This paper reports the plans and design of positron microscopes being built at KEK (High Energy Accelerator Research Organization), Tsukuba, Japan. A used electron microscope is remodeled. The kinetic energies of positrons produced by accelerators or by nuclear decays do not have a unique value but show a spread over in a wide range. Positron beam is guided to a transmission electron microscope (JEM100SX). Positrons are moderated by a tungsten foil, accelerated and focused on a nickel sheet. The monochromatic, focused beam is injected into an electron microscope. The focusing and aberration of positrons are the same as electrons in a magnetic system which is used in commercial electron microscopes. Imaging plates are used to record positron images for the transmission electron microscope. (C) 2002 Published by Elsevier Science B.V.