Instrument Science Report ACS 2003-009
On-orbit Calibration of ACS
CTE Corrections for
Photometry
Adam Riess
August 15, 2003
ABSTRACT
We present the first on-orbit calibration of the photometric losses due to imperfect CTE
on ACS HRC and WFC. We utilized images of 47 Tuc from a CTE calibration program
(GO 9648; PI Riess) to measure the dependence of stellar photometry on the number of
parallel and serial transfers. For WFC, photometric losses are apparent for stars undergoing numerous parallel transfers (y-direction) and are ~1-2% for typical observing
parameters rising to ~10% in worst cases (faint stars, low background). The size of the
photometric loss appears to have a strong power-law dependence on the stellar flux, as
seen for other CCD’s flown on HST. However, the dependence on background is surprisingly weak implying that post-flashing may have little advantage to mitigate CTE. No
losses are apparent for WFC due to serial transfer (x-direction). Also for HRC, photometric losses arise from parallel transfer (~1% for typical observations, ~5% for worst case)
but are not seen for serial transfer. Correction formulae are presented to correct photometric losses as a function of a source’s position, flux, background, time, and aperture
size. The time dependence term will be better constrained from future data but is currently
found to be approximately linear from measurements of charge deferred tails in dark
frames.
Copyright© 1999 The Association of Universities for Research in Astronomy, Inc. All Rights Reserved.
Instrument Science Report ACS 2003-009
1. Introduction
To date, all CCD’s flown in the harsh radiation environment of HST suffer degradation
of their charge transfer efficiency (CTE). The effect of CTE degradation is to reduce the
apparent brightness of sources, requiring the application of photometric corrections to
restore measured integrated counts to their “true” value.
The principle of correcting for CTE losses to achieve unbiased measurements is
straightforward, but in practice it can be quite difficult to utilize. The charge loss due to
imperfect CTE depends on combinations of scene characteristics such as the total counts
and the physical extent of a source on the detector, its background (global and local), the
number of parallel and serial transfers, and elapsed time in the life of the detector. It is difficult to quantify and calibrate the degree to which each of these factors affects the
measurements of a source over time. The general solution has been to use repeated observations of cluster fields to quantify the impact of CTE on point sources, to use internal
measures of CTE degradation to track the changes between costly, external calibrations,
and to do additional studies of the impact to more complicated sources (e.g., extended
sources) when the CTE losses become large.
ACS has two CCD’s which clock charge, WFC and HRC, and therefore are subject to
CTE losses. In this report we describe the first external calibration of their photometric
losses due to imperfect CTE. The order of this report is to first describe the dataset used to
measure CTE, its reduction, how it was photometered, the measurement of CTE trends,
and the derivation and constraining of a CTE correction formula.
The measurement and application of CTE corrections requires the careful utilization
of statistics from large numbers of stars, which individually give a very weak and poor
constraint on CTE. The inference of CTE corrections is further challenged by the wideassortment of photometry practices (and pitfalls) as well as the continual degradation of
CTE (i.e., the calibration is not static, it is always changing).
We have been careful to describe our choices and procedures here to allow others to
match them (or at least compare them) to the photometry methods they use before accepting and applying our CTE corrections. Experience from WFPC2 suggests that differences
in photometry methods may somewhat alter the overall size of CTE corrections, but by
significantly less than ~25% of the size of the correction (B. Whitmore, private communication). An equally viable though far more time consuming approach for those ACS users
who demand the very highest photometry precision is to retrieve the CTE calibration data
from the archive and apply their own photometry methods in identical fashion as to their
own data.
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Instrument Science Report ACS 2003-009
2. CTE Calibration from 47Tuc
From Jan-March, 2003, we initiated a calibration program, GO 9648 (P.I. Riess) to
obtain a sequence of observations of the off-core field (6’ West) of the rich cluster 47 Tuc
(00h 22m 37.2s +/- 1", -72d 4’ 14" +/- 1”). For each camera, our goal was to compare the
relative photometry of individual stars as a function of the number of pixel transfers during read-out. Because the read-out architecture of the WFC and HRC are dissimilar, a
different observing strategy was designed for each camera.
WFC
For WFC, pixels are clocked away from the center and towards the corners to be read
out by 1 of 4 corner amplifiers as shown in Figure 1. Each pixel requires from 1 to 2048
transfers in the parallel and serial directions.
2 Dither Positions used for
Parallel CTE calibration
Figure 1: Schematic showing the location of the read-out amplifiers and the WFC
direction of read-out. The right panel illustrates the two FOVs used to vary the
number of parallel transfers for individual stars.
To vary the relative positions and hence the number of pixel transfers of individual
stars we utilized 2 large scale dithers of ~1/2 the size of the WFC (102”) along each axis to
reposition stars relative to the fixed framework of corner amplifiers. For the large-scale
dither in the parallel (y coordinate) direction, this shift resulted in the displacement of the
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Instrument Science Report ACS 2003-009
entire field-of-view of chip 1 onto chip 2 as shown in the right panel of Figure 1. Because
of the corner placement of the amplifiers, individual stars which undergo n parallel pixel
transfers when imaged on chip 1 (where 1 < n < 2048), will undergo ~(2048-n ) transfers
when imaged on chip 2. In this case the differential number of transfers is (2048-2n ).
This technique of reimaging the field of view with mirror symmetry with respect to
the read-out direction using two different chips is similar to the strategy employed by
Whitmore, Heyer, and Casertano (1999) to measure the degradation of CTE on WFPC2.
Small differences in the zeropoints of the two chips are removed in the analysis by measuring the change in flux (here and elsewhere flux refers to total counts, not counts per unit
time) with pixel transfer for the two chips (i.e., the slope of the relation), ignoring any offset at n =1024 (where the differential transfer would be zero). To measure the affect of
differential transfers in the serial direction, we reimaged the field with a large scale dither
(102”) in the x-direction.
To assess the impact of background on CTE losses, we varied the background of the
image pairs by utilizing different exposure times and different filters. Specifically we used
F606W for 30 sec, 400 sec, and 1100 sec, F775W for 30sec and 400 sec, and F502N for
30 sec and 400 sec. The resulting sky backgrounds varied from <1 e to 120 e per pixel.
B
D
Figure 2: Schematic showing the location of the read-out amplifiers and the HRC
direction of read-out. The right panel illustrates two independent amplifiers used
to vary the number of parallel transfers for individual stars.
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Instrument Science Report ACS 2003-009
HRC
Like WFC, HRC pixels can be clocked away from the center towards read-out amplifiers in the chip corners as shown in Figure 2. An important difference is that the field of
view is not unavoidably divided into 4 quadrants (via the physical and electronic bifurcations of WFC) allowing the field of view to be read-out entirely by any individual corner
amplifier (routine science data is readout through the C Amp). As a result, we can obtain
pairs of images on the HRC with a different number of pixel transfers for individual stars
by using a sequence of different corner read-out amplifiers as shown in Figure 2. This
technique of reimaging the field of view with mirror symmetry with respect to read-out
direction using different amplifiers is the same as that employed by Goudfrooij et al for
the STIS CCD. To fill the orbits, we were able to obtain an exposure for each unique corner amplifier with every combination of filter and exposure time.
As for WFC, the impact of background was assessed by using combinations of filters
and exposure times; F606W, F775W, and F502N each for 30sec and 360sec.
3. Analysis
Each aforementioned combination of FOV position, amplifier read-out, filter, and
exposure time was obtained and processed through the standard OPUS pipeline (overscan
and bias correction, dark frame subtraction, flat correction, and drizzled using the geometric distortion table.) Cosmic ray splits were not utilized but cosmic rays are accounted for
in the analysis by using robust analytic tools.
For both WFC and HRC, a deep, clean master image was made by combining the long
exposure F606W images (3600 sec for WFC, 2400 sec for HRC) with min-max rejection.
From these a master star list was generated with DAOfind run in IDL (find.pro). The list
of sources was visually inspected to verify its purity. For WFC the final star list contained
~19,800 stars, half of which were present in any pair of large scale dithers. For HRC, the
master star list contained ~250 stars.
WFC
For WFC images, the master star list was used to provide an initial guess for the stellar
positions in the shifted 400-sec F606W images. A more precise coordinate list in the
shifted (and unshifted) frames was then derived using individual centroids with a box
width of 1.3*FWHM (~5) pixels. For every WFC image, these deep, centroided master
star lists were used as an initial guess to derive coordinate lists by (re)centroiding on the
stars. These two lists (master and individual) were then differenced and a median of the
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Instrument Science Report ACS 2003-009
differences was used to determine the size of any global shift between the 400 sec F606W
images and other images obtained at the same commanded position. The final coordinate
list utilized for the photometry of individual frames was the list of stellar centroids in the
matching 400 sec F606W with the addition of the individual, global shifts. The intent of
this procedure was to derive star lists which are globally precise but do not ‘overfit’ to the
noise of individual, faint stars.
