Autofocus Correction of Azimuth Phase Error and Residual Range Cell Migration in Spotlight SAR Polar Format Imagery

Synthetic aperture radar (SAR) images are often blurred by phase perturbations induced by uncompensated sensor motion and /or unknown propagation effects caused by turbulent media. To get refocused images, autofocus proves to be useful post-processing technique applied to estimate and compensate the unknown phase errors. However, a severe drawback of the conventional autofocus algorithms is that they are only capable of removing one-dimensional azimuth phase errors (APE). As the resolution becomes finer, residual range cell migration (RCM), which makes the defocus inherently two-dimensional, becomes a new challenge. In this paper, correction of APE and residual RCM are presented in the framework of polar format algorithm (PFA). First, an insight into the underlying mathematical mechanism of polar reformatting is presented. Then based on this new formulation, the effect of polar reformatting on the uncompensated APE and residual RCM is investigated in detail. By using the derived analytical relationship between APE and residual RCM, an efficient two-dimensional (2-D) autofocus method is proposed. Experimental results indicate the effectiveness of the proposed method.

💡 Research Summary

This paper addresses the dual problem of azimuth phase error (APE) and residual range cell migration (RCM) that jointly degrade the focus of spotlight synthetic aperture radar (SAR) images processed with the polar format algorithm (PFA). While conventional autofocus techniques are limited to correcting one‑dimensional APE, the increasing resolution of modern SAR systems makes the two‑dimensional defocus caused by RCM a critical issue. The authors begin by revisiting the mathematical foundation of PFA, showing that the raw SAR data are reorganized into polar coordinates ((k_r,\theta)) before a two‑dimensional Fourier transform reconstructs the image. In this representation, APE appears as a phase function (\phi_a(\theta)) dependent only on azimuth angle, whereas RCM manifests as a non‑linear shift (\Delta r(k_r,\theta)) along the range dimension. By analytically differentiating the polar reformatting equations, they derive a concise relationship:

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