Method for designing error-compensating phase-calculation algorithms for phase-shifting interferometry

Abstract

We propose a general approach to eliminating some error source effects in phase-calculation algorithms for phase-shifting interferometry. We express the actual phase shift in a convenient form that takes the errors into account and develop in series the detected phase from a generic algorithm. Setting to zero the terms of the series that involve unwanted errors leads to a set of linear equations for the algorithm coefficients, which can thus be found. By using this approach, one could develop an algorithm series for an individual interferometer based on relevant concerns about the main error sources in it and eliminate the error source effects to any desired order. Two examples of algorithm series, to eliminate distorted phase shifts caused by the geometric effect in an interferometer with a spherical Fizeau cavity and to eliminate vibration effects, are discussed.

Moving ahead with phase

“…Although three frames are normally sufficient for estimating the phase, it has now become a well-established fact that additional data frames need to be acquired to minimize the effects of various systematic [41][42][43][44][45][46][47][48][49][50][51][52][53] and random errors [54][55][56][57][58][59]. The use of large number of data frames has been shown to decrease the sensitivity to these errors.…”

Ultrafast Three-Dimensional Imaging System Based on Phase-Shifting Method and Hybrid Dispersion Laser Scanning

“…Since the phase-shifting method has less sensitivity to the ambient light, no strict measurement environment is required. Numerous algorithms have been put forward for phaseshifting method, including three-step algorithm, four-step algorithm, Carré algorithm, Hariharan algorithm and least-square algorithm [4], [13]- [16]. The phase-shifting method could be a promising approach for real-time 3-D imaging.…”

Generation of phase-shifting algorithms with N arbitrarily spaced phase-steps

“…Many PS algorithms have been developed that minimize absolute phase errors that are due to the phase-shift error (see, e.g., [1][2][3][7][8][9], and the references therein). The quantitative detection and compensation of PS errors is of interest also in PS digital holography [10].…”