Photometry of all stars in the starlists was measured using the aperture photometry
package in IDL (aper.pro). The sky background was determined from a global median of
matching portions of the FOV (see Figure 1). A comparison of regional median sky values shows agreement to better than 0.1% indicating no significant gradient in the sky
across the field and attests to the suitability of a single sky value. Individual sky annuli
can avoid the problems of sky gradients but can be biased high by inclusion of flux from
faint cluster members. More importantly, any systematic sky errors for individual stars
due to sky gradients effectively “cancel out” in the process of calculating the magnitude
differences of individual stars at different large dither positions as seen in Figure 1 (assuming the origin of any sky gradients were from the cluster and not from errors in flat
fielding).
To evaluate the dependence of CTE loss on stellar flux, background and aperture size,
the relative photometry of individual stars for each filter and exposure time combination
was compared in 2 mag wide flux bins. The specific procedure was to measure a linear
relationship between relative photometry and relative pixel transfer for all filter, exposure
time, flux bin, and aperture size combinations. Because CR splits were not implemented
(to save orbits), star pairs whose relative photometry differed by more than 0.5 mag were
rejected. To further mitigate against CR contamination, the linear relationships were
determined using the least-absolute-deviation method (LAD; a more robust, less tail
weighted statistic) and cross-checked with a 4 sigma-clipped least-squares fit. The yintercept of the fits were not constrained to provide a net photometric loss of 0.0 magnitudes at 0 relative transfers to allow for possible zeropoint differences between the two
chips (though any seen were quite small).
Figure 3 shows a single example of the linear relationship determined for one filter and
exposure time (F606W for 30 sec providing a sky background of 3.6 electrons) at one fitted brightness range (stars with an average of ~400 electrons and a full range of +/-1 mag)
contained within a r=3 pixel aperture. For the example shown, the stars would have an
average magnitude of F606W=23.3 mag and have a signal-to-noise ratio of ~10 in the
aperture in the 30 sec exposure. The upper panel shows the parallel CTE quantification.
For individual stars, their difference in parallel read-out transfers in shown versus their
magnitude differences for the paired observations illustrated in Figure 1. The dashed line
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Instrument Science Report ACS 2003-009
shows the results of the LAD fit and the dotted line shows the results from the sigma
clipped least squares fit. Fit errors were determined from the least squares fit. For the
example shown, a 4% +/-0.6 % photometric loss was measured after 2048 transfers (the
maximum possible transfers), a 7 σ detection of imperfect CTE. The lower panel of Figure 3 shows a similar example relationship for serial transfer CTE. In contrast, the
photometric loss due to 2048 serial transfers was 0.3% +/- 0.6%, a result consistent with
no loss due to imperfect CTE. In the Appendix we show all the linear relationships (i.e.,
as in Figure 3) for all combinations of filter and exposure time and stellar flux bins used to
derive our constraints on CTE.
Figure 3 and the ~50 fits in the Appendix give a clear and consistent snapshot of the
impact of imperfect CTE on photometry in early 2003. The statistics are sufficient to
detect non-trivial CTE losses from individual bins (~a few hundred stars) at the ~5-10
sigma confidence level for faint stars. All photometric losses are given in units of the
amount expected for 2048 reads, the maximum possible of parallel transfers. Observed
values range from 0.0% +/- 0.2% for bright stars (with ~10^5 electrons) and significant
backgrounds (sky ~ ten’s of electrons) to as much as 7%-10% for faint stars (with a few
hundred electrons) and faint backgrounds (e.g., < 5 electrons).
For each fit, the resultant loss per 2048 reads and its uncertainty were tabulated along
with the sky level, median stellar flux inside the aperture. (The sky level includes the contribution from dark current, calculated as the exposure time times the mean dark rate.)
The tabulated values were then used to fit for the CTE loss as a function of the sky and
stellar flux using a fitting formula.
Parallel CTE for WFC
As seen in Figure 4 the parallel WFC CTE loss appears to be a strong function of the
stellar flux. This is not surprising given similar experience with WFPC2 and STIS.
Charge traps may be present at varying depths of the silicon substrate of WFC. Larger
charge packets (from brighter stars) may be subject to greater absolute flux losses by
accessing deeper traps, but smaller charge packets (from fainter stars) appear to lose a
larger fraction of their flux. As seen in Figure 4, the data suggests a power-law relationship between CTE loss and stellar flux which we have utilized in the following correction
formulae.
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Instrument Science Report ACS 2003-009
F606W,30.00s, <f>=402.616(e), <s>=3.5602(e), ap=3
WFC
0.4
Parallel CTE
delta mag
0.2
0.0
-0.2
-0.4
-2000
% loss=4.076
% error=0.578
-1000
0
delta y transfers
1000
2000
F606W,30.00s, <f>=391.664(e), <s>=3.7983(e), ap=3
0.4
Serial CTE
delta mag
0.2
0.0
-0.2
-0.4
-2000
% loss=0.328
% error=0.590
-1000
0
delta x transfers
1000
2000
Figure 3: An example of the linear relationship determined for WFC for one filter and
exposure time (F606W for 30sec providing a sky level of <s>=3.6 electrons) at one
brightness range (stars with an average of <f>~400 electrons and a full range of +/-1
mag) contained within a r=3 pixel aperture. The upper panel shows a parallel
transfer relation, the lower panel illustrates the serial transfer dependence.
In Figure 5 we show the relationship between CTE loss and background. Increased
background can mitigate the CTE losses (presumably by filling traps in advance of the
arrival of the stellar charge packet during read-out) and this phenomenon has been seen for
WFPC2 and STIS. For WFC, the dependence of CTE loss on background appears significantly weaker than on stellar flux (in the sense of a geometric progression) and is even
insignificant for larger aperture sizes. Nevertheless, we used a power-law fitting function
for both parameters to keep them on the same footing.
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Instrument Science Report ACS 2003-009
Low Background (2-4 e) Parallel CTE
0.10
-1.0
log(mag loss @ 2048 parallel trans)
mag loss @ 2048
0.08
0.06
0.04
0.02
-1.5
-2.0
-2.5
0.00
0
5.0•103 1.0•104 1.5•104 2.0•104
stellar flux (electrons, r=3 pix)
-3.0
1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
log(stellar flux) (electrons, r=3 pix)
Figure 4: The dependence of parallel transfer CTE loss versus stellar flux
contained within an r=3 pixel aperture (all images at low sky level). As shown the
relation is strong and suggests a power-law relation which was utilized in the
correction formulae. The panel on the right shows the same in log-log space.
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Instrument Science Report ACS 2003-009
Parallel CTE Loss @ Stellar Flux ~1000 e, r=3
0.08
mag loss @ 2048
0.06
0.04
0.02
0.00
-0.02
0.01
0.10
1.00
sky (electrons)
10.00
100.00
Figure 5: The relationship between parallel transfer CTE loss and sky background
for WFC. As seen, the correlation is weak (and is insignificant for apertures of
r=5 and 7) and in the sense of reduced loss with higher background. The
measurement was made for stars with a flux ~1000 electrons to remove the
dependence on stellar flux.
Our resulting parallel CTE parameterization was:
B
C
Y
( MJD – 52333 )
A
YCTE = 10 × SKY × FLUX × -------------- × ---------------------------------------Y total ( 52714 – 52333 )
The term, Y/Ytotal reflects the linear relationship of the CTE loss with pixel transfer as
seen in Figure 3 and the Appendix analogues. The maximum number of y-transfers,
Ytotal is 2048 pixels for the WFC and 1024 pixels for the HRC. The last term involving the
modified Julian date (MJD) characterizes the time evolution of the degradation of CTE
away from the calibration date (MJD=52714) and will be justified in the next section1.
The full range of sky values sampled extends from ~0.1 e (F502N for 30 sec)
1.
Another viable time-dependence matching equation 1 at the current time is a power-law of the
form: YCTE = 1 –  1 – A × SKY × FLUX ×
B
C
Y N
, where N is the number of years past launch.
2048
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Instrument Science Report ACS 2003-009
to 125 e (F606W for 1100 sec). The full range of aperture flux values sampled ranged
from ~100 e to 300,000 e. However, due to the limited depth of the master star image, the
faintest count levels are only sampled from short exposures (and hence low background).
In the future we plan to add sampling of low flux levels with large backgrounds by utilizing the postflash/pre-readout capability of ACS. This future CTE+postflash calibration
may also provide calibration of CTE losses for large backgrounds encountered in scenes
with high apparent surface brightness (e.g., nearby galaxies). However, the fitting formula
appears to be appropriate over the large dynamic range currently studied and should even
be suitable as an estimate (or guide) for modest extrapolations.
