equation (E-25) may be written 



F(x,j) = e"-^''-^ - ^1 ~ ^2 ^°^ ^ X ^ b/2 



and 



F(x,y) = f^ - f 2 for x& b/2 



(the solution for x<0 will be the niirror image of that for x^O) 



(E-26) 



Computations may be made by use of equation E-23 and Figure E-7, which 

 show real and imaginary parts of f(-u), Ifriting f(-u) as 



f (-u) = s + iw 

 equation (19) may be written as 



f(x,y'i = e"^^^ (l-s^-s^) + i(-w-j^-W2) for ^ x^ b/2 



f(x,y) = e""^^ (3^-82) + i(w^-W2) for x^ b/2 

 S-. and w- corresoond to u^ which is defined by 



2 ii(r^-y) 



(E-27) 



(E-28) 



"1 



= h 



_MfW-i] 



(E-29^) 



and Sp and w correspond to Up which is defined by 



2 h{r^-y) 



= U 



f(Xj_bZ2)^(g )' 



■d 



If equation (S-26) is written 



F(x,y) = e"^^ (s + iW) 



(E-30) 



(E-31) 



where S and W represent the sums of the real and imaginary parts respectively, 

 of equation (E-28) comparison with equation (E-9) shoxirs that a diffraction 

 coefficient K' may be defined as 



VI - lF(x ,y)| for diffracted wave |„/ J _ ,.„„ . , /r< -,o\ 

 ^ - mx,j)\ for incident wave = 1^^^^^^ ^°^ diffracted (E-32) 

 s ' ' wave 



which is equal to 



K' = \/s^ + W^ (E-33) 



E-9 



