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The diffusion coefficient depends on absorption

Optica Publishing Group
Optics Letters
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The diffusion approximation is widely invoked to model the propagation of light in turbid media. When absorption is not weak in comparison with scattering, there is currently a controversy as to if, and how, the diffusion coefficient depends on absorption. Here it is shown that better agreement with random walk simulation is obtained if the photon-diffusion coefficient is taken as D = c / 3 μ s ′ + μ a . One can reconcile this result with recent work advocating D = c / 3 μ s ′ by noting that the diffusion equation must be correspondingly changed to a telegrapher’s equation.
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... Here, J (r) is a source term. The quantity , which is the diffusivity divided by the light velocity in the material1 = / is given by [20] ...
... where 0 (r, ) is the solution of the equation with = 0. Therefore, it was argued in [21][22][23] that the diffusivity should not depend on the absorptivity . The counter argument is that the proper generalization of the steady-state diffusion equation (2) is not equation (5), but a damped telegrapher's equation [19,20], which obeys the proper scaling. However, this equation should reduce to the wave equation of light for short times [20]. ...
... The counter argument is that the proper generalization of the steady-state diffusion equation (2) is not equation (5), but a damped telegrapher's equation [19,20], which obeys the proper scaling. However, this equation should reduce to the wave equation of light for short times [20]. This condition enforces the form (3) of the diffusivity, rather than the form = [3( + )] −1 according to the conventional literature (e.g. ...
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... Here J (r) is a source term. The quantity D, which is the diffusivity divided by the light velocity in the material 2 v = c/n is given by [20] ...
... The counter argument is, that the proper generalization of the steady-state diffusion equation Eq. (2) is not Eq. (5), but a damped telegrapher's equation [20], which obeys the proper scaling. However, for this property to be obeyed, the absorptivity dependence of the diffusivity is given by (3) and not by D = [3(λ a + λ t )] −1 according to the conventional literature (e.g. ...
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... The optical parameters for the various transmission medium used in the study is specified in Fig.3i. 72,73 The LED domain uses the optical parameters of pure water. This is to reasonably simplify the model to simulate the LED domain as a whole to be the light source. ...
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... where µ a and a respectively denote the absorption coefficient and the adjusting numerical factor which depends on the form of the diffusion equation [26,27]. When a = 1 and 0, Eq. (3) reduces to the classical (D = [3(µ s ′ + µ a )] −1 ) and newly proposed (D = (3µ s ′ ) −1 ) [28] definitions of the diffusion coefficient. ...
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