Contribution for 2002 HST Calibration Workshop proceedings available here.
Equations last updated July 19, 2008.
Previous equations:
Since SM3B (March 2002), WF4 data have suffered from what is called the "WF4 Anomaly". Further details about this can be found at STScI's WFPC2 pages, most notably ISR 0502.
From the residuals to the CTE and zero point correction solutions presented here, two key times can be located. Beginning at the time of SM3B (March 2002), an increasing number of images with low bias appeared (as has been documented well in the STScI sources referenced above). In addition, my preliminary analysis indicates a significant change to the XCTE losses at this time (perhaps tripled or more).
The second key time was the temperature reductions in the WF4 electronics that were designed to combat the anomaly. This had the effect of significantly reducing the YCTE loss (perhaps by 20%).
The photometric effects have not yet been adequately calibrated in this work, so I have omitted all WF4 data from March 2002 onwards in deriving the equations below. This means that calibration of WF4 data may not be as reliable as the other chips, even if one applies the streak and count level corrections as recommended in ISR 0502.
The remaining data (PC, WF2, and WF3) fit the lifetime curves very well, with average residuals under 1% per chip or filter, and less than 0.02 magnitudes per dex of star brightness or background level.
The recommended CTE correction below is more complex than usual CTE equations, to allow for the fact that the star brightness is not constant as it is read out, and therefore that the CTE loss per pixel changes during readout. The recipe for correction is as follows:
First, calculate the following variable values:
Second, correct for the CTE loss in X readout:
Third, recalculate lct using:
Finally, correct for the CTE loss in Y readout:
Uncertainties of the parameters:
Note that the background level should equal the true background of the image. For a sky measured near the star, there is usually some starlight in the sky annulus that can cause confusion. For images with low background levels, this can become a major fraction of the measured background.
Also note that the choice of photometry parameters can affect the CTE solution, as CTE loss affects the PSF for very faint sources. The solution here is for the default HSTphot parameters -- a PSF-fit inside a small (3 pixel PC, 2 pixel WFC) aperture.
GAIN=7 | GAIN=14 | |||||||
---|---|---|---|---|---|---|---|---|
Filter | PC1 | WFC2 | WFC3 | WFC4 | PC1 | WFC2 | WFC3 | WFC4 |
F439W | 0.058 +/- 0.007 | 0.060 +/- 0.004 | 0.054 +/- 0.004 | 0.066 +/- 0.004 | 0.036 +/- 0.002 | 0.058 +/- 0.001 | 0.034 +/- 0.001 | 0.058 +/- 0.001 |
F555W | 0.035 +/- 0.002 | 0.038 +/- 0.001 | 0.034 +/- 0.002 | 0.040 +/- 0.001 | 0.029 +/- 0.002 | 0.028 +/- 0.001 | 0.029 +/- 0.001 | 0.043 +/- 0.001 |
