Scattering Media Research Articles

Finite Difference Time Domain Analysis of Diffusion Equations with Nonuniform Grids for Time-Resolved Reflectance of an Optical Pulse in Three-Dimensional Scattering Medium

An integral form of diffusion equations and their finite difference time domain (FDTD) analysis have been formulated. The analysis is extended to FDTD analysis with nonuniform grids in three-dimensional (3-D) scattering medium. It has been confirmed that 600 time steps in calculation sequences of the time-resolved reflectance for 3-D medium 80 × 80 × 30 mm3 in volume is completed within 4 seconds by utilizing 23 and 43 mm3 nonuniform cubic grids, when a conventional personal computer with 3 GHz CPU clock is used. The conditions for keeping numerical accuracies comparable to those in 23 mm3 uniform grids are made clear. The proposed analysis greatly reduces time to run and memory space in 3-D scattering medium numerical analysis.

Least-Squares Finite Element Analysis for Transient Radiative Transfer in Absorbing and Scattering Media

In some radiative transfer processes, the time scales are usually on the order of 10−9-10−15s, so the transient effect of radiation should be considered. In present research, a finite element model, which is based on the discrete ordinates method and least-squares variational principle, is developed to simulate the transient radiative transfer in absorbing and scattering media. The numerical formulations and detailed steps are given. Moreover, two transient radiative transfer problems are investigated and the results are compared with those by integral method and finite volume method. It indicates that the present model can simulate the transient radiative transfer effectively and accurately.

Radiative Characteristics of Beds of Spheres Containing an Absorbing and Scattering Medium.

The aim of this paper is to characterize the radiative behavior of beds made of spherical particles containing an homogeneous absorbing and scattering medium whose radiative properties (extinction coefficient, scattering albedo, and scattering phase function) are known. In the beds studied, the spherical particles could be far apart, close to each other, or even compressed. When the particles are sufficiently distant from each other to scatter independently, the radiative properties of the whole bed are determined from the radiative characteristics of one particle alone. These characteristics are determined using a Monte Carlo procedure applied to one bead alone. On the other hand, when particles get closer to each other independent scattering theory is no longer valid, and dependent scattering effects have to be taken into account. We then apply a Monte Carlo procedure to the whole bed and identify the extinction coefficient, scattering albedo, and scattering phase function of the equivalent homogeneous absorbing and scattering medium that best matches the radiative behavior of the bed. The simulation permits us to characterize the evolution of the radiative properties of the bed with the inside medium properties and the characteristics of the bed. Moreover, we investigate the limit of validity of the independent scattering hypothesis.

TierSPECT: Leistungsparameter einer dedizierten Kleintier-SPECT-Kamera und erste in vivo Messungen

This paper presents the performance of a new small-animal camera (TierSPECT) devised for the in vivo measurements of radiolabeled substances in small laboratory animals such as mice and rats. In a scatter medium, the camera has a tomographic spatial resolution of 2.87 mm and a sensitivity of 22 cps/MBq in a usable Field-of-View (FOV) with a diameter of 82mm. The planar homogeneity amounts to 3.3%, the tomographic homogeneity lies between 3.2% and 3.5%. The deviation between filled and measured concentration of activity in a cylindrical 4-chamber-phantom was smaller than 2.6%. Using a novel rat head phantom with chamber volumes in the order of magnitude of the spatial resolution (between 0.065 ml and 0.19 ml) it could be demonstrated that studies of the rat neostriatal dopaminergic system are feasible under observance of physiological conditions. In vivo studies using [99mTc]diphosphonato-1,2-propandicarbonic acid (99mTc-DPD) and [123I]N-ω-fluoropropyl-2β-carbomethoxy-3β-(4-iodophenyl)-nortropane (123I-FP-CIT) proved that bone metabolism and dopamine transporter binding can be visualized with the TierSPECT. The fusion of 99mTc-DPD and 123I-FP-CIT images allowed the differentiation between intra- and extracerebral structures. Pretreatment with methylphenidate resulted in blockade of striatal dopamine transporter binding.

P1-61 Spectroscopic Three-Dimensional Imaging of Light Scattering Medium by Detection of Ultrasonic Velocity Change Due to Light Illumination

P1-61 Spectroscopic Three-Dimensional Imaging of Light Scattering Medium by Detection of Ultrasonic Velocity Change Due to Light Illumination

Coherent Transverse Speckle Dynamics in the Case of Probing of Stationary Bulk Scattering Media by a Laser with Frequency Deviation

A coherent transverse dynamics of scattered speckle fields that arises upon propagation of tunable laser radiation through stationary optically inhomogeneous bulk media has been discovered. The dynamic photochromic speckle effect can be observed experimentally if the deviation of the laser radiation frequency is comparable with or greater than the effective phase delays arising upon scattering of waves in a random or partly organized medium. It was found experimentally that, with an increase in the frequency tuning range of a probing laser diode (λ = 650 nm) or a compact YAG:Nd laser (λ = 532 μm), which can reach hundreds of gigahertz for multiply scattering bulk media from several millimeters to two centimeters thick (fluoroplastic phantoms), the two-dimensional correlation coefficient of speckle structures decreased monotonically, and the characteristic drop for thicker structures was observed at smaller frequency detunings.

