Face-on Surface Density at Disk Inner Boundary σ
(m2 of grain cross-section per m2 of disk)

if α = 0,    σ =   2 · f
ln( r2 / r1 )

if α ¹ 0,    σ =   2 · α · f
( r2 / r1 )α - 1

α = disk surface density power law exponent
r2 , r1 = disk outer and inner boundary radii
f = infrared excess
LIR/Lstar