In order to achieve realization of ultra-high-precision positioning. of grating a method of complementary calibration is proposed to realize high-precision displacement detection. The grating ruler is used as the positioning measuring device of the nano-positioning platform and the dual-frequency laser interferometric displacement measuring system is used as the measuring reference to compensate and calibrate the measuring error of the grating ruler to improve the measuring precision of the grating ruler. To achieve the purpose of precise positioning. Based on the measurement principle of dual-frequency laser interferometry

the formulas of the interference displacement and the compensation formulas are deduced

and the ultra-high precision measurement optical path are established. An effective wavelength compensation method is given by Edlen formula to improve the precision of the displacement measurement. Step-by-step sampling and comparing method is used to validate the feasibility of system is verified. The precision calibrated system is improved from ± 0. 5 μm to ± 0. 1 μm

which meets the requirements of grating scoring precision detection. By experimental verification

the proposed system is feasible for nano-scale positioning detection.