 Time-lag focusing

Time-lag focusing in time-of-flight mass spectrometry uses a controlled delay between creation of an ion packet and application of its extraction electric field. During this delay, different initial velocities produce different positions. The later extraction pulse can then give initially faster ions less accelerating work than initially slower ones, reducing their arrival-time spread at a chosen detector plane.^[ref]

Suppose two equal-mass, equal-electric charge ions differ in their initial forward velocity by $\Delta u$. A field-free delay $\tau$ creates a position differenceFor example, $\Delta u=100\mathrm{m}{\mathrm{s}}^{-1}$ and $\tau =1\mu \mathrm{s}$ give $\Delta x=100\mu \mathrm{m}$. In a subsequently applied uniform field, an ion farther toward the exit experiences a smaller remaining accelerating electric potential difference. Choosing the delay and fields appropriately allows the slower-starting ion to catch up later.

The delay creates a useful correlation between position and velocity; waiting alone does not focus the packet. Space focusing compensates an initial position distribution, whereas time-lag focusing exploits motion during the delay to address an initial velocity distribution. An instrument's focusing condition must state the geometry, fields, reference mass-to-charge ratio and initial-distribution assumptions.