Collimation testing by use of the Lau effect coupled with moiré readout

We present an easy, simple, and inexpensive technique for checking the quality of the collimation of optical beams using the Lau effect combined with moiré readout. The experimental arrangement consists of a modified Lau-based interferometer in which a white-light incoherent source illuminates a set of two gratings. A collimating lens is placed between the two gratings such that the self-images of the second grating are formed. The third grating is positioned at one of the self-imaging planes forming moiré fringes. The type of the moiré fringe demonstrates the quality of collimation of the optical beam. The necessary theoretical background is presented and the results of our experimental investigation are reported. The technique can also be used for accurate determination of the focal length of a collimating lens using low-cost components.     

Concealed holographic coding for security applications by using a moiré technique

We present an optical coding technique that enhances the anticounterfeiting power of security holograms. The principle of the technique is based on the moiré phenomenon. The code in the hologram has a phase pattern that is invisible and cannot be detected by optical equipment, so that imitation is extremely difficult. Holographic, photographic, and embossing techniques are used in fabricating coded holograms and decoders.     

Distributed load sensor by use of a chirped moiré fiber Bragg grating

A chirped moiré fiber Bragg grating has been demonstrated to be capable of measuring the magnitude, position, and footprint of a transverse load. The device provides an average spatial resolution of 164 microm and has a load accuracy of 0.15 N/mm, or 50 microepsilon.     

Construction of a high-resolution moiré interferometer for investigating microstructural displacement fields in materials

A high-magnification moiré interferometer has been constructed with a spatial resolution of the order of 1 microm to measure the local in-plane displacement field associated with a material's microstructure. Laser illumination passes through phase-stepping optics and is delivered to the microscope head by polarization-preserving single-mode optical fibres. The head itself is a compact unit consisting of collimating optics, an objective lens and a charge coupled device (CCD) camera. Thin-phase gratings are cast onto the sample surface with a compliant epoxy resin and coated with ca. 5 nm of gold to enhance the fringe contrast and reduce speckle noise. By switching between the laser illumination and white-light illumination, the underlying microstructure is viewed in exact registration with the measured displacement fields. The application of the instrument is illustrated here by visualization of displacement fields in polymer-bonded explosives (PBXs) during deformation to failure. PBXs are highly filled polymers consisting of up to 95% by weight crystalline explosive bound in a variety of polymeric binders. The mechanical properties of PBXs are highly dependent on the microstructure, and moiré interferometry is an ideal tool for investigating the relationship between the 1-100 microm sized crystals and the displacement fields. Methods such as this are required if computer models of inhomogeneous materials are to be accurately validated.     

Improved phase-shifting method for automatic processing of moiré deflectograms

An improved moiré deflectometry phase-shifting technique is presented. A squared grating is used to multiplex the information of the deflections in two orthogonal directions in one image. This procedure avoids the need to rotate the gratings to obtain complete deflection information. However, the use of these gratings makes impossible the application of standard phase-shifting algorithms. Specifically, the problems associated with the nonsinusoidal profile of the moiré fringes and the low-modulation areas produced by the square gratings are solved. A modified moiré deflectometry phase-shifting method is designed to deal with these problems. In addition, a method to obtain the zero order of the prismatic effect is developed. The technique configures a complete and automatic method of mapping ray deflections. From them the refractive power maps can be derived. Experimental results obtained with a progressive-addition lens are shown.     

Digital moiré fringe-scanning method for centering a circular fringe image

A digital moiré fringe-scanning method for centering a circular fringe image is proposed. The image of a nondiffracting beam, whose cross section is a circular fringe, is first downloaded onto a computer. The image is then superposed with a digital circular grating, whose center is close to the center of the image, to generate circular moiré fringes. Changing the phase of a digital grating can cause moiré fringe scanning. The global center of the image can be calculated by use of sets of the scanned picture. Because all the image data are used for the calculation, the effect of random noise on centering is greatly reduced and the center position resolution can reach the order of a subelement of a CCD. The measurement of spatial straightness is discussed.     

Comparison of reference image generation techniques for projection moiré interferometry

Three different approaches of generating reference images for projection moiré interferometry are compared. An interpolation-based phase-shift technique that phase shifts the actual reference images is shown to reduce error by over 25% and to reduce processing time compared with the common cosine-wave- and square-wave-based approaches.     

