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We present the DONUTS autoguiding algorithm, designed to fix stellarpositions at the sub-pixel level for high-cadence time-series photometry, whichis also capable of autoguiding on defocused stars. DONUTS was designed tocalculate guide corrections from a series of science images and re-centretelescope pointing between each exposure. The algorithm has the unique abilityof calculating guide corrections from under-sampled to heavily defocused pointspread functions. We present the case for why such an algorithm is importantfor high precision photometry and give our results from off and on-sky testing.We discuss the limitations of DONUTS and the facilities where it soon will bedeployed.

DONUTS: A science frame autoguiding algorithm with sub-pixel precision, capable of guiding on defocused stars