Phase Properties of a Strong Field Interacting with Many Atoms with and Without Initial Atomic Coherences

Abstract

The phase distributions of an initially strong, coherent, single-mode field interacting with one, two, three and four identical atoms with and without initial atomic coherences using the Pegg-Barnett Hermitian phase operator formalism have been examined. A number of interesting features of the phase distributions are revealed. A link between the coincidences of the peaks in the phase probability distribution and the revivals in the two-atom case is also shown.     

Heuristic analysis of closed queueing networks

In this paper we consider closed queueing networks having M single server queueing stations with arbitrary interconnections and general service time distributions. Here we propose an iterative approximation procedure, based on a decomposition approximation. Numerical results are reported to demonstrate the accuracy of the method. We also discuss the sensitivity of the results to the initial guess for the server utilizations.     

Kinetics of growth of γ′- precipitates in Ni–6·75AI alloy

Abstract

The size distributions of γ precipitates in a Ni-based alloy containing 6·75 wt–% aluminium have been measured, using dark-field electron microscopy, at five temperatures ranging from 600 to 825°C and the corresponding volume fractions have been assessed. From these distributions, the average particle sizes were obtained and plotted against time according to the kinetics laws proposed by theory for diffusion–controlled growth, interface-controlled growth, and growth in the transition region where neither process dominates. The particle-size distributions were reconstructed in terms of the ratio of the actual particle size/average size, and the resulting distributions were compared with those predicted by theory for the three controlling conditions. Although the values of activation energy obtained from the plots of particle size against annealing time are equally consistent for the three processes, the agreement between the predicted distributions and the experimental distribution is distinctly better for growth in the transition region than for the two alternative processes.

MST/167     

Optimally Generalized Regularization Methods for Solving Linear Inverse Problems

In order to solve ill-posed linear inverse problems, we modify the Tikhonov regularization method by proposing three different preconditioners, such that the resultant linear systems are equivalent to the original one, without dropping out the regularized term on the right-hand side. As a consequence, the new regularization methods can retain both the regularization effect and the accuracy of solution. The preconditioned coefficient matrix is arranged to be equilibrated or diagonally dominated to derive the optimal scales in the introduced preconditioning matrix. Then we apply the iterative scheme to find the solution of ill-posed linear inverse problem. Two theorems are proved that the iterative sequences are monotonically convergent to the true solution. The presently proposed optimally generalized regularization methods are able to overcome the ill-posedness of linear inverse problems, and provide rather accurate numerical solution.     

An application of an expert system in layout compaction of VLSI design

Abstract

Recent research in knowledge‐based expert systems of VLSI design tools has concentrated on placement, routing, and cell generation. This paper presents an alternative application for artificial intelligence (AI) techniques on compaction design for a VLSI mask layout‐expert compactor. In order to overcome the shortcomings of iterative search through a large problem space within a working memory, and therefore, to speed‐up the runtime of compaction, a set of rule‐based region query operations and knowledge‐based techniques for the plane sweep method are proposed in this system. Experimental results have explored the possibility of using expert system technology (EST) to automate the compaction process by “reasoning” out the layout design and applying sophisticated expert rules to its knowledge base.     

On the Synthesis of a Single Offset Reflector with Dielectric Cone Feed

Abstract

The synthesis of a shaped single offset reflector with dielectric cone feed is studied theoretically under geometric-optics assumptions using the method of complex coordinates to track ray directions and polarizations. Reflection losses are included in the theory presented. The problem of shaping the reflector and dielectric surfaces to control aperture power and phase distributions is shown to require the solution of a Monge-Ampère equation for which numerical techniques are available.     

Influence of Non-uniform Amplitude on PSF

Abstract

The effects of the following three different non-uniform real amplitude distributions on the PSF are investigated: polynomial distribution; a Gaussian distribution; and the distribution that occurs when there is a central obstruction.     

Beam reflection from multilayers with periodic and fractal distributions

Abstract

An impedance model is used to solve the reflection problem from a multilayer with periodic and Cantor bar fractal distributions. It is based on the calculation of the input surface impedance of such a structure. The method consists of replacing the multilayer reflection problem by a simple reflection problem on a single surface. This approach has the additional advantage that only the fields above the surface should be taken into account. Numerical calculation leads to an iterative method which can be implemented for each polarization mode. The results for the input impedance function of the system and for the reflectance are presented for different iteration states. Also to quantify the comparison between both types of structures we introduce a self-similarity function which correlates orders or states of the same type.     

