Clustering-based robust three-dimensional phase unwrapping algorithm.

Relatively recent techniques that produce phase volumes have motivated the study of three-dimensional (3D) unwrapping algorithms that inherently incorporate the third dimension into the process. We propose a novel 3D unwrapping algorithm that can be considered to be a generalization of the minimum spanning tree (MST) approach. The technique combines characteristics of some of the most robust existing methods: it uses a quality map to guide the unwrapping process, a region growing mechanism to progressively unwrap the signal, and also cut surfaces to avoid error propagation. The approach has been evaluated in the context of noncontact measurement of dynamic objects, suggesting a better performance than MST-based approaches.

Fast and robust three-dimensional best path phase unwrapping algorithm.

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.

Spatial fringe pattern analysis using the two-dimensional continuous wavelet transform employing a cost function.

We present a novel ridge extraction algorithm for use with the two-dimensional continuous wavelet transform to extract the phase information from a fringe pattern. A cost function is employed for the detection of the ridge. The results of the proposed algorithm on simulated and real fringe patterns are illustrated. Moreover, the proposed algorithm outperforms the maximum ridge extraction algorithm and it is found to be robust and reliable.

Residue vector, an approach to branch-cut placement in phase unwrapping: theoretical study.

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.

Two-dimensional phase unwrapping using a hybrid genetic algorithm.

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 nearest-neighbor 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.

Spatial carrier fringe pattern demodulation by use of a two-dimensional continuous wavelet transform.

A novel technique that uses a fan two-dimensional (2D) continuous wavelet transform (CWT) to phase demodulate fringe patterns is proposed. The fan 2D CWT algorithm is tested by using computer generated and real fringe patterns. The result of this investigation reveals that the 2D CWT technique is capable of successfully demodulating fringe patterns. The proposed algorithm demodulates fringe patterns without the requirement of removing their background illumination prior to the demodulation process. Also, the algorithm is exceptionally robust against speckle noise. The performance of the 2D CWT technique in fringe pattern demodulation is compared with that of the 1D CWT algorithms. This comparison indicates that the 2D CWT outperforms its 1D counterpart for this application.

Comparative study of the conditions required to image live human epithelial and fibroblast cells using atomic force microscopy.

Successful imaging of living human cells using atomic force microscopy (AFM) is influenced by many variables including cell culture conditions, cell morphology, surface topography, scan parameters, and cantilever choice. In this study, these variables were investigated while imaging two morphologically distinct human cell lines, namely LL24 (fibroblasts) and NCI H727 (epithelial) cells. The cell types used in this study were found to require different parameter settings to produce images showing the greatest detail. In contact mode, optimal loading forces ranged between 2-2.8 x 10(-9) and 0.1-0.7 x 10(-9) (N) for LL24 and NCI H727 cells respectively. In tapping (AC) mode, images of LL24 cells were obtained using cantilevers with a spring constant of at least 0.32 N/m, while NCI H727 cells required a greater spring constant of at least 0.58 N/m. To obtain tapping mode images, cantilevers needed to be tuned to resonate at higher frequencies than their resonance frequencies to obtain images. For NCI H727 cells, contact mode imaging produced the clearest images. For LL24 cells, contact and tapping mode AFM produced images of comparable quality. Overall, this study shows that cells with different morphologies and surface topography require different scanning approaches and optimal conditions must be determined empirically to achieve images of high quality.

Three-dimensional shape measurement of non-full-field reflective surfaces.

We describe a technique for the measurement of non-full-field reflective surfaces by using phase-stepping profilometry. We explain the principles of phase demodulation and discuss three-dimensional (3-D) height reconstruction in the case of measuring surfaces with reflective properties such as plain glass and mirrored glass. A number of required calibration algorithms are described to obtain surface slopes and reconstructed 3-D heights of the whole surface. Masking for non-full-field objects and the surface reconstruction procedure are demonstrated mathematically and algorithmically. Several experimental results are given for glass with different shapes and defects. Measurement of a spherical mirror with a known radius has also allowed us to show the performance of the proposed technique. This allows for the possibility to compare 3-D data from the known object with data taken from the measurement system.

Agglomerative clustering-based approach for two-dimensional phase unwrapping.

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.

Quantization error of CCD cameras and their influence on phase calculation in fringe pattern analysis.

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.

Fast two-dimensional phase-unwrapping algorithm based on sorting by reliability following a noncontinuous path.

We describe what is to our knowledge a novel technique for phase unwrapping. Several algorithms based on unwrapping the most-reliable pixels first have been proposed. These were restricted to continuous paths and were subject to difficulties in defining a starting pixel. The technique described here uses a different type of reliability function and does not follow a continuous path to perform the unwrapping operation. The technique is explained in detail and illustrated with a number of examples.

Robust, fast, and effective two-dimensional automatic phase unwrapping algorithm based on image decomposition.

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 areas), the algorithm reacts satisfactorily to random noise and breaks in the wrap distributions. Execution times for a 512 x 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.

Technique for phase measurement and surface reconstruction by use of colored structured light.

We present a new method for improving the measurement of three-dimensional (3-D) shapes by using color information of the measured scene as an additional parameter. The widest used algorithms for 3-D surface measurement by use of structured fringe patterns are phase stepping and Fourier fringe analysis. There are a number of problems and limitations inherent in these algorithms that include: that the phase maps produced are wrapped modulo 2pi, that in some cases the acquired fringe pattern does not fill the field of view, that there may be spatially isolated areas, and that there is often invalid and/or noisy data. The new method presented to our knowledge for the first time here uses multiple colored fringe patterns, which are projected at different angles onto the measured scene. These patterns are analyzed with a specially adapted multicolor version of the standard Fourier fringe analysis method. In this way a number of the standard difficulties outlined above are addressed.

Fringe pattern demodulation with a two-frame digital phase-locked loop algorithm.

A novel technique called a two-frame digital phase-locked loop for fringe pattern demodulation is presented. In this scheme, two fringe patterns with different spatial carrier frequencies are grabbed for an object. A digital phase-locked loop algorithm tracks and demodulates the phase difference between both fringe patterns by employing the wrapped phase components of one of the fringe patterns as a reference to demodulate the second fringe pattern. The desired phase information can be extracted from the demodulated phase difference. We tested the algorithm experimentally using real fringe patterns. The technique is shown to be suitable for noncontact measurement of objects with rapid surface variations, and it outperforms the Fourier fringe analysis technique in this aspect. Phase maps produced withthis algorithm are noisy in comparison with phase maps generated with the Fourier fringe analysis technique.

Fringe pattern demodulation with a two-dimensional digital phase-locked loop algorithm.

A novel technique called a two-dimensional digital phase-locked loop (DPLL) 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 two-dimensional 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.