Quantitative absorption imaging: The role of incoherent multiple scattering in the saturating regime

In this paper, we study the modification of coherent scattering processes in dense ensembles. Using absorption imaging, we experimentally demonstrate that the absorption cross section in dense ⁸⁷Rb cold atom ensembles is reduced, with respect to the single-particle response. This reduction is linearly dependent on the optical density and well reproduced by a one-dimensional model of coherent field propagation in an ensemble of quantum two-level systems that self-consistently incorporates multiple scattering contribution. Our model shines light upon the key role of incoherent scattering on the modification of the optical response of dense ensembles and leads to a generalization of the Beer-Lambert law. Our result applies to any effective two-level system ensemble and allows for quantitative and absolute in situ absorption imaging.