Various signal processing methods have been developed for application with specifically modified Michelson interferometers and the novel diffraction grating interferometers for the accurate measurement of translational and rotational motion quantities at sinusoidal and shock-shaped time-dependencies. After a survey of these methods and their particular ranges of applicability, the methods based on the determination of the time-intervals between the zero crossings of the interferometer signals are presented. Different versions of time interval determination are described, which are adapted to either homodyne or heterodyne interferometers. It is shown that time interval analysis can be applied in two different ways -either to identify the phase-modulation of the interferometer signal as a measure of the displacement or rotational angle, or to identify the frequency-modulation of the interferometer signal as a measure of the velocity or angular velocity. Results of the theoretical and experimental investigations and of the application of the time interval analysis for the calibration of accelerometers and angular accelerometers are presented.
The paper presents a method for measuring of the amplitude and phase angle of a sinusoidal vibration in the nanometer range. The method is proposed for the calibration of accelerometers in the frequency range from 1 kHz to 50kHz using heterodyne interferometer signals. The developed method is based on quadrature signals generated by digital signal processing. The vibration signal is regenerated as discrete-time phase sequence of quadrature signals using an arc tangent subroutine. The displacement amplitude and the phase angle of the vibration are obtained by applying least squares estimation to the phase sequence. The theoretical background and details of the generation of quadrature signals and of the estimation of displacement amplitude and phase angle are given. Results of an investigation into the errors due to various disturbing arameters are presented. The performance of the proposed signal processing method was examined by means of computer simulation and experimental data taken from both a test measuring system and a measuring system for the calibration of accelerometers.
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.
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