Ill- 108 



,^ ^ lK(i.n)y f f ^-m. Bn) ^3 ,^(,^^) ,, ,^ („,.,3^^^ 



-00 -05 



iC(§,-n) I I e"'^^^^^"^^ v5, (X,u)cl\dM an-136d) 



-00 -co 



CO 03 



r r e"^(^^+^^>$3(X,u)dXdu (III-136e) 



Substituting for $i (X, u) in (III-136d), we have 



l3=iC(^..)(0*2iv[c(?.Ti)e-^^°^^^^^>]-^) 



(III-137) 



Substituting (III-135a) in (III-136c), and recalling that \^ + u^ + v^ = 1, we see that 

 Iq + I, = 0. Then Ig + I3 - 0, and -Ig is the Fourier transform of §2 (^. u)- From 

 this we have 



is (Ku) =[-13]'' 



= ^2v[c(5,ri)]-^ *(v[c(?,^)e-^<^^^^^)]") (III-138) 



The first three terms $q, §;^, $2 must be considered to obtain the lowest 

 order correction to the intensity in the specular direction. With § = $q + a 1^ + 



0^ §s + , the component §ois associated with the specular direction and $j 



with the non-specular direction. The energy in the non-specular wave must come 



from the incident wave and be ?aC^ i^ + ; hence, the energy in the specular 



direction must be sJ. - o^ §? + (where the incident plane wave has unit amplitude) . 



Consequently, there cannot be a correction of order a to the specular term, for this woulc 

 require an energy correction of order o — since Tl - O (o)j ^ = 1 - 2 [0(a)j + 0(a^ ) . 



Arthur 21.1LittleJnf. 



S-7001-0307 



