Planck. A body at temperature T radiates spectral radiance B(λ,T) = 2hc²/λ&sup5; · 1/(e^(hc/λkT) − 1). Integrating over all wavelengths gives the exitance M = σT⁴ (Stefan–Boltzmann) and the peak sits at λmax = 2898 µm·K / T (Wien): about 9.7 µm at 300 K, which is why room-temperature scenes are imaged at 8–14 µm.
Radiometric equation. The detector sees W = ετW(Tobj) + (1−ε)τW(Trefl) + (1−τ)W(Tatm), where each W is the Planck radiance integrated over the camera band. A shiny metal (ε = 0.05) mostly reflects its surroundings, so it looks cold even at 80 °C. The camera inverts the equation with the ε, reflected temperature and distance you give it; a wrong ε gives a wrong temperature (see the spot panel and the ε-error graph).
Atmosphere. Water vapour and CO₂ absorb outside two transmission windows, 3–5 µm (MWIR) and 8–14 µm (LWIR). The transmittance here is a hand-built illustrative model (Gaussian absorption features at the real band centres, scaled with absolute humidity, plus a water-vapour continuum): it shows the right trends (humidity and range lower τ; smoke particles much smaller than the wavelength scatter LWIR far less than visible light) but is not a line-by-line code such as MODTRAN. Smoke and fog values are illustrative.
Camera. A microbolometer pixel is a thermally isolated membrane: C dT/dt = P − G(T−T0), time constant τth = C/G (about 10 ms). The instantaneous field of view is IFOV = pitch / f (17 µm / 12.5 mm = 1.36 mrad). A target needs roughly 3 × IFOV to be measured rather than just seen. NETD is the temperature difference that equals the noise; low-ε surfaces amplify it by 1/ε. Fixed-pattern noise drifts until the shutter does a flat-field correction (NUC).
Buildings. Steady conduction gives Q = U A ΔT; the inside surface of a wall is at Tsi = Tin − U Rsi ΔT (Rsi = 0.13 m²K/W) and outside Tse = Tout + U Rse ΔT (0.04). Thermal bridges have a higher local U, so they show as lines. Lateral conduction is modelled by a blur of about 7 cm; pipes behind plaster use a resistance-ratio estimate. Condensation starts when Tsi falls below the dew point; mould risk is assessed at 80 % surface humidity (fRsi ≥ 0.75 criterion).
Animals and engines. Fur is a thermal resistance: Tcoat = Tair + (Tskin − Tair) Rs/(Rs + t/k) with k about 0.05 W/m·K, so a thick winter coat shows only a few kelvin above the air while eyes, ears and muzzle show the warm skin. A cooling engine follows Newton’s law T(t) = Tair + (T0 − Tair) e^(−t/τ) with a lumped time constant τ = m c/(hA) per part. All starting values are generic textbook numbers.
Honest limits. No solar loading, no view-angle dependence of ε, no spectral ε, no lens vignetting, no glass transmission (glass is opaque in LWIR), simplified wind and humidity effects. Civil uses only: building surveys, firefighting visibility and search and rescue, wildlife surveys, vehicle inspection (medical thermography uses the same physics with skin at 33–35 °C, ε about 0.98 and an NETD below 0.05 K, but is not simulated here). This is a physics teaching model and not an instrument; it is not affiliated with any camera maker.