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CANARY is the multi-object adaptive optics (MOAO) on-sky pathfinder developedin the perspective of Multi-Object Spectrograph on Extremely LargeTelescopes~(ELTs). In 2013, CANARY was operated on-sky at the William Herscheltelescope~(WHT), using three off-axis natural guide stars~(NGS) and fouroff-axis Rayleigh laser guide stars~(LGS), in open-loop, with the on-axiscompensated turbulence observed with a H-band imaging camera and a Truthwave-front sensor~(TS) for diagnostic purposes. Our purpose is to establish areliable and accurate wave-front error breakdown for LGS MOAO. This will enablea comprehensive analysis of \cana on-sky results and provide tools forvalidating simulations of MOAO systems for ELTs. To evaluate the MOAOperformance, we compared the CANARY on-sky results running in MOAO, in SingleConjugated Adaptive Optics~(SCAO) and in Ground Layer Adaptive Optics~(GLAO)modes, over a large set of data acquired in 2013. We provide a statisticalstudy of the seeing. We also evaluated the wave-front error breakdown from bothanalytic computations, one based on a MOAO system modelling and the other onthe measurements from the CANARY TS. We have focussed especially on thetomographic error and we detail its vertical error decomposition~(VED). We showthat CANARY obtained 30.1\%, 21.4\% and 17.1\% H-band Strehl ratios in SCAO,MOAO and GLAO respectively, for median seeing conditions with 0.66" of totalseeing including 0.59" at the ground. Moreover, we get 99\% of correlation over4,500 samples, for any AO modes, between two analytic computations of residualphase variance. Based on these variances, we obtain a reasonableStrehl-ratio~(SR) estimation when compared to the measured IR image SR. Weevaluate the gain in compensation for the altitude turbulence brought by MOAOwhen compared to GLAO.

Wave-front error breakdown in LGS MOAO validated on-sky by CANARY