Model for continuously scanning ultrasound vibrometer sensing displacements of randomly rough vibrating surfaces

An analytic model is developed for the time-dependent ultrasound field reflected off a randomly rough vibrating surface for a continuously scanning ultrasound vibrometer system in bistatic configuration. Kirchhoff’s approximation to Green’s theorem is applied to model the three-dimensional scattering interaction of the ultrasound wave field with the vibrating rough surface. The model incorporates the beam patterns of both the transmitting and receiving ultrasound transducers and the statistical properties of the rough surface. Two methods are applied to the ultrasound system for estimating displacement and velocity amplitudes of an oscillating surface: incoherent Doppler shift spectra and coherent interferometry. Motion of the vibrometer over the randomly rough surface leads to time-dependent scattering noise that causes a randomization of the received signal spectrum. Simulations with the model indicate that surface displacement and velocity estimation are highly dependent upon the scan velocity and projected wavelength of the ultrasound vibrometer relative to the roughness height standard deviation and correlation length scales of the rough surface. The model is applied to determine limiting scan speeds for ultrasound vibrometer measuring ground displacements arising from acoustic or seismic excitation to be used in acoustic landmine confirmation sensing.