  For high-contrast imaging (HCI) systems, such as VLT/SPHERE, the performance
of the system at small angular separations is contaminated by the wind-driven
halo in the science image. This halo is a result of the servo-lag error in the
adaptive optics (AO) system due to the finite time between measuring the
wavefront phase and applying the phase correction. One approach to mitigating
the servo-lag error is predictive control. We aim to estimate and understand
the potential on-sky performance that linear data-driven prediction would
provide for VLT/SPHERE under various turbulence conditions. We used a linear
minimum mean square error predictor and applied it to 27 different AO telemetry
data sets from VLT/SPHERE taken over many nights under various turbulence
conditions. We evaluated the performance of the predictor using residual
wavefront phase variance as a performance metric. We show that prediction
always results in a reduction in the temporal wavefront phase variance compared
to the current VLT/SPHERE AO performance. We find an average improvement factor
of 5.1 in phase variance for prediction compared to the VLT/SPHERE residuals.
When comparing to an idealised VLT/SPHERE, we find an improvement factor of
2.0. Under our 27 different cases, we find the predictor results in a smaller
spread of the residual temporal phase variance. Finally, we show there is no
benefit to including spatial information in the predictor in contrast to what
might have been expected from the frozen flow hypothesis. A purely temporal
predictor is best suited for AO on VLT/SPHERE.
