| Description |
1 online resource (xxii, 274 pages) : illustrations |
| Series |
SPIE Press monograph ; PM193 |
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SPIE monograph ; PM193
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| Contents |
Acknowledgements -- Disclaimer -- List of Acronyms -- List of Symbols -- 1. Introduction -- References |
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I. THEORY. 2. Scattering and absorption properties of diffusive media -- 2.1. Approach followed in this book -- 2.2. Optical properties of a turbid medium. 2.2.1. Absorption properties; 2.2.2. Scattering properties -- 2.3. Statistical meaning of the optical properties of a turbid medium -- 2.4. Similarity relation and reduced scattering coefficient -- 2.5. Examples of diffusive media -- References |
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3. The radiative transfer equation and diffusion equation -- 3.1. Quantities used to describe radiative transfer -- 3.2. The radiative transfer equation -- 3.3. The Green's function method -- 3.4. Properties of the radiative transfer equation. 3.4.1. Scaling properties; 3.4.2. Dependence on absorption -- 3.5. Diffusion equation. 3.5.1. The diffusion approximation -- 3.6. Derivation of the diffusion equation -- 3.7. Diffusion coefficient -- 3.8. Properties of the diffusion equation. 3.8.1. Scaling properties; 3.8.2. Dependence on absorption -- 3.9. Boundary conditions. 3.9.1. Boundary conditions at the interface between diffusive and non-scattering media; 3.9.2. Boundary conditions at the interface between two diffusive media -- References |
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II. SOLUTIONS. 4. Solutions of the diffusion equation for homogeneous media -- 4.1. Solution of the diffusion equation for an infinite medium -- 4.2. Solution of the diffusion equation for the slab geometry -- 4.3. Analytical Green's functions for transmittance and reflectance -- 4.4. Other solutions for the outgoing flux -- 4.5. Analytical Green's function for the parallelepiped -- 4.6. Analytical Green's function for the infinite cylinder -- 4.7. Analytical Green's function for the sphere -- 4.8. Angular dependence of radiance outgoing from a diffusive medium -- References |
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5. Hybrid solutions of the radiative transfer equation -- 5.1. General hybrid approach to the solutions for the slab geometry -- 5.2. Analytical solutions of the time-dependent radiative transfer equation for an infinite homogeneous medium. 5.2.1. Almost exact time-resolved Green's function of the radiative transfer equation for an infinite medium with isotropic scattering; 5.2.2. Heuristic time-resolved Green's function of the radiative transfer equation for an infinite medium with non-isotropic scattering; 5.2.3. Time-resolved Green's function of the telegrapher equation for an infinite medium -- 5.3. Comparison of the hybrid models based on the radiative transfer equation and telegrapher equation with the solution of the diffusion equation -- References |
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6. The diffusion equation for layered media -- 6.1. Photon migration through layered media -- 6.2. Initial and boundary value problems for parabolic equations -- 6.3. Solution of the DE for a two-layer cylinder -- 6.4. Examples of reflectance and transmittance of a layered medium -- 6.5. General property of light re-emitted by a diffusive medium. 6.5.1. Mean time of flight in a generic layer of a homogeneous Cylinder; 6.5.2. Mean time of flight in a two-layer cylinder; 6.5.3. Penetration depth in a homogeneous medium; 6.5.4. Conclusion -- References |
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7. Solutions of the diffusion equation with perturbation theory -- 7.1. Perturbation theory in a diffusive medium and the born approximation -- 7.2. Perturbation theory: solutions for the infinite medium. 7.2.1. Examples of perturbation for the infinite medium -- 7.3. Perturbation theory: solutions for the slab. 7.3.1. Examples of perturbation for the slab -- 7.4. Perturbation approach for hybrid models -- 7.5. Perturbation approach for the layered slab and for other geometries -- 7.6. Absorption perturbation by use of the internal pathlength moments -- References |
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III. SOFTWARE AND ACCURACY OF SOLUTIONS. 8. Software -- 8.1. Introduction -- 8.2. The diffusion & perturbation program -- 8.3. Source code: solutions of the diffusion equation and hybrid models. 8.3.1. Solutions of the diffusion equation for homogeneous media; 8.3.2. Solutions of the diffusion equation for layered media; 8.3.3. Hybrid models for the homogeneous infinite medium; 8.3.4. Hybrid models for the homogeneous slab; 8.3.5. Hybrid models for the homogeneous parallelepiped; 8.3.6. General purpose subroutines and functions -- References |
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9. Reference Monte Carlo results -- 9.1. Introduction -- 9.2. Rules to simulate the trajectories and general remarks -- 9.3. Monte Carlo program for the infinite homogeneous medium -- 9.4. Monte Carlo programs for the homogeneous and the layered slab -- 9.5. Monte Carlo code for the slab containing an inhomogeneity -- 9.6. Description of the Monte Carlo results reported in the CD-ROM. 9.6.1. Homogeneous infinite medium; 9.6.2. Homogeneous slab; 9.6.3. Layered slab; 9.6.4. Perturbation due to inhomogeneities inside the homogeneous slab -- References |
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10. Comparisons of analytical solutions with Monte Carlo results -- 10.1. Introduction -- 10.2. Comparisons between Monte Carlo and the diffusion equation: homogeneous medium. 10.2.1. Infinite homogeneous medium; 10.2.2. Homogeneous slab -- 10.3. Comparison between Monte Carlo and the diffusion equation: homogeneous slab with an internal inhomogeneity -- 10.4. Comparisons between Monte Carlo and the diffusion equation: layered slab -- 10.5. Comparisons between Monte Carlo and hybrid models. 10.5.1. Infinite homogeneous medium; 10.5.2. Slab geometry -- 10.6. Outgoing flux: comparison between Fick and extrapolated boundary partial current approaches -- 10.7. Conclusions. 10.7.1. Infinite medium; 10.7.2. Homogeneous slab; 10.7.3. Layered slab; 10.7.4. Slab with inhomogeneities inside; 10.7.5. Diffusive media -- References |
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Appendix A: The first simplifying assumption of the diffusion approximation -- Appendix B: Fick's law -- Appendix C: Boundary conditions at the interface between diffusive and non-scattering media -- Appendix D: Boundary conditions at the interface between two diffusive media -- Appendix E: Green's function of the diffusion equation in an infinite homogeneous medium -- Appendix F: Temporal integration of the time-dependent Green's function -- Appendix G: Eigenfunction expansion -- Appendix H: Green's function of the diffusion equation for the homogeneous cube obtained with the Eigenfunction method -- Appendix I: Expression for the normalizing factor -- References -- Index |
| Summary |
This book provides foundational information on modeling light propagation through diffusive media, with special emphasis on biological tissue. A summary of the theoretical background on light propagation through diffusive media is provided with the aid of easy-to-use software designed to calculate the solutions of the diffusion equation |
| Bibliography |
Includes bibliographical references and index |
| Subject |
Light -- Transmission -- Mathematical models
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Tissues -- Optical properties
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Tissues -- Optical properties
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| Form |
Electronic book
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| Author |
Martelli, Fabrizio, 1969-
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Society of Photo-Optical Instrumentation Engineers
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| ISBN |
9780819481832 |
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0819481831 |
