Contribution for 2002 HST Calibration Workshop proceedings available here.
Equations last updated December 20, 2004.
Previous equations:

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 roughly constant, 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. Using smaller apertures appears to increase the X-CTE to approximately 0.022*x/800 (with a minimal background dependence).

| GAIN=7 | GAIN=14 | |||||||
|---|---|---|---|---|---|---|---|---|
| Filter | PC1 | WFC2 | WFC3 | WFC4 | PC1 | WFC2 | WFC3 | WFC4 |
| F439W | 0.057 +/- 0.009 | 0.046 +/- 0.004 | 0.051 +/- 0.005 | 0.066 +/- 0.004 | 0.044 +/- 0.002 | 0.053 +/- 0.001 | 0.045 +/- 0.001 | 0.058 +/- 0.001 |
| F555W | 0.038 +/- 0.003 | 0.034 +/- 0.001 | 0.033 +/- 0.002 | 0.035 +/- 0.001 | 0.027 +/- 0.002 | 0.029 +/- 0.001 | 0.031 +/- 0.001 | 0.042 +/- 0.002 |
| F675W | 0.034 +/- 0.006 | 0.040 +/- 0.003 | 0.031 +/- 0.003 | 0.046 +/- 0.003 | 0.025 +/- 0.002 | 0.043 +/- 0.001 | 0.034 +/- 0.001 | 0.034 +/- 0.002 |
| F814W | 0.019 +/- 0.002 | 0.022 +/- 0.001 | 0.025 +/- 0.003 | 0.020 +/- 0.001 | 0.013 +/- 0.002 | 0.020 +/- 0.001 | 0.012 +/- 0.001 | 0.016 +/- 0.001 |
| Filter | Std Filt | offset |
|---|---|---|
| F300W | F336W | -0.000 +/- 0.000 |
| F380W | F439W | 0.076 +/- 0.004 |
| F410M | F439W | 0.066 +/- 0.004 |
| F450W | F439W | -0.006 +/- 0.003 |
| F467M | F439W | -0.060 +/- 0.003 |
| F547M | F555W | -0.006 +/- 0.002 |
| F569W | F555W | -0.020 +/- 0.003 |
| F606W | F555W | -0.020 +/- 0.002 |
| F622W | F675W | -0.004 +/- 0.005 |
| F702W | F675W | 0.010 +/- 0.002 |
| F785LP | F814W | 0.006 +/- 0.002 |
| F791W | F814W | -0.023 +/- 0.005 |
| F850LP | F814W | 0.005 +/- 0.004 |
| F1042M | F814W | -0.000 +/- 0.000 |

| Filter | PC1 | WFC2 | WFC3 | WFC4 |
|---|---|---|---|---|
| F380W | 20.991 +/- 0.010 | 20.990 +/- 0.006 | 21.002 +/- 0.006 | 20.987 +/- 0.005 |
| F410M | 19.366 +/- 0.010 | 19.365 +/- 0.006 | 19.377 +/- 0.006 | 19.363 +/- 0.005 |
| F439W | 20.866 +/- 0.009 | 20.865 +/- 0.004 | 20.877 +/- 0.005 | 20.862 +/- 0.004 |
| F450W | 21.962 +/- 0.010 | 21.961 +/- 0.005 | 21.973 +/- 0.006 | 21.959 +/- 0.005 |
| F467M | 19.896 +/- 0.010 | 19.895 +/- 0.005 | 19.907 +/- 0.006 | 19.892 +/- 0.005 |
| F547M | 21.609 +/- 0.004 | 21.616 +/- 0.003 | 21.622 +/- 0.003 | 21.595 +/- 0.003 |
| F555W | 22.501 +/- 0.003 | 22.508 +/- 0.001 | 22.514 +/- 0.002 | 22.487 +/- 0.001 |
| F569W | 22.175 +/- 0.004 | 22.182 +/- 0.003 | 22.189 +/- 0.004 | 22.161 +/- 0.003 |
| F606W | 22.840 +/- 0.004 | 22.847 +/- 0.002 | 22.853 +/- 0.003 | 22.825 +/- 0.002 |
