where we get 



-It 



Thus if the energy distribution as a function of direction is the same 

 for P(fi) = P(fo) then we also get 



A(e,fi) = A(e,fo). 



Consider now (assuming A(e,f) can be so expressed) a Fourier series 

 expansion of A(9,f) for fixed f. Clearly it is periodic in 9 with 

 period Iv . Thus for any given f = fg we can write AC9,f) as 



00 ^ 



(7.17) 



Substituting this expansion into Equation (7.15) we get 



OR P*(xx -f ) = If [co5 (ait KD cos(e - 1|))) ole +£ (a^ Icos ^ 



4- ^l^* UiM (atr KD cos (6 - tj)ie + 



^. I e^ .... 



tisi ^ ■'-Tr 



y'[a„fcos>iesiM(2LtrKDCos(e-if^ 



b^ siMTje SiM(aiyHD cos(d-iK))de;( (7.18) 



-It 



36 