LASER LIGHT SCATTERING AS A METHOD OF DETECTING AND SIZING PARTICULATES ON SMOOTH PLANAR SURFACES

ABSTRACT

Currently available techniques for particulate detection on smooth planar surfaces using laser light scattering are discussed. A comparison of the response of these instruments using spherical and aspherical latex spheres on silicon wafers is presented. Actual measurement data for wafers with known particle size distributions will be used to illustrate the instrument response.

A first order model of the effects of substrate reflectivity on the measurement is developed. This model is verified with experimental data on silicon surfaces and oxide films.     

Interactive direct illumination in dynamic scenes using graphics APIS

Abstract

We present a progressive refinement system for rendering direct illumination at interactive rates for dynamic scenes using available graphics APIs. We achieve the progression by subdividing object surfaces using a quad‐tree approach. Integrating the visibility and illumination, we can render scenes with soft shadows, taking into account the BRDFs of the scene objects. Our system allows a user to specify the desired frame rates, and the system will achieve such rates with the available time budget. Our system can also render dynamic scenes where the system restores the initial meshes and calculates illumination, producing finer but accurate soft shadows during iterative refinements.     

Image SR-based NLM and DCNN improved IBP with cubic B-spline

ABSTRACT

Image super-resolution (SR) techniques aim to estimate high-resolution (HR) image from low-resolution (LR) image. Existing SR method has slow convergence and recovery of high-frequency details are inaccurate. To overcome these issues, two algorithms have been proposed for image SR based on non-local means improved iterative back projection (NLM-IIBP), deep convolutional neural network improved iterative back projection (DCNN-IIBP) to produce high-resolution images with low noise, minimal blur by restoring high-frequency details. In NLM-IIBP denoised images have been interpolated using cubic B-spline interpolation and processed using IIBP based on guided bilateral method. NLM preserves the edges effectively, but does not consider high dimensional information and over smoothing during noise minimization. To further improve the resolution, NLM is replaced by DCNN. DCNN denoising method suppresses different noises at different noise levels. The proposed algorithms have been analysed and compared with existing approaches using various parameters to prove the effectiveness.     

Wavelength Dependence of Optical Bistability in Molecular-beam-deposited ZnSe Interference Filters

Abstract

Complete ZnSe interference filters exhibiting optical bistability have been fabricated using ultrahigh-vacuum molecular-beam techniques. The wavelength dependence of the critical switching power was measured at five wavelengths between 521 and 676 nm for a filter with two-period ZnSe/BaF₂ multilayer reflectors and an initial assessment has been made of their long-term operational stability.     

Initial water impact of a wedge at vertical and oblique angles

This paper examines initial asymmetric wedge-impact flows with horizontal as well as vertical impact velocity. The method of two-dimensional vortex distributions is employed to model the initial-boundary-value problem. The numerical analysis involves discretization of the body surface and an iterative solution technique. Experimental drop tests of a prismatic wedge were performed to gain understanding and provide data for comparison of initial water impact when asymmetry and horizontal impact velocity are present. The experimental investigation of initial flow separation off the wedge vertex (i.e., keel) during impact is described. Initial separation-ventilation of the flow from the vertex due to asymmetric impact or horizontal-vertical impact velocity is examined in relation to the present theory. Agreement between the data and the numerical predictions was demonstrated for small degrees of asymmetry and small ratios of horizontal to vertical impact velocity. The initial flow detachment from the vertex also revealed interesting hydrodynamic characteristics.     

The vectorization of ITPACK 2C

ITPACK 2C¹⁴ is a package of seven iterative algorithms for solving sparse linear systems represented by Au = b, where A is symmetric and positive definite or mildly non-symmetric. This paper describes the techniques used to vectorize the iterative algorithms in the ITPACK 2C package for the Cyber 205 and Cray X-MP vector computers. The resulting package was named ITPACKV 2C.¹⁵ The basic iterative methods in ITPACK 2C are described in terms of matrix–vector multiplications and forward and backward solutions, and the techniques used in the vectorization of these and other computational kernels are given. Results of experiments using ITPACK 2C and ITPACKV 2C are given, including a comparison of megaflop rates and timings for two model problems.     

