# A tensor approach to double wave vector diffusion-weighting experiments on restricted diffusion

**ABSTRACT** Previously, it has been shown theoretically that in case of restricted diffusion, e.g. within isolated pores or cells, a measure of the pore size, the mean radius of gyration, can be estimated from double wave vector diffusion-weighting experiments. However, these results are based on the assumption of an isotropic orientation distribution of the pores or cells which hampers the applicability to samples with anisotropic or unknown orientation distributions, such as biological tissue. Here, the theoretical considerations are re-investigated and generalized in order to describe the signal dependency for arbitrary orientation distributions. The second-order Taylor expansion of the signal delivers a symmetric rank-2 tensor with six independent elements if the two wave vectors are concatenated to a single six-element vector. With this tensor approach the signal behavior for arbitrary wave vectors and orientation distributions can be described as is demonstrated by numerical simulations. The rotationally invariant trace of the tensor represents a pore size measure and can be determined from three orthogonal directions with parallel and antiparallel orientation of the two wave vectors. Thus, the presented tensor approach may help to improve the applicability of double wave vector diffusion-weighting experiments to determine pore or cell sizes, in particular in biological tissue.

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**ABSTRACT:**Experiments with two diffusion-weighting periods applied successively in a single experiment, so-called double-wave-vector (DWV) diffusion-weighting experiments, are a promising tool for the investigation of material or tissue structure on a microscopic level, e.g. to determine cell or compartment sizes or to detect pore or cell anisotropy. However, the theoretical descriptions presented so far for experiments that aim to investigate the microscopic anisotropy with a long mixing time between the two diffusion weightings, are limited to certain wave vector orientations, specific pore shapes, and macroscopically isotropic samples. Here, the signal equations for fully restricted diffusion are re-investigated in more detail. A general description of the signal behavior for arbitrary wave vector directions, pore or cell shapes, and orientation distributions of the pores or cells is obtained that involves a fourth-order tensor approach. From these equations, a rotationally invariant measure of the microscopic anisotropy, termed MA, is derived that yields information complementary to that of the (macroscopic) anisotropy measures of standard diffusion-tensor acquisitions. Furthermore, the detailed angular modulation for arbitrary cell shapes with an isotropic orientation distribution is derived. Numerical simulations of the MR signal with a Monte-Carlo algorithms confirm the theoretical considerations. The extended theoretical description and the introduction of a reliable measure of the microscopic anisotropy may help to improve the applicability and reliability of corresponding experiments.Journal of Magnetic Resonance 10/2009; 202(1):43-56. DOI:10.1016/j.jmr.2009.09.015 · 2.32 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Summary form only given, as follows. Negative electron affinity (NEA) GaAs photocathodes are widely used in imaging tubes such as image intensifiers, streak cameras and photomultipliers, and recently proposed for applications in electron beam lithography and NEA-based microelectronics. GaAs activation to NEA requires an atomically clean crystal surface which is obtained by a chemical process followed by heating in ultrahigh vacuum. In this work, we prepare GaAs(100) NEA photocathodes by atomic hydrogen bombardment. Atomic hydrogen is known to cause a homogeneous desorption of carbon and oxide contaminants from GaAs surfaces, which can replace the chemical cleaning process and reduce the GaAs cleaning temperature. The preparation of the photocathodes by atomic hydrogen is performed at 450°C while the conventional heat cleaning is performed at 600-700°C. The high temperature cleaning causes preferential desorption of As and can destroy the photocathode. The samples are then activated to NEA by alternately depositing cesium and oxygen to maximize the photoemission. Cesium and oxygen are known to reduce the vacuum level below the bulk conduction band minimum producing a NEA surface with high quantum efficiency (QE) defined as the number of emitted electrons per incident photon. When we exposed the photocathodes to atomic hydrogen before activation, a QE of ~8.3% and ~5.3 % was produced when excited with 632.8 nm and 780 nm lasers, respectively. For a current of 1 μA, the QE is reduced by ~25% after continuous operation for 13 hoursPlasma Science, 1998. 25th Anniversary. IEEE Conference Record - Abstracts. 1998 IEEE International on; 07/1998 -
##### Conference Paper: Study of a triode-dynode amplifier for low intensity near-infrareddetection with a photodiode

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**ABSTRACT:**Summary form only given, as follows. This study is motivated by the observation that PIN photodiodes have excellent quantum efficiency for photon detection well into the near-infrared where the quantum efficiency of photocathodes falls below 1%. Coupling the high quantum efficiency of solid state diodes with the low noise, high gain, and fast time response of dynode chain electron multipliers, we hope to produce a design for a near-infrared detector capable of very low signal detection with fast time response (>10 MHz bandwidth) in the near-infrared (~1 micron). Such a detector would be useful not only for plasma diagnostics, but also in other areas of optical sensing such as communications. In order to couple electrons into a dynode chain, we are examining triode assemblies based on field emission tips, thermionic cathodes with energy filters, and photoemissive cathodes. The advantages and difficulties associated with each technique will be reportedPlasma Science, 1998. 25th Anniversary. IEEE Conference Record - Abstracts. 1998 IEEE International on; 07/1998