Abstract

Pulsed radiation propagating through a layer of a scattering medium undergoes distortions caused by multiple scattering. The results of numerical calculations of pulse waveforms for media with different scattering phase functions are presented. It is demonstrated that the scattered radiation waveform is not described by diffusion theories even for sufficiently large optical thicknesses (τ1020) but is described, as a rule, by a bimodal distribution. Only when the optical thickness significantly increases (τ>100150), the photon distribution over the free paths acquires the unimodal diffusion form.

© 2007 Optical Society of America

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2006 (1)

N. M. Budnev, G. P. Kokhanenko, R. R. Mirgazov, and B. A. Tarashchansky, "Numerical simulation of the anomalous spatial distribution of irradiance in measurements of the absorption coefficient of Baikal water," Atmos. Ocean Opt. 19, 351-359 (2006).

2005 (1)

N. M. Budnev, G. P. Kokhanenko, M. M. Krekova, R. R. Mirgazov, I. E. Penner, B. A. Tarashansky, and V. S. Shamanaev, "Measurements of the asymmetry of aerosol scattering by observation of the light field from a point source," Atmos. Ocean Opt. 18, 109-114 (2005).

1998 (1)

1995 (2)

1994 (1)

V. A. Korshunov, L. N. Pavlova, N. P. Romanov, and V. S. Shuklin, "Experimental investigation of pulsed optical radiation transmitted through a cloud medium," Izv. Akad. Nauk SSSR , Fiz. Atmos. Okeana 30, 39-45 (1994).

1990 (2)

V. V. Vergun, E. V. Genin, G. P. Kokhanenko, V. A. Krutikov, and D. S. Mezhevoi, "Peculiarities of the temporal radiation structure in dence scattering media. P.3. Pulse waveform described in diffusion approximations," Atmos. Opt. 3, 921-928 (1990).

V. V. Korshunov, "Amplitude and temporal properties of pulsed optical radiation transferred through a cloudy layer," Atmos. Opt. 11, 1154-1158 (1990).

1988 (2)

V. V. Vergun, M. V. Kabanov, G. P. Kokhanenko, and V. A. Krutikov, "Distortion and depolarization of the optical pulse at large optical depth in the scattering medium," Atmos. Opt. 1, 97-99 (1988).

H. Leelavathi and J. P. Pichamuthu, "Propagation of optical pulses through dense scattering media," Appl. Opt. 27, 2461-2468 (1988).
[CrossRef] [PubMed]

1987 (2)

D. B. Rogozkin, "Propagation of a pulsed light beam in media with anisotropic scattering," Izv. Akad. Nauk SSSR , Fiz. Atmos. Okeana 23, 366-375 (1987).

R. F. Bonner, R. Nossal, S. Havlin, and G. H. Weiss, "Model for photon migration in turbid biological media," J. Opt. Soc. Am. 4, 423-432 (1987).
[CrossRef]

1986 (1)

A. K. Zakharov and Yu. A. Goldin, "Monte Carlo calculations of the structure of the narrow nonstationary light beam in sea water at a large optical depth," Izv. Akad. Nauk SSSR , Fiz. Atmos. Okeana 22, 533-540 (1986).

1984 (2)

V. V. Vergun, M. V. Kabanov, G. P. Kokhanenko, and V. A. Krutikov, "Numerical investigation of the space-time structure of the light field. Possibilities of the use of small-angle diffusion approximation," Dep. VINITI, Reg. No. 5645-84 (1984).

S. Ito, "Comparison of diffusion theories for optical pulse waves propagated in discrete random media," J. Opt. Soc. Am. A 1, 502-505 (1984).
[CrossRef]

1983 (3)

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

L. S. Dolin, "Parameters of the spatially bounded light beam in attenuating media with narrow scattering phase function," Izv. Akad. Nauk SSSR , Fiz. Atmos. Okeana 19, 400-404 (1983).

V. S. Remizovich, D. B. Rogozkin, and M. I. Ryazanov, "Pulse signal propagation in turbid media," Izv. Akad. Nauk SSSR , Fiz. Atmos. Okeana 19, 1053-1061 (1983).

1982 (2)

1981 (3)

1980 (4)

1979 (2)

V. N. Pelevin, A. M. Gurfink, and Yu. A. Goldin, "Influence of the scattering phase function on the nonstationary light field in the sea," Oceanology 19, 8-3 (1979).

G. C. Mooradian, M. Geller, L. B. Stotts, D. H. Stephens, and R. A. Krautwald, "Blue-green pulsed propagation through fog," Appl. Opt. 18, 429-441 (1979).
[CrossRef] [PubMed]

1978 (2)

1977 (1)

L. B. Stotts, "The radiance produced by laser radiation transferring a particulate multiple scattering medium," J. Opt. Soc. Am. A 67, 815-819 (1977).
[CrossRef]

1974 (1)

V. V. Ivanov and S. D. Gutshabash, "Propagation of a brightness wave through the optically thick atmosphere," Izv. Akad. Nauk SSSR , Fiz. Atmos. Okeana 10, 851-863 (1974).

1973 (3)

1970 (1)

L. M. Romanova, "Nonstationary light field in the boundary layer of turbid media with anisotropic scattering under illumination by a narrow beam," Izv. Akad. Nauk SSSR , Fiz. Atmos. Okeana 6, 489-498 (1970).

1969 (2)

E. P. Zege and I. L. Katsev, "Asymptotic solutions of nonstationary radiative transfer equation," Dokl. Akad. Nauk BSSR 13, 254-260 (1969).

