A problem when working with optical satellite or airborne images is the need to compensate for changes in the illumination conditions at the time of acquisition. This is particularly critical when working with time series of data. Atmospheric correction strategies based on radiative transfer codes may provide a rigorous solution but it may not be the best solution for situations where a huge amount of hyperspectral images may need to be processed and computational time is a critical factor. The GMES ("Global Monitoring for Environment and Security") initiative has promoted the creation of a new generation of satellites (the SENTINEL series) with "ultra-high resolution" and "superspectral imaging" capabilities [1]. Therefore, there is an urgent need to quickly and reliably compensate for changes in the atmospheric transmittance and varying solar illumination conditions. In this paper three different forms of affine transformation models (general, particula...