Resolution and mass accuracy in matrix-assisted laser desorption ionization-time-of-flight

A mathematical model of time-of-flight mass analyzers employing uniform electric fields is presented that allows "exact" calculations of flight times as functions of mass-to-charge ratio, initial velocity and position, applied voltages, and instrument geometry. An "approximate" equation based on a series expansion of the "exact" result is derived which allows focusing conditions and limits on resolution to be determined for different instrument geometries and operating conditions. The fundamental theory is applied to predicting resolution and mass accuracy in matrix-assisted laser desorption ionization-time of flight. In this case higher order velocity focusing can provide excellent correction for the initial velocity distribution of a selected mass-to-charge ratio, but the focusing is mass-to-charge ratio dependent. There is generally a trade-off between ultimate resolution at a particular mass-to-charge ratio and resolution and mass accuracy over a broad mass range. In most practical applications the latter is more important. Calculations are compared with experimental results for a particular analyzer geometry, both at theoretical optimum velocity focus and at operating conditions where ultimate resolution is sacrificed for a broader range of relatively high resolution and better mass accuracy.