Astronomers collect light, nothing more. The formalism of radiative transfer is a macroscopic treatment of microscopic interplay between light and matter; it employs macroscopic variables that parameterize microscopic interactions. In this chapter we describe the radiation and photon field and define the fundamental macroscopic quantity – the specific intensity. The geometry of radiative transfer is key as it involves an origin and an observer defined line-of-sight perspective. The observed solid angle is expressed for a cosmologically distant observer, from which flux vectors and the observed flux are derived. The equation of radiative transfer is introduced, including the macroscopic parameters known as the emission and extinction coefficients and the optical depth and mean free path. The solution for pure absorption is given including illustrations of the anatomy of an absorption line in terms of optical depth. The details hidden within a beam-averaged astronomical absorption spectrum are described, followed by a treatment of partial covering, from which the covering factor is derived. Finally, a formal definition of column density is provided.

Chapter 4 introduces phenomenologically the radiative transfer equation of the directional distribution of the energy density for a given anisotropic scattering coefficient of scalar waves in random media. We solve the radiative transfer equation analytically by using the Legendre expansion for isotropic radiation from a point source. By probabilistically interpreting the Born scattering coefficient and the Eikonal angular spectrum function and the traveling distance fluctuation for scalar waves, we construct the corresponding pseudo-random number generators, where the rejection sampling method is introduced. Then, we synthesize the space–time distribution of the energy density for isotropic radiation from a point source using the MC simulation and compare it with the analytical solution of the radiative transfer equation.

Radiant light is what we see from stars.Radiant light carries the energy outward through the star's photosphere.This chapter gives us the terms and vocabulary to describe radiation processes.