Reconciliation of theories of synthetic aperture radar imagery of ocean waves

Several theories of synthetic aperture radar (SAR) imagery of ocean waves, especially those dealing with the focusing issue, are examined. We show that the “time-dependent” theories of Lyzenga (1988) and of Kasilingam and Shemdin (1988) and the “velocity-bunching” theory of Bruning, Alpers, and Shroter (1991) are identical for short integration times but diverge on the focusing issue for long integration times. The reason for the divergence is simply that velocity bunching theory assumes that integration times are short compared with ocean wave periods. The inference is that the phase speed of the ocean wave plays a secondary, nearly negligible, role to that of orbital velocity and acceleration in determining the optimum focus setting for short integration times but becomes dominant as integration times are increased. For the case of zero focus adjustment, these focus-dependent theories are shown to reduce to those of Plant and Keller (1983) and of Hasselmann et al. (1985). Thus several of the apparently differing theories of SAR imagery of the ocean are reconciled and shown to be a single consistent theory.