dk~ [Jee(k-il' k~, ku)f:e(k.u, k~, k u in Java

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dk~ [Jee(k-il' k~, ku)f:e(k.u, k~, k u
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+ ki-i - k~, ku)]
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+ Jee(k.u, k~, kU)f:e(k.u, k u . W(k.u - k-i)W(k -i
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(1.3.62) (1.3.63)
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Thus if we define incoherent field as
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~2) = E~2) _ (E~2))
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and calculate Poynting's vector for an incoherent wave as
X \7 X ~~2)* (1") ) 2 -ZWJL then the product is similar to that of the previous section. For horizontal polarization incidence ei = e( -k iz ) we have
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~ Re (z . ~2)
'Yhh (Os ,cPs; 1f - cPi, cPi) 41fk 2 cos 2 Os = 0 cos i
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{lex> dk W (k -/ -/ - k
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-/ -u )J: : (k -/ - k ki-i) k
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[f:e(k-i' k~, k u ) + f:e(k-i' k-i
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'Yvh(Os,cPs; 1f - cPi, cPi) 41fk 2 cos 2 Os = 0 cos i
k~ + k u ,k u )] }
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(1.3.64a)
{lex> dk-iW(k-i- -/ -/ - - : : - -/ -u ) -/ - k-i)W(k-i ki-i)!he(k-i,k-i,k
-ex>
[he (k-i , k~, ku)
+ he(k-i' k-i - k~ + k u ,k u )] }
(1.3.64b)
Thus for vertical polarization incidence
'Yhv(Os,cPs; 1f - cPi, cPi) 41fk 2 cos 2 Os = 0 cos i
ei =
11.( -kiz )
{lex> dk-iW(k-i- -/ -/ - - :; - -/ -u ) -/ - k-i)W(k-i h-i)Jeh(k-i,k-i,k
-ex>
. [f:h(k-i' k~, ki-i)
+ f:h(k-i' k-i - k~ + k u ,k u )] }
(1.3.64c)
1 2-D RANDOM ROUGH SURFACE SCATTERING BASED ON SPM
'Yvv(()s,<Ps; 7T - <Pi, <Pi) 47Tk2 COS 2
()s {joo dk
i- W(ki-
- ki-)W(k i-
kU)!hh(ki-, k i-, k u )
(1.3.64d)
. [hh(ki-' k~, k u ) + hh(ki-, ki- -
k~ + k u ,k U )] }
To compute numerical results from (1.3.64a-d) , Eqs. (1.3.60) and (1.2.75) need to be used.
R.EFERENCES
REFERENCES AND ADDITIONAL READINGS
Bahar, E. and M. A. Fitzwater (1989), Depolarization and backscatter enhancement in light scattering from random rough surfaces: Comparison of full-wave theory with experiment, J. Opt. Soc. Am. A, 6, 33-43. Bass, F. G. and I. M. Fuks (1979), Wave Scattering from Statistically Rough Surfaces, translated by C. B. Vesecky and .1. F. Vesecky, Pergamon Press, Oxford, UK. Baylard, C., .1.-.1. Greffet, and A. A. Maradudin (1993), Coherent reflection factor of a random rough surface: applications, J. Opt. Soc. Am. A, 10, 2637-2647. Beckmann, P. and A. Spizzichino (1963), The Scattering of Electromagnetic .Waves from Rough Surfaces, Pergamon Press, Oxford. Broschat, S. L. (1993), The small slope approximation reflection coefficient for scattering from a "Pierson-Moskowitz" sea surface, IEEE Trans. Geosci. Remote Sens., 31(5), 1112-1114. Broschat, S. L., L. Tsang, A. Ishimaru, and E. I. Thorsos (1988), A numerical comparison of the phase perturbation technique with the classical field perturbation and Kirchhoff approximations for random rough surface scattering problems, J. Electromag. Waves and Appl., 2(1), 85-102. Brown, G. S. (1978), Backscattering froIll a Gaussian distributed perfectly conducting rough surface, IEEE Trans. Antennas Propagat., 26, 472-482. Brown, G. S. (1985), Simplification in the stochastic Fourier transform approach to random rough surface scattering, IEEE Trans. Antennas Propagat., 33, 48-55. Chen, K. S. and A. K. Fung (1995), A comparison of backscattering models for rough surfaces, IEEE Trans. Geosci. Remote Sens., 33(1),195-199. Chen, K. S., T. D. Wu, M. K. Tsay. and A. K. Fung (2000), A note on the multiple scattering of the IEM model, IEEE Trans. Geosci. Remote Sens., 38(1), 249-256. Collin, R. E. (1994), Full wave theories for rough surface scattering: An updated assessment, Radio Sci., 29, 1237-1254. De Roo, R. D. and F. T. Ulaby (1994), Bistatic specular scattering from rough dielectric surfaces, IEEE Trans. Antennas Propagat., 42(2), 220-231. DeSanto, J. A. (1974), Green's function for electromagnetic scattering from a random rough surfaces, J. Math. Phys., 15, 283-288. DeSanto, .J. A. and O. Shisha (1974), Numerical solution of a singular integral equation in random rough surface scattering theory, J. of Compo Phys., 15, 286-292. DeSanto, J. A. and R. J. Wombell (1991), Rough surface scattering, Waves in Random Media, 1,41-56. Durden, S. L. and .1. F. Vesecky (1985), A physical radar cross-section model for a wind driven sea with swell, IEEE J. Ocean. Eng., 10, 445-451. Durden, S. L. and .1. F. Vesecky (1990), A numerical study of the separation wavenumber in the two scale scattering approximation, IEEE Trans. Geosci. Remote Sens., 28, 271-272. Fung, A. K. (1994), Microwave Scattel'ing and Emission Models and Their Applications, Artech House, Norwood, Massachusetts. Fung, A. K. and G. W. Pan (1987), A scatter model for perfectly conducting random surface: I. Model development. II. Range of validity, Int. J. Remote Sens., 8(11),1579-1605. Greffet, J . .1. and M. Nieto-Vesperinas (1998), Field theory for generalized bidirectional reflectivity: derivation of Helmholtz's reciprocity principle and Kirchhoff's law, J. Opt. Soc. Am. A, 15(10), 2735-2744.