~ ; att + es 
R, E(x,.y,) {exp jk [x, cosa y,COs8 p(x ,, y,)(cosy(x,, y,) 1)]}a4, 
where (x., y,)is some point in AA,. Then the directivity 
function fs approximately u 
pew ial 
U 
i=1 
or 
N 
ee ° + + —_ 
R ) Ble, y, texp jax, cosa y, cose p(c,. y, Kcosy(a,, y,) 1)]}a4, 
i=l 
Letting 7-0 as max |a4,|>0 
R= { Fx, y) {exp jk xcosatycosstp (x, y)(cosy(x, y)-1) ]}dA (5) 
B 
This equation is for the uncompensated array. If the array 
is compensated for a planar wave front whose direction is 
defined by (cosag, COS85, COSy,), then the directivity function 
is 
R= i Ex, y) {exp jz[x«(cosa- cosa, )+y(cos8- CosB, ) 
B 
+o (x, y(cos¥ (x, y)-1)]}d4A (6) 
If a spherical wave front is compensated for, the directivity 
function is 
Be i E(x, y) {exp jx[ x(cosa- cosa, )+y(cos8- cosBo) 
B 
+o(x, ycosy(x, y)-1)-05 (x, y (cosy (x, y)-1) ] }aA 
