The material impulse response for broadband pulses in lossy media

Effects of loss are most often handled in the frequency domain. An example of this approach is the material transfer function, MTF, a closed form causal function describing absorption, dispersion and delay as a function of frequency and increasing distance z. For power law absorption, α=α₀f^y this function can be written in terms of a parameter a=^y√α₀z, MTF(f)=M(af). The material impulse response function, mirf, is the inverse Fourier transform of this function, mirf(t)=m(t/a)/a. In time, loss can be seen as a decay of amplitude according to 1/a and a broadening of the response by a time stretching factor of 1/a with increasing distance z. This function encodes all absorption, dispersion and delay effects into a compact time domain expression. Properties of the material impulse response include delta function like behavior at z=0 and similarity in shape with distance. This real time function convolved with an input waveform at z=0 describes the changes of pulse shape for propagation in a lossy medium. Application of this approach to broadband pulse echoes from a scanning acoustic microscope are presented. The mirf can be combined with the spatial impulse response for fast computation of combined diffraction and absorption effects.