A Signal Processing Method for Homodyne Laser Interferometer Based on Model Parameter Self-Calibration With Redundant Information

In lithography wafer stage systems, laser interferometers are one of the most important precision measuring instruments. The homodyne interferometer is based on the single-frequency laser interference effect and is able to provide displacement resolution smaller than sub-nanometer. However, its accuracy is affected by ac amplitude variation, dc offset, and quadrature-phase error of the interference signal. In this article, a high-precision signal processing method is proposed, which can make full use of the redundant multiphase information, obtain higher accuracy than the quadrature interferometer, and is more practical than the existing signal processing method in multiphase interferometers because it can approach the theoretical upper limit of accuracy for any number of detection signals. In this method, multiple detectors are installed on the interference optical path, and the Gauss–Newton algorithm is used to solve nonlinear equations containing redundant information. All the parameters are calibrated simultaneously, so the calculation accuracy is improved by avoiding the error transfer in different calculation processes. The simulation shows that using the above methods, when the noise level is 66 dB, the relative errors of calibrated parameters are less than 0.03%, the standard deviation (STD) of the phase error is $5.13 \times 10^{-4}$ rad, and the equivalent STD of the displacement error is 15.9 pm. In the experiment, the root-mean-square error (RMSE) of the displacement is 0.846 nm under the signal noise level of 37.4 dB.