Principles of Modern Radar - Volume 2 1891121537

298 CHAPTER 7 Stripmap SAR≥r√ − ru 2∣ r02 + 1∣( ) −1/2 ≥∣ r 1 + u2r02 − r∣∣u2≥r − r∣ 2r02 − r∣u2≥−r ∣ ∣2r 2 0(7.81)We are interested in the magnitude of the error on the right sideλ u2≥ |r|8 2r02 (7.82)Defining u Max as the maximum positive or negative along-track location of the platformduring the collection (with aperture center set to u = 0), the restriction becomes|r| ≤ λr 024u 2 MaxThe DOF is twice this limit (one-half up-range plus one-half down-range)DOF = 2|r| ≤ λr 2 02u 2 Max(7.83)(7.84)Now, D SAR = 2u MaxDOF = 2 λr 02DSAR2 (7.85)Finally, substituting the expression for cross-range resolution in (7.16) into (7.85) andignoring any disparity between wavelength at the center frequency and away from thecenter frequency yieldsDOF = 8 CR2(7.86)λ cGiven a fixed resolution and carrier frequency, (7.86) tells us that the depth of focusis independent of range to the swath. For the simulated example in Figure 7-37, wherethe cross-range resolution was 0.5 m and the wavelength was 0.0316 m, the DOF isequal to 63.3 m, just over 30 m up-range and down-range. At very fine resolutions andlow frequencies the DOF grows so restrictive it becomes comparable to the down-rangeresolution, making this algorithm unwieldy.7.4.3.3 Frequency-Domain PSR for RDAA closed-form expression for the frequency-domain PSR given in (7.75) is needed toimplement RDA as described already. The first step to solving (7.75) is to reindex timedelay to place the closest point of approach of the hyperbola at time zero. This operation