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We present the DONUTS autoguiding algorithm, designed to fix stellar positions at the sub-pixel level for high-cadence time-series photometry, which is also capable of autoguiding on defocused stars. DONUTS was designed to calculate guide corrections from a series of science images and re-centre telescope pointing between each exposure. The algorithm has the unique ability of calculating guide corrections from under-sampled to heavily defocused point spread functions. We present the case fordoi:10.1086/670940 fatcat:sjuflczvxzcjvpuy5rlegx4k2a