After having crossed an absorbing cloud, the intensity of a source, I,is received by the observer as I() = I, where is the optical depth of the cloud.
Let's connect to the physical parameters.
N : column density a( : line absorption coefficient
: broadening function ao = l : lower level of the atomic transition k : upper level of the atomic transition : rest wavelength of the transition gl : statistical weight of the lower level gk : statistical weight of the upper level akl : spontaneous transition probability
flk = upward oscillator strength