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Determination of the optical turbulence parameters from the adaptive optics telemetry: critical analysis and on-sky validation.

It has been demonstrated by several authors that the optical turbulence parameters associated with a given adaptive optics (AO) run-the seeing angle and outer scale-can be determined from a statistical analysis of the commands of the system's deformable mirror (DM). The higher the accuracy on these parameters, the more we can make use of them, allowing for instance a better estimation of the seeing statistics at the telescope location or a more accurate assessment of the performance of the AO system. In the context of a point spread function reconstruction project (PSF-R) for the W. M. Keck observatory AO system, we decided to identify, in the most exhaustive way, all the sources of systematic and random errors affecting the determination of the seeing angle and outer scale from the DM telemetry, and find ways to compensate/mitigate these errors to keep them under 10%. The seeing estimated using our improved DM-seeing method was compared with more than 70 nearly simultaneous seeing measurements from open-loop PSFs on the same optical axis, and with independent seeing-monitor measurements acquired at the same time but far from the telescope (DIMM/MASS): the correlation with the open-loop PSF is very good (the error is about 10%), validating the DM-seeing method for accurate seeing determination, while it is weak and sometimes completely uncorrelated with the DIMM/MASS seeing monitor data. We concluded that DM-based seeing can be very accurate if all the error terms are considered in the DM data processing, but that seeing taken from non-collocated seeing monitors is of no use even when moderate accuracy is required.