Diffraction of short waves modelled using new mapped wave envelope finite and infinite elements

We consider a two‐dimensional wave diffraction problem from a closed body such that the complex progressive wave potential satisfies the Sommerfield condition and the Helmholtz equation. We are interested in the case where the wavelength is much smaller than any other length dimensions of the problem. We introduce new mapped wave envelope infinite elements to model the potential in the far field, and test them for some simple Dirichlet boundary condition problems. They are used in conjuction with wave envelope finite elements developed earlier [1] to model the potential in the near field. An iterative procedure is used in which an initial estimate of the phase is iteratively improved. The iteration scheme, by which the wave envelope and phase are recovered, is described in detail. Copyright © 1999 John Wiley & Sons, Ltd.     

Structural characterization of the ac conductivity in Ag ion conducting glasses

The material trends in various silver ion conducting glasses have been studied recently by focusing on the relationship between the first sharp diffraction peak (FSDP) wave number Q, and the fitting parameters of the ac conductivity, precisely the ratio (log A)/n, where A and n represent the pre-exponential factor and the power law exponent of Jonscher’s law, respectively. In the present paper, a model for the FSDP wave number dependence of the ratio (log A)/n has been proposed and a good agreement has been found with the experiments. By using the concept of bond fluctuation in superionic conductors, the results have been successfully explained, leading to the conclusion that the universal aspect of the power law reflects the universal pattern of the potential barrier at intermediate length scales. The result reconfirms that the ion transport in glasses is intimately related with the FSDP wave number.     

Super-resolution pupil filtering for visual performance enhancement using adaptive optics

Ocular aberration correction can significantly improve visual function of the human eye. However, even under ideal aberration correction conditions, pupil diffraction restricts the resolution of retinal images. Pupil filtering is a simple super-resolution (SR) method that can overcome this diffraction barrier. In this study, a 145-element piezoelectric deformable mirror was used as a pupil phase filter because of its programmability and high fitting accuracy. Continuous phase-only filters were designed based on Zernike polynomial series and fitted through closed-loop adaptive optics. SR results were validated using double-pass point spread function images. Contrast sensitivity was further assessed to verify the SR effect on visual function. An F-test was conducted for nested models to statistically compare different CSFs. These results indicated CSFs for the proposed SR filter were significantly higher than the diffraction correction (p < 0.05). As such, the proposed filter design could provide useful guidance for supernormal vision optical correction of the human eye.     

Phase-space interferences as the source of negative values of the Wigner distribution function

It is shown that the negative values of the Wigner distribution function in classical optics are a consequence of the phase-space interference among the Gaussian beams into which an arbitrary light distribution (or a superposition of light distributions) can be decomposed. These elementary Gaussian beams partition the phase space in wave optics in adjacent, interacting, finite-area cells, in contrast to geometrical optics, where the phase space is continuous and a light beam can be decomposed into a number of perfectly localized, non-interacting rays.     

The Bayes procedure in exponential reliability family models using conjugate convex tent prior family

A Bayes procedure for estimating the unknown parameter indexed to some of one parameter exponential family distributions is presented. In such a procedure, we shall use a new conjugate prior family that we shall call a conjugate convex tent family. A member of this family could be constructed by assuming a little information about the unknown parameter. Some of the needed parameters for constructing prior density function are the values r, p and q. Bayes estimators for using a priori symmetrical convex tent density can be obtained as special cases of the present work. Numerical simulation study is introduced by using the Monte Carlo method. In this study we have investigated the influence of the prior parameters r, p and q on the accuracy of the Bayes estimators.     

Diffraction-attenuation resistant beams: their higher-order versions and finite-aperture generations

Recently, a method for obtaining diffraction-attenuation resistant beams in absorbing media has been developed in terms of suitable superposition of ideal zero-order Bessel beams. In this work, we show that such beams keep their resistance to diffraction and absorption even when generated by finite apertures. Moreover, we shall extend the original method to allow a higher control over the transverse intensity profile of the beams. Although the method is developed for scalar fields, it can be applied to paraxial vector wave fields, as well. These new beams have many potential applications, such as in free-space optics, medical apparatus, remote sensing, and optical tweezers.     

Fourier array illuminators with 100% efficiency: Analytical Jones-matrix construction

Abstract

Fourier-type spot-array illuminators are designed for electromagnetic fields in the paraxial domain of diffractive optics. An analytical construction of the periodic, spatially variable Jones matrix is presented, which produces 100% conversion efficiency from an arbitrarily polarized incident plane wave into M × N=2 ^P × 2 ^Q (P and Q are integers) diffraction orders. Such perfect performance is not possible within the scalar theory of paraxial diffractive optics.     

