Principles of Diffuse Light Propagation

The following sections are included:

• Foreword

• Preface

• Contents

The following sections are included:

• Introduction

• The Classical Picture of Light Interaction With Matter

• Light Absorbers in Nature
  • Tissue Absorption

• Light Emitters in Nature
  • Coherent and Incoherent Light Sources
  • Fluorescence
  • Bioluminescence

• Light Scatterers in Nature
  • Tissue Scattering

• Optical Molecular Imaging

The following sections are included:

• Definition of Scattering

• Poynting’s Theorem and Energy Conservation
  • The Time-Averaged Expressions

• Single Scattering
  • The Scalar Theory of Scattering
  • Far-Field Approximation

• Main Optical Parameters of a Particle
  • The Absorption Cross-Section
  • The Scattering Cross-Section
  • The Total or Extinction Cross-Section and the Optical Theorem
  • The Phase Function
  • The Anisotropy Factor

• Multiple Scattering
  • The Scattering and Absorption Coefficients

• Extinction by a Slab of Absorbing Particles

• Polarization Effects

• Self-Averaging

The following sections are included:

• Radiative Transfer
  • Volume Averaged Flow of Energy

• Specific Intensity, Average Intensity and Flux
  • The Specific Intensity
  • The Average Intensity
  • The Energy Density
  • The Total Flux Density

• The Detected Power
  • The Numerical Aperture

• Isotropic Emission and its Detection

• Reflectivity and Transmissivity

• Derivation of the Radiative Transfer Equation
  • The Source Term
  • The Equation of Energy Conservation
  • Summary of Approximations: How Small is ‘Small Enough’?

• Some Similarity Relations of the RTE

• The RTE and Monte Carlo
  • Photon Density

The following sections are included:

• Historical Background

• Diffuse Light
  • Reduced and Diffuse Intensity
  • Angular Distribution of Diffuse Light

• Derivation of the Diffusion Equation
  • The Diffusion Coefficient
  • The Diffusion Coefficient In Absorbing Media

• The Diffusion Equation

• The Mean Free Path

• Limits of Validity of the Diffusion approximation

The following sections are included:

• The Diffusion Equation in Infinite Homogeneous Media

• Green’s Functions and Green’s Theorem
  • The Diffusion Equation and Green’s Theorem

• The Time-dependent Green’s Function

• The Constant Illumination Green’s Function

• Waves of Diffuse Light

• The Diffusion Equation in Inhomogeneous Media

• Summary of Green’s Functions
  • 1D Green’s functions
  • 2D Green’s functions
  • 3D Green’s functions

The following sections are included:

• Propagation of Diffuse Light
  • The Diffusion Wavenumber

• The Angular Spectrum Representation
  • Angular spectrum of a point source: The Green Function in K-space

• Spatial Transfer Function and Impulse Response
  • Spatial Transfer Function and Impulse Response

• Spatial Resolution
  • Resolution of Propagating Scalar Waves
  • Resolution of Diffuse Waves

• Backpropagation of Diffuse Light

The following sections are included:

• General Solution
  • Solution for a point source

• Solution for a collimated source

• Point Source Approximation to a collimated source
  • Limits of Validity

• Accounting for the Source Profile

The following sections are included:

• Diffusive/Diffusive (D-D) Interfaces
  • D-D Boundary Conditions
  • D-D Reflection and Transmission Coefficients
  • Frequency independent coefficients

• Diffusive/Non-diffusive (D-N) Interfaces
  • D-N Boundary Conditions
  • D-N Reflection and Transmission Coefficients

• Layered Diffusive Media
  • Expression for a Slab in a Diffusive medium
  • Expression for a Slab in a Non-Diffusive medium

• Multiple layered media

• The Detected Power in Diffuse Media
  • Accounting for the Detector Profile

• Non-contact Measurements
  • Free-space source
  • Free-space detector

The following sections are included:

• Fluorescence in Diffuse Media

• Bioluminescence in Diffuse Media

• Why is imaging in diffuse media an ill-posed problem?
  • Recovering size and position in diffuse media

• Reducing Ill-posedness
  • Introducing a spatial dependence on the emission
  • Normalized measurements
  • Multispectral imaging
  • Phase Information
  • Background Signal
  • Prior Information

The following sections are included:

• The Forward and Inverse Problem

• The Born Approximation

• The Rytov Approximation

• The Normalized Born Approximation and the Sensitivity Matrix

• Direct Inversion Formulas

The following sections are included:

• 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

• Bibliography

• Index