Principles of Modern Radar - Volume 2 1891121537

254 CHAPTER 6 Spotlight Synthetic Aperture RadarFIGURE 6-23Steps for the phasegradient algorithm.(Adapted fromJakowatz et al. [5].)Complex imageCenter shiftbrightest pixelDetermine window widthand apply windowFourier transformin cross-rangeEstimate phase errorDoes RMSphase error exceedthreshold?NoDoneYesApply phase correctionInverse Fourier Transformback into image domainindependent point scatterers. These and other basic signal processing concepts were thenused to develop the the range and cross-range sampling and resolution constraints forspotlight SAR imaging. We also presented the features of a spotlight-mode SAR imagecollection, noting that the geometry affects the appearance of the image through the waythat ground reflections are projected into the slant plane. An important point to rememberis that most spotlight collections employ a linear flight path even though the data aremotion compensated to appear as if the flight path were circular.Spotlight-mode image reconstruction can be carried out using a number of differentalgorithms. The most popular of these is the polar format algorithm. It relies on thenotion that the spherical waves radiated by the sensor are approximately planar over thescene to be imaged. This amounts to a narrow-beam restriction, and many fine resolutionSAR applications fall into this category. Wide-beam collections are encountered whenusing low frequencies, as in foliage penetration, or when imaging at short ranges. Thelatter is also known as near-field imaging. These situations call for image reconstructiontechniques such as the ω-k algorithm [4,17] or backprojection that account for the sphericalnature of the propagating wavefronts. Backprojection is the most general form of imagereconstruction, but it is also very expensive compared with PFA.The nature and impact of linear, quadratic, sinusoidal, and random phase errors werediscussed. Phase error effects tend to fall into the following categories: (1) loss of resolution