The acceleration of multi-MeV protons from the rear surface of thin solid foils irradiated by an intense (approximately 10(18) W/cm2) and short (approximately 1.5 ps) laser pulse has been investigated using transverse proton probing. The structure of the electric field driving the expansion of the proton beam has been resolved with high spatial and temporal resolution. The main features of the experimental observations, namely, an initial intense sheath field and a late time field peaking at the beam front, are consistent with the results from particle-in-cell and fluid simulations of thin plasma expansion into a vacuum.