Orbital angular momentum in phase space

A comprehensive theory of the Weyl–Wigner formalism for the canonical pair angle–angular momentum is presented. Special attention is paid to the problems linked to rotational periodicity and angular-momentum discreteness.     

Neurosensory tissue morphology with intraoperative optical fiber probe in aqueous medium

In this work, the author has demonstrated cross-sectional imaging of a retina of an ex vivo fish sample using a common path frequency domain optical coherence tomography at 0.8 μm range. It has been introduced that an integrated surgical hypodermic needle fiber probe can stabilize the flexible glass optical fiber and provides a close proximity to the specimen for intraoperative image guiding. In addition, the light source characteristics were matched to the common path interferometer while operating in the aqueous medium (saline solution), in order to mimic the in vivo condition, in that it shows greater bandwidth and shorter center wavelength for larger input current or output power to sustain the appropriate level of coherence reference peak by the partial reflection at the glass fiber probe interface.     

软X射线层析摄影在HL—1装置上的应用

本文描述我们建立的含有22道探测器阵列及数据采集和处理系统的软X射线层析摄影诊断,并成功地应用于HL-1托卡马克装置,获得了软X射线辐射的二维层析图的时间分辨,初步观察了等离子体MHD不稳定性发展变化的局部过程。     

On the shape–from–moments problem and recovering edges from noisy Radon data

We consider the problem of reconstructing a planar convex set from noisy observations of its moments. An estimation method based on pointwise recovering of the support function of the set is developed. We study intrinsic accuracy limitations in the shape–from–moments estimation problem by establishing a lower bound on the rate of convergence of the mean squared error. It is shown that the proposed estimator is near–optimal in the sense of the order. An application to tomographic reconstruction is discussed, and it is indicated how the proposed estimation method can be used for recovering edges from noisy Radon data.Mathematics Subject Classification (2000):62C20, 62G20, 94A12     

Single-shot tomography by means of VIPA and spatial phase modulator installed optical interferometer

A VIPA (virtually imaged phased array) installed optical interferometer has been proposed for scanless tomography. Also, a spatial phase modulator and a line-image sensor were installed into the interferometer to realize single-shot measurement by displaying the delay time on a line-image sensor. The correlation peak function was observed on the line-sensor at same time. The envelope of the peak was given by the inverse Fourier transformation of the light source spectrum. The peak position on the image-sensor reflects the sample structure. Furthermore, the correlation peaks are appeared repeatedly along the delay time of the interferometer. The repeated correlation function raise an alignment flexibility of the sample set position, which has been limited in the traditional time-domain interferometry involving the delay time to be zero. The flexibility was experimentally confirmed at 25 mm related to the VIPA coherency. The resolution was experimentally 52.5 μm when the ASE (amplified spontaneous emission) light source of the optical fiber amplifier was used. The single-shot measurement was realized by a line-image sensor of the 30 frames per second. The repeatability of the interfered peak position was 5 μm by the tunable mirror position. The one-dimensional scanless measurement was demonstrated by use of 3-layer glass plates.     

Digital speckle photography and speckle tomography in heat transfer studies

The line-of-sight speckle photography of transparent media is used for quantitative measurements of the instantaneous temperature fields in 3D unsteady flows. Both electronic and photographic methods are employed for specklegram recording. The subsequent specklegram treatment uses the Young's fringes method as well as cross-correlation analysis of small interrogation areas of the recordings. Experimental data for three different heat transfer configurations are obtained and discussed. The first one is natural convection over extended vertical heated plates with forward facing steps, the second is unsteady 3D convective flow around a suddenly heated vertical thin wire, and the third one is a convective plume above a multi-jet flame. Both local and global Nusselt numbers are determined via measuring local surface temperature gradients for these convective flows. The results are compared with Ostrach's theory for a single vertical plate and with the data obtained by Mach–Zehnder interferometry. The 3D temperature fields are reconstructed for axisymmetric convective flows around a suddenly heated vertical wire using quasi-double projection measurement and the Radon inversion. 3D temperature distributions above the combustion zone are reconstructed using multi-projection speckle photography measurements and computerised tomography.     

A Penalization Approach for Tomographic Reconstruction of Binary Axially Symmetric Objects

We propose a variational method for tomographic reconstruction of blurred and noised binary images based on a penalization process of a minimization problem settled in the space of bounded variation functions. We prove existence and/or uniqueness results and derive a penalized optimality system. Numerical simulations are provided to demonstrate the relevance of the approach.     

Detection of Wave Front Set Perturbations via Correlation: Foundation for Wave-equation Tomography

We discuss the mathematical aspects of wave field measurements used in traveltime inversion from seismograms. The primary information about the medium is assumed to be carried by the wave front set and its perturbation with respect to a hypothetical background medium is to be estimated. By a convincing heuristics a detection procedure for this perturbation was proposed based on optimization of wave field correlations. We investigate its theoretical foundation in simple mathematical case studies using the distribution theoretic definition of oscillatory integrals.     

Generalized Hyperinterpolation on the Sphere and the Newman—Shapiro Operators

Hyperinterpolation on the sphere, as introduced by Sloan in 1995, is a constructive approximation method which is favorable in comparison with interpolation, but still lacking in pointwise convergence in the uniform norm. For this reason we combine the idea of hyperinterpolation and of summation in a concept of generalized hyperinterpolation. This is no longer projectory, but convergent if a matrix method A is used which satisfies some assumptions. Especially we study A partial sums which are defined by some singular integral used by Newman and Shapiro in 1964 to derive a Jackson-type inequality on the sphere. We could prove in 1999 that this inequality is realized even by the corresponding discrete operators, which are generalized hyperinterpolation operators. In view of this result the Newman—Shapiro operators themselves gain new attention. Actually, in their case, A furnishes second-order approximation, which is best possible for positive operators. As an application we discuss a method for tomography, which reconstructs smooth and nonsmooth components at their adequate rate of convergence. However, it is an open question how second-order results can be obtained in the discrete case, this means in generalized hyperinterpolation itself, if results of this kind are possible at all. March 9, 2000. Date revised: October 2, 2000. Date accepted: March 8, 2001.     

电阻层析成像技术在两相流测量中的应用

过程层析成像技术能实时提供封闭管道、容器等过程设备内物场运动状态的二／三维测量信息,它为解决两相流参数的检测问题提供一种新的途径。本文以基于电学敏感原理的电阻层析成像技术为测量手段,实现在多相流实验装置上对气／水、油／水两相流二维／三维时空分布信息的实际测量;介绍了基于测量数据特性分析的在线流型识别技术和相含率的估计方法,应用现代数据处理和模式识别技术进行数据融合与提取,实现两相管流流型识别和分相含率的估计;通过开展相关测量的研究,初步实现两相流中离散相流量的测量。