Some considerations of reduction of reference phase error in phase-stepping interferometry

Abstract

Positioning errors and miscalibrations of the phase-stepping device in a phase-stepping interferometer lead to systematic errors proportional to twice the measured phase distribution. We discuss the historical development of various error-compensating phase-shift algorithms from a unified mathematical point of view. Furthermore, we demonstrate experimentally that systematic errors can also be removed a posteriori. A Twyman-Green-type microlens test interferometer was used for the experiments.

Multi-frequency inverse-phase fringe projection profilometry for nonlinear phase error compensation

“…Recently, it has been established that object phase retrieval from a single-frame projection fringe pattern using TV-G-Shearlet image decomposition is more accurate than either the well-known Fourier transform method or the wavelet transform method [4]. In particular, both the measurement accuracy and repeatability of FPP have been greatly improved because of the introduction of the phase-shifting (PS) method [5][6][7]. White light is typically used in FPP, and a set of sinusoidal fringes are projected onto an object's surface by a projector.…”

Invited Review Article: Measurement uncertainty of linear phase-stepping algorithms

“…Linear phase step miscalibration can be eliminated either by measuring the effective average phase step angle [12][13][14] or by using an insensitive algorithm, such as the so-called five-bucket algorithm. Error minimization for linear phase step miscalibration has been specifically treated by several authors, [17][18][19][20][21][22][23][24][25][26][27][28] and quadratic and cubic nonlinearities of the phase stepper have been addressed as well. 7-9, 19, 29-31 Numerical a posteriori correction techniques have been developed based on, e.g., iterative least-squares and so-called FIG.…”

Measurement of surface figure of plane optical surfaces with polarization phase-shifting Fizeau interferometer

“…506-510]. Accuracy of PSI technique, sources of errors, susceptibility and sensitivity of different algorithms, techniques of reduction of errors and calibration of phase shifter have been discussed in details in reports [11][12][13][14][15][16][17]4, pp. 373-374, 6, pp.…”