EEG

Electroencephalograph.  This is one of the primary ways that scientists study sleep.  The EEG measures the electrical activity of the brain, via electrodes attached to a subject's scalp.  Hans Berger is usually credited with its invention (c. 1920), although scientists had been experimenting with charting the electrical activity of the brain in the late 19th century.

Sources:

Dement, The Promise of Sleep

Lavie, The Enchanted World of Sleep