Principles of Modern Radar - Volume 2 1891121537

266 CHAPTER 7 Stripmap SARFor stripmap collections it was found that the achievable integration angle is limited tono more than the 3 dB beamwidth of the physical radar antenna. Applying a common antennarule-of-thumb—that the 3 dB beamwidth is equal to wavelength divided by aperturesize—to (7.2), a constraint on stripmap cross-range resolution was established asCR(stripmap) ≥ D 2(7.3)where D is the horizontal length of the real antenna. For example, an antenna1minsizecan produce a stripmap SAR image with a cross-range resolution no better than 0.5 m.To record data unambiguously, information along-track must be sampled at a sufficientlyhigh spatial rate. The maximum interval between samples d is set by the null-to-nullbeamwidth of the real antenna. Using another rule-of-thumb—that the peak-to-null extentis equal to wavelength divided by aperture size—it was found that the interval betweensamples must bed ≤ D 4(7.4)For example, an antenna 1 m in size requires an along-track sampling interval no largerthan 0.25 meters. If the platform is moving at 100 m/s this requirement is met by a pulserepetition frequency (PRF) of 400 Hz or higher.7.2.2 Point Spread ResponseA second tenet from the signal processing paradigm is that high-fidelity image formationtechniques may be developed through knowledge of the point spread response (PSR), themanifestation of a point target in the measured data.Figure 7-3 shows domains and transformations over the full end-to-end SAR procedure.The top diagram depicts the data acquisition geometry. Cross-track (down-range)and along-track (cross-range) dimensions are denoted by r and x, respectively. In this developmentr is distance in the slant plane (along the line of sight from the platform to theground); later in the chapter we discuss mappings from down-range in the slant plane todownrange in the ground plane. The complex scene content is represented by the functiong(x,r). The diagram at left depicts the recorded data as a function of fast-time delay tand along-track position of the platform u. The complex data content is represented bythe function d(u,t). The last diagram depicts the final SAR image, which is hopefully anaccurate rendering of the original scene. Hence, it shares the same dimensions, x and r.The complex image content is represented by the function f (x,r).The slant-range R from the platform to a location in the scene is calculated by referringto Figure 7-4 and applying the Pythagorean theorem:√R(u; x,r) = (u − x) 2 + r 2 (7.5)This function takes the form of a hyperbola. The shape of the PSR is the same for allscatterers at the same cross-track location (constant r) and different along-track locations.However, the shape changes as cross-track varies, so the PSR for scatterers near theground-track are severely bowed whereas the PSR for scatterers farther away is flatter.