Modified Kubelka-Munk equations for localized waves inside a layered medium

Haney, Matthew M.; Wijk, Kasper van

doi:10.1103/physreve.75.036601

Cited by 8 publications

(4 citation statements)

References 23 publications

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“…It is decay by −1/δ t , which is obtained in [HvW,(A.8)]. However even for the γ = 0.5 case, the penetration to outside does not finish because the total density inside [−50, 50] decreases as in Figure 12.…”

Section: Localization In Poisson Point Process Of the B-impuritymentioning

confidence: 54%

New theory of diffusive and coherent nature of optical wave via a quantum walk

et al. 2017

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We propose a new theory on a relation between diffusive and coherent nature in one dimensional wave mechanics based on a quantum walk. It is known that the quantum walk in homogeneous matrices provides the coherent property of wave mechanics. Using the recent result of a localization phenomenon in a one-dimensional quantum walk (Konno Quantum Inf. Proc. (2010) 9 405-418), we numerically show that the randomized localized matrices suppress the coherence and give diffusive nature.

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Section: Localization In Poisson Point Process Of the B-impuritymentioning

confidence: 54%

New theory of diffusive and coherent nature of optical wave via a quantum walk

et al. 2017

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“…Derived from the K-M theory, the most widely used equation for spectral measurement can be expressed by Eq. (5) , where

and

are, respectively, absorption and reflection [ 40 , 41 , 42 , 43 ].

…”

Section: Methodsmentioning

confidence: 99%

Using an ultra-compact optical system to improve lateral flow immunoassay results quantitatively

Chiu

Kong²,

Chueh³

et al. 2022

Heliyon

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“…Youngquist et al [15] applied the model in optical coherence tomography and Haney and van Wijk [16] in geology. Hébert and Becker [17] examine the relation between continuous and lattice versions of Kubelka-Munk in an effort to give a more physical interpretation of the two-flux model.…”

Section: Introductionmentioning

confidence: 99%

Light scattering as a Poisson process and first-passage probability

Zeller¹,

Cordery

2020

J. Stat. Mech.

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A particle entering a scattering and absorbing medium executes a random walk through a sequence of scattering events. The particle ultimately either achieves first-passage, leaving the medium, or it is absorbed. The Kubelka–Munk model describes a flux of such particles moving perpendicular to the surface of a plane-parallel medium with a scattering rate and an absorption rate. The particle path alternates between the positive direction into the medium and the negative direction back towards the surface. Backscattering events from the positive to the negative direction occur at local maxima or peaks, while backscattering from the negative to the positive direction occur at local minima or valleys. The probability of a particle avoiding absorption as it follows its path decreases exponentially with the path-length λ. The reflectance of a semi-infinite slab is therefore the Laplace transform of the distribution of path-length that ends with a first-passage out of the medium. In the case of a constant scattering rate the random walk is a Poisson process. We verify our results with two iterative calculations, one using the properties of iterated convolution with a symmetric kernel and the other via direct calculation with an exponential step-length distribution. We present a novel demonstration, based on fluctuation theory of sums of random variables, that the first-passage probability as a function of the number of peaks n in the alternating path is a step-length distribution-free combinatoric expression involving Catalan numbers. Counting paths with backscattering on the real half-line results in the same Catalan number coefficients as Dyck paths on the whole numbers. Including a separate forward-scattering Poisson process results in a combinatoric expression related to counting Motzkin paths. We therefore connect walks on the real line to discrete path combinatorics.

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Modified Kubelka-Munk equations for localized waves inside a layered medium

Cited by 8 publications

References 23 publications

New theory of diffusive and coherent nature of optical wave via a quantum walk

New theory of diffusive and coherent nature of optical wave via a quantum walk

Using an ultra-compact optical system to improve lateral flow immunoassay results quantitatively

Light scattering as a Poisson process and first-passage probability

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