Skew-focus phased array imaging: Application to multidimensional velocity estimation

A novel method for multi-dimensional velocity estimation using phased arrays is introduced. The method is based on the `skew-focus' beam recently discovered by the author. The skew-focus can be steered and focused like any normal phased array beam, except that the phase fronts within the resolution cell are slanted off the main direction of propagation. Using two complementary skew-focus beams with skew angles on both sides of the main beam direction, one can obtain two independent estimates of the velocity vector. The true velocity vector can be estimated from these measurements in a straightforward manner. Skew-focus beams can be optimally synthesized in the CW case using a technique previously introduced by the author. It was discovered that the CW synthesis leads to a family of apodization functions largely independent of frequency and are directly applicable in the wideband case. These apodization functions can be expressed analytically and evaluated numerically for a given slant angle (in addition to the steering angle and focal depth). It is important to note that, the resulting apodization functions are smooth and do not result from an ill-posed synthesis procedure. Therefore, these solutions are robust to quantization and discretization effects.