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The signal filtering of the grating encoder is of great significance to the measurement accuracy, aiming at eliminating the background noise potentially from the temperature changes, airflow fluctuations, and mechanical vibrations. Compared with the traditional time-frequency analysis methods, including wavelet transform, fast Fourier transform (FFT), and time Fourier transforms (TFT), the empirical mode decomposition (EMD) algorithm owing to no basis functions and high adaptability, is widely applied for signal decomposition. Here, we extended the EMD algorithm for the background-noise-based signal filtering in a grating encoder, with the experimental parameters of 5 µm/s moving speed and ~19 mm stroke. Simultaneously, a laser interferometer, as a reference, was additionally assembled to calibrate the measurement results of the grating encoder. The measurement signal was collected by NI acquisition card with a 1000 Hz sample rate and processed by EMD algorithm. Here, EMD decomposed the signal into multiple intrinsic mode functions (IMFs), which were reconstructed by removing the noise and DC components according to the correlation coefficients. Compared with the measurement results of the laser interferometer, the measurement displacement with a 6.2 µm error was solved by the phase correction and arctangent calculation from the reconstructed signals. Finally, our proposed signal-filtering approach based on the EMD algorithm exhibits a stable, accurate, and real-time calculation performance applicable for the grating encoder with ultra-high precision positioning.

The signal processing of the grating encoder has a great impact on its accuracy and resolution. We proposed a new type of signal processing method for a grating encoder using a two-phase differential algorithm based on the two-phase physical structure. The interference signal could be divided into two phases with 90 degrees phase delay, capable of effectively reducing the number of optical devices and the space occupied by the reading head. Owing to the rapid elimination of the DC component in the measurement signal, the measurement displacement was solved swiftly by the two-phase signal using the algorithm. In the experiment, a 660 nm laser and a 1 µm-period grating were used, and the scale grating was actuated at a speed of 1 µm/s by a linear stage. With a sampling rate of 20 kHz, the system resolution of the grating encoder was enabled to reach 50 pm. Simultaneously, there was a measurement error of ±1 µm at a stroke of 4 mm, and the error within a single cycle was 2 nm. Compared with the four-phase algorithm, our proposed two-phase differential algorithm exhibits a compact physical structure and fast solution without reducing the accuracy and resolution, which will be of great significance to the real-time measurement and miniaturization of grating encoders.