This information can be used together with Equation (3.9) to obtain an 

 approximation to S(Jl,m,f). Numerical details for finding the spectral 

 matrix are given in Bennett, et al (June 1964). 



It should be pointed out that negative frequencies are still con- 

 sidered in the relationships being discussed. We do not know P*(X,Y,f) 

 for continuous values of (X,Y) . We do know from the spectral matrix 

 the values of 



where X. . = (x. - x.) 

 ij 3 1 



Y, . = (y . - y.) . 



We also have from Equation (4.7) that 

 From Equation (3.9) we get 



S(t,«,f) = ff[F*(X.Y, <) cost^1T(!lX*wY)] 

 -iP7x.Y,(UiNl.2it(lx.i-»Y)j}AxAY 



or, since S(jJ,m, f) is real 



-Q(X.Y.f)siNUTt(i!X^>nY)]] clxar 



(4.15) 



Let us consider treating the points of (X,Y) where we know C(X,Y,f) and 

 Q(X,Y,f) as weighted Dirac delta functions; e.g., at (X^2» "^12) ^^ ^^^ 



C(x.y.O= W,^C(x,„Vf) ^ (^-'^.t)<{(Y-Y,^^ . 



17 



