A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

A self-scanned 1024 element photodiode array and minicomputer are used to measure the phase (wavefront) in the interference pattern of an interferometer to lambda/100. The photodiode array samples intensities over a 32 x 32 matrix in the interference pattern as the length of the reference arm is varied piezoelectrically. Using these data the minicomputer synchronously detects the phase at each of the 1024 points by a Fourier series method and displays the wavefront in contour and perspective plot on a storage oscilloscope in less than 1 min (Bruning et al. Paper WE16, OSA Annual Meeting, Oct. 1972). The array of intensities is sampled and averaged many times in a random fashion so that the effects of air turbulence, vibrations, and thermal drifts are minimized. Very significant is the fact that wavefront errors in the interferometer are easily determined and may be automatically subtracted from current or subsequent wavefrots. Various programs supporting the measurement system include software for determining the aperture boundary, sum and difference of wavefronts, removal or insertion of tilt and focus errors, and routines for spatial manipulation of wavefronts. FFT programs transform wavefront data into point spread function and modulus and phase of the optical transfer function of lenses. Display programs plot these functions in contour and perspective. The system has been designed to optimize the collection of data to give higher than usual accuracy in measuring the individual elements and final performance of assembled diffraction limited optical systems, and furthermore, the short loop time of a few minutes makes the system an attractive alternative to constraints imposed by test glasses in the optical shop.

Digital wavefront measuring interferometer for testing optical surfaces and lenses

Reliability-guided phase unwrapping algorithm: a review ☆

Nondestructive evaluation (NDE) research on composite materials has been ongoing for several decades, during which time their use has expanded significantly in the aerospace, marine, petrochemical, energy, construction and transport sectors. Initially, many composites were employed as fairings or reinforcements, but they are being increasingly used in primary and secondary load-bearing structures, where a mechanical failure has significantly greater safety implications. This increased scope has resulted in composite structures of significant thickness and complexity. Despite this, there has not been a corresponding increase in research pertinent to the detection and characterisation of defects in thick structures, apart from a brief period of interest by the NDE community in the early 1990s. This review critically assesses advances reported in the NDE of thick-section composites (structures of thickness above 15 mm are considered for the purposes of this review), and identifies future research opportunities to overcome the limitations of existing technologies.

Nondestructive evaluation of thick-section composites and sandwich structures: A review

Advances, limitations and prospects of nondestructive testing and evaluation of thick composites and sandwich structures: A state-of-the-art review

A newly developed path-independent phase unwrapping algorithm, which is simple and concise, is presented. The algorithm is based on a parallel elimination of local phase jumps and the subsequent shifts of them, through iterations, to the boundary or to cancel with others in the midway. The number of iterations never exceeds the sum of the width and height of the processed map, whereas for cellular automata algorithm, a multiplier of the cycle of iterations by the proposed algorithm herein is easily needed for successful treatment of a same map. The proposed noise-immune algorithm is applied to a phase map of electronic speckle pattern interferometry (without any filtering work) to prove its effectiveness.

Phase unwrapping based on a parallel noise-immune algorithm

Branch cutting algorithm for unwrapping photoelastic phase map with isotropic point

Phase unwrapping through region-referenced algorithm and window-patching method

A local histogram-data-orientated filtering algorithm is proposed to remove noise from the deformation phase map obtained by a phase stepping electronic speckle pattern interferometry (ESPI). The proposed filter can successfully eliminate any speckle-generated residues of a real dislocation free map. Since the filtered result is totally free from any phase inconsistency, a simple unwrapping rule, like Macy's method, can be applied for the correct phase retrieval. The motivation and theory of the proposed method is described. A simulated noisy wrapped map is employed to detail its implementation. An intercomparison of the present study and two well-known methods is performed to present the performance of the proposed method. In addition, several ESPI experiments are conducted to provide successful filtering of practical phase maps and to prove the effectiveness of the proposed method.

Histogram-data-orientated filter for inconsistency removal of interferometric phase maps

In this paper, a simple isoclinic phase map unwrapping method is proposed to retrieve map with ambiguities at photoelastic isotropic points. Regional phase unwrapping method is also utilized to enhance the retrieving efficiency after all phase inconsistencies have been fully detected and branch cutting works have been properly done to ensure blockings of all the paths which could cause incorrect integrations while involuntarily crossing them. The correctly retrieved isoclinic data are then fed into isochromatic formulation, and as a consequence an inconsistency free isochromatic phase map will be obtained. This map can be unwrapped by any simple and fast unwrapping algorithm accurately and effectively. Circular disk and ring under diametric compression samples are both applied for the verification of the proposed algorithm. The experimental results show the proposed algorithm can successfully solve the annoying problems occurred at photoelastic isotropic points with a processing time of roughly 2 seconds for a 420 x 420 pixels map by a general personal computer.

M. J. Huang

Papers

Phase unwrapping based on a parallel noise-immune algorithm

Branch cutting algorithm for unwrapping photoelastic phase map with isotropic point

Phase unwrapping through region-referenced algorithm and window-patching method

Histogram-data-orientated filter for inconsistency removal of interferometric phase maps

Regional phase unwrapping algorithm for photoelastic phase map