The ACS CCDs have default gain values of approximately 2
/DN for both the WFC and HRC (prior to Cycle 14 the WFC default was 1
/DN). The relative values of gains 1 and 2 for the WFC are determined to an accuracy of about 1 part in 10,000. Although the original default settings were used to establish adjustments to basic quantum efficiency curves, current gains have consistent values. Minor errors in the default gain values would therefore be absorbed into revisions of the QE curves. There is no compelling reason to seek refinement in the quantitative values of the default used for primary calibrations and the bulk of the science program.
The default gain for the WFC does sample the full well depth of the CCDs.
However, for HRC, the default fell short by 22%. Use of the next higher gain value of approximately 4
/DN for the HRC provided full sampling of the 165,000
full well depth; since the readout noise was only marginally higher than with the default gain, and the readout noise for the HRC is nearly critically sampled, even at the higher gain value, (much more so than any WFPC2 data ever taken), many science and calibration programs may have logically chosen the higher gain.
ACS gain values in use between on-orbit installation (in March 2002) and January
2004 can be traced to ground test results. The primary tool for measuring gain values is the photon-transfer method which is described in the Appendix at
This technique relies on analysis of pairs of identical exposure flat fields taken at a
range of intensity levels. Over an ensemble of pixels at a given exposure level, the relation between differences of intensity values (noise) and the direct signal level depends on the readout noise and the gain. This relation can be fit at a range of intensity levels to uniquely determine these two quantities. This technique can also provide limited information on linearity1
and the saturation count level2
by determining where the photon-transfer curve departs from linearity at high signal levels. Errors of about 0.6% in the gain values are quoted for the WFC determinations, and similar values hold for the HRC as given at
On the WFC, with two CCDs and the default use of two readout amplifiers per
CCD, errors of 0.6% in the normalization of gains, quadrant-to-quadrant, would leave easily visible steps in observations of spatially flat sources. A redetermination of the WFC gains (ACS ISR 2002-03
), maintaining the same mean over all amplifiers at a given gain setting but using a continuity constraint across quadrant boundaries, provided an improvement in amplifier-to-amplifier gains at better than 0.1% for the default gains. Any steps of intensity seen in data across quadrant boundaries are likely to reflect minor errors in bias and overscan values (see Section 4.2
), rather than errors in relative gains.
As documented in ACS ISR 2004-01
, on-orbit data was used to redetermine the mean absolute gain values relative to the standard adopted for the default gains on each camera, e.g., WFC GAIN
1 and HRC GAIN
2 values were retained and other gains adjusted relative to these. Through analysis of observations of the same stellar field, in the same filter and at the two gain settings, it is possible to obtain accurate adjustments of these gain values relative to the default gain levels. The results discussed in the above-mentioned ISR supply these to better than 0.1%, removing errors that averaged about 1% for the two cameras prior to updates made in January 2004.
Absolute errors of about 0.6% could remain in the default gain values, but these are
of no real consequence since redetermination of the CCD quantum efficiency would compensate for this, since the QE adjustments were based on data acquired with the default gains. Basic photometric calibrations apply with equal accuracy to data acquired at all supported gains (assuming for the non-default gains that reprocessing was done after January 6, 2004 to include the revised values).
Tables Table 4.6
and Table 4.7
show the CCD gain values for pre-SM4 ACS operations, based on pre-launch and on-orbit calibrations.
Following SM4, the gains available with the new electronics are, in units of e−
/DN, 0.5, 1.0, 1.4, and 2.0. Only GAIN
2.0 is currently supported. New relative gain values were measured and are discussed in ACS ISR 2009-03
. The average absolute gain remains unchanged.
Conceptually, full well depths can be derived by analyzing images of a rich star
field taken at two significantly different exposure times, identifying bright but still unsaturated stars in the short exposure image, calculating which stars will saturate in the longer exposure and then simply recording the peak value reached for each star in electrons (using a gain that samples the full well depth, of course). In practice, as discussed in ACS ISR 2004-01
, it is also necessary to correct for a ~10% “piling-up” effect of higher values being reached at extreme levels of over-saturation relative to the value at which saturation and bleeding begins to neighboring pixels in the column.
Since the full well depth may vary over the CCDs, it is desired to have a rich star
field observed at a gain that samples the full well depth, and for which a large number of stars saturate. Calibration programs have serendipitously supplied the requisite data of rich fields observed at two different exposure times.
The HRC shows large scale variation of about 20% over the CCD. The smallest full
well depth values are at about 155,000
and the largest at about 185,000
, with 165,000
representing a rough estimate at an area- weighted average value. See Figure 3 of ACS ISR 2004-01
As with the HRC, there is a real and significant large scale variation of the full well
depth on the WFC CCDs. The variation over the WFC CCDs is from about 80,000
with a typical value of about 84,000
. There is a significant offset between the two CCDs. The spatial variation may be seen as Figure 4 in ACS ISR 2004-01
Rich star fields observed at quite different exposure times provide a simple, direct
test for linearity. In Figure 4.29
the results of such tests are shown in two ways. The first is a simple plot of aperture sum values in the long exposures versus the same stars on the same pixels in the short exposures—no deviations from linearity are evident.
