How successfully the charge can be restored to a pixel depends mainly on the background level (or number of filled traps) and the position of the object relative to the readout amplifier (or number of traps traversed by the charge packet). In the worst case, a star far from the readout register on a zero background with counts of less than 20 e- will be lost within the pixel-to-pixel noise as the CCD is read out. Such large losses can never be reconstructed with a pixel-based scheme.
From an analysis of all of the Cycle 18 ACS observations, we find that the typical ACS background is in the range of 15 to 40 e–. Our analysis of hot pixels in short dark exposures shows that even 15 electrons is enough to keep a large number of the traps filled, so that instead of losing 90% of its electrons, as it would on zero background, a faint star on a background of 15 to 40 e– would lose between 50% and 25% of its original counts if placed far from the read-out amplifier.
In summary, extensive testing has shown that for typical ACS backgrounds, the CTE correction algorithm has a 75% reconstruction accuracy. Users are encouraged to compare the CTE-corrected output images (_flc or _drc.fits) with their uncorrected equivalents (_flt or _drz.fits) to check the accuracy themselves.
Comparison with empirical photometric-based CTE correction
The standard method of correcting for CTE losses is to apply a formula to correct the measured photometry for CTE losses, depending on chip position, background, flux and observation date (Chiaberge et al. ACS ISR 2009-01).
We compared the pixel-based CTE correction (pixel-CTE) with the CTE Photometric Correction Formula derived by Chiaberge et al (ACS-ISR 09-01). In the figure we show the magnitude loss for stars that undergo 2000 pixel transfers (i.e. at the center of the whole ACS/WFC field of view, near the chip gap) plotted against the stellar flux within a 3-pixel aperture radius, in a logarithmic scale. The top and bottom panels show results for low and high sky background levels, respectively.
Results from photometry performed on non-corrected images (DRZ files) are shown in black, while results derived using CTE corrected images (DRC files) are shown in blue. The green points show the residual Δmag obtained after the photometry performed on DRZ images is corrected using an improved version of the CTE Photometric correction formula (Chiaberge, M., priv. comm.). The two methods produce similar results in stellar photometry, except on faint stars on low sky background. Note that the improved formula is appropriate for post-SM4 data, while the formula published in ISR 09-01 is still accurate for data taken before the ACS failure.
These results were obtained by performing photometry on a stellar field 5’ off the center of 47 Tuc. The data were taken in November 2010. A minimum of 100 stars for each bin of stellar flux are used.