Phase shifting for nonsinusoidal waveforms with phase-shift errors

Abstract

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 j th 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.

An integral approach to phase shifting interferometry using a super-resolution frequency estimation method

“…These phase increments are generally applied using a piezoelectric device (PZT). Although three frames are normally sufficient to compute the phase distribution, the measurement process is sensitive to various systematic [6][7][8][9][10][11][12][13][14][15][16][17][18] and random errors [19][20][21][22][23][24]. The large number of frames has been shown to decrease the sensitivity to these errors.…”

“…The algorithm proposed by Hibino et al [14] offers the possibility to reduce the calibration error in the presence of higher order harmonics. Hibino et al [14] and Surrel [11] showed that 3 2 + κ and 2 2 + κ samples are respectively necessary to minimize the effect of the th κ order harmonic, with the phase step ( )…”

High-resolution frequency estimation technique for recovering phase distribution in interferometers

“…The algorithm proposed by Hibino et al 5 offers the possibility of reducing calibration error in the presence of higher-order harmonics. Hibino et al 5 and Surrel 2 showed that kth-order harmonics can be minimized with phase step 2p͑͞k 1 2͒ between acquired data frames.The objective of this Letter is to propose a novel approach to obtaining phase measurements in the presence of PZT miscalibration and multiple-order harmonics in the sampled waveform. This method, which permits free choice of the phase shifts from 0 to p, completely avoids imposing conditions on the phase shift that must be applied by establishing a high-resolution technique 6 for estimating the phase step.…”

“…The algorithm proposed by Hibino et al 5 offers the possibility of reducing calibration error in the presence of higher-order harmonics. Hibino et al 5 and Surrel 2 showed that kth-order harmonics can be minimized with phase step 2p͑͞k 1 2͒ between acquired data frames.…”

“…(1) has been changed to a subscript of I in Eq. (5). Equation (5) shows that at least N $ 4k 1 2 samples are required for extraction of the roots of polynomial P ͑z͒, enabling us to find the unknown value z k .…”