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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 $\hat{b}$ givesIf the true constant baseline is $b$, its contribution to the charge error is $(b-\hat{b})T_g$. 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 $\Delta t$,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.^[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.

The temporal energy centroid of an optical pulse is its energy-weighted mean time. For nonnegative radiant power $P(t)$ with finite positive energy $U$ and finite absolute first moment,The normalization uses radiant energy as integrated radiant flux.^[ref] The centroid is a moment of the energy-normalized pulse profile; it need not coincide with the largest power value, a threshold crossing or the middle of the FWHM interval.

For an original two-component example, let ninety percent of the energy belong to a symmetric narrow component centred at zero and ten percent to a symmetric component centred at $20\mathrm{ns}$. Linearity of the integral gives $t_E=0.9(0)+0.1(20)=2\mathrm{ns}$. Weak delayed energy can move the centroid even when the dominant peak remains near zero. Multiplying the whole power trace by a positive constant leaves $t_E$ unchanged; translating it by $t_0$ shifts its centroid by $t_0$.

A detector response can shift the measured centroid too. Suppose a normalized impulse response $h$ and normalized optical profile $p$ have finite absolute first moments. For their convolution $q=p\ast h$, direct integration with $t=s+u$ givesThus a causal exponential detector response of time constant $2\mathrm{ns}$ shifts the recorded centroid by $2\mathrm{ns}$ in this model. NIST's pulsed-radiometer characterization explicitly measures detector impulse responses and uses convolution to assess reproduced waveforms.^[ref] The centroid identity is the independent moment calculation above.

Baseline drift can cause a separate shift. Suppose a true pulse has $U=1\mathrm{nJ}$ and $t_E=0$, but a positive residual baseline of $1\mathrm{mW}$ remains across the analysis window from $-10$ to $90\mathrm{ns}$. Its added energy is $0.10\mathrm{nJ}$, centred at $40\mathrm{ns}$. The resulting centroid isA waveform measurement should therefore record the time window, baseline estimate and detector timing response with its reported centroid. A negative background-subtracted trace also needs care: it is not automatically a nonnegative energy distribution.