For a more sensitive test the bottom plot shows the results of summing counts over
all stars within a defined magnitude range in the short and long exposure cases, separately, before then taking the ratio and normalizing to the relative exposure times.
The linearity of the HRC at low and moderate intensity levels, as evidenced by
comparing stars observed with exposures differing by a factor of 60, appears to be excellent.
The upper panel shows aperture sums over 9 pixels for all stars used over a range emphasizing
results at low to moderate count levels. The plotted line has a slope set by the relative exposure time. In the lower panel the ratio of counts in ensembles of stars divided into factor of two intensity bins, and further normalized by the relative exposure time are shown. One sigma error bars are derived based on the ensemble signal-to-noise of the short exposure case. The lowest bin has 81 stars, with typical values of 400 stars per bin above this.
In April 2002, one month after ACS’s installation, small-aperture stellar
photometry with WFC was very linear down to exposure levels of about 5
in the central pixel (Figure 4.31
). At this level, stars are not recognizable in single exposures. Since then, the degradation of CTE by radiation damage has significantly affected the photometric linearity of the WFC, especially for faint sources and low sky background. Figure 4.30
shows the measured and predicted CTE losses for point sources measured with small apertures and different sky background levels. As early as 2003, up to 5% of the signal from a faint source (30 sec. exposure of 20th mag. star through narrow band filters) was lost from the 3-pixel photometric aperture. Thus, any intrinsic non-linearity in the WFC CCDs at low signal levels became negligible compared with the normal losses expected from degraded CTE only a few months after ACS had been placed aboard HST.
The upper panel shows simple aperture sums, for long and short exposures, for all stars of low to
moderate intensity; the line has a slope set by the relative exposure times. The lower panel shows ratio of counts summed over all stars within intensity bins (in factor of two steps) for the 1200 sec. to mean 22.5 sec. exposures after normalization to the relative exposure time. To account for minor encirled energy differences for the very small 9 pixel (total, not radius) apertures used, all points have been normalized by 1.006, the initial value for the brightest bin. The error bars show ±
1σ deviations based on the total signal-to-noise of the short exposure sums. The number of stars per bin is typically about 400, although the lowest bin contains only 33 stars.
The response of the ACS CCDs remains linear not only up to, but well beyond,
the point of saturation when using a gain3
value that samples the full well depth. ACS ISR 2004-01
shows the well-behaved response of the ACS: electrons are clearly conserved after saturation. This result is similar to that of the STIS CCD (Gilliland et al., 1999, PASP, 111 1009-1020
) and the WFPC2 camera (Gilliland, R. L. 1994, ApJ, 435, L63-66). It is possible to perform photometry on point sources that remain isolated simply by summing over all of the pixels affected by bleeding if the gain value samples the full well depth. Given the larger dynamic range afforded before saturation at GAIN = 24
for WFC, and the only modestly-increased readout noise coupled with the potentially beneficial aspect of being able to recover photometry on saturated objects, a gain value of 2 for WFC, currently the default, remains an optimal choice for saturated star photometry.
The extent to which accurate photometry can be extracted for point sources in
which one or more pixels have exceeded the physical full well depth is explored in this section. Only the cases of GAIN
for the HRC and GAIN
for the WFC are considered, which provide direct sampling of the count levels independent of whether saturation has occurred. Ideal data for these tests consist of multiple exposures taken back-to-back on a moderate-to-rich star field with a broad range of exposure times resulting in both unsaturated and saturated data for many stars.
illustrates linearity beyond saturation. In the lower panel, peak values in the long exposure are plotted against peak values from the short exposure. Over the expected linear domain, points fall within a narrow cone centered on a line that has a slope equal to the exposure time ratio while above this the values in the long exposure saturates as expected. Deviations from lying perfectly along the line here result primarily from a 0.1
pixel offset between the images used for this test leading to different relative fractions of light falling on the central pixel.
The upper panel of Figure 4.32
shows the same stars but now using identical extraction apertures in the two exposures. The vertical line, near 205,000
on the x-axis is a separation point where stars below have a central pixel that remained unsaturated, while stars above had a saturated central pixel. There is no difference between the aperture photometry of point sources that are saturated up to 5 times the pixel-well depth, and those that are not. Within the domain sampled here the accuracy of saturated star photometry is much better than 1%.
The lower panel shows peak pixel values for many stars observed for 350 seconds (long) and 60 sec
onds (short) with the HRC. Over the range for which stars are unsaturated in both exposures, there is a linear relation with slope equal to exposure time ratio. Brighter stars in the long exposure saturate at values near the full well depth. The upper panel shows the same stars using photometry sums from identical apertures in both exposures; stars above the vertical mark near 205,000
, on the x-axis, separates stars that are saturated in the long exposure. The photometric response when summing over saturated pixels that have been bled into remains perfectly linear far beyond saturation of the central pixel at GAIN=4.
