Superconducting tunnel junctions as sensitive elements in detectors intended for application to X-ray astronomy provide the possibility to improve the energy resolution by more than one order of magnitude compared to standard semiconductor detectors. We present our results with a detector system consisting of a separate absorber film and superconducting aluminum tunnel junctions attached to its edges. The arrangement of our detector, exploiting 'quasiparticle trapping', provides position resolution in addition to very high energy resolution. Progress in resolving power is expected as a result of the implementation of our epitaxially grown vanadium absorber films, exhibiting a long mean free path for electrons. Details of the absorber film fabrication are discussed and several methods of characterizing the quality of our absorber films are presented. In addition to the experimental results with our detectors, we report on our model of electronic noise in tunnel junctions.