At the Munich 15 MV tandem accelerator a new two-stage microprobe system is under construction. It will demagnify a beam spot by a factor 200 in both transversal directions for ions up to an energy of 200 MeV . q(2)/A. The second stage of the system is a superconducting quadrupole doublet lens, with overlayed 2n-poles, n=4, 6 and 8. The multipole components of this lens have been determined by a ray tracing program with a special treatment of the fringing fields. As a result of these calculations, the overall geometrical aberrations at the focal point are 180 nm horizontally and 280 nm vertically at full angular acceptance (image coordinates +/-9 and +/-20 mrad, respectively). A main part of the superconducting lens is a central ceramic tube which defines the exact positions of the poles. Superconducting NbTi foils are used to shape the field to the desired one. Superconducting current loops automatically serve for a suppression of all odd harmonic field components.