F675W | 0.048 +/- 0.006 | 0.048 +/- 0.003 | 0.040 +/- 0.004 | 0.055 +/- 0.004 | 0.030 +/- 0.002 | 0.048 +/- 0.001 | 0.039 +/- 0.001 | 0.042 +/- 0.002 |
F814W | 0.006 +/- 0.001 | 0.031 +/- 0.000 | 0.026 +/- 0.001 | 0.024 +/- 0.001 | 0.015 +/- 0.001 | 0.031 +/- 0.001 | 0.019 +/- 0.001 | 0.022 +/- 0.001 |
Filter | Std Filt | offset |
---|---|---|
F300W | F336W | -0.000 +/- 0.000 |
F380W | F439W | 0.079 +/- 0.003 |
F410M | F439W | 0.052 +/- 0.004 |
F450W | F439W | -0.006 +/- 0.004 |
F467M | F439W | -0.068 +/- 0.003 |
F547M | F555W | -0.004 +/- 0.002 |
F569W | F555W | -0.022 +/- 0.002 |
F606W | F555W | -0.018 +/- 0.002 |
F622W | F675W | -0.015 +/- 0.005 |
F702W | F675W | 0.006 +/- 0.002 |
F785LP | F814W | 0.005 +/- 0.003 |
F791W | F814W | -0.020 +/- 0.006 |
F850LP | F814W | 0.004 +/- 0.005 |
F1042M | F814W | 0.069 +/- 0.009 |
Filter | PC1 | WFC2 | WFC3 | WFC4 |
---|---|---|---|---|
F380W | 20.994 +/- 0.008 | 21.007 +/- 0.005 | 21.008 +/- 0.005 | 20.991 +/- 0.005 |
F410M | 19.353 +/- 0.008 | 19.366 +/- 0.005 | 19.367 +/- 0.006 | 19.349 +/- 0.005 |
F439W | 20.866 +/- 0.007 | 20.879 +/- 0.004 | 20.880 +/- 0.004 | 20.863 +/- 0.004 |
F450W | 21.963 +/- 0.008 | 21.975 +/- 0.005 | 21.976 +/- 0.006 | 21.959 +/- 0.005 |
F467M | 19.888 +/- 0.008 | 19.900 +/- 0.005 | 19.901 +/- 0.005 | 19.884 +/- 0.005 |
F547M | 21.609 +/- 0.003 | 21.622 +/- 0.003 | 21.625 +/- 0.003 | 21.601 +/- 0.003 |
F555W | 22.498 +/- 0.002 | 22.511 +/- 0.001 | 22.515 +/- 0.002 | 22.491 +/- 0.001 |
F569W | 22.171 +/- 0.003 | 22.184 +/- 0.003 | 22.188 +/- 0.003 | 22.164 +/- 0.003 |
F606W | 22.839 +/- 0.003 | 22.853 +/- 0.002 | 22.856 +/- 0.003 | 22.832 +/- 0.002 |
F622W | 22.314 +/- 0.008 | 22.324 +/- 0.006 | 22.323 +/- 0.006 | 22.309 +/- 0.006 |
F675W | 22.020 +/- 0.006 | 22.031 +/- 0.003 | 22.030 +/- 0.004 | 22.016 +/- 0.004 |
F702W | 22.420 +/- 0.007 | 22.430 +/- 0.004 | 22.429 +/- 0.005 | 22.415 +/- 0.004 |
F785LP | 20.626 +/- 0.003 | 20.662 +/- 0.003 | 20.664 +/- 0.003 | 20.633 +/- 0.003 |
F791W | 21.431 +/- 0.006 | 21.467 +/- 0.006 | 21.469 +/- 0.006 | 21.438 +/- 0.006 |
F814W | 21.583 +/- 0.001 | 21.619 +/- 0.000 | 21.621 +/- 0.001 | 21.590 +/- 0.001 |
F850LP | 19.888 +/- 0.005 | 19.924 +/- 0.005 | 19.926 +/- 0.005 | 19.895 +/- 0.005 |
F1042M | 16.180 +/- 0.009 | 16.216 +/- 0.009 | 16.218 +/- 0.009 | 16.187 +/- 0.009 |
Filter | PC1 | WFC2 | WFC3 | WFC4 |
---|---|---|---|---|
F380W | 20.227 +/- 0.004 | 20.251 +/- 0.004 | 20.232 +/- 0.004 | 20.254 +/- 0.004 |
F410M | 18.586 +/- 0.004 | 18.610 +/- 0.004 | 18.591 +/- 0.004 | 18.613 +/- 0.004 |
F439W | 20.099 +/- 0.002 | 20.123 +/- 0.001 | 20.104 +/- 0.001 | 20.126 +/- 0.001 |
F450W | 21.196 +/- 0.004 | 21.220 +/- 0.004 | 21.201 +/- 0.004 | 21.223 +/- 0.004 |
