Approximate analytical optical transfer function for a wavefront-coded imaging system with two-dimensional rectangularly separable phase masks

Wavefront coding can be used to extend the depth of field of incoherent imaging systems and is a powerful system-level technique. In order to assess the performance of a wavefront-coded imaging system, defocused optical transfer function (OTF) is the metric frequently used. Unfortunately, to the best of our knowledge, among all types of phase masks, it is usually difficult to obtain the analytical OTF except the cubic one. Although numerical computation seems good enough for performance evaluation, the approximate analytical OTF is still indispensable because it can reflect the relationship between mask parameters and system frequency response in a clearer way. Thus, a method is proposed to derive the approximate analytical OTF for two-dimensional rectangularly separable phase masks. The analytical results are well consistent with the direct numerical computations, but the proposed method can be accepted only from engineering point of view and needs rigorous proof in future. (c) 2010 Society of Photo-Optical Instrumentation Engineers. [DOI: 10.1117/1.3485759]

Analytical method of predicating the instabilities of a micro arch-shaped beam under electrostatic loading

An arch-shaped beam with different configurations under electrostatic loading experiences either the direct pull-in instability or the snap-through first and then the pull-in instability. When the pull-in instability occurs, the system collides with the electrode and adheres to it, which usually causes the system failure. When the snap-through instability occurs, the system experiences a discontinuous displacement to flip over without colliding with the electrode. The snap-through instability is an ideal actuation mechanism because of the following reasons: (1) after snap-through the system regains the stability and capability of withstanding further loading; (2) the system flips back when the loading is reduced, i.e. the system can be used repetitively; and (3) when approaching snap-through instability the system effective stiffness reduces toward zero, which leads to a fast flipping-over response. To differentiate these two types of instability responses for an arch-shaped beam is vital for the actuator design. For an arch-shaped beam under electrostatic loading, the nonlinear terms of the mid-plane stretching and the electrostatic loading make the analytical solution extremely difficult if not impossible and the related numerical solution is rather complex. Using the one mode expansion approximation and the truncation of the higher-order terms of the Taylor series, we present an analytical solution here. However, the one mode approximation and the truncation error of the Taylor series can cause serious error in the solution. Therefore, an error-compensating mechanism is also proposed. The analytical results are compared with both the experimental data and the numerical multi-mode analysis. The analytical method presented here offers a simple yet efficient solution approach by retaining good accuracy to analyze the instability of an arch-shaped beam under electrostatic loading.

Analytical solution of a multidimensional Langevin equation at high friction limits and probability passing over a two-dimensional saddle

The analytical solution of a multidimensional Langevin equation at the overdamping limit is obtained and the probability of particles passing over a two-dimensional saddle point is discussed. These results may break a path for studying further the fusion in superheavy elements synthesis.

低β四分之一波长腔中的束流偏转的分析性研究(英文)；Analytical Study on Beam Steering in Low-β Superconducting Quarter Wave Resonators

目前加速速度范围在0.01c—0.3c的粒子的超导腔主要使用四分之一波长腔型。用于不同加速器上的频率范围在50—240MHz的四分之一波长腔在建造或者预研中。这种腔型的一个不足是其横向电磁成分会造成束流偏转效应,从而导致发射度的增长和束流的溢漏,在强流重离子加速器中这种效应尤为严重。对中国科学院近代物理研究所超导直线加速器中的频率为80.5和161MHz的四分之一波长腔的偏转效应进行了分析,计算结果表明,在四分之一腔体的设计时需要考虑到束流偏转的修正,这通常需要在漂移管端面上削适当大小的倾角来实现。

Analytical potential energy function and spectroscopic parameters for the ground and excited states of NaH

set of energies at different internuclear distances for the ground electronic state and two excited electronic states of NaH molecule have been calculated using valence internally contracted multireference configuration interaction(MRCI) including Davidson correction and three basis sets. Then, a potential energy curve (PEC) for each state was determined by extrapolating MRCI energies to the complete basis sets limit. Based on the PECs, accurate vibrational energy levels and rotational constants were determined. The computational PECs are were fitted to analytical potential energy functions using the Murrell-Sorbie potential function. Then, accurate spectroscopic parameters were calculated. Compared with experimental results, values obtained with the basis set extrapolation yield a potential energy curve that gives accurate vibrational energy levels, rotational constants and spectroscopic parameters for the NaH molecule. (C) 2004 Elsevier B.V. All rights reserved.

Theoretical study on analytical potential function and spectroscopic parameters for CaF molecule

The equilibrium properties and potential energy curves of the ground electronic state of CaF have been calculated using the Brueckner Doubles calculation with a triples contribution added [BD(T)] and the gradient-corrected density functional theory with three-parameter exact exchange mixing (B3LY-P) method, with 6-311 + G*,6-311 + G(2df,2pd) and 6-311 + G(3df,3pd) basis sets. All the computational PECs are fitted to analytical potential energy functions using Murrell-Sorbie, Huxley and Tang-Toennies potentials. Based on this, the spectroscopic parameters are calculated, and then compared with some other theoretical and experimental data. (C) 2004 Elsevier B.V. All rights reserved.

Article: Overview of Analytical Methodologies for Sea Water Analysis: Part I-Metals

A comprehensive, critical and up-to-date review of analytical methods developed during the last decade for metals present in sea water is presented. Separate sections are devoted to singular and multimetal determinations. Furthermore, a critical comparison of relative merits or demerits of a particular procedure is made in terms of sensitivity, selectivity and precision. Various aspects of analysis of sea water samples for metals are summarized, and the future trends are discussed.

Analytical intercomparison results from the 1990 Intergovernmental Oceanographic Commission open-ocean baseline survey for trace metals: Atlantic Ocean

“Dissolved” (< 0.4 μm filtered) and “total dissolvable” (unfiltered) trace element samples were collected using “clean” sampling techniques from four vertical profiles in the eastern Atlantic Ocean on the first IOC Trace Metals Baseline expedition. The analytical results obtained by 9 participating laboratories for Mn, Fe, Co, Ni, Cu, Zn, Cd, Pb, and Se on samples from station 4 in the northeast Atlantic have been evaluated with respect to accuracy and precision (intercomparability). The data variability among the reporting laboratories was expressed as 2 × SD for a given element and depth, and was comparable to the 95% confidence interval reported for the NASS seawater reference standards (representing analytical variability only). The discrepancies between reporting laboratories appear to be due to inaccuracies in standardization (analytical calibration), blank correction, and/or extraction efficiency corrections.Several of the sampling bottles used at this station were not adequately pre-cleaned (anomalous Pb results). The sample filtration process did not appear to have been a source of contamination for either dissolved or particulate trace elements. The trace metal profiles agree in general with previously reported profiles from the Atlantic Ocean. We conclude that the sampling and analytical methods we have employed for this effort, while still in need of improvement, are sufficient for obtaining accurate concentration data on most trace metals in the major water masses of the oceans, and to enable some evaluation of the biogeochemical cycling of the metals.

The application of microwave radiation to analytical and environment chemistry

This review presents the latest advances in the application of microwave energy to analytical chemistry. The fundamental principles of microwave field interaction with the matter are presented and their significance for the chemist is discussed, followed by the basic principles of microwave equipment construction and operation. Examples of the techniques that utilized microwave energy for digestion, extraction, chemical reaction, preconcentration, and desorption of the analytical sample are presented. A separate section describes the examples of usage of microwave technology in catalysis, environmental, and nuclear chemistry and engineering.