Relative tilting in-plane of one of gratings in coherent gradient sensor: Error analysis and correction

Coherent gradient sensor (CGS) has a widespread application in surface morphology measurements and mechan-ical analysis. The key component of CGS is a pair of gratings whose the relative position plays an important role in measuring accuracy. The CGS system requires two gratings to be absolutely parallel to each other, but it is difficult to achieve in experiment. In addition, the effect of grating tilt has hardly been studied at present. In this paper, the influence of in-plane relative tilting angle of grating on the measured gradients and curvatures is studied theoretically and experimentally. The results demonstrate that tilting angle induces the errors in gradient and twist curvature. By using the proposed method for correction, the measured results can be compared with the actual results of standard sample.