F467M | 19.121 +/- 0.004 | 19.145 +/- 0.003 | 19.126 +/- 0.003 | 19.148 +/- 0.003 |
F547M | 20.857 +/- 0.003 | 20.857 +/- 0.002 | 20.865 +/- 0.003 | 20.877 +/- 0.003 |
F555W | 21.747 +/- 0.002 | 21.747 +/- 0.001 | 21.754 +/- 0.001 | 21.767 +/- 0.001 |
F569W | 21.420 +/- 0.003 | 21.420 +/- 0.002 | 21.427 +/- 0.003 | 21.439 +/- 0.003 |
F606W | 22.088 +/- 0.003 | 22.088 +/- 0.002 | 22.095 +/- 0.002 | 22.108 +/- 0.002 |
F622W | 21.550 +/- 0.006 | 21.571 +/- 0.005 | 21.567 +/- 0.005 | 21.568 +/- 0.005 |
F675W | 21.257 +/- 0.002 | 21.277 +/- 0.001 | 21.273 +/- 0.001 | 21.274 +/- 0.002 |
F702W | 21.656 +/- 0.003 | 21.677 +/- 0.002 | 21.673 +/- 0.003 | 21.674 +/- 0.003 |
F785LP | 19.890 +/- 0.003 | 19.908 +/- 0.003 | 19.901 +/- 0.003 | 19.903 +/- 0.003 |
F791W | 20.695 +/- 0.006 | 20.712 +/- 0.006 | 20.706 +/- 0.006 | 20.707 +/- 0.006 |
F814W | 20.847 +/- 0.001 | 20.864 +/- 0.001 | 20.858 +/- 0.001 | 20.859 +/- 0.001 |
F850LP | 19.152 +/- 0.005 | 19.170 +/- 0.005 | 19.163 +/- 0.005 | 19.164 +/- 0.005 |
F1042M | 15.444 +/- 0.009 | 15.462 +/- 0.009 | 15.455 +/- 0.009 | 15.456 +/- 0.009 |
note: WFPC2mag = -2.5 log (DN/s) + ZP(FG) - CTE
ZP(FG) from above tables
CTE calculated from above equations
Filter | SMAG | SCOL | ZP(PC1) | ZP(WFC2) | ZP(WFC3) | ZP(WFC4) | T1 | T2 | Cmin | Cmax |
---|---|---|---|---|---|---|---|---|---|---|
F380W | B | (B-V) | 21.019 | 21.032 | 21.033 | 21.016 | -0.581 | 0.777 | ... | 0.5 |
F380W | B | (B-V) | 21.371 | 21.384 | 21.385 | 21.368 | -0.943 | 0.103 | 0.5 | ... |
F410M | B | (B-V) | 19.663 | 19.676 | 19.677 | 19.659 | -0.183 | -0.287 | ... | ... |
F439W | B | (U-B) | 20.853 | 20.866 | 20.867 | 20.850 | -0.103 | -0.046 | ... | ... |
F439W | B | (B-V) | 20.866 | 20.879 | 20.880 | 20.863 | 0.003 | -0.088 | ... | ... |
F439W | B | (B-R) | 20.860 | 20.873 | 20.874 | 20.857 | 0.019 | -0.049 | ... | ... |
F439W | B | (B-I) | 20.863 | 20.876 | 20.877 | 20.860 | 0.005 | -0.023 | ... | ... |
F450W | B | (B-V) | 21.965 | 21.977 | 21.978 | 21.961 | 0.230 | -0.003 | ... | ... |
F467M | B | (B-V) | 19.895 | 19.907 | 19.908 | 19.891 | 0.480 | -0.299 | ... | 0.5 |
F467M | B | (B-V) | 19.846 | 19.858 | 19.859 | 19.842 | 0.432 | -0.002 | 0.5 | ... |
F547M | V | (B-V) | 21.604 | 21.617 | 21.620 | 21.596 | 0.031 | -0.039 | ... | 1.0 |
F547M | V | (B-V) | 21.556 | 21.569 | 21.572 | 21.548 | 0.056 | -0.016 | 1.0 | ... |
F547M | V | (V-I) | 21.604 | 21.617 | 21.620 | 21.596 | 0.027 | -0.032 | ... | 1.1 |
F547M | V | (V-I) | 21.556 | 21.569 | 21.572 | 21.548 | 0.049 | -0.013 | 1.1 | ... |
F555W | V | (U-V) | 22.479 | 22.492 | 22.496 | 22.472 | -0.014 | 0.005 | ... | ... |
F555W | V | (B-V) | 22.498 | 22.511 | 22.515 | 22.491 | -0.060 | 0.033 | ... | ... |
F555W | V | (V-R) | 22.503 | 22.516 | 22.520 | 22.496 | -0.121 | 0.120 | ... | ... |
F555W | V | (V-I) | 22.498 | 22.511 | 22.515 | 22.491 | -0.052 | 0.027 | ... | ... |
