Probabilistic methods for stationary problems of linear transport theory

The steady state of a system of independent particles which undergo elastic collisions can be expressed in terms of the absorption probabilities of the associated Markov process. For the slab albedo problem, this representation enables the application of probabilistic methods to obtain explicit upper and lower bounds on the steady-state density. In particular, the bounds prove the 1/L, decrease of the steady-state flux as a function of the slab widthL (Fick's law).Supported in part by U.S. National Science Foundation grant MCS 75-21684 A02.On leave of absence from Fachbereich Physik, UniversitÄt Mönchen. Work supported by a DFG research fellowship.     

Some problems in the classical theory of radiation

The article considers the problem of the complete radiation of the energy of a charged particle moving in constant and homogeneous electric and magnetic fields and in the field of a plane wave. Exact formulas are obtained for these cases. The problem is al so considered of the instantaneous radiation of an arbitrary moving charge. The problems are considered according to classical theory.     

Optical polarization echo: Manifestation and study by methods of quantum tomography of states and processes

The polarization echo effect is demonstrated, which is manifested in the identity of a composite polarization transformation irrespective of the spectrum of the input polarization state. The pure input state transfers during its evolution to a completely mixed state and then returns to the initial state. The stages of this evolution are completely analogous to the corresponding stages of the “classical” spin echo effect. The adequacy of transformations performed for conditionally prepared one-photon polarization states is verified by the tomography of the quantum process.     

Some abalytical methods in neutron transport theory

In this paper, whose purpose is pedagogic, we discuss some distinctive features of neutron transport theory. The linearized transport equation is similar to those met in theories of gas dynamics and radiative transfer. We describe the analytical techniques that have been most successful in analyzing the neutron equation. Among these are: The method of separated solutions (in space and angle co-ordinates), and the construction of velocity-dependent collision models.     

Optical coherence tomography using broad-bandwidth XUV and soft X-ray radiation

We present a novel approach to extend optical coherence tomography (OCT) to the extreme ultraviolet (XUV) and soft X-ray (SXR) spectral range. With a simple setup based on Fourier-domain OCT and adapted for the application of XUV and SXR broadband radiation, cross-sectional images of semiconductors and organic samples becomes feasible with current synchrotron or laser-plasma sources. For this purpose, broadband XUV radiation is focused onto the sample surface, and the reflected spectrum is recorded by an XUV spectrometer. The proposed method has the particular advantage that the axial spatial resolution only depends on the spectral bandwidth. As a consequence, the theoretical resolution limit of XUV coherence tomography (XCT) is in the order of nanometers, e.g., 3 nm for wavelengths in the water window (280–530 eV). We proved the concept of XCT by calculating the reflectivity of one-dimensional silicon and boron carbide samples containing buried layers and found the expected properties with respect to resolution and penetration depth confirmed.     

Note on half-space problems in the restricted two-group transport theory

Explicit solutions are presented for half space problems in the restricted two-group transport theory.     

非定常辐射输运问题的蒙特卡罗自适应偏倚抽样

用蒙特卡罗(MC)方法模拟高温、高压、多介质、大变形辐射输运问题时,由于网格体积悬殊,导致各网格通量的统计误差涨落很大,随着时间步的增加,误差积累甚至会导致计算结果失真.为此,发展了针对全局网格计算的源偏倚抽样技巧.用于源偏倚抽样的价值函数基于上个时间步各网格通量及误差,通过加权构造产生,它比传统MC通过解伴随方程获取价值的性价比要高得多.数值试验表明,全局源偏倚抽样通过自适应分配当前时间步各网格的粒子数,有效地降低了当前步重要网格通量误差. 关键词： 非定常 辐射输运 蒙特卡罗 源偏倚抽样     

Nonstationary two-flux model of radiation transport for optical tomography of scattering media

