= Detection time gate
{title2=$T_g$}
A \b[detection time gate] is a selected interval during which a <photodetector>'s output contributes to a measurement. Its start delay and duration $T_g$ are measured relative to a trigger or another time reference. The gate may control an <integrating amplifier>, an electronic counter or a software selection of recorded events; it need not physically switch off the light.
A gated integrator supplies a concrete apparatus. Stanford Research Systems' SR250 uses a triggerable gate generator, a fast integrator and a readout normalized by gate width. Its gate monitor can be displayed alongside the signal on an <oscilloscope> to check their relative timing.<SR250 Gated Integrator by Stanford Research Systems>[PDFpp1–2, Overview and Gate Timing]{ref} An integrated area and a gate-averaged amplitude are different output quantities: dividing an area by $T_g$ changes its units.
An original <photon counting> example shows the gate-width tradeoff. Suppose an ideal decaying signal has expected count rate $s(t)=S_\infty e^{-t/\tau}/\tau$ for $t\geq0$, and a constant background has rate $b$. A gate from0 to $T_g$ collects expected counts
$$
S(T_g)=S_\infty(1-e^{-T_g/\tau}),\qquad B(T_g)=bT_g.
$$
If signal and background counts are independent <Poisson distributions> and the background mean is known exactly, the background-corrected count has variance $S+B$. Its <signal-to-noise ratio> is $S/\sqrt{S+B}$. With chosen values $S_\infty=100$ and $b\tau=100$, a gate of width $\tau$ gives about63.2signal counts,100background counts and ratio4.95. A gate of width $3\tau$ collects95.0signal counts but300background counts, reducing that ratio to4.78. More collected signal alone does not guarantee a better measurement.
This example assumes ideal event registration; <detector dead time>, non-Poisson backgrounds or an estimated rather than known background alter the calculation. <Gate timing jitter> can also vary the admitted part of a rapidly changing signal. Gate placement and duration should therefore be checked against the actual waveform, background and measurement objective, rather than chosen solely from the nominal pulse width.
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