= T. J. Spencer
{disambiguate=optical physicist}
{c}
\b[T. J. Spencer] is a coauthor of the Central Laser Facility's1999 report on a single-shot instrument for <third-order intensity autocorrelation> and <optical pulse temporal contrast> measurements.<A Single Shot 3rd Order Cross-Correlator for Pulse Contrast and Pulse Shape Measurements by J. Collier and others>[Printedpp194–195, byline and instrument description]{ref}
An original calculation illustrates a pulse-characterization issue relevant to that work. Let a <Gaussian pulse> have intensity
$$
I(t)=I_0\exp\!\left(-\frac{t^2}{2\sigma^2}\right).
$$
Completing the square in its <third-order intensity autocorrelation> gives
$$
A_3(\tau)=\int_{-\infty}^{\infty}I(t)^2I(t+\tau)\,dt
=I_0^3\sigma\sqrt{\frac{2\pi}{3}}
\exp\!\left(-\frac{\tau^2}{3\sigma^2}\right).
$$
The pulse's intensity <full width at half maximum> is $2\sqrt{2\ln2}\,\sigma$, while the correlation width is $2\sqrt{3\ln2}\,\sigma$. Their ratio is therefore
$$
\frac{w_{A_3}}{w_I}=\sqrt{\frac32}\simeq1.225.
$$
A measured correlation width cannot simply be reported as the original pulse width. The conversion depends on the assumed pulse shape and the correlation being measured. This Gaussian example explains that distinction; it is not a reconstruction of Spencer's individual experimental tasks or a fit to the1999 data.
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