A low-energy electron point source microscope equipped with a position-sensitive energy analyzer is constructed. A nanometer-sized feature can be zoomed in and its energy-loss spectrum can be measured with a retarding field-type energy analyzer mounted in front of the imaging screen. The geometric and the electronic structures of carbon nanotubes are measured with the present system. Interference between the scattered and the transmitted electron beams through the carbon nanotubes is observed using an atomically sharp field emitter. The electron energy-loss spectrum shows two prominent peaks at similar to 7 and 16-17 eV, which are identified as the pi plasmon and (pi + sigma) surface-plasmon peaks. This result is consistent with the measurements of high-energy electron energy-loss spectroscopy as well as the theoretical calculation. (C) 1999 American Institute of Physics. [S0034-6748(99)02011-0].