Spectral and geometric relationships for thermal modeling. Top: reflected solar radiance (black curve) and thermally emitted radiance (red curve) emerging from the subsolar point at lunar noon, given a constant reflectance of r = 0.1, an emissivity of e = 0.95 and A_dh = 0.07. The spectral domain of the M³ instrument (0.6–3.0 μm) is dominated by solar reflection, but the thermal component increases to the same order of magnitude at 3 μm. The spectral domain of GF-4’s MIR channel (3.5–4.1 μm) is dominated by thermal emission, but roughly 10% of reflected radiance remains. The spectral range of MERTIS (7–14 μm) and Diviner’s channel four (8.10–8.40 μm) are entirely dominated by thermal emission. Bottom: illumination and observation geometry. The shape model is divided into N surface elements. We are interested in the radiance I_n(λ) that emerges from the nth facet. The vectors s, v, and n indicate the illumination vector, the viewing vector, and the surface normal vector.