Temporal demodulation of fringe patterns with sensitivity change

Abstract

There are many phase measuring experimental setups in which the rate of temporal phase variation cannot be easily determined. In the case of phase stepping techniques, asynchronous phase measuring techniques were developed to solve this problem. However, there are situations for which the standard asynchronous techniques are not appropriated, like experiments with a sensitivity variation in the phase. In this work, we present an asynchronous demodulation technique for which the only requirement is the monotonicity of the phase in time. The proposed method is based in the computation of the quadrature sign (QS) of the fringe pattern and afterwards the demodulation is performed by a simple arccos calculation, that thanks to the QS extends its range from half fringe to a modulo 2p calculation. The presented demodulation method is asynchronous, direct, fast and can be applied to a general n-dimensional case. We have applied the proposed method to a load stepping experimental fringe pattern obtaining good results.

Multiplicative phase-shifting interferometry using optical flow

“…In the past there have been reported works about multiplicative PSI [4,5]. References [4,5] present techniques for demodulating multiplicative phaseshifting interferograms obtained from a photoelastic sample in a load-stepping experiment [4] and from a surface topography measurement by means of an RGB shadow moiré technique [5].…”

“…References [4,5] present techniques for demodulating multiplicative phaseshifting interferograms obtained from a photoelastic sample in a load-stepping experiment [4] and from a surface topography measurement by means of an RGB shadow moiré technique [5]. In both cases, the method is based on determining the sign of the quadrature signal I Q defined as I Q x; y − sinαΦx; y, where α is the multiplicative phase shift between two patterns.…”

“…In order to obtain this sign, the first step is to normalize the fringe patterns, which consist in background suppression and modulation equalization. After this, we obtain the sign of I Q calculating the gradient of the normalized intensity with respect to n. Note that this method assumes that the phase is monotonic with respect to n [4]. The monotonicity restriction limits the application of this method, and there are interesting problems that cannot be processed using this approach.…”

“…The monotonicity restriction limits the application of this method, and there are interesting problems that cannot be processed using this approach. Some examples are interferograms with an arbitrary phase variation between them, as deformation measurement in speckle interferometry or lens testing by moiré deflectometry [4]. Additionally, the performance of this method depends on the value of the phase variation between samples that must be high enough [4].…”

“…Finally, the modulating phase can be obtained from the spiral phase transform (SPT) [7]. Note that this method is not affected by the monotonicity restriction as the method used in [4,5] and it is also robust against noise because its regularizating character imposes continuity in the reconstructed phase. However, it is important to mention that the proposed method requires the phase difference between successive interferograms not to be higher than π rad.…”