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.

Roles of sorting and chemical weathering in the geochemistry and magnetic susceptibility of Xiashu loess；East China

IEECAS SKLLQG

Environmental geochemistry and health of fluorine in Chinese coals

IEECAS SKLLQG

Geochemistry of rare earth elements in Permian coals from the Huaibei Coalfield；China

IEECAS SKLLQG

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.