4.12.1 Charge Transfer Efficiency

The WFPC2 CCDs have a small but significant charge transfer efficiency (CTE) problem which causes some signal to be lost when charge is transferred down the chip during readout. This has the effect of making objects at higher row numbers (more charge transfers) appear fainter than they would if they were at low row numbers. The effect depends on the temperature of the CCDs. At the original temperature of -76°C, as much as 10-15% of the light within a 0.5" radius aperture around a bright star could be lost for objects at the highest rows. As a result, the CCD operating temperature was changed to -88°C on 23 April, 1994. This reduced the effect to a maximum amplitude of 4% for stars with more than 1,500 total detected electrons. This ~4% amplitude seems to remain in effect for stars up to 20,000 total electrons. However, for fainter stars (few electrons) seen against a low background, the effect appears to have grown much larger (up to tens of percent) over the last 8 years. We also note that the effect depends on the amount of background light on the chip. There is significantly less CTE effect in the presence of even a moderate (several tens of electrons) background. Hence, the effect is not well described by either a constant fractional loss or a constant additive loss per charge transfer, but must be calculated as a function of target counts, background light, and epoch.

Our basic understanding is that CTE problems are caused by electron traps in the CCD's silicon. During the readout process these traps capture charge from the image electron packets as they are clocked across the CCD towards the readout amplifier. After some time delay, the charge is released from the traps, but by that time the affected electron packet has moved away, so the re-deposition occurs at some distance from the electron's original position in the image. Hence this has the effect of producing "tails" on images. We believe that larger electron packets fill a larger volume in the bulk silicon, hence brighter images are able to access larger numbers of traps than faint ones. This simple paradigm also suggests that images with high background levels will tend to have less CTE problems, since the background will fill some of the traps, and prevent them from robbing charge as the CCD is read out.

CTE: photometric effects

The primary observational consequence of CTE loss is that a point source at the top of the chip (Y=800) appears to be fainter than if observed at the bottom of the chip (Y=1), due to loss of electrons as the star is read out down the chip (see Figure 4.13). This is called Y-CTE. There also appears to be a similar, but weaker tendency, for stars on the right side of the chip (X=800) to be fainter (called X-CTE). The effects also depend on the brightness of the star and the background level.

The photometric calibration of the instrument presented in this Handbook is based on Holtzman, et al. (1995b). It has been corrected for CTE by assuming a 4% loss across the 800 rows of the CCD (i.e. 2% correction for CCD centers). All of the frames considered in the primary photometric calibration are short exposures of bright stars. While correction formulae have been developed, as discussed below, the 4% ramp is still a reasonable approximation. Hence, for data taken at -88°C, a 4% correction ramp was applied to the measured 0.5" radius aperture photometry, in the sense that objects at row 800 were made brighter by 4%, but the brightness of objects at the first row was not changed. The correction was applied to bring measurements to the values they would have had in the absence of CTE, or equivalently, the values they would have had if measurements had been made at row 0.

Several studies were done on the photometric effects of the Charge Transfer Efficiency (CTE) problem for WFPC2. This work was based on analysis of observations of the globular cluster Cen (NGC 5139). The first study provides a set of formulae that can be used to correct for CTE loss when doing aperture photometry, based on a data set taken on June 29, 1996 (Whitmore and Heyer 1997, ISR WFPC2 97-08), reducing the observational scatter in these test data from 4-7% to 2-3%, depending on the filter. The second study found evidence that CTE loss for faint stars has increased with time (Whitmore 1998).

Figure 4.13: Ratio of count rates observed for the same star (i.e., Throughput Ratio) as a function of the change in row position for stars in 4 different brightness ranges. The negative slope shows that a star appears brighter when it is at low row number, thus closer to the "bottom" of the chip and the readout amplifiers, than when it is at high row number. The effect is larger for fainter stars (top right panel) as compared to bright stars (bottom left panel). See Whitmore and Heyer (1997) for details.

A continuation of this analysis using observations of Cen confirmed that the CTE loss for WFPC2 was time dependent (Whitmore, Heyer, and Casertano 1999). The datasets cover the time range from April 28, 1994 (shortly after the cooldown to -88°C), to February 1999. For bright stars (i.e., brighter than 200 DN when using gain = 14 e^-/DN; equivalent to 400 DN for gain = 7 e^-/DN) there is only a modest increase in the amount of CTE loss as a function of time. However, for faint stars the CTE loss has increased more rapidly. For example, for very faint stars (i.e., 20-50 DN at a gain of 14 e^-/DN) the CTE loss has increased from 3% to 40% for a star at the top of the chip.

