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The ACS Team is currently testing a new version of CALACS containing two significant improvements: automatic removal of bias stripes using the pre-scan region, and pixel-based CTE correction. In an effort to quantify the accuracy of the pixel-based CTE correction and to monitor the evolution of the transfer losses, we developed a comprehensive analysis that we present in this web page. Figure 1 shows the structure of an actual isolated CTE trail produced by a hot pixel with ~1000 electrons. The schematic on the right shows the position of the hot pixel with the label HP and the first, second and third pixels in the trail are marked as P1, P2, and P3, respectively.

Figure 1: A detail of the WFC2 chip of image jbmncoakq_flt.fits, a 1040 sec dark frame taken on 27DEC2010. The vertical trails extending upward from the hot pixels are indicative of imperfect CTE. The color schematic zooms into one hot pixel to show the CTE trail structure and our notation. The amplifier for this image is located towards the bottom.

Figure 2 shows the evolution of the assigned number of electrons in P1 for each ACS/WFC anneal cycles. We represent the maximum of the distribution for two types of images: those not corrected for imperfect CTE (FLT images) and those corrected for imperfect CTE (FLC images). The red points represent the FLT data that was obtained while ACS was operating at a temperature of -77 ℃. Blue points correspond to FLT data obtained with an instrument temperature of -81 ℃. Green points represent the data from the CTE corrected images (FLC) regardless of the instrument temperature.

Figure 2: Evolution of number of electrons in P1 as a function of time. This plot corresponds to hot pixels with 1000±50 electrons. The black lines represent linear fits to the empirical data. The data obtained after the temperature switch has been scaled and aligned with the data obtained at a temperature of -77 ℃.

The following sections are a detailed explanation of the method that we used for this study. Further information and a more elaborate set of figures can be found in the ACS ISR 2011-XX (Ubeda & Anderson; in prep.)

Detailed discussion of the procedure

Introduction

The ACS Team is currently testing a new version of CALACS containing two significant improvements: automatic removal of bias stripes using the pre-scan region, and pixel-based CTE correction. Currently there are some standard data products: _CRJ files (CR-rejected image), _FLT files (flat fielded image), and _DRZ files (geometrically corrected image). In the near future, there will be three new files (_CRC, _FLC and _DRC) which will contain the CTE-corrected data products. Users will be able to choose whether to use the standard or CTE-corrected products. Both sets of data will be corrected for bias striping. This new version of CALACS applies the CTE correction to the raw science images and requires CTE-corrected dark reference files.

In an effort to quantify the accuracy of the pixel-based CTE correction and to monitor the evolution of the transfer losses, we developed a comprehensive analysis that we present in the following sections.

CTE losses are created during the CCD readout process and it is an issue found in several instruments on board the Hubble Space Telescope, such as the Wide Field and Planetary Camera 2, Wide Field Camera 3 UVIS, Space Telescope Imaging Spectrograph, and the Advanced Camera for Survey's Wide Field Channel (ACS/WFC) and High Resolution Camera.

Method

The new CALACS incorporates a refined version of the Anderson & Bedin (2010) code. This algorithm first develops a model that reproduces the observed trails and then inverts the model to convert the observed pixel values in any image into an estimate of the original pixel values. The original version of the code works very well for intermediate to high flux levels (> 200 electrons). The new version has been improved in order to become more effective at low flux levels (< 100 electrons), and employs a more accurate time and temperature dependence for CTE over the ACS lifetime.

The Dark-Current Data Set

Most of HST's orbits experience some occultation by the Earth. The observatory regularly takes advantage of this downtime to collect calibration images such as dark frames, bias frames, and flats. As a result, the Archive contains an enormous number of such calibration data sets. Usually, the observatory obtains four ACS/WFC ~1000 sec dark frames four times a week.

We begin our analysis using the _RAW dark-current observations. These are 4144 X 4136 2 byte integer images (34.3 Mb) that contain the raw number of counts recorded by the analog-to-digital converter for each pixel. The typical post-SM4 dark current in the ACS/WFC is 0.006 electron/pixel/sec, but like all CCDs operated in Low Earth Orbit radiation environment, the ACS CCDs are subject to radiation damage by energetic particles trapped in the radiation belts. In agreement with the ACS Instrument Handbook, we define hot pixels as all pixels with a discernible dark-current excess ( > 0.08 electron/sec/pixel).

Figure 3 shows a detail of a single dark exposure jbmncoakq_flt.fits. The field shown covers a region near the top of WFC2 and is therefore ~2000 pixels away from the read out amplifier. The hot pixels trails are quite obvious.

Figure 3: Detail of dark frame showing CTE trails.

We extend our study over the whole history of the ACS/WFC, starting from December 2002 until the present time. We sort the dark-frames according to their date of observation, and in groups of anneal dates. The histogram in Figure 4 shows the number of dark-frames that were considered in each anneal cycle.

Figure 4: Distribution of number of dark frames used for each anneal cycle. During an anneal cycle, the CCDs and the thermal electric coolers are turned off and the heaters are turned on to warm the CCDs to ~19 ℃.

The Calibration process

In order to test the pixel-based CTE correction, we calibrated all _RAW dark frames using the latest version of CALACS. The automated pipeline performs: a bias correction, the removal of bias stripes, the pixel-based CTE correction, and a transformation from counts (DN) to units of electrons using the appropriate gain for each of the four amplifiers.

This process generates two calibrated FITS images with extensions _FLT and _FLC with 167.8 Mb each (Figure 5). We processed a total of 240Gb of raw data and delivered almost 2.0Tb of calibrated files. The resulting corrected images look extremely good; the trails appear to be removed nicely.

