Extracted ion mass window

An extracted ion mass window is the set of mass-to-charge ratio coordinates included when reconstructing an extracted ion profile or extracted ion chromatogram. A common choice is an interval centered at $m_0$ with half-width $w$: $|m-m_0|\le w$. The profile definition permits one value or a set of values; specifying the window makes that selection reproducible.^[ref]

A relative half-width can be stated in parts per million:where $p$ is the stipulated ppm half-tolerance and $m,m_0$ use the same displayed mass-coordinate scale. At $m_0=500$, a5ppm half-tolerance gives $w=0.0025$ and interval $499.9975\le m\le 500.0025$. At $m_0=1000$, the same relative tolerance gives $w=0.005$. Conversely, fixed $w=0.005$ corresponds to10ppm at500 and5ppm at1000. State whether a quoted width means half-width or full width.

Finite peak width makes window choice a signal-selection operation. A target whose measured center shifts from500.000 to500.003 moves outside the first window, although part of its broadened signal may remain inside. Widening the window can recover more target signal while admitting a neighboring ion. The extracted-ion window capture fraction depends on the peak shape, width and coordinate offset, not merely on the nominal target formula.

Mass resolving power describes separation of nearby ion peaks; coordinate accuracy and the chosen extraction tolerance are different properties. A narrow software window does not improve instrumental resolving power or recreate information that was not acquired. Nor does fitting the expected window establish a unique ion identity. The window should be interpreted together with acquisition conditions, reference measurements and the other evidence used for assignment.

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.