Vibrational Displacement and Mode-Shape Measurement by a Laser Interferometer

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.

Wide dynamic range homodyne interferometry method and its application for piezoactuator displacement measurements

“…A method described by Pernick in 1973 [20] was among the first proposed to detect the value of the modulation index x from the spectral components of the photodetected signal. This method was not specially named, as happened with the J 1 max, J 1 null, J 1 ∕J 2 , J 1 ∕J 3 [21], J 1 …J 4 [18], and J 1 …J 6 [19] methods, for example. In this text, it will be referred to as the Pernick method, in honor of its creator.…”

Calibration of accelerometers by using an extrinsic fiber optic probe

“…Large dynamic range of measurands and the geometrical versatility of fiber optic sensors make them generally superior to other schemes for sensing and calibrating devices [1][2][3][4][5]. Some of the earliest methods for calibration of vibration transducers and vibration amplitude measurement were based on interferometric techniques [6,7]. In the recent times, optical fibers have been used as sensors for measuring vibration amplitude and several other physical parameters [8][9][10][11].…”

Minimum detectable phase shift in spectrum-analysis techniques of optical interferometric vibration detection

“…Here the Vi's stand for the voltage amplitude of the ith frequency component in Eq. (1). As the J, ... J4 method utilizes the components V, to V 4 , the error introduced by the noise floor gets translated into inaccuracy in the measurement of x, resulting in a MDPS.…”

“…A recent report 4 utilized the asymptotic relationship, J 2 (x) + J+ 1 2 (x) = 2x, between the Bessel functions of the first kind to determine the amplitude x of the dynamic phase shift. This method involves measuring the photodetector voltage amplitude at the heterodyne carrier frequency with and without vibration and that of the first-order spectra.…”