Error compensation of subdivision in grating interferometry based on the least square method
                                                                 SHU Mingyang，CHEN Jian
               (The 55th Research Institute，China Electronics Technology Group Corporation，Nanjing 211100，China)

Abstract: Aiming at solving the problem of subdivision error in grating interferometry for nanometer resolution, the subdivision principle of grating interferometry, noise in sensing signal and nonlinear error were investigated. Digital subdivision was adopted and the noise in photoelectric signal was removed with the help of digital filtering. Meanwhile, an error compensation method based on the least square method was proposed in order to compensate the nonlinear error which caused by the amplitude fluctuation, DC shift and the nonorthogonal in the sensing signal. The grating interferometry system was tested by the twocoordinate nanopositioning stage. The experimental results show that the standard deviation of the measured series after corrected is significantly lower than that before in 50 nm and 200 nm measurements with constant displacement，which indicate that this method can enhance subdivision accuracy by compensate the subdivision error noteworthy.

Key words: grating; interferometry; digital subdivision; error compensation