Abstract: In an interferential measurement device for at least one direction of measurement for measuring the relative position of objects, the collimated light beam bundle emanating from a light source is split into three diffraction beams in the at least one direction of measurement at a scanning grid. These three diffraction beams are divided into eight diffraction beams at a cross grid of a material measure and in turn come to interference at a scanning grid under renewed diffraction. The resultant diffraction beams fall on detectors for the generation of measured positional values for the at least one direction of measurement. The cross grid of the scale extends diagonally to the at least one direction of measurement and has an effective grid constant de in the direction of measurement, which agrees with the grid constant d of the scanning grid.