Evaluation of the pitch deviation of a diffraction scale grating having a pitch shorter than the light wavelength of a measuring laser beam

Abstract A major modification has been made to an optical head for the measuring method that evaluates the pitch deviation of a diffraction scale grating based on the angular information of the diffracted beams. In the conventional method, the angular information of the positive and negative diffracted beams obtained by projecting a laser beam onto a scale at a right angle is utilized to evaluate the pitch deviation. Meanwhile, this method cannot measure scales having a nominal pitch shorter than the wavelength of the laser beam; this fundamental limitation has restricted the applicability of this method. To address the issue, in this study, the optical head has been modified in such a way that a laser beam is projected onto a grating with an oblique incidence so that the negative first-order diffracted beam can be obtained even when the nominal pitch of the scale is shorter than the wavelength of the laser beam. By detecting the changes in the angle of diffraction of the diffracted beam and the angle of reflection of the reflected beam, the pitch deviation of a diffraction grating can be evaluated without being affected by the angular error motion of the scale, as well as the local slope of the grating. Numerical calculations are carried out to verify the effectiveness of the extended principle. In addition, a modified optical head using a Littrow configuration is newly designed and constructed. Experiments have been carried out, and a pitch deviation on the order of 0.001 nm has successfully been detected, verifying the feasibility of the modified optical head with the Littrow configuration.