Instrument Science Report WFPC2 97-08
New Results on Charge Transfer
Efficiency and Constraints on Flat-Field
Accuracy
B. Whitmore and I. Heyer
July 17, 1998
ABSTRACT
The primary new results based on observations from calibration proposal 6195 are:
1. A set of new formulae has been developed to correct for CTE loss, with dependencies on
the X and Y positions, the background counts, and the brightness of the star. The use of
this formula reduces the observational scatter in this particular dataset from 4-7% to 23%, depending on the filter.
2. A small correction is required to normalize results from aperture photometry on the
three WF chips. This normalization can be understood as the product of different aperture
corrections (i.e., variations in the PSF) and different gain ratios for the three chips.
3. The uncertainties in aperture photometry of point sources due to flat-fields are less than
(probably considerable less than) 1.5 % across the chip and 0.6 % chip-to-chip.
1. Introduction
The stated goal of the Cycle 5 “Flat Field Check” calibration proposal (ID = 6195) was
to check the quality of the flat fields and to estimate the errors at the 1 - 2 % rms level.
However, before this could be done the effects of non-optimal charge transfer efficiency
(CTE) needed to be removed from the data. As it turns out, the most valuable contribution
of this proposal was what we learned about CTE.
The observational consequence of the CTE problem is that a point source observed at
the top of the chip appears to be fainter than if observed at the bottom of the chip. The
standard solution has been to use a 4 % linear ramp in cases with low background, and no
correction for cases with high background (Holtzman et al. 1995a). The apparent cause of
the problem is that the efficiency of transporting the packet of electrons from pixel to pixel
as the charge is read down the column is ~ 0.99995 under certain conditions, rather than
1.00000. Hence more of the charge gets “trapped” during the readout for the stars near the
1
top of the chip. The trapped electrons eventually free themselves, and some can be
observed as residual images in subsequent exposures (Biretta, 1997).
Proposal 6195 consisted of observations of the same crowded ω Cen (= NGC 5139)
field centered in each of the four chips during four successive orbits. The standard broadband filters were used (F336W, F439W, F555W, F675W, and F814), along with F606W in
order to compare the effects of using a skyflat developed by the Medium Deep Survey
project for this filter. The F555W observations were taken with and without a preflash. A
gain of 7 was used for all the observations.
The observing log, as well as values of the mean, midpoint over the region
[100:700,100:700], and an estimate of the “background”, are listed for the raw observations (i.e., before cosmic ray removal) in Table 1. The midpoints (from the IMSTAT task)
provide a rough estimate of the background, but turn out to be considerably noisier than
our background measurement which was determined using the mean in a blank region
with an area of about 500 pixels near the center of the chip. Note that the “preflash”
planned for the F555W exposure on WF2 apparently did not occur, or was very faint, since
the mean, midpoint, and background estimates are all similar to the un-preflashed values.
2
Table 1: Means, Midpoints, and Background for the Raw Observations
image name
u34d0101t.c0h
u34d0102t.c0h
u34d0103t.c0h
u34d0104t.c0h
u34d0105t.c0h
u34d0106t.c0h
u34d0107t.c0h
u34d0108t.c0h
u34d0109t.c0h
u34d010at.c0h
u34d010bt.c0h
u34d010ct.c0h
u34d010dt.c0h
u34d010et.c0h
u34d010ft.c0h
u34d010gt.c0h
u34d010ht.c0h
u34d010it.c0h
u34d010jt.c0h
u34d010kt.c0h
u34d010lt.c0h
u34d010mt.c0h
u34d010nt.c0h
u34d010ot.c0h
u34d010pt.c0h
u34d010qt.c0h
u34d010rt.c0h
u34d010st.c0h
u34d010tt.c0h
u34d010ut.c0h
u34d010vt.c0h
u34d010wt.c0h
u34d010xt.c0h
u34d010yt.c0h
u34d010zt.c0h
u34d0110t.c0h
u34d0111t.c0h
u34d0112t.c0h
u34d0113t.c0h
u34d0114t.c0h
u34d0115t.c0h
u34d0116t.c0h
u34d0117t.c0h
u34d0118t.c0h
sequence-filter
chip
mean on chip*
midpoint on chip*
1-555 (preflash)
1.
24.9
23.27
2-555
1.
1.263
0.7333
1-336
1.
0.4925
0.3972
2-336
1.
0.642
-0.03933
1-439
1.
0.2903
0.03169
2-439
1.
0.3381
-0.04355
1-675
1.
0.966
0.5656
2-675
1.
1.318
1.13
1-814
1.
0.8775
0.4527
2-814
1.
0.8211
0.05544
1-606
1.
1.231
0.2556
1-555 (preflash?)
2.
6.005
0.9092
2-555
2.
5.372
0.9278
1-336
2.
0.71
-0.1157
2-336
2.
0.5784
0.0638
1-439
2.
0.5337
-0.002806
2-439
2.
0.5988
0.4042
1-675
2.
3.063
1.768
2-675
2.
2.942
0.4442
1-814
2.
2.865
1.301
2-814
2.
2.954
-0.1678
1-606
2.
4.832
3.172
1-555 (preflash)
3.
28.43
24.44
2-555
3.
5.211
3.642
1-336
3.
0.7688
0.1555
2-336
3.
0.6141
0.1646
1-439
3.
0.6256
-0.02867
2-439
3.
0.5804
0.06774
1-675
3.
3.113
0.9154
2-675
3.
3.151
0.6835
1-814
3.
2.958
0.6743
2-814
3.
3.053
0.2976
1-606
3.
4.934
0.2173
1-555 (preflash)
4.
30.92
27.51
2-555
4.
5.004
0.7388
1-336
4.
0.7257
0.1577
2-336
4.
0.7761
0.4041
1-439
4.
0.5536
-0.04243
2-439
4.
0.5772
0.1013
1-675
4.
3.124
1.577
2-675
4.
3.085
2.32
1-814
4.
3.042
0.2904
2-814
4.
2.94
0.3817
1-606
4.
4.674
0.684
* In region [100:700,100:700]. Units are DN (i.e., ~electrons/7).
** Mean in blank region near the center. Roughly 500 pixels. Units are DN.
3
background**
22.87
0.203
0.020
0.063
0.003
0.050
0.197
0.280
0.193
0.134
0.319
2.339
2.21
0.135
0.079
0.074
0.068
0.929
0.826
0.756
0.726
1.512
25.37
1.99
0.062
0.156
0.124
0.050
1.007
0.996
0.746
0.841
1.541
29.52
1.87
0.173
0.084
0.071
0.080
1.001
0.938
0.745
0.729
1.540
The observations were taken on MJD = 50263.17 through 50263.39, = June 29, 1996.
This was roughly 6.3 days after a decontamination on MJD = 50256.9. Effects of the
monthly contamination have been taken out using the contamination rates listed in Whitmore et al. (1996). The data have been corrected for the geometric distortion by
multiplying by the f1k1552bu.r9h image (see Holtzman 1995a, or the HST Data Handbook (Leitherer, 1995) for details). Stars that fell within 2 pixels of “bad” pixels (i.e.,
anything with a non-zero value in the .c1h image such as saturated pixels, bad columns,
etc.) were filtered out, as were stars with neighboring stars within 5 pixels.
