WFPC2 Instrument Science Report 97-05
Charge Trapping and CTE Residual
Images in the WFPC2 CCDs
John Biretta and Max Mutchler
May 20, 1998
ABSTRACT
We have studied the charge trapping problem in the WFPC2 CCDs by examining residual
images in dark calibration exposures taken at various intervals after non-saturated planetary exposures. Charge is trapped during read-out of the planet image, followed by a slow
release of charge during the dark frame, hence resulting in a residual image. Our results
indicate the dissipation timescale for charge caught in the traps is approximately 16 (+10
-5) minutes, and that the amount of trapped charge in a pixel appears to correlate with the
maximum intensity clocked through it during read-out of the previous exposure. Our model
predicts a photometric ramp similar to that observed on bright stars, suggesting that
charge trapping may account for at least some of the observed photometric anomalies. We
propose a “noiseless” preflash scheme which might significantly reduce the photometric
effects of CTE.
1. Introduction
The WFPC2 CCDs have a significant charge transfer efficiency (CTE) problem whereby a
small number of electrons in an image are lost with each vertical clocking of the CCD during readout. This CTE problem is one of the most significant systematic calibration
uncertainties that can affect photometry with the WFPC2, yet it’s cause and characteristics
are not well understood.
The most obvious manifestation of the CTE problem is that the same target will be
brighter if it is located near the readout register (y~1), than if it is located at the opposite
end of the chip (y~800; Holtzman, et al. 1995). This problem appears to be getting worse
with time; shortly after launch the difference between the top and bottom of the chip was
~4%, while currently it can be as much as 30% for faint stars on a faint background (Whitmore, 1997). Another possibly related effect, is that short exposures appear to be missing
charge relative to long exposures of the same target (or similarly faint targets are missing
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charge relative to bright ones; c.f. Casertano and Ferguson 1996). A third effect, is that
weak residual images tend to appear in exposures following a bright target. It seems possible that these three effects are related, and can all be explained by a single process where
each pixel temporarily “traps” a small number of image electrons during read-out. The
actual “traps” are thought to be phosphorus impurity atoms which are known to be present
in the CCDs (Trauger 1995). CTE-related problems have been discussed previously by a
number of references (Biretta, et al. 1995, 1996; Holtzman, et al. 1995a and 1995b; Whitmore and Heyer 1997; various WFPC2 STAN electronic newsletters). So far, most
detailed studies of CTE have focussed on the observed photometric effects. It seems likely
that additional insights might come from studying the residual or “ghost” images seen following bright exposures, and this is the focus of the present report. In particular, if one can
understand the time evolution of the trapped charge, it may be possible to establish onorbit procedures for mitigating the CTE effects.
For this study we have used data already present in the HST archive. We searched the
archive for normal dark calibration exposures which happened to closely follow planetary
exposures. Planetary exposures were chosen as a source of CTE residual images, since the
residual image extends over many pixels, thus allowing good statistics when measuring
intensities. The planetary images also have high exposure levels which tend to produce
more prominent residual images. The subsequent dark exposures present an ideal opportunity to reclaim and analyze the residual charge. As we will see, the 30-minute dark
exposures drain most of the residual charge, creating a prominent residual trail in an otherwise mostly blank image. Figures 1 and 2 show a typical planetary image and the residual
seen in the subsequent dark image. The maximum intensity in this planetary image is
~2800 DN/pixel (Figure 3), and the residual image averages about 0.26 DN/pixel (Figure
4).
In the following sections we develop a simple model for the amount of the trapped charge,
and its evolution with time. We then use on-orbit data to constrain parameters in this
model. In the final section we consider the viability of preflash schemes to reduce the CTE
effect, and propose a “noiseless” preflash which might reduce CTE while adding little or
no noise to science images.
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Figure 1. A 20-second WFPC2 image of Venus with the F218W filter at gain 15.
Figure 2. A 30-minute dark exposure which started 13 min after the Venus image.
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Figure 3. Maximum intensity in each CCD column of the Venus image of Figure 1. The
broad peak is due to the bright limb of Venus, while the narrow spikes are due to cosmic rays
and bad pixels.
venusAmax.hhh: rows 1 to 1
3000
2000
1000
0
200
400
600
800
Column (pixels)
Figure 4. Mean intensity in each column of the dark exposure (Figure 2) which started 13
minutes after the VenusA image.