I. L. Katsev, "Integral properties of nonstationary light scattering," Dokl. Akad. Nauk BSSR 13, 118-121 (1969).

1968 (3)

V. C. Hulst, "Radiative transfer in thick atmospheres with an arbitrary scattering function," Bull. Astron. Inst. Neth. 20, 77-85 (1968).

G. M. Krekov, G. A. Mikhailov, and B. A. Kargin, "Monte Carlo algorithms for solving the problems of narrow light beam propagation," Izv. Vyssh. Uchebn. Zaved. Fiz. 5, 54-59 (1968).

G. M. Krekov, G. A. Mikhailov, and B. A. Kargin, "Algorithms of Monte Carlo method for resolving problems of narrow beams propagation," Izv. Vyssh. Uchebn. Zaved. Fiz. 4, 5-10 (1968).

1959 (1)

I. N. Minin, "Solution of the nonstationary radiation transfer problems," Leningrad Univ. Bull. 3, 131-141 (1959).

1943 (1)

S. Chandrasekhar, "Stochastic problems in physics and astronomy," Rev. Mod. Phys. 15, 1-89 (1943).
[CrossRef]

Bonner, R. F.

R. F. Bonner, R. Nossal, S. Havlin, and G. H. Weiss, "Model for photon migration in turbid biological media," J. Opt. Soc. Am. 4, 423-432 (1987).
[CrossRef]

Bradley, R. G.

Bucher, E. A.

Budnev, N. M.

N. M. Budnev, G. P. Kokhanenko, R. R. Mirgazov, and B. A. Tarashchansky, "Numerical simulation of the anomalous spatial distribution of irradiance in measurements of the absorption coefficient of Baikal water," Atmos. Ocean Opt. 19, 351-359 (2006).

N. M. Budnev, G. P. Kokhanenko, M. M. Krekova, R. R. Mirgazov, I. E. Penner, B. A. Tarashansky, and V. S. Shamanaev, "Measurements of the asymmetry of aerosol scattering by observation of the light field from a point source," Atmos. Ocean Opt. 18, 109-114 (2005).

G. P. Kokhanenko, B. A. Tarashchansky, N. M. Budnev, and R. R. Mirgazov, "Investigations of Baikal Lake water absorption with ASP-15 device: measurement method and experimental data," Proc. SPIE 6160, 616023 (2005).

Chandrasekhar, S.

S. Chandrasekhar, "Stochastic problems in physics and astronomy," Rev. Mod. Phys. 15, 1-89 (1943).
[CrossRef]

Chievro, A. P.

Darbinyan, R. A.

G. I. Marchuk, G. A. Mikhailov, M. A. Nazaraliev, R. A. Darbinyan, B. A. Kargin, and B. S. Elepov, Monte Carlo Method in Atmospheric Optics (Nauka, 1976).

Dolin, L. S.

L. S. Dolin, "Parameters of the spatially bounded light beam in attenuating media with narrow scattering phase function," Izv. Akad. Nauk SSSR , Fiz. Atmos. Okeana 19, 400-404 (1983).

L. S. Dolin, "Small angle approximation of the radiative transfer equation in stratificated turbid media taking into account the photon distribution with free paths," Izv. Akad. Nauk SSSR , Fiz. Atmos. Okeana 16, 55-64 (1980).

Elepov, B. S.

G. I. Marchuk, G. A. Mikhailov, M. A. Nazaraliev, R. A. Darbinyan, B. A. Kargin, and B. S. Elepov, Monte Carlo Method in Atmospheric Optics (Nauka, 1976).

Elliott, R. A.

Epstein, D. J.

Freeman, J. D.

Furutsu, K.

Gashko, V. A.

Yu. A. Goldin, V. A. Gashko, G. G. Karlsen, V. N. Pelevin, and K. S. Shifrin, "Experimental investigations of nonstationary light fields in the ocean," in Hydrophysical and Hydro-optical Investigations in the Atlantic and Pacific Oceans, D. S. Monin, ed. (Nauka, 1974), pp. 228-241.

Gavrikov, V. K.

V. K. Gavrikov and V. G. Korenev, "Registration of distortion of the temporal structure of an optical pulse transmitted through an aerosol layer," Izv. Akad. Nauk SSSR , Fiz. Atmos. Okeana 17, 763-765 (1981).

Geller, M.

Genin, E. V.

V. V. Vergun, E. V. Genin, G. P. Kokhanenko, V. A. Krutikov, and D. S. Mezhevoi, "Peculiarities of the temporal radiation structure in dence scattering media. P.3. Pulse waveform described in diffusion approximations," Atmos. Opt. 3, 921-928 (1990).

Goldin, Yu. A.

A. K. Zakharov and Yu. A. Goldin, "Monte Carlo calculations of the structure of the narrow nonstationary light beam in sea water at a large optical depth," Izv. Akad. Nauk SSSR , Fiz. Atmos. Okeana 22, 533-540 (1986).

V. N. Pelevin, A. M. Gurfink, and Yu. A. Goldin, "Influence of the scattering phase function on the nonstationary light field in the sea," Oceanology 19, 8-3 (1979).

Yu. A. Goldin, V. A. Gashko, G. G. Karlsen, V. N. Pelevin, and K. S. Shifrin, "Experimental investigations of nonstationary light fields in the ocean," in Hydrophysical and Hydro-optical Investigations in the Atlantic and Pacific Oceans, D. S. Monin, ed. (Nauka, 1974), pp. 228-241.

Gurfink, A. M.

V. N. Pelevin, A. M. Gurfink, and Yu. A. Goldin, "Influence of the scattering phase function on the nonstationary light field in the sea," Oceanology 19, 8-3 (1979).

