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.^[ref]

In an ideal drift, $t_{\mathrm{drift}}=L\sqrt{m/(2qU)}$ 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 iswhere $x$ 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 $12\mu \mathrm{s}$ and $x=100$ at $22\mu \mathrm{s}$. Since the square roots are 5 and 10, $k=2\mu \mathrm{s}$ and $t_0=2\mu \mathrm{s}$. An unknown arriving at $17\mu \mathrm{s}$ then has $x=((17-2)/2{)}^2=56.25$. Ignoring the offset and scaling from the first standard alone would instead give $25(17/12{)}^2\approx 50.17$. 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.

A time-of-flight timing offset, $t_0$, is an additive time-origin parameter in a model connecting recorded ion arrival time with physical flight time. In a simple time-of-flight mass spectrometer calibration,where $x$ is the numerical mass-to-charge ratio in declared units. A 2017 instrument-analysis paper uses this equation and determines instrument-dependent constants from identified isotope peaks.^[ref]

An original error calculation shows why the offset matters. Suppose the physical flight contribution is $20\mu \mathrm{s}$ and $t_0=3\mu \mathrm{s}$, so the recorded time is $23\mu \mathrm{s}$. With $k_0$ held fixed, ignoring the offset multiplies the inferred coordinate bya $32.25\%$ overestimate. This deliberately large example isolates the effect; it does not describe a measured instrument error.

With $k_0$ fixed, a small error in the fitted offset propagates approximately asAn offset uncertainty of $0.05\mu \mathrm{s}$ at a corrected flight time of $20\mu \mathrm{s}$ therefore contributes about $0.5\%$ relative uncertainty in this approximation. The same absolute offset error has greater relative impact on earlier arrivals.

This parameter concerns timing, whereas time-lag focusing is a physical delayed-extraction technique affecting the ion packet. Fitting an offset does not by itself sharpen a peak. More detailed instruments can require additional calibration terms; the stated equation is a model, not a universal transfer function.