Extracted-ion window capture fraction

An 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 $W$,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.^[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,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.

Window-capture sensitivity to mass offset describes how the extracted-ion window capture fraction changes when an ion peak shifts relative to a fixed extracted ion mass window. The shift is in the reported mass coordinate; it can change the selected signal even if the target's total peak area is constant.

For a normalized peak shape $p(m-\delta )$ with offset $\delta$ and window boundaries $a,b$, writeDifferentiation givesThe first-order response is determined by the signal density at the two boundaries. A symmetric peak centered in a symmetric window has equal boundary densities and hence zero first derivative. Zero first derivative does not mean perfect immunity: finite offsets can still reduce capture.

For an original Gaussian function model with standard deviation $\sigma$ and half-width $w$, let $\varphi$ and $\Phi$ be the standard normal density and standard normal cumulative distribution function. ThenFor small offsets the leading loss is consequently quadratic:With $w=2\sigma$, the exact capture is 0.9545 at zero offset and 0.9270 at $\delta =0.5\sigma$. The quadratic approximation gives 0.9275, close for this stipulated displacement. At the boundary $\delta =2\sigma$, capture is about 0.5000 and a small-offset approximation is no longer appropriate.

An experimental check can re-extract the same recorded spectra with deliberately shifted windows while retaining the same time limits and extracted-ion chromatogram baseline. This isolates a software-selection effect. IUPAC's selected-mass profile definition supplies the measurement setting, rather than a claim that all instruments have Gaussian peaks.^[ref] Wider windows may reduce target losses but admit interfering ions; mass resolving power and instrument calibration remain separate instrumental considerations.