研究目的
To investigate the impact of discretization on the Markov chain approximation of anisotropic multiple scattering through a turbid slab, recommend appropriate discretization schemes, and optimize the mathematical realization to reduce computational costs while maintaining accuracy.
研究成果
Non-uniform discretization schemes (e.g., finer resolution near boundaries and forward directions) improve accuracy in Markov chain approximations for photon multiple scattering. An iterative matrix inversion method significantly reduces computational costs (from minutes to seconds) while maintaining accuracy, enabling more efficient inverse problems and applications in diagnostics. Optimal parameters were identified, but further analytical investigation is needed for generalization.
研究不足
The study is limited to 1D turbid slabs with uniform optical properties and specific phase functions; it does not fully address the rationale behind optimal discretization parameters (e.g., OD=0.022 for boundary layers). The iterative method's stopping criterion may need adjustment for different accuracy requirements, and the approach may not generalize to highly inhomogeneous media or other scattering regimes.
1：Experimental Design and Method Selection:
The study uses Markov chain approximations to model photon multiple scattering, comparing with Monte Carlo simulations as a benchmark. Non-uniform discretization schemes for optical depth (OD) and zenith angle are tested, and an iterative matrix inversion method is proposed to reduce computational costs.
2：Sample Selection and Data Sources:
Simulations are performed for turbid slabs with uniform OD distributions and three different phase functions (Mie scattering with specific parameters).
3：List of Experimental Equipment and Materials:
Computational tools include MATLAB for Markov chain calculations and C language for Monte Carlo simulations, run on an Intel Xeon X5650 CPU.
4：Experimental Procedures and Operational Workflow:
The domain is discretized into states; transition probabilities are calculated based on scattering physics. For Markov chain, matrix manipulations are performed; for Monte Carlo,
5：5 billion photons are simulated per case. Results are compared to evaluate errors and computational costs. Data Analysis Methods:
Absolute relative error is calculated between Markov chain and Monte Carlo results. Computational times are measured, and iterative methods are assessed for efficiency.
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