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