Phase shifting for nonsinusoidal waveforms with phase-shift errors

In phase measurement systems that use phase-shifting techniques, phase errors that are due to nonsinusoidal waveforms can be minimized by applying synchronous phase-shifting algorithms with more than four samples. However, when the phase-shift calibration is inaccurate, these algorithms cannot eliminate the effects of nonsinusoidal characteristics. It is shown that, when a number of samples beyond one period of a waveform such as a fringe pattern are taken, phase errors that are due to the harmonic components of the waveform can be eliminated, even when there exists a constant error in the phase-shift interval. A general procedure for constructing phase-shifting algorithms that eliminate these errors is derived. It is shown that 2j 1 3 samples are necessary for the elimination of the effects of higher harmonic components up to the jth order. As examples, three algorithms are derived, in which the effects of harmonic components of low orders can be eliminated in the presence of a constant error in the phase-shift interval.