venusAdarkCR.hhh: rows 80 to 320
N = 0.26
1
.8
.6
.4
200
400
Column (pixels)
4
600
800
2. A Model for Trapped Charge
In an effort to better understand the CTE trapping process, we now attempt to develop a
simple model to describe the amount and evolution of the trapped charge. In the subsequent section we will use observed residual images to constrain free parameters in the
model. In our model we will let N0 represent the trapped charge remaining in any pixel
(x,y) immediately after the target exposure is read-out. From examining Figures 1 and 2, it
is apparent that the amount of trapped charge must be some function f of the image intensity I(x, y′; y′>y) clocked through the pixel in question. Hence:
N 0 ( x, y ) = f ( I ( x, y′ ;y > y′ ) )
Since the trapped charge is visible and is therefore read-out in subsequent images, it must
escape the traps with some time constant t. This process appears analogous to a radioactive decay, and hence we will assume an exponential “dissipation” similar to that used to
describe nuclear decay (Semat and Albright, 1972). The number of residual electrons N
still trapped in a CCD pixel at any time after readout of a bright exposure is thus:
N = N0 e - λt
(1)
and is illustrated in Figure 5.
N0
N
1/λ
time
time
Figure 5. Exponential dissipation of the initial charge N0 over time.
For the available 30-minute dark exposures, the amount of escaped charge forming the
visible residual image is thus:
N = Nt - Nt+30 = N0 * (e-λt - e-λ(t+30))
where:
N0 is the initial amount of trapped charge (at t = 0),
t is the time between readout of the target exposure and the start of the dark
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exposure, and
λ is the “dissipation constant”.
We note that the second exponential term in the equation above, e-λ(t+30), will be close to
zero and can be ignored if the mean life (1/λ) is small compared to the 30-minute duration
of the dark exposure. We also note the formal definitions of “mean life” and “half-life” as
follows:
Tmean = 1 / λ
Thalf = 0.693 / λ
In the following section we attempt to estimate λ and the function f (I(x,y′; y′>y)) using
the observed residual images.
3. Constraints from On-Orbit Data and Analyses
A query of the HST data archive revealed many instances of routine dark calibration exposures taken at various intervals after a planetary exposure. The planetary images and
subsequent dark exposures were examined, and several sets of these were selected for
quantitative measurement (Table 1). All dark exposures are 30 min. at gain 7.
Table 1: Planetary images and subsequent dark frames selected for CTE study.
Planet
name
CCD
used
Archive
root name
of planet
image
Archive
root name
of dark
image
Obs.
Date
Planet
Exp.
Time
(sec)
Planet
Exp.
Gain
Dark
start
time*
t
(min)
Maximum
intensity in
planet image**
i
Mean residual
in dark image
N
Jupiter9
WF3
u3fw0504t
u2ry4x01t
9/3/96
160
7
5
700 - 900 DN
<0.09 DN
MarsA
PC1
u2h50205t
u2fd2a01t
8/23/94
6
7
6
1900 - 3610 DN
0.45 DN ± 13%
MarsB
PC1
u2h50b05t
u2en100at
4/8/95
4
7
6
1900 - 3700 DN
0.30 DN ± 10%
JupiterY
WF3
u2fi2k0bt
u28u3t01t
8/24/94
0.11
15
6
1800 - 2900 DN
0.40 DN ± 8%
JupiterX
WF3
u2fi2l0dt
u28u3u01t
8/25/94
60
7
7
1400 - 1600 DN
0.34 DN ± 9%
VenusA
WF2
u2lw0202t
u28u6v01t
1/24/95
20
15
13
2100 - 2850 DN
0.26 DN ± 15%
* delay between readout of planet image and start of the 30-min dark exposure
** the range of maximum intensities that produced the listed mean residual
Figures 1 and 2 show a typical planet image and subsequent dark frame. Two conclusions
can be immediately drawn from these images. First, the residual image occurs in and
below the region of the planet image. Hence the trapping is primarily associated with the
“vertical” transfers during readout. (Some trapping has been seen to occur in the horizontal or serial transfer register, but the effect is very small; Whitmore and Heyer 1997.)
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Second, the residual intensity at the target location appears nearly identical to that below
the target area. This implies that the amount of trapped charge does not depend on how
long the target charge resides in any given pixel, at least for the timescales involved in
these images (~1 second to transfer the planet image by its own diameter, or the 20 - 40
seconds the charge is stationary at the location of the planet). Hence, the timescale for
charge to be captured by the traps must be short (< 1 second), and the trapping process
must go to completion on this timescale.
Intensity variations across the planet image are also reflected in the residual image. Hence
the intensity of the residual image must increase as counts in the target image increase.
Careful examination of the images suggests that the intensity of the residual image in a
pixel depends primarily on the maximum intensity clocked through that pixel during
readout of the planetary image. This is illustrated in Figures 3 and 4. Figure 3 shows the
maximum planet intensity in a given column, and Figure 4 shows the residual image intensity for each column (averaged along the columns). The two curves appear very well
correlated. In contrast, the correlation between the total charge clocked through a pixel,
and the residual intensity is rather poor. From examining Figure 1, we can see that the total
charge per column would be strongly peaked near the center of the planet image, whereas
the residual image intensity has a flat profile (Figure 4).