| F622W | 22.311 +/- 0.008 | 22.328 +/- 0.006 | 22.326 +/- 0.006 | 22.312 +/- 0.006 |
| F675W | 22.006 +/- 0.006 | 22.023 +/- 0.003 | 22.020 +/- 0.003 | 22.007 +/- 0.003 |
| F702W | 22.410 +/- 0.007 | 22.427 +/- 0.004 | 22.424 +/- 0.004 | 22.411 +/- 0.004 |
| F785LP | 20.641 +/- 0.003 | 20.654 +/- 0.003 | 20.665 +/- 0.004 | 20.630 +/- 0.003 |
| F791W | 21.441 +/- 0.005 | 21.455 +/- 0.005 | 21.465 +/- 0.006 | 21.430 +/- 0.005 |
| F814W | 21.597 +/- 0.002 | 21.610 +/- 0.001 | 21.620 +/- 0.003 | 21.585 +/- 0.001 |
| F850LP | 19.903 +/- 0.005 | 19.916 +/- 0.004 | 19.927 +/- 0.005 | 19.892 +/- 0.005 |
| F1042M | 16.125 +/- 0.002 | 16.138 +/- 0.001 | 16.148 +/- 0.003 | 16.113 +/- 0.001 |
| Filter | PC1 | WFC2 | WFC3 | WFC4 |
|---|---|---|---|---|
| F380W | 20.232 +/- 0.004 | 20.243 +/- 0.004 | 20.240 +/- 0.004 | 20.252 +/- 0.004 |
| F410M | 18.607 +/- 0.004 | 18.618 +/- 0.004 | 18.615 +/- 0.004 | 18.627 +/- 0.004 |
| F439W | 20.107 +/- 0.002 | 20.117 +/- 0.001 | 20.115 +/- 0.001 | 20.126 +/- 0.001 |
| F450W | 21.203 +/- 0.004 | 21.214 +/- 0.003 | 21.211 +/- 0.003 | 21.223 +/- 0.003 |
| F467M | 19.137 +/- 0.004 | 19.148 +/- 0.003 | 19.145 +/- 0.003 | 19.157 +/- 0.003 |
| F547M | 20.853 +/- 0.003 | 20.856 +/- 0.003 | 20.864 +/- 0.003 | 20.873 +/- 0.003 |
| F555W | 21.745 +/- 0.002 | 21.748 +/- 0.001 | 21.756 +/- 0.001 | 21.765 +/- 0.002 |
| F569W | 21.420 +/- 0.003 | 21.423 +/- 0.003 | 21.431 +/- 0.003 | 21.440 +/- 0.003 |
| F606W | 22.084 +/- 0.002 | 22.087 +/- 0.002 | 22.095 +/- 0.002 | 22.104 +/- 0.002 |
| F622W | 21.557 +/- 0.005 | 21.577 +/- 0.005 | 21.574 +/- 0.005 | 21.572 +/- 0.005 |
| F675W | 21.252 +/- 0.002 | 21.272 +/- 0.001 | 21.268 +/- 0.001 | 21.267 +/- 0.002 |
| F702W | 21.655 +/- 0.003 | 21.676 +/- 0.003 | 21.672 +/- 0.003 | 21.670 +/- 0.003 |
| F785LP | 19.889 +/- 0.003 | 19.898 +/- 0.003 | 19.895 +/- 0.003 | 19.898 +/- 0.003 |
| F791W | 20.689 +/- 0.005 | 20.698 +/- 0.005 | 20.696 +/- 0.005 | 20.698 +/- 0.005 |
| F814W | 20.845 +/- 0.002 | 20.854 +/- 0.001 | 20.851 +/- 0.001 | 20.853 +/- 0.001 |
| F850LP | 19.151 +/- 0.005 | 19.160 +/- 0.004 | 19.157 +/- 0.005 | 19.159 +/- 0.005 |
| F1042M | 15.373 +/- 0.002 | 15.382 +/- 0.001 | 15.379 +/- 0.001 | 15.381 +/- 0.001 |
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) | 21.016 | 21.015 | 21.027 | 21.012 | -0.581 | 0.777 | ... | 0.5 |
| F380W | B | (B-V) | 21.368 | 21.367 | 21.379 | 21.364 | -0.943 | 0.103 | 0.5 | ... |
| F410M | B | (B-V) | 19.676 | 19.675 | 19.687 | 19.673 | -0.183 | -0.287 | ... | ... |
