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 use of interferometers is usually divided into two areas. One of them is that of single-dimensional length measurement where the distance along an optical axis is measured, often with more than one wavelength for absolute distance determination. Here one "beam" is considered. The other area is interferometric surface or wavefront measurement where the laterally varying phase distribution of a largely extended wavefront is the property of interest. In this presentation a combination of the two types of use which opens up quite new and challenging applications will be presented.One of the applications which requires simultaneous measurement of distance, slope and curvature is high-accuracy form measurement of aspheres and free form surfaces by the Large Area Curvature Scanning (LACS) method. For a high-accuracy LACS set-up it is most important to measure (and control) the absolute distance between the interferometer and the surface under test (including the multiples of the half wavelength), as well as the slope of the wavefront. In the present set-up, a commercial general purpose interferometer is used.The simultaneous measurement of distance, slope, curvature and shape with this instrument is presented. Special emphasis is laid on the specific fringe evaluation method adapted to the determination of these quantities. It uses a model of the real interferogram image and the superimposed disturbing effects. A suitable global optimization method allows the desired quantities to be determined rapidly and reliably.For the future use of LACS, a new, specifically designed multi-purpose interferometer is introduced which can be used in LACS systems with nanometer form measurement accuracy.
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