Spectroscopic response factor ($I=kn$)

A spectroscopic response factor relates a specified measured signal in spectroscopy to an amount of material under fixed measurement conditions. In the convention$I$ 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.^[ref]

For an original calibration, two standards with amounts $10\mu \mathrm{mol}$ and $20\mu \mathrm{mol}$ give raw integrated signals 25 and 45 in fixed instrument units. Fitting $I_{\mathrm{raw}}=I_0+kn$ givesAn unknown with raw signal 35 therefore hasRatios 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.^[ref]