Formulation of moiré fringes based on spatial averaging

The use of moiré technique in measurements often involves locating the position of moiré fringe and in some cases determining its profile. Due to intensity fluctuation in the fringe pattern, these measurements are accompanied by some errors. It is possible to define a smoothed version of the original fringe pattern and then formulate the related subject in accordance with the characteristics of this new pattern. This procedure reduces these types of errors and gives a well-defined profile of the fringes. In this paper a formulation of moiré phenomenon based on spatial averaging is presented which, without ignoring any of frequencies, leads to a smooth profile.     

Measurement of the thermal expansion coefficients of ferroelectric crystals by a moiré interferometer

A moiré interferometer is used to measure the thermal expansion of two ferroelectric crystals, LiNbO₃ and KTiOPO₄. The crystal samples are patterned with a chromium reflective grating and used as a diffractive component in a reflective grating interferometer. The thermal expansion of all the three axes of congruent LiNbO₃ and of x and y axes of the flux-grown KTiOPO₄ were measured from room temperature to 200 °C. For this temperature range the thermal expansion coefficient has been modeled by a second-order polynomial and its coefficients have been estimated by accurate analysis of the resulting moiré fringe pattern.     

A study on the 3-D measurement by using digital projection moiré method

Moiré topography method is a well-known non-contacting 3-D measurement method. Recently, the automatic 3-D measurement technique by moiré topography has been developed in order to apply to the engineering and medical fields. The projection moiré topography is very attractive because of its high measuring speed and high sensitivity. In this paper, using the two-wavelength methods of projection moiré topography was investigated to measure the 3-D shape of an object with 2π-ambiguity problems. Rapid measurement can be accomplished by the synchronization between CCD camera and projector. The experimental results prove that the proposed scheme is capable of finding absolute fringe orders, so that the 2π-ambiguity problems can be effectively overcome so as to treat large step discontinuities in measured objects.     

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.     

TDI imaging and scanning moiré for online defect detection

This paper explains the application of scanning moiré in association with TDI (Time Delay and Integration) imaging for complete peripheral inspection of cylindrical objects. Based on the structured light technique, a grating pattern modulated by deformations, such as dents on the surface of a rotating cylindrical object, is recorded using a TDI camera. The illumination system consists of an intensity modulated, line generating laser diode aligned at an angle to the camera axis. By using the TDI option for recording every nth line, an online scanning moiré pattern is generated. After providing a simple explanation of the scanning moiré, the effects of object rotation speed and TDI scan speed on the fringe pattern are discussed and demonstrated. The techniques presented here offer low cost solutions to industrial machine vision tasks related to peripheral imaging and inspection of cylindrical objects.     

Deformation and profile measurement using the digital projection grating method

This paper presents a digital projection grating method for full field measurement of out-of-plane deformation and shape of an object. Two grating patterns on an object before and after deformation are captured by a CCD camera and stored in a computer. With the aid of Fast Fourier Transform (FFT) and signal demodulating techniques, a wrapped phase map is generated. The phases are expanded in the range of 0–2π and compared with the resulting moiré pattern. An unwrapping procedure is used to obtain a continuous phase. In addition, a digital method for fractional fringe multiplication is also developed. Results on deformation and object profile measurements are presented.     

Superposition of Cantor gratings II: Fractality of the moiré profiles

Here, we treat the fractality condition for the moiré fringe profiles obtained from the superposition of two Cantor gratings. These Cantor structures are built through the product of periodic components. We restrict the study to the case in which both gratings have the same fractal parameters (dimension and lacunarity). However, the period of each component can be different. The contribution of each periodic component is also shown, and the total moiré is expressed as a product of the moiré from pairs of such components (Optik 113 (2002) 13-24). Considering the normalized fringe profiles as sets and based on the theory of dynamical systems, the fixed points are obtained. Finally, the calculation of the perimeter-yardstick relation (Richardson method) permits to obtain a power law and the fractality condition is accomplished for such normalized fringe profiles.     

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.     