F569W | V | (V-I) | 22.169 | 22.182 | 22.186 | 22.162 | 0.089 | -0.003 | ... | 2.0 |
F569W | V | (V-I) | 22.501 | 22.514 | 22.518 | 22.494 | -0.125 | 0.022 | 2.0 | ... |
F606W | V | (B-V) | 22.848 | 22.862 | 22.865 | 22.841 | 0.293 | 0.015 | ... | 1.7 |
F606W | V | (B-V) | 23.638 | 23.652 | 23.655 | 23.631 | -0.284 | 0.081 | 1.7 | ... |
F606W | V | (V-I) | 22.848 | 22.862 | 22.865 | 22.841 | 0.254 | 0.012 | ... | 2.0 |
F606W | V | (V-I) | 23.638 | 23.652 | 23.655 | 23.631 | -0.247 | 0.065 | 2.0 | ... |
F622W | R | (V-R) | 22.328 | 22.338 | 22.337 | 22.323 | -0.252 | -0.111 | ... | ... |
F675W | R | (U-R) | 22.040 | 22.051 | 22.050 | 22.036 | 0.039 | -0.007 | ... | ... |
F675W | R | (B-R) | 22.021 | 22.032 | 22.031 | 22.017 | 0.092 | -0.017 | ... | ... |
F675W | R | (V-R) | 22.020 | 22.031 | 22.030 | 22.016 | 0.253 | -0.125 | ... | ... |
F675W | R | (R-I) | 22.011 | 22.022 | 22.021 | 22.007 | 0.273 | -0.066 | ... | ... |
F702W | R | (V-R) | 22.425 | 22.435 | 22.434 | 22.420 | 0.343 | -0.177 | ... | 0.6 |
F702W | R | (V-R) | 22.303 | 22.313 | 22.312 | 22.298 | 0.486 | -0.079 | 0.6 | ... |
F785LP | I | (V-I) | 20.629 | 20.665 | 20.667 | 20.636 | 0.091 | 0.020 | ... | ... |
F791W | I | (V-I) | 21.431 | 21.467 | 21.469 | 21.438 | -0.029 | -0.004 | ... | 1.0 |
F791W | I | (V-I) | 21.472 | 21.508 | 21.510 | 21.479 | -0.084 | 0.011 | 1.0 | ... |
F814W | I | (U-I) | 21.559 | 21.595 | 21.597 | 21.566 | -0.018 | 0.002 | ... | ... |
F814W | I | (B-I) | 21.579 | 21.615 | 21.617 | 21.586 | -0.031 | 0.007 | ... | ... |
F814W | I | (V-I) | 21.583 | 21.619 | 21.621 | 21.590 | -0.062 | 0.025 | ... | ... |
F814W | I | (R-I) | 21.583 | 21.619 | 21.621 | 21.590 | -0.112 | 0.084 | ... | ... |
F850LP | I | (V-I) | 19.870 | 19.906 | 19.908 | 19.877 | 0.160 | 0.023 | ... | ... |
F1042M | I | (V-I) | 16.127 | 16.163 | 16.165 | 16.134 | 0.350 | 0.022 | ... | ... |
Filter | SMAG | SCOL | ZP(PC1) | ZP(WFC2) | ZP(WFC3) | ZP(WFC4) | T1 | T2 | Cmin | Cmax |
---|---|---|---|---|---|---|---|---|---|---|
F380W | B | (B-V) | 20.252 | 20.276 | 20.257 | 20.279 | -0.581 | 0.777 | ... | 0.5 |
F380W | B | (B-V) | 20.604 | 20.628 | 20.609 | 20.631 | -0.943 | 0.103 | 0.5 | ... |
F410M | B | (B-V) | 18.896 | 18.920 | 18.901 | 18.923 | -0.183 | -0.287 | ... | ... |
F439W | B | (U-B) | 20.086 | 20.110 | 20.091 | 20.113 | -0.103 | -0.046 | ... | ... |
F439W | B | (B-V) | 20.099 | 20.123 | 20.104 | 20.126 | 0.003 | -0.088 | ... | ... |
F439W | B | (B-R) | 20.093 | 20.117 | 20.098 | 20.120 | 0.019 | -0.049 | ... | ... |
F439W | B | (B-I) | 20.096 | 20.120 | 20.101 | 20.123 | 0.005 | -0.023 | ... | ... |
F450W | B | (B-V) | 21.198 | 21.222 | 21.203 | 21.225 | 0.230 | -0.003 | ... | ... |
F467M | B | (B-V) | 19.128 | 19.152 | 19.133 | 19.155 | 0.480 | -0.299 | ... | 0.5 |
