Abstract

Ray theory plays an important role in determining the propagation properties of high-frequency fields and their statistical measures in complicated random environments. According to the ray approach, the field at the observer can be synthesized from a variety of field species arriving along multiple ray trajectories resulting from refraction and scattering from boundaries and from scattering centers embedded in the random medium. For computations of the statistical measures, it is desirable therefore to possess a solution for the high-frequency field propagating along an isolated ray trajectory. For this reason, a new reference-wave method was developed to provide an analytic solution of the parabolic-wave equation.

© 2002 Optical Society of America

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References

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  1. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1998).
  2. S. M. Rytov, Yu. A. Kravtsov and V. I. Tatarskii, Principles of Statistical Radiophysics (Springer-Verlag, Berlin, 1988), Vols. 1–4.
    [CrossRef]
  3. V. I. Klyatskin, Stochastic Equations and Waves in Randomly Inhomogeneous Media (Nauka, Moscow, 1980).
  4. R. Mazar and L. B. Felsen, “Stochastic geometrical diffraction theory in a random medium with inhomogeneous background,” Opt. Lett. 12, 301–303 (1987).
    [CrossRef] [PubMed]
  5. R. Mazar and L. B. Felsen, “Stochastic geometrical theory of diffraction,” J. Acoust. Soc. Am. 86, 2292–2308 (1989).
    [CrossRef]
  6. J. B. Keller, “Geometrical theory of diffraction,” J. Opt. Soc. Am. 52, 116–130 (1962).
    [PubMed]
  7. R. Mazar, “High-frequency propagators for diffraction and backscattering in random media,” J. Opt. Soc. Am. A 7, 34–46 (1990).
    [CrossRef]
  8. R. Mazar and A. Bronshtein, “Multiscale solutions for the high-frequency propagators in an inhomogeneous background random medium,” J. Acoust. Soc. Am. 91, 802–812 (1992).
    [CrossRef]
  9. S. Frankenthal, M. J. Beran, and A. M. Whitman, “Caustic corrections using coherence theory,” J. Acoust. Soc. Am. 71, 348–358 (1982).
    [CrossRef]
  10. M. J. Beran, A. M. Whitman, and S. Frankenthal, “Scattering calculations using the characteristic rays of the coherence function,” J. Acoust. Soc. Am. 71, 1124–1130 (1982).
    [CrossRef]
  11. R. Mazar, L. Kodner, and G. Samelsohn, “Modeling of high-frequency wave propagation with application to the double-passage imaging in random media,” J. Opt. Soc. Am. A 14, 2809–2819 (1997).
    [CrossRef]
  12. R. Mazar, “Uncertainty in the modeling of high-frequency propagators in random media,” Comput. Struct. 67, 119–124 (1998).
    [CrossRef]

1998

R. Mazar, “Uncertainty in the modeling of high-frequency propagators in random media,” Comput. Struct. 67, 119–124 (1998).
[CrossRef]

1997

R. Mazar, L. Kodner, and G. Samelsohn, “Modeling of high-frequency wave propagation with application to the double-passage imaging in random media,” J. Opt. Soc. Am. A 14, 2809–2819 (1997).
[CrossRef]

1992

R. Mazar and A. Bronshtein, “Multiscale solutions for the high-frequency propagators in an inhomogeneous background random medium,” J. Acoust. Soc. Am. 91, 802–812 (1992).
[CrossRef]

1990

1989

R. Mazar and L. B. Felsen, “Stochastic geometrical theory of diffraction,” J. Acoust. Soc. Am. 86, 2292–2308 (1989).
[CrossRef]

1987

1982

S. Frankenthal, M. J. Beran, and A. M. Whitman, “Caustic corrections using coherence theory,” J. Acoust. Soc. Am. 71, 348–358 (1982).
[CrossRef]

M. J. Beran, A. M. Whitman, and S. Frankenthal, “Scattering calculations using the characteristic rays of the coherence function,” J. Acoust. Soc. Am. 71, 1124–1130 (1982).
[CrossRef]

1962

Beran, M. J.

S. Frankenthal, M. J. Beran, and A. M. Whitman, “Caustic corrections using coherence theory,” J. Acoust. Soc. Am. 71, 348–358 (1982).
[CrossRef]

M. J. Beran, A. M. Whitman, and S. Frankenthal, “Scattering calculations using the characteristic rays of the coherence function,” J. Acoust. Soc. Am. 71, 1124–1130 (1982).
[CrossRef]

Bronshtein, A.

R. Mazar and A. Bronshtein, “Multiscale solutions for the high-frequency propagators in an inhomogeneous background random medium,” J. Acoust. Soc. Am. 91, 802–812 (1992).
[CrossRef]

Felsen, L. B.

Frankenthal, S.

M. J. Beran, A. M. Whitman, and S. Frankenthal, “Scattering calculations using the characteristic rays of the coherence function,” J. Acoust. Soc. Am. 71, 1124–1130 (1982).
[CrossRef]

S. Frankenthal, M. J. Beran, and A. M. Whitman, “Caustic corrections using coherence theory,” J. Acoust. Soc. Am. 71, 348–358 (1982).
[CrossRef]

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1998).

Keller, J. B.

Klyatskin, V. I.

V. I. Klyatskin, Stochastic Equations and Waves in Randomly Inhomogeneous Media (Nauka, Moscow, 1980).

Kodner, L.

R. Mazar, L. Kodner, and G. Samelsohn, “Modeling of high-frequency wave propagation with application to the double-passage imaging in random media,” J. Opt. Soc. Am. A 14, 2809–2819 (1997).
[CrossRef]

Kravtsov, Yu. A.