A. M. Gurfink, "Calculations of the temporal structure of the signal, recorded with the receiver with small angular aperture placed at an arbitrary point of a medium," in Light Fields in the Ocean, K. S. Shifrin, ed. (Inst. Okeanol. Akad. Nauk SSSR, Moscow, 1980), pp. 115-165.

Gutshabash, S. D.

V. V. Ivanov and S. D. Gutshabash, "Propagation of a brightness wave through the optically thick atmosphere," Izv. Akad. Nauk SSSR , Fiz. Atmos. Okeana 10, 851-863 (1974).

Hall, G. J.

Havlin, S.

R. F. Bonner, R. Nossal, S. Havlin, and G. H. Weiss, "Model for photon migration in turbid biological media," J. Opt. Soc. Am. 4, 423-432 (1987).
[CrossRef]

Hulst, V. C.

V. C. Hulst, "Radiative transfer in thick atmospheres with an arbitrary scattering function," Bull. Astron. Inst. Neth. 20, 77-85 (1968).

Ishimaru, A.

Ito, S.

Ivanov, A. P.

E. P. Zege, A. P. Ivanov, and I. L. Katsev, Image Transfer in Scattering Media (Nauka i Tekhnika, 1985).

A. P. Ivanov, Physical Principles of Hydro-optics (Nauka i Tekhnika, 1975).

Ivanov, V. V.

V. V. Ivanov and S. D. Gutshabash, "Propagation of a brightness wave through the optically thick atmosphere," Izv. Akad. Nauk SSSR , Fiz. Atmos. Okeana 10, 851-863 (1974).

Kabanov, M. V.

V. V. Vergun, M. V. Kabanov, G. P. Kokhanenko, and V. A. Krutikov, "Distortion and depolarization of the optical pulse at large optical depth in the scattering medium," Atmos. Opt. 1, 97-99 (1988).

V. V. Vergun, M. V. Kabanov, G. P. Kokhanenko, and V. A. Krutikov, "Numerical investigation of the space-time structure of the light field. Possibilities of the use of small-angle diffusion approximation," Dep. VINITI, Reg. No. 5645-84 (1984).

Kargin, B. A.

G. M. Krekov, G. A. Mikhailov, and B. A. Kargin, "Monte Carlo algorithms for solving the problems of narrow light beam propagation," Izv. Vyssh. Uchebn. Zaved. Fiz. 5, 54-59 (1968).

G. M. Krekov, G. A. Mikhailov, and B. A. Kargin, "Algorithms of Monte Carlo method for resolving problems of narrow beams propagation," Izv. Vyssh. Uchebn. Zaved. Fiz. 4, 5-10 (1968).

G. I. Marchuk, G. A. Mikhailov, M. A. Nazaraliev, R. A. Darbinyan, B. A. Kargin, and B. S. Elepov, Monte Carlo Method in Atmospheric Optics (Nauka, 1976).

Karlsen, G. G.

Yu. A. Goldin, V. A. Gashko, G. G. Karlsen, V. N. Pelevin, and K. S. Shifrin, "Experimental investigations of nonstationary light fields in the ocean," in Hydrophysical and Hydro-optical Investigations in the Atlantic and Pacific Oceans, D. S. Monin, ed. (Nauka, 1974), pp. 228-241.

Katsev, I. L.

E. P. Zege, I. L. Katsev, and I. D. Sherbaf, "Space-time structure of the light field from the point source," Izv. Akad. Nauk SSSR , Fiz. Atmos. Okeana 9, 937-946 (1973).

E. P. Zege and I. L. Katsev, "Asymptotic solutions of nonstationary radiative transfer equation," Dokl. Akad. Nauk BSSR 13, 254-260 (1969).

I. L. Katsev, "Integral properties of nonstationary light scattering," Dokl. Akad. Nauk BSSR 13, 118-121 (1969).

E. P. Zege, A. P. Ivanov, and I. L. Katsev, Image Transfer in Scattering Media (Nauka i Tekhnika, 1985).

Kennedy, R. S.

Kokhanenko, G. P.

N. M. Budnev, G. P. Kokhanenko, R. R. Mirgazov, and B. A. Tarashchansky, "Numerical simulation of the anomalous spatial distribution of irradiance in measurements of the absorption coefficient of Baikal water," Atmos. Ocean Opt. 19, 351-359 (2006).

N. M. Budnev, G. P. Kokhanenko, M. M. Krekova, R. R. Mirgazov, I. E. Penner, B. A. Tarashansky, and V. S. Shamanaev, "Measurements of the asymmetry of aerosol scattering by observation of the light field from a point source," Atmos. Ocean Opt. 18, 109-114 (2005).

V. V. Vergun, E. V. Genin, G. P. Kokhanenko, V. A. Krutikov, and D. S. Mezhevoi, "Peculiarities of the temporal radiation structure in dence scattering media. P.3. Pulse waveform described in diffusion approximations," Atmos. Opt. 3, 921-928 (1990).

V. V. Vergun, M. V. Kabanov, G. P. Kokhanenko, and V. A. Krutikov, "Distortion and depolarization of the optical pulse at large optical depth in the scattering medium," Atmos. Opt. 1, 97-99 (1988).

V. V. Vergun, M. V. Kabanov, G. P. Kokhanenko, and V. A. Krutikov, "Numerical investigation of the space-time structure of the light field. Possibilities of the use of small-angle diffusion approximation," Dep. VINITI, Reg. No. 5645-84 (1984).

