Extracted-ion chromatogram baseline (source code)

= Extracted-ion chromatogram baseline

An <extracted-ion chromatogram baseline> is a model of the signal underlying a selected chromatographic peak in an <extracted ion chromatogram>. Subtracting it helps assign an <extracted-ion chromatogram peak area> to the feature of interest. The baseline need not be zero or constant, and it is not automatically the signal from a separate reagent blank.

Let $E_W(t)$ be the signal from an <extracted ion mass window> $W$ and let $b(t)$ be the baseline over $[t_1,t_2]$. The assigned <extracted-ion chromatogram peak area> is
$$
Q=\int_{t_1}^{t_2}\bigl(E_W(t)-b(t)\bigr)\,dt.
$$
The time-ordered mass selection follows the IUPAC <extracted ion profile> definition; the baseline is an additional integration-model choice.<Extracted ion profile in IUPAC Gold Book>[Entry 12410, signal from selected mass-to-charge values across time-dependent spectra.]{ref}

An original example takes $0\le t\le4\,\mathrm{min}$ and a baseline rising linearly from 1 to 3 signal units. Its integrated area is $4(1+3)/2=8$ signal-unit minutes. If the recorded trace has total area 20, the corrected area is 12. Using a constant baseline 1 would subtract only 4 and assign area 16: a 33% overestimate relative to 12. No recorded ion signal changed; only its allocation between baseline and peak changed.

If a fitted baseline is $b(t)=a+kt$ over a duration $L$ starting at $t=0$, then the subtracted area is $B=aL+kL^2/2$. <Chromatographic baseline-area uncertainty> therefore includes the joint uncertainty of the fitted intercept and slope:
$$
u_B^2\approx L^2u_a^2+\frac{L^4}{4}u_k^2+L^3\operatorname{Cov}(a,k).
$$
This is a direct application of correlated-input <uncertainty propagation>.<Evaluation of measurement data — Guide to the expression of uncertainty in measurement by JCGM>[§5.2, covariance contributions.]{ref}

Candidate baseline regions should be inspected for neighboring peaks, broad tails and drifting background. Two overlapping compounds can generate one smooth trace; subtracting a convenient baseline cannot establish chemical specificity. Record the integration boundaries, baseline model and treatment of negative corrected values. Those choices are necessary to interpret or reproduce a reported <extracted-ion chromatogram peak area>.