ABSTRACT
Remember that for spaceborne SAR, the maximum range is limited by the earth curvature [6,7], depending on the satellite height and elevation angle. If the transmitted signal is of the form given by Equation 1.54, the received signal as a function of fast time is the output of the matched filter:
s A s A t s t dt
A p
( ) ( ) ( ) ( )τ τ τ= ⊗ = −
=
τ pi τ pi τ−
−
+ −
2 2
2 2 2
R
c f
R
c a
R
cc r cos
(3.3)
where A0 is the scatter amplitude [4] and, without loss of generality, is assumed constant. Equation 3.3 is indeed also dependent on the slow time because the slant range R is varying with the sensor position within the target exposure time. Referring to Figure 1.6, the slow time-dependent slant range can be expanded about R(ηc), with the beam center crossing time, ηc:
R R u
R
u
( ) ( ) ( )
( ) cos
( ) (,η η η
η η η θ
η η= + − + −
ηc )2 +… (3.4)
where θc is look angle to the scene center and
η θ η θc c c c R
u
R
u = =
0 tan ( )sin . (3.5)
Due to the time variation of the range, a point target response will continuously appear along the path according to Equation 3.4 within the synthetic aperture length. A coherent sum of these responses during the course of the target exposure time will be out of focus if no range-induced phase variation is corrected. Figure 3.2
schematically illustrates data collection and mapping from the target (object) to the SAR data domain.
