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.     

Exploring the statistical applicability of the Poincaré inequality: a test of normality

A new test of normality based on Poincaré inequality is proposed and analyzed. It rests on the characterization of the normal distribution given by Borovkov and Utev, i.e., a r.v. is normal if and only if its Poincaré constant is equal to its variance.     

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     

Effect of noise-induced crisis of attractor on characteristics of Poincaré recurrence

The effect of noise on the Poincaré recurrence time has been studied in a one-dimensional map with quasi-attractor. The validity of the Kac theorem in application to noise systems is substantiated. Results of calculations of the distribution of recurrence times in a noisy system are presented.     

Effect of inorganic salts on the inhibition of hydrolyzing halo‐ester in a two‐phase solution

Abstract

Effect of the inorganic salts on the conversion of halo‐ester (ethyl‐2‐bromoisobutyrate, EtOBuBr) hydrolyzing in an alkaline aqueous solution/organic solvent two‐phase medium was investigated. The rate of hydrolyzing EtOBuBr and the conversion are obviously affected by the inorganic salts. The experimental data verify the proposed mechanism of hydrolysis. The reaction steps which hydrolyze these bromo‐alkyl bonds (Br‐C bond) and ester functional groups (–COOR) are developed and discussed. A kinetic model of the main reaction steps was established in which the rate expressions were derived. The intrinsic rate constants of the reactions were determined from the experimental data of EtOBuBr hydrolysis via parameter estimation. The results indicated that the conversion of hydrolyzing EtOBuBr is highly dependent on the concentration of alkaline compound in the aqueous solution. It is also found that sodium carbonate, sodium chloride, sodium nitrate and sodium sulfate inhibit the reaction, while calcium carbonate enhances it. The corresponding rate constants of hydrolyzing EtOBuBr in a variety of inorganic salt concentrations were searched.     

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.     

Statistical characteristics of Poincaré return times within the local approach under presence of noise

The dependences of the mean time and dispersion of Poincaré return times on the ? vicinity of the initial state have been analyzed in the absence and in the presence of external noise.     

The mean Poincaré return time locking: A criterion of chaos induced synchronization

A new method for diagnostics of the induced synchronization of chaotic self-oscillation is proposed, which is based on the local theory of Poincaré recurrences. It is established that, in the region of synchronization, the mean Poincaré return time is locked by an external harmonic signal.     

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.     

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.     

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.