Abstract

Multiple scattering processes in a heterogeneous medium with rough boundaries lead inevitably to coupling of volume and surface effects. Our study of this problem using a statistical wave theory shows the nature of this coupling, brings forth the issues involved, and gives the approximations required to separate volume and surface effects. We hence understand that, only under rather special conditions, these two effects can be decoupled according to the “splitting rule” suggested by Guerin and Sentenac [J. Opt. Soc. Am. A 24, 385 (2007) [CrossRef]  ]. One situation where the two effects approximately separate is when the boundary roughness is small. In this case our results are in agreement with [J. Opt. Soc. Am. A 24, 385 (2007) [CrossRef]  ] and [Waves Random Media 7, 303 (1997)]. Apart from this special situation, we find that volume and boundary effects always get coupled. Therefore, it is apparent that a splitting rule is a special property rather than a general law.

© 2012 Optical Society of America

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References

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  1. M. A. Zuniga, T. M. Habashy, and J. A. Kong, IEEE Trans. Geosci. Electron. 17, 296 (1979).
    [CrossRef]
  2. J. M. Elson, Waves Random Media 7, 303 (1997).
  3. G. S. Brown, A Theoretical Study of the Effects of Vegetation on Terrain Scattering (Rome Air Development Center, 1988).
  4. R. J. Papa and D. Tamasanis, in Advisory Group for Aerospace Research and Development Conference Proceedings, Vol. 46 (NATO, 1991), AGARD-CP-501, pp. 4.1–4.12.
  5. C. M. Lam and A. Ishimaru, Waves Random Media 3, 111 (1993).
    [CrossRef]
  6. F. T. Ulaby, R. K. Moore, and A. K. Fung, Microwave Remote Sensing: Active and Passive (Artech, 1986).
  7. J. Caron, C. Andraud, and J. Lafait, J. Mod. Opt. 51, 575 (2004).
    [CrossRef]
  8. K. Pak, L. Tsang, L. Li, and C. H. Chan, Radio Sci. 28, 331 (1993).
    [CrossRef]
  9. K. Sarabandi, O. Yisok, and F. T. Ulaby, IEEE Trans. Geosci. Remote Sens. 34, 425 (1996).
    [CrossRef]
  10. C. A. Guerin and A. Sentenac, J. Opt. Soc. Am. A 24, 385 (2007).
    [CrossRef]
  11. A. Sentenac, H. Giovannini, and M. Saillard, J. Opt. Soc. Am. A 19, 727 (2002).
    [CrossRef]

2007 (1)

2004 (1)

J. Caron, C. Andraud, and J. Lafait, J. Mod. Opt. 51, 575 (2004).
[CrossRef]

2002 (1)

1997 (1)

J. M. Elson, Waves Random Media 7, 303 (1997).

1996 (1)

K. Sarabandi, O. Yisok, and F. T. Ulaby, IEEE Trans. Geosci. Remote Sens. 34, 425 (1996).
[CrossRef]

1993 (2)

C. M. Lam and A. Ishimaru, Waves Random Media 3, 111 (1993).
[CrossRef]

K. Pak, L. Tsang, L. Li, and C. H. Chan, Radio Sci. 28, 331 (1993).
[CrossRef]

1979 (1)

M. A. Zuniga, T. M. Habashy, and J. A. Kong, IEEE Trans. Geosci. Electron. 17, 296 (1979).
[CrossRef]

Andraud, C.

J. Caron, C. Andraud, and J. Lafait, J. Mod. Opt. 51, 575 (2004).
[CrossRef]

Brown, G. S.

G. S. Brown, A Theoretical Study of the Effects of Vegetation on Terrain Scattering (Rome Air Development Center, 1988).

Caron, J.

J. Caron, C. Andraud, and J. Lafait, J. Mod. Opt. 51, 575 (2004).
[CrossRef]

Chan, C. H.

K. Pak, L. Tsang, L. Li, and C. H. Chan, Radio Sci. 28, 331 (1993).
[CrossRef]

Elson, J. M.

J. M. Elson, Waves Random Media 7, 303 (1997).

Fung, A. K.

F. T. Ulaby, R. K. Moore, and A. K. Fung, Microwave Remote Sensing: Active and Passive (Artech, 1986).

Giovannini, H.

Guerin, C. A.

Habashy, T. M.

M. A. Zuniga, T. M. Habashy, and J. A. Kong, IEEE Trans. Geosci. Electron. 17, 296 (1979).
[CrossRef]

Ishimaru, A.

C. M. Lam and A. Ishimaru, Waves Random Media 3, 111 (1993).
[CrossRef]

Kong, J. A.

M. A. Zuniga, T. M. Habashy, and J. A. Kong, IEEE Trans. Geosci. Electron. 17, 296 (1979).
[CrossRef]

Lafait, J.

J. Caron, C. Andraud, and J. Lafait, J. Mod. Opt. 51, 575 (2004).
[CrossRef]

Lam, C. M.

C. M. Lam and A. Ishimaru, Waves Random Media 3, 111 (1993).
[CrossRef]

Li, L.

K. Pak, L. Tsang, L. Li, and C. H. Chan, Radio Sci. 28, 331 (1993).
[CrossRef]

Moore, R. K.

F. T. Ulaby, R. K. Moore, and A. K. Fung, Microwave Remote Sensing: Active and Passive (Artech, 1986).

Pak, K.

K. Pak, L. Tsang, L. Li, and C. H. Chan, Radio Sci. 28, 331 (1993).
[CrossRef]

Papa, R. J.