A nonstationary two-flux model is formulated for the transport of radiation in an inhomogeneous scattering medium and is applied to the situation where such a medium is irradiated by the narrow beam of a pulsed laser. It is shown that when the time distribution of the transmitted photons is measured it is possible simultaneously to reconstruct the two spatial functions (the coefficients of absorption coefficient and of scattering of the radiation by the medium) by means of an inverse Radon transformation and the solution of a system of nonlinear differential equations on the projection lines. An analytic solution is obtained in quadratures for these differential equations. The results constitute a method of solving problems in optical tomography in an inhomogeneous scattering medium Zh. Tekh. Fiz. 67, 61–65 (May 1997)     

Condensed history Monte Carlo methods for photon transport problems

We study methods for accelerating Monte Carlo simulations that retain most of the accuracy of conventional Monte Carlo algorithms. These methods - called Condensed History (CH) methods - have been very successfully used to model the transport of ionizing radiation in turbid systems. Our primary objective is to determine whether or not such methods might apply equally well to the transport of photons in biological tissue. In an attempt to unify the derivations, we invoke results obtained first by Lewis, Goudsmit and Saunderson and later improved by Larsen and Tolar. We outline how two of the most promising of the CH models - one based on satisfying certain similarity relations and the second making use of a scattering phase function that permits only discrete directional changes - can be developed using these approaches. The main idea is to exploit the connection between the space-angle moments of the radiance and the angular moments of the scattering phase function. We compare the results obtained when the two CH models studied are used to simulate an idealized tissue transport problem. The numerical results support our findings based on the theoretical derivations and suggest that CH models should play a useful role in modeling light-tissue interactions.     

Optical methods for the generation of terahertz radiation and subterahertz acoustics of solids

Various methods to increase the efficiency of the generation of broadband terahertz radiation based on optical rectification have been analyzed. The solutions of self-consistent optical terahertz equations have been studied using the inclined front technique. The effect of symmetric and asymmetric resonant impurity centers incorporated into a crystal has been examined. Transient and asymptotic stages of generation have been considered. Attention has been focused on the evolution of the spectra of both generated terahertz and input optic signals. One- and two-frequency generation modes have been discussed. Acoustic analogs that would provide the possibility of the generation of the gigahertz acoustic supercontinuum using subterahertz elastic signals in a solid have been analyzed. The main similarities and differences between terahertz optics and subterahertz acoustics have been revealed.     

An overview on recent radiation transport algorithm development for optical tomography imaging

Optical tomography belongs to the promising set of non-invasive methods for probing applications of semi-transparent media. This covers a wide range of fields. Nowadays, it is mainly driven by medical imaging in search of new less aggressive and affordable diagnostic means. This paper aims at presenting the most recent research accomplished in the authors’ laboratories as well as that of collaborative institutions concerning the development of imaging algorithms. The light transport modelling is not a difficult question as it used to be. Research is now focused on data treatment and reconstruction. Since the turn of the century, the rapid expansion of low cost computing has permitted the development of enhanced imaging algorithms with great potential. Some of these developments are already on the verge of clinical applications. This paper presents these developments and also provides some insights on still unresolved challenges. Intrinsic difficulties are identified and promising directions for solutions are discussed.     

An analytical study of space-dependent evolution problems in particle transport theory

Summary Space-dependent evolution problems arising in particle transport theory are analytically studied via a systematic application of the Boltzmann equation. Some explicit solutions, that can improve our knowledge of the spatial effects in such a class of problems, are constructed and briefly commented on a physical ground.

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Riassunto Problemi spaziali di evoluzione che si incontrano nella teoria del trasporto di particelle sono studiati analiticamente per mezzo di una sistematica applicazione dell'equazione di Boltzmann. Alcune soluzioni esplicite, che possono migliorare la nostra conoscenza degli effetti spaziali in tale classe di problemi, sono costruite e commentate brevemente su base fisica.

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Резюме Аналитически, используя уравнение Больцмана, исследуются проблемы пространственной эволюции, зозниакющие в теории переноса частиц. Конструируются некоторые точные решения, которые могут уточнить наше понимание пространственных эффектов в таком классе проблем. Проводится обсуждение этих решений.

