Nonlinear real-time correction in homodyne interferometers by multi-area spatial sampling and dimensionality-reduced ellipse fitting

Homodyne interferometers are susceptible to signal instability, including the amplitude, relative phase, and DC bias of interference signals, which lead to dynamic nonlinear errors that require real-time correction to ensure full-range displacement measurement accuracy. To address these issues, this paper proposes a real-time, non-iterative FPGA-based nonlinear correction method, designed to balance accuracy and computational efficiency. The method employs peak detection to simplify the elliptical fitting matrix and utilizes feature-based segmented sampling to perform reduced-order correction. Experimental results show that when elliptical signals are unstable, this method reduces residual error from 1.14 nm to 0.12 nm, effectively compensating for nonlinear errors. In a 25 µm displacement test, this method maintains nonlinear error deviation within the sub-nanometer range compared to traditional correction methods, while reducing the computational load by two orders of magnitude, achieving a balance between correction accuracy and efficiency.