Scaling Law for Photon Transmission through Optically Turbid Slabs Based on Random Walk Theory

Li, Xuesong; Ma, Lin

doi:10.3390/app2010160

Cited by 6 publications

(4 citation statements)

References 13 publications

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“…Beyond using RTE and MC approaches, many studies focused on developing reduced models for multiple scattering processes. Such efforts include the Random Walk theorem [11,12], empirical predictions [13], and addingdoubling methods [14], among others. These methods typically use simplified analytical expressions to predict the behavior of experimental details, such as the distribution of total transmission, average cosine of scattering, and distance traveled.…”

Section: Reduced Models For Multiple Scattering Simulationmentioning

confidence: 99%

Advances in the simulation of light–tissue interactions in biomedical engineering

2019

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Monte Carlo (MC) simulation for light propagation in scattering and absorbing media is the gold standard for studying the interaction of light with biological tissue and has been used for years in a wide variety of cases. The interaction of photons with the medium is simulated based on its optical properties and the original approximation of the scattering phase function. Over the past decade, with the new measurement geometries and recording techniques invented also the corresponding sophisticated methods for the description of the underlying light-tissue interaction taking into account realistic parameters and settings were developed. Applications, such as multiple scattering, optogenetics, optical coherence tomography, Raman spectroscopy, polarimetry and Mueller matrix measurement have emerged and are still constantly improved. Here, we review the advances and recent applications of MC simulation for the active field of the life sciences and the medicine pointing out the new insights enabled by the theoretical concepts.

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Section: Reduced Models For Multiple Scattering Simulationmentioning

confidence: 99%

Advances in the simulation of light–tissue interactions in biomedical engineering

2019

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“…Figure 3, to further study the performance of Markov chain approximations. Note that other algorithms, such as the random walk [7], adding doubling [34], and the imperialist competitive algorithm [35] are also frequently used to evaluate such computational tasks. Since we have incorporated such comparisons in our previous work [22], we will not elaborate on such comparisons in this work.…”

Section: Uniform Discretizationsmentioning

confidence: 99%

“…The reason that simplification assumptions usually do not apply well for such problems is that the multiple scattering phenomenon is intrinsically stochastic, particularly in the intermediate regime where the optical depth (OD) of the media is somewhere between two and 10. Many have attempted to interpret multiple scattering through modeling using Monte Carlo methods [1][2][3][4], or other approaches grounded on the random walk theory or empirical approximations [5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Markov Chain Investigation of Discretization Schemes and Computational Cost Reduction in Modeling Photon Multiple Scattering

Yang

Xiao

et al. 2018

Applied Sciences

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Establishing fast and reversible photon multiple scattering algorithms remains a modeling challenge for optical diagnostics and noise reduction purposes, especially when the scattering happens within the intermediate scattering regime. Previous work has proposed and verified a Markov chain approach for modeling photon multiple scattering phenomena through turbid slabs. The fidelity of the Markov chain method has been verified through detailed comparison with Monte Carlo models. However, further improvement to the Markov chain method is still required to improve its performance in studying multiple scattering. The present research discussed the efficacy of non-uniform discretization schemes and analyzed errors induced by different schemes. The current work also proposed an iterative approach as an alternative to directly carrying out matrix inversion manipulations, which would significantly reduce the computational costs. The benefits of utilizing non-uniform discretization schemes and the iterative approach were confirmed and verified by comparing the results to a Monte Carlo simulation.

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“…The most commonly seen methods to solve the multiple scattering problem are solving the radiative transfer equation (RTE) [5][6][7] or using Monte Carlo simulations [4,[8][9][10]. As an analytical method, RTE can be solved to obtain the exact solutions, while it is challenging and time-consuming unless strong assumptions are made [11][12][13][14]. The Monte Carlo simulation method is also popular in that the algorithm itself is relatively simple.…”

Section: Introductionmentioning

confidence: 99%

Numerical Study of Turbid Slab Optical Properties Reconstruction from Multiple Scattering Signals Using Time-Based Markov Chain Model

Pan

et al. 2021

Applied Sciences

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The reconstruction of optical properties for opaque mediums is highly desired for medical, atmosphere and aerosol applications. However, the modeling and reconstruction process is highly related with multiple scattering phenomena, which elevates both the complexity and computational costs for such efforts. This work introduces a time-based Markov chain method, which uses a sparse transition matrix to represent the likelihood for a photon to transit in the turbid media. The accuracy of the time-based Markov chain model was verified against the forwarding calculations of the scattering-based Markov chain model and Monte Carlo simulations. Then, reconstruction was performed with backscattered photon angular distributions. Based on the characteristics of the sparse transition matrix, the optical properties (droplet diameters) could be obtained layer by layer with transmitted photon distributions at different time durations. It is shown that the time-based Markov chain model can reconstruct the optical properties of a turbid slab with satisfactory accuracy and lower computational costs.

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Scaling Law for Photon Transmission through Optically Turbid Slabs Based on Random Walk Theory

Cited by 6 publications

References 13 publications

Advances in the simulation of light–tissue interactions in biomedical engineering

Advances in the simulation of light–tissue interactions in biomedical engineering

Markov Chain Investigation of Discretization Schemes and Computational Cost Reduction in Modeling Photon Multiple Scattering

Numerical Study of Turbid Slab Optical Properties Reconstruction from Multiple Scattering Signals Using Time-Based Markov Chain Model

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