Table 1 contains the best fit values of the parameters A,B, and C and their uncertainties
for equation 1 for 3 different aperture sizes. Observers should select the appropriate aperture size, measure the flux in the aperture and the sky value (if working with drizzled data
in electrons/sec one must multiply by the exposure time), the number of parallel transfers,
Y (Y=y coordinate for 1<y<2048, Y=4096-y for y>2048), and the MJD, and evaluate the
correction. The correction must be derived for the actual exposures, not for a “stack”. Figure 6 shows the corrections derived from the formula for different observing parameters.
Table 1: CTE Correction Coefficients for WFC Parallel Transfer
A( σ )
B(σ )
C( σ )
ap
0.45(0.10)
-0.11(0.03)
-0.65(0.04)
3
0.78(0.20)
0.01(0.05)
-0.77(0.07)
5
0.79(0.32)
0.14(0.09)
-0.79(0.11)
7
In principle, first fitting the CTE trends in bins of stellar flux (and individual sky levels) followed by the step of constraining the multi-parameter fitting formula could result in
information loss. However, the combination of contaminants (CR’s) and the large range of
photon statistics (requiring different sigmas for sigma-clipping) dicatated the adopted
approach.
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Instrument Science Report ACS 2003-009
predicted mag loss at y=1024
Predicted Photometric Losses for WFC from Parallel CTE*
0.25
extrapolation
0.20
M31 Faint-end CMD
0.15
SN Ia at peak, z~1.8
0.10
PSF flux=zeropoint
1/2 orbit integration
0.05
0.00
10
100
1000
flux in r=3 (e)
10000
Figure 6: The predicted photometric losses for WFC due to imperfect
parallel CTE. The three functions are derived from the correction
formula, equation 1, and the coefficients from Table 1 for r=3 pixels.
The upper, middle, and lower lines are for 3 different background levels,
3 e, 30 e, and 100 e. The corrections are calculated for a typical
source position, i.e., y=1024. Three specific science applications
are shown as examples: the measurement of the faint end of M31’s
CMD (GO 9453), the measurement of high-redshift supernovae (GO 9528),
and the measurement of any PSF whose brightness is the zeropoint (i.e.,
1 e/sec), for a half-orbit integration.
Serial CTE for WFC
Using the same methodology described above for parallel CTE, we measured the
impact of imperfect serial CTE on the relative photometry of stars in 47Tuc. An example
is show in Figure 3. Our conclusion is that we see no evidence of photometric losses due
to imperfect serial CTE on the WFC. Figure 7 shows the mag loss per 2048 pixel transfers
in the x-direction versus stellar flux for a narrow range of sky (2-4 e), and versus sky for a
narrow range of stellar flux (1000-5000 e). With low sky and low stellar flux, the parameter ranges where we would expect the largest impact of imperfect CTE, our
measurements are consistent with 0.00 mag loss with a dispersion of ~0.01 mag. There is
also no evidence of a loss trend with decreasing stellar flux as seen for parallel CTE. Utilizing a simple fitting formula for photometric loss versus stellar flux and sky yields
correlation coefficients which are negligible (i.e., predicting losses of less than 0.01 mag
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Instrument Science Report ACS 2003-009
for the explored range of stellar fluxes and sky values) and are also consistent with zero.
As a result, we believe there are no photometric corrections for photometric losses due to
imperfect serial CTE on WFC required at this time.
Figure 7: The dependence of photometric losses due to imperfect serial CTE on
WFC on stellar flux and sky background. As seen, the losses and dependencies
are negligible.
HRC
The same procedure described above for WFC was utilized to analyze the HRC data
and to quantify the photometric losses due to imperfect CTE. By utilizing all 4 read-out
amplifiers, we obtained 2 independent measures of the CTE loss trend for all combinations of filter and exposure time and stellar flux. The parallel transfer losses are measured
by differencing stellar magnitudes in exposure pairs from amplifiers A and C and from B
and D. The serial transfer losses were measured with the A and B pairing and the C and D
pairing. An example of a photometric loss trend as a function of parallel and serial transfers is shown in Figure 8. In this example, (F606W for 30 sec yielding a sky of 0.75 e,
stellar flux ~3300 e, i.e., a 22.0 mag star), a significant parallel transfer loss is detected for
individual frames. The A-C and B-D amplifier read-outs yield 5%+/-1% losses after 1024
transfers (the maximum possible), a ~5 σ detection of imperfect parallel CTE. The A-B
and C-D pairings show negligible loss (~0.2% +/- 1.3%).
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Instrument Science Report ACS 2003-009
HRC Tuc_F606W_30.00s r=5 <f>=3355, s=0.75
0.4
0.4
0.2
0.2
0.0
-0.2
-0.4
-0.6
0.6
-400
0
400
delta y transfers
0.0
-0.6
800
0.6
Amp A-B
0.2
0.2
delta mag
0.4
0.0
-0.2
-0.6
-400
0
400
delta x transfers
800
Amp C-D
-0.2
-0.6
800
-400
0
400
delta y transfers
0.0
-0.4
% loss=0.254
% error=1.228
-800
% loss=5.075
% error=0.937
-800
0.4
-0.4
Amp B-D
-0.2
-0.4
% loss=5.509
% error=1.152
-800
delta mag
0.6
Amp A-C
delta mag
delta mag
0.6
% loss=-0.11
% error=1.483
-800
-400
0
400
delta x transfers
800
Figure 8: An example of the linear relationship determined for HRC for one filter
and exposure time (F606W for 30 sec providing a sky background of 0.75 electrons)
at one brightness range (stars with an average of ~3000 electrons and a full
range of +/-1 mag). The upper panels show the relation for parallel transfer,
the bottom for serial transfer.
Parallel and Serial CTE for HRC
Overall, the quantification of photometric losses due to imperfect CTE on HRC is of
much lower accuracy than for WFC due to the small field of view of HRC (45 times less
area) and the resulting paucity of stars. Only ~250 stars were culled from the HRC master
images and many of these are undetected in the frames with shorter exposure times of 30
sec as well as in the F502N images. In future iterations of this calibration program we
intend to move the HRC field a few arcminutes closer to the core of 47 Tuc to increase the
number of stars in the field (though not too close in order to avoid “crowding”). Despite
the rather limited statistics, small but significant photometric losses are detected arising
from parallel transfers. As shown in Figure 8, the size of the losses depends on stellar flux
and the sky level in the same sense as for WFC (as well as WFPC2 and STIS). For typical
observing parameters (well-detected stars of a few 1000 e, moderate sky values of ~5 electrons, and sources in the middle of the detector) the losses are ~1%, but rise to ~5-6% for
the worst case: sky~1 electron, stars with ~100 electrons which are located far from the
amplifier. One interesting difference suggested by the data is that the dependence of loss
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Instrument Science Report ACS 2003-009
on the background is greater for HRC than for WFC (where the background dependence is
slight). Conversely, the dependence of loss on stellar flux is somewhat weaker for HRC
than for WFC.
Table 2: CTE Correction Coefficients for HRC Parallel Transfer
A( σ )
B(σ )
C( σ )
ap
-0.89(0.26)
-0.24(0.13)
-0.21(0.07)
3
-0.87(0.36)
-0.27(0.17)
-0.21(0.09)
5
-2.22(1.10)
-0.58(0.46)
0.12(0.28)
7
The origin of these differences may come from the differences in the pixel size and
sampling of the two detectors. We tentatively suggest that the greater sampling of HRC
results in more “self-background” trap-filling for stars. That is, the leading edge of the
charge packet likely fills the traps in advance of the trailing edge. In the limit of extreme
sampling, the situation would mimic what is seen for extended sources for WFPC2 (Riess
2000) and hence the specific stellar flux is less indicative of the quantity of charge trapping. Background counts generally fill the shallower traps (which reemit charge on
shorter time scales) and its impact would be counter to the self-background scenario.
We utilized the same fitting formula as for WFC, equation 1, to derive a correction for
the photometric loss due to parallel transfers for HRC.
The method to correct HRC data is the same as for WFC. Observers should select the
appropriate aperture size, measure the flux in the aperture and the sky value (if working
with drizzled data in electrons/sec one must multiply by the exposure time), the number of
parallel transfers, Y (Y=y coordinate for read-outs with amps C or D, Y=1024-y for readouts with amps A or B), and the MJD, and solve for the correction. For most observations
the default amplifier, C, is used but users can determine which amplifier was used by consulting the header keyword CCDAMP.
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Instrument Science Report ACS 2003-009
Low Flux (2000-5000 e)
0.10
0.10
0.08
0.08
0.06
mag loss @ 1024
mag loss @ 1024
Low Background (0.5-1.5 e)
0.04
0.06
0.04
0.02
0.02
0.00
0.00
-0.02
1000
10000
stellar flux (electrons, r=4 pix)
1
10
sky (electrons)
Figure 9: The dependence of parallel transfer CTE loss versus stellar flux (left panel)
at low background and on background (right panel) for low flux. As shown,
both dependencies and associated losses are of significance. Derived correction
formulae and a range of uncertainty are shown.