     

Special problems and methods in the study of water vapor transport in polymers

Water presents special and unique difficulties in diffusion and sorption measurements because of its high cohesive energy and hydrogen-bonding capacity. In the case of transport measurements in hydrophilic polymers the time-lag method is complicated by the tendency of the water vapor to be adsorbed onto the glass receiving sections of the equipment. On the other hand, with more hydrophilic polymers where nonsteady-state direct sorption methods can be used the large amount of heat liberated during the sorption process again causes considerable difficulty. A discussion of these and other problems concerned with transport studies with water vapor is presented and various practical solutions are offered.     

输运问题蒙特卡罗模拟方法回顾及展望北大核心CSCD

蒙特卡罗(MC)方法具有复杂几何处理能力强,方法通用灵活,核数据完备,模拟忠实于物理过程等特点,成为中子学数值模拟的首选方法之一。在核能领域,MC方法得益于计算机的快速发展,在辐射屏蔽、反应堆堆芯临界安全分析、乏燃料后处理、放射性废物处置、核设施退役、核事故应急、放射性石油测井、核医学等领域均有广泛应用。对MC方法及软件输运计算做简要回顾,并对未来发展进行展望。     

Analytical and numerical solutions of some integral equations in radiation transport theory

Summary We discuss some mathematical and computational problems relevant to the solutions of both linear and non-linear integral equations arising in radiation transport. By means of a functional-operator approach, analytic solutions for the FEL (Free Electron Laser) integral equations are found in terms of Bessel-Clifford functions. As for applications of this method to non-linear equations, the same technique allows us to obtain an efficient yet simple algorithm for the numerical solution of the Ambartsumian-ChandrasekharH-equation corresponding to a Neumann-series expansion. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Synchrotron radiation time spectra affected by diffusion: theory

Hyperfine Interactions - The general theory and a qualitative picture of time spectra in nuclear resonant scattering of synchrotron radiation in the presence of diffusive motion of atoms are...     

基于声偶极辐射的磁感应磁声层析成像研究

基于声偶极辐射模型提出磁感应磁声层析成像理论来解决点声源理论所不能解释的边界信号和反相振动问题,理论分析了洛伦茨力引起的一维组织振动和自由空间的三维声偶极辐射,推导了磁声激发、磁声衍射传播和换能器磁声波形接收的解析公式。对二层柱状组织模型进行的数值模拟和实验测量结果证明声偶极传播的指向性会使磁声信号在不同传播方向上产生衰减,接收到的磁声波形在声压突变处产生反映电阻抗分布边界信息的脉冲串,重构的层析图像显示不同电阻抗组织的外形和尺寸。本研究为磁感应磁声层析成像技术在医学成像中组织电阻抗分布的重建提供了理论基础。     

Optical diffraction tomography microscopy with transport of intensity equation using a light-emitting diode array

Optical diffraction tomography (ODT) is an effective label-free technique for quantitatively refractive index imaging, which enables long-term monitoring of the internal three-dimensional (3D) structures and molecular composition of biological cells with minimal perturbation. However, existing optical tomographic methods generally rely on interferometric configuration for phase measurement and sophisticated mechanical systems for sample rotation or beam scanning. Thereby, the measurement is suspect to phase error coming from the coherent speckle, environmental vibrations, and mechanical error during data acquisition process. To overcome these limitations, we present a new ODT technique based on non-interferometric phase retrieval and programmable illumination emitting from a light-emitting diode (LED) array. The experimental system is built based on a traditional bright field microscope, with the light source replaced by a programmable LED array, which provides angle-variable quasi-monochromatic illumination with an angular coverage of ±37 degrees in both x and y directions (corresponding to an illumination numerical aperture of ∼0.6). Transport of intensity equation (TIE) is utilized to recover the phase at different illumination angles, and the refractive index distribution is reconstructed based on the ODT framework under first Rytov approximation. The missing-cone problem in ODT is addressed by using the iterative non-negative constraint algorithm, and the misalignment of the LED array is further numerically corrected to improve the accuracy of refractive index quantification. Experiments on polystyrene beads and thick biological specimens show that the proposed approach allows accurate refractive index reconstruction while greatly reduced the system complexity and environmental sensitivity compared to conventional interferometric ODT approaches.