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WFC3 Data Handbook > Chapter 6: Charge Transfer Efficiency (CTE) > 6.3 The Pixel-Based Model

6.3
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 that almost all 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 to j=2048 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 the model parameters, 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 the long-dark exposures, then fitting the trailed model to the 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 issue is a serious one. An empty image will be read-out 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 is clearly counter-productive, 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 this 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 minimum 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. In the near future, the WFC3/UVIS team plans to use overscan and charge-injection data to construct a rough model of the specific trap distribution within in each column. Until then, the one-size-fits-all model will suffice.
The pixel-based CTE correction is available for download from the CTE-tools webpage. The routine is currently available only as a FORTRAN stand-alone program, but the eventual plan is to include it in the WFC3/UVIS pipeline as has been done for ACS/WFC. At present, the routine requires both the *_raw.fits and the *_flt.fits images and produces a corrected *_flc.fits image. The routine requires access to both input images since the post-flash electrons have been removed from the *_flt.fits images, and the routine needs the *_raw.fits exposures to tell it about the total number of electrons were present in the pixels during readout (since the presence of background mitigates CTE losses).
The webpage provides a link to a document with additional information on the construction of the model and the operation of the routine, as well as what accuracy users should expect from the pixel-based reconstruction. Since its initial launch, the routine has been adapted to operate on the seven subarrays that contain pre-scan pixels. Although the subarray's readout cadence is slightly different than for the full chip, it appears that the model still does a satisfactory job correcting them.
In general, the pixel-based correction should be good to about 25%. However, in low-signal/low-background situations where the losses can become greater than 50%, it can be hard to trust any reconstruction procedure.

WFC3 Data Handbook > Chapter 6: Charge Transfer Efficiency (CTE) > 6.3 The Pixel-Based Model

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