= Spectroscopic response factor
{title2=$I=kn$}
A <spectroscopic response factor> relates a specified measured signal in <spectroscopy> to an amount of material under fixed measurement conditions. In the convention
$$
I=kn,
$$
$I$ is the signal after <blank correction>, $n$ is the <amount of substance>, and $k$ has units of signal per amount. Specify whether the signal is a peak height or an integrated feature, and retain the same acquisition conditions during <measurement calibration> and unknown-sample measurement. Some literature instead defines a response factor as amount per signal: it is the reciprocal of $k$ in this simple model.<Rigorous evaluation of chemical measurement uncertainty: Liquid chromatographic analysis methods using detector response factor calibration by Blaza Toman and others>[Introduction, equations 1–3: calibrated factor RF multiplies the peak-area response to obtain mass fraction]{ref}
For an original calibration, two standards with amounts $10\,\mathrm{\mu mol}$ and $20\,\mathrm{\mu mol}$ give raw integrated signals 25 and 45 in fixed instrument units. Fitting $I_{\rm raw}=I_0+kn$ gives
$$
k=\frac{45-25}{20-10}=2\;\text{signal units per }\mathrm{\mu mol},\qquad I_0=5.
$$
An unknown with raw signal 35 therefore has
$$
\boxed{n=\frac{35-5}{2}=15\,\mathrm{\mu mol}.}
$$
Ratios of uncorrected signal to amount would give 2.5 and 2.25 for the standards, falsely suggesting a changing response. Here the cause is an additive background, not a changing $k$.
Two standards fit this illustrative straight line exactly. Additional standards and repeats are needed to test the useful linear range. The inferred amount inherits <measurement uncertainty> in the signal, background and response factor. Samples calibrated using the same uncertain factor can have correlated inferred amounts; repeating the unknown measurement does not independently average away that shared calibration contribution.<Rigorous evaluation of chemical measurement uncertainty: Liquid chromatographic analysis methods using detector response factor calibration by Blaza Toman and others>[Introduction, discussion after equation 3 and equation 4, positive correlation from a shared response factor]{ref}
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