Time-lag focusing
= 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.<Time-of-Flight Mass Spectrometer with Improved Resolution by W. C. Wiley and I. H. McLaren>[Time-lag focusing analysis; compensation of initial velocity spread by delayed extraction]{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 difference
$$
\Delta x=\Delta u\,\tau.
$$
For example, $\Delta u=100\,\mathrm{m\,s^{-1}}$ 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.