A Real-time Determination Method for Homodyne Grating Interferometer Signal Nonlinear Error Based on Duty Cycle Measurement of States

Nonlinear error is a serious obstruction for inc- reasing the resolution and accuracy of the homodyne grating interferometer. To eliminate the nonlinear error, this article presents a real-time method to determine the nonlinear error in the homodyne grating interferometer signal. Two thresholds separate the signal into four states, and the duty cycle of each state will be measured and used to determine the nonlinear error parameters separately. The method proposed was implemented using MATLAB and a field-programmable gate array (FPGA) for the determination process. The simulation and experimental results indicated that the proposed method is easier to achieve with similar accuracy and precision compared with the methods based on the fitting algorithm. The nonlinear error could be reduced to about 37 nm from 79 nm in a 100- $\mu $ m test, similar to the fitting algorithms.