A measuring head system for a coordinate measuring machine, having a scanning element for contacting a measured object as a contacting part, which can be moved such that an object to be measured can be mechanically scanned using the scanning element. An optical sensor is fixed on the measuring head base. Means are provided to generate a projection on the sensor line using at least one radiation source. The means have at least one first mask element to generate a first partial projection on the sensor line such that said partial projection is optimized to determine an x displacement and a y displacement of the contacting part in relation to the measuring head base in the x direction or y direction. An analysis unit is configured to determine the x displacement and the y displacement from signals only generated by the one sensor line.