A Unified Complex-Fresnel Model for Physically Based Long-Wave Infrared Imaging and Simulation

Accurate modelling of reflection, transmission, absorption, and emission at material interfaces is essential for infrared imaging, rendering, and the simulation of optical and sensing systems. This need is particularly pronounced across the short-wave to long-wave infrared (SWIR-LWIR) spectrum, where many materials exhibit dispersion- and wavelength-dependent attenuation described by complex refractive indices. In this work, we introduce a unified formulation of the full Fresnel equations that directly incorporates wavelength-dependent complex refractive-index data and provides physically consistent interface behaviour for both dielectrics and conductors. The approach reformulates the classical Fresnel expressions to eliminate sign ambiguities and numerical instabilities, resulting in a stable evaluation across incidence angles and for strongly absorbing materials. We demonstrate the model through spectral-rendering simulations that illustrate realistic reflectance and transmittance behaviour for materials with different infrared optical properties. To assess its suitability for thermal-infrared applications, we also compare the simulated long-wave emission of a heated glass sphere with measurements from a LWIR camera. The agreement between measured and simulated radiometric trends indicates that the proposed formulation offers a practical and physically grounded tool for wavelength-parametric interface modelling in infrared imaging, supporting applications in spectral rendering, synthetic data generation, and infrared system analysis.