= Extracted-ion window capture fraction
An \b[extracted-ion window capture fraction] is the fraction of a particular ion peak's integrated mass-coordinate signal retained by an <extracted ion mass window>. For a nonnegative signal-density model $s(m)$ and window $W$,
$$
F_W=\frac{\int_Ws(m)\,dm}{\int_{-\infty}^{\infty}s(m)\,dm},
$$
assuming the denominator is finite and positive. This is a fraction of the specified peak model, not necessarily a fraction of analyte molecules or of the entire <total ion current>. The extraction window selects which mass-coordinate signal enters a profile.<Extracted ion profile in IUPAC Gold Book>[Entry 12410, selected mass-coordinate values and time-dependent profile.]{ref}
An original <Gaussian function> model makes <window-capture sensitivity to mass offset> explicit. Let the peak center be displaced by $\delta$ from the nominal window center, with standard deviation $\sigma$ and symmetric half-width $w$. If $\Phi$ is the <standard normal distribution>'s cumulative distribution function,
$$
F_W=\Phi\!\left(\frac{w-\delta}{\sigma}\right)
-\Phi\!\left(\frac{-w-\delta}{\sigma}\right).
$$
At zero offset and $w=2\sigma$, the retained fraction is approximately $0.9545$. Shifting the peak center to the upper window boundary, $\delta=2\sigma$, reduces it to approximately $0.5000$. The model's total peak area has not changed; the selected fraction has.
A wider window admits more of this peak but can also admit another ion. The measured window sum can therefore increase for two different reasons: greater target capture or added interference. They cannot generally be distinguished from the summed trace alone.
The Gaussian shape is a stipulated teaching model, not a universal instrument response. Real peak asymmetry, finite recorded ranges, background and overlapping signals can change the fraction. <Mass resolving power> and mass-coordinate accuracy remain instrumental properties; a software window only selects from the information available.
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