Limitations imposed by optical turbulence profile structure and evolution on tomographic reconstruction for the ELT

The performance of tomographic adaptive optics (AO) systems is intrinsically linked to the vertical profile of optical turbulence. First, a sufficient number of discrete turbulent layers must be reconstructed to model the true continuous turbulence profile. Secondly over the course of an observation, the profile as seen by the telescope changes and the tomographic reconstructor must be updated. These changes can be due to the unpredictable evolution of turbulent layers on meteorological time-scales as short as minutes. Here, we investigate the effect of changing atmospheric conditions on the quality of tomographic reconstruction by coupling fast analytical AO simulation to a large data base of 10 691 high-resolution turbulence profiles measured over two years by the Stereo-SCIDAR instrument at ESO Paranal, Chile. This work represents the first investigation of these effects with a large, statistically significant sample of turbulence profiles. The statistical nature of the study allows us to assess not only the degradation and variability in tomographic error with a set of system parameters (e.g. number of layers and temporal update period), but also the required parameters to meet some error threshold. In the most challenging conditions where the profile is rapidly changing, these parameters must be far more tightly constrained in order to meet this threshold. By providing estimates of these constraints for a wide range of system geometries as well as the impact of different temporal optimization strategies we may assist the designers of tomographic AO for the extremely large telescope to dimension their systems.