Variance of a pedestal-corrected sample

The variance of a pedestal-corrected sample quantifies the random spread remaining after subtracting an estimated baseline from a signal acquisition. Subtracting a mean reset charge-injection pedestal removes an offset; it does not automatically remove reset pedestal variance. For a raw signal sample $Y$ and pedestal estimate $B$,The covariance term determines whether subtraction suppresses shared fluctuations or adds independent noise. The GUM's correlated-input rule gives this identity directly for the linear measurement model $f(Y,B)=Y-B$.^[ref]

Two correction procedures have different statistical consequences. First suppose signal acquisitions have independent pedestals $P_i$ of variance ${\sigma }_P^2$ and independent readout noise ${\eta }_i$ of variance ${\sigma }_{\eta }^2$. A separate mean of $M$ independent blank acquisitions, with individual variance ${\sigma }_B^2$, is reused for every signal sample:After removing any constant means, independence givesConsequently, averaging $N$ corrected samples givesThe shared blank correction creates a common uncertainty floor, as in shared calibration error.

Alternatively, a baseline and signal reading from the same acquisition can share a fluctuating pedestal. In an idealized correlated double sampling model, $R=B_0+e_R$ and $Y=s+B_0+e_Y$, so $Y-R=s+e_Y-e_R$: the common $B_0$ cancels. Independent readout noises remain and their variances add. More generally, if paired readings each have standard deviation0.20millivolt and correlation coefficient0.9, their difference has standard deviationTreating that pair as independent would predict0.283millivolt instead.

An experimental assessment records paired zero-input samples at the actual acquisition delays and estimates their covariance, then distinguishes that procedure from reusing a separate blank mean. The ACF2101 datasheet specifies output noise and charge-transfer errors separately; a charge-transfer limit is not itself a pedestal variance or evidence for a particular correlation.^[ref]