Viewing angle of liquid-crystal displays: representation on the Poincaré sphere

Using the extended Jones calculus for oblique incidence, we have succeeded in representing light propagation through birefringent media on the Poincaré sphere for arbitrary propagation directions. The situation is far more complicated than for the case of perpendicular transmission. To achieve a simple representation method we had to define appropriate conventions. One can use the method to evaluate the efficiency of existing viewing-angle compensation foils. The Poincaré sphere turns out to be a valid geometrical method for the design of new compensation foils that optimize the contrast ratio. The different parameters of a homogeneous compensation foil that is applied to a liquid-crystal display to improve the viewing-angle properties can be systematically determined.     

Poincaré sphere representation of the fixed-polarizer rotating-retarder optical system

The trajectory of the polarization state of a monochromatic light beam after it passes through a fixed linear polarizer and a rotating linear retarder of arbitrary retardance delta is determined on the Poincaré sphere. The three-dimensional figure-8 contour is shown to be the line of intersection of a right-circular cylinder with the sphere. The cylinder is parallel to the polar (S3) axis, touches the sphere at the equator (at the point that represents the linear polarization transmitted by the fixed polarizer), and has a radius r = sin2(delta/2). Projections of the trajectory in the coordinate planes of the normalized Stokes parameter space (s1, s2, S3) are also determined.     

Analysis of clusters and uniformity of distribution of states of polarization on the Poincaré sphere

An analysis of the clusters and the uniformity of distribution of states of polarization on the surface of a Poincaré sphere generated by rotating wave plates is given. The analysis of clusters of the states of polarization is based on a spherical radial distribution function. For uniform analysis of the distribution, two methods are proposed. The first method is based on calculation of the correlation coefficient; the second method is based on calculation of the angles between pairs of the states of polarization on the Poincaré sphere. For polarization scramblers consisting of eight or more rotating wave plates, nonclustered and near-uniform distribution of states of polarization is obtained.     

Visualization and calculation of polarized light. I. The polarization ellipse, the Poincaré sphere and the hybrid polarization sphere

We describe the historical and mathematical development of the polarization ellipse and the Poincaré sphere. We point out the limitations of the Poincaré sphere in its present use. To overcome these limitations we describe a new polarization sphere that we call the hybrid polarization sphere. This name is used because phase shifting and rotation of polarization components are described by small circles. Furthermore, longitudinal and latitudinal great circles are introduced so that the coordinates of a point on the sphere can be read. The hybrid polarization sphere is described and applied to polarizers, wave plates, and rotators. As a result, the hybrid polarization sphere can be used for both visualization and calculation and enables the difficulties associated with the Poincaré sphere to be overcome.     

On the computation of hilbert—Poincaré series

We prove a theorem, which provides a formula for the computation of the Poincaré series of a monomial ideal ink[X₁,, X_n], via the computation of the Poincaré series of some monomial ideals ink[X ₁,, X_i,, X_n]. The complexity of our algorithm is optimal for Borel-normed ideals and an implementation in CoCoA strongly confirms its efficiency. An easy extension computes the Poincaré series of graded modules over standard algebras.The paper was partly written while the third author was visiting Queen's University, during the academic year 1989/90. It was partly supported by the Natural Sciences & Engineering Research Council of Canada, Queen's University (Kingston, Canada) and Consiglio Nazionale delle Ricerche     

A two‐phase approach for single machine scheduling problems: Minimizing the total absolute deviation

Abstract

This paper presents a heuristic for solving a single machine scheduling problem with the objective of minimizing the total absolute deviation. The job to be scheduled on the machine has a processing time, p_i , and a preferred due date, d_i . The total absolute deviation is defined as the sum of the earliness or tardiness of each job on a schedule 5. This problem is proved to be NP‐complete by Garey et al. [8]. As a result, we developed a two‐phase procedure to provide a near‐optimal solution to this problem. The two‐phase procedure includes the following steps: First, a greedy heuristic is applied to the set of jobs, N, to generate a “good” initial sequence. According to this initial sequence, we run Garey's local optimization algorithm to provide an initial schedule. Then, a pairwise switching algorithm is adopted to further reduce the total deviation of the schedule. The effectiveness of the two‐phase procedure is empirically evaluated and has been found to indicate that the solutions obtained from this heuristic procedure are often better than other heuristic approaches.     

