Diffractive element design for resonant scanner angular correction

We propose an optical corrective element with zooming capability to convert nonlinear sinusoidal scanning into linear scanning. Such a device will be useful for linearizing the angular scan of a resonant mirror scanner. The design methodology is to create a graded index of refraction device as the reference design, with its index of refraction parameters based on the propagation of an electromagnetic field in inhomogeneous media. The algorithm for converting this refractive element to the corresponding binary diffractive version is also presented. Design and simulation data are shown.     

Diffractive phase elements for beam shaping: a new design method

A design method based on the Yang-Gu algorithm [Appl. Opt. 33, 209 (1994)] is proposed for computing the phase distributions of an optical system composed of diffractive phase elements that achieve beam shaping with a high transfer efficiency in energy. Simulation computations are detailed for rotationally symmetric beam shaping in which a laser beam with a radially symmetric Gaussian intensity distribution is converted into a uniform beam with a circular region of support. To present a comparison of the efficiency and the performance of the designed diffractive phase elements by use of the geometrical transformation technique, the Gerchberg-Saxton algorithm and the Yang-Gu algorithm for beam shaping, we carry out in detail simulation calculations for a specific one-dimensional beam-shaping example.     

Diffractive variable beam splitter: optimal design

The analytical expression of the phase profile of the optimum diffractive beam splitter with an arbitrary power ratio between the two output beams is derived. The phase function is obtained by an analytical optimization procedure such that the diffraction efficiency of the resulting optical element is the highest for an actual device. Comparisons are presented with the efficiency of a diffractive beam splitter specified by a sawtooth phase function and with the pertinent theoretical upper bound for this type of element.     

Diffractive optical element design with memory-matrix-based identification methodology

We present a new technique for the design of diffractive optical elements (DOE's) that is based on previous nonlinear least squares (NLS) and phase-shifting quantization methods [Appl. Opt. 36, 7297-7306 (1997)]. The technique uses a memory-matrix-based identification (MMBI) optimization procedure. We compare results from the MMBI method with those from iterative Fourier transform and NLS methods. In comparison, the MMBI DOE designs produce better-quality reconstructions for DOE's with eight or more fabrication phase levels and generally have a higher signal-to-noise ratio and better uniformity.     

Phase-aberration correction with a 3-D ultrasound scanner: feasibility study

We tested the feasibility of using adaptive imaging, namely phase-aberration correction, with two-dimensional (2-D) arrays and real-time, 3-D ultrasound. Because of the high spatial frequency content of aberrators, 2-D arrays, which generally have smaller pitch and thus higher spatial sampling frequency, and 3-D imaging show potential to improve the performance of adaptive imaging. Phase-correction algorithms improve image quality by compensating for tissue-induced errors in beamforming. Using the illustrative example of transcranial ultrasound, we have evaluated our ability to perform adaptive imaging with a real-time, 3-D scanner. We have used a polymer casting of a human temporal bone, root-mean-square (RMS) phase variation of 45.0 ns, full-width-half-maximum (FWHM) correlation length of 3.35 mm, and an electronic aberrator, 100 ns RMS, 3.76 mm correlation, with tissue phantoms as illustrative examples of near-field, phase-screen aberrators. Using the multilag, least-squares, cross-correlation method, we have shown the ability of 3-D adaptive imaging to increase anechoic cyst identification, image brightness, contrast-to-speckle ratio (CSR), and, in 3-D color Doppler experiments, the ability to visualize flow. For a physical aberrator skull casting we saw CSR increase by 13% from 1.01 to 1.14, while the number of detectable cysts increased from 4.3 to 7.7.     

Optimal design of a beam stop for Indus-2 using finite element heat transfer studies

This paper describes the design of an in-vacuum, water-cooled beam stop (X-ray shutter) for the materials science (X-ray diffraction) beamline proposed to be built on the wavelength shifter in the Indus-2 (2.5 GeV) synchrotron radiation source. The radiation source impinges ∼ 1 kW power on the beam stop and the heat transfer capabilities of the beam stop have been evaluated. Temperature distribution in the beam stop has been obtained under various cooling conditions using the finite element analysis calculations with ANSYS software. Design parameters of the beam stop have been optimised. It is also shown that radiation cooling alone is not sufficient for taking away the heat load. Water-cooling of the beam stop is essential.     

