Hence, as D>», the directivity function becomes that of a 
planar wave front. The corresponding result for a planar 
wave front and direction of compensation can similarly be 
derived and is 
R= i Elx, y, 2) \exp.jit [x(cosa- cosa )ty(cosB- cosB, ) 
See 
+z(cosy-cosy,)]}dV 
(c) Generalization of Results (a) and (b) 
Let F be a region containing elements (x, y,z). Then the 
generalized directivity function is 
Rs Jim. Ys Z) | exp jk[2(cosa- cosa, )ty(cos8- cosB,) 
+z(cosy-cosy7o )to(x, y, z(cosW(x, y, z)-1) 
-00 (x, ys z)(cosvo (x, y, z)-1)] } dF 
where 
(Ce Ube) = \f (oe- 200 P+(y- yo)? (2-2 )? 
NxXo* tyo*t+Z07 -(xcosatycos8tzcos 7) 
o (x, Yy> 2) 
Nico +Yo* +Z0* =) 
cosy(x, y, Z) 
where 
3. Shading 
In the foregoing expressions, F(x, y,z) and #, are called the 
shading coefficients. These functions are wéighting factors 