Similar to WFC, we see no significant photometric loss in HRC due to serial transfers.
Figure 10 shows the serial transfer loss at low background and low flux, parameters where
the CTE loss should be maximized. Instead, we find measurements consistent with 0%
loss with a dispersion of 1-2%. At this time we suggest no corrections be applied to
images for serial transfer loss on HRC.
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Instrument Science Report ACS 2003-009
Low Flux (2000-5000 e)
0.10
0.10
0.05
0.05
mag loss @ 1024
mag loss @ 1024
Low Background (0.5-1.5 e)
0.00
-0.05
0.00
-0.05
-0.10
-0.10
1000
10000
stellar flux (electrons, r=4 pix)
1
10
sky (electrons)
Figure 10: The dependence of photometric losses due to imperfect serial CTE on
HRC on sky background and stellar flux. As seen, the losses and dependencies
are negligible.
4. CTE Trending and Evolution
The observations of 47 Tuc obtained in the first half of 2003 provide the first calibration of the photometric losses due to imperfect CTE using external, on-orbit data.
Experience with all CCD’s flown on HST as well as radiation testing of ACS flight spares
indicates that on-going radiation damage will cause continuous growth of the charge trap
population and the photometric losses will evolve (grow) with time. As a result, we intend
to bi-annually recalibrate the photometric losses in order to derive time-dependent CTE
correction formulae which are applicable to users at any time. Because this process has
only just begun, it is too early to be able to derive the time-dependence of the correction
formulae from the external data.
Nevertheless we included a linear time-dependence term which is bounded by the condition that the photometric losses due to imperfect CTE were zero at launch (MJD=52333)
and as measured at the approximate time of the first calibration (MJD=52714), one year
17
Instrument Science Report ACS 2003-009
after launch. While future data will help refine the time-dependence, we believe the linear
time-dependence is well motivated by other, on-orbit data. Still, other time dependencies
such as a power-law of the form included as a footnote to equation 1 may be possible.
Such an evolution would provide similar results at the current epoch but may diverge
somewhat in the future.
Figure 11: The time-dependence of a CTE metric: the charge deferred
tails of cosmic rays and hot pixels due to short time-scale trapping
and releasing of charge. Strong tails are seen for WFC for parallel transfers
and weak tails for HRC parallel transfers, in good accord with the photometric
results presented here. The approximately linear trends allow us to provide
a preliminary time-evolution term in the photometric correction formulae.
18
Instrument Science Report ACS 2003-009
We utilized a tracer of CTE degradation, the flux contained in the charge deferred tails
(CDTs) of cosmic rays and hot pixels from dark frames (Riess, Biretta, and Casertano
1999) to track the evolution of CTE since launch. This is the same technique successfully
employed for WFPC2 and STIS to track changes in CTE and has been shown to correlate
with photometric loss measurements for WFPC2. The upper panel of Figure 11 (Riess
2002) shows the development of the CDTs for WFC. As seen, the CDTs were negligible
at launch and grew linearly (to the precision of the data) and are now well-detected in a
single dark frame. In contrast, the serial transfer tails have remained negligibly small and
show little evidence of any growth. The same summary applies to the CDTs for HRC as
seen in the bottom panel of Figure 11. This internal data from dark frames matches what
is seen from the external data (imperfect CTE is significant for HRC and WFC for parallel
transfers and negligible for serial transfers) and additionally motivates the two aspects of
the time-dependence of equation (1), i.e., at launch it was nearly perfect and has been
degrading linearly with time since then.
5. The Relationship between field-dependent Charge Diffusion and CTE
The CCDs in HRC and WFC are both thinned and the thinning process inevitably
results in large-scale variations in the CCD thickness. Because the charge diffusion of the
CCD depends on thickness (thicker regions suffer greater diffusion), the breadth of the
PSF and aperture corrections can also exhibit a field-dependence. Krist 2003 has characterized the spatial variation of charge diffusion as well as its impact on fixed-aperture
photometry. For intermediate and large apertures (r> 4 pixels), the spatial variation of
photometry is very small (less than 1%), but becomes significant for small apertures (r<3
pixels).
It may be of interest to decouple the impact of imperfect CTE and charge diffusion on
the field dependence of photometry. In principle, it is not necessary for observers to
consider these two effects separately. The correction formulae given in this report
include both effects and hence corrects photometry for both effects (as long as the user
seeks to correct photometry to a perfect CTE and fiducial PSF width standard). However,
it is possible that the impact of charge diffusion is at least as large as imperfect CTE and
that the validity of the fitting formula used here could be invalid in form if charge diffusion produces a different signature (i.e., invalidating a linear characterization of charge
loss with transfers or an extrapolation of the time dependence back to ~zero at launch).
19
Instrument Science Report ACS 2003-009
5 pixel aperture
0.005
% loss=-0.22
delta mag
0.000
-0.005
-0.010
-0.015
-2000
-1000
1000
delta y transfers
2000
3 pixel aperture
0.03
% loss=-0.82
0.02
delta mag
0.01
0.00
-0.01
-0.02
-0.03
-0.04
-2000
-1000
1000
delta y transfers
2000
Figure 12: The difference magnitude of the maps of encircled energy
(whose spatial variation is induced by charge diffusion; see Krist
2003), WFC1-WFC2 versus parallel read-out position. This plot
shows the small contribution to the imperfect CTE signature, e.g., Figure 3,
and acts as a net CTE gain. Both effects are included in the correction
formulae in this report. The solid line shows the bin median and the dashed
shows the LAD fit.
To investigate the impact of charge diffusion on our analysis of WFC we used the
results of Krist 2003 (see their Figure 16) and divided the encircled energy maps for
WFC1 by the maps for WFC2 for r=3 pixels and r=5 pixels. We then examined the magnitude of these ratios as a function of parallel read-out position. The result, plotted in bins
of 128 by 128 pixels is shown in Figure 12 and is directly analogous to the CTE trend
plots shown throughout this report (e.g., Figure 3 and the Appendix). As seen, the effect
of charge diffusion is to act as a net linear CTE-like gain in our analysis though very small
in size (a 0.82% gain for r=3 pixel aperture, a 0.22% gain for r=5 pixel aperture). An
importance difference is that this effect is independent of the brightness of the star, time
20
Instrument Science Report ACS 2003-009
since launch, or background level. Indeed some evidence of this may appear in our analysis as the four bins in our analysis with the brightest stars and largest backgrounds have
modestly negative CTE measurements. For the vast majority of users it is not necessary to
decouple the effects of charge diffusion and imperfect CTE, but special or unusual applications may require such a consideration.
6. Implications
Based on even the preliminary CTE calibration provided here, a few interesting inferences can be drawn.
1) For WFC, post-flashing may be ineffective at mitigating CTE
This statement is a direct implication of the weak dependence of photometric loss on
sky background. However, it is too soon to know for sure if this holds at sky levels much
higher than those studied here but are readily achieved by post-flashing. Perhaps sky levels of a few hundred electrons will mitigate CTE (though such behavior would appear to
conflict with the extrapolation of the WFC correction formula), but if the sky levels
required are too high, the added shot noise may make such post-flashing undesirable.
An additional curiosity would be why post-flashing would appear more effective in
ground-testing than on orbit. The source of such a difference may be the difference in the
spectrum of damaging radiation and the trap species formed in the detector.
2) The future photometric losses for WFC can now be predicted and are expected
to grow faster than for WFPC2
Assuming the linear time-dependence justified by the internal data is correct, predictions can be made. In N years, the typical/worst case losses will be N*(2%/10%). By the
end of life for HST (2010), 8 years after launch, we can anticipate typical case losses of
16% and worst case losses of 50%-80% (here the range of predictions reflects the difference given by linear and power-law time dependence). For comparison WFPC2 had
typical/worst case losses of 6%/40% 7 years after launch (Whitmore et al 2000). Such a
faster rate of degradation for WFC is expected from the greater number of transfers edgeto-amplifier (2048 for WFC versus 800 for WFPC2). (Indeed, ACS WFC may even
have lower CTE per pixel than WFPC2. An even comparison at y=800 would yield a
lower expected net loss for ACS WFC than WFPC2.)
21
Instrument Science Report ACS 2003-009
Acknowledgements
We wish to thank Max Mutchler who provided an important spot-check of the HRC
analysis, Stefano Casertano, Brad Whitmore, John Krist, Ron Gilliland, and Roeland van
der Marel for helpful consultations, and the ACS phot-cal group for commenting on earlier versions of these results.
References
Riess, Biretta, and Casertano 1999, ISR WFPC2 99-04
Whitmore, Heyer, and Casertano, 1999, PASP, 111, 1559
Goudfrooij, P. and Kimble, R. A., 2002, HST Calibration Workshop, page 105
Krist, J., 2003, ACS ISR, 2003-006
Appendix
Here we show a large subset of the range of CTE linear relationships for WFC and
HRC used to derive the correction formulae. These are provided to give a better “sense”
of the impact of CTE. We also provide a table of the individual linear relations for WFC
in the parallel direction. The contents of each plot and table entry are labeled (albeit with
very small print) for r=3 pixels.
