Advanced successive phase unwrapping algorithm for quadrature output Michelson interferometers

The majority of National Metrology Institutes applies interferometric methods for absolute calibration of reference accelerometers. The standard ISO 16063-11 [Methods for the calibration of vibration and shock transducers-Primary vibration calibration by laser interferometry] describes three basic methods: the fringe counting, the minimum-point, and the so-called “sine-approximation”. Although the third method has many advantages compared to the other ones (wider frequency range, better immunity against noise or harmonic distortion, possibility of phase calibration), it is not widely used yet. One of the possible reasons of this delay is its higher hardware requirement. The same standard recommends a high speed and high capacity waveform recorder to sample the photodetector signals. The outlined Successive Phase Unwrapping (SPU) algorithm needs high sampling rate and a huge memory indeed, especially at low frequency calibrations. This paper presents an SPU algorithm that is able to restore the displacement-time function from heavily undersampled photodetector signals. The undersampling ratio can be high enough that a slow (⩽100 kHz) and small capacity (2, … , 8 several ksample/channel) data acquisition board can meet the requirements of the calibrations.