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

a_{o}=

l : lower level of the atomic transition

k : upper level of the atomic transition

: rest wavelength of the transition

g_{l}: statistical weight of the lower level

g_{k}: statistical weight of the upper level

a_{kl}: spontaneous transition probability

f_{lk}= upward oscillator strength