Parallel plate interferometer with a reflecting mirror for measuring angular displacement

A parallel plate interferometer with a reflecting mirror for measuring angular displacement is proposed. A deflection angle of a beam caused by an angular displacement is amplified by use of a reflecting mirror to increase the optical path difference (OPD) in the plane-parallel plate, which provides high sensitivity of the phase measurement. Detection of light transmitted through the plane-parallel plate with a position sensitive detector (PSD) enables high accurate measurement of the initial angle of incidence to the plane-parallel plate with insensitivity to stray light. The improved parallel plate interferometer achieves a measurement repeatability of 10(-8) rad. (C) 2007 The Optical Society of Japan.

A multiple scattering problem

The present work deals with the problem of the interaction of the electromagnetic radiation with a statistical distribution of nonmagnetic dielectric particles immersed in an infinite homogeneous isotropic, non-magnetic medium. The wavelength of the incident radiation can be less, equal or greater than the linear dimension of a particle. The distance between any two particles is several wavelengths. A single particle in the absence of the others is assumed to scatter like a Rayleigh-Gans particle, i.e. interaction between the volume elements (self-interaction) is neglected. The interaction of the particles is taken into account (multiple scattering) and conditions are set up for the case of a lossless medium which guarantee that the multiple scattering contribution is more important than the self-interaction one. These conditions relate the wavelength λ and the linear dimensions of a particle a and of the region occupied by the particles D. It is found that for constant λ/a, D is proportional to λ and that |Δχ|, where Δχ is the difference in the dielectric susceptibilities between particle and medium, has to lie within a certain range.

The total scattering field is obtained as a series the several terms of which represent the corresponding multiple scattering orders. The first term is a single scattering term. The ensemble average of the total scattering intensity is then obtained as a series which does not involve terms due to products between terms of different orders. Thus the waves corresponding to different orders are independent and their Stokes parameters add.

The second and third order intensity terms are explicitly computed. The method used suggests a general approach for computing any order. It is found that in general the first order scattering intensity pattern (or phase function) peaks in the forward direction Θ = 0. The second order tends to smooth out the pattern giving a maximum in the Θ = π/2 direction and minima in the Θ = 0 , Θ = π directions. This ceases to be true if ka (where k = 2π/λ) becomes large (> 20). For large ka the forward direction is further enhanced. Similar features are expected from the higher orders even though the critical value of ka may increase with the order.

The first order polarization of the scattered wave is determined. The ensemble average of the Stokes parameters of the scattered wave is explicitly computed for the second order. A similar method can be applied for any order. It is found that the polarization of the scattered wave depends on the polarization of the incident wave. If the latter is elliptically polarized then the first order scattered wave is elliptically polarized, but in the Θ = π/2 direction is linearly polarized. If the incident wave is circularly polarized the first order scattered wave is elliptically polarized except for the directions Θ = π/2 (linearly polarized) and Θ = 0, π (circularly polarized). The handedness of the Θ = 0 wave is the same as that of the incident whereas the handedness of the Θ = π wave is opposite. If the incident wave is linearly polarized the first order scattered wave is also linearly polarized. The second order makes the total scattered wave to be elliptically polarized for any Θ no matter what the incident wave is. However, the handedness of the total scattered wave is not altered by the second order. Higher orders have similar effects as the second order.

If the medium is lossy the general approach employed for the lossless case is still valid. Only the algebra increases in complexity. It is found that the results of the lossless case are insensitive in the first order of k_imD where k_im = imaginary part of the wave vector k and D a linear characteristic dimension of the region occupied by the particles. Thus moderately extended regions and small losses make (k_imD)² ≪ 1 and the lossy character of the medium does not alter the results of the lossless case. In general the presence of the losses tends to reduce the forward scattering.

