基于超限化的吸收层析反演算法研究

针对吸收光谱层析（tomographic absorption spectroscopy，TAS）中的反问题，利用超限化（superiorization）在重建中引入平滑性、稀疏性等先验条件，对现有的层析反演算法提出了改进.通过计算机仿真，对代数重建（algebraic reconstruction technique，ART）算法、最大似然期望最大化（maximum likelihod expectation maximization，MLEM）算法的超限化在TAS反演中的应用进行了研究.在仿真中，对比了不同二维火焰场、不同目标约束函数下超限化算法的效果，研究了噪声对重建的影响以及超限化算法在不同条件下的计算效率.研究结果证实了超限化对于层析反演算法在计算精度、收敛速度等方面的提升效果.      

Tomographic representation of kinetic equations in classical statistical mechanics

A tomographic representation of kinetic equations is constructed using the Radon transform. Liouville’s equation is considered for one and many particles. The reduced Liouville’s equation is obtained in the tomographic representation and the Bogolyubov chain is investigated in this representation. An example of the relativistic kinetic equation in the tomographic representation is considered.     

Few-Projection Tomography. II. Radioastronomical Method CLEAN for Three-Dimensional Problems

The radioastronomical method CLEAN is extended to problems of three-dimensional (3D) tomographic reconstruction. We consider two options, namely, 3D_1D (reconstruction using one-dimensional projections) and 3D_2D (reconstruction based on using two-dimensional projections). Deconvolution with the use of the synthesized beam (equivalent total transfer function) makes it possible to reduce several times the number of aspects in comparison with the conventional approach. We point out the relationship between the maximum level of sidelobes of the synthesized ray constructed for the Gaussian transfer functions and the number of used projections. In the case of 3D_2D -reconstruction, the reconstruction quality similar to that for the 2D_1D case is only achieved if the same number of uniformly distributed projections are used in both cases. The use of one-dimensional projections for the 3D_1D -reconstruction requires doubling of the number of projections. The reconstruction process is illustrated by an example of the three-dimensional model of an optically thin radiating object. We consider the possibilities of using the developed approach in astrotomography and remote sensing based on introducing the transfer functions which determine resolution of the receiving beam patterns and spectrographs, as well as temporal resolution of the sensing profiles. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 5, pp. 367–381, May 2005.     

TOMOGRAPHIC RECONSTRUCTION OF THREE-DIMENSIONAL TEMPERATURE FIELD USING LIQUID CRYSTAL SCANNING THERMOGRAPHY

Liquid crystal thermography (LCT) generates two-dimensional temperature information in a fluid layer. A three-dimensional temperature field can be reconstructed using the two-dimensional temperature fields obtained at various locations with the help of synchronized movements of the light sheet and camera. However, in many cases it may not be feasible to generate a large number of two-dimensional liquid crystal thermographs that are needed to represent a high-resolution, three-dimensional temperature field. In the present article, a tomographic reconstruction method is suggested that can be used to produce a high-resolution, three-dimensional reconstruction from a limited number of two-dimensional images of the full temperature field. The two-dimensional temperature fields generated from the LCT experiments can be used to obtain integrated information of the three-dimensional field from various directions. These estimated projections of the actual three-dimensional field can be used to reconstruct a high-resolution volumetric temperature field within an acceptable error.     

Equation for wave processes in inhomogeneous moving media and functional solution of the acoustic tomography problem based on it

The paper considers the derivation of the wave equation and Helmholtz equation for solving the tomographic problem of reconstruction combined scalar-vector inhomogeneities describing perturbations of the sound velocity and absorption, the vector field of flows, and perturbations of the density of the medium. Restrictive conditions under which the obtained equations are meaningful are analyzed. Results of numerical simulation of the two-dimensional functional-analytical Novikov–Agaltsov algorithm for reconstructing the flow velocity using the the obtained Helmholtz equation are presented.     

Radon transform and kinetic equations in the tomographic representation

Statistical properties of classical random processes are considered in the tomographic representation. The Radon integral transform is used to construct the tomographic form of the kinetic equations. The relationship between the probability density on the phase space for classical systems and the tomographic probability distribution is elucidated. Examples of simple kinetic equations like the Liouville equations for one and many particles are studied in detail.     

Analysis of algebraic reconstruction technique for accurate imaging of gas temperature and concentration based on tunable diode laser absorption spectroscopy

An improved algebraic reconstruction technique(ART) combined with tunable diode laser absorption spectroscopy(TDLAS) is presented in this paper for determining two-dimensional(2D) distribution of H_2O concentration and temperature in a simulated combustion flame.This work aims to simulate the reconstruction of spectroscopic measurements by a multi-view parallel-beam scanning geometry and analyze the effects of projection rays on reconstruction accuracy.It finally proves that reconstruction quality dramatically increases with the number of projection rays increasing until more than 180 for 20 × 20 grid,and after that point,the number of projection rays has little influence on reconstruction accuracy.It is clear that the temperature reconstruction results are more accurate than the water vapor concentration obtained by the traditional concentration calculation method.In the present study an innovative way to reduce the error of concentration reconstruction and improve the reconstruction quality greatly is also proposed,and the capability of this new method is evaluated by using appropriate assessment parameters.By using this new approach,not only the concentration reconstruction accuracy is greatly improved,but also a suitable parallel-beam arrangement is put forward for high reconstruction accuracy and simplicity of experimental validation.Finally,a bimodal structure of the combustion region is assumed to demonstrate the robustness and universality of the proposed method.Numerical investigation indicates that the proposed TDLAS tomographic algorithm is capable of detecting accurate temperature and concentration profiles.This feasible formula for reconstruction research is expected to resolve several key issues in practical combustion devices.     

