Colour imperfections in structured light projection for freeform measurement – a rapid test

Three-dimensional (3D) optical measuring systems using structured light are often limited in practice by imperfections in the light patterns projected onto the object under test. An understanding of the fine structure of the patterns enables limits to be placed on the accuracy and precision of 3D measurements that can be obtained with such systems. A simple technique has been studied that reveals imperfections in patterns of parallel lines projected in white light. Colour fringing has been revealed using a reference grid in the form of a diffusely reflective grating or a lenticular array, to obtain magnification by means of moiré effects. The moiré magnifier gives a representation of the average error over an area. It is a very simple and robust device which may be convenient to use in an industrial production environment to provide a rapid check for the presence of colour fringing in light patterns with regular structures.     

3-D Contouring of Diffuse Objects by Talbot-projected Fringes

Abstract

Talbot fringe projection, a moiré technique, is applied to three-dimensional contouring of diffuse targets for absolute shape measurement. The basic system relies on depth coding the test target surface by projecting the Talbot image of a linear grating. A second grating, similar to that used for the Talbot image, is employed to obtain the moiré fringes. These fringes represent surface contours of equal depth. Using a phase measurement technique and digital image processing algorithms, the surface shape information is obtained from the contour maps. Experimental results, merits and limitations of the system are discussed.     

Interpretation of Fringes Produced by Time‐Averaged Projection Moiré

Abstract: New exact formulas describing the observed shift of projected moiré grating lines on a surface of an object are derived for the paraxial model. These formulas enable to construct more accurate explicit relationship among the amplitude of oscillation, the pitch of the projected grating and the order of the fringe. Analytical derivations and numerical illustrations are used throughout the text to explain the process of formation of double‐exposure and time‐averaged projection moiré fringes.     

Appareillage semi-automatique pour l'interprétation des clichés moirés. Validité et précision de la technique expérimentale

Résumé La méthode expérimentale du moiré par réflexion Ligtenberg a été peu utilisée jusqu'à présent pour des études complètes du champ des moments élastiques dans des structures de grandes dimensions. Ceci est d? essentiellement à la lourdeur expérimentale des techniques traditionnelles d'interprétation des clichés moirés. Cependant, cette méthode peut s'avérer être un complément utile et parfois nécessaire des méthodes numériques actuelles. C'est pourquoi, nous avons développé, dans une première étape, un appareillage, architecturé autour d'un microprocesseur, permettant l'interprétation semi-automatique des clichés. Dans une seconde étape, nous avons montré la validité de la technique expérimentale proposée et nous en avons analysé la précision. Il s'avère ainsi qu'on peut attendre une erreur moyenne inférieure à 5% sur les moments de flexion et de l'ordre de 7% sur le moment de torsion.

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Summary The experimental moiré Method due to Ligtenberg has only scarcely been used, until now, for the study of moment distribution in large flat structures. It seems that the little success encountered by this method, very powerful in theory, results from the tedious and repetitive manual operations implied in the interpretation of the moiré photographs. Therefore, the author has tried to develop some automatization of these operations. With this object, it has been shown that the variations in the intensity of the light reflected from the clear and the dark parts of print of a filtrate moiré photograph reveal a suitable objective criterion for the detection of moiré fringes. On that principle, an apparatus, built around a microprocessor, has been developed to perform, following a given section, the automatic detection of the centers of the moiré fringes, with about 0.15 mm accuracy. The apparatus stored these data and used them, thereafter, to compute the first derivatives of the experimental curves numerically (curvatures or angle of twist) by means of linear regression using a third order polynomial in the current coordinate. In order to demonstrate the validity of the technique and to determine the accuracy of results obtained, the author has performed the experimental study of a problem whose theoretical solution is available. This study, whose full results can be obtained from the author, has been conclusive and has shown that the mean relative error on the curvatures (δ²w/δx² and δ²w/δy²), the bending moments (M_x and M_y), the torsion angle (δ²w/δxδy) and the bending moment (M_xy) are respectively about 5, 4, and 7%. On the contrary, the relative errors on the third derivatives (δ²w/δx³ and δ³w/δy³) are unacceptable and therefore, the shear forces cannot be determined with accuracy. To conclude, the apparatus and the experimental approach for interpretation of moiré photographs described in this paper are intended to liberate the experimenter from the most tedious parts of the Moiré method of Ligtenberg. They are hoped to favour the use of this powerful method for the study of very large flat structures.

     

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.     

