The high velocities and the two square root terms lead to the presence of high-order terms in
slant range history and Doppler history which cannot be ignored.
([x.sub.c], [r.sub.c] cos [[theta].sub.0]) represents the observed scene center, where [[theta].sub.0] is the squint angle, and [r.sub.c] is the
slant range between the synthetic aperture center and the observed scene center.
In Section 3, the derivation of 2D frequency spectrum of the target echo signal is given based on the accurate approximation of the
slant range history, in which the high-order terms cannot be ignored owing to the presence of high velocities and accelerations.
The shortest
slant range between P and the platform is [r.sub.0] and the
slant range between them in the squint angle direction is [R.sub.0] = [r.sub.0]/cos[[theta].sub.s].
where [sigma] is the backscattering coefficient of the target, c is the velocity of light, and [R.sub.n,m]([eta]) is the
slant rangeMoreover, the interpolation for WDA is carried out in wavenumber domain where the dependency of velocity variable on the
slant range cannot be accounted.
[[eta].sub.c] is the slow-time when SAR is closest to the jammer in
slant range. [K.sub.[eta]] is the chirp rate of Linear Frequency Modulation (LFM).
However, all the above analysis is only consider the conference
slant range, so it is necessary to study the characteristic of UMC along
slant range.
where G([theta], [[phi].sub.k]) indicates the 2D antenna pattern, [theta] is the squinted angle in azimuth, [[phi].sub.k] is the antenna arriving angle in elevation, [f.sub.c] is the carrier frequency, c is the light speed, the subscript k (k = 1,2) is used to distinguish different transmitted sub-pulses, [K.sub.r] is the transmitted pulse chirp rate, [tau] is the range time, [[tau].sub.k] is the delay between two transmitted sub-pulses, [R.sub.k] and [R.sub.mn,k] are the range from target to the transmit sub-aperture Tx and receive [Rx.sub.mn], respectively, [R.sub.0] is the
slant range, [DELTA][x.sub.n] is the physical along-track distance between the transmit sub-aperture Tx and the receive sub-aperture [Rx.sub.mn].
Figure 1 shows the geometric relation of the high squint diving SAR, where [H.sub.0] is the initial platform height; platform dives in a speed V; [V.sub.y] is the horizontal speed; [V.sub.z] is the vertical speed; a is the squint angle of SAR imaging; [phi] is the angle between beam centre and platform motion direction, defined as equivalent squint angle; [theta] is the angle between horizontal speed and resultant speed of platform, defined as trajectory inclination angle; [R.sub.0] is the reference
slant range between platform and target at the initial time; [R.sub.t] is instantaneous
slant range at time t; P is the starting point of the motion, and T is point target on the ground.
Therefore, target
slant range history has large spatial variance.
[r.sub.R] (x) is the receiver
slant range of closed approach.