Using elastic scattering theory we show that a small set of energy dispersive x-ray spectroscopy (EDX) measurements is sufficient to experimentally evaluate the scattering function of electrons in high-angle annular dark field scanning transmission microscopy (HAADF-STEM). We then demonstrate how to use this function to transform qualitative HAADF-STEM images of InGaN layers into precise, quantitative chemical maps of the indium composition. The maps obtained in this way combine the resolution of HAADF-STEM and the chemical precision of EDX. We illustrate the potential of such chemical maps by using them to investigate nanometer-scale fluctuations in the indium composition and their impact on the growth of epitaxial InGaN layers.