DAOFIND was used to identify the stars, and the PHOT task in the DAOPHOT package was used to perform aperture photometry. Two different aperture sizes were used for
the analysis in order to help isolate effects due to differences in the Point Spread Function
(PSF) from effects due to CTE or the flat fields. The first aperture employed a 2-pixel
radius with a sky value defined by the centroid of the values in a 5- to 10-pixel radius
annulus around the star. The second setup used the same sky but a 5-pixel radius aperture
for the stars (i.e., the standard 0.5 arcsec aperture for the WF). Pairs of images were available for the F336W, F439W, F675W, and F814W images. These were combined using
GCOMBINE and COSMICRAYS to remove hot pixels. The images in F555W and
F606W were single images with a fair number of cosmic rays. The procedure in these
cases, and also for a comparison between individual subexposures for the paired exposures, was to find all objects and then compare them with the F675W master list to filter
out cosmic rays. In general this worked quite well, but did filter out a few of the bright
stars in the F336W and F439W images that were saturated in the F675W image (and
hence removed from the master list). An enhancement to the current analysis (included in
the list of possible enhancements in Appendix A) would be to go back and correct this
problem since it limits the information on CTE at high count rates for these filters.
Figure 1 shows the fields-of-view for the various pointings. Note that the direction of
the readout (and hence the definition of the X and Y axis) changes by 90 degrees for each
chip. The result is that a star at the top of the chip in WF2 (e.g. stars A and C) will be on
the bottom of the chip when the field-of-view is centered on the WF4, hence providing an
excellent measurement of the CTE loss. The situation is not quite as optimal for comparisons between the other chips, but shifts in the Y position are still present; hence it is
possible to measure the CTE loss with roughly 50 % larger uncertainties. Another thing to
note is that while this report will only consider field 1, since it appears in all four chips,
there are other fields that appear in two chips (namely fields 2 and 6, and to a lesser
degree, fields 3,4,7,8). This is listed as a possible enhancement in Appendix A.
4
Figure 1: Fields of view for the various pointings of the Wide Field/Planetary
Camera.
1a: centered on PC
1b: centered on WF2
1c: centered on WF3
1d: centered on WF4
2. Results - Charge Transfer Efficiency
2.1 Comparison of CTE Loss on the WF Chips
Figure 2 shows the effect of CTE loss for observations with the F675W filter. The
throughput ratio is defined as the difference between measurements of the same star. The
5
difference in Y positions of a star on the two different chips is plotted along the X-axis. A
comparison is made between the three different chips.
Figure 2: The ratio of the difference in the brightness of the same star (i.e. the
throughput ratio) as a function of the difference in Y position for stars with counts in
the range 2000 to 10000 DN. The three panels show comparisons between the three
WF chips.
The three determinations of the CTE loss in Figure 2 (i.e., the slope in the relation) are
in good agreement. A more comprehensive compilation of all six filters, broken into five
magnitude bins, results in mean values of the ratio of CTE loss of 1.029 +/- 0.047 for WF2
vs. WF3 (NOTE: the +/- value in this report are the uncertainties in the mean, based on the
empirical scatter and the value of N), 0.965 +/- 0.018 for WF2 vs. WF4, and 1.006 +/0.049 for WF3 vs. WF4, where the mean of the three comparisons has been normalized to
1.00. This is based on only 19 of the 30 possible determinations (six filters times five
magnitude bins) since it was not possible to obtain good determinations for all five magnitude bins for some filters (e.g., there are very few bright stars in the F336W and F439W
observations). We conclude that CTE is identical for each of the 3 WF chips, with any
deviations being less than the statistical noise which is about 5 %. Given this result, we
will average all three determinations together to obtain our best estimate in the following
discussion.
6
Figure 3 shows the throughput ratios for each of the six filters, with the different panels showing the data for different brightness ranges. The value of CTE loss in percentage
over 800 pixels is given in each panel.
2.2 Dependence of CTE Loss on Filter
Figure 4 shows the measurements deemed most reliable (i.e with uncertainties in the
slope less than 4%/800 pixels) for each of the six filters. Only the WF2 vs. WF4 measurements are shown. However, the value of CTE is the weighed mean of comparisons
between all three chips. The X-axis locations are approximate in Figure 4, adopting mean
values of 3500, 1000, 330, 100, and 35 DN for the five bins, and offsetting the longer
wavelengths +0.03. In addition, shorter wavelengths have symbols with fewer vertices
(e.g. F336W datapoints are triangles) while longer wavelengths have more vertices (e.g.
F814W datapoints are circles). This makes it easier to see the wavelength dependence.
Table 2 provides our weighed mean values of CTE. Values have been determined both
for GCOMBINED data, and for the individual subexposures (i.e., 1336 is the first observation with the F336W filter while 2336 is the second observation). Comparisons between
the first and second images are made in Section 2.4.
7
3b: F439W
3a: F336W
Figure 3: The Throughput Ratio vs. ∆Y for each of the six filters. The different panels show the data for WF2 vs. WF4 for different stellar brightnesses (in DN).
8
3d: F606W
3c: F555W
Figure 3 continued
9
3f: F814W
3e: F675W
Figure 3 continued.
10
Figure 4: The values of CTE loss in units of % loss over 800 pixels vs. the brightness of the star in DN. A small horizontal offset has been made as a function of the
wavelength in order to reduce overlaps, and to show the dependence on wavelength.
The top panel used an aperture with a 2-pixel radius while the bottom panel used an
aperture with a 5-pixel radius.
11
Table 2. Weighed Mean Values of CTE Loss
Y-CTE
+/-
filter
ap.
counts
-10.11461
-9.191489
-14.55661
-11.86014
-10.26196
-1.792433
-3.978529
-5.031162
-4.719245
-3.259289
-6.932115
-5.656327
-5.022976
-5.882444
-4.455164
-9.526449
-9.593287
-6.666245
-6.498224
-6.788136
-9.535663
-9.976768
-6.575353
-5.324374
-4.967148
-10.70564
-10.18564
-16.39119
-12.26482
-9.686418
-3.024903
-2.231701
-3.041081
-4.224268
-7.860149
-8.339637
-7.002929
-7.314975
-7.711159
-6.476827
-8.641953
-5.663993
-5.505311
-5.014957
-14.888
1.04231
1.171636
1.044465
1.047698
1.649528
1.935278
1.04077
0.779038
0.481895
0.466499
1.687402
0.871414
0.7159144
0.5650335
0.497291
1.646911
0.7317722
0.6096819
0.3854237
0.5959795
1.518046
0.7297708
0.5265434
0.3571874
0.5419394
1.316359
1.297883
1.267091
1.179334
1.317898
1.54268
0.9622505
0.5896671
0.528083
1.585789
0.9530129
0.7343895
0.4926722
0.6404739
1.533442
0.7913548
0.6404739
0.4095338
0.5711918
3.24
336
336
439
439
439
555
555
555
555
555
606
606
606
606
606
675
675
675
675
675
814
814
814
814
814
1336
1336
1439
1439
1439
1555
1555
1555
1555
1675
1675
1675
1675
1675
1814
1814
1814
1814
1814
2336
2.
2.
2.
2.
2.
2.
2.
2.
2.
2.
2.
2.
2.
2.
2.
2.
2.
2.
2.
2.
2.
2.
2.
2.
2.
2.
2.
2.
2.
2.
2.
2.
2.
2.
2.
2.
2.
2.
2.
2.
2.
2.
2.
2.
2.
100.
330.
100.
330.
1000.
35.
100.
330.
1000.
3500.
35.
100.
330.
1000.
3500.
35.
100.
330.
1000.
3500.
35.
100.
330.
1000.
3500.
100.
330.
100.
330.
1000.
100.
330.
1000.
3500.
100.
330.
1000.
3500.
100.
330.
1000.
3500.
35.
12
mean on
chip
X-CTE
+/-
backgr.