S. M. Rytov, Yu. A. Kravtsov and V. I. Tatarskii, Principles of Statistical Radiophysics (Springer-Verlag, Berlin, 1988), Vols. 1–4.
[CrossRef]

Mazar, R.

R. Mazar, “Uncertainty in the modeling of high-frequency propagators in random media,” Comput. Struct. 67, 119–124 (1998).
[CrossRef]

R. Mazar, L. Kodner, and G. Samelsohn, “Modeling of high-frequency wave propagation with application to the double-passage imaging in random media,” J. Opt. Soc. Am. A 14, 2809–2819 (1997).
[CrossRef]

R. Mazar and A. Bronshtein, “Multiscale solutions for the high-frequency propagators in an inhomogeneous background random medium,” J. Acoust. Soc. Am. 91, 802–812 (1992).
[CrossRef]

R. Mazar, “High-frequency propagators for diffraction and backscattering in random media,” J. Opt. Soc. Am. A 7, 34–46 (1990).
[CrossRef]

R. Mazar and L. B. Felsen, “Stochastic geometrical theory of diffraction,” J. Acoust. Soc. Am. 86, 2292–2308 (1989).
[CrossRef]

R. Mazar and L. B. Felsen, “Stochastic geometrical diffraction theory in a random medium with inhomogeneous background,” Opt. Lett. 12, 301–303 (1987).
[CrossRef] [PubMed]

Rytov, S. M.

S. M. Rytov, Yu. A. Kravtsov and V. I. Tatarskii, Principles of Statistical Radiophysics (Springer-Verlag, Berlin, 1988), Vols. 1–4.
[CrossRef]

Samelsohn, G.

R. Mazar, L. Kodner, and G. Samelsohn, “Modeling of high-frequency wave propagation with application to the double-passage imaging in random media,” J. Opt. Soc. Am. A 14, 2809–2819 (1997).
[CrossRef]

Tatarskii, V. I.

S. M. Rytov, Yu. A. Kravtsov and V. I. Tatarskii, Principles of Statistical Radiophysics (Springer-Verlag, Berlin, 1988), Vols. 1–4.
[CrossRef]

Whitman, A. M.

S. Frankenthal, M. J. Beran, and A. M. Whitman, “Caustic corrections using coherence theory,” J. Acoust. Soc. Am. 71, 348–358 (1982).
[CrossRef]

M. J. Beran, A. M. Whitman, and S. Frankenthal, “Scattering calculations using the characteristic rays of the coherence function,” J. Acoust. Soc. Am. 71, 1124–1130 (1982).
[CrossRef]

Comput. Struct.

R. Mazar, “Uncertainty in the modeling of high-frequency propagators in random media,” Comput. Struct. 67, 119–124 (1998).
[CrossRef]

J. Acoust. Soc. Am.

R. Mazar and A. Bronshtein, “Multiscale solutions for the high-frequency propagators in an inhomogeneous background random medium,” J. Acoust. Soc. Am. 91, 802–812 (1992).
[CrossRef]

J. Acoust. Soc. Am.

S. Frankenthal, M. J. Beran, and A. M. Whitman, “Caustic corrections using coherence theory,” J. Acoust. Soc. Am. 71, 348–358 (1982).
[CrossRef]

M. J. Beran, A. M. Whitman, and S. Frankenthal, “Scattering calculations using the characteristic rays of the coherence function,” J. Acoust. Soc. Am. 71, 1124–1130 (1982).
[CrossRef]

R. Mazar and L. B. Felsen, “Stochastic geometrical theory of diffraction,” J. Acoust. Soc. Am. 86, 2292–2308 (1989).
[CrossRef]

J. Opt. Soc. Am. A

R. Mazar, L. Kodner, and G. Samelsohn, “Modeling of high-frequency wave propagation with application to the double-passage imaging in random media,” J. Opt. Soc. Am. A 14, 2809–2819 (1997).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Lett.

Other

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1998).

S. M. Rytov, Yu. A. Kravtsov and V. I. Tatarskii, Principles of Statistical Radiophysics (Springer-Verlag, Berlin, 1988), Vols. 1–4.
[CrossRef]

V. I. Klyatskin, Stochastic Equations and Waves in Randomly Inhomogeneous Media (Nauka, Moscow, 1980).

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Equations (11)

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

gσ=i2kr12g+iknr1,σg,g(r1,σ0|r10,σ0)=δr1-r10.
Πσ=ikν·qΠ-i2kq2Π+iknν+q,σΠ,
Π¯(ν,ρ,σ|ν0,ρ0,σ0)=k2π2-dqdq0×Π(ν,q,σ|ν0,q0,σ0)exp-ikρ·q-ρ0·q0.
Π¯σ+ρ·νΠ¯-iknν+ikρ,σΠ¯=ikρ22Π¯.
dνdσ=ρ,    dρdσ=νnν,σ,
dΠ¯dσ=ikρ22Π¯+iknν,σΠ¯.
g(r,σ|r0,σ0)=k2π2-dρδr-σ0σdξρfξ-r0×expikσ0σdξnrfζ,ζexpik2σ0σdζρf2ζ,
Wp,ρ,σ=k2π2-dsΓp,s,σexpikρ·s,
Aη,s,σ=-dpΓp,s,σexp-ikη·p.
Aη,s,σ=-dp0dρ0Wp0,ρ0,σ0×gWA(η,s,σ|p0,ρ0,σ0),
g2(p,s,σ|p0,s0,σ)=k2π2-dρ0dη×expikη·p-p0-ρ0σ-σ0expikρ0·s-s0×expikσ0σdζFp+ρ0ζ-σ,s+ηζ-σ,ζ,

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