9 figures, 3 tablesInternational audienceWe present experimental results obtained for a one-dimensional pedestrian flow using high precision motion capture. The full pedestrians' trajectories are obtained. In this paper, we focus on the fundamental diagram, and on the relation between instantaneous velocity and spatial headway (distance to the predecessor). While the latter was found to be linear in previous experiments, we show that it is rather a piecewise linear behavior which is found if larger density ranges are covered. Indeed, our data clearly exhibits three distinct regimes in the behavior of pedestrians that follow each other. The transitions between these regimes occur at spatial headways of about 1.1 and 3 meters respectively. Th...