Multiplicative moiré two-beam phase-stepping and fourier-transform methods for the evaluation of multiple-beam fizeau patterns: a comparison

A phase-evaluation method of multiple-beam Fizeau patterns that combines two-beam phase-stepping algorithms with the moiré effect was previously reported [Appl. Opt. 34, 3639-3643(1995)]. The method is based on a multiplicative moiréimage-formation process obtained by the direct superposition of high-frequency multiple-beam Fizeau carrier fringes upon a transmission grating (working as a phase modulator). We present a comparison between this multiplicative moiré two-beam phase-stepping method and the well-known Fourier-transform method for the topographic measurement of an undoped silicon wafer. The discrepancy between the two methods yields a rms phase-difference value of the order of(~2pi/90).     

Effective wavelength calibration for moiré fringe projection

The fringe patterns seen when using moiré instruments are similar to the patterns seen in traditional interferometry but differ in the spacing between consecutive fringes. In traditional interferometry, the spacing is constant and related to the wavelength of the source. In moiré fringe projection, the spacing (the effective wavelength) may not be constant over the field of view and the spacing depends on the system geometry. In these cases, using a constant effective wavelength over the field of view causes inaccurate surface height measurements. We examine the calibration process of the moiré fringe projection measurement, which takes this varying wavelength into account to produce a pixel-by-pixel wavelength map. The wavelength calibration procedure is to move the object in the out-of-plane direction a known distance until every pixel intensity value goes through at least one cycle. A sinusoidal function is then fit to the data to extract the effective wavelength pixel by pixel, yielding an effective wavelength map. A calibrated step height was used to validate the effective wavelength map with results within 1% of the nominal value of the step height. The error sources that contributed to the uncertainty in determining the height of the artifact are also investigated.     

Improvement of measurement accuracy in shadow moiré by considering the influence of harmonics in the moiré profile

A method for high-resolution three-dimensional shape measurement for a shadow moiré system is proposed. To increase the resolving power of the method, the problem caused by the harmonics of the moiré profile needs to be solved. It is well known that moiré fringes in a shadow moiré system have a nonsinusoidal profile caused by harmonics. The influence of the harmonics in moiré profile on the measurement accuracy of the method is discussed. The method is improved to eliminate the error caused by the harmonics in the moiré profile. Both simulation and experimental results show that the improved method can effectively reduce the influence of harmonics.     

Moiré technique for spatial coherence measurements of soft-x-ray lasers

We present a novel moiré diagnostic that allows the time-averaged spatial coherence properties of soft-x-ray lasers to be measured. The technique is an extension of the theoretical work in a recent paper [J. Opt. Soc. Am. A 16, 323 (1999)] and is based on the concept of decompositions of the far-field divergence for partially coherent beams. An appealing feature of the approach is that the spatial coherence width at other planes can be evaluated from the measured one at a given plane on the assumption of shape-invariant beams.     

Instantaneous velocity displacement and contour measurement by use of shadow moiré and temporal wavelet analysis

A temporal wavelet analysis method is proposed for velocity, displacement, and three-dimensional surface-profile measurement of a continuously deforming object by use of the shadow moiré technique. A grating is placed close to a deforming object, and its shadow is observed through the grating. The moiré fringe patterns, generated by the interference of the grating lines and their shadows, are captured by a high-speed CCD camera with a telecentric gauging lens. Instantaneous frequency of gray-value variation is evaluated point by point with the continuous wavelet transform. From the instantaneous frequency of each point on the object, the velocity, displacement, and high-quality surface profile at different instants can be retrieved. In this application, two specimens are tested to demonstrate the validity of the proposed method: One is a small coin with a rigid body motion, and the other is a simply supported beam subjected to a central point load. The results are compared with those obtained from temporal Fourier-transform and mechanical stylus methods.     

Effects of strain rate on transverse tension properties of a carbon/epoxy composite: studied by moiré photography

The dependence on strain rate of the mechanical properties of a high performance carbon fibre/epoxy composite loaded in transverse tension has been investigated. Dog-bone shaped specimens have been tested in quasi-static and dynamic loading conditions. The dynamic tests were performed in a split Hopkinson bar at strain rates between 100 and 800 s⁻¹. A moiré technique combined with high-speed photography, at framing rates of 0.25–1 MHz, was used for extraction of the local strain fields. The transverse mechanical properties were found to have weak or no dependence on strain rate. The average transverse modulus did not depend on strain rate, whereas the strain to and stress at failure were found to increase slightly with increased strain rate. For these dog-bone shaped specimens the strain evaluated by conventional Hopkinson bar technique was found to underestimate the true strain field measured by moiré technique. Finally, the moiré technique facilitated crack-propagation monitoring in real time. Crack speeds up to 2300 m s⁻¹ were measured at transverse crack propagation.     