G. P. Kokhanenko, B. A. Tarashchansky, N. M. Budnev, and R. R. Mirgazov, "Investigations of Baikal Lake water absorption with ASP-15 device: measurement method and experimental data," Proc. SPIE 6160, 616023 (2005).

G. P. Kokhanenko and V. A. Krutikov, "Temporal structure of the signal in scattering media illuminated with an isotropic source," in Abstracts of Seminar on Numerical Methods of Solution of the Radiative Transfer Equation, G. Berezenkova, ed. (Akad. Nauk Est. SSR, Tartu, 1988), pp. 98-101.

Korenev, V. G.

V. K. Gavrikov and V. G. Korenev, "Registration of distortion of the temporal structure of an optical pulse transmitted through an aerosol layer," Izv. Akad. Nauk SSSR , Fiz. Atmos. Okeana 17, 763-765 (1981).

Korshunov, V. A.

V. A. Korshunov, L. N. Pavlova, N. P. Romanov, and V. S. Shuklin, "Experimental investigation of pulsed optical radiation transmitted through a cloud medium," Izv. Akad. Nauk SSSR , Fiz. Atmos. Okeana 30, 39-45 (1994).

Korshunov, V. V.

V. V. Korshunov, "Amplitude and temporal properties of pulsed optical radiation transferred through a cloudy layer," Atmos. Opt. 11, 1154-1158 (1990).

Krautwald, R. A.

Krekov, G. M.

G. M. Krekov, G. A. Mikhailov, and B. A. Kargin, "Algorithms of Monte Carlo method for resolving problems of narrow beams propagation," Izv. Vyssh. Uchebn. Zaved. Fiz. 4, 5-10 (1968).

G. M. Krekov, G. A. Mikhailov, and B. A. Kargin, "Monte Carlo algorithms for solving the problems of narrow light beam propagation," Izv. Vyssh. Uchebn. Zaved. Fiz. 5, 54-59 (1968).

Krekova, M. M.

N. M. Budnev, G. P. Kokhanenko, M. M. Krekova, R. R. Mirgazov, I. E. Penner, B. A. Tarashansky, and V. S. Shamanaev, "Measurements of the asymmetry of aerosol scattering by observation of the light field from a point source," Atmos. Ocean Opt. 18, 109-114 (2005).

Krutikov, V. A.

V. V. Vergun, E. V. Genin, G. P. Kokhanenko, V. A. Krutikov, and D. S. Mezhevoi, "Peculiarities of the temporal radiation structure in dence scattering media. P.3. Pulse waveform described in diffusion approximations," Atmos. Opt. 3, 921-928 (1990).

V. V. Vergun, M. V. Kabanov, G. P. Kokhanenko, and V. A. Krutikov, "Distortion and depolarization of the optical pulse at large optical depth in the scattering medium," Atmos. Opt. 1, 97-99 (1988).

V. V. Vergun, M. V. Kabanov, G. P. Kokhanenko, and V. A. Krutikov, "Numerical investigation of the space-time structure of the light field. Possibilities of the use of small-angle diffusion approximation," Dep. VINITI, Reg. No. 5645-84 (1984).

G. P. Kokhanenko and V. A. Krutikov, "Temporal structure of the signal in scattering media illuminated with an isotropic source," in Abstracts of Seminar on Numerical Methods of Solution of the Radiative Transfer Equation, G. Berezenkova, ed. (Akad. Nauk Est. SSR, Tartu, 1988), pp. 98-101.

Leelavathi, H.

Lerner, R. M.

Lutomirski, R. F.

Marchuk, G. I.

G. I. Marchuk, G. A. Mikhailov, M. A. Nazaraliev, R. A. Darbinyan, B. A. Kargin, and B. S. Elepov, Monte Carlo Method in Atmospheric Optics (Nauka, 1976).

Matter, J. C.

McLean, J. W.

Mezhevoi, D. S.

V. V. Vergun, E. V. Genin, G. P. Kokhanenko, V. A. Krutikov, and D. S. Mezhevoi, "Peculiarities of the temporal radiation structure in dence scattering media. P.3. Pulse waveform described in diffusion approximations," Atmos. Opt. 3, 921-928 (1990).

Mikhailov, G. A.

G. M. Krekov, G. A. Mikhailov, and B. A. Kargin, "Algorithms of Monte Carlo method for resolving problems of narrow beams propagation," Izv. Vyssh. Uchebn. Zaved. Fiz. 4, 5-10 (1968).

G. M. Krekov, G. A. Mikhailov, and B. A. Kargin, "Monte Carlo algorithms for solving the problems of narrow light beam propagation," Izv. Vyssh. Uchebn. Zaved. Fiz. 5, 54-59 (1968).

G. I. Marchuk, G. A. Mikhailov, M. A. Nazaraliev, R. A. Darbinyan, B. A. Kargin, and B. S. Elepov, Monte Carlo Method in Atmospheric Optics (Nauka, 1976).

Minin, I. N.

I. N. Minin, "Solution of the nonstationary radiation transfer problems," Leningrad Univ. Bull. 3, 131-141 (1959).

Mirgazov, R. R.

N. M. Budnev, G. P. Kokhanenko, R. R. Mirgazov, and B. A. Tarashchansky, "Numerical simulation of the anomalous spatial distribution of irradiance in measurements of the absorption coefficient of Baikal water," Atmos. Ocean Opt. 19, 351-359 (2006).

N. M. Budnev, G. P. Kokhanenko, M. M. Krekova, R. R. Mirgazov, I. E. Penner, B. A. Tarashansky, and V. S. Shamanaev, "Measurements of the asymmetry of aerosol scattering by observation of the light field from a point source," Atmos. Ocean Opt. 18, 109-114 (2005).

