Wavefront reconstruction of discontinuous phase objects from optical deflectometry.

One of the challenges of phase measuring deflectometry is to retrieve the wavefront from objects that present discontinuities or non-differentiable gradient fields. Here, we propose the integration of such gradient fields based on an -norm minimization problem. The solution of this problem results in a nonlinear partial differential equation, which can be solved with a fast and well-known numerical method and does not depend on external parameters.

Two-dimensional phase unwrapping based on Fourier transforms and the Yukawa potential spectrum.

The two-dimensional phase unwrapping problem (PHUP) has been solved with discrete Fourier transforms (FTs) and many other techniques traditionally. Nevertheless, a formal way of solving the continuous Poisson equation for the PHUP, with the use of continuous FT and based on distribution theory, has not been reported yet, to our knowledge. The well-known specific solution of this equation is given in general by a convolution of a continuous Laplacian estimate with a particular Green function, whose FT does not exist mathematically.

Direct phase unwrapping method based on a local third-order polynomial fit.

When recovering smooth phases by phase unwrapping algorithms, many noniterative algorithms are available. However, normally those algorithms offer approximations of the current phase that cannot be accurate enough. This is because the majority of them are based on global approaches instead of local ones.

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.

Total variation regularization cost function for demodulating phase discontinuities.

We introduce a method based on the minimization of a total variation regularization cost function for computing discontinuous phase maps from fringe patterns. The performance of the method is demonstrated by numerical experiments with both synthetic and real data.

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.

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.

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.

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.

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.

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.

Quadratic cost functional for wave-front reconstruction.

A quadratic cost functional for reconstruction of a high-resolution wave front from a coarse wave front is presented. The functional uses as data the position and the direction of the coarse wave front that had previously been computed with a ray-tracing method. This functional uses an optical relationship between the ray information and the wave front's shape to reconstruct a high-density wave front.