Photon diffusion coefficient in an absorbing medium

Aronson, Raphael; Corngold, Noel

doi:10.1364/josaa.16.001066

Cited by 94 publications

(62 citation statements)

References 15 publications

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“…It must be noted that it is yet to reach a consensus regarding whether the diffusion coefficient in steady-state measurement shall include the absorption coefficient. [29][30][31][32][33] We argue that, as the DPF is unbiasedly defined by the use of mean time of flight through time-dependent DE, the definition of DPF in steady-state may agree with the one in the time-resolved condition only if the diffusion coefficient is not dependent upon the absorption coefficient. Therefore, this study uses the diffusion coefficient as D ¼ 1∕ð3μ 0 s Þ.…”

Section: Geometries Considered and Analyticmentioning

confidence: 91%

On the geometry dependence of differential pathlength factor for near-infrared spectroscopy. I. Steady-state with homogeneous medium

Piao

Barbour

Graber³

et al. 2015

J. Biomed. Opt

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Abstract. This work analytically examines some dependences of the differential pathlength factor (DPF) for steady-state photon diffusion in a homogeneous medium on the shape, dimension, and absorption and reduced scattering coefficients of the medium. The medium geometries considered include a semi-infinite geometry, an infinite-length cylinder evaluated along the azimuthal direction, and a sphere. Steady-state photon fluence rate in the cylinder and sphere geometries is represented by a form involving the physical source, its image with respect to the associated extrapolated half-plane, and a radius-dependent term, leading to simplified formula for estimating the DPFs. With the source-detector distance and medium optical properties held fixed across all three geometries, and equal radii for the cylinder and sphere, the DPF is the greatest in the semi-infinite and the smallest in the sphere geometry. When compared to the results from finite-element method, the DPFs analytically estimated for 10 to 25 mm source-detector separations on a sphere of 50 mm radius with μ a ¼ 0.01 mm −1 and μ 0 s ¼ 1.0 mm −1 are on average less than 5% different. The approximation for sphere, generally valid for a diameter ≥20 times of the effective attenuation pathlength, may be useful for rapid estimation of DPFs in near-infrared spectroscopy of an infant head and for short source-detector separation. © The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.

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Section: Geometries Considered and Analyticmentioning

confidence: 91%

On the geometry dependence of differential pathlength factor for near-infrared spectroscopy. I. Steady-state with homogeneous medium

Piao

Barbour

Graber³

et al. 2015

J. Biomed. Opt

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“…Notice that here we take into account unavoidable losses to calculate ℓ ⋆ , as in Refs. [44][45][46]. For lossless scatterers σ ext = σ sca , so that ℓ ⋆ = ℓ sca /(1 − cos θ ), where ℓ sca = 1/(ρσ sca ) is the scattering mean free path.…”

Section: B Lorenz-mie Efficiencies and Multiple Scatteringmentioning

confidence: 99%

Electromagnetic energy and negative asymmetry parameters in coated magneto-optical cylinders: Applications to tunable light transport in disordered systems

2016

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We investigate electromagnetic scattering of normally irradiated gyrotropic, magneto-optical coreshell cylinders using Lorenz-Mie theory. A general expression for time-averaged electromagnetic energy inside a coated gyroelectric and gyromagnetic scatterer is derived. Using realistic material parameters for a silica core and InSb shell, we calculate the stored electromagnetic energy and the scattering anisotropy. We show that the application of an external magnetic field along the cylinder axis induces a drastic decrease in electromagnetic absorption in a frequency range in the terahertz, where absorption is maximal in the absence of the magnetic field. We demonstrate not only that the scattering anisotropy can be externally tuned by applying a magnetic field, but also that it reaches negative values in the terahertz range even in the dipolar regime. We also show that this preferential backscattering response results in an anomalous regime of multiple light scattering from a collection of magneto-optical core-shell cylinders, in which the extinction mean free path is longer than the transport mean free path. By additionally calculating the energy-transport velocity and diffusion coefficient, we demonstrate an unprecedented degree of external control of multiple light scattering, which can be achieved by either applying an external magnetic field or varying the temperature.

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“…Here, l s is the scattering coefficient and g is the anisotropy factor, which equals the average cosine of the scattering angle. When the absorption coefficient is not small compared to the reduced scattering coefficient, the accuracy of the cw diffusion approximation decreases, as has been shown earlier [4][5][6][7][8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 96%

“…Application of this latter approach led to discrepancies, because the results with this diffusion coefficient for the steady-state solution calculated with this approach are not in agreement with the more rigorous solution of the equation of transport [6][7][8][9][10][11][12]. The apparent diffusion coefficient of the diffusion equation, which is in agreement with the rigorous solution of the transport equation, depends on the absorption coefficient as well [10,11,23]. Furthermore, it depends on the phase function, which describes the angular distribution of the scatterers [9].…”

Section: Introductionmentioning

confidence: 99%

Telegrapher’s equation for light derived from the transport equation

Hoenders

Graaff

2005

Optics Communications

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Shortcomings of diffusion theory when applied to turbid media such as biological tissue makes the development of more accurate equations desirable. Several authors developed telegrapherÕs equations in the well known P 1 approximation. The method used in this paper is different: it is based on the asymptotic evaluation of the solutions of the equation of radiative transport with respect to place and time for all values of the albedo. Various coefficients for the telegrapherÕs equations were derived, restricted to the case of isotropic scattering, and their properties are discussed. A correct diffusion coefficient for the stationary case could be obtained. However, this solution did not lead to the correct phase velocity. Correct phase velocities in combination with a correct diffusion coefficient were found for a dispersion relation that corresponds with anisotropic Henyey-Greenstein scattering with g = 0.22. It provides a time-dependent description of the fluence rate with validity for all values of the albedo.

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Photon diffusion coefficient in an absorbing medium

Cited by 94 publications

References 15 publications

On the geometry dependence of differential pathlength factor for near-infrared spectroscopy. I. Steady-state with homogeneous medium

On the geometry dependence of differential pathlength factor for near-infrared spectroscopy. I. Steady-state with homogeneous medium

Electromagnetic energy and negative asymmetry parameters in coated magneto-optical cylinders: Applications to tunable light transport in disordered systems

Telegrapher’s equation for light derived from the transport equation

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