Imaging ocean waves by synthetic aperture radars with long integration times

Previously developed theories for the imaging mechanism of ocean waves by synthetic aperture radars (SAR's) apply only for short integration times
T
(typically,
T < 1
s). To what extent long integration times modify these theories is investigated. First, an analytical expression describing the effect of systematic wave motions on radar imagery valid for an arbitrary integration time is derived. Numerical evaluation of the expression shows only small deviations from the previous expression valid for short integration times. Thus the restriction of the previous theory, (
\hat{\omega}T/2) \ll 1
, where
\hat{\omega}
is the radian frequency of the long waves, can be relaxed to
(\hat{\omega}T/2) \lsim 1
. Second, the influence of the coherence time of the scene, randomness of wave field, on the imaging mechanism is investigated. It is argued that the scene coherence time is usually larger than the SAR coherent integration time
T
, implying that the azimuthal "image smear" for the case of ocean wave imaging is usually due to systematic wave motion rather than the scene coherence time.