For each planet image, the maximum intensity in each CCD column was determined and
plotted as in Figure 3. And for each subsequent dark exposure, cosmic rays were removed
and the mean residual image intensity in each CCD column was determined and plotted as
in Figure 4, so that the residual charge due to the CTE problem could be estimated. These
plots were then used to read off the planet maximum, and the residual image intensity
above the background. In all cases the planet image had different maximum values in different columns, so we noted the range in maximum values for the same columns we
averaged to obtain the residual image intensity. These ranges of planet maximum intensities, and the residual image intensities, are given in Table 1. For example, maximum
intensities in different columns of the Venus image (VenusA in Table 1) vary from 2100 to
2850 DN/pixel, while the residual image averages 0.26 DN/pixel.
We now apply the model discussed above, and these observed results, and attempt to constrain parameters in the model.
To estimate the dissipation timescale of the residual charge, λ, we take the ratio of the
residual intensity for different delays between the planet and dark exposures. To simplify
the problem, we will choose images with roughly the same maximum intensity level, so
that the unknown N0 cancels. From Table 1, we see that a 30-minute dark exposure was
started 13 minutes after the “VenusA” exposure, and 6 minutes after the “JupiterY” exposure, and therefore:
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NVenusA / NJupiterY = (0.26 DN ± 15%)/(0.40 DN ± 8%) = (e -13λ - e - 43λ ) / ( e -6λ - e -36λ )
Solving this equation for the dissipation constant yields:
λ = 0.061 (+0.029 -0.023)
(2)
Thus the “mean life” and “half-life” of the charge dissipation are:
Tmean = 1/λ = 16.3 (+10.1 -5.2) minutes
Thalf = 0.693/λ = 11.3 (+7.0 -3.6) minutes
While the data are limited and noisy, this timescale must essentially be correct. If the
timescale were much shorter, we would see no residual at all in the t=13 min darks. And if
it were much longer, we would start to see residual images in darks taken at long delays (t
>30 min), but none were seen in the images we examined.
Next we would like to deduce the relationship between the planet image intensity and the
residual intensity. We have already noted a correlation between the maximum intensity in
a column of the planet image and the residual image intensity, and will attempt to relate
these quantities. In effect, we are attempting to define f in
N 0 ( x, y ) = f ( I max ( x, y′ ;y > y′ ) )
where Imax is the maximum intensity clocked through pixel (x, y). We note that there is no
data at t=0 (i.e. no dark exposures that started immediately after the planet image), so we
will instead use the measurements made at t~6 min. This distinction is important, since the
CCDs are “wiped” before the start of the dark exposure, so any charged released between
t=0 and t=6 minutes is lost. We can later extrapolate back to t=0 to estimate the initial
amount of residual charge N0.
Figure 6 shows a log-log plot of the five data points from Table 1 with t ~ 6 minutes. While
the data have much scatter, the formal best linear fit in log-log space is:
ln Nt~6 = - (9.06 ± 0.23) + (1.00 ± 0.03) ln Imax
Nt~6 = (0.000116 ± 0.000027) e([1.00 ± 0.03] ln Imax)
The resulting exponent is effectively unity, indicating that the amount of trapped charge is
roughly proportional to Imax , the maximum charge clocked through a pixel during readout.
Using equations (1) and (2), and extrapolating backwards 6 minutes to t=0 yields the
residual charge trapped immediately after reading-out the planet exposure (i.e. charge per
pixel in DN at gain 7):
N0 = (0.00017 ± 0.00005) e([1.00 ± 0.03] ln Imax)
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(3)
where N0 is the residual trapped charge in a pixel, and Imax is the maximum intensity
clocked through the pixel during readout of the planet exposure. According to this fit, the
trapped charge increases roughly linearly with Imax , at least at these high count levels.
ln Nt~6
ln Nt~6 = -9.06 + 1.00 ln Imax
ln Imax
Figure 6. Mean CTE residual Nt~6 for data with t~6 vs. maximum planet intensity Imax, both in DN at gain 7. The line is
a log-log fit to the data. The error bars for N were estimated while measuring from plots such as Figure 4. For Imax we
used the geometric mean of the range given in Table 1, with the DN values doubled for gain=15 data.
It is interesting to compare these results with the CTE effects seen in stellar photometry.
An important question is whether there is a direct connection between charge trapping, the
residual images, and the CTE photometric effects. From our results, we can attempt to predict the photometric ramp which would be seen, if indeed the residual charge we see is the
“missing” charge in stellar photometry. If we assume a stellar image with say Imax=1000
DN in the central pixel (corresponding to ~3300 DN total counts for WFC image) is
clocked across the CCD, we would predict from equation (3) that 0.17 DN is trapped per
clocked pixel, or ~140 DN is lost for 800 transfers. Hence we predict a photometric ramp
of 140 DN / 3300 DN = 4% arising in the CCD column containing the core of the PSF.
