Computation of the acoustic field of arbitrary plane or spherical transducer

For a transducer excited with an uniformly distributed velocity, the pressure is usually calculated as a convolution process between the diffraction impulse response h(r,t) and the time derivative function of the uniform distributed velocity applied to the transducer v₀(t). h(r,t) functions are only known for few typical shapes, and their sampling leads to a long computation time. Thus, we propose to solve the convolution process between the time derivative function of h(r,t) and v₀(t). We show that for an arbitrary plane or spherical transducer, this equation leads to a simple line integral. Experimental results confirm the validity of the method