1. A blur correction apparatus comprising: a photographic optical system that comprises a blur correction optical system that corrects a blur, with the blur correction optical system comprising a transmitting member; a detection unit that is provided at the photographic optical system and is capable of detecting a vibration of the photographic optical system; an imaging unit that is provided at an image side of the photographic optical system and captures an image formed through the photographic optical system; a drive unit, with at least part of the drive unit connected to the transmitting member, that drives only the transmitting member in the photographic optical system; a correction unit that comprises a processor and corrects the image captured by the imaging unit while the blur correction optical system is driven by the drive unit; and an output unit that outputs a deviation between a target drive position for the drive unit to drive the blur correction optical unit and an actual drive position of the blur correction optical system, wherein: the correction unit corrects the image captured by the imaging unit in accordance with the deviation.