Scattering from a cylindrical reflector: modified theory of physical optics solution

The problem of scattering from a perfectly conducting cylindrical reflector is examined with the method of the modified theory of physical optics. In this technique the physical optics currents are modified by using a variable unit vector on the scatterer's surface. These current components are obtained for the reflector, which is fed by an offset electric line source. The scattering integral is expressed by using these currents and evaluated asymptotically with the stationary phase method. The results are compared numerically by using physical optics theory, geometrical optics diffraction theory, and the exact solution of the Helmholtz equation. It is found that the modified theory of physical optics scattering field equations agrees with the geometrical optics diffraction theory and the exact solution of the Helmholtz equation.     

General method to design spherically symmetric GRIN axicons

Abstract

A general method is presented for designing spherically symmetric gradient-index axicons, which produce a variety of different intensity patterns along the axis, and with a boundary index larger than or equal to the index of the surrounding medium. As the design method is based on geometrical optics, tools to analyse the axicon using wave optics are given.     

Drop Calorimetry Studies on 9Cr–1W–0.23V–0.06Ta–0.09C Reduced Activation Steel

The temperature dependence of enthalpy increment (H _T − H ₂₉₈) of 9 mass% Cr–1 mass% W–0.23 mass% V–0.06 mass% Ta–0.09 mass% C reduced activation steel has been measured by inverse drop calorimetry in the temperature range 400 K to 1273 K. A critical comparison of present isothermal enthalpy measurements with the results of our previous dynamic calorimetry studies has been made to reveal clearly the occurrence of various diffusional phase transformations that occur at high temperature. These phase changes are marked by the presence of distinct inflections or cusps in an overall nonlinear variation of enthalpy values with temperature. The principal thermal relaxation step of the martensitic microstructure obtained through quenching from the high-temperature γ-austenite phase is observed around 793 K. The ferromagnetic-to-paramagnetic transition of the α-ferrite phase is found to occur at 1015 K. The equilibrium values of γ-austenite start (Ae ₁) and finish (Ae ₃) temperatures are found to be 1063 K and 1148 K, respectively. A value of 12 J · g⁻¹ has been estimated for Δ°H ^α→γ the latent heat associated with the α → γ transformation. The measured enthalpy increment variation of the α-ferrite phase with temperature has been fitted to a suitable empirical function to estimate the temperature-dependent values of the specific heat. A comparison of the drop calorimetry-based indirect estimate of the specific heat with the direct differential scanning calorimetry-based values revealed that the drop calorimetry estimates are systematically lower than its dynamic calorimetry counterpart. This difference is attributed to the fact that, under finite heating rate conditions that are typical of dynamic calorimetry, measurements are made under nonequilibrium conditions. Notwithstanding this limitation, there is a good overall agreement between the two C _p values and also among the phase transformation temperatures so that a reliable assessment of thermal properties and phase transformation characteristics of reduced activation steel can be determined by a combined analysis of the results of drop and differential scanning calorimetry.     

The Effect of Parameter Estimation on Upper‐sided Bernoulli Cumulative Sum Charts

The Bernoulli cumulative sum (CUSUM) chart has been shown to be effective for monitoring the rate of nonconforming items in high‐quality processes where the in‐control proportion of nonconforming items (p₀) is low. The implementation of the Bernoulli CUSUM chart is often based on the assumption that the in‐control value p₀ is known; therefore, when p₀ is unknown, accurate estimation is necessary. We recommend using a Bayes estimator to estimate the value of p₀ to incorporate practitioner knowledge and to avoid estimation issues when no nonconforming items are observed in phase I. We also investigate the effects of parameter estimation in phase I on the upper‐sided Bernoulli CUSUM chart by using the expected value of the average number of observations to signal (ANOS) and the standard deviation of the ANOS. It is found that the effects of parameter estimation on the Bernoulli CUSUM chart are more significant than those on the Shewhart‐type geometric chart. The low p₀ values inherent to high‐quality processes imply that a very large, and often unrealistic, sample size may be needed to accurately estimate p₀. A methodology to identify a continuous variable to monitor is highly recommended when the value of p₀ is low and the required phase I sample size is impractically large. Copyright © 2012 John Wiley & Sons, Ltd.     

Two-phase approach to GT cell formation using efficient p-median formulations

The purpose of this paper is to develop an efficient p-median approach applicable to large cell formation (CF) problems. A two-phase methodology that seeks to minimize the number of exceptional elements is proposed. In phase I, two efficient p-median formulations which contain fewer binary variables than existing p-median formulations are constructed. For a CF problem with m machines existing p-median formulations contains m² or more binary variables, whereas the new formulation proposed in phase I contains not more than 5m binary variables at the expense of a slightly increased number of continuous variables and constraints for practical values of p less than 32. This makes it possible to implement large CF problem within reasonable computer runtime with commercially available linear integer programming codes. Given the initial cell configuration found with the new p-median formulation, in phase II bottleneck machines and parts are reassigned to reduce the number of exceptional elements. This procedure has the flexibility of providing the cell designer with alternative solutions. Test results on large CF problems show a substantial increase in the efficiency of the new p-median formulations compared with existing p-median formulations.     

