The concept of a scanning positron microscope which is under construct
ion in Munchen and Trento will be shown. A beam with a variable energy
from 1 to 30 keV and a spot diameter of 1 mu m, which can be scanned
over an area of (0.6 x 0.6) mm(2), is formed after a double stage stoc
hastic cooling of the positrons emitted from a radioactive source. Add
itionally, the beam will be pulsed to have a well-defined time base fo
r positron lifetime measurements. The design of the microscope is domi
nated by special demands of positron physics. Therefore, the microscop
e contains electron optical elements which are well known but rarely u
sed. These are the through the lens reflection remoderator and the opt
ical column with a magnetic side gap lens as probe forming lens.