Infrared Interference Thickness Inversion Based on Hilbert Analytic Signal and Full-Spectrum Phase Regression

Abstract

This paper proposes a unified algorithmic framework that integrates physical modeling and signal processing for the stable extraction of interference fringe information and the inversion of epitaxial layer thickness in infrared reflectance spectroscopy. First, an optical interference model is established based on phase difference theory, explicitly linking the thickness parameter to the phase-wavenumber relationship, and unifying the description of model parameters through a refractive index correction term. At the signal processing level, Savitzky–Golay filtering is employed for baseline subtraction, and the Hilbert transform is utilized to construct an analytical signal, thereby separating the amplitude and phase of the interference signal and converting the original oscillatory structure into a continuous phase representation. Building on this, phase expansion and linear fitting methods are introduced to propose a full-spectrum phase regression model, transforming the thickness estimation into a global parameter solving problem and thereby reducing dependence on local features. Furthermore, a dual-path inversion mechanism is constructed by combining extreme value spacing calculation methods, and the stability of the results is enhanced through statistical averaging of multiple sets of fringes. Concurrently, a multi-beam interference expansion expression based on the Airy model is introduced, enabling the algorithm to maintain a consistent computational form under varying reflection conditions. Experimental results demonstrate that this method exhibits excellent numerical consistency and noise resistance under diverse data conditions, and the overall framework possesses strong versatility and scalability.