G. P. Kokhanenko, B. A. Tarashchansky, N. M. Budnev, and R. R. Mirgazov, "Investigations of Baikal Lake water absorption with ASP-15 device: measurement method and experimental data," Proc. SPIE 6160, 616023 (2005).

Mooradian, G. C.

Nazaraliev, M. A.

G. I. Marchuk, G. A. Mikhailov, M. A. Nazaraliev, R. A. Darbinyan, B. A. Kargin, and B. S. Elepov, Monte Carlo Method in Atmospheric Optics (Nauka, 1976).

Nossal, R.

R. F. Bonner, R. Nossal, S. Havlin, and G. H. Weiss, "Model for photon migration in turbid biological media," J. Opt. Soc. Am. 4, 423-432 (1987).
[CrossRef]

Paik, W. H.

Pavlova, L. N.

V. A. Korshunov, L. N. Pavlova, N. P. Romanov, and V. S. Shuklin, "Experimental investigation of pulsed optical radiation transmitted through a cloud medium," Izv. Akad. Nauk SSSR , Fiz. Atmos. Okeana 30, 39-45 (1994).

Pelevin, V. N.

V. N. Pelevin, A. M. Gurfink, and Yu. A. Goldin, "Influence of the scattering phase function on the nonstationary light field in the sea," Oceanology 19, 8-3 (1979).

Yu. A. Goldin, V. A. Gashko, G. G. Karlsen, V. N. Pelevin, and K. S. Shifrin, "Experimental investigations of nonstationary light fields in the ocean," in Hydrophysical and Hydro-optical Investigations in the Atlantic and Pacific Oceans, D. S. Monin, ed. (Nauka, 1974), pp. 228-241.

Penner, I. E.

N. M. Budnev, G. P. Kokhanenko, M. M. Krekova, R. R. Mirgazov, I. E. Penner, B. A. Tarashansky, and V. S. Shamanaev, "Measurements of the asymmetry of aerosol scattering by observation of the light field from a point source," Atmos. Ocean Opt. 18, 109-114 (2005).

Pichamuthu, J. P.

Remizovich, V. S.

V. S. Remizovich, D. B. Rogozkin, and M. I. Ryazanov, "Pulse signal propagation in turbid media," Izv. Akad. Nauk SSSR , Fiz. Atmos. Okeana 19, 1053-1061 (1983).

Rogozkin, D. B.

D. B. Rogozkin, "Propagation of a pulsed light beam in media with anisotropic scattering," Izv. Akad. Nauk SSSR , Fiz. Atmos. Okeana 23, 366-375 (1987).

V. S. Remizovich, D. B. Rogozkin, and M. I. Ryazanov, "Pulse signal propagation in turbid media," Izv. Akad. Nauk SSSR , Fiz. Atmos. Okeana 19, 1053-1061 (1983).

Romanov, N. P.

V. A. Korshunov, L. N. Pavlova, N. P. Romanov, and V. S. Shuklin, "Experimental investigation of pulsed optical radiation transmitted through a cloud medium," Izv. Akad. Nauk SSSR , Fiz. Atmos. Okeana 30, 39-45 (1994).

Romanova, L. M.

L. M. Romanova, "Nonstationary light field in the boundary layer of turbid media with anisotropic scattering under illumination by a narrow beam," Izv. Akad. Nauk SSSR , Fiz. Atmos. Okeana 6, 489-498 (1970).

Ryazanov, M. I.

V. S. Remizovich, D. B. Rogozkin, and M. I. Ryazanov, "Pulse signal propagation in turbid media," Izv. Akad. Nauk SSSR , Fiz. Atmos. Okeana 19, 1053-1061 (1983).

Shamanaev, V. S.

N. M. Budnev, G. P. Kokhanenko, M. M. Krekova, R. R. Mirgazov, I. E. Penner, B. A. Tarashansky, and V. S. Shamanaev, "Measurements of the asymmetry of aerosol scattering by observation of the light field from a point source," Atmos. Ocean Opt. 18, 109-114 (2005).

Shapiro, J. H.

Sherbaf, I. D.

E. P. Zege, I. L. Katsev, and I. D. Sherbaf, "Space-time structure of the light field from the point source," Izv. Akad. Nauk SSSR , Fiz. Atmos. Okeana 9, 937-946 (1973).

Shifrin, K. S.

Yu. A. Goldin, V. A. Gashko, G. G. Karlsen, V. N. Pelevin, and K. S. Shifrin, "Experimental investigations of nonstationary light fields in the ocean," in Hydrophysical and Hydro-optical Investigations in the Atlantic and Pacific Oceans, D. S. Monin, ed. (Nauka, 1974), pp. 228-241.

Shimizu, K.

Shuklin, V. S.

V. A. Korshunov, L. N. Pavlova, N. P. Romanov, and V. S. Shuklin, "Experimental investigation of pulsed optical radiation transmitted through a cloud medium," Izv. Akad. Nauk SSSR , Fiz. Atmos. Okeana 30, 39-45 (1994).

Smelov, V. V.

V. V. Smelov, Lectures on the Neutron Transfer Theory (Atomizdat, 1978).

Sobolev, V. V.

V. V. Sobolev, Scattering of Light in the Planet Atmospheres (Nauka, 1972).

Stephens, D. H.

Stotts, L. B.