Displacement measurement of concrete bridges by the sampling Moiré method based on phase analysis of repeated pattern

Measuring accurate deformation distribution of large-scale structures inexpensively and efficiently is a crucial challenge of structural health monitoring. Phase-based imaging technique has great potential for accurate and robust multipoint displacement measurement in the field. In this study, the sampling Moiré method—one of the promising optical techniques—was applied to the displacement measurement of a concrete bridge for the high-speed railway in Japan. Using retroreflective Moiré markers, the two-dimensional in-plane displacements at multiple locations could be easily measured from recorded digital images at a distance of 20 m regardless of day and night. Results of the dynamic deflection obtained from the sampling Moiré method were in good agreement with those from a conventional laser Doppler vibrometer. The time series of two-dimensional displacement analyses when the outbound or inbound trains passed at the speed of 150 or 320 km/h through the bridge revealed that the points at the centre and the quarter of the bridge span demonstrated complex deformation behaviour showing elliptical rotation. The effects of random noise of the recorded image were quantitatively investigated, and the air fluctuation was discussed from the field experiments. We proved that measurements using the sampling Moiré method could be more stable at night than daytime.     

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.     

Dependence of the Coordinate Measurement Error of Geometric Elements’ Shape Characteristics on the Control Point Number

Measurement Techniques - This article presents issues in estimating the coordinate measurement error of geometric elements’ shape characteristics of products depending on the control point...     

Comment on ‘Operator formalism for the Wigner phase distribution’

Abstract

The operator associated with the radially integrated Wigner function is found to lack justification as a phase operator.     

Effect of hot working on flow behavior of Ti–6Al–4V alloy in single phase and two phase regions

Hot deformation behavior of the alloy Ti–6Al–4V was investigated via conducting hot compression tests at temperatures of 800–1150 °C and at strain rates, ranging from 0.001 s⁻¹ to 1 s⁻¹, at an interval of an order of magnitude. The apparent differences of flow stress curves obtained in dual phase α + β and single phase β regions were analyzed in term of different dependence of flow stress to temperature and strain rate and different microstructural evolutions. The values of strain rate sensitivity and apparent activation energy were obtained respectively as 0.20 and 530 kJ/mol for two phase microstructure. However, for single phase β microstructure they were approximated as 0.19 and 376 kJ/mol, respectively. It was found that in two phase region the values of strains corresponding to peak point, ε_p, and the highest rate of flow softening, ε^*, are almost independent to Zenner–Hollomon parameter. In single phase region, ε_p and ε^* exhibited a direct relationship to Z parameter and the corresponding empirical equations were proposed.     

The Sénarmont Compensator: An Early Application of the Geometric Phase

Abstract

The Sénarmont compensator has been used for many years to measure the phase retardation between the two components of an elliptically polarized beam of light. This letter shows how the operation of this device actually makes use of the geometric phase.     

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.     

Temperature-dependence on the optical properties and the phase separation of polymer–fullerene thin films

A detailed study on the thermal transition of poly(3-hexylthiophene) (P3HT) and blends was investigated by differential scanning calorimetry, while the morphological, phase separation and the transformation in the optical properties were probed by thermal-atomic force microscopy (AFM), polarized optical microscopy (POM) and spectroscopic ellipsometry (SE). The inclusion of fullerenes on the polymer structure confirms the formation and evolution of a new endothermic transition at high temperatures. SE revealed that the refractive index and extinction coefficient of the films increased with annealing temperature up to 140 °C due to the suppressed diffusion of PCBM molecules into the blend. Annealing above 140 °C resulted in a decrease in the optical constants due to the formation of large “needle-like” crystals. This is due to the depletion of PCBM clusters near the “needle-like” structures; resulting from the diffusion of the PCBM molecules into the growing PCBM crystals or “needle-like” crystals as is evidenced by in situ thermal-AFM and POM. These findings indicate that annealing temperature of 140 °C is suitable for a P3HT:PCBM film to obtain the desired phase separation for solar cell application.     

Moiré interferogram phase extraction: a ridge detection algorithm for continuous wavelet transforms

We present a procedure using continuous wavelet transforms (CWTs) to extract the phase information from moiré interferograms. The relationship between precise ridge detection of the two-dimensional CWT magnitude map and accurate phase extraction is detailed. A cost function is introduced for the adaptive selection of the ridge, and a computationally inexpensive implementation of the cost function ridge detection algorithm is explored with dynamic programming optimization. The results of the proposed ridge detection algorithm on actual interferograms are illustrated. Moreover, the resulting extracted phase is demonstrated to be smooth and accurate. As a result, the sensitivity of the moiré interferometry method is improved to obtain a pixel-by-pixel in-plane strain distribution map.     

