In this thesis a new detector concept for a cryogenic imaging spectrometer has been experimentally developed. The new detector scheme consists of a large dielectric absorber (sapphire), which is simultaneously read out with two superconducting phase transition thermometers (SPTs). An X-ray absorbed in the sapphire creates a non-equilibrium phonon flux. Each thermometer detects a share of the initially deposited energy. The measurement of the coincident signals allows the reconstruction of both the energy and the position of the X-ray event. With a prototype detector an energy resolution of 224 eV (#+-# 6 keV) with imaging over a length of 1 cm was demonstrated. The spatial resolution was determined to be better than #approx#200 #mu#m. In addition, with a single SPT an energy resolution of 27.6 eV (#+-# 1.5 keV) was shown, which indicates the potential of such a detector. Further investigations showed the ability to extend this concept to larger areas, higher count rates (>#approx#kHz) and better energy and position resolution. (author)SIGLEAvailable from British Library Document Supply Centre-DSC:D207929 / BLDSC - British Library Document Supply CentreGBUnited Kingdo