Simulation and Experimental Validation of Long-Wave Infrared Polarization Characteristics Based on the Smith-pBRDF Model

Long-wave infrared (LWIR, 8–14 μm) polarization detection supports target recognition, but measuring target polarization characteristics is costly and sample-limited, and existing polarized bidirectional reflectance distribution function (pBRDF) models suffer from energy divergence at grazing angles, over-reliance on empirical parameters, and neglect of the temperature dependence of the complex refractive index. To address these issues, a Smith-pBRDF analytical model is proposed: a closed-form Smith masking–shadowing function embedded in the microfacet specular term suppresses grazing-angle divergence; two-dimensional directional–hemispherical reflectance (DHR) integration coupled with Kirchhoff’s law models rough-surface emission polarization; and wavelength-dependent optical constants are integrated over the 8–14 μm detector band, with the thermo-optic effect included through dynamic complex-refractive-index evolution. Division-of-focal-plane (DoFP) LWIR polarization imaging of silicon carbide and alumina at 338 K, 358 K and 378 K over viewing angles of 0°–80° is used to compare the proposed model with the original Priest–Germer (P–G) and the Minnaert-modified models. The measured degree of linear polarization (DoLP) increases with both viewing angle and temperature; this rise is governed primarily by the Planckian target–background radiance contrast, while the thermo-optic term provides a secondary refinement. The original P–G model—which obtains its emission polarization from the smooth-interface Fresnel relation, neglecting the microfacet distribution—overestimates the DoLP by roughly an order of magnitude (RMSE 0.036–0.089). The Minnaert and Smith models both reproduce the measurements well, with RMSE 0.0004–0.0011 for alumina and 0.0032–0.0070 for silicon carbide. The proposed three-parameter Smith model attains the lowest AICc and BIC for both materials while using fewer parameters than the Minnaert model, demonstrating improved physical fidelity and parameter efficiency.