A Cartesian numerically controlled machine tool for high-precision machining includes a footing, a first part with first movement elements for the movement of a second part with respect to a first controlled axis, a second part with second movement elements for the movement of a third part with respect to a second controlled axis, and a third part with third movement elements for the movement of a machining head with respect to a third controlled axis. The Cartesian machine tool further includes a machining head, and, on board, optical elements for detecting and monitoring the position of at least one reference nodal point for each of one or more of the controlled axes with respect to a reference that is integral with a part of the machine tool.