Modeling two-dimensional opto-acoustic studies of excited media

The use of the opto-acoustic effect in tomographic studies of excited media under strong absorption of the initiating laser radiation is discussed. We present the results of two-dimensional model experiments showing the possibility of good reconstruction of a secondary acoustic source even in the case of significant absorption of the initiating radiation. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 42, No. 1, pp. 83–86, January, 1999.     

Method of holographic imaging of inhomogeneities in the density of a substance of a semitransparent medium using plane-parallel laser radiation

A new method for coherent superbroadband sounding of a semitransparent substance with the aim to construct a three-dimensional image of its inner structure is proposed and justified. The method is based on irradiating the studied medium with a plane ray, spectral analysis by the two-dimensional Fresnel–Fourier transform, interferometric comparison of spatial spectra of scattered and reference signals, and holographic construction of a series of two-dimensional images of the medium followed by tomographic reconstruction of its three-dimensional image. The stochastic image model has been justified in a coherent approach for the first time both in the region of high frequencies and after the transfer of the radiation spectrum to the lowfrequency range of spatial frequencies to the surface of the radiation recorder. The spectral correlation characteristics of the speckle structure of the reconstructed image have been studied. Calculations and investigations of the spread function of the structure implementing the proposed method have been carried out.     

Nondestructive rare earth element imaging of fish teeth from deep‐sea sediments

X‐ray fluorescence computed tomography is an emerging imaging modality that allows for the nondestructive reconstruction of the internal distribution of elements within a sample. The common use of X‐ray excitation energy (up to approximately 20 keV) has necessitated the use of l ‐shell fluorescence for heavy elements. In this study, based on high energy X‐ray at BL13W1 of the Shanghai Synchrotron Radiation Facility, we employed high‐energy excitation for tomographic imaging of the heavy metals (rare earth elements) in fish teeth from deep‐sea sediments on the micrometer scale using K‐shell X‐ray fluorescence. The virtual cross‐sectional distribution of La, Ce, Pm, Pr, Nd, and Sm were obtained, thereby providing a feasible approach for analyzing the enrichment mechanism of rare earth elements. Copyright © 2015 John Wiley & Sons, Ltd.     

A high order kinetic flux-vector splitting method for the reduced five-equation model of compressible two-fluid flows

We present a high order kinetic flux-vector splitting (KFVS) scheme for the numerical solution of a conservative interface-capturing five-equation model of compressible two-fluid flows. This model was initially introduced by Wackers and Koren (2004) [21]. The flow equations are the bulk equations, combined with mass and energy equations for one of the two fluids. The latter equation contains a source term in order to account for the energy exchange. We numerically investigate both one- and two-dimensional flow models. The proposed numerical scheme is based on the direct splitting of macroscopic flux functions of the system of equations. In two space dimensions the scheme is derived in a usual dimensionally split manner. The second order accuracy of the scheme is achieved by using MUSCL-type initial reconstruction and Runge–Kutta time stepping method. For validation, the results of our scheme are compared with those from the high resolution central scheme of Nessyahu and Tadmor [14]. The accuracy, efficiency and simplicity of the KFVS scheme demonstrate its potential for modeling two-phase flows.     

Application of X‐Ray Computerized Tomography to Characterize Particle Retention Within Depth Filters

Local measurements of solid concentration in depth wound cartridge filters using X‐ray computerized tomography (XCT) are described. The filters were contaminated with glass bead particles, which exhibit high contrast in the tomographic images. Segmentation of the successive original slices was applied and solid profile concentrations along the filters were obtained. 3D reconstruction techniques permitted the modeling of the spatial distribution of the solid particles captured by the filters.     

Variance-reduced DSMC for binary gas flows as defined by the McCormack kinetic model

A variance-reduced direct simulation Monte Carlo method is presented for binary gas flows as defined by the McCormack kinetic model. Two types of flow configuration, namely pressure driven flow between two parallel plates and through rectangular channels, are considered. The kinetic model is transformed into one- and two-dimensional projected formalisms. Both cases are modeled by the variance-reduced DSMC. Simulations are performed to compare the method to the analytical discrete ordinate and discrete velocity methods. For both flow configurations, very good agreement is obtained between the results of different approaches. The results of the approach are also compared to the prediction of the moment method and the results of hard-sphere gases. The model can be beneficial for computing slow rarefied gaseous mixture flows, especially in nano- and microscale devices.     

