Effects of atmospheric dispersion on the PSF background level

Atmospheric dispersion represents a relatively overlooked problem in connection with the ultimate quality of ELT images corrected by adaptive optics (AO). The aim of this paper is to evaluate the contribution from atmospheric dispersion to the background level of the point-spread function (PSF). Since proper suppression of this level is important for the prospects for direct exo-planet observation, it is necessary to quantify the contributions from all possible sources to it. Atmospheric dispersion will in principle result in three different kinds of contributions. The first one is related to the fact that two rays of different color following the same path through the atmosphere to the telescope do not have the same optical path-length difference (OPD). The second one is related to the fact that two coinciding rays of different color entering the atmosphere at a non zero zenith angle will be separated due to refraction before they reach the telescope. The third one is related to the fact that rays are diffracted by inhomogeneities in the atmosphere and that the diffraction angle is dependent on color. This last effect is small[2] and will not be treated here. As a consequence of dispersion phase fluctuations can, in principle, only be compensated at a single wavelength by AO systems with deformable mirrors (DMs). Hence looking for an exo-planet in a certain spectral bandwidth there will be a contribution from the parent star uncorrected background level. Hence it will be crucial to perform observations in a narrow spectral bandwidth and to ensure that the wavefront measurements used for AO correction are performed within the same narrow bandwidth. The last point affects the needed magnitude of the parent star, which is used for wavefront measurements