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.     

The role of Fourier theory and of modulation in the prediction of visible moiré effects

Modern moiré theory is largely based on the Fourier approach. And yet, it seems that the Fourier theory by itself cannot answer all questions related to moiré effects. We present some visible phenomena in the superposition of periodic structures (such as line gratings) that are not captured by the Fourier approach. We discuss their significance, and provide possible explanations. In particular, we introduce the infinite module spanned by the frequencies of the original individual layers as a main tool in the moiré theory. We discuss its significance on the visible periodicities in the layer superposition–either real moiré effects, or pseudo-moiré (modulation) effects having no corresponding impulses in the Fourier spectral domain.     

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.     

Experimental evidence of the spatial coherence moiré and the filtering of classes of radiator pairs

Evidence of the physical existence of the spatial coherence moiré is obtained by confronting numerical results with experimental results of spatially partial interference. Although it was performed for two particular cases, the results reveal a general behavior of the optical fields in any state of spatial coherence. Moreover, the study of the spatial coherence moiré deals with a new type of filtering, named filtering of classes of radiator pairs, which allows changing the power spectrum at the observation plane by modulating the complex degree of spatial coherence, without altering the power distribution at the aperture plane or introducing conventional spatial filters. This new procedure can optimize some technological applications of actual interest, as the beam shaping for instance.     

Measurement of residual stress for ITO/PET substrates by the double beam shadow moiré interferometer

This study constructed a measurement system that can quickly and accurately analyze the residual stress of flexible electronics. A double beam shadow moiré interferometer was set up to measure and evaluate the residual stress of tin-doped indium oxide films on a polyethylene terephthalate substrate. However, this system required only two symmetrical fringes to evaluate the residual stress of transparent conductive oxide films on flexible substrate. Applying the grating translation techniques to the double beam shadow moiré interferometer greatly improved the measurement resolution and accuracy, and the relative error was reduced to 1.2%.     

Unification of formulation of moiré fringe spacing in parametric equation and Fourier analysis methods

Inspections of moiré fringe characteristics, such as period and orientation, conventionally are done by two approaches; namely, parametric equation and Fourier analysis methods. In some cases these methods yield different results. This inconsistency is removed by revising the derivation of the indicial equation for moiré fringes by the parametric equation method.     

Projection method of resolving ambiguities by determining the order of colors in moiré fringes

From the scientific literature there are some well-known methods used to resolve the arising problem of ambiguities in moiré patterns. The main disadvantage of these methods is that for image processing one must use several patterns. It means that it is impossible to work with dynamic objects in a real-time operation mode. We present a projection method to resolve ambiguities by determining the order of colors in moiré patterns. This method is based on the application of color rulings to gratings in a projection moiré technique.     

Investigation on certain optical,thermal, and Z-scan studies of nonlinear optical tris–sarcosine calcium chloride single crystal

Slow solvent evaporation was used to produce single crystals of Tris–Sarcosine Calcium Chloride (TSCC) from aqueous solution. The cell parameters of the grown crystals were determined using the single-crystal X-ray diffraction analysis. The existence of functional groups in TSCC was confirmed using the Fourier Transform Infrared spectrum analysis. Energy-Dispersive X-ray Analysis verified the chemical composition of the TSCC crystal. The optical transmittance of TSCC was greater than 90%, according to the UV–Vis–NIR transmittance spectrum measurements. This indicates TSCC is an appropriate material for NLO applications. The optical characteristics of the grown crystal, including band gap energy, were determined. The photoluminescence characteristics of TSCC crystal were also studied in order to better understand its optical device manufacturing. The thermal behavior of TSCC was investigated using the TGA/DTA and DSC studies. For various temperatures, the fluctuation of the dielectric constant and dielectric loss with regard to frequency variation was examined and the results were described in depth. The TSCC susceptibility χ⁽³⁾ and nonlinear refractive index n₂ values were evaluated. The saturation absorption of TSCC was revealed by open aperture Z-scan technique, and the self-defocusing performance was revealed by closed aperture Z-scan measurements.

     

Analysis of the tilt angle of the moiré fringes produced by two inclined gratings in talbot interferometry

Abstract

Features of the moiré fringes produced by the inclined grating planes in Talbot interferometry are studied under the illumination of a plane wave. Inclinations of the two grating planes are introduced by rotating the beam-splitter and the detector gratings around the axes parallel to the line directions of each grating, when the line directions of the two grating are different. Theoretical analyses indicate that the tilt angle of the moiré fringes is sensitive to the inclination angle, and the analyses are supported by experimental results. Some simple and practical methods for judging and removing the inclinations are also discussed.     

Definition and measurement of the shear-lag parameter, β, as an index of the stress transfer efficiency in polymer composites

The shear-lag parameter, , employed in various problems of shear-lag analysis of composites is an unknown parameter which, in certain cases, is impossible to define. In this paper, a new methodology is proposed for the definition and subsequent experimental measurement of for various single-fibre model composites. It is argued that, if is defined as a fitting parameter for the solution of the shear-lag differential equation, then it can effectively serve as a stress-transfer efficiency index. The dependence of upon the conditions prevailing at the fibre–matrix interface will be demonstrated by measuring as a function of the fibre sizing in a carbon–epoxy composite system. © 1998 Chapman & Hall     

Parameter design of a parallax barrier based on the color moiré patterns in autostereoscopic display

We propose a parameter design of the parallax barrier (PB) based on the color moiré patterns in autostereoscopic displays. First, the display device and the PB are approximated as two corresponding binary gratings. In order to obtain different corresponding predominant Fourier low-frequency terms, the superposition of the equivalent grating for the display device and the special radial grating is analyzed, referring to the indicial equation method and Fourier theory. Moreover, the two transition regions are considered as the regions where moiré patterns vary gently. Finally, the appropriate parameter of the PB can be obtained. The validity of the proposed design is verified in the experiment.     