High‐Speed 3D Printing of Millimeter‐Size Customized Aspheric Imaging Lenses with Sub 7 nm Surface Roughness

Advancements in three‐dimensional (3D) printing technology have the potential to transform the manufacture of customized optical elements, which today relies heavily on time‐consuming and costly polishing and grinding processes. However the inherent speed‐accuracy trade‐off seriously constrains the practical applications of 3D‐printing technology in the optical realm. In addressing this issue, here, a new method featuring a significantly faster fabrication speed, at 24.54 mm³ h^?1, without compromising the fabrication accuracy required to 3D‐print customized optical components is reported. A high‐speed 3D‐printing process with subvoxel‐scale precision (sub 5 µm) and deep subwavelength (sub 7 nm) surface roughness by employing the projection micro‐stereolithography process and the synergistic effects from grayscale photopolymerization and the meniscus equilibrium post‐curing methods is demonstrated. Fabricating a customized aspheric lens 5 mm in height and 3 mm in diameter is accomplished in four hours. The 3D‐printed singlet aspheric lens demonstrates a maximal imaging resolution of 373.2 lp mm^?1 with low field distortion less than 0.13% across a 2 mm field of view. This lens is attached onto a cell phone camera and the colorful fine details of a sunset moth's wing and the spot on a weevil's elytra are captured. This work demonstrates the potential of this method to rapidly prototype optical components or systems based on 3D printing.     

Fourier‐series‐based virtual fields method combining with moiré interferometry for characterising elastic modulus distribution of laser repaired GH4169

Laser cladding is an effective technology for repairing damaged components with high efficiency and low cost. Characterisation for the mechanical properties of the repaired structure is of great importance to evaluate its reliability. In this study, the mechanical properties of laser repaired GH4169 are investigated by Fourier‐series‐based virtual fields method and moiré interferometry. The elastic modulus distribution of the whole structure is identified to understand the mechanical performance of the repaired zone and base material. A uniaxial tensile test is performed and the full‐field deformation is measured by moiré interferometry. With the measured strain field, the distribution of modulus in repaired structures can be calculated. In addition, simulation experiments of moiré interferometry are conducted to optimise the parameters of Fourier‐series‐based virtual fields method to improve the accuracy of the proposed method. On the basis of these results, experiments on the repaired GH4169 material are performed and the variation of modulus in the whole structure is identified. The results verify that the proposed method is effective for characterising modulus distribution of the laser repaired structures, and will have a good prospect for further application.     

Accurate pixel-to-pixel correspondence adjustment in a digital micromirror device camera by using the phase-shifting moiré method

A camera based on the digital micromirror device (DMD) technology has been previously developed. In this optical system, the correspondence of each mirror of the DMD to each pixel of the CCD cannot readily be done since the pixel sizes of the DMD and the CCD are very small. An accurate pixel-to-pixel correspondence adjustment in the DMD camera by means of the phase-shifting moiré method is proposed. To perform high accurate adjustment of the optical system, the phase distribution of a moiré fringe pattern is analyzed when the CCD pixels and the DMD mirrors have a mismatch and/or misalignment with each other. This technique does not need a complicated setting or complex image processing to generate the moiré fringe pattern, and it needs only one captured image. In the adjustment experiment, the proposed method provided very accurate adjustment whose error was less than 1/25 pixel. An experiment of phase analysis to demonstrate the usefulness was performed.     

Automated small tilt-angle measurement using Lau interferometry

A technique for a tilt-angle measurement of reflecting objects based on the Lau interferometry coupled with the moire readout has been proposed. A white-light incoherent source illuminates a set of two gratings, resulting in the generation of the Fresnel image due to the Lau effect. The Fresnel image is projected onto a reflecting object. The image reflected from the object is superimposed onto an identical grating, which results in the formation of a moiré fringe pattern. The inclination angle of moiré fringes is a function of tilt angle of the object. Theory and experimental arrangement of the proposed technique is presented and results of the investigation are reported.     

Self‐Sorting of 10‐µm‐Long Single‐Walled Carbon Nanotubes in Aqueous Solution

Single‐walled carbon nanotubes (SWCNTs) are a class of 1D nanomaterials that exhibit extraordinary electrical and optical properties. However, many of their fundamental studies and practical applications are stymied by sample polydispersity. SWCNTs are synthesized in bulk with broad structural (chirality) and geometrical (length and diameter) distributions; problematically, all known post‐synthetic sorting methods rely on ultrasonication, which cuts SWCNTs into short segments (typically <1 µm). It is demonstrated that ultralong (>10 µm) SWCNTs can be efficiently separated from shorter ones through a solution‐phase “self‐sorting”. It is shown that thin‐film transistors fabricated from long semiconducting SWCNTs exhibit a carrier mobility as high as ≈90 cm² V^?1 s^?1, which is ≈10 times higher than those which use shorter counterparts and well exceeds other known materials such as organic semiconducting polymers (<1 cm² V^?1 s^?1), amorphous silicon (≈1 cm² V^?1 s^?1), and nanocrystalline silicon (≈50 cm² V^?1 s^?1). Mechanistic studies suggest that this self‐sorting is driven by the length‐dependent solution phase behavior of rigid rods. This length sorting technique shows a path to attain long‐sought ultralong, electronically pure carbon nanotube materials through scalable solution processing.     

