Formation of unsymmetric moiré fringes and their use in moiré topography

An analytical method of predicting the intensity profile of the moiré fringes formed by a three-dimensional grating is proposed. The proposed method is proved to be effective in determining the appropriate structure of the grating and the experimental conditions for directional moiré topography.     

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.     

Phase shifting SEM moiré method

A new phase shifting scanning electron microscope (SEM) moiré method is proposed in this paper. The phase shifting technique is realized in four steps from 0 to 2π by shifting electron beam in the y-axis direction controlled by the SEM system. It is successfully applied to determine the residual strain of a deformed holographic grating with a frequency of 1200 lines/mm in an electronic package. As a further application, it is used to measure the virtual strain of a MEMS structure with a 5000-line/mm grating and to determine the phase distribution of a SEM moiré formed with a 6000-line/mm grating fabricated by electron beam lithography. The experiments show the feasibility of this method. It provides a new way for disposal of fringes pattern in sub-micro moiré method.     

A moiré fringe alignment aid

The task of accurately superimposing two photographic transparencies is frequently encountered in some areas of optical metrology. By recording a suitable line structure, along with the image, on each photograph, moiré fringes formed when two of the structures are superimposed can be used to give an accurate indication of the alignment of the transparencies.     

In-plane deformation measurement using holographic moiré

The present paper analyses the factors affecting the quality of the moiré fringes for an arbitrary displacement and deformation of the object surface. Methods for the generation of auxiliary fringes are considered and their localisation is investigated. The physical significance of speckle displacement, both in the image plane and in the pupil plane, is pointed out.     

Holographic implementation of holographic moiré inspection

Implementation of holographic moiré inspection is demonstrated using one hologram to project the reference grating and a further hologram to produce moiré patterns. Well contrasted moiré fringes are obtained. Results of calibration tests are reported and an example of object contouring is presented.     

Localisation of fringes in moiré topography

The moiré pattern produced by two separate gratings is characterised by a fringe localisation phenomenon. A theory based on the geometric shadow of light can account for the spatial location of moiré fringes in topographical applications. The fringe location depends on the optical arrangement of the system and also on the surface slope of the specimen. Experimental results are introduced into practical usage.     

Frequency marker based on moiré deflectometry

We propose a new method for frequency marking based on measuring the diffraction angle by moiré deflectometry. The method is demonstrated experimentally.     

Electron moiré method and its application to micro-deformation measurement

In this paper, the single and two deposited metal layers method were proposed to produce the model grating for electron moiré method. The measurement principle of electron moiré method and the techniques for manufacturing model grid are expounded in detail. The accuracy of measuring strain using this method is discussed. The gratings with single deposited layer and two deposited layers with high frequency up to 5000 lines/mm were produced on different substrates. From the experimental results, both single deposited metal layer and two deposited metal layers gratings showed their heat resistance ability. Using the gratings produced and a replicated model grid, the electron moiré method was applied to measure the deformation of the strain around holes in a polyimide resin substrate, thermal strain of electronic packaging component and tensile creep around grain boundary in a pure copper specimen.     

Automatic fringe analysis for moiré topography

Two digital systems are developed for the automatic measurement of 3-D shapes using moiré techniques—an automatic 3-D shape measuring system using the scanning moiré method and an interactive fringe analysing system for moiré fringe photographs. In the automatic 3-D shape measuring system, a deformed grating is scanned and sampled with an electronic image scanning device so that moiré fringes are generated in a computer. This technique of electronic fringe generation eliminates ambiguity with regard to the sign of the moiré fringes. The interactive fringe analyser provides a flexible and versatile tool for moiré fringe analysis. Medical applications of these analysing systems are discussed.     

Defects analysis of Al/Si artificial nanocluster with moiré fringes

In this paper, it is demonstrated the defects play a very important role in determining the quality of artificial nanoclusters grown. The surface strain (stress) distribution around defects in Al artificial nanocluster is analyzed by Moiré fringes pattern. The moiré fringes generated by scanning lines in monitor and nanocluster array can be used as a “magnifier” to study surface imperfections with scanning tunneling microscopy (STM). As moiré fringes’ exist in many ordered nanostructures and adsorbate systems, the method is expected to have wide applications.     