Perturbation theory for the effective diffusion constant in a medium of random scatterers

We develop perturbation theory and physically motivated resummations of the perturbation theory for the problem of a tracer particle diffusing in a random media. The random media contains point scatterers of density $\rho$ uniformly distributed through out the material. The tracer is a Langevin particle subjected to the quenched random force generated by the scatterers. Via our perturbative analysis we determine when the random potential can be approximated by a Gaussian random potential. We also develop a self-similar renormalisation group approach based on thinning out the scatterers, this scheme is similar to that used with success for diffusion in Gaussian random potentials and agrees with known exact results. To assess the accuracy of this approximation scheme its predictions are confronted with results obtained by numerical simulation.

Finite Element Simulation of Radiative Heat Transfer in Absorbing and Scattering Media

References 1Whiting, E. E., Yen, L., Arnold, J. O., and Paterson, J. A., “NEQAIR96, Nonequilibrium and Equilibrium Radiative Transport and Spectra Program: User’s Manual,” NASA RP-1389, Dec. 1996. 2Hottel, H. C., and Sarofim, A. F., Radiative Transfer, McGraw–Hill, New York, 1967, p. 258. 3Lockwood, M., “Titan Aerocapture Systems Analysis,” AIAA Paper 2003-4799, July 2003. 4Olejniczak, J., Prabhu, D., Wright, M., Takashima, N., Hollis, B., Sutton, K., and Zoby, V., “An Analysis of the Radiative Heating for Aerocapture at Titan,” AIAA Paper 2003-4953, July 2003. 5Takashima, N., Hollis, B., Olejniczak, J., Wright, M., and Sutton, K., “Preliminary Aerothermodynamics of Titan Aerocapture Aeroshell,” AIAA Paper 2003-4952, July 2003.

Radiation with Mixed Convection in an Absorbing, Emitting, and Anisotropic Scattering Medium

Radiation with Mixed Convection in an Absorbing, Emitting, and Anisotropic Scattering Medium

An Approach of Three-Dimensional Vector Radiative Transfer (3-D–VRT) Equation for Inhomogeneous Scatter Media

To solve a three-dimensional vector radiative transfer (3-D-VRT) equation for the model of spatially inhomogeneous scatter media, the finite enclosure of the scatter media is geometrically divided, in both the vertical z and horizontal (x,y) directions, to form very thin multiboxes. The zeroth-order emission, first-order Mueller matrix of each thin box, and an iterative approach of high-order radiative transfer are applied to deriving high-order scattering and emission of whole inhomogeneous scatter media. Numerical results of polarized brightness temperature at microwave frequency from an inhomogeneous scatter model such as vegetation canopy are calculated and discussed.

Effective diffusion constant in a two-dimensional medium of charged point scatterers

We obtain exact results for the effective diffusion constant of a two dimensional Langevin tracer particle in the force field generated by charged point scatterers with quenched positions. We show that if the point scatterers have a screened Coulomb (Yukawa) potential and are uniformly and independently distributed then the effective diffusion constant obeys the Volgel-Fulcher-Tammann law where it vanishes. Exact results are also obtained for pure Coulomb scatterers frozen in an equilibrium configuration of the same temperature as that of the tracer.

MEAN AND VARIANCE OF THE FORWARD FIELDS PROPAGATED THROUGH 3D RANDOM INTERNAL WAVES WITH RAYLEIGHT-BORN SCATTERING

The mean and variance of the acoustic field forward propagated through an ocean waveguide containing random internal waves is modelled using a normal mode formulation [1] that takes into account the 3-D interaction of the acoustic field with medium inhomogeneities. The effects of dispersion, attenuation and redistribution of modal energy due to random multiple scattering in the forward azimuth are treated analytically. The inhomogeneous medium's scatter function density is modelled using the Rayleigh-Born approximation to Green's theorem to account for random fluctuations in density and compressibility caused by the internal waves. The generalized waveguide extinction theorem [2] is applied to determine the attenuation due to scattering from the internal wave inhomogeneities. Simulations for typical continental shelf environments quantitatively show how coherent and incoherent acoustic field intensities vary with range, depth and internal wave field properties

Analysis of Gain Volume in Random Laser in a Spherical Multiple Scattering Medium

We performed numerical simulation of a random laser in a spherical multiple scattering medium in order to examine the saturation absorption in the excitation process and the resultant increasing process of the gain volume under the random laser action. The size of the gain volume increases with 1/3 power of the excitation pulse energy in the weak excitation region, and then approaches a critical value Lth when the excitation pulse energy is increased above the threshold. The dependence of Lth, as well as the dependence of the threshold excitation pulse energy on the dye concentration, transport mean free path, stimulated emission cross section and excited state lifetime were also examined. These results of the simulation well correspond to the experimental results by a two-beam spatial-correlation method.

