A regression analysis method is applied for data transforming and error evaluation in the sine-approximation method (SAM) for the calibration of vibration pick-ups by laser interferometry. A new simple algorithm for phase unwrapping in the SAM is also proposed. To make a more valuable comparison of this modified SAM with other techniques, i.e. the fringe counting method (FCM) and the minimum point method (MPM), the resolution of the measuring system is increased by using a double optical path difference homodyne interferometer. Additionally the uncertainty of the FCM is suppressed by implementing the procedure of fringe phase analysis in the turning points of the vibration cycle. This paper presents a theoretical analysis of the above mentioned problems.

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The regression analysis method applied for data transforming and error evaluation in the sine-approximation method (SAM) for the calibration of vibration pick-ups is experimentally verified. The new algorithm used for phase unwrapping in the SAM has also been examined. Detailed procedures for the analysis of data obtained from the SAM, the modified fringe counting method (FCM) and the minimum point method (MPM) are presented and a comparison of measurements taken has been carried out. The uncertainty of the FCM, suppressed by implementing fringe phase analysis in a single vibration cycle, is evaluated experimentally. The influence of distortions of the modulation phase signal is shown. The error budgets for all applied methods are given and compared. Expanded measurement uncertainties of about 0.2% for acceleration measurements and about 0.5% for sensitivity measurements (with a 99% confidence level) have been obtained.

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