The phase shift method applied to cross grating moiré measurements

The automatic evaluation of the grating deformation in a moiré image is greatly enhanced by the phase shift method. Based on three or more local grey values of a related number of phase shifted moiré patterns, the local displacement of a deformed grating against a reference grating, and hence the total displacement in one direction, is calculated. In this paper an extension to cross gratings is presented yielding a two- dimensional displacement field.     

Dynamic diffraction moiré: Theory and applications

As advanced structural materials such as graphite epoxy, metal matrix and ceramic matrix composites or optical mirror substrate materials such as beryllium and silicon carbide are increasingly used in high performance systems, their ability to withstand environments that will cause loss of system survivability must be taken into account. The concept of survivability includes cases where the system is not destroyed, but is inoperable because of subtle effects on the system. These effects can be delamination from weak shock events, critical platform misalignment from large slew motions, or even mirror coating and substrate deformations of as little as a fraction of a micron from their specifications. All the effects listed above, in the system survivability realm, are very subtle and are due to transient deformations at a local or micromechanical level. This paper describes recent work at the Idaho National Engineering Laboratory, under the Office of Naval Research funding, to understand the transient mechanisms in composite interfaces that lead to impact delamination. The principal tool of investigation was dynamic moiré interferometry coupled with continuum analysis. Results for two configurations under impact loading are presented. The first result shows dynamic interfacial shears in a AS4/3501-6 [0/90]_s composite. The second result shows similar effects in a [0₂/90₂]_s configuration of the same material. Similarities and dissimilarities will be discussed, as will future work.     

Fringe formula for projection type moiré topography

The rays that form moiré fringes in projection type moiré topography are discussed. It is shown that the nodal-ray formula conventionally used in projection type moiré topography gives erroneous results for an object located close to the lenses. An alternative formula based on principal rays is proposed and compared with the conventional nodal ray formula. The principal ray formula proposed can be applied to a wide class of optical systems, including a telecentric system.     

Suppression of moiré fringes due to sampling of halftone screened images

When a halftone screened image is discretely sampled by, for example, a CCD array, moiré fringes sometimes appear. These moiré fringes are caused by aliasing errors due to the improper sampling rate. To suppress these fringes, a dual sampling method is proposed. In this method, halftone screened images are sampled twice with different sampling rates, and the selection of proper frequency components less suffering from aliasing errors can effectively suppress moiré fringes.     

Application of moiré method to the study of plastic deformation processes

The moiré method can be broadly applied in metal forming processes. Many moiré fringe patterns of plastic working processes have been obtained. Based on this information, the principle of flowing metal and the distribution of strain and stress have also been obtained. These results should help us to improve the metal forming processes.     

Stress analysis of fibrous composites using moiré interferometry

A sensitive moiré fringe interferometer has been developed for measuring in-plane strains in engineering materials and structures. The specific advantage of this system is that it does not have to be used in an environment isolated from external vibration. As a result, it is possible to record deformation contours with a sensitivity and spatial resolution sufficient for the accurate measurement of strains even in areas of high strain gradient. The technique has been used to investigate the behaviour of a carbon fibre reinforced plastic material under fatigue loading. The changes in strain distribution have been measured as a function of the number of cycles undergone, and have been compared with theoretical predictions of the strain distribution around a hole in an orthotropic plate.     

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.     

A moiré method of visualizing electromagnetic force lines

We propose a simple moiré method of visualizing electromagnetic force lines. The indicial equation is first derived for the tangent (or normal) curve to the electric field (or magnetic induction) around two parallel-line charges (or currents). The derived equation is then shown to have a one-to-one correspondence with that of the moiré fringe formed by two overlapped radial gratings. Since the tangent (or normal) curve to the electric field (or the magnetic induction) corresponds to the direction of the electric (or magnetic) force on a test charge (or current), the radial grating moirés can be used for the visualization of electric (or magnetic) force lines.     

Finite fringe moiré deflectometry for the measurement of radius of curvature: an alternative approach

Moiré deflectometry, based on infinite fringe detection, is a sensitive and advantageous method for the precise measurement of optical parameters. An alternative approach, based on accurate finite-fringe detection moiré deflectometry, is described for the measurement of radius of curvature. An error estimation of the method, supported by experimental verification, is also presented. Extension of the method for the measurement of a long radius of curvature has also been suggested.