Multiple path analysis of reflectance from turbid media

Rogers, GL

doi:10.1364/josaa.25.002879

Cited by 17 publications

(15 citation statements)

References 15 publications

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“…semi-infinite medium, T 5 0 and the second term in R vanishes with the result reducing to the reflectance as found in Ref. 10.…”

Section: Reflection and Transmissionsupporting

confidence: 66%

“…In the following the reflection and transmission path length probability densities for a finite thickness medium are obtained by considering a photon random walk within the medium . One derives expressions for μ R ( ξ ) and μ T ( ξ ) the probability densities for path length ξ before reflecting or transmitting, respectively.…”

Section: Path Length Probability Densitiesmentioning

confidence: 99%

“…A path length probability density is found by considering a photon random walk through the medium. Reference treats the case of a semi‐infinite medium, for which there is only reflection. The current work uses a random walk analysis to calculate the reflection and transmission of a finite thickness turbid medium.…”

Section: Introductionmentioning

confidence: 99%

“…Another numerical technique is a Monte Carlo simulation. 9 An article 10 has recently appeared that uses a photon random walk to calculate the reflectance of light from turbid media. This approach uses the Beer-Lambert law 2 but for each path individually.…”

Section: Introductionmentioning

confidence: 99%

“…Because different rays have different path lengths in turbid media, and Ref. 10 applies the Beer-Lambert law to each path and all paths are summed, with each path weighted by its probability. A path length probability density is found by considering a photon random walk through the medium.…”

Section: Introductionmentioning

confidence: 99%

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Random walk analysis for reflection and transmission of turbid media

Rogers

2016

Color Research & Application

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The reflection and transmission of light from a turbid slab is determined by considering a photon random walk within the medium. The reflection and transmission is obtained using the Beer-Lambert law on each path through the slab. Path length probability densities are derived, then all paths are summed weighted by their probabilities. The results are simple expressions for the reflection and the transmission in terms of the physical properties of the medium.

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“…semi-infinite medium, T 5 0 and the second term in R vanishes with the result reducing to the reflectance as found in Ref. 10.…”

Section: Reflection and Transmissionsupporting

confidence: 66%

Section: Path Length Probability Densitiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Random walk analysis for reflection and transmission of turbid media

Rogers

2016

Color Research & Application

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Fixed point characterizations of continuous univariate probability distributions and their applications

Betsch

Ebner

2019

Ann Inst Stat Math

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By extrapolating the explicit formula of the zero-bias distribution occurring in the context of Stein's method, we construct characterization identities for a large class of absolutely continuous univariate distributions. Instead of trying to derive characterizing distributional transformations that inherit certain structures for the use in further theoretic endeavours, we focus on explicit representations given through a formula for the density-or distribution function. The results we establish with this ambition feature immediate applications in the area of goodness-of-fit testing. We draw up a blueprint for the construction of tests of fit that include procedures for many distributions for which little (if any) practicable tests are known.To illustrate this last point, we construct a test for the Burr Type XII distribution for which, to our knowledge, not a single test is known aside from the classical universal procedures.MSC 2010 subject classifications. Primary 62E10 Secondary 60E10, 62G10Over the last decades, Stein's method for distributional approximation has become a viable tool for proving limit theorems and establishing convergence rates. At it's heart lies the well-known Stein characterization which states that a real-valued random variable Z has a standard normal distribution if, and only if,holds for all functions f of a sufficiently large class of test functions. To exploit this characterization for testing the hypothesisof normality, where P X is the distribution of a real-valued random variable X, against general alternatives, Betsch and Ebner (2019b) used that (1.1) can be untied from the class of test functions with the help of the so-called zero-bias transformation introduced by Goldstein and Reinert (1997). To be specific, a real-valued random variable X * is said to have the X-zero-bias distri-bution ifholds for any of the respective test functions f . If EX = 0 and Var(X) = 1, the X-zero-bias distribution exists and is unique, and it has distribution function(1.3)By (1.1), the standard Gaussian distribution is the unique fixed point of the transformation P X → P X * . Thus, the distribution of X is standard normal if, and only if,where F X denotes the distribution function of X. In the spirit of characterization-based goodnessof-fit tests, an idea introduced by Linnik (1962), this fixed point property directly admits a new class of testing procedures as follows. Letting T X n be an empirical version of T X and F n the empirical distribution function, both based on the standardized sample, Betsch and Ebner (2019b) proposed a test for (1.2) based on the statisticwhere w is an appropriate weight function, which, in view of (1.4), rejects the normality hypothesis for large values of G n . As these tests have several desirable properties such as consistency against general alternatives, and since they show a very promising performance in simulations, we devote this work to the question to what extent the fixed point property and the class of goodness-of-fit procedures may be generalized to othe...

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How Physicists Made Stable Lévy Processes Physically Plausible

Schınckus

2013

Braz J Phys

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Multiple path analysis of reflectance from turbid media

Cited by 17 publications

References 15 publications

Random walk analysis for reflection and transmission of turbid media

Random walk analysis for reflection and transmission of turbid media

Fixed point characterizations of continuous univariate probability distributions and their applications

How Physicists Made Stable Lévy Processes Physically Plausible

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