C4 - surface brightness profiles

considering the angle subtended by a square patch of a galaxy, with side $D$ , on the sky
if $d >> D : α = D / d$
the intensity, or energy per unit area:

I = \frac{F}{α^{2}} = (\frac{L_{t o t}}{4 π d^{2}}) {(\frac{d}{D})}^{2} = \frac{L_{t o t}}{4 π D^{2}}

definitions	symbol	units
linear	$I (Σ)$	$L_{⊙} p c^{- 2}$
log	$μ$	magnitudes arcseconds $^{- 2}$

μ = - 2. 5 \log_{10} (\frac{F}{α^{2}}) + c