Impedance-matching properties of an inhomogeneous matching layer with continuously changing acoustic impedance

This paper analyzes the impedance-matching properties of an inhomogeneous layer whose specific acoustic impedance varies smoothly across the layer, from the effective value of the transducer specific acoustic impedance to the value of the output medium specific acoustic impedance. In this paper we first derive the energy reflection and transmission coefficients for an inhomogeneous layer with no attenuation and constant propagation speed, and the results are presented for selected profiles. Next, the performance of an inhomogeneous matching layer with an exponential impedance profile is compared with a quarter-wavelength matching plate. Finally, the general case in which both sound speed and density of the inhomogeneous matching layer may vary is analyzed; the specific acoustic impedance profile as a function of travel time is found to be a principal factor, determining the transmission and reflection properties. The spatial functions of the acoustic parameters are determined for the case where both density and sound speed vary exponentially with travel time.