Diffractive optical elements for beam shaping of monochromatic spatially incoherent light

Fresnel-type diffractive optical elements (DOEs) for general beam shaping of monochromatic, spatially incoherent light are demonstrated. Direct and indirect methods, i.e., adding a lens' phase to the designed Fraunhofer-type DOEs, are used for the design. The indirect method can reduce the calculation time by approximately half without loss of design accuracy. Two different design examples are shown. For one design the direct method gives a maximum sidelobe intensity of 5.0% of the maximum intensity in the signal window. For the second design the indirect method gives 23.0% of this value. The generated patterns can maintain their basic shapes over a long distance. The elements have been fabricated by directly using gray-scale commercial slides as masks. Experimental results are in close agreement with numerical predictions.     

Development of a HTS magnet and application to a beam scanner

A solenoid magnet using high-temperature superconductor tape was designed, fabricated, and tested for its suitability as beam scanner. After successful cooling tests, the magnet performance was studied using DC and AC currents. With DC current the magnet was successfully operated as mirror coils for a 2.45 GHz ECR ion source. The coils could be operated at 100 A and frequencies above 1 Hz. The installation of iron pole pieces and return yokes, enabled us to generate fields in excess of 2 T at 197 A DC. In AC mode this magnet can be operated in the ranges of 0.14–1.73 and 1.22–1.67 T at frequencies of 0.05 and 0.25 Hz, respectively.     

Finite element simulation of internal flows with heat transfer using a velocity correction approach

This paper enumerates finite-element based prediction of internal flow problems, with heat transfer. The present numerical simulations employ a velocity correction algorithm, with a Galerkin weighted residual formulation. Two problems each in laminar and turbulent flow regimes are investigated, by solving full Navier-Stokes equations. Flow over a backward-facing step is studied with extensive validations. The robustness of the algorithm is demonstrated by solving a very complex problem viz. a disk and doughnut baffled heat exchanger, which has several obstructions in its flow path. The effect of wall conductivity in turbulent heat transfer is also studied by performing a conjugate analysis. Temporal evolution of flow in a channel due to circular, square and elliptic obstructions is investigated, to simulate the vortex dynamics. Flow past an in-line tube bank of a heat exchanger shell is numerically studied. Resulting heat and fluid flow patterns are analysed. Important design parameters of interest such as the Nusselt number, Strouhal number, skin friction coefficient, pressure drop etc. are obtained. It is successfully demonstrated that the velocity correction approach with a Galerkin weighted residual formulation is able to effectively simulate a wide range of fluid flow features.     

A microprocessor controlled on-line beam profile scanner for polarized beams

A beam profile scanner system for measuring the distribution of polarization and intensity is described. The thickness of a special scatterer can be adjusted easily, so that it does not disturb the actual measurement. The scatterer is moved through through the beam at a given speed. Whenever a scattered event of interest occurs, the system records its location. In this way the intensity and polarization distribution spectra are obtained. The deceleration and acceleration at the turning points of the motion are carefully programmed so as to minimize wear of the mechanical components.     

A modified extended finite element method approach for design sensitivity analysis

This paper describes a modified extended finite element method (XFEM) approach, which is designed to ease the challenge of an analytical design sensitivity analysis in the framework of structural optimisation. This novel formulation, furthermore labelled YFEM, combines the well‐known XFEM enhancement functions with a local sub‐meshing strategy using standard finite elements. It deviates slightly from the XFEM path only at one significant point but thus allows to use already derived residual vectors as well as stiffness and pseudo load matrices to assemble the desired information on cut elements without tedious and error‐prone re‐work of already performed derivations and implementations. The strategy is applied to sensitivity analysis of interface problems combining areas with different linear elastic material properties. Copyright © 2015 John Wiley & Sons, Ltd.     

Polarization distribution in a Gaussian beam reflected from a resonant medium

It is shown that the distribution of parameters of light polarization in the cross section of a Gaussian beam reflected from a resonant medium is substantially inhomogeneous. This inhomogeneity is especially pronounced in the wavelength range of light absorption by metals.     

