Location and estimation of the defective area in a diaphragm: an a posteriori moiré method

A moiré method based on holographic interferometry is shown to be a powerful tool for non-destructive testing of diaphragms.     

Lau phase interferometry with a vibrating object

In this paper, we have demonstrated experimentally the vibration analysis of a reflecting object in a time-averaged mode using Lau phase interferometry. Experimental results provide information about the tilt at every point of a vibrating plate. The Lau phase interferometry is robust and simple. Experimental results are compared with conventional shadow-moiré method.     

Monitoring/measurement of out-of-plane vibrations using shearing interferometry and interferometric grating

In this paper, an application of shear plate interferometry combined with moiré readout to monitor/measure out-of-plane vibrations is presented. Moiré fringes are produced between the fringe pattern from the shear plate and interferometric grating recorded by photographing the interference pattern generated from the shear plate. It is demonstrated that the method can be used to study periodic and non-periodic vibrations.     

Experimental tire mechanics by moiré

Tires and their component parts are made from various low modulus rubbers and cord/rubber laminates. In service they typically undergo large deformations of about 1–30%. The accurate measurement of these deformations by either pointwise (strain gage) or full-field (optical) techniques is rendered difficult in these circumstances. Ordinary strain gages reinforce these soft structures and inhibit their deformation, whereas most optical methods are too sensitive to measure large motions. These difficulties can be overcome by the judicious use of various moiré methods: moiré interferometry, geometric moiré and shadow moiré.Several applications of moiré methods to tire mechanics problems are presented. The emphasis is on the range of problems that has been successfully approached and on the results obtained. Examples are drawn from work on belt-edge strains, tread groove strains, sidewall strains, dynamic sidewall deformations and material properties determination. Proprietary details of technique are not included.     

Moiré interferometric fringe patterns about crack tips: Experimental observations and numerical simulation

The local deformation about fatigue cracks has been investigated by the coherent optics method of moiré interferometry. The complexity of the interference fringe patterns motivated the parallel development of companion numerical models for simulating moiré interferometric response for known boundary conditions. Experimental patterns are here examined in the light of computer-generated fringe systems for a stationary crack in elastic as well as elastic-plastic solids. Various effects due to material plasticity, specimen-dependent non-singular stress, and mixed mode loading are identified in the fringe patterns.     

The optimization of three-mirror illuminating system for the four-beam Moiré interferometer

The three-mirror illuminating system for moiré interferometry consists of a Lloyds mirror and two additional mirrors at right angles to each other. This arrangement makes possible the design of a four-beam moiré interferometer system for a cross-lined specimen grating, to determine the u and v displacement components of the object under test. The design problems, including optimization of dimensions of the optical elements and adjustment by a user, are discussed and analytically solved. The analysis was verified by the construction and laboratory use of the interferometer.     

Refractive power mapping of progressive power lenses using Talbot interferometry and digital image processing

A method of refractive power mapping of a lens is presented which is based on Talbot interferometry and utilizes a digital image processor. By adding a digital image processing system, fast measurement of a lens power distribution is feasible. A test lens is placed in front of two collinearly arranged gratings. The light passing through the test lens produces a shifted Talbot image of the first grating on the second grating and generates moiré fringes. Given the inclination angle of moiré fringes, the refractive power of the lens can be calculated. The calculation is performed using a digital image processor. This method is effective in finding the refractive power distribution of progressive power lenses.     

Talbot and fourier moiré deflectometry and its applications in engineering evaluation

With the aim of providing a metrical and detection method used in plate-shell mechanics and NDE, moiré interferometry (shearing interferometry) based on the Talbot effect and Fourier principle is proposed in this paper. This method does not require the use of an imaging lens, it is simple to use, and gives accurate results. The feature of this system is entirely based on the ability of an ordinary grating as the object and reference gratings, the optical differential and multiplicative element simultaneously. This will be a further step toward the realization of the aim mentioned above.     