22
Instrument Science Report ACS 2003-009
Linear CTE Relationships for WFC
F502N,30.00s, <f>=838.103(e), s=0.0437(e), ap=3
0.4
0.2
0.2
0.2
0.0
-0.4
-2000
-1000
0
1000
delta y transfers
-0.4
2000
-2000
-0.2
% loss=5.123
% error=0.758
-1000
0
1000
delta y transfers
-0.4
2000
-2000
F502N,30.00s, <f>=54.5465(e), s=0.0437(e), ap=3
0.2
0.2
-0.4
-2000
delta mag
0.4
0.2
0.0
0.0
-0.2
% loss=8.245
% error=1.585
-1000
0
1000
delta y transfers
-0.4
2000
-2000
F775W,30.00s, <f>=6585.36(e), s=2.4550(e), ap=3
-1000
0
1000
delta y transfers
-0.4
2000
-2000
0.2
0.2
-2000
delta mag
0.2
delta mag
0.4
-0.4
0.0
-0.2
-1000
0
1000
delta y transfers
-0.4
2000
-2000
F775W,30.00s, <f>=408.553(e), s=2.4550(e), ap=3
-1000
0
1000
delta y transfers
-0.4
2000
-2000
0.2
-2000
delta mag
0.2
delta mag
0.4
0.2
-0.4
0.0
-0.2
-1000
0
1000
delta y transfers
-0.4
2000
-2000
F606W,30.00s, <f>=16780.7(e), s=3.5602(e), ap=3
-1000
0
1000
delta y transfers
-0.4
2000
-2000
F606W,30.00s, <f>=7158.45(e), s=3.5602(e), ap=3
0.2
-2000
delta mag
0.2
delta mag
0.2
-0.4
0.0
-0.2
-1000
0
1000
delta y transfers
-0.4
2000
-2000
-1000
0
1000
delta y transfers
2000
% loss=6.881
% error=1.491
-1000
0
1000
delta y transfers
2000
F606W,30.00s, <f>=2423.92(e), s=3.5602(e), ap=3
0.4
% loss=0.670
% error=0.195
% loss=3.137
% error=0.372
-0.2
% loss=7.078
% error=0.775
0.4
-0.2
2000
0.0
0.4
0.0
0
1000
delta y transfers
F775W,30.00s, <f>=109.139(e), s=2.4550(e), ap=3
0.4
% loss=5.625
% error=0.531
-1000
-0.2
% loss=1.639
% error=0.265
F775W,30.00s, <f>=234.602(e), s=2.4550(e), ap=3
-0.2
% loss=0.360
% error=0.212
0.0
0.4
0.0
2000
F775W,30.00s, <f>=928.708(e), s=2.4550(e), ap=3
0.4
% loss=0.789
% error=0.248
0
1000
delta y transfers
-0.2
% loss=3.037
% error=2.055
F775W,30.00s, <f>=2621.99(e), s=2.4550(e), ap=3
-0.2
-1000
0.0
0.4
0.0
% loss=7.731
% error=1.037
F775W,30.00s, <f>=15326.9(e), s=2.4550(e), ap=3
0.4
delta mag
delta mag
0.0
0.4
-0.2
delta mag
0.0
-0.2
% loss=2.202
% error=1.105
F502N,30.00s, <f>=189.679(e), s=0.0437(e), ap=3
delta mag
delta mag
0.4
-0.2
delta mag
F502N,30.00s, <f>=393.520(e), s=0.0437(e), ap=3
0.4
delta mag
delta mag
F502N,30.00s, <f>=1609.86(e), s=0.0437(e), ap=3
0.0
-0.2
% loss=1.091
% error=0.254
-1000
0
1000
delta y transfers
23
-0.4
2000
-2000
% loss=1.284
% error=0.321
-1000
0
1000
delta y transfers
2000
Instrument Science Report ACS 2003-009
F606W,30.00s, <f>=397.508(e), s=3.5602(e), ap=3
0.4
0.2
0.2
0.2
0.0
-0.4
-2000
-1000
0
1000
delta y transfers
-0.4
2000
-2000
-0.2
% loss=4.234
% error=0.588
-1000
0
1000
delta y transfers
-0.4
2000
-2000
F502N,400.0s, <f>=21845.0(e), s=1.3348(e), ap=3
0.2
0.2
-0.4
-2000
delta mag
0.4
0.2
0.0
0.0
-0.2
% loss=3.553
% error=1.473
-1000
0
1000
delta y transfers
-0.4
2000
-2000
F502N,400.0s, <f>=5598.88(e), s=1.3348(e), ap=3
-1000
0
1000
delta y transfers
-0.4
2000
-2000
0.2
0.2
-2000
delta mag
0.2
delta mag
0.4
0.0
-0.2
% loss=2.712
% error=0.407
-1000
0
1000
delta y transfers
-0.4
2000
-2000
F502N,400.0s, <f>=314.089(e), s=1.3348(e), ap=3
-1000
0
1000
delta y transfers
-0.4
2000
-2000
0.2
-2000
delta mag
0.2
delta mag
0.4
0.2
-0.4
0.0
-0.2
-1000
0
1000
delta y transfers
-0.4
2000
-2000
F775W,400.0s, <f>=88783.6(e), s=24.644(e), ap=3
-1000
0
1000
delta y transfers
-0.4
2000
-2000
F775W,400.0s, <f>=34208.7(e), s=24.644(e), ap=3
0.2
-2000
delta mag
0.2
delta mag
0.2
0.0
-0.2
% loss=-0.24
% error=0.152
-1000
0
1000
delta y transfers
-0.4
2000
-2000
-1000
0
1000
delta y transfers
2000
% loss=-0.16
% error=0.178
-1000
0
1000
delta y transfers
2000
F775W,400.0s, <f>=12569.9(e), s=24.644(e), ap=3
0.4
-0.4
% loss=5.341
% error=0.890
-0.2
% loss=3.177
% error=1.381
0.4
-0.2
2000
0.0
0.4
0.0
0
1000
delta y transfers
F775W,400.0s, <f>=211783.(e), s=24.644(e), ap=3
0.4
% loss=5.378
% error=1.195
-1000
-0.2
% loss=3.451
% error=0.620
F502N,400.0s, <f>=143.148(e), s=1.3348(e), ap=3
-0.2
% loss=2.419
% error=0.425
0.0
0.4
0.0
2000
F502N,400.0s, <f>=916.799(e), s=1.3348(e), ap=3
0.4
-0.4
0
1000
delta y transfers
-0.2
% loss=1.418
% error=0.626
F502N,400.0s, <f>=2470.53(e), s=1.3348(e), ap=3
-0.2
-1000
0.0
0.4
0.0
% loss=5.573
% error=0.831
F502N,400.0s, <f>=11763.1(e), s=1.3348(e), ap=3
0.4
delta mag
delta mag
0.0
0.4
-0.2
delta mag
0.0
-0.2
% loss=2.390
% error=0.405
F606W,30.00s, <f>=102.156(e), s=3.5602(e), ap=3
delta mag
delta mag
0.4
-0.2
delta mag
F606W,30.00s, <f>=215.640(e), s=3.5602(e), ap=3
0.4
delta mag
delta mag
F606W,30.00s, <f>=951.765(e), s=3.5602(e), ap=3
0.0
-0.2
% loss=-0.07
% error=0.179
-1000
0
1000
delta y transfers
24
-0.4
2000
-2000
% loss=0.123
% error=0.222
-1000
0
1000
delta y transfers
2000
Instrument Science Report ACS 2003-009
F775W,400.0s, <f>=3001.78(e), s=24.644(e), ap=3
0.4
0.2
0.2
0.2
0.0
-0.4
-2000
% loss=0.483
% error=0.275
-1000
0
1000
delta y transfers
-0.4
2000
-2000
% loss=1.005
% error=0.326
-1000
0
1000
delta y transfers
-0.4
2000
-2000
F775W,400.0s, <f>=247.977(e), s=24.644(e), ap=3
0.2
0.2
0.2
-0.4
-2000
delta mag
0.4
0.0
0.0
-0.2
% loss=4.178
% error=1.328
-1000
0
1000
delta y transfers
-0.4
2000
-2000
F606W,400.0s, <f>=97195.9(e), s=38.415(e), ap=3
-1000
0
1000
delta y transfers
-0.4
2000
-2000
F606W,400.0s, <f>=32656.6(e), s=38.415(e), ap=3
0.2
-2000
delta mag
0.2
delta mag
0.2
0.0
-0.2
% loss=-0.24
% error=0.167
-1000
0
1000
delta y transfers
