The Thomson optical depth is optical depth due to Thomson scattering and is of interest when the latter is the primary type of scattering, e.g., when electromagnetic radiation (EMR) passes through a medium in which it is likely to pass close to electrons, i.e., an ionized medium. Determining the Thomson optical depth is of interest in studying distant EMR such as the cosmic microwave background, that passed for a long distance through reionized media, since the opaqueness due to Thomson scattering produces tends to cover up interesting detail in the primordial CMB such as deviations and polarization.
The term Thomson thick refers to material with considerable Thomson optical depth. Similarly, the terms Compton optical depth, and Compton thick are used for Compton scattering, which is a subject of study regarding X-rays from active galactic nuclei. Particular spectral energy distribution features are used to determine whether such scattering is occurring, and to work out what sort of EMR produced the observed results.