A compact, robust and versatile moiré interferometer

A moiré interferometer was designed and constructed based on a general system design using a reflective crossed-line diffraction grating to produce the four beams of light necessary for moiré interferometry. The design concept, basic design and tuning procedures are discussed. The important features of the interferometer, i.e. compactness, versatility, polarization insensitivity, relaxed collimation requirements, low laser power and remote optics, are addressed. Several such interferometers have been constructed and successfully applied to engineering problems. These include examining the displacement fields surrounding drilled and preformed holes in composite laminates loaded in tension, and the evaluation of nonhomogeneous behavior in textile composites.     

Display of tilt information of vibrating object in time average mode using lateral shearing interferometry and interferometric grating

We have experimentally demonstrated vibration analysis of a reflecting object in time-average mode using shearing interferometry and interferometric grating. Experimental results show that time-average moiré fringes, formed between fringe pattern reflected from object and sinusoidal grating are modulated spatially by the amplitude of vibrating tilt. From the experimental results, information regarding tilt of vibrating objects can be determined.     

A new real-time method of moiré interferometry for displacement derivative fringe patterns

A new method of moiré interferometry is proposed in this paper to obtain the strain fringe pattern in real time. The specimen grating is illuminated by dual beams whose optical path-difference is larger than the coherence length of the laser. The diffractions of the grating are sheared by a glass wedge to fulfil the optical differentiation. The principles based on wavefront analysis are shown and an experimental verification is reported.     

The Effects of Motion on Dynamic Moiré Interferometry

Experimental techniques (e.g. laser interferometry, photoelasticity) that generate fringe data are currently being utilized for analyzing full-field surface deformations in a variety of dynamic problems in experimental mechanics. As opposed to static problems, the transience of surface deformations in dynamic problems poses a unique problem in accurately resolving the fringe data that is acquired. Neumann determined that for time-lapse, double-exposure holographic interferometry the fringe contrast depends on the data acquisition time, wavelength of the light source, and transience of the dynamic phenomena. Dally performed a similar analysis for dynamic photoelasticity, where the dependence was on the stress gradients instead of the wavelength of the light source. This paper attempts to extend the analysis of Neumann and Dally to the analysis of transient fringe intensity data obtained from using dynamic moiré interferometry. It is found that the fringe contrast can depend on the frequency of the fringe field rather than the wavelength of the light source or stress gradients, and the fringe contrast will decay more rapidly for Gaussian light sources than constant intensity light sources. © 1997 Elsevier Science Ltd. All rights reserved.     

Strain analysis of a bonded, dissimilar, composite material T-joint using moiré interferometry

High-sensitivity moiré interferometry and finite-element analysis are used to analyze the state of deformation and stress in the region of contact between a plane orthotropic rectangular punch bonded to a foundation with dissimilar elastic properties which models a highly loaded region of a composite material rocket motor casing. Stress distributions are presented for the contact region and an estimate of the maximum shear stress in the foundation is given. The displacement components show good qualitative agreement between analysis and experiment. The lack of quantitative agreement between the experimental and the finite-element analysis is attributed to uncertainty of the material properties.     