0.696
0.696
0.578
0.578
0.578
5.200
5.200
5.200
5.200
5.200
4.813
4.813
4.813
4.813
4.813
3.080
3.080
3.080
3.080
3.080
2.969
2.969
2.969
2.969
2.969
0.696
0.696
0.578
0.578
0.578
25.290
25.290
25.290
25.290
3.080
3.080
3.080
3.080
3.080
2.969
2.969
2.969
2.969
2.969
0.696
-5.017
-2.937
-6.418
-6.688
-10.135
-6.062
-6.303
-4.613
-5.084
-2.928
2.157
-3.955
-4.143
-4.861
-3.509
-4.786
-3.558
-3.079
-4.384
-2.072
-9.220
-6.427
-2.464
-4.093
-0.865
-2.610
-1.926
-6.727
-6.502
-8.834
-0.762
-3.711
-4.423
-3.804
-6.113
-8.773
-2.676
-4.270
-0.751
-5.532
-3.980
-2.611
-4.416
-1.297
-0.271
1.609
2.253
1.645
1.521
2.894
3.142
1.983
1.041
0.695
0.762
2.884
1.387
1.110
0.974
0.756
2.578
1.212
0.950
0.648
0.891
2.509
1.235
0.761
0.533
0.970
2.221
2.451
1.891
1.673
2.527
2.571
1.590
0.879
0.702
2.370
1.431
1.198
0.397
1.141
2.625
1.360
0.971
0.564
0.874
4.357
0.115
0.115
0.078
0.078
0.078
2.02
2.02
2.02
2.02
2.02
1.540
1.540
1.540
1.540
1.540
0.950
0.950
0.950
0.950
0.950
0.757
0.757
0.757
0.757
0.757
0.123
0.123
0.090
0.090
0.090
19.08
19.08
19.08
19.08
0.979
0.979
0.979
0.979
0.979
0.749
0.749
0.749
0.749
0.749
0.106
Y-CTE
+/-
filter
ap.
counts
mean on
chip
X-CTE
+/-
backgr.
-12.03499
-10.82073
-16.25918
-10.64444
-9.223102
-8.183213
-8.982924
-6.048081
-5.358417
-4.048478
-6.733097
-9.600081
-7.713207
-4.692548
-3.817884
-7.051493
-8.285187
-4.02515
-11.96342
-11.18256
-10.80812
-1.964629
-4.716091
-3.665416
-3.213291
-3.249155
-3.325771
-4.752463
-4.861613
-5.809546
-5.906372
-5.812048
-5.898314
-5.364728
-5.350156
-4.949152
-4.359361
-9.063997
-9.973407
-12.86479
-11.30308
0.6336962
-1.754313
-3.028596
-6.8389
-5.654282
-6.326442
1.199349
1.567314
1.317898
1.171636
1.451844
1.622739
0.88681
0.717454
0.4480238
0.7851964
1.672006
0.84832
0.6250779
0.4233902
0.5234643
1.631977
1.35023
1.764382
1.62782
1.019678
1.080492
1.867536
1.325596
0.6543003
0.4572614
1.479556
1.236299
0.6666471
0.4464842
1.268323
0.9300728
0.4278396
0.4253609
1.442606
0.7682608
0.4803554
0.3695042
3.344
1.920502
2.40982
1.077721
1.974242
1.105433
0.6127611
1.670467
1.114671
0.5881275
2336
2336
2439
2439
2439
2675
2675
2675
2675
2675
2814
2814
2814
2814
2814
336
336
336
439
439
439
555
555
555
555
606
606
606
606
675
675
675
675
814
814
814
814
1336
1336
1439
1439
1555
1555
1555
1675
1675
1675
2.
2.
2.
2.
2.
2.
2.
2.
2.
2.
2.
2.
2.
2.
2.
5.
5.
5.
5.
5.
5.
5.
5.
5.
5.
5.
5.
5.
5.
5.
5.
5.
5.
5.
5.
5.
5.
5.
5.
5.
5.
5.
5.
5.
5.
5.
5.
100.
330.
100.
330.
1000.
35.
100.
330.
1000.
3500.
35.
100.
330.
1000.
3500.
100.
330.
1000.
100.
330.
1000.
100.
330.
1000.
3500.
100.
330.
1000.
3500.
100.
330.
1000.
3500.
100.
330.
1000.
3500.
100.
330.
100.
330.
330.
1000.
3500.
100.
330.
1000.
0.696
0.696
0.578
0.578
0.578
3.080
3.080
3.080
3.080
3.080
2.969
2.969
2.969
2.969
2.969
0.696
0.696
0.696
0.578
0.578
0.578
5.200
5.200
5.200
5.200
4.813
4.813
4.813
4.813
3.080
3.080
3.080
3.080
2.969
2.969
2.969
2.969
0.696
0.696
0.578
0.578
25.290
25.290
25.290
3.080
3.080
3.080
-6.28
-7.701
-7.489
-6.423
-4.381
-4.733
-2.967
-4.218
-3.444
-1.560
-7.153
-6.111
-3.000
-3.270
0.377
-5.127
-1.215
-1.482
-4.297
-4.754
-4.376
-2.736
-3.769
-2.406
-1.228
-1.908
-1.563
-1.909
-2.350
-2.583
-3.247
-2.096
-2.208
-7.360
-3.567
-2.916
-2.878
-2.027
-3.636
-3.707
-3.326
-1.717
-2.496
-0.888
-8.257
-3.479
-1.062
1.996
2.997
2.081
1.870
2.825
2.420
1.397
1.170
0.807
0.827
2.978
1.414
0.888
0.760
1.012
2.526
2.097
3.385
2.517
1.722
1.742
3.103
2.190
0.974
0.844
2.562
2.288
1.255
0.687
2.339
1.617
0.710
0.806
2.458
1.229
0.928
0.670
4.173
2.515
3.572
1.983
3.006
1.714
0.914
2.857
1.782
1.121
0.106
0.106
0.066
0.066
0.066
0.920
0.920
0.920
0.920
0.920
0.765
0.765
0.765
0.765
0.765
0.115
0.115
0.115
0.078
0.078
0.078
2.02
2.02
2.02
2.02
1.54
1.54
1.54
1.54
0.950
0.950
0.950
0.950
0.757
0.757
0.757
0.757
0.123
0.123
0.90
0.90
19.08
19.08
19.08
0.979
0.979
0.979
13
Y-CTE
+/-
filter
ap.
counts
mean on
chip
X-CTE
+/-
backgr.
-6.996896
-6.025214
-5.746727
-4.279703
-4.377519
-7.967961
-7.367838
-13.421
-9.723362
-11.52346
-3.429119
-4.891324
-5.381503
-3.941726
-6.553308
-5.831608
-3.231557
-3.329856
0.4911326
1.328675
0.9607109
0.6158403
0.420311
2.021496
1.933739
2.324967
1.174715
1.510348
1.628898
1.182413
0.5634938
0.6558699
1.38718
0.9083644
0.7928944
0.5096079
1675
1814
1814
1814
1814
2336
2336
2439
2439
2439
2675
2675
2675
2675
2814
2814
2814
2814
5.
5.
5.
5.
5.
5.
5.
5.
5.
5.
5.
5.
5.
5.
5.
5.
5.
5.
3500.
100.
330.
1000.
3500.
100.
330.
100.
330.
1000.
100.
330.
1000.
3500.
100.
330.
1000.
3500.
