two-photon excitation fluorescence in scattering media: Experiments and time-resolved Monte Carlo simulations,” Opt. Commun.272(1), 269–278 (2007).
[CrossRef]

Y. Le Grand, A. Leray, T. Guilbert, and C. Odin, “Non-descanned versus descanned epifluorescence collection in two-photon microscopy: Experiments and Monte Carlo simulations,” Opt. Commun.281(21), 5480–5486 (2008).
[CrossRef]

A. Leray, C. Odin, and Y. Le Grand, “Out-of-focus fluorescence collection in two-photon microscopy of scattering media,” Opt. Commun.281(24), 6139–6144 (2008).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Mater.

S. N. Kasarova, N. G. Sultanova, C. D. Ivanov, and I. D. Nikolov, “Analysis of the dispersion of optical plastic materials,” Opt. Mater.29(11), 1481–1490 (2007).
[CrossRef]

Photochem. Photobiol.

S. L. Jacques, “Light distributions from point, line and plane sources for photochemical reactions and fluorescence in turbid biological tissues,” Photochem. Photobiol.67(1), 23–32 (1998).
[CrossRef] [PubMed]

Phys.- Usp.

V. V. Tuchin, “Light scattering study of tissues,” Phys.- Usp.40(5), 495–515 (1997).
[CrossRef]

Science

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

SIAM Rev.

G. Marsaglia and T. A. Bray, “A Convenient Method for Generating Normal Variables,” SIAM Rev.6(3), 260–264 (1964).
[CrossRef]

Other

V. V. Tuchin, Handbook of Biomedical Diagnostics, PM107 (SPIE Press, 2002).

L.-V. Wang and H. Wu, Biomedical Optics, Principles and Imaging (Wiley Inter-Science 2007).

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Figures (9)

Fig. 1
Fig. 1

Geometry of the collection paths used in the Monte Carlo simulations and useful parameters. f: focal length of the objective; wd: working distance; θNA: numerical aperture angle; rfov: linear field of view; θ fov DS and θ fov NDS : angular field of view of the confocal (or descanned DS) and non-descanned NDS ports, respectively.

Fig. 2
Fig. 2

Monte Carlo simulations of the z-profile of collection efficiencies ηconf (pinhole 1 and 4) and ηNDS, without absorption (full lines) and with absorption µa = 10cm−1 (dashed lines), for g = 0.85 (empty square) and g = 0.95 (full triangle). The vertical scale is logarithmic and µs = 100cm−1.

Fig. 3
Fig. 3

Monte Carlo simulations of the z-profile of collection efficiencies ratio ηconfNDS for pinhole 4, without absorption (full lines) and with absorption µa = 10cm−1 (dashed lines), for g = 0.85 (empty square) and g = 0.95 (full triangle). The vertical scale is logarithmic.

Fig. 4
Fig. 4

(a) Epi-collection efficiencies for the ballistic fluorescence photons produced by two-photon excitation at focus of a water immersion objective with NA = 0.9, as a function of the imaging depth z0 in a turbid medium with various scattering coefficients. Dots were obtained from numerical integration of Eq. (3) whereas full lines are the corresponding linear regressions. (b) apparent scattering coefficient μsapp derived from curve fitting of Fig. 4(a) as function of the true scattering coefficient µs. The full line is a guide for the eye (bisector).

Fig. 5
Fig. 5

(a) Corrected scattering coefficient μ s corr from Eq. (4) versus true scattering coefficient μs ; (b) Relative error between μ s corr and μs.

Fig. 6
Fig. 6

Semi-log representation of the confocal-to-nondescanned ratios of the two-photon excitation fluorescence intensity versus imaging depth measured from six scattering gels with scattering coefficients of ~50cm−1 and ~100cm−1, and three distinct anisotropy factors (see Table 4). The confocal pinhole has a diameter of 200µm (pinhole 4). Straight lines stand for linear fits of experimental data (dots), allowing to determine the true scattering coefficients through Eq. (4).

Fig. 7
Fig. 7

(a) Confocal-to-NDS fluorescence intensity ratios as a function of the imaging depth inside a ~130cm−1 scattering gel containing polystyrene beads of 1.53µm in diameter (g = 0.93), for the four confocal pinholes of our scanning microscope and a much larger aperture. (b) Table reporting the apparent and corrected scattering coefficient for the five apertures.

Fig. 8
Fig. 8

(a) Intensities ratios versus imaging depth in the case of superposed gels with different scattering properties. Points represent the experimental data. Dash line is the fit of the ratio for the top gel, and continuous line for the bottom gel. Inserts are ~50 × 50µm2 images of the gels through the NDS pathway (left: 4.52µm beads top layer imaged at 30µm depth, right: 0.54µm beads bottom layer imaged at 90µm depth). (b) Table reporting the apparent and corrected scattering coefficient of the two layers.

Fig. 9
Fig. 9

Scattering coefficient imaging of two abreast gels. The left part is a 0.54µm beads gel with low µs, and the right part is a 4.52µm beads gel with high µs. (a) ~50 × 50µm2 image of the sample through the NDS pathway, for an imaging depth of 30µm. (b) Reconstructed scattering coefficient map. (c) Histogram of µsapp. (d) Histogram of the correlation coefficient R2. Note that 90% of the data are included within the grey areas.

Tables (5)

Tables Icon

Table 1 Slopes of the curves of Fig. 2 (in cm−1). The correlation coefficient R2 of the linear fit is shown in brackets. For pinholes 1 and 4, these values represent the apparent scattering coefficient μsapp (or attenuation coefficient in the case of absorption), obtained directly from the collection efficiency η.

Tables Icon

Table 2 Slopes of the curves of Fig. 3. The correlation coefficient R2 of the linear fit is shown in brackets. These values represent the apparent scattering coefficient μsapp, obtained from the collection efficiency ratio ηconfNDS, for pinhole 4.

Tables Icon

Table 3 Corrected scattering coefficient μscorr from the apparent scattering coefficients μsapp obtained from Monte Carlo simulations for a scattering medium with µs = 100cm−1 (see Table 2).

Tables Icon

Table 4 Microsphere diameters and concentrations, and resulting scattering properties of agarose gels used as tissue-mimicking samples. Error bars were estimated from the uncertainty on volumes taken from stock solutions of microbeads.

Tables Icon

Table 5 Scattering coefficients of agarose gel mixtures for three bead diameters, i.e. three different anisotropy factors g. The scattering coefficients are from left to right: the scattering coefficient anticipated from Mie theory (µsant), the apparent coefficient derived from the confocal-to-NDS ratio (µsapp), the corresponding scattering coefficient as obtained after correction (µscorr) and the ones obtained from the collimated transmission method (µstrans). Errors bars on the experimental scattering coefficients were obtained from statistics on two-photon images and from repetitive measurements for the collimated method.

Equations (5)

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F conf coll = f exc ( P ¯ ,τ,f,C, σ TPEF ,Φ, µ s exc , z 0 ) η conf
F NDS coll = f exc ( P ¯ ,τ,f,C, σ TPEF ,Φ, µ s exc , z 0 ) η NDS
F conf coll / F NDS coll η conf exp( µ s app z 0 )
η bal ( z 0 , μ s )= I( z 0 , μ s ) I 0 = 1 2 1 C A 1 exp( μ s z 0 u ) u 2 du
μ s corr = 2A μ s app 1+ 12 μ s app z corr B

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