The serial calibration activities have been performed a total of 26 times during the mission, with the first run at On-Board Mission Time 1484 revolutions, and a final acquisition at OBMT revolution 16381, on the 14th of January 2025, shortly before the end of Gaia science operations.

The data recorded from these activities consist of the measurement of the signal from a limited number of pixels: the final 12 CCD image area pixels of each line, to estimate the level of injected charge in the blocks, and the measurements in 20 (24 for devices in the first AF strip) post-scan pixels samples, that show the characteristic charge trails from the release of trapped electrons in the serial register.

Data from all epochs have been fitted using the CtiPixel serial readout modelling task.

Within a block, the injected charge level is only approximately uniform, with the signal falling slightly from one line to the next despite a constant commanded injection voltage, due to the ‘injection droop’ phenomenon.

In our analyses, the signal from the 10th line in a block is used to estimate the amount of injected charge, calculating the median of its values in the 70 blocks acquired at the same injection setting.

The signal in the post-scan pixels must be evaluated precisely to detect levels of trailing charge as low as 0.1 electrons per pixel, on average.

To this end, particular care has been given to accurately calibrate the electronic offsets, applying the required bias non–uniformity corrections (Hambly et al. 2018).

The bias offset level for each pixel in the serial readout sequence is characterised using line scans made between the injection blocks with the first TDI blocking gate (Crowley et al. 2016b) in operation.

Use of the gate ensures negligible photoelectric signal contamination to the offset values, but may introduce gate–dependent effects relative to the trail measurements that are made with no TDI gate active.

The vector of offset values is measured relative to the final post-scan sample and then applied in conjunction with the prescan level on a line–by–line basis for the trail measurements.

In this way any global gate–mode dependent effect is removed, although there likely remains some very low level of scan position dependent effects in the measurements.

We note that in AF mode the 12th sample (9th in XP mode) in the post-scan trail sequences follows a readout pause and is subject to a large ‘glitch’ offset (Hambly et al. 2018).

Any inadequacies in the electronic offset correction manifest as a discontinuity in residual level from the 11th to the 12th trail sample in AF mode (8th to 9th in XP mode); in general no such discontinuity is observed but may be visible for one problematic device (see Section 6).

Two more lines of lower signal with respect to those of the five charge injection levels commanded in the blocks were included in the CtiPixel serial readout processing and the fits, with the goal of better constraining the model parameters.

The signal in the lines immediately after a block are dominated by the typical exponential charge trails from parallel CTI due to traps present in the CCD image area that release electrons during the parallel readout.

The first line of the release trail immediately following a block presents the highest such deferred signal, and therefore its serial trail charge in the serial post-scan pixels has the higher signal to noise when compared to the other lines following a block, but this was not employed in the analysis to avoid possible blooming charge contamination from the charge injection block.

Instead, the signal from the second line following a charge injection block was preferred and added to the fits.

Finally, the 100th line after an injection block, dominated by the diffuse background signal integrated over 4500 TDI line trans-
fers, was included in the fits.

This line represents the lowest signal level in the fits.

The calibration datasets were fitted with the CtiPixel model employing standard non–linear least-squares minimisation using a Levenberg–Marquardt Algorithm (LMA) implementation.

The fits were weighted by the inverse of the sample measurement variance, derived from a robust determination of the scatter of the input data.

Initially the most problematic aspect of the fits were found to be the large excess residuals often seen in the first sample of the trails.

Investigating this issue, evidence of charge blooming from the charge injection line into the neighbouring pixel was found in the case of red devices (RP and RVS CCDs), especially at the highest commanded injection voltage levels.

To mitigate this effect, the flux values of the first sample in the case of the red devices has been corrected using the signal measured in the second pre-scan sample, i.e. that nearest the image section at the opposite end of the serial register.

This of course assumes that any charge bleeds at the same rate forwards and backwards and affects only the pixels adjacent to the image section.