Jonathan M. Huntley

Temporal phase-unwrapping algorithm for automated interferogram analysis

A new algorithm is proposed for unwrapping interferometric phase maps. Existing algorithms search the two-dimensional spatial domain for 2π discontinuities: only one phase map is required, but phase errors can propagate outward from regions of high noise, corrupting the rest of the image. An alternative approach based on one-dimensional unwrapping along the time axis is proposed. It is applicable to an important subclass of interferometry applications, in which a sequence of incremental phase maps can be obtained leading up to the final phase-difference map of interest. A particular example is quasi-static deformation analysis. The main advantages are (i) it is inherently simple, (ii) phase errors are constrained within the high-noise regions, and (iii) phase maps containing global discontinuities are unwrapped correctly, provided the positions of the discontinuities remain fixed with time. The possibility of real-time phase unwrapping is also discussed.

Noise-immune phase unwrapping algorithm

A new phase unwrapping algorithm is proposed which combines noise immunity with computational efficiency. It is based on the requirement that the unwrapped map should be independent of the route by which unwrapping takes place.

Temporal phase unwrapping: application to surface profiling of discontinuous objects

The recently proposed technique of temporal phase unwrapping has been used to analyze the phase maps from a projected-fringe phase-shifting surface profilometer. A sequence of maps is acquired while the fringe pitch is changed; the phase at each pixel is then unwrapped over time independently of the other pixels in the image to provide an absolute measure of surface height. The main advantage is that objects containing height discontinuities are profiled as easily as smooth ones. This contrasts with the conventional spatial phase-unwrapping approach for which the phase jump across a height discontinuity is indeterminate to an integral multiple of 2pi. The error in height is shown to decrease inversely with the number of phase maps used.

Improved noise-immune phase-unwrapping algorithm

An algorithm for unwrapping noisy phase maps has recently been proposed, based on the identification of discontinuity sources that mark the start or end of a 2π phase discontinuity. Branch cuts between sources act as barriers to unwrapping, resulting in a unique phase map that is independent of the unwrapping route. We investigate four methods for optimizing the placement of the cuts. A modified nearest neighbor approach is found to be the most successful and can reliably unwrap unfiltered speckle-interferometry phase maps with discontinuity source densities of 0.05 sources pixel(-1).

Unwrapping noisy phase maps by use of a minimum-cost-matching algorithm

An algorithm for unwrapping noisy phase maps by means of branch cuts has been proposed recently. These cuts join discontinuity sources that mark the beginning or end of a 2π phase discontinuity. After the placement of branch cuts, the unwrapped phase map is unique and independent of the unwrapping route. We show how a minimum-cost-matching graph-theory method can be used to find the set of cuts that has the global minimum of total cut length, in time approximately proportional to the square of the number of sources. The method enables one to unwrap unfiltered speckle-interferometry phase maps at higher source densities (0.1 sources pixel(-1)) than any previous branch-cut placement algorithm.

Error-reduction methods for shape measurement by temporal phase unwrapping

Temporal phase unwrapping is a method of analyzing fringe patterns in which the fringe phase at each pixel is measured and unwrapped as a function of time t. We propose two methods for improving th ...

Shape measurement by temporal phase unwrapping : comparison of unwrapping algorithms

Projected fringes can be used to measure surface profiles unambiguously, even in the presence of surface discontinuities, if the fringe pitch is changed over time. We investigate by numerical, analytical and experimental means the reliability of two recently proposed algorithms for unwrapping the resulting phase histories. The first, which unwraps through a sequence of phase maps produced with a linear change in spatial frequency with time, is found to be superior to the second, which uses only the first and last maps in the sequence. A new method is proposed in which the spatial frequency is changed exponentially with time. It is shown to be significantly more robust than either of the other algorithms under most conditions. The computation time required to unwrap through a given phase range is proportional to and therefore also results in a reduction in computational effort by a factor compared with the linear algorithm.

Deformation, strengths and strains to failure of polymer bonded explosives

This paper describes a study of the strength and failure properties of a range of polymer bonded explosives (PBXS). These are composite systems in which small (typically micrometre up to millimetre-sized) explosive crystals are bonded by a polymer (typically 2–10% (by mass)). In PBXS it is important to optimise the mechanical properties, while maintaining a low sensitiveness (i. e. the material is safe to manufacture, store and handle) and high explosiveness (i. e. reacts powerfully to a prescribed stimulus). The Brazilian test, in which a disc-shaped specimen is loaded diametrically, was chosen for the study. The advantages are that relatively small specimens of typically 10 mm diameter and 4 mm thickness can be used, and that the tensile stresses on the central axis are achieved by applying compressive stresses at the anvil so that complicated gripping arrangements are not required. The technique of double-exposure laser speckle photography was chosen to measure the in-plane displacement field. The technique can measure displacements to sub-micrometre accuracy and provide information over the whole specimen surface. These are distinct advantages over strain gauge methods that involve attaching gauges to the specimen and which only give pointwise information. The double-exposure speckle pattern records were interpreted using an automated Young’s fringes method. The PBXS were of three explosive types and those based on HMX were studied systematically for two crystal sizes and three different binder materials, of two different weight percents. In general, compositions based on micronized crystals were the strongest. Polishing techniques were developed to study the deformation of the individual crystals, the points of nucleation of failure and the fracture paths through the PBXS. The failure modes are discussed in terms of various theoretical models. The mechanical twinning which was shown in earlier work to be an important failure mode in β-HMX also takes place in PBXS based on HMX. The general applicability of the techniques developed in this research for other composite systems is emphasized.

Automated fringe pattern analysis in experimental mechanics : a review

Abstract The paper reviews the main numerical techniques that have been developed to carry out fully automated analysis of fringe patterns resulting from solid mechanics experiments. These include temporal and spatial phase shifting interferometry, temporal and spatial phase unwrapping, and calculation of strain fields from the phase maps. Systematic and random errors associated with the various procedures are also analysed. A unified treatment for both speckle and smooth-wavefront interferograms is presented, and the common features underlying many of the algorithms are emphasized. The paper is illustrated with applications that include ball impact (moiré photography), bending waves in orthotropic plates (double-pulsed dual-reference wave holography) and finite strains in propellant grains (fine grid technique).

Phase-shifted dynamic speckle pattern interferometry at 1 kHz

We describe a phase-shifting out-of-plane speckle interferometer operating at 1 kHz for studying dynamic events. The system is based on a Pockels cell that is synchronized to a high-speed video camera to ensure that the phase shifting occurs between frames. Phase extraction is performed by use of a standard four-frame algorithm, and temporal phase unwrapping allows sequences of several hundred absolute (rather than relative) displacement maps to be obtained fully automatically. The maximum theoretical surface velocity of 67 microm s(-1) is a factor of 40 greater than can be achieved with a speckle interferometer based on a conventional video camera. We test the system using a target that is displaced with constant speed in a direction normal to its surface by means of a piezoelectric transducer. The systems performance in a practical situation is illustrated with measurements on a thin plate undergoing out-of-plane deformation.