Resolution of a controversy surrounding the focusing mechanisms of synthetic aperture radar images of ocean waves

This paper addresses key problems regarding the focusing of synthetic aperture radar (SAR) images of ocean surface waves, explaining why applying a processor defocus will generally yield an enhanced image, why the same defocus applies to both image modulations brought about by the radar cross section and by the velocity bunching process, and why the effects apply to both single-look and multilook systems independently of look relocation. Two interpretations are given for the case when surface scatterers are stationary, but modulated in reflectivity (radar cross section) by a propagating wavefield. The first interpretation is what will be called a “degrade-and-shift” model. In it, a processor focusing adjustment degrades a point image. However, the overall image can be enhanced because an appropriate defocus results in a shifting of points in such a way that the image can most closely resemble the image of the time-invariant (or “frozen”) reflectivity. The second interpretation is a “defocus-and-refocus” model in which the image of a time-varying reflectivity is defocused and may be refocused to enhance the image. In justifying this “defocus-and-refocus” model, it is shown that the radar return from stationary scatterers of time-varying reflectivities is identical to that from physically moving scatterers of constant reflectivity. Thus, the two interpretations are not contradictory; they are, fundamentally, equivalent. The models support the use of a processor defocus corresponding to one half the wave phase velocity. Both qualitative and quantitative illustrations of the effects are given. Finally, it is shown that the same defocusing effect applies to image modulations brought about by the velocity bunching process