Currently, observations of space debris are primarily performed with ground-based sensors. These sensors have a detection limit at some centimetres diameter for objects in Low Earth Orbit (LEO) and at about 20 cm diameter for objects in Geostationary Orbit (GEO). The few space-based debris observations stem mainly from in-situ measurements and from the analysis of returned spacecraft surfaces. Both provide information about mostly sub-millimetre-sized debris particles. As a consequence, the population of centimetre- and millimetre-sized debris objects remains poorly understood. The development, validation and improvement of debris reference models drive the need for measurements covering the whole diameter range. In 2003 the European Space Agency (ESA) initiated a study entitled "Space-Based Optical Observation of Space Debris". The first tasks of the study were to define user requirements and to develop an observation strategy for a space-based instrument capable of observing uncatalogued millimetre-sized debris objects. Only passive optical observations were considered, focussing on mission concepts for the LEO, and GEO regions respectively. Starting from the user requirements and the observation strategy, an instrument system architecture and an associated operations concept have been elaborated. The instrument system architecture covers the telescope, camera and onboard processing electronics. The proposed telescope is a folded Schmidt design, characterised by a 20 cm aperture and a large field of view of 6 degrees. The camera design is based on the use of either a frame-transfer charge coupled device (CCD), or on a cooled hybrid sensor with fast read-out. A four megapixel sensor is foreseen. For the onboard processing, a scalable architecture is selected. Performance simulations have been executed for the system as designed, focussing on the orbit determination of observed debris particles, the estimation of the limiting debris particle size, and on the analysis of the object detection algorithms in terms of limiting magnitude. In this paper we present some of the main results of the study. A short overview of the user requirements and observation strategy is given. The architectural design of the instrument is discussed, and the main trade-offs are outlined. An overview of the results of the performance simulations is provided. The main conclusion is that with the proposed architecture, observation of centimetre-sized debris is possible and in many cases the orientation of the orbit can be determined from a single observed FOV crossing event.