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The 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,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.^[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 $0.20\mu \mathrm{J}$. Their total is $36\mu \mathrm{J}$, 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 $0.20\mu \mathrm{J}$, despite both the missing pulses and the unremoved background. Removing the background but still using the nominal rate would instead infer $0.18\mu \mathrm{J}$, 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.

The conditional pulse-energy mean given emission averages over emitted optical pulses rather than all commands or all detected events. If $E$ denotes an emission event and energy is zero when no pulse is emitted, the conditional expectation identity givesThe left side is energy per trigger. The conditional mean is energy per emitted pulse. Missing-pulse bias in average-power inference explains the corresponding rate denominator.

For an original distribution, let emission probability be $0.75$. Conditional on emission, energies $2$ and $6\mathrm{nJ}$ are equally likely. The emitted-pulse mean is $4\mathrm{nJ}$, whereas the per-trigger mean is $3\mathrm{nJ}$. At $2\mathrm{MHz}$ nominal triggering, average pulse power is $6\mathrm{mW}$; the actual $1.5\mathrm{MHz}$ emission rate gives the same power when multiplied by $4\mathrm{nJ}$.

Now let a perfect threshold receiver detect only energies above $4\mathrm{nJ}$. Its detected-event mean is $6\mathrm{nJ}$ and its event probability per trigger is $0.375$. This is detection-threshold selection bias in pulse-energy means: the detector conditions on a narrower event than emission. The undetected records include both failed emissions and the weaker emitted pulses.

A calibrated pulse monitor, trigger counter and known detection response help distinguish the denominators. A total-energy measurement alone need not identify the missing weak-pulse distribution. Historical calorimetric inference combines total energy, injection time and pulse rate, so the rate must match the population whose mean is reported.^[ref]