IV-46 



The phase and tiie amplitude fluctuations at a point are therefore essentially 

 uncorrelated for ranges of propagation long compared to the focusing distance of 

 the inhomogeneities. On the other hand, they are quite strongly correlated in- 

 side the focusing range. 



We can also calculate the cross correlation of the amplitude or the phase 

 at two distinct points in space. Chernov computes some typical correlation dis- 

 tances (i.e., distances over which the correlation is appreciable) for two receiving 

 points. We must distinguish between two points located relative to each other in 

 the longitudinal direction of wave propagation and two points located transversely, 

 i.e., in a constant phase plane of the incident plane wave . We find that a typical 

 distance of longitudinal correlation is of the order of magnitude of the focusing 

 range, which is approximately ka . 



Longitudinal correlation can therefore extend over appreciable distances. 

 In the transverse direction, however, the correlation distance of the single fluctua- 

 tions is of the same order of magnitude as the correlation of the refractive index, 

 i.e. , of the order of magnitude of a. Figures IV- 14 and IV- 15 show some trans- 

 verse correlation functions of the phase and the amplitude computed by Chernov 

 on the basis of a Gaussian correlation function of the index of refraction. These 

 quantitative conclusions about signal correlation appear to be borne out by experi- 

 mental evidence such as that shown in Figure IV- 16 (after Skudrzyk). 



S-7001-0307 



