For monitoring the position and shape of fast moving and, especially, rotating objects such as turbo machine rotors, contactless and compact sensors with a high measurement rate as well as high precision are required. We present for the first time, to the best of our knowledge, a novel laser Doppler sensor employing a single fan-shaped interference fringe system, which allows measuring for the position and shape of fast moving solid bodies with known tangential velocity. It is shown theoretically as well as experimentally that this sensor offers concurrently high position resolution and high temporal resolution in contrast to conventional measurement techniques, since its measurement uncertainty is, in principle, independent of the object velocity. Moreover, it can be built very compact, because it features low complexity. To prove its operational capability and its potential for practical applications, radial and axial shape measurements of rotating bodies are demonstrated in comparison with triangulation. An average position resolution of about 2 microm could be achieved.