Methods for the calibration of vibration pick-ups by laser interferometry: I. Theoretical analysis

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 ct 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.