<title>Evaluation of uncertainty in interferometric vibration measurements</title>

Abstract

The ISO "Guide to the Expression of Uncertainty in Measurement" (GUM, 1993) establishes a unified method for evaluating and stating measurement uncertainties, that has been accepted by nearly all calibration services and most test cooperations in all parts of the world. In vibration measurements and calibrations using laser interferometry, the application of the GUM may be difficult and very time-consuming unless some possibilities of simplification are made use of. After a brief introduction to the basic procedure specified in the GUM for the calculation of the measurement uncertainty, a survey is given of the problems typically encountered in uncertainty calculations when vibrations are measured or accelerometers calibrated by laser interferometry. It is shown how a model function of simple structure can be established for the usually complex relationship between the output quantity (e.g. sensitivity of an accelerometer), the quantity to be measured (e.g. acceleration) and various influence quantities (noise, transverse motion, base strain etc.). Among other things, non-linear effects such as the influences of distortion, hum and noise can be properly taken into account. The uncertainty evaluation is demonstrated and explained by the example of the measurement of the displacement amplitude of a sinusoidal vibration using Michelson interferometry and by the example of the primary vibration calibration of an accelerometer.

Metrology of vibration measurements by laser techniques

“…Uncertainty evaluations for measurements using laser interferometry [ 4 ] had demonstrated that relative expanded uncertainties (k = 2) < 0.1 % can be attained, e.g., 0.028 % in a measurement of a displacement amplitude 2 µm, and 0.065 % in a measurement of an accelerometer sensitivity (magnitude) of 0.123 pC/(m/s²) at a vibration frequency of 800 Hz using the fringe-counting method. Experimental investigations [ 5 ], [ 7 ] verified such high accuracy (expanded uncertainties < 0.1 %) attainable in vibration measurements and calibrations.…”

“…The example was selected because it characterizes a real measurement where all the metrological aspects have been observed and the specifications stated in the table are precisely documented. Uncertainty of measurement As specified in ISO 16063-11 or ISO 16063-21 in accordance with GUM [ 14 ]; for tools see [ 4 ] or [ 27 ] Complete result including uncertainty Uncertainty budget(s), Combined standard uncertainty, Expanded uncertainty with coverage factor k = 2…”

“…For the fringe counting method [ 12 ] a theoretical description was given in [ 4 ] demonstrating that a stimulated appropriate drift can be used to suppress the error component due to quantization. For the Sineapproximation method in the homodyne and heterodyne versions, specific formulae have been established which functionally relate the offset variations to the maximum modulus of amplitude and phase measurement errors due to drift [ 7 ].…”

Additional error sources for microscopic laser Doppler measurements

“…Therefore, we can consider the electrical-field amplitude E(t) ofthe electrical-field vector E(t)= E1 cos(wt + °)ht)+ P22 cos(wt + E3 cos(wt+ q,) (1) with E1 , E2, and E3 the amplitude of the reference beam, the amplitude of the measurement beam, and the amplitude of the back reflection respectively. In addition, w = 2irv is the frequency of the laser, Wh = 2ftVh is the heterodyne frequency shift of an acousto-optical oscillator, 0(t) is the time-dependent phase shift, and is the phase of the backreflected light relative to the measurement light.…”

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Laser-Doppler Vibrometry has been proven to be an accurate method to measure vibration amplitudes with a known error budget [1]. Therefore, vibrometer technique is used to realize primary standards in vibration-amplitude measurements at national metrology institutes (e.g.

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