Compact angular support beams for space-invariant vector flow mapping

The authors define a special class of compact angular spectrum beams (CASBs) that can be used to provide space-invariant estimation of the velocity vector from a single coplanar aperture. By space-invariance the authors mean both range and azimuth flow shift-invariance of velocity estimation. They analytically show that some of the non-diffractive beams, e.g., Bessel beams, are sub-classes of CASBs. They show that CASBs have infinite spatial support and thus, they cannot be generated in practice. They discuss finite support approximation of such beams. These approximations can be implemented using currently available annular and two-dimensional transducer arrays. The authors also describe the related class of spatially modulated CASBs. These beams provide range-invariant true-velocity estimation from frequency shift measurements