A rather narrow field of view (FOV) has always been considered as an essential limitation of spectral imagers based on acousto-optical tunable filters (AOTFs). We demonstrate a computational technique to overcome this constraint. It is based on preliminary precise spectral-angular characterization of beam transformation caused by light diffraction on an acoustic wave and consequent correction of acquired stack of spectral images. This technique is applicable for any geometry of acousto-optic interaction and opens the way for the development of AOTFs with significantly expanded FOV.