Numerical spatial impulse response evaluations of lossy media

The spatial impulse response in lossless media can be evaluated exactly with analytical expressions that are specific to individual transducer shapes. These expressions describe the effect of diffraction in the time domain by analytically evaluating the Rayleigh integral. No exact analytical expressions are presently available for lossy media, so numerical methods must be used instead. The spatial impulse response is numeri-cally computed by superposing contributions from time-domain Green's functions weighted by the area of the corresponding section of the piston source. The causal time-domain Green's function for the Power Law Wave Equation is used to evaluate these individual contributions. The spatial impulse response can be numerically evaluated this way for lossy media and for any shape of transducer. The numerically computed lossy result converges to the analytical lossless result as the value of the attenuation constant decreases. Conversely, as the attenuation constant increases, the temporal extent increases, and the sharp edges become increasingly smooth curves.