Emissivity and reflected temperature correction

An infrared camera measures radiance, not temperature. The radiance reaching the detector is a mixture of three things: radiation emitted by the target, scaled by its emissivity ε; radiation from the surroundings reflected off the target, scaled by (1−ε); and radiation emitted by the air in between, which also attenuates the first two by the transmission τ. The camera converts the total into a temperature, so unless the correct ε, reflected apparent temperature and transmission are entered, the number on the screen is not the surface temperature.

Working in the broadband approximation where radiance goes as the fourth power of absolute temperature, the measurement equation rearranges to T_obj = [(T_meas⁴ − (1−ε)·τ·T_refl⁴ − (1−τ)·T_atm⁴)/(ε·τ)]^(1/4), with every temperature in kelvin. All three corrections push in the same direction on a hot target in cool surroundings: the reading understates the true temperature, and the lower the emissivity the worse it gets. Where the view passes through an infrared window or protective optic — routine on energised switchgear — the window's transmission τ_win multiplies everything behind it and the window adds its own emission, so the same rearrangement carries a τ_win divisor and a (1−τ_win)·T_win⁴ term.

Reflected apparent temperature is the parameter most often left at ambient by default and most often wrong. It is not the air temperature — it is the effective temperature of everything radiating onto the target, which near a furnace, a flare or a sunlit sky can be hundreds of degrees away from ambient. Measure it with the crumpled-aluminium-foil reflector method, or by reading a diffuse reflector placed at the target and pointing away from the object.

Emissivity itself is a property of the surface, not the material: polished aluminium sits near 0.05 while the same alloy oxidised is 0.25, and paint, rust or a scale layer takes carbon steel to 0.9. It also varies with viewing angle, wavelength band and temperature. Because the correction divides by ε, low-emissivity surfaces amplify every error — which is why the sensitivity figure matters: it shows how many degrees the answer moves for a 0.05 change in the emissivity assumed. Where that number is large, apply a high-emissivity tape or paint patch and measure the surface temperature there instead of arguing about the value.

T_obj = [ (T_meas⁴ − τw·(1−ε)·τ·T_refl⁴ − τw·(1−τ)·T_atm⁴ − (1−τw)·T_win⁴) / (ε·τ·τw) ]^0.25
all temperatures in kelvin: K = °C + 273.15
no window, short path (τw = τ = 1):  T_obj = [ (T_meas⁴ − (1−ε)·T_refl⁴) / ε ]^0.25