The diffuse series is a series of spectral lines in the atomic emission spectrum caused when electrons jump between the lowest p orbital and d orbitals of an atom. The total orbital angular momentum changes between 1 and 2. The spectral lines include some in the visible light, and may extend into ultraviolet or near infrared. The lines get closer and closer together as the frequency increases never exceeding the series limit. The diffuse series was important in the development of the understanding of electron shells and subshells in atoms.  The diffuse series has given the letter d to the d atomic orbital or subshell.
The diffuse series has values given by
The series is caused by transitions from the lowest P state to higher energy D orbitals.
One terminology to identify the lines is: 1P-mD But note that 1P just means the lowest P state in the valence shell of an atom and that the modern designation would start at 2P, and is larger for higher atomic numbered atoms.
The terms can have different designations, mD for single line systems, mδ for doublets and md for triplets.
Since the Electron in the D subshell state is not the lowest energy level for the alkali atom (the S is) the diffuse series will not show up as absorption in a cool gas, however it shows up as emission lines.
The Rydberg correction is largest for the S term as the electron penetrates the inner core of electrons more.
The limit for the series corresponds to electron emission, where the electron has so much energy it escapes the atom.
In alkali metals the P terms are split   and .  This causes the spectral lines to be doublets, with a constant spacing between the two parts of the double line.
This splitting is called fine structure.  The splitting is larger for atoms with higher atomic number.  The splitting decreases towards the series limit. Another splitting occurs on the redder line of the doublet.  This is because of splitting in the D level  and .  Splitting in the D level has a lesser amount than the P level, and it reduces as the series limit is approached.