In Figure 4.33
, results for the WFC show that over a range of nearly 4 magnitudes beyond saturation, photometry remains linear to <
The lower panel shows peak pixel values for many stars observed for 340 seconds (long) and 10 sec
onds (short) with the WFC. Over the range for which stars are unsaturated in both exposures, there is a linear relation with slope equal to the exposure time ratio. Brighter stars in the long exposure saturate at values near the full well depth. The middle panel shows the same stars using photometry sums from identical apertures in both exposures; stars above the vertical mark near 12,350
, on the x-axis, separates stars that are saturated in the long exposure. The upper panel shows the ratio of long to short aperture sums normalized by the relative exposure time plotted against the degree of over-saturation in the central pixel of the long exposure. The lines in the top and middle panels represent the ideal case of perfect linearity in the pixel response. The fact that the data falls on the lines (or are symmetrically scattered about the lines) indicates that the WFC CCDs are close to perfectly linear. The photometric response when summing over saturated pixels that have been bled into remains perfectly linear far beyond the saturation of the central pixel at GAIN=2.
These linearity results are based upon comparisons of flt.fits
images. A comparison of long and short drizzled images show that the conservation of flux property by Drizzle leads to equally good results for linearity beyond saturation. An analysis of the drizzled data sets corresponding to Figure 4.33
showed equally impressive results.
For each detector, the shutter consists of two blades located in front of the CCD
entrance window. The optical path is blocked by one blade. When a command is sent to begin an exposure, the blade sweeps uniformly across the detector by 90°
to open the aperture, exposing the CCD for the commanded integration time. When the exposure is complete, the shutter rotates by another 90°
in the same direction so the second blade covers the aperture. A single exposure, therefore, rotates the shutter mechanism by 180°
, i.e., one blade opens the aperture while the other closes it. If the blades sweep at a uniform speed, all pixels will be exposed for an identical integration time. The shortest possible exposure time for WFC is 0.5 seconds, where the blade rotates continuously through 180°.
(A 0.6 sec integration time is not allowed.) For more information about the shutter, please refer to the report “WFC and HRC Shutter Shading and Accuracy (Feb. 2001)
,” by Martel, G. Hartig, and M. Sirianni.
For short exposure times, field dependent timing (shutter shading), “A
” versus “B
” blade shutter5
control dependence, stability, and timing accuracy were assessed for the HRC and WFC during ground-based testing and through utilizing on-orbit data. The ground results using time variable flat-field sources suggested deviations in actual versus nominal exposure times up to, but no larger than ~1% for short exposures of less than 1.0 sec.
Even at the shortest exposures, shutter shading measures did not exceed ~0.5%
center-to-edge for either camera. This supports a previous decision to not actively invoke a shading correction in calacs
No systematic biases in timing reach the 0.5% level for any average over multiple
pairs at any exposure time when switching between A
shutter control. This supports not actively utilizing a record of which shutter was used.
Stability of shutter timing was a bit more problematic. For the HRC, stability
appeared excellent when measured as rms across several exposures, and the errors remain well under 0.5%. At exposure times of 1.0 second, peak-to-peak fluctuations on the HRC were at the 0.1% level. Only at 0.1 seconds
the HRC exposures exhibit peak-to-peak fluctuations up to ~1.0% (and part of this may have been measurement error).
The WFC shutter timing stability was not as good, but was also more difficult to
quantify given a higher level of systematic errors. Again, measured as an rms across several exposures, errors were well under 0.5%. However, out of 7 pairs of back-to-back 1.0 second exposures, two of the pairs had individual components differing by > 1.3%. Where such differences existed on WFC, it was always the case that shutter timing under A
control was shorter than the following B
exposure. At 0.5 seconds on WFC (where shutter operation is one continuous rotation), the greatest discrepancy between A
remained < 0.3%. These results suggest that if generally short WFC exposures are required (where short is taken to be < 2 seconds), then 0.5 second exposures appear to be stable and would likely support 1% accuracy, but exposures in the range of 0.7 seconds to less than 2.0 seconds may experience timing fluctuations that could compromise such accuracy. This conclusion regarding WFC exposures is not regarded as robust, but is offered as that most consistent with a simple and conservative interpretation of the test data.
In adopting a threshold of 0.5% in absolute timing, only 4 exposure times over
HRC and WFC required revisions from pre-launch values. The 0.1 second HRC exposure is actually larger by 4.1%, while WFC exposures at 0.5 seconds, 0.7 seconds and 0.8 seconds in reality differ
by +1.6%, -1.0% and -0.6% respectively. For these four exposures, using revised exposure times in calacs
was recommended in order to support accurate photometry; retrievals made after March 11, 2004 will have invoked use of these corrected values.