Yves Surrel

Design of algorithms for phase measurements by the use of phase stepping

If the best phase measurements are to be achieved, phase-stepping methods need algorithms that are 112 insensitive to the harmonic content of the sampled waveform and 122 insensitive to phase-shift miscalibration. A method is proposed that permits the derivation of algorithms that satisfy both requirements, up to any arbitrary order. It is based on a one-to-one correspondence between an algorithm and a polynomial. Simple rules are given to permit the generation of the polynomial that corresponds to the algorithm having the prescribed properties. These rules deal with the location and multiplicity of the roots of the polynomial. As a consequence, it can be calculated from the expansion of the products of monomials involving the roots. Novel algorithms are proposed, e.g., a six-sample one to eliminate the effects of the second harmonic and a 10-sample one to eliminate the effects of harmonics up to the fourth order. Finally, the general form of a self-calibrating algorithm that is insensitive to harmonics up to an arbitrary order is given.

Phase stepping : a new self-calibrating algorithm

A new (N + 1)-bucket algorithm is proposed for phase-stepping systems. It eliminates most of the errors caused by the phase-shifter miscalibration.

ADDITIVE NOISE EFFECT IN DIGITAL PHASE DETECTION

The characteristic polynomials associated with the algorithms used in digital phase detection are used to investigate the effects of additive noise on phase measurements. First, it is shown that a loss factor eta can be associated with any algorithm. This parameter describes the influence of the algorithm on the global signal-to-noise ratio (SNR). Second, the variance of the phase error is shown to depend mainly on the global SNR. The amplitude of a modulation of this variance at twice the signal frequency depends on a single parameter beta. The material presented here extends previously published results, and as many as 19 algorithms are analyzed.

Moire and grid methods: a signal-processing approach

This presentation is a formulation of moire and grid methods with the vocabulary of signal processing. It addresses basically the case of in-plane geometrical moire, but, as is well known, any geometrical moire setup can be related to in-plane moire. We show that the moire phenomenon is not a measurement method by itself, but only a step in a process of information transmission by spatial frequency modulation. The distortion of a grid bonded onto the surface of a loaded specimen or structure will cause locally a modulation (Delta) F of the spatial frequency vector F of the grid. The modulation (Delta) F is linearly related to the strain and rotation tensors. An equivalent point of view is to consider the same phenomenon as a phase modulation, caused by the inverse displacements. In this approach, moire is presented merely as an analog means of frequency substraction. The interpretation of the classical fringe processing techniques -- temporal and spatial phase shifting, Fourier transform method -- is made, and some consequences of the zoom-in effect induced by the moire phenomenon are given.

DESIGN OF PHASE-DETECTION ALGORITHMS INSENSITIVE TO BIAS MODULATION

For digital phase detection, the characteristic polynomial method permits algorithms that are insensitive to the harmonic content of the signal and insensitive to miscalibration to be designed easily. It is shown here that this method can also be used to design algorithms that are insensitive to a possible bias modulation of the intensity.

Whole-field assessment of the effects of boundary conditions on the strain field in off-axis tensile testing of unidirectional composites

The objective of this paper is to present an experimental assessment of the effects of boundary conditions on the strain field in 10° off-axis tensile tests on unidirectional carbon/epoxy composites. It is shown experimentally by using a whole-field phase stepped grid technique that oblique tabbing of off-axis coupons results in a homogeneous strain field over the whole specimen, thus preventing premature failure near the tabs. A numerical sensitivity study reveals that the oblique angle is not very sensitive to the elastic moduli values. Therefore only estimates of the moduli are needed to derive the oblique angle. It is also shown by finite-element analysis that a 3° error on the oblique angle is acceptable in terms of stress concentrations near the tabs, but that a 7° error leads to significant stress concentrations for this material.

Effect of quantization error on the computed phase of phase-shifting measurements

The effect of the quantization of fringe intensity on the phase error in phase-shifting measurements is formulated by a characteristic polynomial method. A numerical simulation is performed, and its result is in good agreement with the analytical one. Several factors influencing the quantization effects are investigated.

Phase shifting: six-sample self-calibrating algorithm insensitive to the second harmonic in the fringe signal

This PDF contains the communication Phase shifting: six-sample self-calibrating algorithm insensitive to the second harmonic in the fringe signal.

Phase-shifting algorithms for nonlinear and spatially nonuniform phase shifts: comment

In the framework of phase-shifting interferometry, the characteristic polynomial theory is extended to deal with nonlinear and nonuniform phase-shift miscalibration. A general procedure for designing algorithms that are insensitive to those errors is presented. It is also shown how analytical expressions for the residual phase errors can be obtained. Finally, it is demonstrated that the coefficients of any algorithm can be given a Hermitian symmetry.

Extended averaging and data windowing techniques in phase-stepping measurements: an approach using the characteristic polynomial theory

The extended averaging technique and the data windowing technique used in phase-stepping are investigated using the characteristic polynomials. It is shown that the phase measurement algorithms derived using the extended averaging technique are not in general more efficient and may require more samples than those obtained directly from the rules of the characteristic polynomial theory.