Electrostatic spraying: a novel technique for preparation of polymer coatings on electrodes

A liquid flow emerging from a tip or a thin tube under the influence of a strong electric field will, due to charging of the dielectric liquid, break up into small droplets. Thus, if a polymer material is dissolved in the liquid, this electrodeposition technique can be utilized for producing polymer coatings on electrodes. The method was applied for in situ formation of ultrathin (～3000 ?) cellulose acetate (CA) phase inversion membranes on glassy carbon electrodes. The purpose of the membrane was to protect the electrode surface from fouling by macromolecular species. The spraying liquid consisted of CA, acetone, and aqueous magnesium perchlorate as pore former, and the spraying voltage was 14 kV. Profilometric measurements showed that the thickness of the spray-cast membranes was much more uniform than that of similar membranes formed by solvent casting. By using cadmium and lead as test analytes and differential pulse anodic stripping voltammetry as detection method, it was found that the membranes prepared by spray casting offered better protection against interference from poly(ethylene glycol) (PEG) 6000 than those prepared by solvent casting. Also, the interference from PEG 2000 was significantly reduced. Experimental details of the electrostatic spraying technique are given.     

Determination of two-dimensional planar displacement by moiré fringes of concentric-circle gratings

We investigate the moiré fringe pattern of two concentric-circle gratings with the aim of measuring the relative two-dimensional planar displacement induced between the gratings. In the first stage we give a comprehensive mathematical approach for the analysis of fringe patterns. Then we suggest a fast computational measurement algorithm that uses a Fourier transformation technique. Finally, our experimental results prove that a measuring accuracy of 0.01 μm can be achieved with this method.     

Measurement of slope of bent plates using phase shifted moiré deflectometry

In this paper, we report the investigations undertaken towards mapping the slope of specularly reflecting bent plates using moiré deflectometry. Towards improvement of the measurement characteristics, the four-step phase shifting technique has been incorporated into the deflectometric setup to obtain quantitative results. The experimental verification of the proposed technique for poly-methyl methacrylate (PMMA) specimens in the form of a cantilever beam and a circular plate, subjected to a well-defined load, has been undertaken. In each case, the experimental results match well with theoretical predictions.     

Application of "parallel" moiré deflectometry and the single beam Z-scan technique in the measurement of the nonlinear refractive index

In this paper, the application of "parallel" moiré deflectometry in measuring the nonlinear refractive index of materials is reported. In "parallel" moiré deflectometry the grating vectors are parallel, and the resulting moiré fringes are also parallel to the grating lines. Compared to "rotational" moiré deflectometry and the Z-scan technique, which cannot easily determine the moiré fringe's angle of rotation and is sensitive to power fluctuations, respectively, "parallel" moiré deflectometry is more reliable, which allows one to measure the radius of curvature of the light beam by measuring the moiré fringe spacing. The nonlinear refractive index of the sample, including the sense of the change, is obtained from the moiré fringe spacing curve. The method is applied for measuring the nonlinear refractive index of ferrofluids.     

Error analysis of the phase-shifting technique when applied to shadow moiré

An exact solution for the intensity distribution of shadow moiré fringes produced by a broad spectrum light is presented. A mathematical study quantifies errors in fractional fringe orders determined by the phase-shifting technique, and its validity is corroborated experimentally. The errors vary cyclically as the distance between the reference grating and the specimen increases. The amplitude of the maximum error is approximately 0.017 fringe, which defines the theoretical limit of resolution enhancement offered by the phase-shifting technique.     

Measurement of strain distribution by the moiré fringe multiplication method at a tip of propagating fatigue crack

The moiré fringe multiplication method which used interference of the +1st and -1st order diffracted beams from a 1000 lines/mm phase-type grating on the specimen surface was applied to the measurement of strain distribution at the tip of a propagating fatigue crack in a steel plate having a central crack. The sensitivity of the measurement was equivalent to the sensitivity obtained from a 2000 lines/mm grating on the specimen when the conventional moiré fringe method is used. The gage length was of the order of 10m. The result of the measurement of strain distribution was applied to the estimation of the fatigue crack propagation rate.

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Résumé La méthode de multiplication des franges de Moiré qui utilise les interférences d'ordre +1 et -1 de rayons lumineux diffractés par une grille de 1000 lignes/millimètre, du type à phase sur la surface de l'éprouvette, a été appliqué à la mesure de la distribution des déformations à l'extrémité d'une fissure de fatigue en cours de propagation dans une tôle d'acier présentant une fissure centrale.La sensibilité de la mesure était équivalente à la sensibilité obtenue par une grille de 2000 lignes/millimètre appliquée sur l'éprouvette et utilisant la méthode de franges de Moiré conventionnelle. La longueur de référence était de l'ordre de 10 microns. Le résultat des mesures de distribution de déformation a été appliqué à l'estimation de la vitesse de propagation d'une fissure de fatigue.