I. H. McLaren

I. H. McLaren coauthored with W. C. Wiley the 1955 Bendix study of time-of-flight mass spectrometry with improved mass resolving power. A notable part of their analysis was time-lag focusing: waiting between ion formation and application of an accelerating pulse lets initial velocities become position differences that can compensate some arrival-time spread.^[ref]

A first-order calculation exposes the mechanism. Let $T(v,s)$ be arrival time after immediate extraction for initial axial velocity $v$ and position $s$. During a field-free delay $\tau$, an ion moves to $s+v\tau$. Apart from the common delay added to all times,The partial derivatives are evaluated at $v=0$ and the reference position. First-order sensitivity to $v$ vanishes ifA positive delay requires opposite signs of these sensitivities. For example, $T_v=2\times 10^{-9}{\mathrm{s}}^2{\mathrm{m}}^{-1}$ and $T_s=-10^{-3}\mathrm{s}{\mathrm{m}}^{-1}$ give $\tau =2\mu \mathrm{s}$. These values illustrate the cancellation, rather than reproducing an instrument setting from the paper.

This also reveals the tradeoff: the cancellation needs a nonzero position sensitivity, whereas ideal first-order space focusing sets $T_s=0$. The paper's delayed-extraction condition and measured spectra therefore address competing sources of broadening, not a universal elimination of every initial-condition effect.^[ref]