= Detector baseline subtraction
\b[Detector baseline subtraction] estimates the non-signal level of a <photodetector> readout and subtracts it before interpreting the desired signal. The baseline can include electronic offset, <dark current> and background light. Subtracting its estimated mean removes a bias contribution; it does not remove the random fluctuations that occurred in the measurement.
For a current readout over a <detection time gate>, a constant baseline estimate $\widehat b$ gives
$$
\widehat Q=\int_{t_0}^{t_0+T_g}i_{\rm meas}(t)\,dt-\widehat bT_g.
$$
If the true constant baseline is $b$, its contribution to the charge error is $(b-\widehat b)T_g$. An original example has $T_g=10\,\mu\mathrm s$ and a baseline overestimate of1nanoampere. The corrected charge is then10femtocoulombs too low. A longer gate amplifies this fixed baseline-estimation error linearly.
A finite baseline record also adds uncertainty. Suppose $n$ equally spaced signal-window samples and $N$ separate baseline samples each have independent zero-mean noise of variance $\sigma^2$, and the baseline estimate is their <arithmetic mean>. With spacing $\Delta t$,
$$
\widehat Q=\Delta t\left(\sum_{j=1}^{n}i_j-n\widehat b\right),\qquad
\operatorname{Var}(\widehat Q)=\sigma^2\Delta t^2\left(n+\frac{n^2}{N}\right).
$$
The same estimated baseline is subtracted from every signal sample, so its error is shared rather than independently redrawn $n$ times. For $n=N=100$, $\sigma=1\,\mathrm{nA}$ and $\Delta t=1\,\mu\mathrm s$, the standard uncertainty is about14.1femtocoulombs. Treating the baseline as known would give only10femtocoulombs. These are stipulated independent-noise values, not a detector specification.
<Baseline drift> motivates measuring the baseline near the signal in time. The SR250's active subtraction mode alternates signal-present and signal-absent triggers, reversing the baseline sample's sign before averaging.<SR250 Gated Integrator by Stanford Research Systems>[PDFp2, Polarity Control and Active Baseline Subtraction]{ref} Cancellation depends on how well those samples represent the baseline during the signal; a source-correlated artifact need not cancel.
In <pulse energy measurement with a photodiode>, charge-to-energy conversion propagates this baseline error through $U=Q/R$, where $R$ is <spectral responsivity>. Baseline characterization is therefore part of the energy measurement, not merely a cosmetic shift of a plotted trace.
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