and that G(£,m) is a measure of the directional resolving power of the 

 assumed probe array. By the nature of g(X,Y) we have from Equation 

 (6.3) 





^ ^ (6.5) 



If we assume that the wave equation (Equation (3.1)) holds, 

 that S(S,,m,fQ) is zero when Z + v[r ^ Icq, the wave number f^^ ^^ 

 From this we have for a given (HqVciq) that the directional resolving 

 power, DRP, is 



we find 

 for f. 



OS oo 



DRP(JI, >.,(,) =:j|<(((iV>,^)-Kt)G(l!«-^ni«->^j)^U 



w 



«■ X 



LET 



Jl^KoCos© , >M = Ko SIN e, WHICH iMPnES ft+m-K. 



and we get, for energy coming from a direction Q^ at frequency f as a 

 function of £ 6 £ 2it, that 



I)RP(e|0o,f.) = G(k.(cos0o-cos0),K.(s»NG.rSlN9)) . 



From Equation (6.5) we get 



E>RP(e|a,t)= l + 2'|^2ios[aTT(x.jK.tos0.-cose>XjK. 

 = l-^2££cos[eir(Ci-k. COS 0)X,^+(V«.-K. SIN 0)^3)] 



NOTE THAT DRP(0j0,O= N(N-|)+I (6.6) 



Compare Equation (6.6) and (5.5). Except for the amplitude term, a2/4M, 

 in Equation (5.5) the equations give identical results. The choice of 

 b-. = [N(N-l) + l]""*" = 1/M is again found convenient. 



25 



