where Jji(Z) is a Bessel function of the first kind of integer order n. 

 Returning to Equation (5.9), the above results give, for n = where 



fp > 0, the result 



Since the above is real 



describe the elements for the spectral matrix of a single frequency 

 isotropic sea. 



The above two special cases for sea waves are the extremes of 

 directionality of real sea waves of frequency f ^ > . These results 

 will have important applications later. 



6. A MEASURE OF ARRAY DIRECTIONAL RESOLVING POWER 



From Equation (3.9) we have the Fourier transform 



S(^>n.n = |rV(X,Y,OE'^P{-i^'^0^ + >"'^))<l>^^Y 



>«e -OB 



In practice we use a probe array with elements at (x^, y^^) . . . , (xj^, yj^.) 

 to obtain P*(X,Y,f) at the separation points (0.0), (X]^2> ^12^' 

 (-Xi2'""^12^-'-' ^^k-l,k' ^k-l,k^' ^"-^k-l.k* "^k-l^k) • 



We do not then know P*(X,Y,f) but the product 



[P*(X,Y,f) g(X,Y)] (6.2) 



23 



