Biological tissues are strongly heterogeneous media, with spatial inhomogeneities occurring on length scales ranging from nanometers (structural proteins), to hundreds of nanometers (cellular organelles), to tens of microns (cells), all the way to millimeters and centimeters (at tissue and organ levels). These inhomogeneities are associated with spatial gradients and discontinuities in physical properties that play key roles in determining the optical properties of tissues, which govern how light propagates within tissues. For example, a discontinuity in the refractive index at a plane or interface causes reflection and refraction of light, whereas, as discussed in Chapters 7 and 8, localized optical inhomogeneities associated with particles result in light scattering, with a wavelength dependence and an angular distribution that depend on the shapes and refractive indices of particles and their sizes relative to the wavelength of light. Further, as described in Chapter 2, a number of molecules found in tissues (e.g., aromatic amino acids, melanin, bilirubin, rhodopsin, hemoglobin, cytochrome c, water, etc.) absorb light with spectral extinction coefficients that determine their wavelength-dependent absorption efficiency. Whereas Chapter 7 developed the theories that describe scattering from single particles, and Chapter 8 described treatment of light transport between a source and detector separated by only a few optical mean free paths, this chapter addresses the diffuse field, for which source and detector are separated by a distance large compared to the mean free path for scattering.

When considering the transport of light in bulk turbid media, it is frequently easier, conceptually, to invoke the particle representation rather than the wave nature of light. (See Section 4.7.1.) In the particle-like description of light propagation as a flow of photons, one may describe the effects of spatial heterogeneities and absorbing molecules in terms of deflections and annihilations, respectively, of traveling photons. This means that the tissue can be seen as a collection of scattering and absorbing centers that interact with photons randomly but according to quantitative rules that specify the probability of interaction and the way in which the tissue constituents deflect or absorb the incident photons. This is conceptually no different than a flow of metal balls in a pinball machine with posts (scattering centers) and holes (absorbing centers).