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For extremely large telescopes, adaptive optics will be required to correctthe Earth's turbulent atmosphere. The performance of tomographic adaptiveoptics is strongly dependent on the vertical distribution (profile) of thisturbulence. An important way in which this manifests is the tomographic error,arising from imperfect measurement and reconstruction of the turbulent phase ataltitude. Conventionally, a small number of reference profiles are used toobtain this error in simulation however these profiles are not constructed tobe representative in terms of tomographic error. It is therefore unknownwhether these simulations are providing realistic performance estimates. Here,we employ analytical adaptive optics simulation that drastically reducescomputation times to compute tomographic error for 10 691 measurements of theturbulence profile gathered by the Stereo-SCIDAR instrument at ESO Paranal. Weassess for the first time the impact of the profile on tomographic error in astatistical manner. We find, in agreement with previous work, that thetomographic error is most directly linked with the distribution of turbulenceinto discrete, stratified layers. Reference profiles are found to providemostly higher tomographic error than expected, which we attribute to the factthat these profiles are primarily composed of averages of many measurementsresulting in unrealistic, continuous distributions of turbulence. We proposethat a representative profile should be defined with respect to a particularsystem, and that as such simulations with a large statistical sample ofprofiles must be an important step in the design process.

Identifying optical turbulence profiles for realistic tomographic error in adaptive optics