Extended averaging technique for derivation of error-compensating algorithms in phase-shifting interferometry

Abstract

Phase-shifting interferometry suffers from two main sources of error: phase-shift miscalibration and detector nonlinearity. Algorithms that calculate the phase of a measured wave front require a high degree of tolerance for these error sources. An extended method for deriving such error-compensating algorithms patterned on the sequential application of the averaging technique is proposed here. Two classes of algorithms were derived. One class is based on the popular three-frame technique, and the other class is based on the 4-frame technique. The derivation of algorithms in these classes was calculated for algorithms with up to six frames. The new 5-frame algorithm and two new 6-frame algorithms have smaller phase errors caused by phase-shifter miscalibration than any of the common 3-, 4- or 5-frame algorithms. An analysis of the errors resulting from algorithms in both classes is provided by computer simulation and by an investigation of the spectra of sampling functions.

Optical method for measuring bed topography and flow depth in an experimental flume

“…The principle of the phase-shifting method consists of generating a series of images where the projected fringe pattern or grating is shifted in its plane (Schmit and Creath, 1995). A minimum of three measurements is necessary to calculate the phase since there are three unknowns in the fringe pattern (1).…”

Phase-shift algorithm for white-light interferometry insensitive to linear errors in phase shift

“…They are 4-frame Carre 4) , simple 4-frame 5) , 5-frame Hariharan 6) , 7-frame Groot 7) , 5-frame in Schmit 8) , and 6-frame in Hibino 9) algorithms. There are many other algorithms and still others may be in development 12) , but they are not identified here, because of restricted space in the paper.…”

“…The estimated algorithms are of 4-frame Carre 4) , simple 4-frame 5) , 5-frame Hariharan 6) , 7-frame Groot 7) , 5-frame in Schmit 8) , and 6-frame in Hibino 9) . Among the algorithms the one satisfying the former requirement is found to be the 7-frame Groot algorithm.…”

Single-step method for fiber-optic probe-based full-range spectral domain optical coherence tomography

“…They can be categorized into the multi-and single-frame methods. As the multi-frame method, the phase shifting [5][6][7][8][9][10] and the simultaneous multiple detection method [11,12] were researched. For the single-frame method, the BM scan [13] (B-scan: lateral scan, M-scan: reference mirror scan), the B-scan-based Hilbert transform reconstruction [14], and the phase shift between two A-lines [15] methods have been proposed.…”