Analyzing SAR ambiguities in the u-v plane

Phased array designers routinely analyze beam patterns in the u-v plane, to ensure that aliasing locations (called grating lobes) remain outside the visible beam region. A related spatial aliasing problem occurs in synthetic aperture radar (SAR) systems, where points that can fold onto other locations in an image (called ambiguities) must be kept out of the radar main beam. A well-known SAR criterion specifies the minimum area of a rectangular antenna for ambiguity-free operation. This paper employs a phased array-inspired approach to solving the SAR problem for general antennas, by overlaying SAR ambiguities onto the antenna beam pattern in the u-v plane. A theorem from Number Theory then provides the maximum beam area that does not illuminate ambiguous points, under general conditions. This maximum beam area criterion extends the classic minimum antenna area expression to non-rectangular antennas in unconventional orientations, while providing intuition and visualization familiar from phased array design.