Repeat-pass Autofocus for airborne polarimetric Synthetic Aperture Radar Tomography

Synthetic aperture radar tomography, or volume imaging with a side-looking radar uses a two-dimensional aperture made of several antenna paths along more or less parallel trajectories. The carrier motion providing the along track extension of the aperture, and the across-track extension is provided by multiple cross-track antenna or by repeated acquisition along parallel lines. The relative position of the individual antenna centres within the aperture is highly demanding (its accuracy requirement is in the order of magnitude of on tenth of wavelength). The absolute positioning is less demanding: it has an impact on the image registration (which does not require accuracy beyond the image resolution, typically several wavelengths) and to a lesser extend to the topographic effects in motion compensation (but DTM resolution is generally even much lower than that of the image). The relative successive positions during the aperture can be refined by autofocus (using the resulting image sharpness to increase the trajectory accuracy) for the along-track separation. For the across-track separation, especially in repeat-pass airborne acquisitions, the same direct approach is not feasible because volume extension of the landscape is low (typically the height of a tree compared to the image stripe length) and the aperture sampling across-track is sparse (each new antenna centre require a new acquisition line that takes tens of minutes of flight). Co-registration by correlating the images obtained from individual acquisition lines is not enough since the autofocus only refines the relative positions within the along-track aperture, leaving error build up at low frequency. Here we propose and evaluate two solutions: The first one is to separately autofocus the acquisition lines and then recover the low frequency positioning errors between the acquisition lines by measuring the distortion field between the images obtained from each acquisition line and deriving the low frequency relative errors. The second is to autofocus the first (or master) acquisition line and then "refocus" the other acquisition lines using the master signal as reference in a way derived from the bistatic autofocus. To compare the methods, we use the 18 calibrations passes of a three week long airborne acquisition campaign with two antenna centre, providing full polarimetric measurement on one side and dual polar measurement on the other side (thus providing 36 separate trajectories for the Vv and Hv channels and 18 for the Hh and Vh channels).