G. C. Mooradian, M. Geller, L. B. Stotts, D. H. Stephens, and R. A. Krautwald, "Blue-green pulsed propagation through fog," Appl. Opt. 18, 429-441 (1979).
[CrossRef] [PubMed]

L. B. Stotts, "The radiance produced by laser radiation transferring a particulate multiple scattering medium," J. Opt. Soc. Am. A 67, 815-819 (1977).
[CrossRef]

Summers, J. D.

Tarashansky, B. A.

N. M. Budnev, G. P. Kokhanenko, M. M. Krekova, R. R. Mirgazov, I. E. Penner, B. A. Tarashansky, and V. S. Shamanaev, "Measurements of the asymmetry of aerosol scattering by observation of the light field from a point source," Atmos. Ocean Opt. 18, 109-114 (2005).

Tarashchansky, B. A.

N. M. Budnev, G. P. Kokhanenko, R. R. Mirgazov, and B. A. Tarashchansky, "Numerical simulation of the anomalous spatial distribution of irradiance in measurements of the absorption coefficient of Baikal water," Atmos. Ocean Opt. 19, 351-359 (2006).

G. P. Kokhanenko, B. A. Tarashchansky, N. M. Budnev, and R. R. Mirgazov, "Investigations of Baikal Lake water absorption with ASP-15 device: measurement method and experimental data," Proc. SPIE 6160, 616023 (2005).

Tebyani, M.

Vergun, V. V.

V. V. Vergun, E. V. Genin, G. P. Kokhanenko, V. A. Krutikov, and D. S. Mezhevoi, "Peculiarities of the temporal radiation structure in dence scattering media. P.3. Pulse waveform described in diffusion approximations," Atmos. Opt. 3, 921-928 (1990).

V. V. Vergun, M. V. Kabanov, G. P. Kokhanenko, and V. A. Krutikov, "Distortion and depolarization of the optical pulse at large optical depth in the scattering medium," Atmos. Opt. 1, 97-99 (1988).

V. V. Vergun, M. V. Kabanov, G. P. Kokhanenko, and V. A. Krutikov, "Numerical investigation of the space-time structure of the light field. Possibilities of the use of small-angle diffusion approximation," Dep. VINITI, Reg. No. 5645-84 (1984).

Walker, R. E.

Weiskopf, V. F.

V. F. Weiskopf, in The Science and Engineering of Nuclear Power, C.Goodman, ed. (Addison-Wesley, 1947), pp. 87-97.

Weiss, G. H.

R. F. Bonner, R. Nossal, S. Havlin, and G. H. Weiss, "Model for photon migration in turbid biological media," J. Opt. Soc. Am. 4, 423-432 (1987).
[CrossRef]

Zakharov, A. K.

A. K. Zakharov and Yu. A. Goldin, "Monte Carlo calculations of the structure of the narrow nonstationary light beam in sea water at a large optical depth," Izv. Akad. Nauk SSSR , Fiz. Atmos. Okeana 22, 533-540 (1986).

Zege, E. P.

E. P. Zege, I. L. Katsev, and I. D. Sherbaf, "Space-time structure of the light field from the point source," Izv. Akad. Nauk SSSR , Fiz. Atmos. Okeana 9, 937-946 (1973).

E. P. Zege and I. L. Katsev, "Asymptotic solutions of nonstationary radiative transfer equation," Dokl. Akad. Nauk BSSR 13, 254-260 (1969).

E. P. Zege, A. P. Ivanov, and I. L. Katsev, Image Transfer in Scattering Media (Nauka i Tekhnika, 1985).

Appl. Opt. (13)

E. A. Bucher, "Computer simulation of light pulse propagation for communication through thick clouds," Appl. Opt. 12, 2391-2400 (1973).
[CrossRef] [PubMed]

E. A. Bucher and R. M. Lerner, "Experiments on light pulse communications and propagations through atmospheric clouds," Appl. Opt. 12, 2401-2414 (1973).
[CrossRef] [PubMed]

W. H. Paik, M. Tebyani, D. J. Epstein, R. S. Kennedy, and J. H. Shapiro, "Propagation experiments in low-visibility atmospheres," Appl. Opt. 17, 899-905 (1978).
[CrossRef] [PubMed]

G. C. Mooradian, M. Geller, L. B. Stotts, D. H. Stephens, and R. A. Krautwald, "Blue-green pulsed propagation through fog," Appl. Opt. 18, 429-441 (1979).
[CrossRef] [PubMed]

J. C. Matter and R. G. Bradley, "Optical pulse propagation through clouds," Appl. Opt. 20, 2220-2229 (1981).
[CrossRef] [PubMed]

S. Ito, "Theory of beam light pulse propagation through thick clouds: effect of beam width and scatterers behind the light source on pulse broadening," Appl. Opt. 20, 2706-2715 (1981).
[CrossRef] [PubMed]

R. M. Lerner and J. D. Summers, "Monte Carlo description of time- and space-resolved multiple forward scatter in natural water," Appl. Opt. 21, 861-869 (1982).
[CrossRef] [PubMed]

G. C. Mooradian and M. Geller, "Temporal and angular spreading of blue-green pulses in clouds," Appl. Opt. 21, 1572-1577 (1982).
[CrossRef] [PubMed]

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

H. Leelavathi and J. P. Pichamuthu, "Propagation of optical pulses through dense scattering media," Appl. Opt. 27, 2461-2468 (1988).
[CrossRef] [PubMed]

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

R. F. Lutomirski, A. P. Chievro, and G. J. Hall, "Moments of multiple scattering," Appl. Opt. 34, 7125-7136 (1995).
[CrossRef] [PubMed]

A. P. Chievro, "Propagation through optically thick media," Appl. Opt. 34, 7137-7148 (1995).
[CrossRef]

Atmos. Ocean Opt. (2)

N. M. Budnev, G. P. Kokhanenko, M. M. Krekova, R. R. Mirgazov, I. E. Penner, B. A. Tarashansky, and V. S. Shamanaev, "Measurements of the asymmetry of aerosol scattering by observation of the light field from a point source," Atmos. Ocean Opt. 18, 109-114 (2005).

