= Time-of-flight mass spectrometer
A <time-of-flight mass spectrometer> is a <mass spectrometer> whose analyzer infers <mass-to-charge ratio> from ion arrival times. A simple arrangement uses an <ion source>, pulsed acceleration, a drift region under <vacuum> and a <mass spectrometer detector>. The 1955 Wiley–McLaren instrument connected such an apparatus to calculations of how initial position and velocity spread affect resolution.<Time-of-Flight Mass Spectrometer with Improved Resolution by W. C. Wiley and I. H. McLaren>[Page 1150, general description; two-field focusing and resolution analysis]{ref}
In an ideal drift, $t_{\rm drift}=L\sqrt{m/(2qU)}$ for flight length $L$, positive charge $q$ and accelerating <electric potential difference> $U$. Recorded arrival time can also include a <time-of-flight timing offset> $t_0$. A useful ideal <instrument calibration> model is
$$
t_{\rm measured}=t_0+k\sqrt{x},
$$
where $x$ is the numerical mass-to-charge coordinate in a declared unit and $k$ absorbs the instrument geometry and unit conversion.
For original invented standards, let $x=25$ arrive at $12\,\mathrm{\mu s}$ and $x=100$ at $22\,\mathrm{\mu s}$. Since the square roots are 5 and 10, $k=2\,\mathrm{\mu s}$ and $t_0=2\,\mathrm{\mu s}$. An unknown arriving at $17\,\mathrm{\mu s}$ then has $x=((17-2)/2)^2=56.25$. Ignoring the offset and scaling from the first standard alone would instead give $25(17/12)^2\approx50.17$. A timing offset becomes a mass-assignment error when omitted from the model.
Real peaks have finite widths. <Space focusing> and <time-lag focusing> address specified sources of that spread; neither is simply a longer wait before detection. Calibration standards, acquisition timing and focusing conditions therefore belong in the interpretation of a measured spectrum.
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