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Baseline-drift bias in pulse-energy integration is the systematic energy error caused by using an inaccurate baseline over the integration gate. Relative to the true signal energy in the same gate,This error is separate from energy excluded by the gate. Historical NIST measurements bracketed each run with baseline observations and subtracted their average to compensate background and thermal drift.^[ref]

An original curvature example shows a limit of endpoint bracketing. On $-T/2\le t\le T/2$, suppose $b(t)=b_0+c{t}^2$. Both endpoint baselines equal $b_0+c{T}^2/4$, so their average and the straight interpolation between them coincide. However, the true integrated baseline is $b_{0}T+c{T}^3/12$. Subtracting the endpoint level over the whole gate therefore givesFor a $20\mu \mathrm{s}$ gate whose endpoints are $3\mathrm{mW}$ above its midpoint baseline, this bias is $-(2/3)(3\mathrm{mW})(20\mu \mathrm{s})=-0.040\mu \mathrm{J}$. A true gated signal energy of $1.00\mu \mathrm{J}$ would be reported as $0.960\mu \mathrm{J}$ under these assumptions.

Thus quadratic baseline curvature in gated energy integration survives a correction that is exact for a linear baseline. For fixed curvature, the error grows with the cube of gate duration. Additional pulse-free samples can test the baseline model, but pulse tails in those samples can themselves corrupt the estimate. Pulse energy baseline correction supplies the broader measurement context.

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 duration quantifies a pulse's temporal extent using a stated observable and width convention. A common optical convention is the full width at half maximum of the background-subtracted radiant power profile. The Ansys source documentation explicitly defines its PULSELENGTH parameter as the power-profile FWHM, rather than the width of the electric-field amplitude.^[ref]

For an original example, choose a triangular power pulseIts nonzero support extends from $-T$ to $T$, giving total support width $16\mathrm{ns}$. Its half-maximum crossings occur at $t=\pm T/2$, giving a power FWHM of only $8\mathrm{ns}$. Neither number is wrong when its convention is specified. The pulse energy shape factor additionally relates a chosen width to integrated energy and peak power.

A fast photodetector and oscilloscope record an electrical response to an optical pulse. For a linear response model, the recorded trace is a convolution with the instrument's impulse response; a slow response can broaden the measured feature. The readout width need not equal the optical width. State the observable, background treatment and instrument response when reporting a duration. Pulse energy baseline correction affects where the half-maximum threshold lies, while Gaussian pulse energy and peak power treats the conversion for a specific power-profile family.