Abstract
Holographic projections of experimental ultrasound measurements generally use the angular spectrum method or Rayleigh integral, where the measured data are imposed as a Dirichlet boundary condition. In contrast, full-wave models, which can account for more complex wave behavior, often use interior mass or velocity sources to introduce acoustic energy into the simulation. Here, a method to generate an equivalent interior source that reproduces the measurement data is proposed based on gradient-based optimization. The equivalent-source can then be used with full-wave models (for example, the open-source k-Wave toolbox) to compute holographic projections through complex media including nonlinearity and heterogeneous material properties. Numerical and experimental results using both time-domain and continuous-wave sources are used to demonstrate the accuracy of the approach.
Highlights
A COUSTIC holography is widely used in ultrasonics for reconstructing the 3-D acoustic field of an ultrasound transducer from hydrophone measurements made in a single plane [1], [2]
A plot of the axial peak pressure through the projected field using the optimized equivalent source and angular spectrum method (ASM) is shown in Fig. 12, with the differences less than 1%
To demonstrate the utility of calculating an equivalent source more generally, i.e., mapping from a Dirichlet boundary condition to an interior source, the calculated equivalent-source plane for the experimental measurement of the H101 transducer shown in the bottom panel of Fig. 4 was used to project the ultrasound field through a heterogeneous nonlinear medium
Summary
A COUSTIC holography is widely used in ultrasonics for reconstructing the 3-D acoustic field of an ultrasound transducer from hydrophone measurements made in a single plane [1], [2]. These methods work very effectively for homogeneous media, but do not allow for projection of the measured data through complex media, e.g., with acoustic nonlinearity and spatially varying sound speed or mass density. Such simulations are of particular interest in medical ultrasonics as the acoustic properties of biological tissue are spatially varying, the wave propagation can be nonlinear, and it is often of interest to study the field of a particular transducer in vivo [6]–[8]. Numerical and experimental results using both time-domain and CW sources are used to demonstrate the approach
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