= Average power of a laser pulse train
{title2=$\overline P=f_{\rm rep}\overline U$}
The \b[average power of a laser pulse train] is its integrated <radiant energy> per observation time. If an interval $T$ contains $N$ complete pulses, with no uncounted edge contributions or continuous background,
$$
\overline P_{\rm pulses}=\frac{\sum_{j=1}^NU_j}{T}
=\frac NT\overline U.
$$
Thus the relevant <pulse repetition frequency> is the actual emitted-pulse rate in the interval. Historical calorimetric calibrations inferred average power and pulse energy from total received energy, injection time and pulse rate.<Calibration Service for Laser Power and Energy at 248 nm by Rodney W. Leonhardt>[§6.2, Laser stability, printedp.23]{ref}
An original counting example exposes a possible cancellation of errors. A nominal $100\,\mathrm{kHz}$ trigger produces 200 triggers in $2\,\mathrm{ms}$. Suppose only 180 complete optical pulses arrive, each carrying $0.20\,\mathrm{\mu J}$. Their total is $36\,\mathrm{\mu J}$, so the pulse contribution is $18\,\mathrm{mW}$, corresponding to an actual 90kHz pulse rate. Add a continuous optical background of $2\,\mathrm{mW}$, and a detector integrating everything reads $20\,\mathrm{mW}$.
Dividing that total by the nominal trigger rate would happen to give $0.20\,\mathrm{\mu J}$, despite both the missing pulses and the unremoved background. Removing the background but still using the nominal rate would instead infer $0.18\,\mathrm{\mu J}$, ten percent below the actual emitted-pulse energy. This <missing-pulse bias in average-power inference> cannot be diagnosed from the apparently reasonable quotient alone. A pulse-resolving monitor and a suitable <background subtraction> distinguish the two contributions.
For bursts or variable repetition, count the pulses in the same interval as the energy measurement. A slow integrating detector can establish their mean energy after these corrections but does not resolve <pulse-to-pulse energy fluctuation> or optical <peak power>. <Laser pulse energy> separates these observables.
Back to article page
