  Timepix3 is a multi-purpose readout ASIC for hybrid pixel detectors. It can
measure time and energy simultaneously by employing time-of-arrival (ToA) and
time-over-threshold (ToT) techniques. Both methods are systematically affected
by timewalk. In this paper, a method for pixel-by-pixel calibration of the time
response is presented. Assemblies of Timepix3 ASICs bump-bonded to thin planar
silicon pixel sensors of different thicknesses between 50 um and 150 um are
calibrated and characterised in particle beams. For minimum ionising particles,
time resolutions down to 0.72 $\pm$ 0.04 ns are achieved.
