Principles of diffuse light propagation light propagation in tissues with applications in biology and medicine - Lorenzo, Jorge Ripoll (World Scientific, 2012)
Includes bibliographical references (pages 321-329) and index
1. Light absorbers, emitters, and scatterers: the origins of color in nature. 1.1. Introduction. 1.2. The classical picture of light interaction with matter. 1.3. Light absorbers in nature. 1.4. Light emitters in nature. 1.5. Light scatterers in nature. 1.6. Optical molecular imaging -- 2. Scattering and absorption. 2.1. Definition of scattering. 2.2. Poynting's theorem and energy conservation. 2.3. Single scattering. 2.4. Main optical parameters of a particle. 2.5. Multiple scattering. 2.6. Extinction by a slab of absorbing particles. 2.7. Polarization effects. 2.8. Self-averaging -- 3. The Radiative Transfer Equation (RTE). 3.1. Radiative transfer. 3.2. Specific intensity, average intensity and flux. 3.3. The detected power. 3.4. Isotropic emission and its detection. 3.5. Reflectivity and transmissivity. 3.6. Derivation of the radiative transfer equation. 3.7. Some similarity relations of the RTE. 3.8. The RTE and Monte Carlo --
- 4. Fick's law and the diffusion approximation. 4.1. Historical background. 4.2. Diffuse light. 4.3. Derivation of the diffusion equation. 4.4. The diffusion equation. 4.5. The mean free path. 4.6. Limits of validity of the diffusion approximation -- 5. The diffusion equation. 5.1. The diffusion equation in infinite homogeneous media. 5.2. Green's functions and Green's Theorem. 5.3. The time-dependent Green's function. 5.4. The constant illumination Green's function. 5.5. Waves of diffuse light. 5.6. The diffusion equation in inhomogeneous media. 5.7. Summary of Green's functions -- 6. Propagation and Spatial Resolution of Diffuse Light. 6.1. Propagation of diffuse light. 6.2. The angular spectrum representation. 6.3. Spatial transfer function and impulse response. 6.4. Spatial resolution. 6.5. Backpropagation of diffuse light --
- 7. The point source approximation. 7.1. General solution. 7.2. Solution for a collimated source. 7.3. Point source approximation to a collimated source. 7.4. Accounting for the source profile -- 8. Diffuse light at interfaces. 8.1. Diffusive/Diffusive (D-D) interfaces. 8.2. Diffusive/Non-diffusive (D-N) interfaces. 8.3. Layered diffusive media. 8.4. Multiple layered media. 8.5. The detected power in diffuse media. 8.6. Non-contact measurements -- 9. Fluorescence and bioluminescence in diffuse media: an ill-posed problem. 9.1. Fluorescence in diffuse media. 9.2. Bioluminescence in diffuse media. 9.3. Why is imaging in diffuse media an ill-posed problem? 9.4. Reducing ill-posedness -- 10. Imaging in diffusive media: the inverse problem. 10.1. The forward and inverse problem. 10.2. The born approximation. 10.3. The Rytov approximation. 10.4. The normalized born approximation and the sensitivity matrix. 10.5. Direct inversion formulas
The main idea behind this book is to present a rigorous derivation of the equations that govern light propagation in highly scattering media, with an emphasis on their applications in imaging in biology and medicine. The equations and formulas for diffuse light propagation are derived from the very beginning and all the necessary analytical expressions needed to complete a complex imaging or characterization problem are presented step by step. This book provides postgraduate and PhD students with the basic framework and sufficient knowledge in light transport and the related mathematical methods to solve most complex problems that may appear in biomedical applications involving multiple scattered light. All results presented are formal analytical derivations from the complete problem, presenting, in those cases which are relevant, approximations to these expressions