About this ArticleJ. Anderson (jander[at]stsci.edu), S. Baggett (sbaggett[at]stsci.edu), and B. Kuhn (bkuhn[at]stsci.edu)
WFC3 was installed on board HST in May of 2009 during Servicing Mission 4. The moment the Space Shuttle Atlantis carried it above the Earth's atmosphere, the CCD detectors began to suffer progressive radiation damage, leading to hot pixels and a degradation in charge-transfer efficiency (CTE). CTE losses became an issue for WFC3/UVIS much more quickly than for ACS, since UVIS was designed to operate with extremely low background, thanks to its low dark current, low readnoise, UV sensitivity, and complement of narrow-band filters. And, as it turns out, the first few electrons in a pixel are particularly vulnerable to charge-transfer loss.
Dealing with Radiation Damage
We started developing a charge-transfer model for WFC3/UVIS in 2012, using a model that is similar to the successful model that had been developed for ACS (Massey et al. 2010; Anderson & Bedin 2010). The model was fully implemented in the pipeline in 2015 and produced images that had their pixels corrected for the blurring that results from imperfect charge transfer. In our exploration of the model, we found that adding 12 e– of post-flash to an image before readout significantly lowered charge-transfer losses for faint sources. The WFC3/UVIS readnoise is about 3 electrons, so the post-flash ended up increasing the per-pixel noise by more than 50%. But this painful addition of noise was necessary in order to preserve flux: without post-flash and/or natural background of 12 e–, a faint source could lose 75% of its electrons during its parallel transfer to the readout, but with post-flash, this loss could be reduced to 15%.
This pixel-based correction and post-flashing to 12 e– worked well for several years, but in 2018 it started to become clear that 12 e– of background was no longer providing as much protection as before. Sources were losing more than 30% of their flux. When losses are more than a perturbation, the pixel-based algorithm (which is essentially a deconvolution) ends up amplifying noise when it tries to reconstruct signal. In 2020, we began to recommend increasing the background level to 20 e–.
Since the UVIS CTE model depends so critically on how the model deals with low backgrounds, we devised new ways to study transfer losses for small charge packets. The initial CTE models involved examining trails behind warm pixels (WPs) in dark exposures and using the flux in the trails to estimate how much charge was lost from each WP. This indirect approach works for moderately bright WPs, but it is hard to study faint WPs and CTE losses for low pixel values this way.
Observing CTE Losses Directly
Given the drawbacks of the indirect approach, we sought a more direct way to measure CTE losses. In December 2020, we took a series of 900s long darks and 30s short darks with various post-flash backgrounds. A WP of ~180 electrons in a long dark will have 6 electrons in a short dark, and we can directly examine the losses as a function of number of transfers and image background. Studying faint WPs allows us to focus on the marginal losses at each particular background level and thus pin down the model more precisely.
Figure 1 shows the surviving fraction of a ~6 e– WP after ~1750 parallel transfers as a function of background. When the background is 12 e– only 40% of the electrons survive, when it is 20 e– nearly 60% survive.
An Updated Model
We used the data in CAL-16440 and similar calibration programs to re-constrain the parameters of the pixel-based model with modern data. The pixel-based model involves the trapping and the release of charge. The first parameter in the model, φ(q), gives the number of traps that a pixel-packet containing q electrons will be subject to in a 2000-pixel shuffle to the register. The second parameter τ(q, Δj) describes how the trapped charge is released into upstream pixels.
Figure 2 shows the two sets of parameters for the recent models for ACS (Anderson & Ryon 2018) and WFC3/UVIS (Anderson 2021), both normalized to late 2016. At the bright end, ACS has more traps than UVIS, which makes sense given that it had spent about twice as long in orbit at that time. Below q ~ 90 e–, however, UVIS has considerably more traps than ACS. Interestingly, the two have very similar power-law release profiles, except for below q ~ 90 e–, where UVIS has an extremely sharp profile. The WFC3/UVIS CCDs were manufactured with a mini-channel, which was designed to protect the smallest charge packets from CTE losses. It is not clear whether the transition behavior at q ~ 90 e– is related to the mini-channel.
The Challenge of Noise Amplification
One of the challenges of the pixel-based reconstruction procedure is that the readout process is not noise-free. Readnoise is added at the amplifier, but the trapping and release of charge is a probabilistic process that must deal with quantized electrons and, as such, it cannot be reversed perfectly. When the marginal losses are more than a simple perturbation on the original charge distribution, then amplification of the noise is unavoidable.
