4. SCATTERER AMPLITUDE DISTRIBUTIONS 
In the computer model, it was assumed that the amplitude and phase of the 
complex return from each of the numerous scatterers in a pixel would be 
statistically distributed. It was assumed that the phases would be uniformly 
distributed over 27 radians and given by UNIFM2. From intuition it appears 
reasonable to assume that the amplitudes from geophysical seatterers may be 
Rayleigh voltage distributed. A Rayleigh distribution R(g) was not available 
from the computer library so that R(g) was ereated from a uniform distribution 
U(g) using the following transformations: (Ref. 6) 
R(g) = v-2 1n [1 - U(g)] 
Other seatterer amplitude distributions are possible and should be considered in 
subsequent efforts. For example, if the pixel scene contains planar specular 
return surfaces, a log-normal distribution may be more representative. A 
diffuse surface would probably be accurately represented by a constant 
amplitude and uniformly random phase of a large number of scatterers in the 
pixel. 
The computer model assumes that the scatterer amplitude remains constant 
during the azlook integration period. This assumption is usually valid for all 
scatterers. A planar specular surface whose normal is oriented towards the SAR 
deserves a special comment. Such a surface with a dimension d less than the 
resolution ó has a monostatic two-way reflection pattern beamwidth of 
about A/(2d) and this beamwidth is broader than the radar illumination angle 
0v Beeause of the broader beamwidth the seatterer amplitude will remain 
nearly eonstant during the azlook integration period. 
It is further assumed that there are no multipath or multiple refleetion effects 
among the seatterers. 
5. PHASES OF SCATTERERS 
When processing the radar signals to create an image, a deterministic reference 
phase is assumed which is assigned to the center of the pixel and all radar signal 
phases are referred to that phase. The relative phase is obtained from the 
difference Rg in the two slant ranges from the SAR, viz., one slant range 
Ryo to pixel center, and the other slant range R.. to individual scatterers 
within the pixel. 
rs 
The difference in phase ¢,g due to the slant range difference Ry is 
\ 
where A- radar wavelength. The net phase of a scatterer is given by the 
difference in the scatterer random phase 6g and 9... 
6. WAVELENGTH DEPEN DENCE 
The speckle effect is dependent on intra-pixel interferometry and hence on 
radar wavelength with respect to the overall geometry. In the sample 
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