Concept of error compensation for non-orthogonality in two-axis displacement measurement system utilizing single grating scale and Littrow configuration

In this study, we proposed a measurement system that compensates for orthogonality in planar stages and demonstrated its principle. The proposed measurement system consists of a single diffraction grating scale placed diagonally across the stage and two interferometers aligned in a Littrow configuration, which are sensitive only to stage displacement in the optical axis direction. The direction of measurement is determined with high accuracy by the pitch of the diffraction grating and optical wavelength of the laser, allowing orthogonality compensation. In the experiments, we demonstrated that the interferometer aligned at Littrow configuration was capable of measuring the stage displacement component in the optical axis direction. In the discussion, our assessment of orthogonality identified two crucial factors: (1) how accurately the Littrow configuration can be aligned and (2) the accuracy of the pitch of the grating scale.