A well collimated thermal beam of argon atoms, moving in the z direction, crosses the electron beam that is to be studied. Those argon atoms that are excited by impact to a metastable state proceed, with very little change in speed or direction, to a detector (windowless electron multiplier) some distance away. The neutral atomic beam of the metastable atom probe (MAP) has a negligible interaction with the electromagnetic fields that govern the behavior of the electron beam; moreover, almost no additional space charge is created when the atomic beam is introduced. Thus, if the cross section of the atomic argon beam is small compared to the characteristic dimensions of the electrode structure that defines the electron beam, the metastable atom count rate, monitored as a function of x and y, gives a virtually nonperturbative measurement of the density profile of the electron beam. In this paper we outline the principles and applications of the method, discuss details of its implementation, and give results obtained with an MAP that has a spatial resolution of better than 0.5 mm.