3.080
2.969
2.969
2.969
2.969
0.696
0.696
0.578
0.578
0.578
3.080
3.080
3.080
3.080
2.969
2.969
2.969
2.969
-1.965
-5.557
-3.046
-3.218
-1.029
1.850
-6.057
-5.807
-7.116
-1.143
-3.274
-5.084
-1.017
-2.052
-5.090
-3.298
-1.906
-2.204
0.779
2.446
1.541
1.078
0.698
4.061
3.292
3.372
1.994
3.529
2.878
1.698
0.937
1.030
2.368
1.411
1.327
0.987
0.979
0.749
0.749
0.749
0.749
0.106
0.106
0.066
0.066
0.066
0.92
0.92
0.92
0.92
0.765
0.765
0.765
0.765
Figure 5 shows a plot of the values from Table 2. Our primary conclusions are:
1. While the “standard” value of 4 % for the CTE ramp is roughly correct for the
F555W filter, where most of the determinations have been made in the past, it is not a
good approximation in many other cases .
2. The effect of CTE is larger for the faint stars, as has been suggested but not quantified in the past (e.g. Holtzman et al. 1995a) . Values of the CTE loss as high as 15 %
are present (i.e., the faint stars with the F439W filter).
3. Wavelengths in the mid-range (e.g., F555W and F606W) have the lowest CTE loss,
with both longer and shorter wavelengths having larger values of CTE loss. This can
be seen by the V-shaped distribution of data points in Figure 4 in the cases with full
wavelength coverage (i.e., 100 and 330 counts). This is probably because the chips
are more efficient at these wavelengths, hence the background is higher. The higher
background appears to reduce the CTE loss, as will be discussed in Section 2.5.
2.3. The Effect of Aperture Size on CTE
The shape of the PSF changes as a function of position on the chip, with a tighter focus
near the center than along the edges. In addition, if the focus near the top of the chip is
worse than at the bottom of the chip, it would mimic a CTE-like effect. One way to check
for this is to see if the value of the CTE loss changes when different sized apertures are
used. A measurement of the spatial changes in the PSF would be the most direct method
14
Figure 5: The values of CTE loss in units of % loss over 800 pixels vs. the brightness of the star in DN. The results from the first, second, and GCOMBINED images
are included for the 2-pixel aperture measurements.
15
to check this possible effect. This has been included in Appendix A as a future
enhancement.
Figure 4b is identical to Figure 4a except an aperture with a 5-pixel radius was used.
The primary effect is to remove much of the tendency for the fainter stars to have larger
values of CTE loss.
Figure 6 shows the difference in CTE loss when the radius of the aperture is changed
from 2 pixels (containing about 75 % of the total light) to 5-pixels (containing about 90 %
of the total light). We find the CTE loss is slightly reduced when the larger aperture is
used, by about 1 % for the bright stars and 3 % for the faint stars with about 100 counts.
Figure 6: The difference in the values of CTE loss between the 2- and 5-pixel apertures as a function of the brightness of the star.
However, we caution the reader from adopting a strategy of using larger apertures in
order to reduce the effects of CTE, since in general the uncertainty in the measurements
dramatically increases for faint stars. This is shown in Figure 7, which plots the ratio of
the uncertainty in the determination of the CTE slope using the two apertures as a function
of the brightness of the star. While there is actually a slight advantage to using the larger
aperture for the very bright stars, or cases where the background is very low (presumably
due to the increased number of photons collected compared to the negligible amount of
sky), most of the measurements indicate that the uncertainty in the measurement of CTE
16
Figure 7: The ratio of the uncertainty in the measurement of CTE loss between 2and 5-pixel apertures vs. the brightness of the star.
loss using the smaller aperture is 60 % of the uncertainty using the larger aperture.
Another manifestation of this is that we were able to determine the CTE loss for stars as
faint as 35 counts using the 2-pixel aperture, but not the 5-pixel aperture.
Holtzman (1995b) suggests that CTE loss may be larger when larger apertures are
used, since the fainter wings may suffer more CTE loss. Figure 7 indicates that this is not
the case, however.
A possible explanation might be that the bottom part of the PSF may act to partially
preflash the top part. This would be more efficient in the wings where the contrast in
brightness level is much lower (i.e., even if a few traps are filled by the bottom half of the
PSF, this will have little effect on the very bright central pixel). However, this is just speculation at this point. It may be possible to examine whether this mechanism is working by
looking for asymmetries in the PSFs.
2.4 Comparison of First and Second Exposures
There are several reasons for comparing the first and second exposures taken in the
CR-SPLIT pairs, as well as comparing the measurements from separate exposures with
17
measurements from the GCOMBINED image. The first reason is to determine whether
any systematic effects are introduced by the presence of cosmic rays in cases where only a
single image is available (e.g., for the F555W or F606W observations in the current proposal, or several other calibration proposals where paired images are not available). The
second reason is to determine if the GCOMBINE task introduces any systematic artifacts.
The third reason is to search for any difference due to some physical effect (e.g., does the
first image act as a preflash for the second image; hence removing some of the CTE for the
second image).
Figure 5 shows a comparison of our measurements of CTE for the first, second, and
GCOMBINED image. Our first conclusion is that the GCOMBINED image is an accurate
representation of the mean of the individual images.
A comparison of the first versus second exposure shows essentially no difference if we
include all the data. However, if we look at the five cases with mean counts higher than
about 1000 counts (excluding F555W since the first exposure was preflashed), we always
find that the value of CTE loss is higher for the first exposure. In the case of F675W the
effect is quite large (e.g., 4 % and a 4-sigma difference for the brightest stars).
Figure 8 shows the ratio of the measurement in the first and second exposures for the
F555W observations (where the first exposure was preflashed), as well as the F675W and
the F814W filters. The S/N for the F336W and F439 filters is too low to search for correlations for the very small difference implied by Figure 5. In the cases with smaller values
of CTE loss for the second exposure we would expect the stars to be slightly brighter in
the second exposure (e.g., for F675W, 4 % for counts near 3500 counts, and 2 % for
counts near 1000 counts). Figure 8b shows that this is indeed the case. In addition, the
difference between the first and second image is a function of Y-position for the F675W
filter, as expected based on Figure 5.
The F555W observations are particularly interesting since they show a very weak
increasing trend for the brightest stars, but a decreasing trend for the 330 count panel. This
is consistent with the results from Figure 5, and is probably due to the preflash in the first
exposure, which seems to have a strong effect for the faint stars but not the bright stars. It
is likely that the number of traps filled by the preflash was sufficient to have an important
effect on the fainter stars, but a lesser effect on the brightest stars where more traps must
be filled to have the same effect in terms of percentage of the total.
The fact that the preflash for the WF2 exposure did not work may explain why CTE
loss was not reduced to nearly zero for our comparison of WF2 vs. WF4 data for F555W
in Figure 5. However, even in the case of WF3 vs. WF4, where large preflashes were
administered in both cases (i.e., ~ 190 electrons), there is still a small non-zero value for
CTE loss (i.e., an average of 2.1 +/- 0.9 % compared to an average for chips WF2 vs. WF3
and WF2 vs. WF4 of 3.6 +/- 0.5 %; using the three brightest bins). This is consistent with
18
8b: F675W
8a: F555W
Figure 8: The ratio between counts in the second and first exposures versus the position on the chip for the three highest S/N filters with two exposures, using just the
WF2 vs. WF4 data.
19
8c: F814W
Figure 8 continued.
the findings of Holtzman (1995a), who advised using a 2 % linear ramp for background in
the range 30 - 250 electrons.
The F814W filter shows essentially no trends, which is roughly consistent with the
smaller differences seen in Figure 5.
Hence, there is evidence that the first image acts to preflash the second image in some
cases (i.e. primarily the F675W filter), with the value of the CTE loss being reduced and
the stars at the top of the chip in the second image being slightly brighter. An obvious
question is why doesn’t the preceeding exposure with a different filter also have the same
effect. Part of the reason might be that the extra time between exposures due to the filter
change may reduce the effect, since there is evidence based on residual images that electrons that fill charge traps responsible for reducing CTE loss (e.g., by preflashing) may
diffuse out of the traps on time scales of about 20 minutes (Biretta, 1997).