It should be noted that CTE loss is strongly dependent on the background level in an image. Figure 4.14 illustrates CTE losses for background levels ranging from 0.03 to 70 DN/pixel. For example, for faint targets (20 - 50 DN, top left panel) a low background of 0.03 DN/pixel results in ~40% CTE loss at late epochs, while a 14 DN/pixel background produces ~4% loss. The results in the previous Figure 4.13 are based on very short (14s) exposures with very low background. By comparison, a typical WFPC2 exposure (300s in F555W) has ~3 DN/pixel background. Hence, the sky background will significantly reduce CTE loss for most science observations. CTE will primarily affect images in the UV and in narrow band filters, where the background is very low.

Figure 4.14: Y-CTE loss in stellar photometry as a function of epoch and background light. Each panel corresponds to a different range of target count levels (1 DN = 14 electrons). Different symbols correspond to different background levels; the larger plotting symbols indicate images with larger backgrounds. The straight lines represent the best-fit multilinear regression for Y-CTE as function of time, log counts (DN), and log background. See Whitmore et al. (1999).

An approximate correction for stellar photometry is given by Whitmore, Heyer, and Casertano (1999) as follows for stellar photometry performed with a 2 pixel radius aperture. For and they give

whereas for and they give

and finally the corrected stellar counts are given by

where parameters are defined as:

= number of counts (DN) measured for the star.

= percent loss over 800 pixels in Y-direction

= percent loss over 800 pixels in X-direction

= X position of star in pixels

= Y position of star in pixels

= mean background counts in image (DN)

Note that these equations are for gain = 7 e-/DN observations, since this is most commonly used for science observations. For gain = 14 e-/DN, multiply CTS_obs and BKG by 2 before using the above equations. For further details, please see Whitmore, Heyer, and Casertano (1999).

Another study analyzed CTE losses and developed formulae to correct them (Dolphin 2000). This paper compares WFPC2 observations with ground based observations of Omega Cen and NGC 2419 and derives CTE corrections using a baseline through March 2000, roughly a year longer than available for a similar study by Whitmore, Heyer, and Casertano (1999, PASP, 111, 1559). In general, Dolphin finds good agreement with the Whitmore et al. results (within a few hundredths of a magnitude) with less scatter in the residuals, except for relatively recent (1998 and later) data at low count levels. Dolphin updated his formula on September 17, 2002. For his most up-to-date formulas, the user is strongly encouraged to check his webpage at http://www.noao.edu/staff/dolphin/wfpc2_calib/. Figure 4.15 shows data on Omega Cen which has been corrected for CTE by the Dolphin (2002) formula. Based on this figure and the comparison presented in Whitmore and Heyer (2002), we find that the Dolphin formula provides better CTE corrections than that of Whitmore et al. formula. Our current recommendation is to use the Dolphin (2002) formula for the CTE loss correction, though caution should always be exercised at the faintest levels (e.g. approximately 4 DN in a 14 sec exposure). We list here Dolphin's "complex" equations which take into account the fact that the magnitude loss per pixel is not constant as the star reads out. These CTE correction equations, expressed in magnitudes of CTE loss, are given as follows:

First, calculate X-CTE, the CTE loss (in magnitudes) in the X readout:

Second, calculate Y-CTE, the CTE loss (in magnitudes) in the Y readout:

where:

ct = counts in electrons lct = ln(ct) - 7 bg = sqrt (background2+1) - 10 lbg = ln( sqrt(background2+1) ) - 1 yr = (MJD - 50193) / 365.25 Counts and background are given in electrons.

Finally, the corrected magnitude of the star is then given by:

mag(corr) = mag - X-CTE - Y-CTE

Figure 4.15: The ratio of counts between a 14 sec. and 100 sec. exposure for stars in Omega Cen vs. the Y position for stars on all three WFC chips. The raw values (filled circles) fall below a ratio of 0.14 due to CTE loss. The different panels represent different target brightnesses (in DN), as selected on the 100 sec. exposure and described by the labels. The filled triangles show the values corrected using the Dolphin (2002) formula.  Note that the extrapolation of the raw data to Y=0 (the sloped line) is consistent with the predicted value of the throughput ratio based on the exposure times; hence, the long-vs-short anomaly is not a problem for this data set (see Section 4.12.2 "The Long vs. Short Photometric Anomaly"). This figure courtesy of A. Dolphin (Dolphin 2002, private comm.).

