Aperture Synthesis With Digital Array Radars and Covariant Change of Wavenumber Variables

Abstract

Attributes of digital array radars are leveraged in enhancements of wideband frequency-wavenumber (omega-k) methods to achieve 1) single-pulse, short-range imaging from a stationary array; 2) single-pulse, all-range, high-density, digital beamforming-on-receive from a stationary array; 3) multiple-pulse aperture synthesis for shortrange imaging with sensor movement; and 4) multiple-pulse inverse aperture synthesis for long-range imaging with tracked object movement. Modifications to conventional omega-k algorithms used in synthetic aperture radar are introduced to accommodate antenna element level data, real array element spacing, large scene size and small array size (compared to scene size). Large scene size with k-space processing is handled by a novel Huygens-Fresnel transfer function that does not fully rely on zero-padding to resolve array and scene size mismatch. Aperture synthesis with generalized pulse-to-pulse sensor-step operations is supported. Connections between omega-k wavenumber migration and a covariant change of variables transform associated with Dirac's spectral models of free and scattered electromagnetic fields are established.