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.     

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.     

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.     

Realization of high sensitivity displacement field from moiré interferometer with rough phase shifting mechanism and pattern matching technique

In this study, phase shifting method is used to modify moiré system into micro moiré interferometer which can measure displacement field with highly improved sensitivity. Apart from existing micro moiré technique, a low cost and less precise translation stage with rough resolution (10 μm resolution) is adapted for the phase shifter. Least square algorithm is applied to estimate the arbitrary phase shifted amount and to minimize the errors induced by lowering the cost. Moreover, specimen grating is phase shifted instead of reference grating which enables simple construction from given moiré system. To compensate for rigid body in-plane translation of specimen that may occur during phase shifting, pattern matching algorithm is put into practice to ensure pixel correspondence for each phase shifted images. To verify the newly constructed micro moiré technique, local displacement fields of Fine pitch Ball Grid Array package and Wafer Level Chip Size Package with elevated sensitivity up to 26 nm per fringe was acquired.     

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.     

Flow visualization by an improved double exposure method in holography

Some optical differential interferometric techniques were investigated in order to measure the density distribution in the air jet flow of a small scale flow cell while excluding the effects of the optical distortion of its glass windows. A technique using moiré fringe formation by rotating the reference wave in one exposure of the double exposure method was found to be most suitable for this purpose. High contrast and multiplication of moiré fringes can be obtained by a moiré fringe sharpening and multiplication method.     

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 application of automatic fringe analysis in fracture mechanics

The likelihood of propagation of a crack in a metallic plate under load can be assessed by evaluating an energy-based contour integral, the J integral, for the loaded specimen. Calculation of the integral requires that the local stresses in the specimen are known. These stresses can be obtained practically by the use of strain gauges or by moiré fringe methods. This paper describes a semi-automatic, computer vision-based method of calculating the J integral when moiré fringe methods are used to evaluate the stresses in the specimen.     

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.     

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.     

Limitation of carrier fringe methods in digital photoelasticity

The carrier fringes method has been proposed in digital photoelasticity in combination with techniques such as Fourier transform and phase shifting method, without considering the influence of the isoclinics on the isochromatic patterns analysis. Unlike other optical methods as moiré and holographic interferometry, in photoelasticity the light intensity emerging from a circular polariscope is related to both the isochromatic retardation and the isoclinic parameter. As it is shown by the theoretical analysis, owing to the misalignment between the principal stresses in the model and in the carrier, the computed retardation is affected by an error which is the same for all photoelastic methods based on the use of carrier fringes. Consequently, the photoelastic analysis carried out by methods that use carrier fringes cannot be applied as a full-field technique. In detail, numerical simulations show that the retardation error is comparable (less than 0.05 fringe orders) with that of other photoelastic methods provided that the misalignment between the principal stresses in the model and in the carrier is less than 30°. On the contrary, in the model zones where the misalignment is higher than 30°, the retardation measurement can be affected by non negligible errors (up to 0.25 fringe orders).     

Frozen strain moiré used in the analysis of impact loading

This paper presents a solution to the problem of the displacement fields and strains in a semi-infinite plate with two half-circular holes during the propagation of a stress wave. The solution was realized experimentally by means of the method of the frozen strain moiré using a double-pulse ruby laser. The load of impact was applied by a pendulum hammer. Two suitable external-trigger mechanisms were used to fire the ruby laser at predetermined intervals. The moiré fringe patterns of the U and V displacement fields were recorded on a holographic film adhered to the specimen at different time delays after impact.     

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.     

Investigation of dynamic displacements of lithographic press rubber roller by time average geometric moiré

Geometric moiré fringe formation method is a classical well-established experimental technique with numerous practical applications. This paper proposes the application of time-average geometric moiré analysis for the determination of dynamic displacements of the lithographic press rubber roller. This optical measurement technique is a natural extension of double-exposure geometric moiré for the identification of dynamic displacements of vibrating elastic structures. Experimental investigations prove the validity and effective practical applicability of the method.     

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.     

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.     

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.     

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.     

A study on the digital moiré technique with circular and radial gratings

A digital moiré technique with circular and radial gratings is proposed to measure in-plane displacement and strain distributions of soft materials in a polar coordinate system. By introducing the coordinate-transform technique, the concentric circles and radial lines in the Cartesian coordinate system are converted to cross gratings in a polar coordinate system. Then, the digital moiré fringes are generated using logical and filter operations on the one-bit binary images. Finally, the in-plane displacement distributions are obtained by means of the four step phase-shifting procedure. Also, the measurement principles and the basic procedures of the new digital moiré technique are explained in detail. An application for rubber sheet with a single-edge crack is studied, and the experimental results show that the presented method is feasible.     

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.