Physical effects of CTE

Late in 1999, efforts were made to better understand the detailed effects of CTE during the read out process (Biretta, Baggett, and Riess 2000). Figure 4.16 illustrates the impact of CTE on a single pixel during the read out process. This image is the average of 700 hot pixels taken from WFPC2 dark frames from late 1999, and it effectively shows the system response to a single bright pixel at the center of a CCD. The CTE problem displaces counts into obvious "tails" extending in both the X and Y directions on the CCD. Three components of CTE can be discerned and characterized by the time delay for trapped charge to be released:

1. A rapidly decaying tail in the Y direction with a decay scale of a few pixels (decay time 10s of milliseconds)
2. A rapidly decaying tail in the X direction (decay time 10s of microseconds)
3. An extended tail in the Y direction which decays slowly over dozens of pixels (decay time 100s of milliseconds).

All of these components have the effect of robbing charge from typical small apertures (few pixel radius) used for stellar photometry. (A fourth component of CTE is responsible for long-lived residual images, and will be discussed later.)

The brightness profile along the Y-CTE tail is shown quantitatively in Figure 4.17. While the count levels in the extended tail are low, they still make up approximately 2/3 of the total counts displaced from the hot pixel. Figure 4.17: also illustrates the effect in 1994, and gives a clear indication of the time evolution. Similar measurements made on hot pixels in separate intensity ranges are illustrated in Figure 4.18; the total charge in the Y-CTE tail (in this case for late 1999 and background level ~1 DN) is approximately

where I is the hot pixel intensity in DN at gain 7 e^-/DN. This relationship together with Figure 4.17: and model PSFs can be used to predict stellar CTE, and the results appear to be in fair agreement with observations.

Cosmic rays in images are also impacted by CTE, and provide another useful probe of CTE effects. Much like the hot pixels, CTE causes tails to appear on the cosmic rays. Though cosmic rays themselves have complex shapes, these tails are still manifest as a statistical asymmetry, and this asymmetry can be used as a quantitative measure of CTE (Riess, Biretta, and Casertano 1999).

The total counts in these cosmic ray "tails" is a useful metric of CTE. As shown in the top panel of Figure 4.19, no significant tail is apparent at low Y. But at high Y an exponentially declining tail is readily apparent with an e-fold decay of 2 pixels (indicating that charge is released on the 10's of milliseconds timescale). This Y dependence closely mimics that seen in stellar photometry. These tails are very similar to those seen for hot pixels.

Figure 4.20 displays the temporal dependence of both parallel-read (Y) and serial-read (X) induced-tails for WFPC2 as measured with cosmic rays. This figure shows results from thousands of WFPC2 dark frames, and sharply delineates the degradation of CTE with time. There is even evidence for mild acceleration in the sense that the counts in the CR tails at late epochs are somewhat higher than expected by a linear extrapolation of the early data. The same growth trend is seen in Figure 4.20: for X-CTE tails except the X-tails are much weaker and have presently converged at 1/3 the size of the Y-tails. This is in good agreement with the relative strengths of X to Y stellar CTE measurements (Whitmore, Heyer, & Casertano 1999).We note that using internal data, such as these cosmic rays in dark frames, saves external HST pointed time and provides a better time sampling, compared to more conventional stellar CTE monitoring.

As mentioned above, a fourth component of CTE is manifest as long-lived residual images. These residual images are seen as faint ghost images in exposures following a highly exposed target, and tend to decay with a timescale of roughly 10 to 20 minutes (Biretta and Mutchler 1997; Baggett, Biretta, and Hsu 2000). They usually appear at both the location of the bright target, and in pixels below the target (smaller Y values than target). Figure 4.21 illustrates this phenomenon. The trail below the target is caused by charge which is trapped during read-out of the highly exposed image, which is then slowly released during subsequent exposures. The effect is most pronounced when long exposures in low throughput filters (narrow band or UV filters) immediately follow a highly exposed image (usually a broad band filter). These long-lived residual images may be related to surface traps on the CCD, whereas the other components are more likely related to traps in the bulk silicon.

Investigations reveal that CTE losses to extended sources are not uniform across the source (Riess 2000). Rather, they are proportionally greater on the side of the source which is closer to the read amplifier (i.e., low-Y), decrease in the direction away from the amplifier, and charge is regained at the opposite side (i.e., high-Y) of a source. The portion of an extended source which is far from the amplifier suffers little charge loss because charge traps encountered have been filled and in addition, charge is deferred. Our knowledge of how CTE affects galaxies and other extended sources is still growing and it is difficult at this point to provide a recipe to restore changes to the shape of a source. Nevertheless, we suggest that users consider that the total CTE loss expected for an extended source (Baggett et al. 2001; Whitmore, Heyer, & Casertano 1999) likely applies only to the side of the source near the amplifier (i.e., low-Y), with the opposite side (i.e., high-Y) facing smaller losses.

