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... Byrom Street. Liverpool. L3 3AF ... Page 5. NEURALNETWORKS IN FRINGEANALYSIS 395 a much smaller network is used to process sections of the phase map, effectively building up an image from a large number of smaller sets of inputs. EXPERIMENTAL WORK ...

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.

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.

Advances in image processing and optics technology, allied to the development of algorithmic techniques such as the fast Fourier transform and phase stepping, have allowed automatic fringe analysis to be successfully applied to many problems in visual inspection and noncontact surface measurement. However, when confronted with complicated or noisy images the algorithmic techniques tend to be less successful, implying an

ABSTRACT The influence of thermal loads on the stress-strain state of oxide-ceramic cutting plates is investigated; in the analysis, the nonlinear properties of aluminum oxide and gray iron are taken into account. Requirements are formulated on the properties of aluminum-oxide cutting plates.