Heterodyne laser interferometers have been widely utilized in the field of precision measurement owing to their wide measurement range, high measurement accuracy, and robust measurement ability. With the development of high-precision science and technology, higher requirements have been proposed for the measurement accuracy of heterodyne laser interferometers, which is significantly affected by the phase measurement accuracy of the interference signal. In multichannel signal acquisition and processing, the crosstalk error between sampled signals is a familiar error source. In this study, the problem of signal crosstalk in interference signal processing is investigated, and a signal crosstalk error model is established. Accordingly, a pre-compensation method based on spectrum analysis is proposed to eliminate signal crosstalk errors and improve the phase measurement accuracy of the interference signal.

The signal crosstalk error was systematically examined through theoretical derivation, simulation analysis, and experimental verification to solve the problem of crosstalk between two sampled signals in heterodyne interferometry. First, a mathematical model of the signal crosstalk error was deduced, and a pre-compensation method based on spectrum analysis was proposed. Then, the influence of the crosstalk coefficient, signal amplitude ratio, and crosstalk signal phase offset on the signal crosstalk error was analyzed via simulation, and the crosstalk compensation method was verified. After the initial verification of the error model and compensation method through simulation, the signal processing algorithm was implemented based on the Red Pitaya FPGA board, and further verification was performed through a phase measurement experiment. The experimental results show that the actual measurement error is consistent with the theoretical calculation error and that the crosstalk compensation method can effectively eliminate the signal crosstalk error. Finally, a heterodyne interferometric measurement system was built to verify that the proposed signal processing system can meet the measurement requirements of practical applications.

This study deduces a mathematical model of the signal crosstalk error and proposes a pre-compensation method based on spectrum analysis. Then, the analysis and verification are conducted through simulations and experiments. According to the derived mathematical model of the signal crosstalk error, the crosstalk coefficient, signal amplitude ratio, and crosstalk signal phase offset affect the magnitude of the crosstalk error. The influence of these three factors on the signal crosstalk error is analyzed via simulation. The crosstalk coefficient and signal amplitude ratio significantly impact the size of the signal crosstalk error (Figs. 3 and 4), and the phase offset of the crosstalk signal affects the size of the crosstalk signal error and the location of the extreme value distribution simultaneously (Fig. 5). After the simulation analysis, the signal processing algorithm is implemented based on the Red Pitaya board, and a phase measurement experiment is performed (Fig. 8). When the amplitude ratios of the two input signals are 1, 2, and 3, the actual measurement and theoretical calculation errors are consistent (Fig. 13). After compensating for the signal crosstalk error, the maximum measurement error drops from 0.34° to 0.01° (Fig. 14). A phase measurement experiment verifies the correctness and effectiveness of the signal crosstalk error model and compensation method. Finally, a heterodyne interferometric measurement system is built to test the performance of the algorithm (Fig. 16). In the range of 250 μm, the measurement error is less than 5 nm (Fig. 17), indicating that the signal processing algorithm can meet the needs of actual measurements.

Phase measurement accuracy is essential for accurate heterodyne laser interferometer measurements, and the signal crosstalk error is a common source in multichannel signal sampling processing. This study deduces the signal crosstalk error model and proposes a pre-compensation method based on spectrum analysis to solve the problem of crosstalk between the reference signal and measurement signal in heterodyne interferometry. The influence of the crosstalk coefficient, signal amplitude ratio, and crosstalk signal phase offset on the signal crosstalk error is analyzed via simulation. When both crosstalk coefficients are 0.01, the signal amplitude ratio is 10, and the phase offset of the crosstalk signal is 0, the maximum crosstalk error of the signal can reach 5.78°, which needs to be effectively compensated. In the phase measurement experiment, when the amplitude ratios of the two signals are 1, 2, and 3, the actual measurement error is the same as the theoretical calculation error, proving that the signal crosstalk error model is correct. After the signal crosstalk error compensation, the measurement error drops from the maximum of 0.34° to 0.01°, proving that the crosstalk error compensation method is effective. In summary, this study systematically analyzes the signal crosstalk error. The proposed compensation method can effectively eliminate the signal crosstalk error and improve the phase-measurement accuracy of the heterodyne interference signal.