Comparison of Particle Size Distributions Measured Using Different Techniques

ABSTRACT

In this article, particle size distributions (PSDs) measured by different techniques, including image analysis (IA), laser diffraction (LD), ultrasonic attenuation spectroscopy (UAS), and focused-beam reflectance measurement (FBRM), are compared for spherical glass beads and nonspherical silica flakes. It is shown that particle shape strongly affects the results obtained by different techniques. For spheres, the PSDs obtained by IA, LD, and UAS agree well. There is no consistent result among different particle measurement techniques for nonspherical particles. The conversion between PSDs obtained by IA, LD, and UAS has been based on particle shape factors. Caution must be exercised when a measured chord length distribution (CLD) is used to indicate the PSD during a process because the CLD result obtained by FBRM is complex, depending not only on the PSD, but also on particle optical properties and shape.     

AN ITERATIVE SOLUTION SCHEME FOR SYSTEMS OF WEAKLY CONNECTED BOUNDARY ELEMENT EQUATIONS

In this paper an iterative scheme of first degree is developed for solving linear systems of equations. The systems investigated are those which are derived from boundary integral equations and are of the form ∑^N_j=1H_ijx_j=c_i, i=1, 2,…,N, where H_ij are matrices, x_j and c_i are column vectors. In addition, N denotes the number of domains and for i≠j, H_ij is considered to be small in some sense. These systems, denoted as weakly connected, are solved using first-order iterative techniques initially developed by the authors for solving single-domain problems. The techniques are extended to solve multi-domain problems. Novel solution strategies are investigated and procedures are developed which are computationally efficient. Computation times are determined for the iterative procedures and for elimination techniques indicating the benefits of iterative techniques over direct methods for problems of this nature.     

Theoretical and experimental properties of a binary linear beam-splitting element with a large fan angle

Abstract

Diffractive beam-splitting elements with a large fan angle of about 45° were realized as binary phase elements for application in a commercial laser device operating at the wavelength of 635 nm. The fan-out elements designated to split a laser beam into a line of 43 equal power spots were fabricated in silica by means of microstructuring techniques and replicated in acrylate by ultraviolet curing. Two different gratings have been designed using scalar unidirectional iterative methods, based on the iterative discrete on-axis and on the direct binary search algorithms. The optical properties of both gratings obtained by these scalar methods were compared with simulations based on rigorous electromagnetic calculations in order to verify and control the application-relevant specifications. The experimentally measured optical performance of the replicated fan-out elements is in good agreement with the theoretical predictions. The complete procedure for realizing the linear beam splitters, that is the design method, the fabrication of the master, and the replication process, will be presented. The optical properties and characteristic data of the replicas will be compared with scalar simulations as well as rigorous calculations; the results will be discussed.     

Characterization of 1D diffractive optical elements by phase inversion

Abstract

We consider the feature dimensions of selected 1D diffractive optical elements (DOE) such that the Fourier transform based Gerchberg-Saxton (GS) iterative scalar phase retrieval algorithm, as calibrated by the results of vector coupled-wave theory, may be used for phase reconstruction. We consider examples only of continuous surface relief and binary (two level, not multi-level) phase-only DOE. Experimental phase distribution for rectangular and blazed gratings with ～ 5λ period agree within experimental limits with scalar theory, and, for the rectangular grating, were shown to agree also with the vector theory. Phase distributions are considered for a continuously varying linear blazed grating with 10λ periodicity, its sampled binary equivalent with minimum feature sizes of 0.1λ and for continuous linear blazed gratings with period varied from ～ 16λ to ～ 2λ. The vector calculations show an average linear dependence of the phase on grating period, but the vector curves are displaced to lower values from the scalar results by an increasing amount as the grating period is reduced. Grating performance is more influenced by the size of the grating period than the subwavelength size of the features in a binary representation. Reasonable equivalence is found in the prediction of correct phase distributions between scalar and vector theory for grating periods > ～ 5λ.     

Non-iterative solution of finite-element equations in incompressible solids

Summary. Finite-element equations for incompressible and near-incompressible media give rise to a matrix with a diagonal block of zeroes or very small numbers. The matrices are not amenable to conventional techniques involving pivoting on diagonal entries. Uzawa methods have been applied to the associated linear systems. They are iterative and converge when the matrix is nonsingular. In the current study an alternate form of the matrix is used which is amenable to a solution without iteration. It likewise is applicable whenever the matrix is nonsingular. The solution process consists of a block LU factorization, followed by Cholesky decomposition of a positive definite diagonal block together with several forward and backward substitution operations. Two illustrative examples are developed.