N. M. Budnev, G. P. Kokhanenko, R. R. Mirgazov, and B. A. Tarashchansky, "Numerical simulation of the anomalous spatial distribution of irradiance in measurements of the absorption coefficient of Baikal water," Atmos. Ocean Opt. 19, 351-359 (2006).

Atmos. Opt. (3)

V. V. Vergun, M. V. Kabanov, G. P. Kokhanenko, and V. A. Krutikov, "Distortion and depolarization of the optical pulse at large optical depth in the scattering medium," Atmos. Opt. 1, 97-99 (1988).

V. V. Korshunov, "Amplitude and temporal properties of pulsed optical radiation transferred through a cloudy layer," Atmos. Opt. 11, 1154-1158 (1990).

V. V. Vergun, E. V. Genin, G. P. Kokhanenko, V. A. Krutikov, and D. S. Mezhevoi, "Peculiarities of the temporal radiation structure in dence scattering media. P.3. Pulse waveform described in diffusion approximations," Atmos. Opt. 3, 921-928 (1990).

Bull. Astron. Inst. Neth. (1)

V. C. Hulst, "Radiative transfer in thick atmospheres with an arbitrary scattering function," Bull. Astron. Inst. Neth. 20, 77-85 (1968).

Dokl. Akad. Nauk BSSR (2)

I. L. Katsev, "Integral properties of nonstationary light scattering," Dokl. Akad. Nauk BSSR 13, 118-121 (1969).

E. P. Zege and I. L. Katsev, "Asymptotic solutions of nonstationary radiative transfer equation," Dokl. Akad. Nauk BSSR 13, 254-260 (1969).

Izv. Akad. Nauk SSSR (10)

L. M. Romanova, "Nonstationary light field in the boundary layer of turbid media with anisotropic scattering under illumination by a narrow beam," Izv. Akad. Nauk SSSR , Fiz. Atmos. Okeana 6, 489-498 (1970).

L. S. Dolin, "Small angle approximation of the radiative transfer equation in stratificated turbid media taking into account the photon distribution with free paths," Izv. Akad. Nauk SSSR , Fiz. Atmos. Okeana 16, 55-64 (1980).

E. P. Zege, I. L. Katsev, and I. D. Sherbaf, "Space-time structure of the light field from the point source," Izv. Akad. Nauk SSSR , Fiz. Atmos. Okeana 9, 937-946 (1973).

V. V. Ivanov and S. D. Gutshabash, "Propagation of a brightness wave through the optically thick atmosphere," Izv. Akad. Nauk SSSR , Fiz. Atmos. Okeana 10, 851-863 (1974).

L. S. Dolin, "Parameters of the spatially bounded light beam in attenuating media with narrow scattering phase function," Izv. Akad. Nauk SSSR , Fiz. Atmos. Okeana 19, 400-404 (1983).

V. S. Remizovich, D. B. Rogozkin, and M. I. Ryazanov, "Pulse signal propagation in turbid media," Izv. Akad. Nauk SSSR , Fiz. Atmos. Okeana 19, 1053-1061 (1983).

D. B. Rogozkin, "Propagation of a pulsed light beam in media with anisotropic scattering," Izv. Akad. Nauk SSSR , Fiz. Atmos. Okeana 23, 366-375 (1987).

V. A. Korshunov, L. N. Pavlova, N. P. Romanov, and V. S. Shuklin, "Experimental investigation of pulsed optical radiation transmitted through a cloud medium," Izv. Akad. Nauk SSSR , Fiz. Atmos. Okeana 30, 39-45 (1994).

V. K. Gavrikov and V. G. Korenev, "Registration of distortion of the temporal structure of an optical pulse transmitted through an aerosol layer," Izv. Akad. Nauk SSSR , Fiz. Atmos. Okeana 17, 763-765 (1981).

A. K. Zakharov and Yu. A. Goldin, "Monte Carlo calculations of the structure of the narrow nonstationary light beam in sea water at a large optical depth," Izv. Akad. Nauk SSSR , Fiz. Atmos. Okeana 22, 533-540 (1986).

Izv. Vyssh. Uchebn. Zaved. Fiz. (2)

G. M. Krekov, G. A. Mikhailov, and B. A. Kargin, "Algorithms of Monte Carlo method for resolving problems of narrow beams propagation," Izv. Vyssh. Uchebn. Zaved. Fiz. 4, 5-10 (1968).

G. M. Krekov, G. A. Mikhailov, and B. A. Kargin, "Monte Carlo algorithms for solving the problems of narrow light beam propagation," Izv. Vyssh. Uchebn. Zaved. Fiz. 5, 54-59 (1968).

J. Opt. Soc. Am. (4)

J. Opt. Soc. Am. A (2)

L. B. Stotts, "The radiance produced by laser radiation transferring a particulate multiple scattering medium," J. Opt. Soc. Am. A 67, 815-819 (1977).
[CrossRef]

S. Ito, "Comparison of diffusion theories for optical pulse waves propagated in discrete random media," J. Opt. Soc. Am. A 1, 502-505 (1984).
[CrossRef]

Leningrad Univ. Bull. (1)

I. N. Minin, "Solution of the nonstationary radiation transfer problems," Leningrad Univ. Bull. 3, 131-141 (1959).

Oceanology (1)

V. N. Pelevin, A. M. Gurfink, and Yu. A. Goldin, "Influence of the scattering phase function on the nonstationary light field in the sea," Oceanology 19, 8-3 (1979).

