No abstract

Four experimental methods are described in a tutorial way for use with a laser interferometer in measuring vibrational displacements and mode shapes of a transducer face. The relative merits and experimental difficulties of the methods are discussed. Quantitative data to show the type of experimental agreement that one might expect between the various methods and two illustrative mode shape measurements are given. In general, by proper choice of one or more of the methods, displacement measurements of magnitude 0.1–6000 Å at sonic and ultrasonic frequencies can be made at a point 0.1 mm in diameter. Mode shapes are determined simply by moving the laser beam a measured distance between points. Displacement data presented show a random error for all methods of 5% in the range 0.5–80 Å and less than 5% above 80 Å.

The calibration and use of a laser heterodyne system for nonsinusoidal vibration measurements are described. A frequency-shifted beam is heterodyned in a photomultiplier with an unshifted central light beam that has been phase modulated by motion of a reflecting surface. The output of the phototube is passed through a limiter-discriminator receiver, and then through an integrator resulting in a linear reproduction of the surface vibration as long as the frequency-amplitude product is within limits. The linearity and calibration technique has been tested out to a product of 13 kHz × 4700 Å. A minimum amplitude measurement of 3.5 Å was obtained. Measurement of time delay or spatial cross-correlation functions is demonstrated, using two heterodyne detectors.