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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.

Laser pulse energy is the radiant energy carried by one specified laser pulse across a measurement plane. For an isolated pulse whose total radiant power is $P(t)\ge 0$ and whose background is zero,Here $P$ is already integrated over the transverse beam area; it is not local irradiance. The unit of $U$ is the joule. Radiant exposure instead divides received energy by a receiving area, so a beam's $U$ alone does not specify the exposure at its centre. The radiant exposure of a Gaussian beam makes that spatial distinction quantitative.

The Gaussian pulse energy and peak power relation gives $P_{\mathrm{pk}}\simeq 0.939437U/\tau$ when $\tau$ is the power full width at half maximum. The pulse energy shape factor records pulse-shape dependence, while the Gaussian pulse field-envelope width is $\sqrt{2}$ times the power width.

For an original example, stipulate $U=0.50\mu \mathrm{J}$ and a Gaussian pulse power full width at half maximum $\tau =10\mathrm{ns}$. Then $P_{\mathrm{pk}}=46.97\mathrm{W}$. Stretching the same model pulse to $40\mathrm{ns}$ while keeping $U$ unchanged reduces its peak power to $11.74\mathrm{W}$. Both curves below integrate to the same energy; their peak heights and widths differ.

A finite detection time gate collects the Gaussian pulse time-gate energy fraction, which depends on its width and alignment. A centred gate as wide as the power full width at half maximum receives only $76.10\%$ of $U$, because Gaussian tails extend beyond it. For a $\tau$-wide gate, a Gaussian gate centring error of $\tau /2$ reduces capture to $49.07\%$.

The average power of a laser pulse train follows by counting complete pulses. If a long observation of duration $T$ contains $N$ pulses of energies $U_1,\dots ,U_N$, with negligible edge contributions and no continuous background,Here $f_{\mathrm{rep}}$ is the pulse repetition frequency, not the inverse pulse width. An average power readout constrains $\overline{U}$ when $f_{\mathrm{rep}}$ is known; it does not resolve pulse-to-pulse energy fluctuation. Identical, well-separated $0.50\mu \mathrm{J}$ pulses at $1.0\mathrm{MHz}$ give $0.50\mathrm{W}$ average power, even though the stipulated $10\mathrm{ns}$ pulses peak near $47\mathrm{W}$.

If a steady optical background is present, state whether the reported energy includes it. For pulse energy above a measured background $P_{\mathrm{bg}}$, the pulse energy baseline correction uses ${\int }_{\mathrm{gate}}[P(t)-P_{\mathrm{bg}}]dt$. Failing to subtract a constant background adds $P_{\mathrm{bg}}{T}_g$ to the inferred energy. This optical-background model is distinct from an offset introduced later by detector electronics.

Historical NIST equipment illustrates what the readouts measure. Its TC-24 reference absorbed the beam in a glass plate, sensed a plate temperature difference with thermocouples, and integrated the thermopile's electric potential difference during beam injection. Before/after readings enabled background subtraction and compensated thermal drift. Counting pulses converted total injected energy to mean pulse energy. The semiconductor pulse photodetector used an integrating amplifier; calibration related the peak output electric potential difference to pulse energy. That electrical peak did not by itself establish optical peak power.^[ref] Pulse energy measurement with a photodiode connects this kind of measurement to collected electric charge; validating the detector response under the actual pulse conditions remains part of that interpretation.

Pulse timing jitter describes variation of pulse arrival times relative to a stated timing reference. Choose a reproducible pulse feature and reference instants $t_j^{\mathrm{ref}}$; define errors $e_j=t_j-t_j^{\mathrm{ref}}$. One measure is their standard deviation ${\sigma }_t$. Edge-time error relative to an ideal reference differs from variation of successive periods or cycle-to-cycle differences; the primary timing guide distinguishes these measurements.^[ref]

For an original distribution, let each error equal $500\mathrm{ps}+ϵ$, where $ϵ$ is equally likely to be $+100$ or $-100\mathrm{ps}$. The mean delay is $500\mathrm{ps}$ and ${\sigma }_t=100\mathrm{ps}$. The root mean square error about zero is instead $\sqrt{500^2+100^2}\approx 510\mathrm{ps}$. A fixed delay changes the mean without increasing the spread. None of these numbers is the individual pulse's duration.

A fast photodetector, reference timing signal and oscilloscope can measure a selected arrival feature. A fixed electrical threshold can also turn amplitude/readout noise into an apparent time change, producing threshold timing noise from amplitude noise. Specify the reference, feature, observation duration and measurement response. A fitted or recovered reference can absorb some timing variation, changing the reported residual.

Timing variation can become gated-energy variation even at constant full pulse energy. The Gaussian gate centring error provides one quantitative model, distinct from pulse-to-pulse energy fluctuation of complete pulses.

A pulse train is a sequence of pulses. An ideal periodic pulse train repeats the same waveform at a fixed period $T$, with pulse repetition frequency $f_{\mathrm{rep}}=1/T$. A finite burst, varying pulse heights or pulse timing jitter can break exact periodicity without removing the useful description as a pulse train. The repetition interval describes spacing; it is distinct from one pulse's duration.

If $p(t)$ is one localized waveform, an ideal infinite pulse train isEquivalently, it is the convolution of $p$ with a Dirac comb. Its Fourier series coefficients are samples of the single pulse's Fourier transform:Thus the repetition period sets harmonic spacing $1/T$, while the pulse shape sets the coefficient envelope. This statement concerns the repeated waveform itself; an optical electric field additionally has carrier phase information that a measured optical-power trace does not contain.

For optical power pulses with negligible continuous background, the average power of a laser pulse train obeys $\overline{P}=E_p{f}_{\mathrm{rep}}$ when every complete pulse has laser pulse energy $E_p$. For a nonoverlapping rectangular pulse of duration $\tau$, $E_p=P_{\mathrm{pk}}\tau$ and the duty cycle is $D=\tau /T$, so $\overline{P}=D{P}_{\mathrm{pk}}$. For other shapes, a width such as the full width at half maximum needs a pulse energy shape factor before it determines peak power.^[ref]

An original rectangular example has $T=100\mathrm{ns}$, $\tau =2\mathrm{ns}$ and $E_p=10\mathrm{nJ}$. The pulse repetition frequency is $10\mathrm{MHz}$, the duty cycle is $0.02$, the peak power is $5\mathrm{W}$ and the average power is $0.10\mathrm{W}$. A slow power meter can report that average while failing to resolve either the $2\mathrm{ns}$ width or individual pulse-to-pulse energy fluctuation.

A fast photodetector and oscilloscope instead display successive electrical responses. Their bandwidth and impulse response limit the optical timing information available. Counting the spacing tests the pulse repetition frequency; integrating calibrated individual responses tests laser pulse energy. Pulse energy measurement with a photodiode explains the charge-integration step. Separating those measurements avoids inferring the pulse width from an average-power reading alone.