1. A system for correcting aberrations of a specimen surface that vary across a visual field on a microscope, the system comprising a lens, a tubular lens, an imaging optics element, a pupil stop disposed in a beam path, and at least one optical element for optical-geometric separation of different image field regions, said optical element for optical-geometric separation of different image field regions being arranged in or near an intermediate image plane and wherein each individual element of the optical element for optical-geometric separation of different image field regions performs a pupil imaging defined by dimensions of a covered area of the intermediate image, such that a distribution of sub-pupils occurs, wherein each sub-pupil is allocated to an angle distribution from the associated image field region, the system further comprising an adaptive element arranged between the optical element for optical-geometric separation of different image field regions and the imaging optics element.