(8.6) Q(x',y',t')=lim j^ 



T-*co 



T X Y 

 2/2/2 



T / X -^ Y 

 2 ■ 2" 2 



7i(x, y, t) Ti(x+x', y+y', t+t') dxdy dt 



«Tr ,oo 



( 



^i) U [A(|a., 6)]^ cos[— (x'cose + y'sine) - HLt'ldfxde 



-IT 



oo c» 



= ^ j [J [A*(c, p)]2cos(ax' + py' - ,/g{a^+ p^)^/^ t')dp] dc 



-CD 



'-OO 



In equation (8. 6), a = (x cos0/g, P = fJ. sinS/g, jx = \^(cl + P ) > 



■li 



and G = tan"^{p/c)„ Also 

 (8.7) 



.2 VF[A{ /g(a2 + p2)l/4^ tan-1 ^/a)f 

 [A*(c, p)]'^ = ^ 



If x' and y' are chosen to be zero, then an average over time can re- 

 place an average over space and time, and the result is 



(8.8) 



Q(t') = lim -^ j Ti(x,y, t)Ti(x, y, t+t')dt 



T-^OO / r|n 



■n yr CO 



if 



[A(|4„ 6)] cosfxt'd(j.de 



.oo 



1 I ? 



[A(|j.)]'^ cos|j.t' diJ. 



61 



