WHT autoguiding

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. rapid oscillations) 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.