However, the fact that the F675W filter shows the largest difference between the first
and second exposure may indicate that this preflashing by the previous image actually is
important, since the previous observation in this particular case was the F439W image
which would not be bright enough to have much effect on the much brighter observations
in the F675W filter. This would predict that the F814W filter observations should show little effect, since the preceeding images in F675W are brighter and should act as an
adequate preflash. This agrees with the observed result. Similarly, this hypothesis may
20
explain why the F336W observations show a slight inverse relation (i.e., the previous
F555W observations acted as a preflash for the first F336W image, but the first F336W
image was too weak to preflash the second F336W image), and may be the reason why the
F555W images show a slight inverse relation (i.e., the first F555W image was preflashed,
which did a better job than relying on the first image to preflash the second image). This
latter result suggests that while the first image can act as a partial preflash, a regular uniform preflash works considerably better, at least for the fainter stars. Perhaps this is
because it takes time for the electrons to diffuse into (and out of ?) charge traps. Another
factor may be that the total number of electrons from the preflash is a factor of about 5
larger than from just the stars.
Hence, in rough terms it appears that many of the small differences between the first
and second exposures seen in Figure 5 can be understood in terms of a consideration of the
previous images. However, the effects are generally quite small, and so this result should
be considered tentative pending a more complete investigation. It is likely that a detailed
understanding will need to take into acount the background level (which fills traps during
the previous exposure), the bright stars (which fills traps during the previous readout), and
the time delay.
2.5 Dependence of CTE on “Background”
Previous results suggest that CTE loss can be greatly reduced or even eliminated if the
“background’’ is sufficiently high. Holtzman et al. (1995a) suggest a ramp of 4 % for
observations with less than about 30 electrons, 2 % for backgrounds of 30 to 250 electrons, and 0 % for higher backgrounds. Ferguson (1996) suggests that a 160 electron
preflash reduces the CTE loss to less than 1 %. The basic model is that electrons fill the
charge traps before (and during?) the readout, so that they are not available to trap the
electrons in the targets as they are read down the column. An open question is if a diffuse
background is required, or if electrons deposited by stars or cosmic rays which are below a
given star are enough to fill the traps during the readout.
Figure 5 suggests that there may be a correlation between CTE loss and the total number of counts on the chip (i.e., the more efficient filters like F555W and F606W have the
lowest values of CTE loss). Figure 9a shows that this is indeed the case, with a good correlation between CTE loss and the mean number of counts on the raw image (i.e., including
stars, cosmic rays, and background), depending on the faintness of the star in a systematic
way. Figure 9b shows the same effect, but using the background measurement as discussed
in section 1. The correlations are only slightly better using the background rather than the
mean number of counts on the chip. A third measurement of the “background”, namely
the midpoint, gives similar, but clearly poorer correlations, supposedly because of the
larger uncertainties in the measurement, as discussed in Section 1.
21
Figure 9: Log of CTE loss vs. log of the mean counts on the chip (9a, top block) or
vs. the log of the background (9b, bottom block). The upper right panels show the
combined results from the other five panels. The low point from the 35-count panel
has been excluded from the combined fit.
22
Figure 10 shows that the residuals from the correlation shown in the upper right hand
panel of Figure 9a are a function of the brightness of the star. A similar result is found
when the blank background is used in Figure 9b.
Figure 10: The residual from the fit of CTE loss vs. mean counts on chip (i.e., the fit
in the upper right panel of Figure 9a) vs. the brightness of the star (Log Counts).
2.6 Evidence for CTE Loss Along the X-axis
One of the surprises in our study was the discovery of what appears to be CTE loss
along the X axis. We will call this X-CTE, and henceforth call the normal CTE down the
columns Y-CTE. Figure 11 shows that after removing a linear dependence on Y-CTE for
the F675W observations, there is still a measureable amount of CTE on the X-axis,
although at a level which is roughly half the normal Y-CTE for the different filters. The
most logical explanation would be that this is due to CTE loss in the shift register at the
bottom of the chip during the readout.
It is possible that the bottom rows might act to preflash the shift register. We might
therefore expect to have less X-CTE at the top of the chip than at the bottom.
Figure 12 shows weak evidence that X-CTE is smaller at the top of the chip in the
present dataset.
23
Figure 11: The throughput ratio for individual stars with counts in the range from
500 - 2000 counts, using the F675W observations. The bottom left panel shows the
raw result. The bottom right shows after the Y-CTE correction has been made. The
upper left shows that there is still some CTE loss along the X-axis. The upper right
panel shows no significant correlation as a function of the distance from the center of
the chip, as expected.
Figure 13 shows the values of X-CTE for all the filters. The values range from about 1
to 5 %. Note that the preflashed observations of F555W show essentially the same amount
of X-CTE loss as the regular F555W observation, as we might expect since the preflash
does not illuminate the shift register. Similarly, the amount of X-CTE does not appear to
depend on the background level at more than a 2-sigma level, only on the brightness of the
star. This is shown more clearly in Figure 14.
2.7 Formulae for Removing the Effects of CTE
The preceeding sections indicate that a correction for CTE will depend on the X and Y
positions, the background, the brightness of the star, and the size of the aperture. In this
section we develop a formula for four different setups: a) 2-pixel aperture using the mean
counts of the chip, b) 5-pixel aperture using the mean counts on the chip, c) 2-pixel aperture using the blank background, and d) 5-pixel aperture using the blank background. Note
24
Figure 12: Similar to Figure 11, but now the two upper panels show the X-CTE for
the upper and lower parts of the chip.
Equation #1 (same for all four cases):
Y -CTE
X -CTE
X
Y
CT S corrected = 1 + ----------------- × --------- + ------------------ × --------- CT S observed
100
100
800
800
where:
•
CTS(corrected) = number of counts in DN for the star, after CTE correction
•
CTS(observed) = raw number of counts in DN for the star
•
Y-CTE = CTE loss in % over 800 pixels in the Y direction (see Equation #2)
•
X-CTE = CTE loss in % over 800 pixels in the X direction (see Equation #3)
•
X, Y = X, Y positions of the star in pixels
•
BKGtotal = mean number of counts in DN over full chip on raw image (incl. stars, cosmic, rays, etc.)
•
BKGblank = mean number of counts in DN for a blank region of the background
that the slight Y-dependence of X-CTE reported in Section 2.7 (Figure 12) is not included
since it is less than a 2-sigma result.
25
Setup A: 2-pixel radius using the mean counts on the chip
Equation #2a
Y -CTE = 10
( 0.9945 – 0.3712 × log BK G total ) + ( 0.2464 – 0.0982 × log CT S obs )
Equation #3a
X -CTE = 7.373 – 1.57 × log CT S observed
Example:
given: CTSobserved = 52 DN, X = 419, Y = 425, and BKG = 2 DN
therefore: Y-CTE = 9.13% and X-CTE = 4.68%
resulting: CTScorrected = 55.80 (i.e. a 7.30% effect)
Setup B: 5-pixel radius using the mean counts on the chip
Equation #2b
Y -CTE = 10
( 0.8946 – 0.4141 × log BK G total )
Equation #3b
X -CTE = 7.040 – 1.63 × log CT S observed
Setup C: 2-pixel radius using the blank background
Equation #2c
Y -CTE = 10
( 0.7994 – 0.2564 × log BK G blank ) + ( 0.2478 – 0.0987 × log CT S obs )
Equation #3c
X -CTE = 7.373 – 1.57 × log CT S observed
Setup D: 5-pixel aperture using the blank background
Equation #2d
Y -CTE = 10
( 0.6930 – 0.2675 × log BK G blank )
Equation #3d
X -CTE = 7.040 – 1.63 × log CT S observed
26
Figure 13: X-CTE loss vs. the brightness of the star for all six filters. Note that
while there is a dependence on brightness, there is no dependence on background
level (i.e., F439W and F336W show similar levels of X-CTE as the more efficient
filters) or on preflash.
