Ultrasonic sensing of vibrations

A noncontact system for vibration measurement using airborne ultrasound is studied as an alternative to optical techniques. An ultrasonic beam is emitted towards the moving surface and is received after reflection from the object under test. Two different physical effects contribute to the phase modulation of the received signal. The first one is simply the Doppler effect. The second one results from the nonlinear parametric interaction of the high frequency probing beam with the low frequency sound field emitted by the vibrating surface. The probing beam is expanded in a sum of Gaussian beams and the parabolic approximation is used in the case of weak nonlinear effects. Then, the parametric interaction of a Gaussian beam with a low frequency plane wave is explored. A given vibration pattern is calculated by the summation of the plane wave contributions. The parametric effect is computed for different geometries and it is shown that the parametric effect may be much larger than the Doppler effect. Moreover, the parametric directivity of the vibration measurement can be very different from the probing beam directivity.