The distance D from the origin of the array to the source 
is given by 
= x.cosoty. singt Oo 
D xy sé y,s 8 ee su. 
Since 
=r.+ 
nr,, 0) ins g(0) 
and 
zg) = D-h(r,, 0) 
Is 0 oe 
i : 
pan = + ap - - 
ay x, cosh y, sind p, cosy, r. g(0) 
But 
=r+t 
Pa aa ey 
hence 
at f el A 
6, kl, coséty, sindtp , (cosy, 1) g(t ,) g(0) ] 
Now 
. ro = =| ° 
au 6, Lo, cose y, sind | 
since y,70 as D-~. Hence for large D, 6, approaches the 
phase difference for a plane wave. if 
The directivity function for an uncompensated discrete 
array is given by 
WV 
= ; ar in§+ -1)+ = 
R ) £, expselo, cose y, sine p, (cost, 1) gy.) g(0)] 
sa 
47 
