CdTe array detectors are being investigated for use in a variety of applications, ranging from medical diagnosis to high-energy astronomy. Herein, we present a study of the spatial resolution of several prototype CdTe arrays of varying thickness as a function of energy and angle of the incident radiation. These measurements were performed at the European Synchrotron Research Facility at Grenoble, France in the first week of July 2002. The energy range employed was between 100 and 500 keV, while the detectors consisted of a set of CdTe arrays containing elements of thicknesses between 3 and 8 mm. The spatial response of the detectors was measured using single site events, while the possibility of using this type of array detector also for measuring the degree of polarisation of the radiation was investigated using multi-site interactions.