Robustness of tomographic reconstructors versus real atmospheric profiles in the ELT perspective

In this article we revisit a subject that has partly already been examined in previous studies: the behavior of tomographic reconstructors in adaptive optics systems, facing to an atmospheric profile (C 2 n ( h )) different from the one they've been optimized for. We develop a new approach for that. The current usual approach is to simulate the performance of the reconstructor when slightly varying the C 2 n ( h ) profile around a nominal one, and show how far the deviation may go. This has the disadvantage that, as the parameter space for potential errors on the C 2 n ( h ) profile is basically infinite, it is particularly uneasy to span. Our approach consists in deriving a sort of sensitivity function, that we call vertical error distribution (VED), from the knowledge of any tomographic reconstructor. This function can be computed even for non-tomographic reconstructors, ground-layers reconstructors, single-conjugate AO reconstructors, etc. In any case, it allows us to derive the error when applied to a particular C 2 n ( h ) profile, have a direct, global visualization of the error variation with layer altitude, for any number at any altitude. This also allows us to understand what a given reconstructor is sensitive to, at what altitudes or altitude range, or explain why some GLAO reconstructors may perform better than optimized MMSE tomographic reconstructors if low-altitude layers pop up. We also discuss the case of ELTs and apply our approach to large scale reconstructors.