Figure 4.16: Average of 700 hot pixels illustrating the CTE effect. Data were taken from dark frames in late 1999 in all four CCDs in region 50<Y<750 and for hot pixels intensities in the range 100 to 4000 DN. The bottom panel is the same image enhanced to illustrate faint pixels.

Figure 4.17: Intensity profile of CTE tail in Y direction for averaged hot pixel (~350 DN) in 1994 and 1999.

Figure 4.18: Dependence of Y-CTE tail on pixel intensity measured on late 1999 data.

Figure 4.19: Cosmic ray tails in a single WFPC2 dark frame. Each individual point represents one cosmic ray and shows the differences between pixels which are equal distances from a cosmic ray pixel. The line is the median of the data. At low Y there are few charge transfers and hence minimal trailing of charge. At high Y the statistical cosmic ray tails are evident.

Figure 4.20: Counts in CTE tails measured on cosmic rays. Separate distributions are shown for the X-CTE and Y-CTE.

Figure 4.21: Images Illustrating CTE Residual Trail. (a) Image of star field taken in broad band filter on PC1. (b) 1500s dark exposure taken immediately following (a). Read out direction is towards bottom of image. Cosmic rays have been removed.

Mitigating CTE during observations

Observers can use a number of strategies to minimize the effect of CTE loss. Longer individual exposures help by increasing both background and source counts, both of which reduce CTE loss. Users thinking of dithering may wish to take this into account if they are considering shortened exposures to allow for more dither positions.

When observing a target significantly smaller than a single detector, it is advisable to place it towards the bottom of a chip (i.e., near the readout amplifier). For example, the aperture WFALL will place the target near the bottom of Chip 3. (Note, however, that targets larger than about 20" centered on WFALL will be split between chips, which itself may lead to photometric problems.) The resulting data can still be corrected using the CTE correction formulae, and the corrections will be smaller.

For faint point sources on low backgrounds, it is recommended that the target be imaged close to the pyramid apex at pixel location (150,150) to reduce the effects of CTE loss. When placing targets closer to the pyramid apex than this position, one risks the target landing near the vignetted regions and affecting the resulting photometry. For the wide field CCDs, aperture = WFALL is recommended. The aperture reference point for WFALL is at pixel (133,149) on the WF3 chip. Therefore, no movement of the target is required to reduce the effects of CTE loss when using this aperture. For PC1 imaging, it is recommended that a POS TARG be used to move the target from the aperture reference point (420.0,424.5) to the recommended position (150,150) using (POS TARG -12.292,-12.491). Table 4.3 presents recommended POS TARGs to position a target at pixel location (150,150) in the respective CCD chip.

Table 4.3: Recommended POS TARGs to mitigate CTE.

Aperture	Reference Point X (pixel)	Reference Point Y (pixel)	POS TARG (arcsec)
PC1-FIX	420.00	424.00	-12.292, -12.491
WF2-FIX	423.00	414.00	27.213, -26.293
WF3-FIX	416.00	424.00	26.536, 27.307
WF4-FIX	423.00	421.00	-27.174, 27.001
WFALL	903.00	904.00	no POS TARG needed

When the very highest possible photometric accuracy is required, another possibility is to include a special calibration observation of Cen, taken close to the time of the science observations and designed so as to reproduce them as closely as possible in exposure and background levels.

A further possible strategy is to preflash the chip to raise the background level. However, tests indicate that the required level of preflash is so high that in general more is lost than gained by this method (due to overhead times and added noise). A variation of this, called "noiseless" preflash, was tested where a flat field exposure is taken immediately prior to a science exposure.1 However, it gave only very modest improvements in CTE (Schultz, et al. 2001).

As part of the Cycle 8 through 12 Calibration Plans, we continued to monitor the CTE for point sources by repeating the key observations of Cen every six months (Proposals 7629, 8447, 8821, 9254, 10076). This will be continued in Cycle 13 (Proposal 10364). We also added observations of a cluster of galaxies (Proposal 8456), which yielded a direct measurement of the effect of CTE for faint extended sources for more typical exposure times and background levels. A proposal in Cycle 10 (Proposal 9255) studied the astrometric effects of CTE.