Figure 5: (Left) A 1000 x 1000 pixel region of the top of the extension 1 chip in image jbmncoakq_flt.fits. The CTE vertical trails are clearly visible. (Right) The reconstructed _FLC image after the execution of CALACS. (Center) An animation of the two adjacent images, blinking at a one second interval.

The Identification of Hot Pixels

In the presence of a high electric field, the dark current of a single pixel can be greatly enhanced. These hot pixels accumulate as a function of time on orbit; however, the reduction of the operating temperature of the WFC CCDs has dramatically reduced the dark current of the hot pixels and therefore many pixels previously classified as hot may now be normal pixels. ACS devices undergo a monthly annealing process which greatly reduces the population of hot pixels and does not affect the normal pixels. In order to identify most of the hot pixels in each anneal period and avoid mistaking them for cosmic rays, we selected only those pixels which comply with the following conditions:

pixel should have dark current greater than 0.08 electrons/second
pixel should be isolated within a 4 pixel radius
pixel should appear consistently in at least 80% of the dark _FLT frames in each anneal period.

This procedure allowed us to create a single hot pixel list for each anneal period by combining the results from individual dark frames.

The Empirical Trails

Figure 1 shows the structure of an actual isolated CTE trail produced by a hot pixel with ~1000 electrons. The schematic shows the position of the hot pixel with the label HP and the first, second and third pixels in the trail are marked as P1, P2, and P3, respectively. Using the list of hot pixels in each anneal period, we scan every single _FLT and _FLC image and record the values of HP, P1, P2, and P3.

Pixel Distribution

In order to analyze how well the pixel-based CTE correction is performing, we propose to study the evolution of the number of electrons in pixels P1, P2, and P3 as a function of time, and as a function of number of electron in the hot pixels.

We create subsets of hot pixels with intensities in the ranges 100±10, 1000±50, 10000±1000, and electrons that are located at least 1500 pixels away from the readout amplifiers and we study their behaviour individually.

Most dark exposures are taken with 1000s integration time, but there are some with longer or shorter exposure times. We scaled the pixel intensities to match a single 1000s exposure in all the cases. Figure 6 represents a typical _RAW dark frame with the four readout amplifiers labeled in the corners as A, B, C, and D. During readout of the CCDs, the charge is shifted in the direction of the white arrows. In order to maximize the CTE signature, we examined the hot pixels that were at least 1500 pixels from the serial registers: y>1500 in the WFC2 and y<500 in the WFC1. We use black rectangles to represent that space.

Figure 6: A typical processed _FLT dark frame. The white arrows represent the readout direction.

Figure 7 shows a typical histogram distribution of the number of electrons in the first upstream pixel (P1) for 66 dark frames obtained around August 2009. They correspond to hot pixels with 1000±50 electrons. These distributions have always the same shape: they present a steep increase, a defined maximum and a slower decline. The distribution is definitely not symmetrical. The assigned value to the most probable number of electrons in P1 is shown with the green vertical line. The dotted lines represent the adopted error in the average.

Figure 7: Histogram distribution of the number of electrons in the first upstream pixel (P1) for 66 dark frames obtained around August 2009. The average number of electrons in this distribution is 42.5±1.6 electrons.

In order to find the maximum we compute an iteratively sigma-clipped mean on the dataset. This yields a value close to the mode of the distribution and allows us to provide an error to the measurement. We perform this analysis on both the _FLT and _FLC images.

Time Dependence

Figure 8 shows the evolution of the assigned number of electrons in P1 for each anneal cycle. We represent the maximum of the distribution for both types of images: not corrected for imperfect CTE (_FLT images) and corrected for imperfect CTE (_FLC images). In this web page we only provide the results based on hot pixels with 1000±50 electrons. Please refer to the ACS ISR (in preparation) for other cases.

The red points represent the FLT data that was obtained while ACS was operating at a temperature of -77 ℃. Blue points correspond to _FLT data obtained with an instrument temperature of -81 ℃. Green points represent the data from the CTE corrected images (_FLC) regardless of the instrument temperature.

Figure 8: Evolution of number of electrons in P1 as a function of time. This plot corresponds to hot pixels with 1000±50 electrons. The black lines represent linear fits to the empirical data.

Comments on the plot

The data in the plot represents a comprehensive study of ~5000 dark frames obtained using the ACS/WFC from 2002 until 2011. The gap in the data represents the time between the ACS failure (January 2007) and the repair mission (May 2009).

Overall, there is a noticeable trend in the _FLT data. A linear fit is provided for two segments: the pre-SM4 _FLT data and the _FLC data. The slope of the linear fits are 6.81 and 0.42 in units of electrons per year.

One significant feature of the plot is the drop observed around July 2006. This was the time in which the electronics on side 1 failed and was switched to side 2. At the same time the operating temperature of ACS was decreased from -77 to -81 ℃.

The data that was empirically corrected for charge transfer inefficiencies is shown as green points. This analysis is showing that the flux from the first pixel in the trail (P1) is indeed being transferred back to the pixels where it originated. This study also shows that the Anderson & Bedin algorithm performs the expected empirical correction on ACS/WFC data obtained in a variety of circumstances such as (1) newly installed camera, (2) electronics switch, (3) decrease in operating temperature, and (4) camera recovery to the expected 10% accuracy. Also note the expected CTE loss at the time when the camera started operations. Finally, we have shown that the integration of the pixel-based CTE correction has been successfully implemented onto CALACS.

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