Transient Discrete Ordinate Method and Experiments of Pulsed Radiative Transfer Through Scattering Absorbing Media

Volume 4 ◽  
2004 ◽  
Author(s):  
Ashish Trivedi ◽  
Soumyadipta Basu ◽  
Kunal Mitra
Keyword(s):  
Radiative Transfer ◽  
Pulse Laser ◽  
Transfer Equation ◽  
Radiative Transfer Equation ◽  
Short Pulse ◽  
Laser Source ◽  
Discrete Ordinates ◽  
Experimental Measurements ◽  
Short Pulse Laser ◽  
Absorbing Media

The objective of this paper is to validate the solution of transient radiation transfer equation with experimental measurements using short pulse laser source having a Gaussian distribution. The transient radiative transfer equation for the case of short pulse laser propagation through scattering absorbing media such as tissue is an integrodifferential equation and is therefore complicated to solve. The time-dependent discrete ordinates method in conjunction with high order upwind piecewise parabolic interpolation scheme is used to solve the transient radiative transfer equation for the case of anisotropically scattering absorbing medium having a rectangular geometry in which an inhomogeneity is embedded. A parametric study involving different scattering and absorption coefficients of the medium, inhomogeneity and inhomogeneity size as well as the detector position is performed. The numerical modeling results and experimental measurements are in excellent agreement for various parameters studied in this paper.

An Efficient Sparse Finite Element Solver for the Radiative Transfer Equation

2009 ◽  
Author(s):  
Gisela Widmer
Keyword(s):  
Linear System ◽  
Radiative Transfer ◽  
Transfer Equation ◽  
Degrees Of Freedom ◽  
Radiative Transfer Equation ◽  
Three Dimensional ◽  
Discrete Ordinates ◽  
Five Dimensions ◽  
Computational Costs ◽  
Dimensional Domain

The stationary monochromatic radiative transfer equation (RTE) is posed in five dimensions, with the intensity depending on both a position in a three-dimensional domain as well as a direction. For non-scattering radiative transfer, sparse finite elements [1, 2] have been shown to be an efficient discretization strategy if the intensity function is sufficiently smooth. Compared to the discrete ordinates method, they make it possible to significantly reduce the number of degrees of freedom N in the discretization with almost no loss of accuracy. However, using a direct solver to solve the resulting linear system requires O(N3) operations. In this paper, an efficient solver based on the conjugate gradient method (CG) with a subspace correction preconditioner is presented. Numerical experiments show that the linear system can be solved at computational costs that are nearly proportional to the number of degrees of freedom N in the discretization.

Analytical solution for temperature field in thin film initially heated by a short-pulse laser source

2005 ◽  
Vol 41 (12) ◽  
pp. 1077-1084 ◽  
Author(s):  
B. S. Yilbas ◽  
M. Pakdemirli ◽  
S. Bin Mansoor
Keyword(s):  
Thin Film ◽  
Temperature Field ◽  
Analytical Solution ◽  
Pulse Laser ◽  
Short Pulse ◽  
Laser Source ◽  
Short Pulse Laser

Error analysis and calibration of a spectroscopic Mueller matrix polarimeter using a short-pulse laser source

2002 ◽  
Vol 13 (10) ◽  
pp. 1563-1573 ◽  
Author(s):  
B Boulbry ◽  
B Le Jeune ◽  
B Bousquet ◽  
F Pellen ◽  
J Cariou ◽  
...  
Keyword(s):  
Error Analysis ◽  
Pulse Laser ◽  
Short Pulse ◽  
Mueller Matrix ◽  
Laser Source ◽  
Short Pulse Laser

Propagation of Ultra-Short-Pulse Radiation in Participating Media: A Laguerre-Galerkin Solution

2007 ◽  
Author(s):  
Tuba Okutucu ◽  
Yaman Yener
Keyword(s):  
Radiative Transfer ◽  
Transfer Equation ◽  
Radiative Transfer Equation ◽  
Transfer Problem ◽  
Short Pulse ◽  
Optical Tomography ◽  
Time Derivative ◽  
Product Analysis ◽  
Participating Media ◽  
Radiative Transfer Problem

