16 
If D-~, then 
+N /2 
RS y H, exp jk(7#1/2)d(sin6- sinh, ) 
t=-W/2 
And if the E, are all equal, and I = 2m 
m 
ip = 25 )) exp ji(i-1/2)d(sine-sing, ) 
wel 
Applying the geometric symmetry of the array 
m 
R= 2B, ) cos(ie(i-1/2)a(sing- sing, )) 
aml 
Then, using the identity* 
ie sin oy 
2 Y cos(i-1/2) x = ————, where = 2m 
sin = 
wail 2 
the directivity function becomes, 
Re Ey sine) o 
where 
= ns (sin§- sin, ) 
*Reference 2, page 16. 
