Michael J. Lalor

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.

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 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.

Multichannel Fourier fringe analysis as an aid to automatic phase unwrapping.

We describe a technique termed multichannel Fourier fringe analysis and its application to the problem of automatic phase unwrapping in the presence of surface discontinuities. The technique is especially useful for the analysis of fringe projection contour maps in order to measure surface height distributions. Use is made of multiple fringe patterns that are separated in the frequency space of the Fourier transform by means of a set of bandpass filters. We also describe the design of a special fiber-optic interferometer with features particularly important in the case of this technique: easily adjustable fringe spacing and rotation. Fringe production by the interferometer is analyzed, and the relationship between the fringe phase and the height distribution of an illuminated surface is derived. A method for measuring phase in the case of multichannel Fourier fringe analysis is presented. The application of the technique to automatic phase unwrapping is shown. An example of the technique in operation is given, and a discussion of implementation of the technique is included.

Frequency normalised wavelet transform for surface roughness analysis and characterisation

This paper proposes a new strategy for surface roughness analysis and characterisation based on the wavelet transform. After a short review of wavelet-based methods used in the field of surface roughness analysis, results obtained using a new tool of analysis called the frequency normalised wavelet transform (FNWT) are presented.

Robust fringe analysis system for human body shape measurement

This paper describes the development and practical application of a fringe analysis system for the high-speed measurement of human body shape and position. The application for this system is in the measurement of patient surface location and shape during the delivery of radiotherapy treatment for cancer. The system uses a twin-fiber interferometer as the basis for fringe production. The fringes are then projected onto the surface to be measured and captured by a CCD camera before being analyzed using Fourier-transform fringe analysis by a computer system. The novel features of this work are in the way in which the system has been realized, with maximum robustness and speed as primary goals. This has led to the development of a number of new techniques in data preprocessing, use of the algorithm itself, and calibration. Particular features include the larger than customary field of view, the use of noncollimated fringes, toleration of the damaging radiation environment, robustness to the variable color, texture, and profile of the surface, and the ability to operate at high speed with a conventional PC platform. The system is capable of measuring in excess of 32,000 surface points per second. Further developments of the system are also described, which are intended to extend its capabilities further.

Spatiotemporal phase unwrapping for the measurement of discontinuous objects in dynamic fringe-projection phase-shifting profilometry

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.

Robust, simple, and fast algorithm for phase unwrapping.

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.

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.

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.