Ramon Rodriguez-Vera

PHASE UNWRAPPING THROUGH DEMODULATION BY USE OF THE REGULARIZED PHASE-TRACKING TECHNIQUE

Most interferogram demodulation techniques give the detected phase wrapped owing to the arctangent function involved in the final step of the demodulation process. To obtain a continuous detected phase, an unwrapping process must be performed. Here we propose a phase-unwrapping technique based on a regularized phase-tracking (RPT) system. Phase unwrapping is achieved in two steps. First, we obtain two phase-shifted fringe patterns from the demodulated wrapped phase (the sine and the cosine), then demodulate them by using the RPT technique. In the RPT technique the unwrapping process is achieved simultaneously with the demodulation process so that the final goal of unwrapping is therefore achieved. The RPT method for unwrapping the phase is compared with the technique of least-squares integration of wrapped phase differences to outline the substantial noise robustness of the RPT technique.

Parallel algorithms for phase unwrapping based on Markov random field models

A general framework is presented for the design of parallel algorithms for two-dimensional, path-independent phase unwrapping of locally inconsistent, noisy principal-value phase fields that may contain regions of invalid information. This framework is based in Bayesian estimation theory with the use of Markov random field models to construct the prior distribution, so that the solution to the unwrapping problem is characterized as the minimizer of a piecewise-quadratic functional. This method allows one to design a variety of parallel algorithms with different computational properties, which simultaneously perform the desired path-independent unwrapping, interpolate over regions with invalid data, and reduce the noise. It is also shown how this approach may be extended to the case of discontinuous phase fields, incorporating information from fringe patterns of different frequencies.

Regularization methods for processing fringe-pattern images

A powerful technique for processing fringe-pattern images is based on Bayesian estimation theory with prior Markov random-field models. In this approach the solution of a processing problem is characterized as the minimizer of a cost function with terms that specify that the solution should be compatible with the available observations and terms that impose certain (prior) constraints on the solution. We show that, by the appropriate choice of these terms, one can use this approach in almost every processing step for accurate and robust interferogram demodulation and phase unwrapping.

FAST ALGORITHM FOR INTEGRATING INCONSISTENT GRADIENT FIELDS

A discrete Fourier transform (DFT) based algorithm for solving a quadratic cost functional is proposed; this regularized functional allows one to obtain a consistent gradient field from an inconsistent one. The calculated consistent gradient may then be integrated by use of simple methods. The technique is presented in the context of the phase-unwrapping problem; however, it may be applied to other problems, such as shapes from shading (a robot-vision technique) when inconsistent gradient fields with irregular domains are obtained. The regularized functional introduced here has advantages over existing techniques; in particular, it is able to manage complex irregular domains and to interpolate over regions with invalid data without any smoothness assumptions over the rest of the lattice, so that the estimation error is reduced. Furthermore, there are no free parameters to adjust. The DFT is used to compute a preconditioner because there is highly efficient hardware to perform the calculations and also because it may be computed by optical means.

Robust procedure for fringe analysis.

A robust procedure for analyzing fringe patterns obtained from speckle interferometric techniques is proposed. The fringes generally are observed only in a region S of a rectangular lattice L. We give a method for computing (from S) the region R, where the unwrapped phase is to be computed; this computation is done by use of a morphological filter (in particular, a closing filter). We then use a fast-unwrapping algorithm to compute the phase: a preconditioned conjugate-gradient algorithm that uses the discrete Fourier transform.

Aeolic vibration of aerial electricity transmission cables

A feasibility study for amplitude and frequency vibration measurement in aerial electricity transmission cable has been made. This study was carried out incorporating a fringe projection method for the experimental part and horizontal taut string model for theoretical one. However, this kind of model ignores some inherent properties such as cable sag and cable inclination. Then, this work reports advances on aeolic vibration considering real cables. Catenary and sag are considered in our theoretical model in such a way that an optical theodolite for measuring has been used. Preliminary measurements of the catenary as well as numerical simulation of a sagged cable vibration are given.

Three-dimensional micro-topography by Talbot-projected fringes

Implementation of a structured light projection technique for measuring the relief of objects, or object areas, of micrometric size (approximately 500 μm x 500 μm), is described. It is well-known that when a fringe pattern is projected on an object, the fringes are deformed according to the topography of its surface. This deformed fringe pattern is a modulated optical signal that allows us to measure the relief of the object. Through one of the oculars of a stereomicroscope, previously focused on the object under study, the fringe pattern of one the Talbot self-image is projected. The deformed fringe patterns are observed by the other ocular, in which a CCD camera is mounted to digitize them. Digitized fringe patterns are demodulated by means of a second virtual reference grating. As a result, a moire fringe pattern is obtained delivering a wrapped phase map when is digitally processed by means of a phase recover technique. Phase recovery techniques for obtaining the wrapped phase maps are phase-shifting and spatial phase synchronous. Experimental results and the conditions, under which the topography of an object section is determined, are shown. Also, comparisons over quality between the phase recovery techniques are discussed.

Real discontinuity preservation algorithm for ESPI fracture measuring

A well-founded and computationally fast method is presented for filtering and interpolating noisy and discontinuous wrapped phase fields that preserves both the 2(pi) discontinuities that come from the wrapping effect and the true discontinuities that may be present. It also permits the incorporation of an associated quality map, if it is available, in a natural way. Examples of its application to the computation recovery of discontinuities phase fields from speckle interferometry fracture measuring are presented.

Spatial phase-stepping using a computer-generated diffractive optical element

A computer-generated diffractive optical element (DOE) is used in electronic speckle pattern interferometry (ESPI). This DOE is applied to calculate the interference phase corresponding to object deformation from a single TV frame. The system is utilized for static and transient deformation measurement with CW and pulse Nd:YAG lasers, respectively. The DOE is a modified phase computer generated hologram or cross grating. For transient deformation measurements the DOE does not need to be translated in order to introduce the phase change between diffracted fields. Thus, spatial phase- stepping becomes feasible and high-speed frame acquisitions do not limit real-time phase measurements. Experimental results for spatial phase-stepping with and without moving the DOE are given.

Complementary analysis by ESPI experimental and FEM numerical methods

In this paper, numerical and experimental methods for vibration mode analysis are reported. Some of the vibration modes of an aluminum plate were investigated by modeling with the finite element method (FEM). An out-of-plane electronic speckle pattern interferometer (ESPI) was the experimental method used to analyze the same vibration modes. Experimental and numerical methods are compared. These results were obtained as part of a project to identify the requirements for correlation between experimental modal measurement data and finite element numerical modal estimation.