Quadratic pseudopotentials for Gl(N, ) principal sigma models

Matrix pseudopotentials for the Gl(n, ) principal sigma model in two-dimensional Minkowski space are derived through the method of closed differential ideals. The structure of the pseudopotential equations is chosen to contain only quadratic nonlinearities of the matrix Riccati type. A set of further constraints is deduced which leads to inner Bäcklund transformations depending on two complex parameters. Through a geometrical interpretation of such matrix Riccati equations and the associated constraints, a linearization procedure is derived and the equations are reduced to those of Zakharov, Mikhaïlov and Shabat [7–10]. An inductive procedure is applied to explicitly solve an iterated sequence of such Bäcklund transformations through a purely algebraic transformation of solutions to the first step. The resulting nonlinear superposition formula is used to demonstrate a permutability theorem, and to analyse the appearance of singularities.fr|Nous déduisons les pseudo-potentiels matriciels pour le modèle sigma principal à valeurs dans Gl(N, ), défini sur l'espace de Minkowski bi-dimensionnel, en utilisant la méthode des idéaux différentiels fermés. On restreint la structure des équations des pseudopotentiels de façon à ce que n'apparaissent que des non-linéarités quadratiques du type Riccati matriciel. Nous déduisons un ensemble de contraintes supplémentaires menant à des transformations de Bäcklund internes dépendantes de deux paramètres complexes. Grâce à l'interprétation géométrique de ces équations de Riccati matricielles et des contraintes associées, nous déduisons un procédé de linéarisation et les équations se réduisent à celles de Zakharov, Mikhailov et Shabat [7–10]. Un procédé inductif est utilisé pour résoudre explicitement une succession de transformations de Bäcklund par une transformation purement algébrique des solutions de la première ètape. La formule de superposition non-linéaire qui en résulte permet de démontrer un théorème de permutabilité et d'analyser l'apparition de singularités.     

Experimental analysis of thermal displacement and strain distributions in a small outline J-leaded electronic package by using wedged-glass phase-shifting moiré interferometry

To evaluate the influence of a printed wiring board (PWB) with a high coefficients of thermal expansion (CTE) on the thermal deformation of a small outline J-leaded electronic package (SOJ), a newly developed phase-shifting method was applied to moiré interferometry. This phase-shifting moiré interferometry method uses a wedged glass plate as a phase shifter to obtain displacement fields with a sensitivity of 100 nm/line. This technique also enabled the quantitative determination of strain distributions in all observation areas. Thermal loading was applied from room temperature (25 °C) to an elevated temperature (100 °C), and then the thermal strains of SOJ with and without the PWB were compared. The results showed that the concentrations of the longitudinal strains ε_xx and ε_yy became increasingly prominent when mounted on the PWB, and the shear strains γ_xy were concentrated at the corners of the silicon chip. The values of these strains increased by about 50% when the SOJ was mounted on the PWB.     

Experimental study of three-dimensional residual stresses in rails by moiré interferometry and dissecting methods

Residual stresses in rails produced by rolling cycles are studied by a destructive testing procedure. Thin slices of rails are cut and small grid elements are made by cutting slots onto the surface of the slice. Residual stresses are believed to be released near the surface of the slice when those grid elements have right angles and are sufficiently small. The resulting deformation produced by the stress relief is measured by moiré interferometry. On assuming all strain components be constant along the longitudinal axis of the rail and this axis is one principal direction, three-dimensional strain and stress components are solved.     

Particles and strings in six-dimensional (2, 0) theory

In 1995, we learned of the rather surprising existence of a completely new class of quantum theories in six space–time dimensions with (2,0) superconformal symmetry. Some important reasons to study these theories are: (i) Finding the right conceptual framework to define them is a very challenging problem, that will probably take a long time to solve. It is likely to involve new interesting mathematical structures with connections in particular to algebra and geometry. (ii) They give rise to certain Yang–Mills theories with maximally extended supersymmetry upon compactification on a two-torus. This may be a way to find an S-dual formulation of these lower dimensional theories. (iii) They arise within string/M-theory as decoupled subsectors localized on certain space–time impurities such as branes or singularities. (This is in fact how these theories were first discovered (see Witten, hep-th/9507121).) This may provide an opportunity to study aspects of these higher dimensional theories without having to deal with the conceptual subtleties of quantum gravity. To cite this article: M. Henningson, C. R. Physique 5 (2004).