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.     

Investigation of the dynamic recording process of thick refractive index gratings in photorefractive crystals by the microphotometric method

Diffraction-efficiency measurements are compared with the microphotometric determination of the intensity pattern at the exit face of a LiNbO₃-sample during the holographic recording process. The special advantage of the microphotometric method is the possibility to determine phase shifts of the refractive index grating and of the light intensity pattern simultaneously and independently. Both quantities are very important for an understanding of dynamical effects during the holographic writing process. Furthermore, direct experimental evidence for the change of the modulation degree, i.e. the change of the contrast of the light pattern writing the grating, has been found. This change is caused by a Moiré-like effect which is closely related to the energy transfer between writing beams.     

Application of computer-aided evaluation for holography and similar techniques

The application of computer based evaluation of fringe patterns achieved by holographic interferometry, projected fringes or moiré technics are demonstrated for

• - vibration analysis;

• - non destructive testing; and

• - contour measurements.

The vibration analysis is carried out on dynamic stressed parts by impact or operation. Even rotating objects can be investigated. Non destructively tested materials are compound materials like glass or carbon fibre reinforced plastics and honeycomb panels for aerospce application and tires.A different evaluation technique is used in droplet analysis. The 3-dimensional image, stored in the hologram, is automatically evaluated for the investigations of injection sprays.     

Measurement of nonlinear refractive index of Ag and Au nano-particles using moiré technique

In this paper we have measured second order nonlinear refractive index of Ag and Au nano-particles using the moiré deflectometry with a CW He-Ne laser at wavelength of 632.8 nm. The main advantages of this technique are its extreme experimental simplicity and low sensitivity to external distribution in comparison with other interfrometric methods that need very stable experimental set-up. Because of self-focusing (or self-defocusing) that is due to intensity dependent refractive index, presence of sample in the moiré deflectometry set-up lead to rotation of moiré fringes. By moving the sample in set-up we have measured these rotation angles in different displacements from focus point of lens used in this set-up and then we have calculated the nonlinear refractive index of Ag and Au nano-particles using their values. Also we have obtained the sign of n₂ regard to the direction of rotations. Consequently by using the Mathematica software we have exhibited the suitable fitness of theoretical curve with experimental results.     

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.     

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.     

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.     

Absolute moiré contouring

A novel absolute moiré contouring principle and the associated experimental system is described. This system enables the absolute distance from the object point to the reference plane and the height of the object to be measured directly to a high degree of accuracy. It is not necessary to judge the hills or valleys to decide the object's shape. A few objects were used as samples to illustrate the procedure. The objects' height, found by using the moiré technique, compares very well with that found by using a mechanical gage.     

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.     

Improved algorithm for image encryption based on stochastic geometric moiré and its application

A technique based on optical operations on moiré patterns for image encryption and decryption is developed. In this method, an image is encrypted by a stochastic geometric moiré pattern deformed according to the image reflectance map. The decryption is performed using pixel correlation algorithm in the encrypted image and the stochastic geometrical moiré pattern. The proposed technique has a number of advantages over existing encryption techniques based on moiré gratings. No original moiré grating can be reconstructed only from the encrypted image. Stochastic moiré grating can be deformed in any direction what is an important factor of encryption security. Finally, the quality of the decrypted image is much better compared to decryption methods based on the superposition of the regular and deformed moiré gratings. The proposed technique has a great potential, because the process is performed using computational algorithms based on optical operations and optical components are avoided.     

Accurate nonlinear phase step estimation in phase shifting interferometry

We propose a new method for the accurate estimation of nonlinear response of the PZT to the applied voltage. The method uses discrete chirp Fourier transform for the coarse estimation followed by a fine search method for the accurate estimation of the phase step and nonlinearity. The method can be extended to the cases of extraction of multiple phases in the configurations involving multiple PZTs such as holographic moiré in the presence of nonlinearity. The robustness of the proposed method is verified by comparing with Cramér-Rao lower bound. Experimental results prove the method’s feasibility.