A three-dimensional vector radiative transfer (3D-VRT) equation for inhomogeneous scatter media *

Abstract To solve 3D-VRT equation for the model of spatially inhomogeneous scatter media, the finite enclosure of the scatter media is geometrically divided, in both the vertical z and horizontal (x, y) directions, to form very thin multi-boxes. The zero-th order emission, first-order Mueller matrix of each thin box and an iterative approach of high-order radiative transfer are applied to deriving high-orderscattering and emission of whole inhomogeneous scatter media. Numerical results of polarized brightness temperature at microwave frequency from inhomogeneous scatter model such as vegetation canopy are calculated and discussed.

Calculation of Photon Path Distribution Based on Photon Behavior Analysis in a Scattering Medium

We calculated the photon path distribution (PPD) in a scattering medium based on a theoretical analysis, which utilizes the relationship between the photon intensity and photon pathlength. This PPD is defined by local photon pathlengths for photons having total pathlengths of l between the light input points and detection points. The PPD of photons that consist of the impulse response at time t (= l/c) was calculated for a 2-D model. Precise analysis of photon migration in the scattering medium is essential in order to carry out image reconstruction of diffuse optical tomography (DOT). We show the PPD at time t (the total pathlength l = ct) and demonstrate its effectiveness. Our method for describing photon migration is intuitive and allows finding weight functions in DOT.

Iterative solution of multiple scattering and emission from inhomogeneous scatter media

An iterative layering method is developed to take into account multiple scattering of random media in vector radiative transfer. By stratifying the random media into multiple thin slabs and employing the low-order approximated Mueller matrix solution of each thin slab, high-order scattering of the whole scatter media can be derived. This approach is applied to simulation of the polarized brightness temperature from an inhomogeneous snowpack, which is modeled as a layer of randomly and densely distributed spherical particles with nonuniform profiles of particle size, fractional volume, and physical temperature. Numerical results are compared with a conventional eigen-analysis approach for a uniform scatter medium. The functional dependence of multiple scattering and emission upon the characteristic parameters, such as the profiles of particle size, fractional volume, physical temperature, etc., are discussed. The results are also compared with microwave remote sensing measurements of a multilayered snowpack.

Iterative layering approach to multiple scattering and emission from inhomogenou s random scatter media

Taking into account the multiple scattering of vector radiative transfer (VRT), an iterative layering method is developed by stratifying the random media into m ulti-slabs and employing the lower-order Mueller matrix solution to derive high- order scatterings. This approach is applied to the simulation of polarized brigh tness temperature from an inhomogeneous snowpack of randomly and densely distrib uted spherical particles with nonuniform profiles of particle size, fractional v olume and physical temperature. Numerical results are compared with conventional eigen-analysis approach for a uniform scatter medium. The functional dependence of multiple scattering and emission upon the characteristic parameters such as particle size, fractional volume, physical temperature etc. are discussed, and a re also compared with the microwave remote sensing measurements of the multi-lay ers snowpack.

Interference effects in backscattering of light by a layer of a discrete random medium

Multiple backscattering of light by a layer of a discrete random medium is considered. A brief derivation of equations for describing the coherent and incoherent components of scattered light is presented. These equations are solved numerically in the approximation of doubled scattering of light by a semi-infinite medium of spherical scatterers having a size comparable with the wavelength in order to study the effect of the properties of particles on the angular dependence of interference effects. Calculations show that the half-width of the interference peak decreases upon an increase in lateral scattering by particles and that the degree of polarization has a complex angular dependence on the properties of the particles. For an optically thin layer of the medium, the relations defining the interference peak half-width and the scattering angle upon extreme linear polarization as functions of the effective refractive index are given.

Solutions of Radiative Heat Transfer in Three-Dimensional Inhomogeneous, Scattering Media

In the present study, we use the Monte-Carlo (MC) method to simulate radiative heat transfer in three-dimensional inhomogeneous scattering unit cube with black or gray walls. The results show that the averaging method of non-uniform radiative properties in each medium element has influence on the results. One reasonable averaging method has been employed in our model. In mean while, several characters of exchange factor have been employed to estimate the performance of pseudo-random numbers generator and the numerical uncertainty of MC simulation.

Iterative approach of high-order scattering solution for vector radiative transfer of inhomogeneous random media

By stratifying a random scatter media into multiple thin layers in the vertical z direction, the first-order scattering solution of each thin layer is employed to derive high-order scattering solution of whole random media. Using the Fourier transform and Mueller matrices in discrete ordinates, an iterative approach to solve high-order scattering solution of vector radiative transfer (VRT) equation is newly developed. Numerical results are well compared with the Mueller matrix solutions of the first order for a single layer medium, second order for a half-space, and the results of the discrete ordinate and eigen analysis method. It demonstrates our approach as feasible, effective and especially applicable to high-order solution of VRT for both bistatic scattering and thermal emission of inhomogeneous non-spherical scatter media.