We consider quantifying the shape of galaxies and the fundamental plane. And P-S profiles for different categories of galaxies in different environments. So, we have some surface brightness, which is the line integral of the luminosity volume density.
R is the cylindrical radius from the center of the galaxy.
In general, galaxies have composite profiles, with several components of different scale lengths, and of course there are deviations from the simple single parameter fit light profile. For example, spirals are typically fit by both an exponential disk, and a bulge, and the bulge may be well fit either by a spheroidal exponential, or a de Vaucouleurs profile. Most galaxies show some significant deviation from these smooth azimuthally symmetric profile fits. Spirals, of course, typically have spiral structure, and frequently also central bars, dust lanes, and they may have rings and point-like nuclei. Type I galaxies have excess light at some radius, after the best fits smooth profile has been subtracted.