基于微波链路的降雨场反演方法研究

本文基于微波雨衰的幂律关系, 研究了使用微波链路反演降雨场的方法, 采用层析技术建立了降雨场反演模型. 并利用SIRT算法与正则化算法实现对降雨场层析反演模型的求解. 数值模拟结果表明, 该模型与反演算法能够较为准确地重建降雨场强度与空间分布特征, 能够提供高时空分辨率的二维降雨强度分布. 因此, 利用微波衰减数据进行降雨探测可以作为常规的雨量计与天气雷达观测手段的有效补充. 关键词： 微波雨衰 微波链路 降雨场重建 层析反演     

Mojette变换层析技术中的投影角度布局方法

Mojette变换是一种最小冗余采样的离散Radon变换,能够用较少角度的投影数据进行精确的计算层析(computed tomography,CT)重建,为少量投影角度CT技术的实现提供了一种新思路.投影角度的空间布局决定了层析重建最少所需投影的数量.为了获得Mojette变换层析技术中的最优投影空间角度布局方案,本文对三维Mojette变换数学模型及其精确重建条件进行了研究.以此为基础,在考虑实际探测器像素数目受限的条件下,提出了确定最优投影角度的方法.研究结果表明:所有探测器围绕被测物体在同一水平面内进行平行投影采集是最优的投影角度布局方案,此时投影模型为二维Mojette变换,所需的投影角度和探测器像素数最少,投影角度范围最小;若在实际的测量中该投影条件无法满足,则投影矢量中|pi|和|qi|的值越小越好.该研究可为实际层析系统的建立提供理论基础.     

Two-dimensional optical tomography of hemodynamic changes in a preterm infant brain

Our preliminary results on two-dimensional (2D) optical tomographic imaging of hemodynamic changes in a preterm infant brain are reported. We use the established 16-channel time-correlated single photon counting system for the detection and generalized pulse spectrum technique based algorithm for the image reconstruction. The experiments demonstrate that diffuse optical tomography may be a potent means for investigating brain functions and neural development of infant brains in the perinatal period.     

Aberrations of self-imaged patterns with two-dimensional periodicity

We develop a geometrical theory of aberration in the self-imaged patterns with two-dimensional periodicity. The patterns are considered to be a crossed-line grating or a periodic array of finite apertures. We first derive the raytracing equations for determining the optical path of a self-imaging ray. We then find the third- and fifth-order contributions to the wavefront aberration which arise from the difference between the optical paths of a self-imaging ray and of an actual ray. We also derive the expression of the ray aberration from the wavefront aberration. The ray aberration is classified into five distinct types by analogy with the cases in a refracting lens system. We show that the overall ray aberration is entirely undercorrected and the aberrated image patch is decentered from an ideal image point in the direction parallel to the direction tangent vector of a chief ray. The image evaluation technique discussed here will be useful in various applications related to self-image formation of two-dimensionally periodic patterns.     

Tomographic reconstruction of two-dimensional radiated power distribution during impurity injection in KSTAR plasmas using an infrared imaging video bolometer

Based on the two-dimensional radiation images obtained by an infrared imaging video bolometer (IRVB) with tangential view, the two dimensional radiation profiles of plasmas in KSTAR were reconstructed. The IRVB installed on KSTAR has a tangential view of the plasma, and thus tomographic reconstruction of the raw images of radiation profiles was performed to remove the chord-integration effect by using a tomographic reconstruction code based on the Phillips-Tikhonov algorithm. Phantom reconstruction tests with various synthetic images were carried out to validate the accuracy of the reconstruction results. It is found that hollow radiation phantoms with strong divertor radiation were reconstructed with high accuracy. Furthermore, the effects of the number of channels of the IR camera, and the number of pixels of the plasma and of the IRVB on reconstruction performance are studied with phantom tests. Two-dimensionally reconstructed images of KSTAR plasmas demonstrated that radiation loss at the plasma edge and near the divertor region increased significantly after gaseous impurity injection. The total radiated power was up to 1.2 MW at the disruption, which was 40% of the NBI power. After argon and krypton gas injection, total radiated power was increased by 325 kW and 180 kW, respectively.     

Aperture properties of multimode conical optical fibers (focons)

The problem on the propagation of meridional rays in conical optical fibers (focons) has been considered in terms of the geometric optics model. A sine condition for the ray parameters at reflection points has been obtained. A general equation that relates the geometric size of a focon with the ray parameters at the entrance and exit of the focon has been deduced. The equation is valid for all physically possible taper angles of a focon. The aperture properties of two types of focons (hollow and dielectric) have been analyzed. The entrance and exit aperture angles appear to be piecewise continuous or piecewise smooth functions of the parameters, which is related to the discreteness of the number of ray reflections. The main properties of the considered types of focons with typical values of the parameters have been illustrated by numerical calculations of the aperture angles.