R. J. Papa and D. Tamasanis, in Advisory Group for Aerospace Research and Development Conference Proceedings, Vol. 46 (NATO, 1991), AGARD-CP-501, pp. 4.1–4.12.

Saillard, M.

Sarabandi, K.

K. Sarabandi, O. Yisok, and F. T. Ulaby, IEEE Trans. Geosci. Remote Sens. 34, 425 (1996).
[CrossRef]

Sentenac, A.

Tamasanis, D.

R. J. Papa and D. Tamasanis, in Advisory Group for Aerospace Research and Development Conference Proceedings, Vol. 46 (NATO, 1991), AGARD-CP-501, pp. 4.1–4.12.

Tsang, L.

K. Pak, L. Tsang, L. Li, and C. H. Chan, Radio Sci. 28, 331 (1993).
[CrossRef]

Ulaby, F. T.

K. Sarabandi, O. Yisok, and F. T. Ulaby, IEEE Trans. Geosci. Remote Sens. 34, 425 (1996).
[CrossRef]

F. T. Ulaby, R. K. Moore, and A. K. Fung, Microwave Remote Sensing: Active and Passive (Artech, 1986).

Yisok, O.

K. Sarabandi, O. Yisok, and F. T. Ulaby, IEEE Trans. Geosci. Remote Sens. 34, 425 (1996).
[CrossRef]

Zuniga, M. A.

M. A. Zuniga, T. M. Habashy, and J. A. Kong, IEEE Trans. Geosci. Electron. 17, 296 (1979).
[CrossRef]

IEEE Trans. Geosci. Electron. (1)

M. A. Zuniga, T. M. Habashy, and J. A. Kong, IEEE Trans. Geosci. Electron. 17, 296 (1979).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (1)

K. Sarabandi, O. Yisok, and F. T. Ulaby, IEEE Trans. Geosci. Remote Sens. 34, 425 (1996).
[CrossRef]

J. Mod. Opt. (1)

J. Caron, C. Andraud, and J. Lafait, J. Mod. Opt. 51, 575 (2004).
[CrossRef]

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

Radio Sci. (1)

K. Pak, L. Tsang, L. Li, and C. H. Chan, Radio Sci. 28, 331 (1993).
[CrossRef]

Waves Random Media (2)

C. M. Lam and A. Ishimaru, Waves Random Media 3, 111 (1993).
[CrossRef]

J. M. Elson, Waves Random Media 7, 303 (1997).

Other (3)

G. S. Brown, A Theoretical Study of the Effects of Vegetation on Terrain Scattering (Rome Air Development Center, 1988).

R. J. Papa and D. Tamasanis, in Advisory Group for Aerospace Research and Development Conference Proceedings, Vol. 46 (NATO, 1991), AGARD-CP-501, pp. 4.1–4.12.

F. T. Ulaby, R. K. Moore, and A. K. Fung, Microwave Remote Sensing: Active and Passive (Artech, 1986).

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Figures (1)

Fig. 1.
Fig. 1.

Geometry of the problem.

Equations (26)

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L0E0=0,L1E1=νE1,
Be[E0E1]=0,Bm[E0E1]=0onΣ,
Ej(r)=Eˇj(r)+G¯ˇj1(r,r)ν(r)E1(r)dr.
Ej(r)v=Eˇj(r)+drdrG¯ˇj1(r,r)M¯v(r,r)E1(r)v,
LjEj(r)v=δj1M¯v(r,r)E1(r)vdr.
LjEj(r)vs=δj1M¯vs(r,r)E1(r)vsdr,
E0(r)=eiki·r{p0eik0ziz+p0+Rp(ki)eik0ziz},
E1(r)=p1eiki·rTp(ki)eiqz,
|E0psvs|2=(2π)2δ(kki)|Rp(k)|2,
E0(r)v=p0eiki·rik0ziz+14π2{q0+Rqp(k,ki)v}eik·r+ik0zzdk,
E1(r)v=14π2{q1Tqp(k,ki)veiqqzz}eik·rdk.
Rpq(k,ki)s=δpqRp(ki)δ(kki),
Tpq(k,ki)s=δpqTp(ki)δ(kki).
EjEj*v=EjvEj*v+G¯j1vG¯j1*vK¯vE1E1*v,
EjEj*vs=EjvEj*vs+G¯j1vG¯j1*vsK¯vsE1E1*vs,
EE*vs=EvsE*vs+E˜E˜*vs.
EvE*vs=EvsE*vs+E˜vE˜v*s.
E˜0E˜0*vs=E0˜vE0*˜vs+G¯01vG¯01*vsK¯vsE1E1*vs.
E1E1*vs=E1vE1*vs+G¯11vG¯11*vsK¯vsE1E1*vs.
E1=E1E1*vs,E˜0=E˜0E˜0*vs,E1s=E1vE1*vs,E˜0s=E0˜vE0*˜vs,G1=G¯11vG¯11*vs,G0=G¯01vG¯01*vs.
E1=E1s+G1KE1s+G1KG1KE1s+.
E˜0=E˜0s+G0KE1s+G0KG1KE1s+G0KG1KG1KE1s.
G¯j1vG¯j1*vsG¯j1vsG¯j1*vs,E1vE1*vsE1vsE1*vs.
G¯j1vsG¯j1vo,E1vsE1vo,
E˜0E˜0*vs=E0˜vE0*˜vs+G¯01voG¯01*voK¯voE1E1*vs,
E1E1*vs=E1voE1*vo+G¯11voG¯11*voK¯voE1E1*vs.

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