High frequency wave propagation in the earth: theory and observation

The wave-theoretical analysis of acoustic and elastic waves refracted by a spherical boundary across which both velocity and density increase abruptly and thence either increase or decrease continuously with depth is formulated in terms of the general problem of waves generated at a steady point source and scattered by a radially heterogeneous spherical body. A displacement potential representation is used for the elastic problem that results in high frequency decoupling of P-SV motion in a spherically symmetric, radially heterogeneous medium. Through the application of an earth-flattening transformation on the radial solution and the Watson transform on the sum over eigenfunctions, the solution to the spherical problem for high frequencies is expressed as a Weyl integral for the corresponding half-space problem in which the effect of boundary curvature maps into an effective positive velocity gradient. The results of both analytical and numerical evaluation of this integral can be summarized as follows for body waves in the crust and upper mantle:

1) In the special case of a critical velocity gradient (a gradient equal and opposite to the effective curvature gradient), the critically refracted wave reduces to the classical head wave for flat, homogeneous layers.

2) For gradients more negative than critical, the amplitude of the critically refracted wave decays more rapidly with distance than the classical head wave.

3) For positive, null, and gradients less negative than critical, the amplitude of the critically refracted wave decays less rapidly with distance than the classical head wave, and at sufficiently large distances, the refracted wave can be adequately described in terms of ray-theoretical diving waves. At intermediate distances from the critical point, the spectral amplitude of the refracted wave is scalloped due to multiple diving wave interference.

These theoretical results applied to published amplitude data for P-waves refracted by the major crustal and upper mantle horizons (the Pg, P*, and Pn travel-time branches) suggest that the 'granitic' upper crust, the 'basaltic' lower crust, and the mantle lid all have negative or near-critical velocity gradients in the tectonically active western United States. On the other hand, the corresponding horizons in the stable eastern United States appear to have null or slightly positive velocity gradients. The distribution of negative and positive velocity gradients correlates closely with high heat flow in tectonic regions and normal heat flow in stable regions. The velocity gradients inferred from the amplitude data are generally consistent with those inferred from ultrasonic measurements of the effects of temperature and pressure on crustal and mantle rocks and probable geothermal gradients. A notable exception is the strong positive velocity gradient in the mantle lid beneath the eastern United States (2 x 10^-3 sec^-1), which appears to require a compositional gradient to counter the effect of even a small geothermal gradient.

New seismic-refraction data were recorded along a 800 km profile extending due south from the Canadian border across the Columbia Plateau into eastern Oregon. The source for the seismic waves was a series of 20 high-energy chemical explosions detonated by the Canadian government in Greenbush Lake, British Columbia. The first arrivals recorded along this profile are on the Pn travel-time branch. In northern Washington and central Oregon their travel time is described by T = Δ/8.0 + 7.7 sec, but in the Columbia Plateau the Pn arrivals are as much as 0.9 sec early with respect to this line. An interpretation of these Pn arrivals together with later crustal arrivals suggest that the crust under the Columbia Plateau is thinner by about 10 km and has a higher average P-wave velocity than the 35-km-thick, 62-km/sec crust under the granitic-metamorphic terrain of northern Washington. A tentative interpretation of later arrivals recorded beyond 500 km from the shots suggests that a thin 8.4-km/sec horizon may be present in the upper mantle beneath the Columbia Plateau and that this horizon may form the lid to a pronounced low-velocity zone extending to a depth of about 140 km.

Specklegram in a multiple-mode fiber and its dependence on longitudinal modes of the laser source

A specklegram in a multimode fiber (MMF) has successfully been used as a sensor for detecting external disturbance. Our experiments showed that the sensitivity in the sensor with a multiple longitudinal-mode laser as its source was much higher than that with a single longitudinal-mode laser. In addition, the near-field pattern observations indicated that the coupling between different transverse modes in the MMF is quite weak. Based on the experimental results, a theoretical model for the speckle formation is proposed, taking a bend-caused phase factor into consideration. It is shown in the theoretical analysis that the interferences between different longitudinal modes make a larger contribution to the specklegram signals. (C) 2007 Optical Society of America.

Specklegram in a grapefruit fiber and its response to external mechanical disturbance in a single-multiple-single mode fiber structure

Specklegram in multimode fiber has successfully been used as a sensor for detecting mechanical disturbance. Speckles in a multimode pure silica grapefruit fiber are observed and compared to that of a step-index multimode fiber, showing different features between them. The sensitivities to external disturbance of two kinds of fiber were measured, based on single-multiple-single mode (SMS) fiber structure. Experimental results show that the grapefruit fiber shows higher sensitivity than does the step-index multimode fiber. The transmission spectrum of the grapefruit fiber was measured as well, showing some oscillation features that are significantly different from that of a step-index multimode fiber. The experiments may provide suggestions to understand the mechanisms of light propagation in grapefruit fibers. (D 2008 Optical Society of America.

