Accurate measurement of orthogonality of equal-period, two-dimensional gratings by an interferometric method

A two-dimensional grating can be used as a key component in planar encoders for measuring two-dimensional displacements or calibrating coordinate measuring machines. Ideally the two main periodic directions of the grating, the directions along which a translation by a grating period leaves the two-dimensional pattern indistinguishable from the untranslated one, should be perfectly orthogonal; any deviation from orthogonality causes cross-talk errors and necessitates system calibration. We present a method to measure the orthogonality, or the non-orthogonality angle of two-dimensional gratings precisely. This method uses interference fringes generated by diffracted beams of different orders to align the grating's periodic directions, and applies a new measurement strategy to directly measure the non-orthogonality angle by an autocollimator. Compared with traditional optical diffractometry, its angular position alignment is of higher sensitivity and its angle measurement is of lower uncertainty, and the measurement uncertainty is reduced. Orthogonalities of four gratings were measured and the standard uncertainty was 0.28 arcsec. The results agree well with the measurement results of optical diffractometry.