Lately, the reconstructed images have been getting noisier and noisier. Figure 3 compares an unreconstructed flt image with a background of 20 e– (with the expected noise) next to the reconstructed flc image. The reconstructed image has five times more 4‑sigma pixels, the bulk distribution has the noise-equivalent of 30 e– background, and the noise distribution is also made asymmetric by the reconstruction. This noise amplification is to be expected, since the marginal electron on a background of 20 e– has nearly a 50% chance of being trapped. Note that this noise is present even though we made an attempt to suppress the amplification that could be related to simple readnoise fluctuations (see AB10). We explored alternative approaches to do restoration without significantly amplifying the noise, but were unsuccessful—it simply is not possible to restore the signal without adding unacceptable levels of noise.
Taking to heart the Hippocratic admonition to "do no harm," in the recently released update to the pipeline, we chose to increase the noise mitigation to a level that would effectively suppress noise amplification in the background. This comes at the cost of not restoring faint sources (which could not be restored well anyway).
Over the years, the community has become accustomed to dealing with CTE loss by simply using the pixel-based correction products (the flc and drc images). It is unfortunate that the losses have risen to the point where reconstruction near the background has become impossible. Other approaches to CTE correction will be necessary.
Still Flux to Be Measured
The good news is that there is still signal to be measured, and when noise is kept down it can be measured. Figure 4 shows observed vertical profiles of stars on eight different backgrounds. The S/N ~10 star on the left can be seen at all backgrounds, but it loses half its flux on a 12 e– background as the left side is whittled away by the CTE traps and the right side is puffed up by the trails. The faintest star (in the right panel) is essentially undetectable on a 12 e– background. Many of these sources still have detectable flux, but it is impossible to restore the pixels to their original distribution, particularly when one realizes that there is readnoise and Poisson noise added to these average profiles in individual exposures (which the restoration is based on).
Figure 5 shows the flux in a 2 × 2‑pixel aperture extracted from the profiles above. These simple trends can be used to correct observed photometry for CTE losses. The trends seen here mirror almost identically the trends shown in marginal WPs in Figure 1.
There is a new Instrument Science Report out (Anderson 2021) with more details on the new model and the new operation of the correction. Even though the pixel-based model can no longer restore all sources, it still cleans up the trails from WPs and CRs, which can reduce the number of pixels they affect by a factor of 5.
In addition to the above ISR, a separate ISR (Kuhn 2021a) will show the effects of the v1.0 and new v2.0 CTE corrections on external star-cluster data. Very soon, we will be coming up with new ways for users to correct their observations for CTE losses (Kuhn 2021c, Anderson 2021b). Finally, the community still has the option of running the pipeline with the old correction (Kuhn 2021b), with the caveat that the added noise may drown out faint sources. Figure 4 shows that even though CTE has a significant impact on faint-star profiles, there is still faint signal to measure. By carefully analyzing the original pixels, faint-source science is still very much possible with WFC3/UVIS.
Finally, the increasing CTE losses in WFC3/UVIS reminds us of how important it is to take observations carefully in the first place. More than ever, it is better to preserve signal in the first place than to correct images for missing signal after the fact. Anderson (2021) provides strategies for optimizing signal-to-noise in the current CTE environment.
Please refer to the WFC3 CTE page for the most up-to-date information on the state of CTE losses in WFC3 and current mitigation strategies.
Anderson, J. & Bedin, L. R. 2010, PASP, 122, 1035, "An Empirical Pixel-Based Correction for Imperfect CTE. I. HST's Advanced Camera for Surveys," aka AB10
Anderson, J. & Ryon, J. 2018, ACS ISR 2018-04, "Improving the Pixel-Based CTE-Correction Model for ACS/WFC"
Anderson, J. 2021a, WFC3/ISR in progress, "Updating the WFC3/UVIS CTE Model and Loss-Mitigation Strategies"
Anderson, J. 2021b, WFC3/ISR in progress, "Table-Based CTE Corrections for WFC3/UVIS Photometry and Astrometry"
Kuhn, B., et al. 2021a, WFC3/ISR in progress, "WFC3/UVIS New FLC External CTE Monitor 2009–2020"
Kuhn, B. 2021b, Jupyter notebook for reverting to the old processing
Kuhn, B. 2021c, WFC3/ISR in progress, "Formula Corrections for CTE in WFC3/UVIS Images"
Massey, R., et al. 2010, MNRAS, 401, 1, "Pixel-Based Correction for Charge Transfer Inefficiency in the Hubble Space Telescope Advanced Camera for Surveys"