Résumé

En 1995, l'existence plutôt surprenante d'une classe complètement nouvelle de théories quantiques en dimensions six avec symétrie superconforme (2,0) a été découverte. Quelques-unes des raisons pour les étudier sont : (i) Trouver le cadre conceptuel correct pour les définir est un challenge qui prendra probablement beaucoup de temps. Il est probable que ce cadre introduira de nouvelles structures mathématiques ayant en particulier des liens avec l'algèbre et la géométrie. (ii) Elles donnent lieu à des théories de Yang–Mills avec une supersymétrie étendue maximale après compactification sur un tore bidimensionnel. Cela pourrait permettre de trouver une formulation S-duale de ces théories en dimension inférieure. (iii) Elles interviennent en théorie M et cordes à travers un sous-secteur découplé localisé sur certaines impuretés de l'espace-temps, comme des branes ou singularités. (C'est en fait ainsi que ces théories ont à l'origine été découvertes (voir Witten, hep-th/9507121).) Ceci pourrait être l'occasion pour étudier des aspects de ces théories en dimension supérieure, sans avoir à faire avec les subtilités conceptuelles de la gravité quantique. Pour citer cet article : M. Henningson, C. R. Physique 5 (2004).     

Supersymmetric backgrounds from generalized Calabi–Yau manifolds

We show that the supersymmetry transformations for type II string theories on six-manifolds can be written as differential conditions on a pair of pure spinors, the exponentiated Kähler form e^iJ and the holomorphic form Ω. The equations are explicitly symmetric under exchange of the two pure spinors and a choice of even or odd-rank RR field. This is mirror symmetry for manifolds with torsion. Moreover, RR fluxes affect only one of the two equations: e^iJ is closed under the action of the twisted exterior derivative in IIA theory, and similarly Ω is closed in IIB. This means that supersymmetric SU(3)-structure manifolds are always complex in IIB while they are twisted symplectic in IIA. Modulo a different action of the B-field, these are all generalized Calabi–Yau manifolds, as defined by Hitchin. To cite this article: M. Graña et al., C. R. Physique 5 (2004).

Résumé

On montre que les transformations de supersymétrie pour les théories des cordes de type II peuvent être traduites dans des équations différentielles pour une paire de spineurs purs, l'exponentiel de la forme de Kähler e^iJ et la forme holomorphe Ω. Ces équations sont symétriques sous l'échange des deux spineurs purs et des formes de RR de rang pair ou impair. Cette propriété est la symétrie miroir pour les variétés avec torsion. On voit aussi que les fluxes de RR entrent seulement dans une des deux équations : e^iJ est fermé sous l'action de la dérivée extérieure « twisted » dans la corde de type IIA, et de la même manière Ω est fermé en type IIB. Cela implique que les variétés supersymétriques de structure SU(3) sont toujours complexes en type IIB ou bien symplectiques « twisted » en IIA. Ces variétés sont donc des variétés des Calabi–Yau généralisées selon la définition de Hitchin, mais avec une action du champ B différente. Pour citer cet article : M. Graña et al., C. R. Physique 5 (2004).     

Higher-loop integrability in gauge theory

The dilatation operator measures scaling dimensions of local operator in a conformal field theory. Algebraic methods of constructing the dilatation operator in four-dimensional N=4 gauge theory are reviewed. These led to the discovery of novel integrable spin chain models in the planar limit. Making use of Bethe ansätze a superficial discrepancy in the AdS/CFT correspondence was found, we discuss this issue and give a possible resolution. To cite this article: N. Beisert, C. R. Physique 5 (2004).

Résumé

L'opérateur de dilatation mesure les dimensions d'échelles des opérateurs locaux des théories conformes des champs. Nous passons en revue les méthodes algébriques de construction de l'opérateur de dilatation pour la théorie de jauge N=4 en quatre dimensions. Ceci nous a conduit à découvrir, dans la limite planaire, de nouveaux modèles intégrables de chaînes de spin. En utilisant l'ansätze de Bethe une incompatibilité avec la correspondance AdS/CFT fut découverte, nous discutons ce problème et une résolution possible. Pour citer cet article : N. Beisert, C. R. Physique 5 (2004).