Distinct dendritic α phase emerging on the surface of primary α phase in a compressed near-α titanium alloy

The characteristic of the surface morphology of primary α phase was studied in a deformed near-α titanium alloy. Dendritic α phase emerged on the surfaces of primary α phase when the alloy was air-cooled in α + β phase field after deformation. The dendritic α grain has the same orientation with its original primary α grain. The formation of the dendritic α phase could be explained by interface instability in epitaxial growth process of the primary α phase. The dislocations induced by deformation could facilitate the formation of dendritic α phase leading to the dendritic α phase and more obvious with the increase of strain. The growth of dendritic α phase was finally limited by the nucleation of second α phase with cooling.     

The Avogadro constant: determining the number of atoms in a single-crystal ²⁸Si sphere

The Avogadro constant, the number of entities in an amount of substance of one mole, links the atomic and the macroscopic properties of matter. Since the molar Planck constant--the product of the Planck constant and the Avogadro constant--is very well known via the measurement of the Rydberg constant, the Avogadro constant is also closely related to the Planck constant. In addition, its accurate determination is of paramount importance for a new definition of the kilogram in terms of a fundamental constant. Here, we describe a new and unique approach to determine the Avogadro constant from the number of atoms in 1 kg single-crystal spheres that are highly enriched with the (28)Si isotope. This approach has enabled us to apply isotope dilution mass spectroscopy to determine the molar mass of the silicon crystal with unprecedented accuracy. The value obtained, N(A)=6.022 140 82(18)×10(23) mol(-1), is now the most accurate input datum for a new definition of the kilogram.     

The intracellular phase in rapidly solidified lloys based on the AlFe system

The nature of the second phase formed in rapidly solidified AlFe alloys has been determined. For those alloys studied exhibiting micro-cellular morphologies, the second phase is T′. The alloy Al-6.8Fe-2Mo-1.1V, in the melt-spun condition, exhibits a different microstructure, consisting of a uniform and extremely fine distribution of second phase particles. These particles possess the icosahedral structure, identical to that observed in rapidly solidified AlMn alloys. The mechanism of formation of these second phase particles is thought to involve the formation of an amorphous material following the nucleation of primary α-Al; this amorphous material is thought to be crystallized as a result of recalescence.     

Influence of the α/β-SiC phase transformation on microstructural development and mechanical properties of liquid phase sintered silicon carbide

The transformation kinetics and microstructural development of liquid phase sintered silicon carbide ceramics (LPS-SiC) are investigated. Complete densification is achieved by pressureless and gas pressure sintering in argon and nitrogen atmospheres with Y2O3 and AlN as sintering additives. Studies of the phase transformation from to -SiC reveals a dependency on the initial -content and the sintering atmosphere. The transformation rate decreases with an increasing -content in the starting powder and in presence of nitrogen. The transformation is completely supressed for pure -SiC starting powders when the additive system consists of 10.34 wt% Y2O3 and 2.95 wt% AlN. Materials without phase transformation showed a homogeneous microstructure with equiaxed grains, whereas microstructures with elongated grains were developed from SiC powders with a high initial /-ratio (>1:9) when phase transformation occurs. Since liquid phase sintered silicon carbide reveals predominantly an intergranular fracture mode, the grain size and shape has a significant influence on the mechanical properties. The toughness of materials with platelet-like grains is about twice as high as for materials with equiaxed grains. Materials exhibiting elongated microstructures show also a higher bending strength after post-HIPing.     

Identification of thermomechanical parameters based on the virtual fields method combined with the sampling moiré method

Thermomechanical parameters are important indicators for evaluating the mechanical properties of superalloys and generally include the coefficients of stiffness and thermal expansion at high temperatures. At present, there are few methods for simultaneously characterising the thermomechanical parameters of superalloys, especially single-crystal superalloys. To satisfy the demand for simultaneously identifying the thermomechanical parameters of orthotropic superalloys, an optimised virtual fields method for decoupling the thermomechanical parameters was developed in this study by combining the self-developed heat-resistant grids and the sampling moiré method. First, several factors, including the oblique angle of the grids, image noise and thermomechanical coupling phenomena, were studied through numerical experiments to analyse their influences on the identification accuracy. Then, an optimised identification strategy was established. Finally, the thermomechanical parameters of Ni-based polycrystalline and single-crystal superalloys were successfully identified and comparatively studied. The identification results demonstrate that the proposed method is highly accurate and robust. This research will provide an effective way to accurately characterise the multiple parameters of superalloys at high temperatures.