Generating a pencil beam from a focused transducer using Stolt migration

Scanning using a strongly focused transducer gives a narrow focus depth and locally a high resolution. To obtain a high resolution at every point along the acoustic axis imaging is applied. Because the focal point can be considered as a second source, the wavefield can be split in its causal and anticausal parts. Imaging can be performed efficiently with a mapping algorithm in the wavenumber domain (f-k or Stolt migration), achieving a pencil beam. This work investigates the potential of this mapping algorithm on simulated and experimentally obtained data. The target geometry consisted of a line of point scatterers (pins) mounted in a water tank. The experimental dataset was obtained by scanning along the line of scatterers using an xyz-system. A 1 MHz transducer was used with diameter 1.5" and focal distance 3". The simulated dataset was created using an in-house implementation of a wavefield extrapolation algorithm. Imaging of the simulated and experimental datasets was performed using a custom implementation of the Stolt mapping algorithm. The aforementioned concept was illustrated on simulated data, where the -6dB lateral point spread functions (PSF) were improved by 91.3%, 0% and 90.5% in the near-field (2.5cm), focus (7.4cm) and far-field (13.5cm), respectively. Measurements confirmed this pattern, and showed improvements in the PSFs by 86.8%, 0% and 60.0% at the same distances. The enhancement of the resolution using the mapping algorithm effectively created a pencil beam from the focused beam of the transducer in both the simulations and the experiments.