Note: The correction equations here were derived from gain 7 data. In order to correct
gain 15 observations, counts should be multiplied by 2 before using them in the CTE
equations.
2.8 CTE on the Planetary Camera
Measuring the CTE loss on the Planetary Camera (=PC) is considerably more difficult
than on the WF chips for a number of reasons, including: 1. roughly a factor of 5 fewer
stars, 2. rather than reversing the positions of identical stars and hence having an effective
∆Y = 1600 pixels, a comparison is made with the mean of the WF2+WF4 values, resulting
in an effective range of only ∆Y = 800 pixels, 3. edge effects due to variations in the PSF
are more important than on the WF where they tend to cancel out, limiting the effective
range still further to ∆Y = 500 pixels, 4. only one determination is possible rather than the
3 available for the WF (i.e. WF2 vs. WF3, WF2 vs. WF4, WF3 vs. WF4).
27
Figure 14: X-CTE loss vs. the brightness of the star (lower panel) and vs. the mean
counts on the chip (upper panel). There is a weak correlation with the brightness of a
star, but essentially no correlation with the total number of counts on the chip (or on
the background).
28
Figure 15: Same as Figure 11, but for the PC. Note the much smaller range in ∆Y
and ∆X for the PC as compared to the WF, and the correspondingly larger uncertainties.
Figure 15 shows our measurement for the F675W filter, where we combine all the
stars brighter than 200 DN. The mean value of the throughput ratio of 0.738 is due to the
use of the same aperture size that was used for the WF, hence the aperture correction is
much larger for the PC. This normalization is 0.693 for the F814W, 0.738 for F675W,
0.775 for F606W, 0.794 for F555W, and 0.833 for F439W. These ratios can be well understood using the encircled energy curves from Holtzman et al. (1995a), a slightly higher
value of CTE (since the background is lower on the PC), and perhaps a slight residual
effect due to the fact that the stars tend to be closer to the edge of the chip (i.e. poorer
focus) on the PC than on the WF.
Figure 16 shows that while the measurement uncertainties on the PC are quite large,
they are in good general agreement with the values from the WF, with the exception of the
preflashed measurement of F555W (at logmean counts = 1.5) which has the largest uncertainty. Note that this implies CTE values on the PC which are typically a factor of about
1.8 higher than on the WF, due to the lower background. Based on this limited dataset, our
current advice is to use the same equations to correct for CTE on the PC and the WF
chips.
29
Figure 16: The measurements of CTE loss for the PC compared to the WF measurements from the upper right panel of Figure 9a.
3. Flat Field Check
The original purpose of proposal 6195 was to check to what degree the flat fields were
responsible for uncertainties in the aperture photometry measurements of point sources.
In this section we look at two aspects of this question. The first is the observational scatter
when measuring individual stars on two different chips. The second is a comparison of the
absolute normalization between the three WF chips.
3.1 Observational Scatter for Observations of the Same Star
We will consider four components to the scatter in measurements of the same star
taken on two different chips:
1) the CTE problem (in both Y and X),
2) the measurement uncertainty (i.e., due to photon statistics, read noise, uncertainty in
sky, centering problems, undersampling, digitization of signal, etc),
3) the variable PSF (i.e., differences in the aperture correction across the chip),
30
4 ) uncertainty in the flat-fields.
Since we can estimate the effects of CTE (see Section 2) and the measurement uncertainty (by comparing the first and second exposures in CR-SPLIT pairs), the resulting
scatter will be due to a combination of the variable PSF and the uncertainty in the flatfields. The effect of the variable PSF has not been well quantified yet, so our results will
only provide an upper limit to the flat field uncertainty.
Table 3 shows the values of the raw scatter, the scatter after corrections for both YCTE and X-CTE have been made (see Section 2.6), and the remaining uncertainty after
the contribution of the measurement uncertainty has been removed. In all cases it is
assumed that the uncertainties add in quadrature (i.e., that the noise is uncorrelated). The
remaining uncertainty column represents our best estimate of the uncertainty due to a
combination of the PSF and flat-field errors. There is evidence based on continuum observations that the flat fields are actually good to a few tenths of a percent (Biretta 1997b,
Fruchter 1997). Hence most of this 0.02 fractional uncertainty is probably due to the PSF
variations, or possibly other sources of noise not considered above.
Table 3. Observational Scatter of the Same Star Using the 2-Pixel Radius Aperture
filter
counts
raw scatter*
scatter after
CTE removed
measurement
uncertainty**
remaining uncertainty
F439W
F675W
1000.
3500.
1000.
330.
3500.
1000.
330.
0.0755
0.0434
0.0489
0.0548
0.0349
0.0398
0.0464
0.0225
0.0242
0.0258
0.0384
0.0201
0.0247
0.0334
0.0174
0.0103
0.0205
0.0355
0.0092
0.0182
0.0334
mean:
mean(3500 cts)):
0.0143
0.0219
0.0157
----0.0179
0.0167
----0.0173 +/- 0.0013 n=5
0.0199 +/- 0.0020 n=2
F814W
Notes to Table 3:
* Values for the raw scatter are for comparisons of the same star on the WF2 and WF4.
** The values of the measurement uncertainty is slightly overestimated since it compares two single subexposures (i.e., with the star at the same position), while the
values of raw scatter, use GCOMBINED pairs with slightly higher S/N. This effect is
larger for the fainter stars, and makes our approach untenable for stars fainter than
1000 counts. The fact that the average for the stars with 3500 counts is slightly larger
is probably due to this effect. The value for the stars with roughly 3500 counts represents our best estimate.
Another question we can ask is how much of the measurement uncertainty is due to
photon statistics and read noise (i.e., unavoidable limitations) and how much is due to
31
other uncertainties (e.g., centering). For the F675W filter, and count rates from 3500 to
100, the photon statistics plus read noise added in quadrature represent a roughly constant
value of 60 % of the observed scatter for repeat measurements at the same position. Hence
the uncertainty introduced by other effects such as centering is comparable.
One final question is whether the measurements with a 5-pixel radius provide less
scatter, and hence more stringent limits on the flatfield (e.g., the centering should be less of
an issue).
Table 4 shows that for very bright sources the 5-pixel aperture does provide smaller
uncertainties, but for fainter stars things deteriorate very fast (i.e., compare the measurement uncertainties for stars with 300 counts between Tables 3 and 4). This is similar to
what we found in Section 2.3.
Table 4. Observational Scatter of the Same Star Using the 5-Pixel Radius Aperture
filter
counts
raw scatter*
scatter after
CTE removed
measurement
uncertainty
remaining uncertainty
F675W
3500.
1000.
300.
3500.
1000.
300.
n=4
n=2
0.0413
0.0463
0.0775
0.0300
0.0472
0.0637
0.0199
0.0318
0.0645
0.0183
0.0371
0.0541
0.0144
0.0257
0.0602
0.0125
0.0261
0.0607
mean:
mean(3500 cts):
0.0137
0.0187
----0.0134
0.0264
----0.0180 +/- 0.0030
0.0136 +/- 0.0002
F814W
Conclusions:
1. For bright stars (i.e., > 500 counts) the removal of Y-CTE and X-CTE improves the
scatter from about 4 - 7 %, to about 2 - 3 %.
