A Nonlinear Error Compensation Method for Heterodyne Interferometry Based on Self-Supervised Physics-Informed Neural
Yao Wang1, Hongyu Sun1, Jiakun Li1
1Key Lab of Luminescence and Optical Information, School of Physical Science and Engineering, Beijing Jiaotong University, Beijing 100044, China.
Sensors (Basel, Switzerland)
|May 27, 2026
Summary
A novel self-supervised Physics-Informed Neural Network (PINN) method precisely calibrates laser heterodyne interferometric sensors. This approach significantly reduces nonlinear errors, enhancing precision metrology sensor performance even in low signal-to-noise ratios (SNR).
Area of Science:
- Precision Metrology
- Optical Sensing Systems
- Artificial Intelligence in Engineering
Background:
- Laser heterodyne interferometric systems have high theoretical resolution but are limited by nonlinear errors from optical imperfections.
- Existing compensation methods are complex, hardware-dependent, and perform poorly under low signal-to-noise ratios (SNR).
Purpose of the Study:
- To develop a novel precision calibration method for laser heterodyne interferometric sensing systems.
- To address limitations of conventional methods by utilizing a self-supervised Physics-Informed Neural Network (PINN).
Main Methods:
- A self-supervised PINN guided by frequency-domain priors was employed for robust nonlinear error compensation.
- Measurement residuals with periodic physical features were extracted using high-precision displacement references.
- Frequency-domain priors were integrated into a physically constrained network, using theoretical frequency characteristics for pseudo-label generation and the error equation as a differentiable physical layer for hard constraints.
Main Results:
- The root-mean-square (RMS) nonlinear error was reduced from 1.90 nm to 0.23 nm.
- A significant nonlinear error compensation rate of up to 88.13% was achieved.
- The method demonstrated effective identification of nonlinear physical properties even in high background noise.
Conclusions:
- The proposed PINN-based method offers a reliable framework for intelligent calibration and self-characterization of heterodyne interferometric industrial sensors.
- This approach enhances the practical precision of interferometric sensing systems, particularly in demanding metrology applications.
- The method overcomes limitations of conventional techniques, offering improved performance and robustness.
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