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A mass analyzer is the part of a mass spectrometer that makes ions distinguishable or selectively transmits them according to mass-to-charge ratio. The measured coordinate can be position, arrival time or transmission under a specified field setting. A separate mass spectrometer detector records the resulting signal.

A quadrupole mass analyzer selects trajectories using combined static and time-varying electric fields: chosen mass-to-charge values remain on stable paths while others are lost from the transmitted beam.^[ref] A time-of-flight mass spectrometer instead encodes the ratio in arrival time after acceleration. Different physical designs can therefore provide the same kind of ionic-mass information through different observables.

An original magnetic example exposes an important assumption. For speed $v$ perpendicular to a uniform magnetic field $B$, balancing the Lorentz force and circular acceleration givesIf the incoming ions have the same selected speed and charge, mass values in the ratio $56/54$ give bending radii in that ratio, about $1.0370$. But if ions instead start negligibly slowly and gain energy from the same electric potential difference $U$, substituting $qU=m{v}^2/2$ gives $r=\sqrt{2mU/q}/B$. Their radius ratio is then $\sqrt{56/54}\approx 1.0184$. The initial-condition choice changes the mapping.

Analysis requires this mapping and its assumptions, not just separated peaks. Mass resolving power describes the ability to distinguish nearby peak coordinates under a stated width criterion; accurate assignment of those coordinates additionally needs instrument calibration and the correct charge-state interpretation.

A mass spectrometer is an instrument that produces or receives ions, separates them according to mass-to-charge ratio, and records their signals. Its major functions are supplied by an ion source, a mass analyzer and a mass spectrometer detector. The result is a mass spectrum; interpreting a peak also requires knowing which ionic chemical species produced it.

The 1955 instrument described by W. C. Wiley and I. H. McLaren provides a concrete apparatus example. An ion source and accelerating fields launch ions into an evacuated drift region toward a collector. Arrival times separate mass-to-charge ratios; the paper analyses how initial positions and velocities broaden the recorded peaks, and uses a two-field ion-gun geometry to improve focusing.^[ref] This is one analyzer design, not a definition requiring every mass spectrometer to measure flight time.

For an ideal time-of-flight mass spectrometer, neglect initial speed and acceleration duration. Across an electric potential difference $U$, an ion of positive electric charge $q$ gains $qU=m{v}^2/2$. A field-free drift of length $L$ then givesIf one peak arrives at $40\mu \mathrm{s}$ and another at $44\mu \mathrm{s}$, identical acceleration and drift conditions imply a mass-to-charge ratio ratio $(44/40{)}^2=1.21$. It is a mass ratio only if the charge states are also equal. Peak position, width and intensity answer different questions: ionic identity, resolving ability and response-weighted abundance.

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.