A Nonlinear Error Compensation Method for Heterodyne Interferometry Based on Self-Supervised Physics-Informed Neural Networks with Frequency-Domain Priors

Although laser heterodyne interferometric sensing systems offer exceptional theoretical resolution, practical precision is constrained by intractable nonlinear errors stemming from optical imperfections. Conventional compensation methods suffer from hardware dependency, complexity, and performance degradation under low signal-to-noise ratios (SNR). To address this, we propose a precision calibration method using a self-supervised Physics-Informed Neural Network (PINN) guided by frequency-domain priors with harmonic distribution characteristics. This approach establishes a robust compensation model by inverting equivalent parameter sets and error curves in a single step. Specifically, leveraging high-precision displacement references, the method extracts measurement residuals containing periodic physical features. Subsequently, it integrates frequency-domain priors into a physically constrained network architecture: theoretical frequency characteristics construct masks to generate high-confidence pseudo-labels, while the error equation is recast as a differentiable physical layer imposing explicit hard constraints during forward propagation. This mechanism enables precise identification of the system’s nonlinear physical properties against high background noise. Experimental results show that the root-mean-square (RMS) value of the nonlinear error was reduced from 1.90 nm to 0.23 nm, with a compensation rate reaching up to 88.13%. This method provides a reliable framework for the intelligent calibration and error self-characterization of heterodyne interferometric industrial sensors in the field of precision metrology sensors.