Methods and apparatuses for the exact determination of an angle of rotation

An apparatus for the accurate determination of an angle of rotation (w), comprising

• an optical detector (1) which comprises a multiplicity of detector elements (2) arranged in series, and
• a rotating body (3) which is connected to the detector (1) so as to be rotatable about an axis (a) and has a multiplicity of pattern elements (5, . . . , 13) arranged around a pattern center (4), a multiplicity of which is arranged one behind the other in the direction of rotation,
• at least some of the pattern elements (5, . . . , 13) being capable of being focused by means of optical beams at least partly on detector elements (2), and
• positions (p) of the focused pattern elements (5, . . . , 13) being capable of being resolved by means of the detector elements (2) of one and the same detector (1),
• wherein
• the optical detector elements (2) and pattern elements (5, . . . , 13) are formed and arranged relative to one another in such a way that
• effects of an eccentricity (e) of the pattern center (4) relative to the axis (a) on the determination of an angle of rotation can be computationally determined from resolved positions (p) of at least one pattern element (5, . . . , 13), and
• the angle of rotation (w) can be accurately determined from resolved positions (p1, p2, p3) of the pattern elements (5, 6, 7) arranged one behind the other, taking into account the effects.