Simulation model for shapiro time delay and light deflection experiments

The time delay experiment proposed by I.I. Shapiro in 1964 and conducted in the seventies was the most precise experiment of general relativity until that time. Further experimentation has improved the accuracy level of both the time delay and the light deflection experiments. A simulation model is proposed that involves only a simple mass and time transformation factor involving velocity of light. The light deflection and the time delay experiments are numerically simulated using this model that does not use the general relativistic equations. The computed values presented in this paper compare well with recent levels of accuracy of their respective experimental results.     

Speckle shear interferometry

A number of speckle shear methods and their applications to ndt are discussed. Experiments using multiple apertures with custom-made optical elements have shown that in-plane displacement, slope and curvature patterns can be obtained by filtering through appropriate haloes.     

Speckle interferometry methods for displacement and strain measurements using photorefractive crystal

Photorefractive crystals offer several attractive features such as high resolution and in situ processing. As the images are erasable, these crystals are suitable for read–write applications and hence find potential use in speckle photography, image processing and holography. The barium titanate (BaTiO₃) crystal as recording medium has been extensively used as a novelty filter for real-time in-plane displacement measurements employing two-beam coupling configuration. This paper presents new optical configurations in speckle shear photography to measure in-plan displacement and the strain in real time using BaTiO₃ crystal as recording medium. Speckle photography studies are made using a simple two-beam coupling configuration. In speckle shear photography, a diffused object illuminated with two parallel narrow laser beams is imaged inside the crystal, and a pump beam is added at this plane. The speckle patterns due to each beam and the pump beam produce index gratings. When the object is deformed, the speckle patterns shift consequently. We now have four speckle fields: two generated from the interaction of pump beam with the index gratings and two pertaining to deformed states directly transmitted through the crystal. Thus, the fields from respective points on the object interfere after passage through the crystal and produce the Young's fringe patterns. Due to strain, the fringes in each pattern are of different width and orientation, resulting in the generation of a Moiré pattern. The strain is obtained from the width and orientation of the fringes in the Moiré pattern. The experiments are conducted on a specimen with a notch, which is subjected to tensile loading. The in-plane displacement is measured separately in another experiment. The above studies are carried out at Nd–Yag laser.     

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.     

Speckle interferometry

Illumination of a rough surface by a coherent monochromatic wave creates a grainy structure in space termed a speckle pattern. It was considered a special kind of noise and was the bane of holographers. However, its information-carrying property was soon discovered and the phenomenon was used for metrological applications. The realization that a speckle pattern carried information led to a new measurement technique known as speckle interferometry (SI). Although the speckle phenomenon in itself is a consequence of interference among numerous randomly dephased waves, a reference wave is required in SI. Further, it employs an imaging geometry. Initially SI was performed mostly by using silver emulsions as the recording media. The double-exposure specklegram was filtered to extract the desired information. Since SI can be configured so as to be sensitive to the in-plane displacement component, the out-of-plane displacement component or their derivatives, the interferograms corresponding to these were extracted from the specklegram for further analysis. Since the speckle size can be controlled by the F number of the imaging lens, it was soon realized that SI could be performed with electronic detection, thereby increasing its accuracy and speed of measurement. Furthermore, a phase-shifting technique can also be incorporated. This technique came to be known as electronic speckle pattern interferometry (ESPI). It employed the same experimental configurations as SI. ESPI found many industrial applications as it supplements holographic interferometry. We present three examples covering diverse areas. In one application it has been used to measure residual stress in a blank recordable compact disk. In another application, microscopic ESPI has been used to study the influence of relative humidity on paint-coated figurines and also the effect of a conservation agent applied on top of this. The final application is to find the defects in pipes. These diverse applications demonstrate the power of this technique.     

An in-plane insensitive multiaperture speckle shear interferometer for slope measurement

A modified two-aperture speckle shear interferometer that eliminates the contribution of the in-plane component and its derivative to the phase change, and yields a fringe pattern corresponding to the first-order partial derivatives of the out-of-plane displacement component, is reported in this note. In this method, two laterally sheared object points are viewed axially. The wave fields from these points are independently combined at the image plane of the imaging system.     

A separable potential model for N-N interaction (II)

A two-term separable potential model for the N-N interaction in ¹S₀, ³S₁?³D₁, ¹D₂, ³D₂, ³D₃, ¹P₁, ³P₀, ³P₁ and ³P₂ partial waves is proposed. Its off-energy-shell behaviour is very similar to that of a local potential.     

Setting sensitivity in Talbot interferometry with modified gratings

A dual field grating has been introduced for use in Talbot interferometry. We report here results of an experimental investigation on setting sensitivity when using these gratings for testing.     

Lateral shear interferometry with holo shear lens

A simple method for obtaining lateral shear using holo shear lenses (HSL) has been discussed. This simple device which produces lateral shears in the orthogonal directions has been used for lens testing. The holo shear lens is placed at or near the focus of the lens to be tested. It has also been shown that HSL can be used in speckle shear interferometry as it performs both the functions of shearing and imaging.     

Schur complement preconditioners for anisotropic problems

We present two new variants of Schur complement domain decompositionpreconditioners suitable for 2D anisotropic problems. Thesevariants are based on adaptations of the probing idea, describedby Chan et al (1992 Fifth Int. Symp. on Domain DecompositionMethods for Partial Differential Equations, Philadelphia: SIAM,pp 236-249), used in conjunction with a coarse grid approximationas introduced by Bramble et al (1986 Math. Comput. 47, 103-134).The new methods are specifically designed for situations wherethe coupling between neighbouring interfaces is stronger thanthe coupling within an interface. Taking into account this strongcoupling, one variant uses a multicolour probing technique toavoid distortion in the probe approximations that appear whenusing the method proposed by Chan et al. The second techniqueuses additional probe matrices to approximate not only the couplingwithin the interfaces but also the coupling between interfacepoints across the subdomains. This latter procedure looks somewhatlike an alternating line relaxation method for anisotropic problems,see Brandt (1977 Math. Comput.. 31, 333-390). To assess therelevance of the new preconditioners, we compare their numericalbehaviour with well known robust preconditioners such as thebalanced Neumann-Neumann method proposed by Mandel (1993 Commun.Numer. Methods Eng.. 9, 233-241).