Motion compensation method for vortex SAR imaging

In synthetic aperture radar (SAR) imaging, the flight trajectory of a carrier aircraft is affected by atmospheric turbulence and vibration, and its flight trajectory deviates from the ideal trajectory. This affects the quality of the imaging and must be compensated for its motion. Electromagnetic vortex waves carry orbital angular momentum with more information modulation and acquisition ability and have been proven to have higher azimuthal resolution in radar imaging compared with plane waves. However, current research on motion compensation algorithms by related scholars is based on plane-wave imaging without considering the errors introduced by vortex wave imaging. In contrast to the compensation algorithms based on planar waves, the motion compensation method relying on vortex electromagnetic waves necessitates consideration of the angular errors inherent in the vortex wave echo formula's Bessel terms and pitch angles and their impact on imaging. This study thus derives expressions for the angular errors in instantaneous azimuth and pitch angles and conducts an analysis of the Bessel amplitude term. It extracts pitch angle errors and designs corresponding matched filters accordingly. Finally, numerical simulations are performed under different modes to compare and contrast the effects of compensation. The azimuthal integrated sidelobe ratio experiences significant enhancement post-compensation, thereby validating the effectiveness of the algorithm and providing insights into motion compensation for vortex SAR imaging.