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.     

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.     

Analysis of moiré fringes for measuring the focal length of lenses

We describe a technique based on fast Fourier transform and least-squares fit for automated analysis of moiré fringe patterns for accurately measuring the focal length of lenses. An interference fringe pattern is produced by a reflective diffraction grating interferometer and illuminates the test lens. Moiré fringes are generated by digitally superimposing the magnified fringe pattern imaged by the lens on the interference fringe pattern without the test lens. We analyze two common ways to generate the digital moiré effect: multiplication and subtraction with successive rectification of the two digitally stored intensity distributions, and we show that in the latter case by means of the described technique it is possible to determine the moiré spatial frequency by a simple and fully automated procedure.     

Enhancement of visibility of fringes and exposure time for moiré topography

The aperture filtering of lenses for the purpose of moiré topography is described. By replacing the circular iris of a lens with a rectangular one whose long side is parallel with the bars of the grating, both the visibility of the fringes and the exposure condition are greatly enhanced. Using this technique, it becomes possible to take pictures of moiré fringes on a moving, living human body.     

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.     

Interpretation of fringes produced by time average reflection moiré on a circular disk

Inverse problem of reconstruction of dynamic displacements from the fringe pattern generated by time average reflection moiré is investigated in this paper. A technique for numerical simulation of time average smoothed reflection moiré fringes is proposed. The smoothing procedure is incorporated into the finite element formulation of the problem. Reconstruction of the field of deflections is illustrated for a centrally clamped disk. Such techniques can be effectively exploited in hybrid numerical–experimental procedures for different objects and grating geometries.     

Moiré fringes

This review paper clarifies the characteristics of the incoherent-and-multiplicative type moiré fringe phenomenon, presents examples of the application of these characteristics to measurement and explains the profile prediction method and the sharpening conditions of moiré fringes formed by two binary gratings.     

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.     

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.     

Measurement of histograms of halftone images

We present theory and experiments for two optical methods for measuring histograms of halftone images. In both methods, the histogram is obtained by spatial filtering of the halftone object. In the first method, we used a phase filter with a comb-type point spread function. In the second method, the filter matched one kind of the differentiated halftone dots. Experiments show that the first method works fast and gives fairly accurate results (errors were about 10%), whereas the second method requires more experimental efforts, but the results are more accurate in this case (errors were about 0.9%).     

Moiré fringes in metrology

Moiré fringe phenomena have been exploited in a wide range of transducers, particularly in the field of engineering metrology. Paying particular attention to developments which have taken place during the last 15 years, the paper presents a cross-section of moiré techniques for the measurement of displacement, surface topography, deformation, vibration and refractive index gradient.     

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.     

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.     

An automatic quantitative approach to additive/subtractive moiré

An automatic fringe-analysis procedure is described for additive and subtractive types of moiré. The procedure is based on the simultaneous introduction of differential phase shifts to the two superposed gratings or fringes.     

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.     

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.     

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.