Evaluation of the pitch deviation of a linear scale based on a self-calibration method with a Fizeau interferometer

Abstract

A self-calibration method, in which the wavefronts of zeroth and first-order diffracted beams from a scale grating measured by a Fizeau interferometer are employed, is applied for the evaluation of the pitch deviation of a reflective-type linear scale with a grating pitch of 2.048 μm used in a commercial interferential scanning-type optical linear encoder. One of the advantages of the self-calibration method is that the pitch deviation of a scale grating can be evaluated while measuring the out-of-flatness of the scale grating under inspection and the Z-directional out-of-flatness (surface profile) of the reference optical flat in the Fizeau interferometer. Meanwhile, in a practical case, the self-calibration method is valid under the condition where the out-of-flatness of the scale grating is on the same order or less than that of the reference optical flat in the Fizeau interferometer. In this paper, theoretical analysis and numerical calculations are thus carried out to investigate the influence of the out-of-flatness of the scale grating on measurement of the pitch deviation and the out-of-flatness of the reference optical flat. Some experiments with a linear scale from a commercial interferential scanning-type linear encoder are also carried out to verify the feasibility of the self-calibration method for the evaluation of the pitch deviation of the scale having an out-of-flatness of approximately 600 nm over the analyzed area.