Laboratory Spectroradiometric Temperature Retrieval of Silicates Using Linearized Wien Approximations and Polynomial Regression

Atilio Efrain Bica Grondona , Luis Morales-Salinas, Bijeesh Kozhikkodan Veettil

Thermal infrared (TIR) remote sensing provides critical diagnostic capabilities for surface temperature and spectral emissivity retrieval. However, extracting these parameters from at-target radiance measurements is fundamentally ill-posed because Planck's radiation law non-linearly couples kinetic temperature and spectral emissivity, creating an underdetermined system of N spectral bands with N+1 unknowns. Conventional temperature-emissivity separation (TES) algorithms mitigate this indeterminacy by imposing empirical constraints or spectral assumptions that frequently rely on external atmospheric profile sounding or specific scene properties. This paper proposes a direct, consistent inversion framework to retrieve both surface kinetic temperature and complete spectral emissivity relying strictly on at-target radiance measurements. The central premise is that spectral emissivity and kinetic temperature are physically coupled, allowing this relationship to be parameterized via a linearized Wien approximation into a polynomial regression model. Controlled spectroradiometric experiments were conducted on a high-purity crystalline hydrothermal quartz sample (SiO2) across 12 distinct thermal regimes (289.45 K to 326.75 K) under stabilized ambient conditions using a portable micro-Fourier transform interferometer (µFT-IR Model 102). Absolute radiometric calibration was conducted using a two-temperature blackbody protocol with liquid nitrogen (LN2, ~77 K) for the cold cycle and a heated blackbody cavity (~325 K). The spectral library was partitioned into calibration/training (8 regimes) and testing/validation sets (4 regimes). Five interpolators were evaluated across strategic diagnostic wavelengths (10.0 µm, 10.1 µm, 11.0 µm, and 12.0 µm): shape-preserving piecewise cubic Hermite (PCHIP), linear, quadratic, cubic, and 4th-degree polynomials. Once calibrated on the target's characteristic response, at-target radiance serves as the sole operational input: the polynomial regression directly predicts kinetic temperature, from which the complete spectral emissivity curve is simultaneously derived across all wavelengths. The experimental results demonstrate that target surface temperature can be retrieved with absolute errors below 0.02 K using simple linear regression, and below 4 × 10⁻⁴ K using 4th-degree polynomials at longer wavelengths (λ ≥ 11.0 µm). Errors below 10⁻³ K reflect algebraic model convergence, whereas physical performance is bounded by instrument noise (NEΔT ≈ 0.05 K). Importantly, this study focuses strictly on controlled laboratory spectroradiometry; operational extrapolation to airborne or orbital sensors is outside the scope of this paper and reserved for future investigations. The complete calibrated spectroradiometric dataset is openly accessible via Zenodo (DOI: 10.5281/zenodo.23571365), providing a reproducible benchmark for forward thermal radiative transfer modeling and sensor calibration.