We use phase-sensitive optical coherence tomography to measure relative motions within the human eye. From a sequence of tomograms, the phase difference between successive tomograms reveals the local axial motion of the tissue at every location within the image. The pulsation of the retina and of the lamina cribrosa amounts to, at most, a few micrometers per second, while the bulk velocity of the eye, even with the head resting in an ophthalmic instrument, is a few orders of magnitude faster. The bulk velocity changes continuously as the tomograms are acquired, whereas localized motions appear at acquisition times determined by the repeated scan of the tomogram. This difference in timing allows the bulk motion to be separated from any localized motions within a temporal bandwidth below the tomogram frame rate. In the human eye, this reveals a map of relative motions with a precision of a few micrometers per second.