Contents -- Foreword -- Preface -- Part I: Light Propagation in Tissues -- 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 -- 1.3.1 Tissue Absorption -- 1.3.1.1 Blood: The Main Absorber In Tissue -- 1.3.1.2 The effect of Water -- 1.3.1.3 The effect of Skin -- 1.4 Light Emitters in Nature -- 1.4.1 Coherent and Incoherent Light Sources -- 1.4.2 Fluorescence -- 1.4.2.1 Fluorescence Lifetime -- 1.4.2.2 Steady-state Fluorescence Intensity -- 1.4.2.3 Quantum Yield -- 1.4.2.4 Tissue Auto-fluorescence -- 1.4.3 Bioluminescence -- 1.5 Light Scatterers in Nature -- 1.5.1 Tissue Scattering -- 1.6 Optical Molecular Imaging -- The definition further elaborates -- Key Points -- Further Reading -- 2. Scattering and Absorption -- 2.1 Definition of Scattering -- 2.2 Poynting's Theorem and Energy Conservation -- 2.2.1 The Time-Averaged Expressions -- 2.3 Single Scattering -- 2.3.1 The Scalar Theory of Scattering -- 2.3.2 Far-Field Approximation -- 2.4 Main Optical Parameters of a Particle -- 2.4.1 The Absorption Cross-Section -- 2.4.2 The Scattering Cross-Section -- 2.4.3 The Total or Extinction Cross-Section and the Optical Theorem -- 2.4.4 The Phase Function -- 2.4.5 The Anisotropy Factor -- 2.5 Multiple Scattering -- 2.5.1 The Scattering and Absorption Coefficients -- 2.6 Extinction by a Slab of Absorbing Particles -- 2.7 Polarization Effects -- 2.8 Self-Averaging -- Key Points -- Further Reading -- 3. The Radiative Transfer Equation (RTE) -- 3.1 Radiative Transfer -- 3.1.1 Volume Averaged Flow of Energy -- 3.2 Specific Intensity, Average Intensity and Flux -- 3.2.1 The Specific Intensity -- 3.2.2 The Average Intensity -- 3.2.3 The Energy Density -- 3.2.4 The Total Flux Density -- 3.3 The Detected Power.

3.3.1 The Numerical Aperture -- 3.4 Isotropic Emission and its Detection -- 3.5 Reflectivity and Transmissivity -- 3.6 Derivation of the Radiative Transfer Equation -- 3.6.1 The Source Term -- 3.6.2 The Equation of Energy Conservation -- 3.6.3 Summary of Approximations: How Small is 'Small Enough'? -- 3.7 Some Similarity Relations of the RTE -- 3.8 The RTE and Monte Carlo -- 3.8.1 Photon Density -- Key points -- Further Reading -- 4. Fick's Law and The Di usion Approximation -- 4.1 Historical Background -- 4.2 Diffuse Light -- 4.2.1 Reduced and Diffuse Intensity -- 4.2.2 Angular Distribution of Diffuse Light -- 4.3 Derivation of the Diffusion Equation -- 4.3.1 The Diffusion Coefficient -- 4.3.2 The Diffusion Coefficient In Absorbing Media -- 4.4 The Diffusion Equation -- 4.5 The Mean Free Path -- 4.6 Limits of Validity of the Diffusion approximation -- Key points -- Further Reading -- Part II: Diffuse Light -- 5. The Diffusion Equation -- 5.1 The Diffusion Equation in Infinite Homogeneous Media -- 5.2 Green's Functions and Green's Theorem -- 5.2.1 The Diffusion Equation 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 -- 5.7.1 1D Green's functions -- 5.7.2 2D Green's functions -- 5.7.3 3D Green's functions -- Key points -- Further Reading -- 6. Propagation and Spatial Resolution of Diffuse Light -- 6.1 Propagation of Diffuse Light -- 6.1.1 The Diffusion Wavenumber -- 6.2 The Angular Spectrum Representation -- 6.2.1 Angular spectrum of a point source: The Green Function in K-space -- 6.3 Spatial Transfer Function and Impulse Response -- 6.3.1 Spatial Transfer Function and Impulse Response -- 6.4 Spatial Resolution -- 6.4.1 Resolution of Propagating Scalar Waves.

6.4.2 Resolution of Diffuse Waves -- 6.5 Backpropagation of Diffuse Light -- Key points -- Further Reading -- 7. The Point Source Approximation -- 7.1 General Solution -- 7.1.1 Solution for a point source -- 7.2 Solution for a collimated source -- 7.3 Point Source Approximation to a collimated source -- 7.3.1 Limits of Validity -- 7.4 Accounting for the Source Profile -- Key points -- Further Reading -- 8. Diffuse Light at Interfaces -- 8.1 Diffusive/Diffusive (D-D) Interfaces -- 8.1.1 D-D Boundary Conditions -- 8.1.1.2 Index Matched Conditions -- 8.1.2 D-D Reflection and Transmission Coefficients -- 8.1.2.1 Approximate reflection and transmission coefficients -- 8.1.2.2 Snell's law for Diffuse Waves -- 8.1.3 Frequency independent coefficients -- 8.2 Diffusive/Non-diffusive (D-N) Interfaces -- 8.2.1 D-N Boundary Conditions -- 8.2.1.1 The Extrapolated Boundary Condition -- 8.2.2 D-N Reflection and Transmission Coefficients -- 8.2.2.1 Black interface -- 8.3 Layered Diffusive Media -- 8.3.1 Expression for a Slab in a Diffusive medium -- 8.3.2 Expression for a Slab in a Non-Diffusive medium -- 8.4 Multiple layered media -- 8.5 The Detected Power in Diffuse Media -- 8.5.1 Accounting for the Detector Profile -- 8.6 Non-contact Measurements -- 8.6.1 Free-space source -- 8.6.2 Free-space detector -- 8.6.2.1 Free-space detection through a system of lenses -- 8.6.2.2 Normalized Fluorescence in Free-space -- Key points -- Further Reading -- 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? -- 9.3.1 Recovering size and position in diffuse media -- 9.3.1.1 Ill-posed nature of Propagating Scalar Waves -- 9.3.1.2 Ill-posed nature of Diffuse Waves -- 9.4 Reducing Ill-posedness.

9.4.1 Introducing a spatial dependence on the emission -- 9.4.2 Normalized measurements -- 9.4.3 Multispectral imaging -- 9.4.3.1 Distinct background absorption features -- 9.4.4 Phase Information -- 9.4.5 Background Signal -- 9.4.6 Prior Information -- Key points -- Further Reading -- 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 -- Key points -- Further Reading -- Appendix A Useful Formulas -- A.1 The Fourier Transform -- A.2 The Hankel Transform -- A.3 The Laplace Transform -- A.4 The Delta Function -- A.5 Gaussian Function -- A.6 Vector Identities -- Appendix B The Solid Angle -- B.1 The solid angle delta function -- B.2 The solid angle and the unit direction vector -- Appendix C An Alternative Derivation of the Radiative Transfer Equation -- C.1 Derivation of the Radiative Transfer Equation -- C.1.1 Volume Averaged Change in Energy Density -- C.1.2 Volume Averaged Absorbed Power -- C.1.3 Volume Averaged Change in Energy Flow -- C.1.4 The Scattering Contribution -- C.1.5 The Radiative Transfer Equation -- C.1.6 Summary of Approximations -- Bibliography -- Index.