20 
Let D-o; then a plane wave front will be incident: 
+11 +e 
ae ee a 
if = ) \ 2, pexp jk [(t41/2)d, cosat(t+1/2)dz cose J 
pata 27M 
2 2 
Applying Euler's Formula and noting that because of 
symmetry the odd function cancels in pairs (letting #, 28 
be equal) ue 
mie 
R= 4B, my )cos(e(i-1/2)a, cosa) * cos(k(2-1/2)ds cosp) 
OA, 2a. 
Then by using the identity of Section (a) 
stn 
yx 
2) cos(i- 2) 4 —————— 
Lig Ot. OG 
SEL oy 
the directivity function becomes 
PzE sin(W,é) , sin(Wsn) 
i, 2 sin(é) sin(n) 
where 
bs kiddy ze kidz 
Ee = 79, ©Osa Metis —z_cosB 
Letting fi. ee 1 and normalizing 
_ sin(W,&)  sin(Izq) * (9) 
Ry eee eames 
N,sin(é) Nz sin(y) 
*Reference 1, page 37, equation (29). 
