Numerical study of reflectivity signals with diffracting airborne ultrasound beams

In this work, we investigate an efficient method for calculating the reflected and transmitted acoustic fields from diffracting ultrasound beams incident to a gas/gas interface. The study is motivated by the application to gas sensors of an experimental setup consisting of air and CO2 separated by a thin membrane and a 40 kHz acoustic incident beam at oblique angles. The numerical method consists of performing a Plane Wave Expansion (PWE) of the incident beam using standard Fourier transform methods. Expressions for the reflected and transmitted acoustic fields are obtained in terms of two-dimensional integrals of simple Kernels. These can be performed numerically in a straightforward way. The main approximation in this method comes from guessing the acoustic pressure field at a plane just in front of the ultrasonic emitter. We compare calculations with the PWE method with Finite Element Method simulations in a 2-D geometry, finding good agreement. Among the advantages of the PWE method we have that there is no need to calculate the whole acoustic fields in a large volume of many cubic wavelengths, while still considering rigorously diffraction effects. We will present predictions for practical airborne ultrasound reflection measurements of interest in developing novel acoustic gas sensors.