Performance of the scanning ultrasound vibrometer for sensing displacements of a randomly rough vibrating surface

An analytic model is developed for the ultrasound field reflected off a randomly rough vibrating surface for a scanning ultrasound vibrometer system in bistatic configuration. Kirchhoff’s approximation to Green’s theorem is applied to model reflection and scattering from the vibrating rough surface. The model incorporates the beampattern of both the transmitting and receiving ultrasound transducers and the statistical properties of the rough surface. Conventional approaches for estimating surface displacement and velocity based on the laser vibrometer, such as incoherent Doppler shift spectra and coherent interferometry, are applied to the ultrasound system. Simulations with the model indicate that surface displacement and velocity estimation is highly dependent upon scan velocity and operating frequency of the ultrasound vibrometer relative to the roughness height and correlation length scales of the rough surface. The model is applied to determine optimal sonar design parameters and measurement geometry for the scanning ultrasound vibrometer for measuring ground displacements from acoustic/seismic excitation in land‐mine detection.