The device has a scanning unit that is displaceable relative to the measuring standard (1.1) in a measuring direction (X). A scanning unit (2.1) has a grating (G2) located at a scanning distance from the grating (G1). A first detector array configured to obtain a first scanning signal for position determination in which the gratings are illuminated with light of a first wavelength. A second detector array configured to obtain a second scanning signal for position determination in which the absolute mark (R1) is illuminated with light of second wavelength.