Abstract

The problem of the propagation of narrow radiation beams in a scattering medium is considered. The previously formulated small-angle approximation solution accounting for the path length spread is further developed. The numerical scheme for practical calculations is implemented, and the simulation results are presented and discussed. Applicability of the new solution to certain problems of optical communications and data transfer techniques is shown.

© 2011 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  28. V. P. Budak and Y. A. Ilyushin, “Separation of the singular part of the light field on the basis of the small angle solutions of the transfer theory,” Atmos. Opt. 24, 93–100 (2011).
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  32. S. D. Gedzelman, M.  Á. López-Álvarez, J. Hernandez-Andrés, and R. Greenler, “Quantifying the “milky sky” experiment,” Appl. Opt. 47, H128 –H132 (2008).
    [CrossRef]
  33. N. L. Swanson, V. M. Gehman, B. D. Billard, and T. L. Gennaro, “Limits of the small-angle approximation to the radiative transport equation,” J. Opt. Soc. Am. A 18, 385–391 (2001).
    [CrossRef]
  34. N. L. Swanson, B. D. Billard, V. M. Gehman, and T. L. Gennaro, “Application of the small-angle approximation to ocean water types,” Appl. Opt. 40, 3608–3613 (2001).
    [CrossRef]
  35. R. A. Elliott, “Multiple scattering of optical pulses in scale model clouds,” Appl. Opt. 22, 2670–2681 (1983).
    [CrossRef]
  36. S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41 –R93 (1999).
    [CrossRef]
  37. F. Hanson and S. Radic, “High bandwidth underwater optical communication,” Appl. Opt. 47, 277–283 (2008).
    [CrossRef]

2011 (3)

Y. Ilyushin and V. Budak, “Analysis of the propagation of the femtosecond laser pulse in the scattering medium,” Comput. Phys. Commun. 182, 940–945 (2011).
[CrossRef]

V. P. Budak and Y. A. Ilyushin, “Separation of the singular part of the light field on the basis of the small angle solutions of the transfer theory,” Atmos. Opt. 24, 93–100 (2011).

Y. A. Ilyushin and V. P. Budak, “Narrow-beam propagation in a two-dimensional scattering medium,” J. Opt. Soc. Am. A 28, 76–81 (2011).
[CrossRef]

2010 (1)

2008 (2)

2005 (1)

V. P. Budak and A. V. Kozelskii, “Accuracy and applicability domain of the small angle approximation,” Atmos. Opt. 18, 32–37 (2005).

2001 (2)

1999 (2)

R. E. Walker and J. W. McLean, “Lidar equations for turbid media with pulse stretching,” Appl. Opt. 38, 2384–2397 (1999).
[CrossRef]

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41 –R93 (1999).
[CrossRef]

1998 (2)

1995 (1)

1990 (2)

K. K. Benke and B. H. J. McKellar, “Modulation transfer function of photographic emulsion: the small-angle approximation in radiative transfer theory,” Appl. Opt. 29, 151–156 (1990).
[CrossRef]

V. G. Peters, D. R. Wyman, M. S. Patterson, and G. L. Frank, “Optical properties of normal and diseased breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334(1990).
[CrossRef]

1989 (1)

1987 (1)

1985 (1)

1984 (1)

1983 (2)

1982 (1)

1981 (2)

1979 (3)

1977 (1)

1976 (1)

B. V. Kaul and I. V. Samokhvalov, “Double scattering approximation of the atmospheric laser location equation taking polarization effects into account,” Russ. Phys. J. 19, 64–67 (1976).
[CrossRef]

1972 (1)

1971 (1)

1963 (1)

1949 (1)

H. S. Snyder and W. T. Scott, “Multiple scattering of fast charged particles,” Phys. Rev. 76, 220–225 (1949).
[CrossRef]

Abramowitz, M.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, 1972).

Alexandrov, M. D.

Arnush, D.

Arridge, S. R.

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41 –R93 (1999).
[CrossRef]

Benke, K. K.

Billard, B. D.

Box, M. A.

Budak, V.

Y. Ilyushin and V. Budak, “Analysis of the propagation of the femtosecond laser pulse in the scattering medium,” Comput. Phys. Commun. 182, 940–945 (2011).
[CrossRef]

Budak, V. P.