Accuracy analysis of parallel plate interferometer for angular displacement measurement

The measurement accuracy of a parallel-plate interferometer for angular displacement measurement is analyzed. The measurement accuracy of angular displacement is not only related to the accuracy of phase extraction, but also related to initial incident angle, refraction index and thickness of plane-parallel plate as well as wavelength's stability of laser diode, etc. Theoretical analysis and computer simulation show that the measurement error of the angular displacement bears a minimum value when choosing an optimal initial incident angle in a large range. These analytical results serve as a guide in practical measurement. In this interferometer, reducing the refraction index or increasing the thickness of the parallel plate can improve the measurement accuracy; and the relative error of the phase measurement is 3.0 x 10(-4) corresponding to 1 degrees C temperature variation. Based on these theoretical and experimental results, the measurement accuracy of the parallel-plate interferometer is up to an order of 10(-8) rad. (c) 2007 Elsevier Ltd. All rights reserved.

Structural Design under Seismic Risk Using Multiple Performance Objectives

Structural design is a decision-making process in which a wide spectrum of requirements, expectations, and concerns needs to be properly addressed. Engineering design criteria are considered together with societal and client preferences, and most of these design objectives are affected by the uncertainties surrounding a design. Therefore, realistic design frameworks must be able to handle multiple performance objectives and incorporate uncertainties from numerous sources into the process.

In this study, a multi-criteria based design framework for structural design under seismic risk is explored. The emphasis is on reliability-based performance objectives and their interaction with economic objectives. The framework has analysis, evaluation, and revision stages. In the probabilistic response analysis, seismic loading uncertainties as well as modeling uncertainties are incorporated. For evaluation, two approaches are suggested: one based on preference aggregation and the other based on socio-economics. Both implementations of the general framework are illustrated with simple but informative design examples to explore the basic features of the framework.

The first approach uses concepts similar to those found in multi-criteria decision theory, and directly combines reliability-based objectives with others. This approach is implemented in a single-stage design procedure. In the socio-economics based approach, a two-stage design procedure is recommended in which societal preferences are treated through reliability-based engineering performance measures, but emphasis is also given to economic objectives because these are especially important to the structural designer's client. A rational net asset value formulation including losses from uncertain future earthquakes is used to assess the economic performance of a design. A recently developed assembly-based vulnerability analysis is incorporated into the loss estimation.

The presented performance-based design framework allows investigation of various design issues and their impact on a structural design. It is a flexible one that readily allows incorporation of new methods and concepts in seismic hazard specification, structural analysis, and loss estimation.

大行程高分辨率微定位机构的设计分析

压电驱动器的位移输出能力有限，因此通常借助于柔性机构对其位移量进行放大。对常用的柔性放大机构的性能进行了分析。提出一种柔性八杆放大机构，并对其进行有限元分析和理论计算。为了提高放大率，提出两级串连式机构。机构整体具有结构紧凑、放大效率较高的优点。

Optimization of Pulse Temporal Contrast in Optical Parametric Chirped Pulse Amplification

In optical parametric chirped pulse amplification (OPCPA), the degradation of temporal contrast of the compressed signal pulse mainly results from spectral clipping in the grating stretcher with finite size of the optics, parametric fluorescence (PF) and the spectral variations transferred from temporal fluctuation of the pump pulse. The temporal contrast of the recompressed amplified pulse in the OPCPA system is studied numerically and a number of solutions are considered and optimized to achieve the highest temporal contrast.

Ultrabroadband infrared luminescence and optical amplification in bismuth-doped germanosilicate glass

This letter reports the ultrabroadband infrared luminescence from 1000- to 1700-nm wavelength range and demonstrate optical amplification at the second optical communication window in a novel bismuth-doped germanosilicate glass. The full-width at half-maximum of the luminescence is about 300 mn and the optical gain is larger than 1.37 within the wavelength region from 1272 to 1348 nm with pump power 0.97 W. This material could be useful to fabricate ultrabroadband optical fiber amplifiers.