2010
DOI: 10.1364/oe.18.009266
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Light diffusion in a turbid cylinder II Layered case

Abstract: This paper is the second of two dealing with light diffusion in a turbid cylinder. The diffusion equation was solved for an N-layered finite cylinder. Solutions are given in the steady-state, frequency, and time domains for a point beam incident at an arbitrary position of the first layer and for a circular flat beam incident at the middle of the cylinder top. For special cases the solutions were compared to other solutions of the diffusion equation showing excellent agreement. In addition, the derived solutio… Show more

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Cited by 60 publications
(90 citation statements)
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“…Simulations have been performed to compare the code to the total diffuse transmittance and total reflectance of van de Hulst, 34 the total reflectance as calculated in the multi layer diffusion model of Liemert and Kienle, 35 the temporal point-spread functions (TPSFs) presented by Martelli et al, 36 and the internal fluence for an optically inhomogeneous sphere inside a semi-infinite slab as derived by Boas et al 37 In each case, excellent agreement is found in regions where the DA is valid.…”
Section: Validationmentioning
confidence: 99%
“…Simulations have been performed to compare the code to the total diffuse transmittance and total reflectance of van de Hulst, 34 the total reflectance as calculated in the multi layer diffusion model of Liemert and Kienle, 35 the temporal point-spread functions (TPSFs) presented by Martelli et al, 36 and the internal fluence for an optically inhomogeneous sphere inside a semi-infinite slab as derived by Boas et al 37 In each case, excellent agreement is found in regions where the DA is valid.…”
Section: Validationmentioning
confidence: 99%
“…In this section we aim to review the theoretical approach given in reference 15 . Figure 1 shows a N-layered cylinder of height L and radius R. The ith layer has an absorption coefficient µ a,i , a reduced scattering coefficient µ s ′ ,i , a refractive index n i and a depth l i (so that L = ∑ N i=1 l i ).…”
Section: Theorymentioning
confidence: 99%
“…This approach was soon extended to three, four and eventually N layers, with the expected increasing complexity of the obtained expressions 12;13 . A better approach has been given by Liemert et al 14;15 , in which laterally finite cylinders instead of infinitely extended parallelepipeds were modeled, making the resulting expressions both, easier to handle and faster to run in computers.…”
Section: Introductionmentioning
confidence: 99%
“…[18][19][20][21][22] A particularly complete set of solutions in time domain and frequency domain in a number of geometries were presented by Arridge et al 18 in 1992; the DPFs could be obtained from the explicit solutions derived for the mean time of flight in a variety of geometries using the zero boundary condition. In 2001, Sassaroli et al 22 developed the corresponding solutions of time-resolved DE using the more widely used extrapolated boundary condition (EBC) 21,23,24 for curved geometries including infinite cylinder and sphere; the DPFs for infinite cylinder and sphere can also be derived or computed from the results that were in excellent agreement with Monte Carlo (MC) simulations.…”
Section: Introductionmentioning
confidence: 99%