We demonstrate a time-to-space mapping of an optical signal with a picosecond time resolution based on an electrooptic beam deflection. A time axis of the optical signal is mapped into a spatial replica by the deflection. We theoretically derive a minimum time resolution of the time-to-space mapping and confirm it experimentally on the basis of the pulse width of the optical pulses picked out from the deflected beam through a narrow slit which acts as a temporal window. We have achieved the minimum time resolution of 1.6+/-0.2 ps.