F467M | B | (B-V) | 19.079 | 19.103 | 19.084 | 19.106 | 0.432 | -0.002 | 0.5 | ... |
F547M | V | (B-V) | 20.852 | 20.852 | 20.860 | 20.872 | 0.031 | -0.039 | ... | 1.0 |
F547M | V | (B-V) | 20.804 | 20.804 | 20.812 | 20.824 | 0.056 | -0.016 | 1.0 | ... |
F547M | V | (V-I) | 20.852 | 20.852 | 20.860 | 20.872 | 0.027 | -0.032 | ... | 1.1 |
F547M | V | (V-I) | 20.804 | 20.804 | 20.812 | 20.824 | 0.049 | -0.013 | 1.1 | ... |
F555W | V | (U-V) | 21.728 | 21.728 | 21.735 | 21.748 | -0.014 | 0.005 | ... | ... |
F555W | V | (B-V) | 21.747 | 21.747 | 21.754 | 21.767 | -0.060 | 0.033 | ... | ... |
F555W | V | (V-R) | 21.752 | 21.752 | 21.759 | 21.772 | -0.121 | 0.120 | ... | ... |
F555W | V | (V-I) | 21.747 | 21.747 | 21.754 | 21.767 | -0.052 | 0.027 | ... | ... |
F569W | V | (V-I) | 21.418 | 21.418 | 21.425 | 21.437 | 0.089 | -0.003 | ... | 2.0 |
F569W | V | (V-I) | 21.750 | 21.750 | 21.757 | 21.769 | -0.125 | 0.022 | 2.0 | ... |
F606W | V | (B-V) | 22.097 | 22.097 | 22.104 | 22.117 | 0.293 | 0.015 | ... | 1.7 |
F606W | V | (B-V) | 22.887 | 22.887 | 22.894 | 22.907 | -0.284 | 0.081 | 1.7 | ... |
F606W | V | (V-I) | 22.097 | 22.097 | 22.104 | 22.117 | 0.254 | 0.012 | ... | 2.0 |
F606W | V | (V-I) | 22.887 | 22.887 | 22.894 | 22.907 | -0.247 | 0.065 | 2.0 | ... |
F622W | R | (V-R) | 21.564 | 21.585 | 21.581 | 21.582 | -0.252 | -0.111 | ... | ... |
F675W | R | (U-R) | 21.277 | 21.297 | 21.293 | 21.294 | 0.039 | -0.007 | ... | ... |
F675W | R | (B-R) | 21.258 | 21.278 | 21.274 | 21.275 | 0.092 | -0.017 | ... | ... |
F675W | R | (V-R) | 21.257 | 21.277 | 21.273 | 21.274 | 0.253 | -0.125 | ... | ... |
F675W | R | (R-I) | 21.248 | 21.268 | 21.264 | 21.265 | 0.273 | -0.066 | ... | ... |
F702W | R | (V-R) | 21.661 | 21.682 | 21.678 | 21.679 | 0.343 | -0.177 | ... | 0.6 |
F702W | R | (V-R) | 21.539 | 21.560 | 21.556 | 21.557 | 0.486 | -0.079 | 0.6 | ... |
F785LP | I | (V-I) | 19.893 | 19.911 | 19.904 | 19.906 | 0.091 | 0.020 | ... | ... |
F791W | I | (V-I) | 20.695 | 20.712 | 20.706 | 20.707 | -0.029 | -0.004 | ... | 1.0 |
F791W | I | (V-I) | 20.736 | 20.753 | 20.747 | 20.748 | -0.084 | 0.011 | 1.0 | ... |
F814W | I | (U-I) | 20.823 | 20.840 | 20.834 | 20.835 | -0.018 | 0.002 | ... | ... |
F814W | I | (B-I) | 20.843 | 20.860 | 20.854 | 20.855 | -0.031 | 0.007 | ... | ... |
F814W | I | (V-I) | 20.847 | 20.864 | 20.858 | 20.859 | -0.062 | 0.025 | ... | ... |
F814W | I | (R-I) | 20.847 | 20.864 | 20.858 | 20.859 | -0.112 | 0.084 | ... | ... |
F850LP | I | (V-I) | 19.134 | 19.152 | 19.145 | 19.146 | 0.160 | 0.023 | ... | ... |
F1042M | I | (V-I) | 15.391 | 15.409 | 15.402 | 15.403 | 0.350 | 0.022 | ... | ... |
note: SMAG = -2.5 log (DN/s) + ZP(FS) + T1 SCOL + T2 SCOL^2 - CTE
ZP(FS), T1, and T2 from above tables
CTE calculated from above equations
"WFPC2 Stellar Photometry with HSTphot." Dolphin, A. E. 2000, PASP, 112, 1383