Optical position measuring device for recording the relative position of at least two scales (30, 40; 130.1, 130.2; 140.1, 140.2) which are movable relative to one another along two measurement directions (x, y) and are arranged in different planes and crossed relative to each other, wherein - the optical position measuring device comprises at least two scales (30, 40; 130.1, 130.2; 140.1, 140.2), a light source and a detection unit, - the two scales (30, 40; 130.1, 130.2; 140.1, 140.2) each comprise at least one measurement graduation (G1, G2, G3; 31, 41; 1131.1, 1131.2, 1141.1, 1141.2) with grating regions that have different optical properties arranged periodically along at least one measurement direction (x, y) and the directions of longitudinal extent (R L1, R L2) of the scales (30, 40; 130.1, 130.2; 140.1, 140.2) are each oriented parallel to a first or second measurement direction (x, y), and - wherein the at least two scales (30, 40; 130.1, 130.2; 140.1, 140.2) are configured such that - an illumination beam emitted by the light source is split into at least two component beams (S1, S2) at the first scale (30; 130.1; 140.1) and - the component beams (S1, S2) subsequently impinge upon the second scale (40; 130.2; 140.2) and experience a reflection back in the direction of the first scale (30; 130.1; 140.1) and - the back-reflected component beams (S1, S2) are incident on the first scale (30; 130.1; 140.1) again and recombined there such that at least one resultant signal beam subsequently propagates in the direction of the detection unit, by means of which one or more position-dependent sensing signals are generable in respect of the relative motion of the scales (30, 40; 130.1, 130.2; 140.1, 140.2) along the first or second measurement direction (x, y), wherein the measurement graduation (G1, G2, G3; 31, 41; 1131.1, 1131.2, 1141.1, 1141.2) of at least one scale (30, 40; 130.1, 130.2; 140.1, 140.2) is in the form of a two-dimensional cross grating (131.1; 231.1, 331.1; 431.1; 531.1; 631.1), characterized - in that the cross grating (131.1; 231.1, 331.1; 431.1; 531.1; 631.1) has such a filter effect that interfering higher orders of diffraction are suppressed at the cross grating (131.1; 231.1, 331.1; 431.1; 531.1; 631.1), - wherein the cross grating (131.1; 231.1; 331.1; 431.1; 531.1; 631.1) has first and second areal measurement graduation regions (M1 1, M1 2) with different optical properties arranged in chequerboard fashion, the said measurement graduation regions being arranged in chequerboard fashion, periodically with a first region periodicity (P B1) along the longitudinal direction of extent (R L1) and periodically with a second region periodicity (P B2) along a transverse direction of extent (R Q1) of the cross grating (131.1; 231.1; 331.1; 431.1; 531.1; 631.1) oriented orthogonally to the longitudinal direction of extent (R L1), wherein a one-dimensional or two-dimensional, periodic line grating is overlaid on the first and second areal measurement graduation regions (M1 1, M1 2). - the optical position measuring device comprises at least two scales (30, 40; 130.1, 130.2; 140.1, 140.2), a light source and a detection unit, - the two scales (30, 40; 130.1, 130.2; 140.1, 140.2) each comprise at least one measurement graduation (G1, G2, G3; 31, 41; 1131.1, 1131.2, 1141.1, 1141.2) with grating regions that have different optical properties arranged periodically along at least one measurement direction (x, y) and the directions of longitudinal extent (R L1, R L2) of the scales (30, 40; 130.1, 130.2; 140.1, 140.2) are each oriented parallel to a first or second measurement direction (x, y), and - wherein the at least two scales (30, 40; 130.1, 130.2; 140.1, 140.2) are configured such that - an illumination beam emitted by the light source is split into at least two component beams (S1, S2) at the first scale (30; 130.1; 140.1) and - the component beams (S1, S2) subsequently impinge upon the second scale (40; 130.2; 140.2) and experience a reflection back in the direction of the first scale (30; 130.1; 140.1) and - the back-reflected component beams (S1, S2) are incident on the first scale (30; 130.1; 140.1) again and recombined there such that at least one resultant signal beam subsequently propagates in the direction of the detection unit, by means of which one or more position-dependent sensing signals are generable in respect of the relative motion of the scales (30, 40; 130.1, 130.2; 140.1, 140.2) along the first or second measurement direction (x, y), - in that the cross grating (131.1; 231.1, 331.1; 431.1; 531.1; 631.1) has such a filter effect that interfering higher orders of diffraction are suppressed at the cross grating (131.1; 231.1, 331.1; 431.1; 531.1; 631.1), - wherein the cross grating (131.1; 231.1; 331.1; 431.1; 531.1; 631.1) has first and second areal measurement graduation regions (M1 1, M1 2) with different optical properties arranged in chequerboard fashion, the said measurement graduation regions being arranged in chequerboard fashion, periodically with a first region periodicity (P B1) along the longitudinal direction of extent (R L1) and periodically with a second region periodicity (P B2) along a transverse direction of extent (R Q1) of the cross grating (131.1; 231.1; 331.1; 431.1; 531.1; 631.1) oriented orthogonally to the longitudinal direction of extent (R L1), wherein a one-dimensional or two-dimensional, periodic line grating is overlaid on the first and second areal measurement graduation regions (M1 1, M1 2).