IV -4 



The incoming (zero- order) wave, therefore, provides the energy to generate a 

 source distribution for the first-order wave. We shall see later that this 

 corresponds to a single scattering approximation, in the sense of Chapter II. 

 In other words, the pov/er series expansion in terms of a slight correction to 

 the index of refraction not only approximates the quadratic expression for the 

 index of refraction in (IV-7), but also removes higher orders of scattering from 

 the first- order approximation. 



The solution to (IV- 11) is given (see Appendix A) by the integral: 



ikr 



/ 



V 



= p''*W = -f?^/ <iiu(i)pW(i>f 



(IV- 12) 



The geometry required to explain the nomenclature of (IV- 12) is shown in Figure 

 IV- 1 . A scattering element at ? acts as a secondary source emitting a spherical 

 wave to an observer at x- The volume of the scattering element is denoted by 

 d? = d?i d?3 d?3 in rectangular coordinates. The integral in (IV- 12) runs 

 over the entire portion of space containing inhomogeneities (i.e. , that portion 

 of space for which u / 0). The vector running from the scattering element to the 

 observer is called r = x - 5 . 



OBSERVER 



T - X- ^ 



SCATTERING ELEMENT 



FIGURE IV- 1 THE GEOMETRY OF SCATTERING 



Arthur H.littlcJnc-. 



8-7001-0307 



