Correlation analysis of the spatial phase of acoustic scattering from a sphere by a vortex beam

Although the pressure amplitude of scattering and related nonlinear effects (e.g., the acoustic radiation force and torque) are widely studied, the modulation of spatial phase resulting from the interaction of vortex beams with scatterers has been less explored. In this paper, we investigate the lateral spatial phase of the backward scattering from an underwater elastic sphere in a Bessel vortex with the angular spectrum method. The resonance scattering is isolated by subtracting the background contribution from the total field based on the resonance scattering theory. A cross correlation method is proposed to locate the positions of singularities of spatial phase from scattering fields precisely. Our theoretical analysis shows that in a limited regime, the offset of the singularities of the spatial phase for the backscattering from a sphere is linearly proportional to the sphere's positions although, beyond this limit, the linear relation breaks. In addition, the modulation of the singularity offset versus the dimensionless frequency ka provides a possible way to evaluate the target size even though the resonance scattering is suppressed at a specific frequency. This work may facilitate an alternative method for the detection/classification of underwater targets with a new degree of freedom of the spatial phase.