  Absorption imaging is a commonly adopted method to acquire, with high
temporal resolution, spatial information on a partially transparent object. It
relies on the interference between a probe beam and the coherent response of
the object. In the low saturation regime, it is well described by a Beer
Lambert attenuation. In this paper we theoretically derive the absorption of a
$\sigma$ polarized laser probe by an ensemble of two-level systems in any
saturation regime. We experimentally demonstrate that the absorption cross
section in dense $^{87}$Rb cold atom ensembles is reduced, with respect to the
single particle response, by a factor proportional to the optical density b of
the medium. To explain this reduction, we developed a model that incorporates,
in the single particle response, the incoherent electromagnetic background
emitted by the surrounding ensemble. We show that it qualitatively reproduces
the experimental results. Our calibration factor that has a universal
dependence on optical density $b$ for $\sigma$ polarized light : $\alpha$ =
1.17(9) + 0.255(2)b allows to obtain quantitative and absolute, in situ, images
of dense quantum systems.
