Apparatus and method for roll invariant reflective position sensing

A position-sensing apparatus that measures the relative displacement of two members, the displacement being characterized by lateral displacement and roll, comprising:

• a diffractive grating track on a diffractive grating scale attached to one member, said track having a periodicity Pg;
• a first pair of beams of quasi-monochromatic light, said first pair of beams propagating at a first predetermined angle with respect to each other and said first pair of beams being incident on said grating at a first predetermined location along said grating, said first pair of beams reflectively diffracting from said grating to form a first set of optical fringes of a first periodicity P1;
• a second pair of beams of quasi-monochromatic light, said second pair of beams propagating at a second predetermined angle with respect to each other and said second pair of beams being incident on said scale at a second predetermined location along said grating, said second pair of beams reflectively diffracting from said grating to form a second set of optical fringes of a second periodicity P2, P2 being different from P1;
• a first periodic, interdigitated detector array, said array being positioned on said second member to detect said first set of optical fringes, said first array having a periodicity N times P1, N being greater than 2, said first array generating a first signal representative of the position of the first set of optical fringes;
• a second periodic, interdigitated detector array, said second array being positioned on said second member to detect said second set of optical fringes, said second array having a periodicity M times P2, M being greater than 2, said second array generating a second signal representative of the position of the second set of optical fringes;
• and
• a signal processor that linearly combines the first and second signals to estimate the lateral displacement or the roll of the diffractive grating scale or both.

A position-sensing apparatus that measures the relative displacement of two members, the displacement being characterized by lateral displacement and roll, comprising:

• a diffractive grating scale attached to one member, said scale having a first diffractive grating track with a first periodicity Pg1, and a second diffractive grating track with a second periodicity Pg2 being different from Pg1;
• a first pair of beams of quasi-monochromatic light, said first pair of beams propagating at a first predetermined angle with respect to each other and said first pair of beams being incident on said first track at a first predetermined location, said first pair of beams reflectively diffracting from said first track to form a first set of optical fringes of a first periodicity P1;
• a second pair of beams of quasi-monochromatic light, said second pair of beams propagating at a second predetermined angle with respect to each other and said second pair of beams being incident on said second track at a second predetermined location, said second pair of beams reflectively diffracting from said second track to form a second set of optical fringes of a second periodicity P2;
• a first periodic, interdigitated detector array, said array being positioned on said second member to detect said first set of optical fringes, said first array having a periodicity N times P1, N being greater than 2, said first array generating a first signal representative of the position of the first set of optical fringes;
• a second periodic, interdigitated detector array, said second array being positioned on said second member to detect said second set of optical fringes, said second array having a periodicity M times P2, M being greater than 2, said second array generating a second signal representative of the position of the second set of optical fringes;
• and
• a signal processor that uses the first and second signals to estimate the lateral displacement or the roll of the diffractive grating scale or both.