Lorenzo J.R. Principles of Diffuse Light Propagation: Light Propagation in Tissues with Applications in Biology and Medicine

World Scientific Publishing Co. Pte. Ltd., Danvers, MA, USA, 2012. – 355 p. – ISBN: 9814293768The 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.Light Propagation in Tissues
Light Absorbers, Emitters, and Scatterers: The Origins of Color in Nature
Scattering and Absorption
The Radiative Transfer Equation (RTE)
Fick’s Law and The Diffusion Approximation
Diffuse Light
The Diffusion Equation
Propagation and Spatial Resolution of Diffuse Light
The Point Source Approximation
Diffuse Light at Interfaces
Fluorescence and Bioluminescence in Diffuse Media: An ill-posed problem
Imaging in Diffusive Media: The Inverse Problem
Appendix A Useful Formulas
The Fourier Transform
The Hankel Transform
The Laplace Transform
The Delta Function
Gaussian Function
Vector Identities
Appendix B The Solid Angle
The solid angle delta function
The solid angle and the unit direction vector
Appendix C An Alternative Derivation of the Radiative Transfer Equation
Derivation of the Radiative Transfer Equation
Volume Averaged Change in Energy Density
Volume Averaged Absorbed Power
Volume Averaged Change in Energy Flow
The Scattering Contribution
The Radiative Transfer Equation
Summary of Approximations