Opt. Lett. (1)

Proc. SPIE (1)

G. P. Kokhanenko, B. A. Tarashchansky, N. M. Budnev, and R. R. Mirgazov, "Investigations of Baikal Lake water absorption with ASP-15 device: measurement method and experimental data," Proc. SPIE 6160, 616023 (2005).

Rev. Mod. Phys. (1)

S. Chandrasekhar, "Stochastic problems in physics and astronomy," Rev. Mod. Phys. 15, 1-89 (1943).
[CrossRef]

Other (12)

V. V. Smelov, Lectures on the Neutron Transfer Theory (Atomizdat, 1978).

V. F. Weiskopf, in The Science and Engineering of Nuclear Power, C.Goodman, ed. (Addison-Wesley, 1947), pp. 87-97.

A. Ishimaru, Wave Propagation and Scattering in Random Media. Vol. 1. Single Scattering and Transport Theory (Academic, 1978).

E. P. Zege, A. P. Ivanov, and I. L. Katsev, Image Transfer in Scattering Media (Nauka i Tekhnika, 1985).

V. V. Sobolev, Scattering of Light in the Planet Atmospheres (Nauka, 1972).

A. P. Ivanov, Physical Principles of Hydro-optics (Nauka i Tekhnika, 1975).

V. V. Vergun, M. V. Kabanov, G. P. Kokhanenko, and V. A. Krutikov, "Numerical investigation of the space-time structure of the light field. Possibilities of the use of small-angle diffusion approximation," Dep. VINITI, Reg. No. 5645-84 (1984).

M. N. Gorshkov and M. A. Nazaraliev, "Some Monte Carlo algorithms for solving problems of point isotropic source radiation transfer in the atmosphere," in Monte Carlo Methods in Computational Mathematics and Mathematical Physics, G. I. Marchuk, ed. (Nauka, 1979), pp. 5-14.

Yu. A. Goldin, V. A. Gashko, G. G. Karlsen, V. N. Pelevin, and K. S. Shifrin, "Experimental investigations of nonstationary light fields in the ocean," in Hydrophysical and Hydro-optical Investigations in the Atlantic and Pacific Oceans, D. S. Monin, ed. (Nauka, 1974), pp. 228-241.

G. I. Marchuk, G. A. Mikhailov, M. A. Nazaraliev, R. A. Darbinyan, B. A. Kargin, and B. S. Elepov, Monte Carlo Method in Atmospheric Optics (Nauka, 1976).

A. M. Gurfink, "Calculations of the temporal structure of the signal, recorded with the receiver with small angular aperture placed at an arbitrary point of a medium," in Light Fields in the Ocean, K. S. Shifrin, ed. (Inst. Okeanol. Akad. Nauk SSSR, Moscow, 1980), pp. 115-165.

G. P. Kokhanenko and V. A. Krutikov, "Temporal structure of the signal in scattering media illuminated with an isotropic source," in Abstracts of Seminar on Numerical Methods of Solution of the Radiative Transfer Equation, G. Berezenkova, ed. (Akad. Nauk Est. SSR, Tartu, 1988), pp. 98-101.

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Figures (5)

Fig. 1
Fig. 1

Results of experimental observations of the light pulse broadening. Here symbols indicate the references: 1 was borrowed from [38], 2 and 3 from [43] for different scattering media, 4 from [45], 5 from [47], 6 and 7 from [49] for two polarized components, 8 from [41], 9 from [39], 10 from [42], 11 from [40], and 12 from [44].

Fig. 2
Fig. 2

Pulse waveforms for media with the normalized scattering phase function g 2 , σ = 0.15 m 1 , and indicated distances Z.

Fig. 3
Fig. 3

Pulse waveforms for the indicated scattering phase functions, and Z = 5 m.

Fig. 4
Fig. 4

Energy of scattered radiation accumulated by the time Δ t for the indicated scattering phase functions, and Z = 5 m.

Fig. 5
Fig. 5

Pulse waveforms for the entire range of variations of the optical thicknesses, scattering phase function g 3 , and distances Z = 10 (curve 1, τ = 1.5 ), 60 (curve 2, τ = 9 ), 100 (curve 3, τ = 15 ), 200 (curve 4, τ = 30 ), 400 (curve 5, τ = 60 ), and 1000 m (curve 6, τ = 150 ).

Tables (1)

Tables Icon

Table 1 Data of Experimental Measurements of Time Pulse Broadening

Equations (7)

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

( 1 c t + s r + ε ) I ( r , s , t ) = Λ 4 π g ( s , s ) I ( r , s , t ) d ω .
1 c U t = D 2 U κ U .
P ( t ) = σ 3 c 8 π 3 / 2 η 3 / 2 ( σ c t ) 3 / 2 exp ( η τ 2 4 σ c t ) .
δ u σ c δ t η τ 2 / 2 , t max δ t / 3 .
F ( r ) = F r i ( r ) + V [ 4 π σ g ( s , s ) I ( r , s ) d ω ] × e τ | r r | 2 s d V .
E ( r 0 ) = 2 π I ( r 0 , s 0 ) cos φ d ω 0 = M n ξ i ( x n , x 0 ) ,
ξ i ( x , x 0 ) = e τ ( r , r 0 ) g ( γ 0 ) 2 π | r r 0 | 2 | ( n 0 , s 0 ) | ,

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