The directivity function becomes 
where 
E = kas (cosa-cosdo )* +(cos8- cosBo )° 
If this directivity function is normalized 
_ 2d, (§) 
Ry z 
Let do = 85 = 90°; then & = Aasiny and 
_ 2/1 (kasiny) ,, 
Ry ~Fasin y 
(f{) Spherical Surface Array 
First, an uncompensated spherical surface array will be 
considered, followed by a compensated hemisphere. 
In the case of the uncompensated spherical surface array, 
the directivity function is given by 
R= fa, v2) exnstdveosntyoost zcosy]}ds 
S 
Let the sphere have radius qa. Then from figure 12, 
x = asingcos6é 
y = asingsiné 
Z = acosg 
oO 
*Reference 1, page 20, equation (17). 
(Up) 
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