Effect of transducer boundary conditions on the generated ultrasonic field

Several investigators have modeled ultrasonic fields in front of finite sized transducers. Most of these models are based on Huygens principle. Following Huygens-Fresnel superposition principle one can assume that the total field of a finite size transducer is obtained by simply superimposing the contributions of a number of point sources uniformly distributed on the transducer face. If the point source solution, also known as the Green's function, is known then integrating that point source solution over the transducer face one can obtain the total ultrasonic field generated by a finite transducer. This integral is known as Rayleigh-Sommerfield integral. It is investigated here how the ultrasonic field in front of the transducer varies for different interface conditions at the transducer face-fluid interface such as 1) when only the normal component of the transducer velocity is assumed to be uniform on the transducer face and continuous across the fluid-solid interface, or 2) when all three components of velocity are assumed to be uniform on the transducer face and continuous across the interface, 3) when the pressure instead of velocity is assumed to be uniform on the transducer face and continuous across the interface. AU these different boundary and interface conditions can be modeled by the newly developed Distributed Point Source Method (DPSM). These results are compared with the Rayleigh-Sommerfield integral representation that gives the fluid pressure in front of the transducer when the transducer-fluid interface is subjected to uniform normal velocity.