Unstable resonator modes: a beam expansion approach

A novel method of computing the modes of unstable resonators is presented. By writing the modes as a series expansion in a set of orthogonal functions, the problem is reduced to finding how the expansion coefficients change in a circuit of the resonator. The eigenvalues of the transfer matrix are shown to be the mode eigenvalues, while the eigenvectors are the expansion coefficients defining the mode in question. The technique is demonstrated in one transverse dimension using Hermite–Gaussian functions as the basis. The approach offers significant advantages over other methods.     

Automatic 3-D crack propagation calculations: a pure hexahedral element approach versus a combined element approach

This article presents an evaluation of two different crack prediction approaches based on a comparison of the stress intensity factor distribution for three example problems. A single edge notch specimen and a quarter circular corner crack specimen subjected to shear displacements and a three point bend specimen with a crack inclined to the mid-plane are examined. The stress intensity factors are determined from the singular stress field close to the crack front. Two different fracture criteria are adopted for the calculation of an equivalent stress intensity factor and crack deflection angle. The stress intensity factor distributions for both numerical methods agree well to available reference solutions. Deviations are recorded at crack front locations near the free surface probably due to global contraction effects and the twisting behaviour of the crack front. Crack propagation calculations for the three point bending specimen give results that satisfy intuitive expectations. The outcome of the study encourages further pursuit of a crack propagation tool based on a combination of elements.     

Rudiments of the design of an immersed polarizing beam divider with a narrow spectral bandwidth and enhanced angular acceptance

A MacNeille type of linear polarizer is designed at a spectral band of +/-20 nm centered at 633 nm. The acceptance angle is +/-10 degrees in the BK-7 glass, or +/-15 degrees in air.     

A new approach for displacement functions of a curved Timoshenko beam element in motions normal to its initial plane

In existing literature, either analytical methods or numerical methods, the formulations for free vibration analysis of circularly curved beams normal to its initial plane are somewhat complicated, particularly if the effects of both shear deformation (SD) and rotary inertia (RI) are considered. It is hoped that the simple approach presented in this paper may improve the above‐mentioned drawback of the existing techniques. First, the three functions for axial (or normal to plane) displacement and rotational angles about radial and circumferential (or tangential) axes of a curved beam element were assumed. Since each function consists of six integration constants, one has 18 unknown constants for the three assumed displacement functions. Next, from the last three displacement functions, the three force–displacement differential equations and the three static equilibrium equations for the arc element, one obtained three polynomial expressions. Equating to zero the coefficients of the terms in each of the last three expressions, respectively, one obtained 17 simultaneous equations as functions of the 18 unknown constants. Excluding the five dependent ones among the last 17 equations, one obtained 12 independent simultaneous equations. Solving the last 12 independent equations, one obtained a unique solution in terms of six unknown constants. Finally, imposing the six boundary conditions at the two ends of an arc element, one determined the last six unknown constants and completely defined the three displacement functions. By means of the last displacement functions, one may calculate the shape functions, stiffness matrix, mass matrix and external loading vector for each arc element and then perform the free and forced vibration analyses of the entire curved beam. Good agreement between the results of this paper and those of the existing literature confirms the reliability of the presented theory. Copyright © 2005 John Wiley & Sons, Ltd.     

Rational design of a diffractive homogenizer for a laser beam

The problem of designing a diffractive optical element (DOE) that produces a uniform-intensity beam from a spatially variable source is considered. Under the thin-lens approximation, the DOE is fully characterized by a phase function. Fresnel approximation is used to simplify the relationship between the input amplitude, the phase function, and the image intensity. The case where the light source has partial coherence is considered. A simple design procedure based on a lenslet array is proposed. It is shown that under certain physical assumptions, this `engineering' solution leads to an effective design capable of producing a uniform intensity from a time-varying, non-uniform source.     

LCC resonant converter with power factor correction for power supply units

This article presents a power supply using an LCC resonant converter having power factor correction with burst mode operation. In order to improve the performance from no load to full load, a microcontroller with an active control has been introduced. The light load efficiency is increased using burst mode operation. The proposed controller provides zero voltage switching. Mathematical analysis is done, and steady state characteristics are drawn. A simple design example is given based on the equations. The proposed converter has good efficiency with good power factor at all loading conditions. This is shown by the simulation and experimental results obtained through testing the prototype.