Autoguiding serves mainly to eliminate slow drifts in pointing,
and with an autoguide loop closed, the WHT typically tracks with accuracy
<~ 0.05 arcsec rms from exposure to exposure. On a timescale of
~ 1 hour, slow monotonic drifts <~ 0.3 arcsec become evident, probably
due to relative flexure
between autoguider and instrument, and to differential refraction
between them (different wavelength responses).
E.g. an undithered series of 300-sec ACAM r-band images of a science target
was observed on 17 February 2016, in 1-arcsec seeing, at airmass ~ 1.0,
over a period of 1 hour.
During the one hour of observing,
there's a small net drift of the star positions,
~ 0.3 arcsec, in azimuth, but apart from this, the exposure-to-exposure
change in star positions is only 0.05 arcsec rms.
(The positions of the stars can be measured from the images with
accuracy < 0.02 arcsec rms.)
Uncorrected rapid motion
Rapid motion won't be corrected by autoguiding.
The cycle time for autoguiding is typically 3 sec
(1 sec exposure, 2 sec overheads), and the loop gain is < 1,
so movements on a timescale <~ 30 sec (e.g.
are not well compensated for.
However, the circularity of images taken in good seeing places a strong
constraint on the amplitude of any such motions. Images of stars
typically have iraf ellipticity (1 - minor-axis/major-axis) < 0.05, which
in 0.5 arcsec seeing implies that the FWHM of any uncorrected motion
is < 0.15 arcsec.