IV -42 



We note t±iat the expected value of the amplitude is now no longer the amplitude 

 of the incident wave but rather a slightly larger number. Note also that the 

 logarithm of the amplitude fluctuation Bi is normally distributed, so that the 

 amplitude itself, as given by (IV- 84), should be expected to have a log normal 

 distribution. 



The mean square value of the amplitude can be obtained similarly by 

 averaging the square of (IV- 84): 



<A^> = A^<e^^'^^K = A^^y^io, -2i) = A^^e'^^^'^ . (IV-86) 



We therefore obtain for the square of the coefficient of variation of the amplitude 

 the expression: 



a < | p|> ' ^ "^ -l-'<Bi^> (IV-87) 



We had earlier computed the coefficient of variation for the entire field p for the 

 interference range. Using the present scheme, the average of the total field is 

 given by: 



<p>=p^<e^S^-^^^>=p^X(l'-i)=Po^'*^^''''"^''''"'"''''''^ 



(IV-88) 



Similarly, the coefficient of variation becomes: 



,,2 <| pl^> - I <p>| ^ (<Bi^> + <Si^>) 2 2 



^ - ^ Jl ^ "6 - 1 ^<Bi^> + <Si^> (IV-89 



p ) <p>l 



As we show later, the mean square fluctuations of Si and Bi become equal in the 

 far field, and this explains, see (IV-88), why the magnitude of the total pressure 

 became equal to the amplitude of the incident wave. It is clear from the above that 

 we should like to evaluate the following averages over the ensemble: 



<B-/> = <(Im>lii)^>, <Si^> ^^{Re^if>, <SiBi> = - <Re i|/i Im\|fi> (IV-90) 



Arthur ai.littlcJnt. 



S-7001-0307 



