High-accuracy and real-time phase solution algorithm based on extended Kalman filter for multi-degree-of-freedom grating interferometer

The heterodyne signal of a grating interferometer is formed by the interference of two coherent light beams with a frequency difference. The frequency of the heterodyne signal is equal to the frequency difference of the two light beams. When one beam undergoes Doppler frequency shift, the heterodyne signal experiences a corresponding frequency change. By calculating the phase difference between the reference and measurement heterodyne signals of the grating interferometer, the displacement of an object can be determined. The accuracy and real-time performance of solving this phase difference affect the overall performance of the grating interferometer. Multi-degree-of-freedom grating interferometers play a crucial role in high-precision fields such as lithography machines and astronomical telescope mirror alignment. The phase calculation of interference signals is an important component. Current algorithms hard to balance real-time performance and accuracy effectively. Therefore, to enhance both the precision and real-time performance of grating interferometers, this paper proposes using an extended Kalman filter (EKF) method to solve the phase difference. In the EKF model, the state variables are set as the phase, frequency, and amplitude of the sinusoidal signal, and the calculation is performed through prediction and correction steps. Since the Kalman filter algorithm only uses the current sampling point data for model calculation, it has lower latency. The algorithm was deployed on an FPGA to test the signals generated by a signal generator, achieving a measurement accuracy of 0.03° and a resolution of 0.01°. This research contributes to improving the real-time performance and accuracy of grating interferometers.