narrow beam. It will instead produce a random pattern of radiation 
going off in all directions. We can no longer speak of the antenna as 
having a beam width A/L, but it can be shown that the random radiation 
pattern will be correlated over angles small compared to A/L. That 
is, the beam width of the smooth antenna becomes the correlation angle 
of the rough antenna. 
Now, let us return to the case of SAR. The rough terrain takes 
the place of the rough antenna. From any given point, the SAR antenna 
illuminates an area of the ground that extends a distance L in the 
azimuth direction. This illuminated terrain reflects the transmitted 
radiation back to the antenna producing a random radiation pattern with 
correlation angle A/L, which translates to a correlation length of 
4/L x R at the antenna. We must assure that our samples are taken 
closely enough to adequately sample this pattern. We might think that 
this means the sample interval must be less than A/L x R, but we must 
be careful. The argument in the paragraph above applies to an antenna 
that originates the transmitted radiation. The terrain, is merely a 
reflector. As in the derivation of SAR azimuth resolution above, the 
phase shifts of radiation reflected from the terrain must be doubled to 
account for the two way path. The correlation length of the signal is 
thus A/2L x R and the samples must be closer than this. The required 
pulse repetition frequency is thus 
fr, oO 
AR D : (3) 
If the pulse repetition frequency is too high, however, we 
will also run into problems. Suppose the ground swath occupies 
an extent W in range. If pulses are transmitted more closely than 
en (4) 
we encounter ambiguities: a pulse reflected from the far end of 
the swath can return simultaneously with a subsequent pulse reflected 
from the near end of the swath. To avoid this ambiguity, the prf must 
satisfy 
y est (5) 
295