Imaging of voids by means of a physical-optics-based shape-reconstruction algorithm

We analyze the performance of a shape-reconstruction algorithm for the retrieval of voids starting from the electromagnetic scattered field. Such an algorithm exploits the physical optics (PO) approximation to obtain a linear unknown-data relationship and performs inversions by means of the singular-value-decomposition approach. In the case of voids, in addition to a geometrical optics reflection, the presence of the lateral wave phenomenon must be considered. We analyze the effect of the presence of lateral waves on the reconstructions. For the sake of shape reconstruction, we can regard the PO algorithm as one of assuming the electric and magnetic field on the illuminated side as constant in amplitude and linear in phase, as far as the dependence on the frequency is concerned. Therefore we analyze how much the lateral wave phenomenon impairs such an assumption, and we show inversions for both one single and two circular voids, for different values of the background permittivity.     

Robust design method for highly efficient beam-shaping diffractive optical elements using an iterative-Fourier-transform algorithm with soft operations

Abstract

Beam-shaping diffractive optical elements give a desired intensity distribution in the diffraction plane over areas much larger than the diffraction limited spot size. Such elements can be designed using geometrical optics methods or iterative-Fourier-transform algorithms (IFTAs). The usefulness of geometrical optics methods is considerably limited for two reasons: first the number of cases for which a solution exists is small and second the design solution, if it exists, often does not work in practice. Then IFTAs can be used. They are applicable for any desired intensity distribution in the diffraction plane with any intensity cross-section of the incident beam. The IFTA presented in this paper uses a novel set of operations that introduce a minimum disturbance of the fields while still leading to an improved performance. This makes the method robust, insensitive to stagnation and capable of iteratively distributing an increasing portion of the light in the diffraction plane into the desired areas thus leading to a high efficiency (～95%). Three design examples are given and one is also tested experimentally.     

On spherical X-ray wave focusing upon backscattering from a parabolic cylinder crystal

The focusing of a spherical X-ray wave upon the Bragg backscattering from a crystal uniaxially bent to form a parabolic cylinder is theoretically studied. Based on geometrical optics, an analytical formula for the size of the crystal surface area involved in the diffraction reflection in the backscattering mode is derived. The analytical expression for the wave intensity distribution at the focus is analyzed and compared to that obtained previously.     

MEASUREMENT OF THE SPECIFIC SURFACE AREA OF POWDERS BY THIN LAYER WICKING

ABSTRACT

The specific surface areas (A) of different clay mineral powders were measured by both the BET method and by thin layer wicking. The values of A for the BET and the wicking experiments coincided within a few percent. Thus, the simple and inexpensive thin layer wicking approach may well suffice to obtain reliable specific surface area values for most powders. From the wicking data it is also possible to obtain a rough estimate of the average particle size.     

Anisotropy of acousto–optic figure of merit in lithium tetraborate crystals

We analyse anisotropy of acousto–optic figure of merit (AOFM) for Li₂B₄O₇ crystals in order to estimate the prospects of these crystals in acousto–optics. We find that the maximal AOFM, 3.44 × 10^?15 s³/kg, is peculiar for the isotropic acousto–optic interaction of the incident ordinary optical wave with the quasi-longitudinal acoustic wave. For the case of anisotropic diffraction in Li₂B₄O₇, the maximum 1.87 × 10^?15 s³/kg can be reached using the interaction of the extraordinary optical wave with the quasi-longitudinal acoustic wave. The case of collinear diffraction is characterized by small AOFMs, with the largest value 0.26 × 10^?15 s³/kg.     

Evolution of diffraction and self-diffraction phenomena in thin films of Gelite Bloom/Hibiscus Sabdariffa

In this work, we present a study of non-linear optical response in thin films elaborated with Gelite Bloom and extract of Hibiscus Sabdariffa. Non-linear refraction and absorption effects were studied experimentally (Z-scan technique) and numerically, by considering the transmittance as non-linear absorption and refraction contribution. We observe large phase shifts to far field, and diffraction due to self-phase modulation of the sample. Diffraction and self-diffraction effects were observed as time function. The aim of studying non-linear optical properties in thin films is to eliminate thermal vortex effects that occur in liquids. This is desirable in applications such as non-linear phase contrast, optical limiting, optics switches, etc. Finally, we find good agreement between experimental and theoretical results.     

Optical collection efficiency function in single-molecule detection experiments

The optical collection efficiency function for an optical system such as that used in single-molecule detection experiments is studied. Closed analytical expressions based on a geometrical optics approximation are presented. Comparison is made with exact wave optics calculations.