709 
CONSIDERATIONS FOR SAR CALIBRATION 
UNIQUE TO ORBITAL SYSTEMS 
R. Keith Raney 
Chief Radar Scientist 
Canada Centre for Remote Sensing 
Ottawa, Ontario, Canada 
ISPRS Commission VII 
ABSTRACT 
For calibration purposes, quantitative expressions are required for the 
response of a synthetic aperture radar (SAR) to both point and distributed scatterers. The 
orbital geometry for satellite SAR systems needs to be included in the analysis. Unlike the 
"flat Earth" case, the spacecraft velocity and the beam footprint velocity are different, and 
enter key expressions in different ways. The impulse response width of a point reflector is 
improved by the velocity ratio, and the peak of the impulse response is enhanced over that 
predicted from the flat Earth model. When imagery of a distributed scene observed by an 
orbital SAR is to be calibrated by comparison to the impulse response of a reference point 
scatterer, the velocity ratio enters the expression for peak power, but does not enter when 
an integral is used over the impulse response. The velocity ratio effect is about -0.5 dB for 
typical systems, and thus is significant when compared to modern SAR calibration goals. 
Image signal to noise ratio is dependent on footprint velocity, but the mean clutter to noise 
ratio for distributed scatterers is dependent on spacecraft velocity. The paper also looks at 
the processing gain resulting from over-lapping image pixels in azimuth through the 
sampling of the pulse repetition frequency. Analysis of the discrete SAR model shows that 
when the pulse repetition frequency exceeds the antenna Doppler bandwidth by only a small 
margin, as is sometimes true for orbital systems, the gain is somewhat greater than that 
normally applied. The general approach uses end to end SAR impulse response rather than 
approximate extrapolation of the standard radar equation to the imaging mode. 
INTRODUCTION 
Calibration of SAR systems is increasing in importance, 
due to the advent of quadrature polarimetry radars (e.g., 
van Zyl 1990), and to more quantitatively demanding 
analysis of SAR data in a variety of Earth applications. 
Experiments based on airborne SAR systems have been 
concerned by variations as small as 0.01 dB as they impact 
the overall radiometric error budget (Kasischke and 
Fowler 1989), and SAR calibration results are headed 
below the 1 dB threshold (Gray et al. 1990). Systematic 
errors or biases are to be avoided. 
References on SAR calibration are appearing at an 
increasing rate, reinforced by encouraging results derived 
from the excellent airborne SAR systems now being oper 
ated by the Jet Propulsion Laboratory, the Canada Centre 
for Remote Sensing, and others. The growing literature 
is timely, given the advent of several major orbital SAR 
systems to operate during this decade. It is natural to 
expect to be able to apply the methodology developed in 
the SAR calibration literature to the orbital situation. 
By way of background, the viewing geometry normally 
used for analysis of SAR azimuth channel response is 
shown in Figure 1. Such a "flat Earth" model is quite 
suitable for the airborne case, from which key azimuth 
performance parameters may be derived. Assuming a 
narrow antenna pattern, the range from the radar to a 
scatterer is, to first order, 
which determines the phase, and hence Doppler, 
properties of the received signal as the aircraft flies past. 
For radar wavelength \ and antenna of beamwidth /3 and 
the geometric definitions implied in the figure, expressions 
are well known for the available integration time 
ß 
V 
(2) 
the antenna limited Doppler bandwidth 
It turns out that a small trap awaits those who would 
apply certain aircraft SAR calibration methods directly to 
the orbital case without accounting for the sphericity of 
the Earth. A systematic error can arise as a result, 
depending on methodology. It would seem that nowhere 
in the calibration literature can be found the basic 
concepts required. 
the time bandwidth product 
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X 
(3) 
(4)