An identification method of mechanical properties of materials based on the full‐field measurement method based on the fringe pattern

With the development of image processing technology, optical methods based on fringe patterns, for example, the grid method, electronic speckle pattern interferometry, moiré techniques (including moiré interferometry and digital moiré), and coherent gradient sensing, have become useful techniques for measuring the full‐field deformation of materials and structures. An important application of these techniques is to offer deformation fields for extracting constitutive parameters in the inverse methods. In this paper, we proposed a novel inversion method based on fringe patterns (IMFP), which can be used to identify constitutive model parameters by comparing simulated fringe patterns obtained using the finite element method with experimentally measured fringe patterns. The feasibility and identification accuracy of IMFP were evaluated through numerical experiments, and an additional series of numerical tests were conducted to analyse the noise immunity of IMFP and its sensitivity to the number of constitutive model parameters. Finally, IMFP was applied in the identification of the mechanical parameters of selective laser melting three‐dimensional printed stainless steel.     

Moiré Superlattice Structure in Two-Dimensional Catalysts: Synthesis,Property and Activity

Two-dimensional (2D) layered materials have been widely used as catalysts due to their high specific surface area, large fraction of uncoordinated surface atoms, and high charge carrier mobility. Moiré superlattice emerges in 2D layered materials with twist angle or lattice mismatch. By manipulating the moiré superlattice structure, 2D layered materials present modulated electronic band structure, topological edge states, and unconventional superconductivity which are tightly associated with the performance of catalysts. Hence, engineering moiré superlattice structures are proposed to be an important technology in modifying 2D layered materials for improved catalytic properties. However, currently, the investigation of moiré superlattice structure in a catalytic application is still in its infancy. This perspective starts with the discussion of structural features and fabrication strategy of 2D materials with moiré superlattice structure. Afterward, the catalytic applications, including electrocatalytic and photocatalytic applications, are summarized. In particular, the promotion mechanism of the catalytic performance caused by the moiré superlattice structure is proposed. Finally, the perspective is concluded by outlining the remaining challenges and possible solutions for the future development of 2D materials with moiré superlattice structure towards the catalytic applications.     

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.     

L'embarras du choix

Résumé Il est nécessaire de considérer les avantages et les limitations des nombreuses méthodes dont on dispose aujourd'hui pour l'analyse des contraintes. Des études systématiques manquent sur cette question. L'auteur s'occupe qualitativement de l'efficacité relative des méthodes dites des éléments-finis par rapport aux méthodes expérimentales d'analyse des contraintes. Il fait quelques considérations aussi sur la valeur relative de: 1^o la photoplasticité et le moiré pour résoudre des problèmes de plasticité; 2^o la photo-ortho-élasticité, la couche photoélastique et le moiré pour résoudre des problèmes d'anisotropie; 3^o plusieurs des méthodes employées maintenant pour résoudre des problèmes de photoélasticité dynamique; 4^o les méthodes employées en photoélasticité tridimensionnelle, et en général sur les méthodes photoélastiques, du moiré, de l'holographie, des pellicules fragiles et des méthodes ponctuelles.

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Summary It is necessary to consider the advantages and limitations of each of the numerous methods available today for the analysis of stress. Systematic studies are lacking on this subject. The author deals in a qualitative manner with the relative efficiency of the so-called finite element methods in respect with the experimental stress analysis methods. He also makes considerations on the relative merits of: 1) photoplasticity and moiré to solve problems in plasticity; 2) photo-ortho-elasticity, photoelastic coatings, and moiré to solve anisotropic problems; 3) several of the methods used today to solve problems in dynamic photoelasticity; 4) the methods used in three-dimensional photoelasticity, and in general about the photoelasticity methods, moiré, holography, brittle coatings, and the point-by-point methods. The analysis presented in the paper can be considered only preliminary. The author, however, gives reasons for his preference for the whole-field methods and for the diffused light polariscopes, for the use of moiré to solve problems in plasticity and in anisotropy, and for the use of the methods of repeated flashes to solve reproduceable problems in dynamic photoelasticity. He also shows that in general the “freezing” method is the most pratical and the most precise to solve three-dimensional problems. He thinks that the method of finite elements has replaced, or will soon replace, two-dimensional static photoelasticity. On the other hand, photoelasticity seems to be the most efficient method to solve dynamic problems, optimization problems, and three-dimensional problems.

