6.4 The Pixel-Based Model

The previous section made reference to the pixel-based model of CTE losses. The WFC3/UVIS model is based on the empirical model that was constructed by Anderson & Bedin (2010), which itself was inspired by the model in Massey et al. (2010) for ACS/WFC.

The basic model assumes that each column contains a number of charge traps distributed evenly among its pixels from j=1 to j=2048. Charge packets for pixels at the top of the chip will see all of the traps, those in the middle at j=1024 will see half of them, and those at j~200 will experience a tenth of them. Each trap will grab and hold a particular electron in a charge packet (the first, the second, the hundredth, etc). The model also has a release profile for each trap. Typically, there is a 20% chance the electron will be released into the first upstream pixel, a 10% chance it will be released into the second upstream pixel, etc. We find for WFC3/UVIS that essentially all trapped electrons are released after 60 transfers. The two sets of parameters for the model are therefore: the distribution of traps as a function of electron-packet size and the release-probability distribution for trapped electrons.

The readout process is simulated by going up through each column from j=1 (close to the readout amplifier) to j=2015 and determining (1) which electrons will be trapped during the journey down the detector to the serial register and (2) when these trapped electrons will be released. Even though this is a stochastic process in reality, the model treats it as deterministic. The end result is that the observed distribution of pixel values gets blurred somewhat in the upstream direction relative to the original distribution, leading to the characteristic CTE trails seen behind sources in CTE-affected UVIS images.

In order to determine optimal parameters for the model, we examined the blurring experienced by hot and warm pixels in a variety of dark exposures taken in August 2012 with both short (100s) and long (900s) exposure times, and with various post-flash background levels (from zero up to 60 electrons). In practice, the model was constrained by first solving for the pre-readout distribution of warm pixels from scaling down the long-dark exposures, then fitting a trailed model to the actual trailed short-dark observations. The variety of background levels provided additional constraints. The first set of parameters (the distribution of traps as a function of charge-cloud size) is shown in Figure 6.1.

In order to use the model on science images, we must invert this procedure: we must determine what original image - when pushed through the readout algorithm- generates the observed distribution. This is formally a non-linear deconvolution process.

There are several challenges to a pixel-based reconstruction. One challenge is that the observed images represent not just the charge that arrived at the readout, but they represent this charge plus a contribution from the readnoise (3.1-3.2 electrons for UVIS). The other challenge is that the model assumes an even distribution of traps throughout the detector, even though in actuality this distribution is stochastic: each column will naturally have a slightly different number of traps and even the distribution of traps within each column will not be perfectly uniform.

The readnoise introduces a serious complication. An empty image will be readout to have a variance of about 3.2 electrons in each pixel due to readnoise. If the original image on the detector had a pixel-to-pixel variation of 3.2 electrons on a background of near zero, then the charge-transfer process would blur the image out so much that the image that reached the amplifier would have a variance of less than 0.5 electron. The CTE reconstruction algorithm determines what the original image would have to be in order to be read out as the observed image. If we include readnoise in this observed target image, then the original image would have to start with an extremely large amount of pixel-to-pixel variation (perhaps 15 electrons of noise) for it to end up with 3.2 electrons noise after the blurring readout process. We would have to increase the noise by a factor of five to arrive at the image that was read out. This clearly will not produce a realistic reconstruction, so we need to find some way to mitigate this "readnoise amplification".

We address this issue by taking the observed image (which has had readnoise added to it) and determining the smoothest possible image that is consistent with the image, modulo readnoise. We choose the smoothest possible image, since the smoother the image, the less the readout algorithm will redistribute charge. While this may not give us the true counts that arrived at the readout register, it should provide us with the most conservative possible CTE correction. The pixel-based reconstruction algorithm then operates on this "smooth" image, and the redistribution of flux is applied to the observed image (which still has the readnoise in it).

The other challenge to a pixel-based reconstruction is that the model assumes that each pixel has the same number of fractional traps, even though in reality the traps are quantized: most pixels have no traps, while some may have several. The WFC3/UVIS team has examined overscan and charge-injection data in an effort to construct a rough model of the specific trap distribution within each column, but since charge injection is possible at only a very high level (15,000 electrons per pixel), it is very difficult to explore the lower-level charge traps, which are the most relevant to science images. So, until we can find a better way to pin down the location of traps, the simplistic uniform trap-density model will have to suffice.

Previously, the pixel-based CTE correction was a standalone FORTRAN program available for download from the CTE-tools web page. However, the pixel-based CTE correction is now part of the automated calibration pipeline for all UVIS full-frame images (calwf3 version 3.3 and later) and most1 UVIS subarray images (calwf3 version 3.4 and later). Controlled via a new header calibration switch (PCTECORR = PERFORM), and associated calibration table (PCTETAB) and CTE-corrected reference files (e.g. DRKCFILE), calwf3 will by default produce two sets of products: the standard non-CTE-corrected (e.g. *_raw.fits, *_flt.fits, *_drz.fits) files as well as the new CTE-corrected results (*_flc.fits, *_drc.fits). Observers can use the *_flc.fits and *_drc.fits data products in the same way as *_flt.fits and *_drz.fits files.

In general, the pixel-based correction should be good to about 25%. The correction can enable recovery of a significant fraction of faint sources ( WFC3 ISR 2016-17). However, in low-signal/low-background situations where the losses can become greater than 50%, it can be hard to trust any reconstruction procedure.

To help evaluate the efficacy of the CTE-correction, the CTE monitor analysis has been performed with and without the correction ( WFC3 ISR 2017-09, and WFC3 ISR 2016-17). Those results show that as of 2017, for images with the recommended minimum 12 e-/pixel background, flux losses are 5-15%, depending on source brightness. With CTE-correction, those losses are effectively 0 or sometimes over-corrected by a few percent. For images with less than the recommended background, the CTE correction is able to reduce flux losses from ~50% down to ~15% for faint sources, from ~15% to < ~5% for intermediate-brightness sources, and from ~5% down to 0 for the brightest sources (e.g., Fig 8 and Fig 10 in WFC3 ISR 2017-09 and Fig 4 in WFC3 ISR 2016-17).

 1For observers utilizing unsupported subarrays (UVIS2-M1K1C-SUB and UVIS2-M512C-SUB), there is a workaround available that uses the standalone FORTRAN CTE-correction code ( STAN Issue 18)