V. P. Budak and Y. A. Ilyushin, “Separation of the singular part of the light field on the basis of the small angle solutions of the transfer theory,” Atmos. Opt. 24, 93–100 (2011).

Y. A. Ilyushin and V. P. Budak, “Narrow-beam propagation in a two-dimensional scattering medium,” J. Opt. Soc. Am. A 28, 76–81 (2011).
[CrossRef]

V. P. Budak and A. V. Kozelskii, “Accuracy and applicability domain of the small angle approximation,” Atmos. Opt. 18, 32–37 (2005).

Deepak, A.

Duntley, S.

Elliott, R. A.

Eloranta, E. W.

Frank, G. L.

V. G. Peters, D. R. Wyman, M. S. Patterson, and G. L. Frank, “Optical properties of normal and diseased breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334(1990).
[CrossRef]

Freeman, J. D.

Gedzelman, S. D.

Gehman, V. M.

Gennaro, T. L.

Greenler, R.

Hanson, F.

Harris, J. F. S.

Helliwell, W. S.

Hernandez-Andrés, J.

Ilyushin, Y.

Y. Ilyushin and V. Budak, “Analysis of the propagation of the femtosecond laser pulse in the scattering medium,” Comput. Phys. Commun. 182, 940–945 (2011).
[CrossRef]

Ilyushin, Y. A.

V. P. Budak and Y. A. Ilyushin, “Separation of the singular part of the light field on the basis of the small angle solutions of the transfer theory,” Atmos. Opt. 24, 93–100 (2011).

Y. A. Ilyushin and V. P. Budak, “Narrow-beam propagation in a two-dimensional scattering medium,” J. Opt. Soc. Am. A 28, 76–81 (2011).
[CrossRef]

Ishimaru, A.

Ito, S.

Kaul, B. V.

B. V. Kaul and I. V. Samokhvalov, “Double scattering approximation of the atmospheric laser location equation taking polarization effects into account,” Russ. Phys. J. 19, 64–67 (1976).
[CrossRef]

Kozelskii, A. V.

V. P. Budak and A. V. Kozelskii, “Accuracy and applicability domain of the small angle approximation,” Atmos. Opt. 18, 32–37 (2005).

Lasher, M.

López-Álvarez, M. Á.

McKellar, B. H. J.

McLean, J. W.

Morton, K. W.

R. D. Richtmyer and K. W. Morton, Difference Methods for Initial-Value Problems (Interscience, 1967).

Patterson, M. S.

V. G. Peters, D. R. Wyman, M. S. Patterson, and G. L. Frank, “Optical properties of normal and diseased breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334(1990).
[CrossRef]

Peters, V. G.

V. G. Peters, D. R. Wyman, M. S. Patterson, and G. L. Frank, “Optical properties of normal and diseased breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334(1990).
[CrossRef]

Radic, S.

Remizovich, V. S.

Richtmyer, R. D.

R. D. Richtmyer and K. W. Morton, Difference Methods for Initial-Value Problems (Interscience, 1967).

Samokhvalov, I. V.

B. V. Kaul and I. V. Samokhvalov, “Double scattering approximation of the atmospheric laser location equation taking polarization effects into account,” Russ. Phys. J. 19, 64–67 (1976).
[CrossRef]

Scott, W. T.

H. S. Snyder and W. T. Scott, “Multiple scattering of fast charged particles,” Phys. Rev. 76, 220–225 (1949).
[CrossRef]

Snyder, H. S.

H. S. Snyder and W. T. Scott, “Multiple scattering of fast charged particles,” Phys. Rev. 76, 220–225 (1949).
[CrossRef]

Sreenivasiah, I.

Stegun, I. A.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, 1972).

Stotts, L. B.

Swanson, N. L.

Tam, W. G.

Tessendorf, J.

Tsang, L.

Walker, P. L.

Walker, R. E.

Wigner, E.

E. Wigner, Group Theory and its Application to the Quantum Mechanics of Atomic Spectra (Academic, 1959).

Wyman, D. R.

V. G. Peters, D. R. Wyman, M. S. Patterson, and G. L. Frank, “Optical properties of normal and diseased breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334(1990).
[CrossRef]

Zardecki, A.

