Geri

Phase unwrapping has been and still is a cumbersome concern that involves the resolution of several different problems. When dealing with two-dimensional phase unwrapping in fringe analysis, the final objective is, in many cases, the realization of that analysis in real time. Many algorithms have been developed to carry out the unwrapping process, with some giving satisfactory results even when high levels of noise are present in the image. However, these algorithms are often time consuming and far removed from the goal of real-time fringe analysis. A new approach to the construction of a simple and fast algorithm for two-dimensional unwrapping that has considerable potential for parallel implementation is presented.

What we believe to be a novel technique of branch-cut placement in the phase unwrapping is proposed. This approach is based on what we named residue vector, which is generated by a residue in a wrapped phase map and has an orientation that points out toward the balancing residue of opposite polarity. The residue vector can be used to guide the manner in which branch cuts are placed in phase unwrapping. Also, residue vector can be used for the determination of the weighting values used in different existing phase unwrapping methods such as minimum cost flow and least squares. The theoretical foundations of the residue-vector method are presented, and a branch-cut method using its information is developed and implemented. A general comparison is made between the residue-vector map and other existing quality maps.

We describe a novel algorithm for two-dimensional phase unwrapping. The technique combines the principles of agglomerative clustering and use of heuristics to construct a discontinuous quality-guided path. Unlike other quality-guided algorithms, which establish the path at the start of the unwrapping process, our technique constructs the path as the unwrapping process evolves. This makes the technique less prone to error propagation, although it presents higher execution times than other existing algorithms. The algorithm reacts satisfactorily to random noise and breaks in the phase distribution. A variation of the algorithm is also presented that considerably reduces the execution time without affecting the results significantly.

This paper presents a thorough discussion on the application of the one-dimensional continuous wavelet transform (1D-CWT) in order to retrieve phase information in temporally and spatially tilted fringe patterns and highlights recent progress and challenges. The paper also suggests some possible future developments for this method. The advantages and drawbacks of the one-dimensional continuous wavelet transform technique are discussed here and in this context are compared to the widely used methods of Fourier fringe analysis, phase stepping and the windowed Fourier transform. A description is given of the manner in which the CWT phase gradient and phase estimation methods may be used to extract the phase of fringe patterns, and these two methods are compared and contrasted. Five different ridge extraction algorithms are explained and the performance of three of these is evaluated. To alleviate the distortions that may occur at the image borders and at regions close to holes in fringe patterns, two methods are described and evaluated for extending the image edges and for filling in holes within fringe patterns. A novel mother wavelet is presented which has been designed to improve the ability of the continuous wavelet transform to analyse fringe patterns that contain sudden phase variations. The sampling and structural conditions that are required to obtain ‘correct’ phase are also discussed.

A novel technique called a two-dimensional digital phase-locked loop ͑DPLL͒ for fringe pattern demodulation is presented. This algorithm is more suitable for demodulation of fringe patterns with varying phase in two directions than the existing DPLL techniques that assume that the phase of the fringe patterns varies only in one direction. The two-dimensional DPLL technique assumes that the phase of a fringe pattern is continuous in both directions and takes advantage of the phase continuity; consequently, the algorithm has better noise performance than the existing DPLL schemes. The twodimensional DPLL algorithm is also suitable for demodulation of fringe patterns with low sampling rates, and it outperforms the Fourier fringe analysis technique in this aspect.

A spatiotemporal phase-unwrapping method is presented that combines the dynamic fringe-projection method and the phase-shifting technique and extends the phase-unwrapping method, which measures two phase maps at different sensitivities. The most important feature of the method is that it makes possible the automatic three-dimensional shape measurement of discontinuous objects with large dynamic range limits and high precision because the effective wavelength of the fringe-projection profilometry can be continuously varied over several orders of magnitude by rotation of the projection grating in its own plane. Only one grating and several steps of rotating the grating are required; therefore the method is inherently simple, fast, and robust. In the experiment, choosing the rotation angle was crucial for optimizing the measurement speed and the measurement accuracy. A criterion is presented for the choice of the minimum number of rotational steps for a given accuracy. The experimental results demonstrate the validity of the proposed method.

