= Pulse energy baseline correction
{title2=$U=\int(P-P_{\rm bg})\,dt$}
\b[Pulse energy baseline correction] subtracts the estimated non-pulse contribution before integrating a measurement trace. For a trace calibrated in power units over a gate $[t_0,t_1]$,
$$
\widehat U=\int_{t_0}^{t_1}\left[P_{\rm measured}(t)-\widehat b(t)\right]\,dt.
$$
The estimate $\widehat b$ must have the same units as the integrated trace. Optical background and a detector-electronics offset enter at different stages of a physical measurement; a voltage offset cannot be subtracted directly from optical power without a response calibration.
An original drift example takes a $10\,\mathrm{\mu s}$ gate. Suppose pulse-free observations establish a baseline increasing linearly from $20$ to $40\,\mathrm{mW}$ across that gate. Its integrated contribution is
$$
U_b=\frac{20+40}{2}\,\mathrm{mW}\times10\,\mathrm{\mu s}
=0.30\,\mathrm{\mu J}.
$$
If the measured trace integrates to $1.50\,\mathrm{\mu J}$, the corrected estimate is $1.20\,\mathrm{\mu J}$. Subtracting only the initial $20\,\mathrm{mW}$ would yield $1.30\,\mathrm{\mu J}$, with a positive $0.10\,\mathrm{\mu J}$ error. This is a <baseline-drift bias in pulse-energy integration> in a stipulated linear model.
Historical NIST measurements took baselines before and after each run and averaged them to correct background and thermal drift. The leakage-background configuration was specified separately from a pulse injection.<Calibration Service for Low-level Pulsed-Laser Radiometers at 1.06 µm: Pulse Energy and Peak Power by Rodney W. Leonhardt>[§3.5, printedp.8; §7.2, Type B component4, Leakage Effect]{ref} Bracketing observations must genuinely represent the non-pulse signal; they cannot include an unrecognized pulse tail. Subtraction also cannot recover energy excluded by a <detection time gate> or repair a nonlinear detector. The <Gaussian pulse time-gate energy fraction> quantifies one profile-specific truncation effect.
Back to article page
