Use of two planar gratings to measure 3-DOF displacements of planar moving stage

This paper presents a 3-DOF displacement (x, y, R_z) measurement method for planar moving stage based on two planar gratings. The measurement system consists of two planar gratings placed in a diagonal line of a planar moving stage while each planar grating can acquire 2-D displacement measurement at one time. The mathematical model is then established to calculate 3-DOF displacements of a planar moving stage according to four outputs of two planar gratings. The presented measurement method not only solves the mounting inconvenience of using three 1-D linear gratings but also calculates and compensates the assembly misalignment errors by mathematical model itself. Experiments are carried out to prove the superiority of the presented measurement method. Experimental results indicate that the presented method can reduce the coupling errors in x and y directions approximately by three and 15 times, respectively, compared with the method of using three 1-D linear gratings. It can be concluded that the presented measurement method can be effectively used to achieve 3-DOF displacement for planar moving stage.