Real-time displacement calculation and offline geometric calibration of the grating interferometer system for ultra-precision wafer stage measurement

Abstract For ultra-precision wafer stage measurement in a photolithography scanner, real-time six-degree-of-freedom displacement calculation and offline geometric calibration methods are proposed to solve the multiple nonlinearities caused by rotation-translation coupling, Abbe error, and cosine error of the grating interferometer system with non-ideal geometry. First, the interference signal phase-shift model related to the displacements of the center of mass of the wafer stage is established. Then, through double approximations, the displacement calculation process is efficiently reduced to polynomials of substitution variables of phase-shift to improve the real-time performance of computing. Finally, the non-ideal geometry of the nonlinear computing model caused by manufacturing and assembly errors is calibrated offline by solving overdetermined equations set up by redundant measurement to improve the calculation precision. The proposed methods are verified through ZEMAX simulation.