Emission measure ($\mathrm{EM}=\int n_e^{2}dl$)

For a hydrogen-dominated fully ionized plasma, the line-of-sight emission measure is $\mathrm{EM}=\int n_e^{2}dl$. Its units distinguish it from a volume-integrated emission measure $\int n_e^{2}dV$. Thermal free-free optical depth is proportional to $\mathrm{EM}{T}^{-3/2}{\nu }^{-2}{\bar{g}}_{\mathrm{ff}}$ in the radio limit. Inferring density also requires depth, ionization and clumping assumptions.^[ref]