Ricardo Legarda-Saenz

Accurate procedure for the calibration of a structured light system

A procedure is proposed to calibrate a generic structured light system, consisting of one camera and one projector. The proposed pro- cedure is based on defining a unique coordinate system for both devices in the structured light system, and thus, a rigidity constraint is introduced into the transformation process. This constraint is used to derivate a simple function for the simultaneous estimation of the parameters, result- ing in parameters that are more reliable. The performance of the pro- posed procedure is shown on examples of the calibration of two different structured light systems.

Improvement of the regularized phase tracking technique for the processing of nonnormalized fringe patterns

One of the powerful approaches to demodulate a single fringe pattern is the regularized phase tracking (RPT) technique. Here, a new improvement in the RPT technique is presented. This new improvement consists in the addition of one term that models the fringe-pattern modulation. With this new term, the RPT technique can be used for the demodulation of nonnormalized fringe patterns. The performance of the improved RPT technique is shown on examples of various fringe patterns.

Fast phase recovery from a single closed-fringe pattern

A new framework for phase recovery from a single fringe pattern with closed fringes is proposed. Our algorithm constructs an unwrapped phase from previously computed phases with a simple open-fringe-analysis algorithm, twice applied for analyzing horizontal and vertical oriented fringes, respectively. That reduces the closed-fringe-analysis problem to that of choosing the better phase between the two oriented computed phases and then of estimating the local sign. By propagating the phase sign [and a tilewise constant (DC) term] by regions [here named tiles] instead of a pixelwise phase propagation, our analysis of closed-fringe patterns becomes more robust and faster. Additionally, we propose a multigrid refinement for improving the final computed phase.

Robust wave-front estimation from multiple directional derivatives

A quadratic cost functional for computing an estimate of a wave front from multiple directional derivatives is presented. This functional is robust to noise and is specially suited for moiré deflectometry, Ronchi testing, and lateral shearing interferometry.

Wavefront reconstruction using multiple directional derivatives and Fourier transform

We present a Fourier-based regularized method for reconstructing the wavefront from multiple directional derivatives. This method is robust to noise, and is specially suited for deflectometry measurement.

Fast half-quadratic regularized phase tracking for nonnormalized fringe patterns

Although one of the simplest and powerful approaches for the demodulation of a single fringe pattern with closed fringes is the regularized phase-tracking (RPT) technique, this technique has two important drawbacks: its sensibility at the fringe-pattern modulation and the time employed in the estimation. We present modifications to the RPT technique that consist of the inclusion of a rough estimate of the fringe-pattern modulation and the linearization of the fringe-pattern model that allows the minimization of the cost function through stable numerical linear techniques. With these changes, the demodulation of nonnormalized fringe patterns is made with a significant reduction in the processing time, preserving the demodulation accuracy of the original RPT method.

Color-fringe pattern profilometry using a generalized phase-shifting algorithm.

In order to overcome the limitations of the sequential phase-shifting fringe pattern profilometry for dynamic measurements, a color-channel-based approach is presented. The proposed technique consists of projecting and acquiring a colored image formed by three sinusoidal phase-shifted patterns. Therefore, by using the conventional three-step phase-shifting algorithm, only one color image is required for phase retrieval each time. However, the use of colored fringe patterns leads to a major problem, the color crosstalk, which introduces phase errors when conventional phase-shifting algorithms with fixed phase-shift values are utilized to retrieve the phase. To overcome the crosstalk issue, we propose the use of a generalized phase-shifting algorithm with arbitrary phase-shift values. The simulations and experimental results show that the proposed algorithm can significantly reduce the influence of the color crosstalk.

GPU based real-time quadrature transform method for 3-D surface measurement and visualization

In this article, we propose a massively parallel, real-time algorithm for the estimation of the dynamic phase map of a vibrating object. The algorithm implements a Fourier-based quadrature transform and temporal phase unwrapping technique. CUDA, a graphic processing unit programming architecture was used to implement the algorithm. It was tested on a fringe pattern sequence using three devices with different capabilities, achieving a processing rate greater than 1600 frames per second (fps).

Wavefront recovery Fourier-based algorithm used in a vectorial shearing interferometer

Vectorial Shearing Interferometer is able to select variable shear and tilt along any wavefront direction. This system is self-referenced and with variable sensibility. We proposed this instrument to measure a phase object without rotational symmetry. Phase recovery is implemented by a Fourier-based algorithm and spatial unwrapping methods. We show results emphasizing the advantage in the easier selection of fringe density and directional derivative orientation for a speci c optical element.

Dynamic 3-D shape measurement method based on quadrature transform.

In this work, it is presented a combination of temporal phase unwrapping technique and Fourier-based quadrature transform to obtain the dynamic phase map from a vibrating object. The proposed combination results on a very simple algorithm which allows an accurate and versatile 3D reconstruction of the object under analysis.