-0.4
2000
-2000
F606W,400.0s, <f>=5326.78(e), s=38.415(e), ap=3
% loss=0.034
% error=0.225
-1000
0
1000
delta y transfers
2000
-2000
0.2
0.2
-2000
delta mag
0.2
delta mag
0.4
-0.4
0.0
-0.2
-1000
0
1000
delta y transfers
-0.4
2000
-2000
F606W,400.0s, <f>=627.859(e), s=38.415(e), ap=3
-1000
0
1000
delta y transfers
-0.4
2000
-2000
F606W,400.0s, <f>=298.729(e), s=38.415(e), ap=3
0.2
-2000
delta mag
0.2
delta mag
0.2
0.0
-0.2
% loss=4.291
% error=1.299
-1000
0
1000
delta y transfers
-0.4
2000
-2000
-1000
0
1000
delta y transfers
2000
% loss=1.950
% error=0.660
-1000
0
1000
delta y transfers
2000
F606W,1100.s, <f>=646670.(e), s=125.66(e), ap=3
0.4
-0.4
% loss=0.277
% error=0.292
-0.2
% loss=1.367
% error=0.449
0.4
0.0
2000
0.0
0.4
-0.2
0
1000
delta y transfers
F606W,400.0s, <f>=1263.37(e), s=38.415(e), ap=3
0.4
% loss=0.679
% error=0.384
-1000
0.0
-0.4
F606W,400.0s, <f>=2764.74(e), s=38.415(e), ap=3
-0.2
% loss=-0.17
% error=0.182
-0.2
0.4
0.0
2000
F606W,400.0s, <f>=12797.2(e), s=38.415(e), ap=3
0.4
-0.4
0
1000
delta y transfers
-0.2
% loss=1.898
% error=3.407
0.4
0.0
-1000
0.0
0.4
-0.2
% loss=2.639
% error=0.564
F606W,400.0s, <f>=231885.(e), s=38.415(e), ap=3
0.4
delta mag
delta mag
0.0
-0.2
0.4
-0.2
delta mag
0.0
-0.2
F775W,400.0s, <f>=536.536(e), s=24.644(e), ap=3
delta mag
delta mag
0.4
-0.2
delta mag
F775W,400.0s, <f>=1352.95(e), s=24.644(e), ap=3
0.4
delta mag
delta mag
F775W,400.0s, <f>=5645.45(e), s=24.644(e), ap=3
0.0
-0.2
% loss=9.643
% error=5.197
-1000
0
1000
delta y transfers
25
-0.4
2000
-2000
% loss=-0.60
% error=0.363
-1000
0
1000
delta y transfers
2000
Instrument Science Report ACS 2003-009
F606W,1100.s, <f>=97946.4(e), s=125.66(e), ap=3
0.4
0.2
0.2
0.2
0.0
-0.4
-2000
0.0
-0.2
% loss=0.488
% error=0.157
-1000
0
1000
delta y transfers
-0.4
2000
-2000
F606W,1100.s, <f>=14779.4(e), s=125.66(e), ap=3
0.0
-0.2
% loss=0.679
% error=0.204
-1000
0
1000
delta y transfers
-0.4
2000
-2000
F606W,1100.s, <f>=7365.42(e), s=125.66(e), ap=3
0.4
0.2
0.2
0.2
-0.2
-0.4
-2000
0.0
-0.2
% loss=0.785
% error=0.418
-1000
0
1000
delta y transfers
-0.4
2000
-2000
F606W,1100.s, <f>=1489.16(e), s=125.66(e), ap=3
0.2
0.2
delta mag
0.4
0.0
-0.2
-2000
-1000
0
1000
delta y transfers
2000
0.0
-1000
0
1000
delta y transfers
-0.4
2000
-2000
0
1000
delta y transfers
2000
0.0
-0.4
-0.2
% loss=-0.71
% error=1.503
-1000
-0.2
% loss=1.006
% error=0.522
F606W,1100.s, <f>=757.809(e), s=125.66(e), ap=3
0.4
-0.4
delta mag
0.4
0.0
% loss=0.772
% error=0.367
F606W,1100.s, <f>=3197.97(e), s=125.66(e), ap=3
0.4
delta mag
delta mag
delta mag
0.4
-0.2
delta mag
F606W,1100.s, <f>=33123.9(e), s=125.66(e), ap=3
0.4
delta mag
delta mag
F606W,1100.s, <f>=257004.(e), s=125.66(e), ap=3
% loss=1.430
% error=3.349
-1000
0
1000
delta y transfers
26
2000
-2000
% loss=0.751
% error=0.845
-1000
0
1000
delta y transfers
2000
Instrument Science Report ACS 2003-009
Linear CTE Relationships for HRC
0.0
Amp C-D
0.6
0.4
0.2
delta mag
delta mag
0.6
0.4
0.2
0.0
HRC Tuc_F606W_30.00s r=5 <f>=497, s=0.75
Amp A-B
0.2
0.0
0.2
0.0
0.0
-0.2
-0.2
-0.4
-0.4
-0.4
-0.4
-0.4
-0.4
-0.4
-0.4
-800 -400 0
400
delta y transfers
-0.6
800
% loss=0.955
% error=0.588
-800 -400 0
400
delta x transfers
-0.6
800
% loss=1.008
% error=0.573
-800 -400 0
400
delta x transfers
-0.6
800
% loss=0.908
% error=3.184
-800 -400 0
400
delta y transfers
Amp A-C
0.6
Amp B-D
0.6
-0.6
800
% loss=0.404
% error=3.682
-800 -400 0
400
delta y transfers
-0.6
800
-800 -400 0
400
delta x transfers
0.6
Amp C-D
0.6
Amp A-C
0.6
Amp B-D
0.6
0.4
0.2
0.2
-0.6
-0.2
-0.4
% loss=2.252
% error=0.926
-800 -400 0
400
delta y transfers
-0.6
800
-0.2
-0.4
% loss=2.217
% error=0.643
-800 -400 0
400
delta y transfers
-0.6
800
-0.2
-0.4
% loss=-0.27
% error=0.868
-800 -400 0
400
delta x transfers
-0.6
800
0.0
-0.2
-0.4
% loss=-0.08
% error=1.043
-800 -400 0
400
delta x transfers
-0.6
800
Amp A-C
0.6
Amp B-D
0.6
0.0
-0.2
-0.4
% loss=1.670
% error=0.490
-800 -400 0
400
delta y transfers
HRC Tuc_F606W_30.00s r=5 <f>=3355, s=0.75
0.6
delta mag
0.4
0.2
0.0
delta mag
0.4
0.2
0.0
delta mag
0.4
0.2
delta mag
0.4
0.2
delta mag
0.4
0.2
0.0
-0.6
800
-0.4
% loss=1.963
% error=4.206
-800 -400 0
400
delta y transfers
-0.6
800
0.6
Amp C-D
0.6
Amp A-C
0.6
Amp B-D
0.6
-0.4
% loss=5.509
% error=1.152
-800 -400 0
400
delta y transfers
-0.6
800
-0.4
% loss=5.075
% error=0.937
-800 -400 0
400
delta y transfers
-0.6
800
-0.2
-0.4
% loss=0.254
% error=1.228
-800 -400 0
400
delta x transfers
-0.6
800
-0.2
-0.4
% loss=-0.11
% error=1.483
-800 -400 0
400
delta x transfers
-0.6
800
-0.2
-800 -400 0
400
delta y transfers
-800 -400 0
400
delta y transfers
-0.4
-0.6
800
-800 -400 0
400
delta y transfers
-0.4
-0.6
0.6
-0.4
% loss=-4.26
% error=2.355
-0.6
800
Amp A-C
Amp A-C
0.6
Amp B-D
0.6
-0.6
800
0.6
0.2
-0.6
800
0.0
-0.2
-0.4
% loss=1.265
% error=0.728
-800 -400 0
400
delta x transfers
-0.6
800
-800 -400 0
400
delta x transfers
-0.4
-0.6
800
0.6
-800 -400 0
400
delta y transfers
-0.4
-0.6
800
0.6
-0.4
% loss=5.014
% error=1.714
-800 -400 0
400
delta y transfers
-0.6
800
0.0
-0.2
-0.4
% loss=2.727
% error=1.760
-800 -400 0
400
delta x transfers
-0.6
800
0.6
Amp C-D
0.6
Amp A-C
0.6
Amp B-D
0.6
Amp A-B
0.6
-800 -400 0
400
delta y transfers
-0.4
-0.6
800
-0.4
% loss=2.242
% error=2.135
-800 -400 0
400
delta y transfers
