Reducing tilt errors in chromatic confocal measurement: a peak extraction algorithm based on the pseudo-Voigt function

In chromatic confocal measurement (CCM), peak extraction is a critical step in converting spectral signals into physical position information, which directly affects the measurement accuracy and reliability. However, when measuring inclined surfaces with CCM techniques, the spectral confocal signal (SCS) becomes distorted and loses its symmetry. Existing peak extraction methods, when applied to asymmetric SCS, introduce high-frequency random errors, significantly reducing measurement accuracy. To address this issue, we first develop an optical transfer model for the CCM system that accounts for tilt angles and analyze the correlation mechanism between tilt angles and errors. Subsequently, we propose a robust asymmetric signal error compensation method. This method integrates the pseudo-Voigt function concept by introducing a damping perturbation with asymmetric parameters and an exponential term that adjusts the compactness of the two curve wings, enabling accurate curve fitting and peak wavelength extraction for asymmetric SCS. Simulations and experiments demonstrate that the proposed method outperforms traditional approaches in goodness-of-fit metrics (R2 and RMSE) and exhibits minimal dependence on inclination angles. Even at a 10° inclination angle, the error stabilizes below 60 nm. Compared to the Gaussian fitting method, the best performing traditional method, our approach improves measurement accuracy by 77.8% at 10° inclination and reduces positional error from 0.13μm to 0.054μm across a 160μm measurement range. The proposed method demonstrates superior robustness and accuracy, offering a feasible solution for complex surface measurements and related applications.