IV-11 



OBSERVER 



INCIDENT 

 PLANE WAVE 



•^- ^1 



e = SCATTERING ANGLE 

 FIGURE IV-2 SCATTERING COORDINATES 



-I'JJt 



If we drop t±ie time dependence e (see IV-9), die incoming plane wave is 

 represented by: 



Pq(x) = e 



ikxi 



(IV-38) 



The inhomogeneity is represented by a distribution u (£) < < 1 which is the deviation 

 from unity of the index of refraction. TTie scattering integral to be evaluated is 

 therefore obtained by substituting the incoming plane wave (IV-38) into the scatter- 

 ing integral (IV- 37): 



Pi(x) = - 



2k^ 



4TT 



H 



ik(r+?i) 



u(?) 



(IV-39) 



V 



To evaluate this integral in the far field (i.e. , at a distance from the inhomogeneity 

 which is large compared to the characteristic size of the inhomogeneity), we must 

 approximate the distance r which is given by: 



r = |x-?| = (x^ + 5^ - 2x . 5 )^ = x (1+%- 2^ .i-)2 (IV-40) 



— — — — . X X x 



arthur B.lLittUMt. 



S-7001-0307 