-0.6
800
0.0
-0.2
-0.4
% loss=-6.76
% error=2.455
-800 -400 0
400
delta x transfers
-0.6
800
0.0
-0.2
-0.4
% loss=0.441
% error=2.749
-800 -400 0
400
delta x transfers
-0.6
800
Amp A-C
0.6
Amp B-D
0.6
-0.4
% loss=0.827
% error=0.940
-800 -400 0
400
delta y transfers
HRC Tuc_F775W_30.00s r=5 <f>=403, s=0.51
0.6
0.0
-0.2
-0.6
800
delta mag
0.0
-0.2
delta mag
0.2
delta mag
0.4
0.2
delta mag
0.4
0.2
delta mag
0.4
0.2
delta mag
0.4
0.2
delta mag
0.4
% loss=4.737
% error=2.103
0.0
-0.2
-0.4
% loss=1.272
% error=1.986
-800 -400 0
400
delta y transfers
-0.6
800
0.0
-0.4
% loss=-0.14
% error=0.580
-800 -400 0
400
delta x transfers
-0.6
800
-800 -400 0
400
delta x transfers
Amp A-B
0.6
Amp C-D
0.6
Amp A-C
0.6
Amp B-D
0.6
Amp A-B
0.6
0.2
-0.4
-0.6
0.0
-0.4
% loss=4.768
% error=3.360
-800 -400 0
400
delta y transfers
-0.6
800
0.0
-0.2
-0.4
% loss=1.806
% error=3.906
-800 -400 0
400
delta y transfers
-0.6
800
0.0
-0.2
-0.4
% loss=-7.52
% error=3.822
-800 -400 0
400
delta x transfers
-0.6
800
0.0
-0.2
-0.4
% loss=-8.36
% error=4.015
-800 -400 0
400
delta x transfers
-0.6
800
Amp A-C
0.6
Amp B-D
0.6
-0.4
% loss=-1.52
% error=2.030
-800 -400 0
400
delta y transfers
HRC Tuc_F606W_360.0s r=5 <f>=18489, s=6.23
0.6
0.0
-0.2
-0.6
800
delta mag
0.4
0.2
delta mag
0.4
0.2
delta mag
0.4
0.2
delta mag
0.4
0.2
delta mag
0.4
0.2
delta mag
0.4
0.2
delta mag
0.4
-0.2
0.0
-0.2
-0.4
% loss=1.453
% error=1.872
-800 -400 0
400
delta y transfers
-0.6
800
-0.4
% loss=0.521
% error=1.035
-800 -400 0
400
delta x transfers
-0.6
800
-800 -400 0
400
delta x transfers
Amp A-B
0.6
Amp C-D
0.6
Amp A-C
0.6
Amp B-D
0.6
Amp A-B
0.6
-0.4
-0.6
-0.4
% loss=0.696
% error=0.320
-800 -400 0
400
delta y transfers
-0.6
800
0.0
-0.2
-0.4
% loss=0.597
% error=0.307
-800 -400 0
400
delta y transfers
-0.6
800
0.0
-0.2
-0.4
% loss=0.147
% error=0.293
-800 -400 0
400
delta x transfers
-0.6
800
0.0
-0.2
-0.4
% loss=-0.16
% error=0.267
-800 -400 0
400
delta x transfers
-0.6
800
Amp A-C
0.6
Amp B-D
0.6
-0.4
% loss=0.304
% error=1.960
-800 -400 0
400
delta y transfers
HRC Tuc_F606W_360.0s r=5 <f>=13548, s=6.23
0.6
0.0
-0.2
-0.6
800
delta mag
0.2
delta mag
0.4
0.2
delta mag
0.4
0.2
delta mag
0.4
0.2
delta mag
0.4
0.2
delta mag
0.4
0.2
delta mag
0.4
0.2
0.0
0.0
-0.2
-0.4
% loss=2.039
% error=1.521
-800 -400 0
400
delta y transfers
-0.6
800
-0.4
% loss=-1.16
% error=1.962
-800 -400 0
400
delta x transfers
-0.6
800
-800 -400 0
400
delta x transfers
Amp A-B
0.6
Amp C-D
0.6
Amp A-C
0.6
Amp B-D
0.6
Amp A-B
0.6
-0.4
-0.6
% loss=0.133
% error=0.689
-800 -400 0
400
delta y transfers
800
-0.4
-0.6
0.0
-0.2
% loss=0.769
% error=0.571
-800 -400 0
400
delta y transfers
800
-0.4
-0.6
0.0
-0.2
% loss=0.431
% error=0.723
-800 -400 0
400
delta x transfers
800
-0.4
-0.6
0.0
-0.2
% loss=-0.07
% error=0.942
-800 -400 0
400
delta x transfers
-0.4
-0.6
800
% loss=0.454
% error=0.331
-800 -400 0
400
delta y transfers
27
0.0
-0.2
800
-0.4
-0.6
delta mag
0.2
delta mag
0.4
0.2
delta mag
0.4
0.2
delta mag
0.4
0.2
delta mag
0.4
0.2
delta mag
0.4
0.2
delta mag
0.4
0.2
0.0
% loss=-2.37
% error=2.249
800
HRC Tuc_F775W_360.0s r=5 <f>=11881, s=4.29
0.4
-0.2
Amp C-D
0.0
0.2
0.0
800
-0.2
0.4
-0.2
% loss=-0.12
% error=3.354
HRC Tuc_F606W_360.0s r=5 <f>=5138, s=6.23
0.4
-0.2
Amp C-D
0.0
0.2
0.0
800
-0.2
0.4
-0.2
% loss=-0.22
% error=3.521
HRC Tuc_F606W_360.0s r=5 <f>=11132, s=6.23
0.2
0.0
Amp C-D
-0.2
0.4
-0.2
800
HRC Tuc_F606W_360.0s r=5 <f>=-31868, s=6.23
Amp A-B
0.2
-0.6
% loss=-3.61
% error=2.337
-800 -400 0
400
delta x transfers
0.4
-0.4
Amp C-D
0.2
0.0
-0.2
0.2
0.0
800
0.4
0.2
0.0
-0.2
% loss=3.976
% error=1.169
Amp A-B
0.4
0.2
0.0
-0.2
% loss=-2.26
% error=2.510
Amp B-D
0.4
-0.2
% loss=-1.80
% error=0.802
-800 -400 0
400
delta x transfers
0.2
0.0
800
Amp C-D
0.4
0.4
-0.2
% loss=2.262
% error=3.227
-800 -400 0
400
delta x transfers
Amp A-B
0.0
-0.4
% loss=1.514
% error=1.287
0.4
HRC Tuc_F775W_30.00s r=5 <f>=988, s=0.51
0.6
0.6
0.2
0.0
-0.2
-800 -400 0
400
delta x transfers
-0.4
% loss=0.834
% error=0.324
-0.2
-800 -400 0
400
delta y transfers
0.4
0.2
0.0
800
Amp C-D
0.4
-0.2
% loss=2.036
% error=2.360
-0.6
800
delta mag
0.6
0.2
0.0
-0.2
% loss=5.208
% error=2.235
Amp A-B
0.4
delta mag
0.0
-0.6
0.6
0.2
delta mag
0.2
-0.2
-0.4
Amp B-D
0.4
delta mag
0.6
0.0
HRC Tuc_F775W_30.00s r=5 <f>=2473, s=0.51
delta mag
Amp A-C
0.4
-0.4
% loss=4.152
% error=0.823
HRC Tuc_F606W_30.00s r=5 <f>=911, s=0.75
0.6
0.0
delta mag
-0.6
-0.2
0.0
delta mag
0.2
0.0
delta mag
0.4
0.2
0.0
delta mag
0.4
0.2
delta mag
0.4
0.2
delta mag
0.4
0.2
delta mag
0.4
-0.4
0.2
-0.2
HRC Tuc_F775W_30.00s r=5 <f>=5625, s=0.51
Amp A-B
0.2
-0.2
800
Amp C-D
0.4
-800 -400 0
400
delta x transfers
0.4
-0.2
0.6
-0.2
0.2
0.0
% loss=-1.62
% error=3.040
-800 -400 0
400
delta x transfers
Amp A-B
0.0
0.4
0.0
-0.6
800
HRC Tuc_F775W_30.00s r=5 <f>=17341, s=0.51
Amp A-B
0.4
0.0
% loss=-4.83
% error=3.198
delta mag
% loss=1.461
% error=0.347
delta mag
-0.6
800
delta mag
% loss=1.645
% error=0.386
delta mag
delta mag
0.2
0.0
-0.2
-0.4
delta mag
0.2
0.0
Amp C-D
0.4
-0.2
-0.2
delta mag
0.6
-0.2
HRC Tuc_F606W_30.00s r=5 <f>=6501, s=0.75
delta mag
Amp A-B
0.4
-0.2
0.6
delta mag
0.6
-0.2
-800 -400 0
400
delta y transfers
delta mag
Amp B-D
0.4
-0.2
-0.6
delta mag
0.6
0.4
0.2
0.0
Amp A-C
delta mag
0.4
0.2
delta mag
0.6
delta mag
0.4