2. The measurement uncertainty is about 1.3 % for the brightest stars, hence there is
about 1.4 % uncertainty remaining. This is the upper limit of the flat-field uncertainty.
However, it is very likely that most of this is due to other sources of noise not included
in the analysis (e.g. changes in the PSF) rather than flat-field uncertainties.
3.2 Normalization Between the Three WF Chips
Figure 17 shows that a comparison between measurements of the same star on the
three WF chips (after Y-CTE has been removed) results in non-statistical scatter. For
example, using a 2-pixel aperture gives ratios between WF2/WF3 and WF2/WF4 of about
1.04 for the F675W filter. We also note that the values are essentially constant versus the
count rate. This allows us to average the results for the three bins into a single value in the
subsequent discussion. We also note that the normalization between the three chips
changes slightly when an aperture with a 5-pixel radius is used.
32
Figure 17: Comparison between the throughput ratios for measurements of the same
star for each of the three WF chips, using the F675W filters, and including measurements with both the 2- and 5-pixel radii.
Figure 18 shows the mean values of the chip-to-chip normalizations for observations
brighter than 500 DN for the various filters, using both the 2- and 5-pixel apertures. In
general there is quite good agreement between the different wavelengths, indicating that a
single normalization correction between the chips is warranted. The values for the 5-pixel
apertures are slightly different, as suggested by Figure 17. The most discrepant points are
the preflashed observations of F555W (offset slightly in the X-axis to make them more
visible). The cause of this difference is unclear at this point. The WF2 vs. WF3, AP = 2
point for F336W, is also discrepant, but that is probably due to the large uncertainties.
We will consider three components to the difference in normalization between the
three WF chips:
1. Differences in the gain ratios (see Holtzman, 1995b),
2. Differences in the point spread functions (i.e., different aperture corrections are
required for each chip),
3. Differences in the flat field normalization.
33
Figure 18: The normalization between the different chips as a function of wavelength, for both the 2- and 5-pixel radii. The preflashed observations of F555W have
been offset slightly in wavelength to make them more visible.
34
We can check if differences in the PSF are part of the reason for the scatter by using
the aperture with a 5-pixel radius, since this should minimize any dependence on aperture
corrections by including a larger fraction of the total light of the stars. Assuming for the
moment that the differences due to the flat fields are negligible, we would expect that the
observations using the 5-pixel aperture should correlate with the Holtzman (1995b) gain
ratios between the different chips. The lower panel in Figure 19 shows that a weak correlation does exist, although the small baseline makes the result somewhat uncertain (i.e.,
formally a 3-sigma result). Table 5 provides the corresponding numbers.
Table 5. Normalization Between the WF Chips using the 5 Pixel Radius Aperture
F336W (observed)
Normalized Ratio
F439W (observed)
Normalized Ratio
F555W (observed)
Normalized Ratio
F555W (obs,preflash)
Normalized Ratio
F606W (observed)
Normalized Ratio
F675W (observed)
Normalized Ratio
F814W (observed)
Normalized Ratio
Holtzman gain ratios**
means ***(observed) n=5
means (normalized) n=5
WF2/WF3
WF2/WF4
WF3/WF4
mean
scatter
pred. scatter*
1.012
1.013
1.008
1.009
1.015
1.016
0.991
0.992
1.003
1.004
1.015
1.016
1.013
1.014
0.999
1.011
+/- 0.002
1.012
1.017
0.992
1.007
0.982
1.033
1.008
1.029
1.004
1.023
0.998
1.026
1.001
1.028
1.003
1.025
1.023
+/- 0.004
0.998
0.996
0.971
1.011
0.985
1.024
0.998
1.040
1.014
1.019
0.993
1.009
0.983
1.022
0.996
1.026
1.017
+/- 0.003
0.991
1.008
0.992
1.009
0.992
1.024
1.007
1.020
1.003
1.015
0.998
1.017
1.000
1.021
1.004
0.011
0.021
0.002
0.015
0.009
0.009
0.026
0.011
0.011
0.006
0.009
0.016
0.008
0.009
0.018
1.017
0.0078
0.0048
1.000
0.0110
0.007
0.007
0.009
0.003
0.004
0.003
Notes to Table 5:
* Predicted scatter is based on the mean of the empirical scatter in the determinations
of the individual chip-to-chip ratios.
** The Holtzman gain ratios have been used to determine the normalized ratios.
*** Means are compiled after the removal of F336W (large predicted uncertainty) and
F1555W (preflashed on WF3 and WF4, but not on WF2).
Our conclusions based on the 5-pixel aperture are:
1. The observed scatter (0.0078) is slightly higher than the predicted scatter (0.0048),
indicating that the three chips do not all have the same normalization. However, the
remaining sources of noise are less than 0.01 mag (i.e.,
35
2
2
0.0078 – 0.0048 = 0.0061 )
Figure 19: A comparison of the observed throughput ratios between the three WF
chips with predictions, as described in the text. For the 5-pixel aperture measurements the predictions are based on Holtzman’s (1995b) gain ratios, with the assumption that the larger aperture have reduced the dependence on the PSF. For the 2-pixel
aperture measurements the prediction is the product of the gain ratios and the aperture corrections from Whitmore et al. (1997).
36
2. The observed ratios can be partially explained by the Holtzman (1995a) gain ratios,
as shown by the 3-sigma correlation in Figure 19. However, normalizing by the gain
ratios does not reduce the scatter.
The measurements with the 2-pixel aperture are probably affected by both the gain
ratios and differences in the PSF between the three WF chips. An estimate of the relative
aperture correction between the three WF chips has been made by Whitmore et al. (1997).
The upper panel in Figure 19 indicates that the product of the gain ratios and the aperture
correction does provide a good prediction of the observed ratios, with a 10-sigma correlation. In addition, Table 6 shows that normalizing by this product reduces the scatter from
0.0227 to 0.0099.
Table 6. Normalization between WF chips using the 2-Pixel Radius Aperture
F336W (observed)
Normalized Ratio
F439W (observed)
Normalized Ratio
F555W (observed)
Normalized Ratio
F555W (obs, preflash)
Normalized Ratio
F606W (observed)
Normalized Ratio
F675W (observed)
Normalized Ratio
F814W (observed)
Normalized Ratio
PSF x Gain Ratios**
means (observed) n=5
means (normalized) n=5
WF2/WF3
WF2/WF4
WF3/WF4
mean
scatter
pred. scatter*
1.010
0.956
1.048
0.991
1.037
0.981
1.010
0.956
1.037
0.981
1.039
0.983
1.045
0.989
1.058x0.999
=1.057
1.041
+/- 0.002
0.985
1.037
0.974
1.032
0.969
1.039
0.976
1.027
0.964
1.037
0.974
1.035
0.972
1.044
0.980
1.039x1.025
=1.065
1.037
+/- 0.002
0.974
0.998
0.990
0.994
0.986
1.000
0.992
1.015
1.007
1.008
1.000
0.998
0.990
1.002
0.994
0.982x1.026
=1.008
1.000
+/- 0.002
0.992
1.015
0.973
1.025
0.982
1.025
0.983
1.017
0.976
1.027
0.985
1.024
0.982
1.030
0.988
0.0200
0.0170
0.0277
0.0115
0.0220
0.0082
0.009
0.0273
0.0167
0.0135
0.0226
0.0091
0.0245
0.0071
0.0132
1.026
0.0227
0.984
0.0099
0.0059
0.0053
0.0059
0.0025
0.0028
0.0029
0.0039
Notes to Table 6:
* Means are compiled after the removal of F336 (large predicted uncertainty) and
F155W (preflashed on WF3 and WF4, but not on WF2).
