48 
Note that if g(g) = 0 for allg, then the above directivity 
function becomes that for a cylindrical wave front. 
If a cylindrical wave front is compensated for (compensa- 
tion indicated by subscript zero), the directivity function 
for a discrete number of elements is 
N 
fe : : va Beate e 
R ) B exp flor, (cos COsfo ) y, (sino sino ) p, (cosy, 1) 
L= 
- Poy (costoz -1 +9(vz)-9(0) | 
The various quantities in this equation are easily obtained 
from geometry: 
p, = (2. = 20 Ea Ue) p or 
ys /(x,-Deose +(y, -Dsiné zaman 
D-(x;cos6+y sind) 
Py 
cost, = 
An example of the function g(g) is sin 4g. Its effect ona 
cylindrical wave front is shown in figure D2, when r =2-5 
that is 
WS 
1 psu : 
n (25.8) = 25+ sin4 9g 