Appl. Opt. (15)

J. F. S. Harris, “Water and ice cloud discrimination by laser beam scattering,” Appl. Opt. 10, 732–737 (1971).
[CrossRef]

I. Sreenivasiah and A. Ishimaru, “Beam wave two-frequency mutual-coherence function and pulse propagation in random media: an analytic solution,” Appl. Opt. 18, 1613–1618(1979).
[CrossRef]

S. Ito, “Theory of beam light pulse propagation through thick clouds: effects of beamwidth and scatterers behind the light source on pulse broadening,” Appl. Opt. 20, 2706–2715 (1981).
[CrossRef]

W. G. Tam and A. Zardecki, “Multiple scattering corrections to the Beer-Lambert law. 1: Open detector,” Appl. Opt. 21, 2405–2412 (1982).
[CrossRef]

R. A. Elliott, “Multiple scattering of optical pulses in scale model clouds,” Appl. Opt. 22, 2670–2681 (1983).
[CrossRef]

W. G. Tam, “Aerosol backscattering of a laser beam,” Appl. Opt. 22, 2965–2969 (1983).
[CrossRef]

P. L. Walker, “Beam propagation through slab scattering media in the small angle approximation,” Appl. Opt. 26, 524–528(1987).
[CrossRef]

K. K. Benke and B. H. J. McKellar, “Modulation transfer function of photographic emulsion: the small-angle approximation in radiative transfer theory,” Appl. Opt. 29, 151–156 (1990).
[CrossRef]

E. W. Eloranta, “Practical model for the calculation of multiply scattered lidar returns,” Appl. Opt. 37, 2464–2472 (1998).
[CrossRef]

J. W. McLean, J. D. Freeman, and R. E. Walker, “Beam spread function with time dispersion,” Appl. Opt. 37, 4701–4711 (1998).
[CrossRef]

R. E. Walker and J. W. McLean, “Lidar equations for turbid media with pulse stretching,” Appl. Opt. 38, 2384–2397 (1999).
[CrossRef]

N. L. Swanson, B. D. Billard, V. M. Gehman, and T. L. Gennaro, “Application of the small-angle approximation to ocean water types,” Appl. Opt. 40, 3608–3613 (2001).
[CrossRef]

F. Hanson and S. Radic, “High bandwidth underwater optical communication,” Appl. Opt. 47, 277–283 (2008).
[CrossRef]

S. D. Gedzelman, M.  Á. López-Álvarez, J. Hernandez-Andrés, and R. Greenler, “Quantifying the “milky sky” experiment,” Appl. Opt. 47, H128 –H132 (2008).
[CrossRef]

F. Hanson and M. Lasher, “Effects of underwater turbulence on laser beam propagation and coupling into single-mode optical fiber,” Appl. Opt. 49, 3224–3230 (2010).
[CrossRef]

Atmos. Opt. (2)

V. P. Budak and Y. A. Ilyushin, “Separation of the singular part of the light field on the basis of the small angle solutions of the transfer theory,” Atmos. Opt. 24, 93–100 (2011).

V. P. Budak and A. V. Kozelskii, “Accuracy and applicability domain of the small angle approximation,” Atmos. Opt. 18, 32–37 (2005).

Comput. Phys. Commun. (1)

Y. Ilyushin and V. Budak, “Analysis of the propagation of the femtosecond laser pulse in the scattering medium,” Comput. Phys. Commun. 182, 940–945 (2011).
[CrossRef]

Inverse Probl. (1)

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41 –R93 (1999).
[CrossRef]

J. Opt. Soc. Am. (6)

J. Opt. Soc. Am. A (6)

Phys. Med. Biol. (1)

V. G. Peters, D. R. Wyman, M. S. Patterson, and G. L. Frank, “Optical properties of normal and diseased breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334(1990).
[CrossRef]

Phys. Rev. (1)

H. S. Snyder and W. T. Scott, “Multiple scattering of fast charged particles,” Phys. Rev. 76, 220–225 (1949).
[CrossRef]

Russ. Phys. J. (1)

B. V. Kaul and I. V. Samokhvalov, “Double scattering approximation of the atmospheric laser location equation taking polarization effects into account,” Russ. Phys. J. 19, 64–67 (1976).
[CrossRef]

Other (3)

R. D. Richtmyer and K. W. Morton, Difference Methods for Initial-Value Problems (Interscience, 1967).

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, 1972).

E. Wigner, Group Theory and its Application to the Quantum Mechanics of Atomic Spectra (Academic, 1959).

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