Generation of the basis sets for multi-Gaussian ultrasonic beam models--an overview

Area of Science:

• Acoustics
• Wave Propagation
• Computational Physics

Background:

• Gaussian beam models offer powerful simulation tools for wave fields from piston transducers.
• These models utilize a superposition of Gaussian basis functions.
• Gaussian beams facilitate transmission through complex geometries and media.

Purpose of the Study:

• To provide an overview of spatial and k-space domain methods for obtaining multi-Gaussian beam model coefficients.
• To relate the expansion coefficients derived from these two methods.
• To demonstrate the applicability of optimized coefficients for circular transducers to rectangular probes.

Main Methods:

• Synthesis of wave fields using a superposition of Gaussian basis functions.
• Comparison of spatial domain and k-space domain methods for determining expansion coefficients.
• Optimization of coefficients for circular piston transducers and their application to rectangular probes.

Main Results:

• Established a relationship between expansion coefficients from spatial and k-space domain methods.
• Demonstrated that coefficients optimized for circular transducers yield improved simulations for rectangular probes.
• Identified limitations in the accuracy of multi-Gaussian beam models in the very near field due to the paraxial approximation.

Conclusions:

• Multi-Gaussian beam models are effective for simulating wave fields from piston transducers.
• The transferability of optimized coefficients between different transducer geometries (circular to rectangular) enhances simulation capabilities.
• The paraxial nature of Gaussian beams imposes inherent accuracy limitations in near-field simulations.