Transient analysis of the radiative transfer problem in participating media has become essential due to the recent applications involving extremely small time scales. In classical radiation problems, the time derivative term in the radiative transfer equation has a negligible order of magnitude compared to the others. Lasers of pico- to femtosecond pulse durations are now being used to investigate the properties of scattering and absorbing media in such applications as, optical tomography, combustion product analysis, and remote sensing. For such applications, the time derivative in the radiative transfer equation can no longer be neglected. Numerous approaches such as, integral formulation, direct numerical approach, discrete ordinates method, Monte Carlo simulations, and Galerkin technique have been introduced for the solution of transient radiative transfer problems in participating media. In the present work, Laguerre-Galerkin solutions for both rectangular and Gaussian incident pulse profiles are presented.

Solution of the Radiative Transfer Equation in Three-Dimensional Participating Media Using a Hybrid Discrete Ordinates: Spherical Harmonics Method

2012 ◽  
Vol 134 (11) ◽  
Author(s):  
Maathangi Sankar ◽  
Sandip Mazumder
Keyword(s):  
Monte Carlo ◽  
Radiative Transfer ◽  
Spherical Harmonics ◽  
Hybrid Method ◽  
Transfer Equation ◽  
Large Range ◽  
Radiative Transfer Equation ◽  
Three Dimensional ◽  
Discrete Ordinates ◽  
Medium Component

In this article, a new hybrid solution to the radiative transfer equation (RTE) is proposed. Following the modified differential approximation (MDA), the radiation intensity is first split into two components: a “wall” component, and a “medium” component. Traditionally, the wall component is determined using a viewfactor-based surface-to-surface exchange formulation, while the medium component is determined by invoking the first-order spherical harmonics (P1) approximation. Recent studies have shown that although the MDA approach is accurate over a large range of optical thicknesses, it is prohibitive for complex three-dimensional geometry with obstructions, both from a computational efficiency as well as memory standpoint. The inefficiency stems from the use of the viewfactor-based approach for determination of the wall-emitted component. In this work, instead, the wall component is determined directly using the control angle discrete ordinates method (CADOM). The new hybrid method was validated for both two-dimensional (2D) and three-dimensional (3D) geometries against benchmark Monte Carlo results for gray media in which the optical thickness was varied over a large range. In all cases, the accuracy of the hybrid method was found to be within a few percent of Monte Carlo results, and comparable to the solutions of the RTE obtained directly using CADOM. Finally, the new hybrid method was explored for 3D nongray media in the presence of reflecting walls and various scattering albedos. As a noteworthy advantage, irrespective of the conditions used, it was always found to be computationally more efficient than standalone CADOM and up to 15 times more efficient than standalone CADOM for optically thick media with strong scattering.

Experimental and Numerical Analysis of Thermal Ablation in Biological Tissues Using Short Pulse Lasers

2010 ◽  
Author(s):  
Amir Sajjadi ◽  
Ogugua Onyejekwe ◽  
Kunal Mitra ◽  
Michael S. Grace
Keyword(s):  
Pulse Laser ◽  
Continuous Wave ◽  
Short Pulse ◽  
Skin Surface ◽  
Biological Tissues ◽  
Tumor Ablation ◽  
Laser Source ◽  
Striated Muscles ◽  
Short Pulse Laser ◽  
Ultra Short Pulse

For the past few years various photothermal methods such as Laser-induced Hyperthermia [1] and Laser Interstitial Thermal Therapy [2] has been developed for tumor ablation. In all of these existing techniques, either continuous wave (CW) or long pulse laser sources have been used, which often produces heat affected zones that are larger than the boundaries of the tumor, which leads to collateral damage of surrounding healthy tissue. Moreover for these applications, either collimated or diffused laser beams are used, resulting in much of the energy being absorbed by tissues at the skin surface and very little remaining energy penetrating the skin. Such drawbacks can be eliminated if a beam from a short pulse laser source is focused directly at the targeted subsurface location. Tight focusing ensures that sufficient intensity to drive nonlinear optical absorption can be achieved with low pulse energy. This technique has been effectively used in applications such as non-ablative dermal remodeling [3] and treatment of striated muscles [4]. However, the use of focused beam from an ultra-short pulse laser source has never been applied to tumor ablation and is investigated in this paper.

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