Adjacent columns on the CCD would trap some additional charge from the wings of the
PSF, thus increasing the total ramp to 5% or 6%. This value is roughly consistent with the
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4% ramp found by Holtzman, et al. (1995) and 4% to 7% ramp found by Whitmore and
Heyer (1997) for bright stars. While our results do have significant uncertainties, the
above suggests that charge trapping may be a significant component of the CTE photometric effect.
We finally caution that these results are based on a very small amount of data at fairly high
count levels. It would be very premature to attempt correction of images already observed
based solely on these results. Moreover, there are various implicit assumptions which cannot be tested with the current data (e.g. that all traps have the same time constant, that all
CCDs have similar CTE properties, etc.). Much more study is needed on the CTE effect.
4. Implications for A Noiseless Preflash
In the preceding section we derived a timescale for trapped charge to escape, and found an
approximate relationship between the intensity of the target, and the residual image it
leaves behind.
An important implication of these results is that conventional preflashing of the CCDs will
only have limited success in removing the CTE problem. As we have seen (equation 3),
the amount of trapped charge appears to increase as the target intensity increases. Hence a
preflash of some intensity is likely to cure the CTE problem only for target pixels at or
below the preflash intensity. When the target intensity exceeds the preflash intensity, some
charge will continue to be trapped. A very large preflash will generally be unacceptable,
since the photon noise of the preflash will become the dominant noise source for faint
objects.
However, another possibility is apparent. If our model is substantially correct and the
charge remains trapped for a significant period of time (timescale ~16 min), it should be
possible to generate a preflash without noise (“noiseless preflash”) by exposing the CCDs
to a uniform high intensity, and then wiping the CCDs before starting the science exposure. This should have the effect of completely filling the traps, which should then remain
substantially filled long enough to take several minutes of data (e.g. ~2/3 of the traps still
filled after 8 minutes). This would contribute essentially no noise, since the preflash image
is cleared from the CCDs prior to the science exposure, leaving only the charge caught in
the traps. Since the preflash could be done at high intensity, it should correct the CTE
problem at all levels of target intensity.
This strategy of “noiseless preflash” should be particularly successful for short target
exposures (<5 min), where most of the traps are still filled when the science exposure is
read out. These same short exposures appear to suffer the greatest photometric effect from
CTE, as there is very little background. For longer exposures (>20 min) the benefit will be
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less, since much of the preflash charge will escape from the traps before the science image
is read out. In the limit of very long exposures, the main effect of this “noiseless” preflash
will be to contribute a low background (<1 DN) to the image, with an intensity equal to
that of the preflash trapped by the CTE effect.
In practice, a noiseless preflash could be accomplished by exposing an INTFLAT through
some broad filter just prior to starting the science exposure. Ideally, the preflash exposure
would not be read-out, but would be allowed to remain on the CCD until the normal “CCD
clear” command executes just before the shutter opens for the science exposure. This
sequence of events would minimize the time interval between the preflash and readout of
the science exposure, and hence would maximize the benefit of the preflash. If the science
filter can be used for the preflash, the extra overhead time might be as little as one minute;
two extra minutes might be required if the filter is changed between the preflash and science exposure. On-orbit testing of this concept is included in Cycle 7 program 7630.
These data have been obtained but are not yet fully analyzed.
5. References
Biretta, J. A. et al., 1995, “A Field Guide to WFPC2 Image Anomalies,” WFPC2 Instrument Science Report 95-06, available on WFPC2 WWW pages.
Biretta, J. A., et al., 1996, “Wide Field and Planetary Camera 2 Handbook,” Version 4.0.
Available from the STScI Science Support Division and on WFPC2 WWW pages.
Casertano, S., and Ferguson, H. 1996, “Status Report on CTE and Photometric Differences Between Long and Short Exposure Times,” WFPC2 WWW pages.
Holtzman, J., et al., 1995a, “The Performance and Calibration of WFPC2 on the Hubble
Space Telescope,” PASP 107, 156.
Holtzman, J., et al., 1995b, “The Photometric Performance and Calibration of WFPC2,”
PASP 107, 1065.
Semat, H., Albright, J., 1972, “Introduction to Atomic and Nuclear Physics,” Holt, Reinhart, and Winston, 5th edition, p. 426.
Trauger, J. 1995, private communication.
Whitmore, B. and Heyer, I. 1997, “New Results on Charge Transfer Efficiency and Constraints on Flat-Field Accuracy,” WFPC2 Instrument Science Report 97-08, available on
WFPC2 WWW pages.
Whitmore, B. 1997, “Time Dependence of the Charge Transfer Efficiency on the
WFPC2,” WWW memo, Dec. 1997.
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