** The PSF x Gain Ratios are used to determine the normalized ratios.
Our conclusions based on the 2-pixel aperture are:
1. The observed scatter (0.0227)is much higher than the predicted scatter (0.0039),
showing that the three WF chips do not have the same normalization when using the 2pixel aperture. The remaining sources of noise are (i.e.,
37
2
2
0.0227 – 0.0039 = 0.0224 ).
The
increased scatter compared to the 5-pixel aperture is probably due to differences in the
PSF, which are accentuated by the smaller aperture.
2. The observed ratios can be explained by the combination of the aperture correction
(taken from the F555W values from Whitmore et al. (1997) and the Holtzman (1995b)
gain ratios), since the mean scatter is reduced from 0.0227 to 0.0099, and Figure 19
shows a good correlation. We note that using the aperture ratios from Miller et al.
(1997) for the other filters does not work nearly as well, perhaps because of the larger
measurement uncertainties in these cases, or the slightly different radii for the annulus
used for the sky values. The F555W aperture correction measurement appears to provide an adequate estimate for all of the filters, with the possible exception of F336W
and preflashed F555W, which have not been included in the final analysis.
3. Using an uncertainty in the aperture corrections of 0.003 from the Whitmore et al.
(1997) measurements, the remaining value for the uncertainty due to the flat fields is
2
2
2
0.0099 – 0.0039 – 0.003 = 0.0085 ,
or less if there are other sources of noise not included
in the analysis.
4. Summary
The observations from WFPC2 calibration proposal 6195 provide a CONFIRMATION of the following effects, as noted in the Holtzman et al. (1995a, 1995b) papers.
1. The Charge Transfer Efficiency (CTE) loss is proportionally larger for fainter point
sources.
2. CTE loss is larger for frames with low background.
3. A 4 % linear ramp provides a reasonable correction for CTE in many cases (but not
all cases, see below).
The 6195 observations led to the following NEW RESULTS concerning CTE:
1. CTE loss is the same on all three WF chips, and appears to be the same on the PC, to
the degree it can be determined
2. CTE loss can range from about 2 % (even for bright stars on a bright background) to
about 15 % (faint stars on a faint background).
3. The dependence on the background has been quantified. A linear correlation in a
log-log plot provides a good characterization.
4. There appears to be a weak CTE problem in the X-axis (i.e., the stars on the right
side of the chip are fainter than on the left side) at the 1 - 5 % level.
5. Differences between the first and second exposure in a CR-SPLIT pair can be
understood in terms of the previous exposure acting as a preflash for the next exposure.
38
6. The formulae included in Section 2.7 can be used to correct for CTE loss when
using aperture photometry.
The 6195 observations also led to the following NEW RESULTS related to FLAT
FIELDS:
1. There is about a 2 % scatter in the normalization of the different chips. Nearly all of
this can be understood in terms of differences in the gain ratios and the aperture corrections. The mean (observed) values from Tables 5 and 6 can be used to normalize the
three WF chips.
2. Making corrections for CTE, aperture corrections, and gain ratios, reduces the RMS
scatter for a random observation from 4 - 7 % to about 2-3 %.
3. The flat fields are uniform to a level of at least 1.5 % across the chips, and 0.6 %
from chip-to-chip. Most of this uncertainty is probably related to other sources of
noise (e.g., variable PSFs), hence the flat-fields are probably much better than even
this level.
One final caveat is in order. It should be kept in mind that the results and formulae presented in this report have been derived from a single data set. While it is very likely that
the results are applicable to all WFPC2 data, especially since in the region of overlap (i.e.,
F555W observations) with past studies (Holtzman, 1995a, 1995b) the agreement is good,
it will be important to test this on other data sets (e.g., to see if there is any dependence on
time).
An update to this study has been posted on the WFPC2 webpage in the advisory section at
http://www.stsci.edu/ftp/instrument_news/WFPC2/wfpc2_advisory.html
39
Appendix A- Future Enhancements
1. Use some of the other fields which show up only in two chips, rather than all four
(see Figure 1).
2. Extend the range of the F336W and F439W CTE measurements to brighter objects
by including saturated stars in the master list used for cross referencing to remove cosmic rays.
3. Make slightly better determinations of CTE loss by using a 3-sigma clip of bad data
rather than constant limits (i.e., current throughput limits of 0.9 and 1.15 for bright
stars and 0.7 to 1.4 for faint stars). This would mainly be useful for aperture = 5 pixel
measurements which have larger errors for faint stars. This appears to be a very minor
problem based on tests using a variety of different cutoffs.
4. Determine if spatial dependence in the PSF is the main source of remaining noise by
mapping out the aperture corrections across the chip.
5. See if the use of the F606W sky flat reduces the scatter.
6. Look for asymmetries in the PSF, since the bottom half may act to help preflash the
top half.
7. Examine other data sets to see how relevant these results are to other observations,
and to see if there is any dependence with time. We are especially interested in
whether CTE increases with time, since ground tests of the STIS CCDs suggest that
they may.
8. Study first vs. second exposure differences in more detail using generic images from
the archives.
Appendix B - Potential Future Observations
1. Preflash F336W or F439W observations to see if higher CTE is really due to low
background rather than a wavelength dependence (Note: current plan is to include
F300W in proposal 7630).
3. Look for CTE in F170W (might be possible from 6935 data).
4. Look for CTE in narrow band images, since they have the same wavelength, but
very low background. Predict large CTE.
5. Test noiseless preflash (i.e., preflash, readout data, then take real data). Take several
very short observations (low background) to see how long (if at all) the improvement
in CTE persists (included in proposal 7630).
6. Look for CTE in short vs. long exposure time data (included in proposal 7630).
40
8. Do a single star at the top and bottom of a chip with no other stars on the chip. Compare this with cases where the background on the chip is the same, but lots of other
bright stars are also present.
References
Biretta, J. S., 1997, WFPC2 ISR-97-03
Burrows, C., 1994, WFPC2 ISR-94-01
Casertano, S., 1996, A Possible Non-Linearity in WFPC2 Observations, http://
www.stsci.edu/ftp/instrument_news/WFPC2/Wfpc2_cte/shortnlong.html
Ferguson, H., 1996, CTE Calibrations, http://www.stsci.edu/ftp/instrument_news/
WFPC2/Wfpc2_cte/cte.html
Fruchter, A., 1997, (private communication)
Holtzman J., et al. (the WFPC2 team), 1995a, PASP, 107, 156
Holtzman J., et al. (the WFPC2 team), 1995b, PASP, 107, 1065
Leitherer, C., 1995, The HST Data Handbook, http://www.stsci.edu/ftp/documents/
html/data-handbook.html
Miller, 1997, AJ, submitted
Whitmore, B. C., 1995, Calibrating the Hubble Space Telescope: Post Servicing Mission, ed. A. Koratkar and C. Leitherer, (STScI)
Whitmore, B. C., Miller, B. M., Schweizer, F., and Fall, S. M., 1997, AJ, submitted
Whitmore, B. C., et al., 1996, WFPC2 ISR-96-04
Whitmore, B. C., Wiggs, M. S., 1995, WFPC2 ISR-95-03
Acknowledgments
This paper has benefitted from discussions with a large number of people, including
John Biretta, Chris Burrows, Stefano Casertano, Harry Ferguson, Andy Fruchter, Ron Gilliland, John MacKenty, Peter Stetson, Massimo Stiavelli, and John Trauger.
41