= Two-load radiometer calibration
{title2=$T_s=T_c+(T_h-T_c)(S_s-S_c)/(S_h-S_c)$}
For a stable <radiometer> with affine output $S=g(T+T_r)$, let $g>0$ be the fixed response coefficient and $T_r$ the <receiver noise temperature>. Two reference loads with known equivalent input <noise temperatures> $T_c<T_h$ give outputs $S_c$ and $S_h$. Subtracting their outputs eliminates $T_r$; dividing source and reference differences eliminates $g$:
$$
S_h-S_c=g(T_h-T_c),\qquad
T_s=T_c+(T_h-T_c)\frac{S_s-S_c}{S_h-S_c}.
$$
This <two-load radiometer calibration> assumes unchanged response and <receiver noise temperature> between readings, with the loads and source referred to the same input. It also eliminates an additional constant output offset. Physical load <temperatures> must first be converted to the applicable equivalent input <noise temperatures> when the classical thermal approximation fails. The <Penzias-Wilson microwave background experiment> gives an original worked example.
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