Approximate scheme by the coupled-wave theory to efficiently analyze the influences of moiré phenomena in liquid-crystal devices

This work studies an approximate scheme by coupled-wave theory to analyze quickly the large-scale moiré phenomena as seen in common liquid-crystal devices. The moiré phenomena are considered to be caused by two periodic structures (with lattice vectors γ?₁ and γ?₂) and show an interference pattern spanning over a length γ_m=|γ?₁|·|γ?₂|/|γ?₁-γ?₂| (with γ?₁?γ?₂). With the coupled-wave theory, the complete analysis of the moiré optics includes at least 2γ_m/λ (λ: wavelength in vacuum) Fourier components and presents an ineffective computation. This work applies a cos^τ type approximation for the openings of unpatterned liquid-crystal pixels, and considers the first-order coupling between the Fourier components of pixels and other (periodic) optical structures. We hence arrive at an effective evaluation, including 4τ|γ?₁|/λ (or 4τ|γ?₂|/λ) Fourier components, and are able to go back to a complete analysis when considering higher-order couplings at an appropriate τ integer value.     

Theoretical error analysis of the sampling moiré method and phase compensation methodology for single-shot phase analysis

Recently, a rapid and accurate single-shot phase measurement technique called the sampling moiré method has been developed for small-displacement distribution measurements. In this study, the theoretical phase error of the sampling moiré method caused by linear intensity interpolation in the case of a mismatch between the sampling pitch and the original grating pitch is analyzed. The periodic phase error is proportional to the square of the spatial angular frequency of the moiré fringe. Moreover, an effective phase compensation methodology is developed to reduce the periodic phase error. Single-shot phase analysis can perform accurately even when the sampling pitch is not matched to the original grating pitch exactly. The primary simulation results demonstrate the effectiveness of the proposed phase compensation methodology.     

Measurement of stress in aluminum film coated on a flexible substrate by the shadow moiré method

This investigation proposes the use of the shadow moiré method (SMM) to measure stress in a thin film that is coated on a flexible substrate. The technique defines the profile of the sample by contour lines without the application of an external force, and the radius of curvature is calculated from these contour lines. The SMM is insensitive to environmental noise and has the same advantages as the interference method, such as being nondestructive and easy to use. For Al film with a thickness of 120 nm coated on a polyimide substrate by a DC magnetron sputtering system (800 W, room temperature), the stress is 0.45 +/- 0.042 GPa.     

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).     

Analysis of the magnetic field and studies of the beam dynamics for H− ions in the University of Manitoba cyclotron

Beam orbit dynamics investigations for H⁻ ions in the completely redesigned central region of the University of Manitoba cyclotron were carried out. The methods and the results of these studies are presented along with an analysis of the cyclotron magnetic field that was previously mapped in 1984.     

Study on the relation between the refractive index of fresh muscle tissue and its water content from 400 to 750 nm

Refractive index dispersion (RID) of fresh tissue is highly related to water content. However, there is no experimental investigation about their relationship for a wide spectral range. In this study, with the aid of a previously proposed lab-made apparatus, the RID of fresh and fully-dehydrated mutton muscle samples were measured over the continuous spectral range from 400 to 750 nm. The mass fractions and volume fractions were also measured. Results showed that the RID of fresh muscle tissue equals to the sum of fully-dehydrated tissue RID and water RID multiplied by their respective volume fractions. The results in this study also experimentally proved that the effective medium theory of refractive index is applicable for tissue analysis.     

Critical comments to the Oliver–Pharr measurement technique of hardness and elastic modulus by instrumented indentations and refinement of its basic relations

A critical analysis was made of the Oliver and Pharr method for determination of the hardness and elastic moduli of materials by instrumented indentations with the continuous recording of the P–hdiagrams (P is the force acting on the indenter, h is the approach of the indenter and a sample). Mistakes and insufficient justification were revealed in the basic theoretical relations of this method. In particular, this refers to an incorrect definition of the depth of the elastic contact h_c, which is the base of these relalations. New refined basic relations and formulas for the determination of hardness and elastic modulus are given, in which the above defects are eliminated and which are based only on the assumption of elastic unloading of the indenter according to the classic theories of the elastic contact. In addition to the foregoing, using the data of the P–h diagram measured in the arbitrary laboratory coordinate system, an improved method of the stable determination of the contact stiffness S = dP/dh at the P–h diagram position have been proposed in the commonly accepted theoretical coordinate system in which its basic classic model relations are recorded. These refinements have been derived without additional assumptions to hypotheses to the Oliver and Pharr method and additional experimental measurements.     

Application of Photothermal Techniques in the Determination of the Water–Vapor Diffusion Coefficient and Thermal Effusivity of Hydrogels

The main objective of this work is to determine the effect of different sodium alginate concentrations in hydrogels on their water–vapor diffusion coefficient (WVDC) and thermal effusivity ( $e_\mathrm{s})$ . These physical parameters were measured by photoacoustic and pyroelectric techniques, respectively. The results indicate that the higher values for the WVDC are presented at a concentration of 2 % sodium alginate. At lower concentrations of sodium alginate, the sample thermal effusivity increases, with a value close to the water thermal effusivity.