Principles of Modern Radar - Volume 2 1891121537

326 CHAPTER 7 Stripmap SARdriven by larger system and resource allocation considerations. For example, a SAR maybe capable of both stripmap and spotlight modes and may be tasked with several suchcollections on a pass. A broadside stripmap collection would be preferred, but perhaps thesystem will be busy performing higher-priority spotlight collections at that time, relegatingthe stripmap task to earlier or later in the pass and therefore requiring squinted operation.Directing beams to broadside or squinting them fore or aft does not affect the hyperbolicslant-range history and the form of the PSR; these are driven solely by the geometry.However, the beam patterns provide a shading to PSR. At broadside the portion of thePSR defined by the mainbeam is symmetric about the closest point of approach. Squintingthe beam highlights the leading side of the PSR at the expense of the trailing side or viceversa. The resulting asymmetry is tantamount to a bulk change in average slant rangeto scatterers as they move through the beam. This linear migration of scatterers throughrange, so-called range walk, is the same for all scatterers at the same down-range location.Range walk is equivalently described in temporal frequencies as a Doppler offset or inalong-track wavenumbers as a spatial-frequency offset.The fix for squint-induced range walk depends on the image formation technique.Because the PSR remains hyperbolic, the filter used by RMA and RDA is still a matchto the data; all that remains is to ensure the data and filter have the same support inthe (k u ,ω) domain. However, the time shifts applied to the data in the spatial frequencydomain in the approximation to RDA become difficult to implement when range walk issignificant. It is prudent to remove range walk from the data prior to the Fourier transformfrom along-track to spatial frequency. Since walk is linear and the same for all scatterers,correction is a straightforward linear shift in time and linear multiply in phase over thealong-track collection. To first order, all that remains after correction is a hyperbolicrange curvature that is symmetric about the closest point of approach. The data are nowready for Fourier transformation to the spatial-frequency domain and application to theestablished time-domain RDA method. This same preprocessing of squinted data to removea bulk, linear range walk and phase progression is also appropriate for the DBS family oftechniques.Squinted operation may also be a consequence of motion outside the platform. Forexample, winds aloft may change the effective motion of an airborne SAR. The apparentvelocity of the platform from the imaged ground is the vector sum of the platform velocitywith respect to the surrounding air and the velocity of the wind with respect to the ground.Similarly, planetary rotation will modify the collection geometry of an orbiting spacebasedSAR. From the point of view of a satellite, the rotating earth is manifested as aspatially variant vector flow field. However, for the typically small SAR beam footprintthe earth’s rotation can be approximated as a spatially invariant velocity vector. Then, likethe airborne system in wind, the velocity of the platform with respect to the imaged groundis the vector sum of the orbital velocity and the rotational velocity.Both airborne winds aloft and space-based planetary rotation may be modeled asmodified platform velocity vectors with respect to the imaged swath. There are fourimportant consequences to this model:1. The apparent motion is still linear, so the hyperbolic PSR development is relevant toimage formation.2. In general, the apparent velocity vector has a modified magnitude, so the along-tracksampling interval is, for a fixed PRF, larger or small or expected. (Or the PRF must bemodified to maintain a desired along-track sampling interval.)