High angle annular dark field (HAADF) scanning transmission electron microscopy has demonstrated the capability to achieve sub-Angstrom resolution in the study of the structure of materials. Furthermore, the sensitivity of HAADF imaging to fine variations of the chemistry of the specimen allows one to derive the relevant chemical map from the intensity distribution in an image. Here, a general approach to calculate the HAADF image intensity for an alloy is derived and applied to experimental images to measure quantitatively the distribution of the chemical species. The calculations of HAADF image contrast have been performed by multi-slicemethods in the framework of the frozen-phononapproximation by developing and using a parallel code to strongly reduce the computing time necessary to obtain a reliable simulation of realistic specimens. The parameters that influence the HAADF image contrast have been studied and their role has been quantified. Experimental examples of quantification of the chemistry of semiconducting heterostructures will be shown. Attention will be focused on the different parameters that influence the HAADF image contrast depending on the material system and on the specimen composition.