In this study we have theoretically and experimentally investigated the behavior of first order approximation contrast function when purely scattering inhomogeneities located at different depths inside a turbid thick slab are considered. Results of model predictions have been compared with Finite element method simulations and tested on phantoms. To this aim, we have developed for the first time to our knowledge a fitting algorithm for estimating both the scattering perturbation parameter and the shift of the inhomogeneity from the middle plane, allowing one to reduce the uncertainties due to depth. This is important for optical mammography because effects of the depth can cause uncertainties in the derived tumor optical properties that are above 20% and the scattering properties of tumors differ from those of the sourrounding healthy tissue by a comparable extent.