713 
Signal to Noise Ratio 
Let the signal to noise ratio for a point scatterer be 
defined in the usual way. Then, from Eqs. 15 and 19, 
SNR - 
S P 
E[g n i 
°K 2 "in: 
N.0 
(26) 
Note that normally N'- M is proportional to range, and also 
inversely proportional to the beam footprint velocity V B . 
Clutter to Noise Ratio 
if uncorrected. The required correction to the measured 
ratio is in proportion to Vg/V s / C . 
The velocity ratio may be readily calculated from the 
geometry sketched in Figure 5. The most compact form 
of the needed equation is in terms of the angle of 
intersection at the centre of the Earth, but a serviceable 
expression is 
(30) 
A measure of the response of the radar to distributed 
scatterers is the clutter to noise ratio. Thus, from Eqs. 15 
and 24, 
CNR - 
E[g d ] 
Elg n ] 
N n 
(27) 
Again, the expected proportionality to appears. 
However, for over-sampling ratios in excess of 1.2, the 
product A G p N int is inversely proportional to V s/c . 
Clearly, the CNR has a different velocity dependence than 
SNR. 
It is of interest to compare Eq. 29 to the receiver clutter 
to noise ratio. Let the antenna pattern illuminate a 
continuous distribution of uniform random scatterers 
described by the surface correlation function of Eq. 20. 
The scatterers are statistically independent over the 
azimuth extent of the beam, so the expected clutter 
(signal) to noise ratio per pulse at the receiver is 
g[|/f] _ 
N0 " W 0 
(28) 
Figure 5. Orbital SAR geometry viewed in 
section along the velocity vectors. 
Now AN int ~Rfi when integration is taken over all 
samples available to the processor. Under this condition, 
comparison of Eqs. 27 and 28 illustrates the role of G P as 
processing gain resulting from azimuth over sampling. 
We turn to the calibration issue for which point reflector 
response is to be compared to mean distributed scatterer 
response. 
Calibration: Peak Method 
One conventional approach to SAR calibration (e.g., 
Kasischke and Fowler 1989) depends on comparing the 
peak point reference response g p divided by the mean 
clutter response E[g d ]. Using Eqs. 15 and 24 one finds 
—^ — (29) 
E[g d \ o 0 AG p ■ 
Now A G p - (V B I V s/c ) ( X/2p ) which is a system constant 
times the velocity ratio. Thus, if the flat Earth expression 
is assumed to apply, calibration attempts of a spacecraft 
SAR based on this method will contain a systematic error 
The velocity ratio is shown in Figure 6 (in deciBels) for 
three typical radar spacecraft altitudes over the incidence 
angles to be used by RADARSAT. For ERS-1, the effect 
is about -0.5 dB, and varies from about -0.5 dB to -0.6 dB 
for RADARSAT as a function of incidence angle. 
Calibration: Integral Method 
Use of integral norms for point reference calibration 
rather than peak impulse response has been suggested by 
several authors (Corr and Smith 1982, Raney 1985, Gray 
et al. 1990). Issues raised in this section add more weight 
to that argument. The response over the image plane to 
a point scatterer is given by Eq. 13 with the input signal 
described by Eq. 14. Using a discrete summation over the 
image plane point reflector response, and recognizing the 
similarity of the form of the calculation to Eq. 21, one 
obtains a simple expression for a digital number 
proportional to the energy of the reference reflector 
% p -°k'nLo p . (31) 
From this equation, and using Eq. 24, the reference