An optical measurement apparatus includes a fixed headstock and an opposed, movable tailstock mounted on a reference support. The movable tailstock is movable along a linear axis to maintain a piece to be measured between the headstock and tailstock. A mobile carriage is movable along the linear axis. The carriage carries a light source directing a beam of collimated light across the linear axis to be interrupted by a piece under measurement. An optical detector aligned with the light source is arranged to receive residual light of the beam that has not been interrupted by the piece under measurement. The measuring apparatus has a rectilinear guide, fastened on the reference support, on which are slideably engaged the optical carriage and the tailstock, whereas the headstock is placed on a headstock carrier that is fastened on the reference support and hangs at least in part over the rectilinear guide.