     

Robust estimation of 3D trajectories from a monocular image sequence

This article describes a new method for object trajectory estimation that uses sequences of images taken from a monocular camera. The method integrates a Kalman filter to estimate the three‐dimensional (3D) parameters of the optical system and a lineal projective model to determine 3D point coordinates projected on the retinal plane. It works with at least three distinctive points in the image, and they are updated with correlation methods. The result is an estimation of the rotation and translation parameters between successive images within the sequence and yield to the 3D coordinates of the points selected for correspondence. The scaling problem related to 3D reconstruction is tackled via a priori information of the objects being observed. The method is tested with synthetic images to evaluate its accuracy, and later, an interesting application in autonomous navigation is presented. © 2002 Wiley Periodicals, Inc. Int J Imaging Syst Technol 12, 128–137, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ima.10020     

Micro 3D measurement method using SEM

Three diamensional (3D) measurement method by Scanning Electron Microscope (SEM) has already been proposed by using the principle of shadow moiré. In the method, the image of original grid in shadow moiré image must be clearly removed in fringe analysis process in order to perform high resolution analysis. A new method based on the principle of projection moiré is proposed to solve the trouble concerning the grid. In this paper, the mechanism of producing some shadows of grid on the surface of the object by back scattering electron beam in the new method is discussed. Fringe image as shadow of grid is analyzed by Wavelet transform. The precise 3D measurement is realized by using the phenomenon of shadows of grid. Furthermore, a 3D micro structure on the head of a hard disk is measured. From the comparison of results obtained by Atomic Force Microscope (AFM), it is confirmed that the proposed method has high-resolution power(about 20nm).     

TENSILE IMPACT DELAMINATION OF A CROSS-PLY INTERFACE STUDIED BY MOIRÉ PHOTOGRAPHY

Abstract Impact induced delamination along a cross-ply interface in carbon fiber/epoxy laminates is studied by high resolution moiré photography. The specimens were loaded in a tensile split-Hopkinson bar giving mode I dominated fracture, and a high speed camera captures images during loading and delamination. The resulting moiré fringes are analysed to produce full field displacement maps of the area around the loaded and propagating crack tips. The displacement map prior to failure shows good agreement with numerical solutions, calculated using a 3D self-adaptive p-version of the finite element method. The calibrated finite element solutions are then used to give further information about the matrix cracking zone size around the crack tip and the energy release rate. In comparison to quasi-static loading, tensile impact loading was found to increase the failure load and the resulting energy release rates; some physical explanations for this behaviour are discussed. It was concluded that the procedures presented have good potential for further determination of rate dependent material properties in carbon/fiber epoxy composites.     

Digital color encoding and its application to the moirétechnique

A moiré pattern color-encoding technique in which a digital image-processing system is used is described. The technique can display color moiré patterns with color sequences that represent the fringe orders. This technique is simple and fast and can be performed automatically. Experimental results demonstrating the feasibility of the technique are reported.     

Moire technique by means of digital image processing

Moiré technique by means of projected fringes is a suitable method for full field measurements of out-of-plane deformations and object contouring. One disadvantage in industrial applications has been the photographic process with the involved time-consuming development of the photographic film. This paper presents a new method using a TV camera and a digital image processor whereby real-time measurements of deformations and comparison of object contours are possible. Also the principles and limitations of the projected moiré method are described.     

Profiling of objects with height steps by wavelet analysis of shadow moiré fringes

A temporal wavelet analysis algorithm is proposed for shadow-moiré-based three-dimensional surface profiling on objects having discontinuous height steps. A grating is positioned close to an object, and its shadow is observed through the grating. The moiré fringe patterns vary when the grating is in-plane rotating. A series of fringe patterns are captured by a CCD camera at different rotating angles. Phase values are evaluated point by point with the continuous wavelet transform. From the phase values of each point on the object, the distance between the object and the grating can be retrieved. The surface profile is obtained without temporal or spatial phase unwrapping. This technique is applicable to objects with discontinuous height steps, which are impossible to measure with conventional shadow moiré topography. Two specimens are tested to demonstrate the validity of the method: One is an object with a height step of 1.6 mm, and another is a small coin with unevenness of less than 0.2 mm. The experimental results are compared with test results by use of the mechanical stylus method.