A work piece carrier is provided with two reference systems for accurately positioning it with regard to a chuck member. The work piece carrier comprises a central aperture with the two opposite ends of the aperture surrounded by one of the reference systems. The two reference systems are independent from each other and allow the work piece carrier to be attached to the chuck member in two different positions. Assigned to each reference system is a protrusion surrounding the central aperture and extending substantially in the direction of the central longitudinal axis of the work piece carrier. The particular protrusion is provided with a shoulder serving as a clamping surface, adapted to be engaged by clamping elements provided in the chuck member. Preferably, also the centering elements for defining the position of the work piece carrier with regard to the chuck member are located on the particular protrusion.