Why is collision broadening homogeneous and Doppler broadening isn't? From what I understand, homogeneous broadening is one for which is the same for all atoms, whilst an inhomogeneous is one that is different. Correct me if I am wrong.
Doppler broadening depends on the current speed of the atom, and as such it is clear that this is a type of inhomogeneous broadening.
However collision broadening, I would say, depends on collisions of individual atoms. An atom undergoing no collisions will not have the same collision broadening as one undergoing many. I would naturally think then that collision broadening is to inhomogeneous. But everywhere I look it is called homogeneous. Why is this?
 A: The distinction appears to be whether the absorption cross-section due to a transition is distributed with frequency in the same way for all atoms (homogeneous broadening) or whether it differs systematically from atom-to-atom (inhomogeneous broadening). Note that any particular atom will emit or absorb a photon that has some uncertainty in its frequency. What matters here is whether the probability function describing that frequency uncertainty is the same for all atoms.
Homogeneous broadening would include natural broadening and could include pressure and collisional broadening, if all the atoms responsible for the spectrum were in the same environment (density, temperature, composition etc.). Collisional broadening cuts-off the interaction between atom and radiation, resulting in an energy uncertainty that is on average the same for all such atoms.
The line shape for an ensemble of atoms would be identical to the line shape probability function calculated for a single atom.
The distinction with inhomogeneous broadening is that the observed spectral line has arisen from atoms that are situated in more than one environment. So that could include where there are temperature, density or composition inhomogeneities or where different parts of the source are travelling with different line-of-sight velocities (for example due to thermal broadening or turbulence) leading to a different Doppler shift, and hence different central line frequency and/or frequency probability distribution, for each atom. In these cases, the line shape for an ensemble of atoms would be a homogeneous profile for one atom convolved with functions (often Gaussian) that represent the differing conditions that are appropriate for each atom.