Amp B-D
delta mag
0.6
delta mag
Amp A-C
delta mag
HRC Tuc_F606W_30.00s r=5 <f>=18060, s=0.75
0.6
0.0
-0.2
% loss=1.187
% error=0.288
-800 -400 0
400
delta y transfers
800
-0.4
-0.6
Amp C-D
0.0
-0.2
% loss=0.381
% error=0.168
-800 -400 0
400
delta x transfers
800
-0.4
-0.6
% loss=0.788
% error=0.737
-800 -400 0
400
delta x transfers
800
Instrument Science Report ACS 2003-009
HRC Tuc_F775W_360.0s r=5 <f>=879, s=4.29
Amp A-C
0.6
Amp B-D
0.6
Amp A-B
0.6
0.4
0.4
0.2
0.2
0.2
0.2
0.0
-0.2
-0.4
-0.6
0.0
-0.2
-0.4
% loss=0.574
% error=0.633
-800 -400 0
400
delta y transfers
-0.6
800
delta mag
0.4
delta mag
0.4
delta mag
delta mag
0.6
0.0
-0.2
-0.4
% loss=1.030
% error=0.803
-800 -400 0
400
delta y transfers
-0.6
Amp C-D
0.0
-0.2
-0.4
% loss=0.390
% error=0.174
800
-800 -400 0
400
delta x transfers
-0.6
800
% loss=0.342
% error=0.882
-800 -400 0
400
delta x transfers
800
HRC Tuc_F775W_360.0s r=5 <f>=32327, s=4.29
Amp A-C
0.6
Amp B-D
0.6
Amp A-B
0.6
0.4
0.4
0.2
0.2
0.2
0.0
0.0
delta mag
0.4
0.2
delta mag
0.4
delta mag
delta mag
0.6
0.0
0.0
-0.2
-0.2
-0.2
-0.2
-0.4
-0.4
-0.4
-0.4
-0.6
% loss=0.784
% error=0.786
-800 -400 0
400
delta y transfers
-0.6
800
% loss=0.173
% error=0.933
-800 -400 0
400
delta y transfers
-0.6
% loss=0.266
% error=0.651
800
-800 -400 0
400
delta x transfers
Amp C-D
-0.6
800
% loss=0.277
% error=1.683
-800 -400 0
400
delta x transfers
800
HRC Tuc_F775W_360.0s r=5 <f>=12102, s=4.29
Amp A-C
0.6
Amp B-D
0.6
Amp A-B
0.6
0.4
0.4
0.2
0.2
0.2
0.0
0.0
delta mag
0.4
0.2
delta mag
0.4
delta mag
delta mag
0.6
0.0
0.0
-0.2
-0.2
-0.2
-0.2
-0.4
-0.4
-0.4
-0.4
-0.6
% loss=1.053
% error=1.333
-800 -400 0
400
delta y transfers
-0.6
800
% loss=0.954
% error=1.879
-800 -400 0
400
delta y transfers
-0.6
% loss=-0.85
% error=1.722
800
-800 -400 0
400
delta x transfers
Amp C-D
-0.6
800
% loss=-0.12
% error=2.739
-800 -400 0
400
delta x transfers
800
HRC Tuc_F775W_360.0s r=5 <f>=5274, s=4.29
Amp A-C
0.6
Amp B-D
0.6
Amp A-B
0.6
0.4
0.4
0.2
0.2
0.2
0.0
0.0
delta mag
0.4
0.2
delta mag
0.4
delta mag
delta mag
0.6
0.0
0.0
-0.2
-0.2
-0.2
-0.2
-0.4
-0.4
-0.4
-0.4
-0.6
% loss=1.429
% error=2.140
-800 -400 0
400
delta y transfers
-0.6
800
% loss=0.670
% error=2.372
-800 -400 0
400
delta y transfers
-0.6
% loss=-2.51
% error=2.207
800
-800 -400 0
400
delta x transfers
Amp C-D
-0.6
800
% loss=-0.00
% error=3.075
-800 -400 0
400
delta x transfers
800
HRC Tuc_F502N_360.0s r=5 <f>=7886, s=0.25
Amp A-C
0.6
Amp B-D
0.6
Amp A-B
0.6
0.4
0.4
0.2
0.2
0.2
0.0
-0.2
-0.4
-0.6
0.0
-0.2
% loss=3.965
% error=3.724
-800 -400 0
400
delta y transfers
800
-0.4
-0.6
delta mag
0.4
0.2
delta mag
0.4
delta mag
delta mag
0.6
0.0
-0.2
% loss=1.697
% error=5.200
-800 -400 0
400
delta y transfers
-0.4
-0.6
800
Amp C-D
0.0
-0.2
% loss=0.977
% error=1.017
-800 -400 0
400
delta x transfers
800
-0.4
-0.6
% loss=0.200
% error=7.212
-800 -400 0
400
delta x transfers
800
Tabulated Linear CTE Relationships for WFC
sky (e)
<flux> (e)
loss/2048 pix
(mag)
error
ap
#
stars
data set
0.086
1624.41
0.041
0.008
3
126
Tuc_F502N_30.00
0.086
845.375
0.057
0.007
3
366
Tuc_F502N_30.00
0.086
393.822
0.072
0.010
3
583
Tuc_F502N_30.00
0.086
188.229
0.084
0.016
3
575
Tuc_F502N_30.00
0.086
57.7970
0.069
0.021
3
578
Tuc_F502N_30.00
2.391
15311.9
0.003
0.002
3
641
Tuc_F775W_30.00
2.391
6605.38
0.007
0.002
3
935
Tuc_F775W_30.00
2.391
2603.52
0.016
0.002
3
1224
Tuc_F775W_30.00
2.391
919.203
0.031
0.003
3
1869
Tuc_F775W_30.00
2.391
404.583
0.056
0.005
3
2703
Tuc_F775W_30.00
2.391
231.126
0.073
0.007
3
2245
Tuc_F775W_30.00
2.391
104.770
0.060
0.014
3
952
Tuc_F775W_30.00
3.523
16741.8
0.006
0.001
3
717
Tuc_F606W_30.00
28
Instrument Science Report ACS 2003-009
sky (e)
<flux> (e)
loss/2048 pix
(mag)
error
ap
#
stars
data set
3.523
7282.32
0.010
0.002
3
820
Tuc_F606W_30.00
3.523
2407.22
0.012
0.003
3
1053
Tuc_F606W_30.00
3.523
925.369
0.020
0.004
3
1682
Tuc_F606W_30.00
3.523
402.938
0.047
0.005
3
2398
Tuc_F606W_30.00
3.523
210.817
0.061
0.008
3
2170
Tuc_F606W_30.00
3.523
97.6159
0.042
0.013
3
1133
Tuc_F606W_30.00
2.239
21834.1
0.017
0.005
3
128
Tuc_F502N_400.0
2.239
11485.2
0.024
0.004
3
362
Tuc_F502N_400.0
2.239
5557.06
0.025
0.004
3
552
Tuc_F502N_400.0
2.239
2473.21
0.033
0.006
3
610
Tuc_F502N_400.0
2.239
919.578
0.048
0.009
3
638
Tuc_F502N_400.0
24.75
210562.
-0.00
0.001
3
671
Tuc_F775W_400.0
24.75
88816.4
-0.00
0.001
3
933
Tuc_F775W_400.0
24.75
34044.9
-0.00
0.001
3
1253
Tuc_F775W_400.0
24.75
12380.5
0.001
0.002
3
1922
Tuc_F775W_400.0
24.75
5589.34
0.003
0.002
3
2732
Tuc_F775W_400.0
24.75
2960.67
0.010
0.003
3
2496
Tuc_F775W_400.0
24.75
1249.33
0.025
0.005
3
1559
Tuc_F775W_400.0
38.19
230330.
-0.00
0.001
3
748
Tuc_F606W_400.0
38.19
97852.4
-0.00
0.001
3
824
Tuc_F606W_400.0
38.19
31996.8
-7.23
0.002
3
1068
Tuc_F606W_400.0
38.19
12476.9
0.002
0.003
3
1729
Tuc_F606W_400.0
38.19
5418.44
0.007
0.004
3
2560
Tuc_F606W_400.0
38.19
2758.87
0.013
0.004
3
2584
Tuc_F606W_400.0
38.19
1217.27
0.025
0.006
3
1742
Tuc_F606W_400.0
127.0
646684.
-0.00
0.003
3
628
Tuc_F606W_1100.
127.0
257017.
0.004
0.001
3
706
Tuc_F606W_1100.
127.0
97963.6
0.007
0.002
3
859
Tuc_F606W_1100.
127.0
33242.1
0.007
0.003
3
1359
Tuc_F606W_1100.
127.0
14954.3
0.008
0.004
3
2105
Tuc_F606W_1100.
127.0
7443.19
0.011
0.004
3
2211
Tuc_F606W_1100.
127.0
3216.53
0.012
0.007
3
1569
Tuc_F606W_1100.
29