Markov chain solution of photon multiple scattering through turbid slabs

Area of Science:

• Optics and Photonics
• Computational Physics
• Applied Mathematics

Background:

• Photon multiple scattering in turbid media is crucial for applications like medical imaging and atmospheric science.
• Existing methods like Monte Carlo simulations face challenges with complex scattering functions and inversions.
• Anisotropic scattering, particularly Mie scattering, complicates accurate modeling.

Purpose of the Study:

• To develop a novel Markov Chain solution for modeling photon multiple scattering in turbid slabs.
• To address the limitations of current stochastic methods in handling complex phase functions and enabling practical inversions.
• To provide a computationally efficient alternative for analyzing light transport in scattering media.

Main Methods:

• Formulating a Markov Chain model for photon transport through turbid media.
• Incorporating anisotropic scattering processes, specifically Mie scattering.
• Converting the scattering problem into a matrix form for efficient computation.
• Solving for transmitted and reflected photon angular distributions using matrix multiplications.

Main Results:

• The Markov Chain model demonstrates strong agreement with Monte Carlo simulations for various media.
• The model successfully handles non-uniform phase functions and absorbing media.
• It provides accurate transmitted and reflected photon angular distributions.
• The matrix-based approach facilitates practical inversions and diagnostics.

Conclusions:

• The proposed Markov Chain solution offers a robust and efficient method for modeling photon multiple scattering.
• This approach overcomes limitations of traditional Monte Carlo methods, enabling practical diagnostic reconstructions.
• Potential applications span medical diagnosis, spray analysis, and atmospheric sciences, enhancing light interaction analysis.