We present an investigation into the phase errors that occur in fringe pattern analysis that are caused by quantization effects. When acquisition devices with a limited value of camera bit depth are used, there are a limited number of quantization levels available to record the signal. This may adversely affect the recorded signal and adds a potential source of instrumental error to the measurement system. Quantization effects also determine the accuracy that may be achieved by acquisition devices in a measurement system. We used the Fourier fringe analysis measurement technique. However, the principles can be applied equally well for other phase measuring techniques to yield a phase error distribution that is caused by the camera bit depth.

In this paper we propose a novel hybrid three-dimensional phase-unwrapping algorithm, which we refer to here as the three-dimensional best-path avoiding singularity loops (3DBPASL) algorithm. This algorithm combines the advantages and avoids the drawbacks of two well-known 3D phase-unwrapping algorithms, namely, the 3D phase-unwrapping noise-immune technique and the 3D phase-unwrapping best-path technique. The hybrid technique presented here is more robust than its predecessors since it not only follows a discrete unwrapping path depending on a 3D quality map, but it also avoids any singularity loops that may occur in the unwrapping path. Simulation and experimental results have shown that the proposed algorithm outperforms its parent techniques in terms of reliability and robustness.

What we believe to be a novel three-dimensional (3D) phase unwrapping algorithm is proposed to unwrap 3D wrapped-phase volumes. It depends on a quality map to unwrap the most reliable voxels first and the least reliable voxels last. The technique follows a discrete unwrapping path to perform the unwrapping process. The performance of this technique was tested on both simulated and real wrapped-phase maps. And it is found to be robust and fast compared with other 3D phase unwrapping algorithms.

We describe what is to our knowledge a novel approach to phase unwrapping. Using the principle of unwrapping following areas with similar phase values ͑homogenous areas͒, the algorithm reacts satisfactorily to random noise and breaks in the wrap distributions. Execution times for a 512 ϫ 512 pixel phase distribution are in the order of a half second on a desktop computer. The precise value depends upon the particular image under analysis. Two inherent parameters allow tuning of the algorithm to images of different quality and nature.

A novel hybrid genetic algorithm (HGA) is proposed to solve the branch-cut phase unwrapping problem. It employs both local and global search methods. The local search is implemented by using the nearestneighbor method, whereas the global search is performed by using the genetic algorithm. The branch-cut phase unwrapping problem [a nondeterministic polynomial (NP-hard) problem] is implemented in a similar way to the traveling-salesman problem, a very-well-known combinational optimization problem with profound research and applications. The performance of the proposed algorithm was tested on both simulated and real wrapped phase maps. The HGA is found to be robust and fast compared with three well-known branch-cut phase unwrapping algorithms.

Purpose: The CT body surface underpins millimeter scale dose computation in radical radiotherapy. A lack of technology has prevented measurement of surface topology changes during irradiation. Consequently, body changes are incorporated into plans statistically. We describe the technology for dynamic measurement of continuous surface topology at submillimeter resolution and suggest appropriately modified planning. Methods and Materials: An interferometer casts cosinusoidal fringes across the surface of a patient on a treatment couch. Motion-induced changes to the spatial phase of the fringes are used to generate dynamic sequences of body height maps. Volume-conserving CT warping, guided by height change, is used to illustrate potential planning perturbations. Results: We present the results for a prone patient with rectal carcinoma. At most of the simultaneously measured 440 ؋ 440 points in each of the 898 body height maps in a dynamic sequence, the standard deviations were <1-2 mm, with occasional points of 6 mm. Surface motion predominantly occurred along the small of the back. This motion was periodic and could take the spine and bladder across the 95% isodose contour. Conclusion: Surface changes are most likely to be within 3 mm during irradiation, despite the effects of breathing and the discomfort of lying prone. The dosimetric effects are acceptable.