Invariance property in inhomogeneous scattering media with refractive-index mismatch

Tommasi, Federico; Fini, Lorenzo; Martelli, Fabrizio; Cavalieri, Stefano

doi:10.1103/physreva.102.043501

Cited by 20 publications

(30 citation statements)

References 43 publications

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“…One important application of the study of path length is to study the optical absorption of a refractive object. If we define the absorption A as the fraction of rays that are absorbed compared to the total number of incident rays, it can be expressed in terms of the path length distribution as [5,29]:…”

Section: Absorption In a Low Scattering Samplementioning

confidence: 99%

“…Rays are then refracted at the boundary and may also be reflected internally or externally, which may increase the path length of some internal rays. Even then, it has been argued recently [28,29] that the mean path length invariance remains valid for scattering samples, and is simply modified by a factor s 2 :…”

mentioning

confidence: 99%

“…Application to physical systems. To investigate the generality of these results, we now consider less symmetric geometries, for which numerical calculations (Monte Carlo ray tracing [29]) can be used to derive L 0 . Figure 4 summarizes these results.…”

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confidence: 99%

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Mean path length inside nonscattering refractive objects

Majic

Somerville

2021

Phys. Rev. A

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Section: Absorption In a Low Scattering Samplementioning

confidence: 99%

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confidence: 99%

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Mean path length inside nonscattering refractive objects

Majic

Somerville

2021

Phys. Rev. A

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“…If such entrance condition is assumed, the result for leads to, at a first glance, quite counter-intuitive and surprising value: a constant quantity that only depends on the basic geometric characteristics of the medium regardless of the distribution of the scattering properties. In the optical case, these results can be generalized, also taking into account the refractive index mismatch between the external environment and the medium and also the mismatches among different regions of the same medium 52 . Indicating with V , S and P the volume, the surface (for a 3D medium) and the perimeter (for a 2D medium) respectively, the predicted values by the IP, in 2D and 3D domains, assume very simple forms 52 : …”

Section: Introductionmentioning

confidence: 99%

“…In the optical case, these results can be generalized, also taking into account the refractive index mismatch between the external environment and the medium and also the mismatches among different regions of the same medium 52 . Indicating with V , S and P the volume, the surface (for a 3D medium) and the perimeter (for a 2D medium) respectively, the predicted values by the IP, in 2D and 3D domains, assume very simple forms 52 : …”

Section: Introductionmentioning

confidence: 99%

Verification method of Monte Carlo codes for transport processes with arbitrary accuracy

Martelli

Tommasi

Sassaroli

et al. 2021

Sci Rep

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In this work, we present a robust and powerful method for the verification, with arbitrary accuracy, of Monte Carlo codes for simulating random walks in complex media. Such random walks are typical of photon propagation in turbid media, scattering of particles, i.e., neutrons in a nuclear reactor or animal/humans’ migration. Among the numerous applications, Monte Carlo method is also considered a gold standard for numerically “solving” the scalar radiative transport equation even in complex geometries and distributions of the optical properties. In this work, we apply the verification method to a Monte Carlo code which is a forward problem solver extensively used for typical applications in the field of tissue optics. The method is based on the well-known law of average path length invariance when the entrance of the entities/particles in a medium obeys to a simple cosine law, i.e., Lambertian entrance, and annihilation of particles inside the medium is absent. By using this law we achieve two important points: (1) the invariance of the average path length guarantees that the expected value is known regardless of the complexity of the medium; (2) the accuracy of a Monte Carlo code can be assessed by simple statistical tests. We will show that we can reach an arbitrary accuracy of the estimated average pathlength as the number of simulated trajectories increases. The method can be applied in complete generality versus the scattering and geometrical properties of the medium, as well as in presence of refractive index mismatches in the optical case. In particular, this verification method is reliable to detect inaccuracies in the treatment of boundaries of finite media. The results presented in this paper, obtained by a standard computer machine, show a verification of our Monte Carlo code up to the sixth decimal digit. We discuss how this method can provide a fundamental tool for the verification of Monte Carlo codes in the geometry of interest, without resorting to simpler geometries and uniform distribution of the scattering properties.

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Anomalous Radiative Transfer in Heterogeneous Media

Tommasi,

Pattelli,

Cavalieri

et al. 2024

Advcd Theory and Sims

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Monte Carlo (MC) simulations are the gold standard for describing various transport phenomena and have largely contributed to the understanding of these processes. However, while their implementation for classical transport governed by exponential step‐length distributions is well‐established, widely accepted approaches are still lacking for the more general class of anomalous transport phenomena. In this work, a set of rules for performing MC simulations in anomalous diffusion media is identified, which is also applicable in the case of finite‐size geometries and/or heterogeneous inclusions. The results are presented in the context of radiative transfer, however their implications extend to all types of anomalous transport. The proposed set of rules exhibits full compatibility with the pathlength invariance property for random trajectories, and with the important radiometric concept of fluence. Additionally, it reveals the counter‐intuitive possibility of introducing interfaces between independent subdomains with identical properties, which arise from the fact that non‐exponential step‐length distributions have a “memory” that can in principle be reset when traversing a boundary. These results have far‐reaching consequences not just for the physical interpretation of the corrections required to handle these discontinuities, but also for their experimental verification, due to their expected effects on the observable pathlength distributions.

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Invariance property in inhomogeneous scattering media with refractive-index mismatch

Cited by 20 publications

References 43 publications

Mean path length inside nonscattering refractive objects

Mean path length inside nonscattering refractive objects

Verification method of Monte Carlo codes for transport processes with arbitrary accuracy

Anomalous Radiative Transfer in Heterogeneous Media

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