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MALDI, short for matrix-assisted laser desorption/ionization, is an ionization method for mass spectrometry. The sample is prepared with a MALDI matrix that absorbs the incident laser light and helps release sample molecules into the gas phase as ions. The MALDI matrix is a chemical preparation component; it is distinct from the mass analyzer that subsequently separates the ions. Combining MALDI with time-of-flight mass spectrometry gives MALDI-TOF. The measured mass-to-charge ratio characterizes the resulting ion, rather than directly reporting the mass of an uncharged molecule.

For an illustrative molecule of nominal mass $20000$ atomic mass units, adding one proton gives a singly charged ion with nominal mass-to-charge ratio $20001$, whereas adding two protons gives approximately $(20000+2)/2=10001$. These are simplified assignments that neglect exact mass defects. A second peak therefore need not mean a second molecular species: charge states, isotopes and attached ions also affect a mass spectrum.

In the 1997 tissue-imaging experiment, a MALDI matrix coated a tissue section or its blotted imprint, and an ordered array of mass spectra supplied a spatial map for a selected mass-to-charge ratio. The investigators mapped insulin in rat pancreas and peptides in rat pituitary. This connects the ion source to mass spectrometry imaging: sample position supplies the image coordinates, while the mass spectrum supplies chemical discrimination. A bright pixel alone does not establish an absolute molecular concentration.^[ref]

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 mass spectrometer detector turns arriving ions into a recorded electrical signal. It is distinct from the mass analyzer that makes mass-to-charge ratio information distinguishable. The measured response can depend on collection, conversion and amplification as well as on how many ions arrived.

A Faraday cup collects electric charge directly. Ideally, a flux $\Phi$ of ions with known charge $q$ gives $I=q\Phi$. For $10^6$ singly charged positive ions per second, the current is $1.602176634\times 10^{-13}\mathrm{A}$, about $0.1602\mathrm{pA}$. Escaping secondary electrons and background currents must be accounted for when inferring particle delivery.^[ref]

An electron multiplier instead uses secondary emission to amplify the initial conversion signal. The manufacturer's detector description shows discrete dynodes, a continuous-dynode alternative, and a conversion dynode before the multiplier.^[ref] In an illustrative equal-stage model, ten stages with mean yield $\delta =4$ give mean gain $G=4^{10}=1048576$. This is a model calculation, not a measured gain for a named instrument.

Detector gain and detection efficiency answer different questions: the size of an output event and the probability of registering an arriving ion. Increasing gain cannot recover missed ions. At high signals, mass spectrometer detector saturation can also invalidate proportionality between ion delivery and recorded response. Quantitative peak comparisons therefore need a tested response range and appropriate instrument calibration, not merely a large signal.

A quadrupole mass analyzer is a mass analyzer that selects ions through stability of motion in combined static and alternating quadrupole electric fields. Selected mass-to-charge ratios follow bounded transverse trajectories through the analyzer; others grow unstable and fail to reach its exit.^[ref]

For an idealized model, define the electric potentialHere $r_0$ is a geometric scale and $U,V$ follow this stated potential convention. An ion with electric charge $Q$ and mass $m$ then obeysAt a given instant the field focuses one transverse direction and defocuses the other. Alternation can nevertheless yield bounded motion in both directions. Rescaling time reduces these equations to forms of the Mathieu equation; a quadrupole stability diagram summarizes the relevant bounded-motion regions.

The equations also show why the filter selects a ratio. Doubling both $m$ and $Q$ leaves the ideal equations unchanged. With fixed geometry, the dimensionless coefficients scale as $QU/(m{\Omega }^2)$ and $QV/(m{\Omega }^2)$. Doubling the drive angular frequency while keeping the potentials fixed divides both coefficients by four; multiplying both potentials by four restores them in this model.

A stable mathematical trajectory is only part of instrument performance. Initial ion positions and velocities, finite flight length, field imperfections and detector response also influence transmission and measured mass resolving power. The ideal potential is an explicit model, not a guarantee about a particular instrument.