Phase error compensation in multi-baseline SAR tomography

This paper explores the main issue surrounding the multidimensional synthetic aperture radar (SAR) image focusing techniques, suchlike those caused by the atmosphere propagation delays or by residual platform motion. The problem brings unknown contributions to the phases of complex received signal that it is generally independent of acquisitions track to track and leads spreading and defocusing in multi-dimensional space. To deal with these issues, in this paper an auto-focusing procedure based on sharpness optimization of the reconstructed signal has been employed. The main concern about this technique is that sharpness optimization by itself however can introduce unwanted and uncontrollable vertical shifts in the focused image. To tackle this issue, the phase error is estimated by multiple integration of second derivative of the phase with respect to baseline. The estimation of the calibration phase is performed by optimizing contrast or entropy of the vertical profile with the constraint of a zero phase derivative. In this way, unwanted vertical shifts are avoided and the correct height reference is preserved. Experimental results from the proposed method are evaluated by vertical profile reconstruction performance in the controlled conditions by simulated dataset over the forested area and multi-baseline data acquired by ONERA in Guyana in the frame of European space agency's campaign TROPISAR.