E. J. Skudrzyk 207 
10 
(ce) 
EW=afes cos bs cos(ks)ds 
(0) 
e) 
i l l 
20| + (beke aa 
for a=0.20 and b=0.27 
TOTAL SQUARED THERMAL DEVIATION (per cent) 
Ol 
| 10 100 
WAVELENGTH (yd) 
Fig. 12.9. Power spectrum obtained from an analysis of the correlation function 
R(p) = e 2-295 0,27 which represents a good fit to the experimental results [1]. 
nates the necessity to perform the Fourier integration over an infinite interval 
of time.) The time function, then, is given by 
fae coslwt + U(]da (10) 
A maximum is attained whenever ot + w(t) =0 for mostof the spectral components 
of the distribution. In the vicinity of such a maximum, the above integral may be 
crudely approximated by the following expression: 
229 i i 
f Acosat dw = Aes, eet = Ado Sin x (11) 
0 @ot x 
It has been assumed that the spectrum is of constant amplitude 4, and that it is 
cut off at the frequency wo. The time function is thus of the form (sinx)/x. The 
amplitude fluctuates, and the period of the fluctuation is equal to the cutoff 
period. Actually, the spectrum is not constant, but is of the Kolmogorov type. 
It can be shown that for such a spectrum the fluctuations are still larger. 
The above conclusions can be easily illustrated by experiments in which 
the space coordinate is replaced by the time. For instance, curves very similar 