| F439W | B | (U-B) | 20.853 | 20.852 | 20.864 | 20.849 | -0.103 | -0.046 | ... | ... |
| F439W | B | (B-V) | 20.866 | 20.865 | 20.877 | 20.862 | 0.003 | -0.088 | ... | ... |
| F439W | B | (B-R) | 20.860 | 20.859 | 20.871 | 20.856 | 0.019 | -0.049 | ... | ... |
| F439W | B | (B-I) | 20.863 | 20.862 | 20.874 | 20.859 | 0.005 | -0.023 | ... | ... |
| F450W | B | (B-V) | 21.964 | 21.963 | 21.975 | 21.961 | 0.230 | -0.003 | ... | ... |
| F467M | B | (B-V) | 19.903 | 19.902 | 19.914 | 19.899 | 0.480 | -0.299 | ... | 0.5 |
| F467M | B | (B-V) | 19.854 | 19.853 | 19.865 | 19.850 | 0.432 | -0.002 | 0.5 | ... |
| F547M | V | (B-V) | 21.604 | 21.611 | 21.617 | 21.590 | 0.031 | -0.039 | ... | 1.0 |
| F547M | V | (B-V) | 21.556 | 21.563 | 21.569 | 21.542 | 0.056 | -0.016 | 1.0 | ... |
| F547M | V | (V-I) | 21.604 | 21.611 | 21.617 | 21.590 | 0.027 | -0.032 | ... | 1.1 |
| F547M | V | (V-I) | 21.556 | 21.563 | 21.569 | 21.542 | 0.049 | -0.013 | 1.1 | ... |
| F555W | V | (U-V) | 22.482 | 22.489 | 22.495 | 22.468 | -0.014 | 0.005 | ... | ... |
| F555W | V | (B-V) | 22.501 | 22.508 | 22.514 | 22.487 | -0.060 | 0.033 | ... | ... |
| F555W | V | (V-R) | 22.506 | 22.513 | 22.519 | 22.492 | -0.121 | 0.120 | ... | ... |
| F555W | V | (V-I) | 22.501 | 22.508 | 22.514 | 22.487 | -0.052 | 0.027 | ... | ... |
| F569W | V | (V-I) | 22.173 | 22.180 | 22.187 | 22.159 | 0.089 | -0.003 | ... | 2.0 |
| F569W | V | (V-I) | 22.505 | 22.512 | 22.519 | 22.491 | -0.125 | 0.022 | 2.0 | ... |
| F606W | V | (B-V) | 22.849 | 22.856 | 22.862 | 22.834 | 0.293 | 0.015 | ... | 1.7 |
| F606W | V | (B-V) | 23.639 | 23.646 | 23.652 | 23.624 | -0.284 | 0.081 | 1.7 | ... |
| F606W | V | (V-I) | 22.849 | 22.856 | 22.862 | 22.834 | 0.254 | 0.012 | ... | 2.0 |
| F606W | V | (V-I) | 23.639 | 23.646 | 23.652 | 23.624 | -0.247 | 0.065 | 2.0 | ... |
| F622W | R | (V-R) | 22.325 | 22.342 | 22.340 | 22.326 | -0.252 | -0.111 | ... | ... |
| F675W | R | (U-R) | 22.026 | 22.043 | 22.040 | 22.027 | 0.039 | -0.007 | ... | ... |
| F675W | R | (B-R) | 22.007 | 22.024 | 22.021 | 22.008 | 0.092 | -0.017 | ... | ... |
| F675W | R | (V-R) | 22.006 | 22.023 | 22.020 | 22.007 | 0.253 | -0.125 | ... | ... |
| F675W | R | (R-I) | 21.997 | 22.014 | 22.011 | 21.998 | 0.273 | -0.066 | ... | ... |
| F702W | R | (V-R) | 22.415 | 22.432 | 22.429 | 22.416 | 0.343 | -0.177 | ... | 0.6 |
| F702W | R | (V-R) | 22.293 | 22.310 | 22.307 | 22.294 | 0.486 | -0.079 | 0.6 | ... |
| F785LP | I | (V-I) | 20.644 | 20.657 | 20.668 | 20.633 | 0.091 | 0.020 | ... | ... |
| F791W | I | (V-I) | 21.441 | 21.455 | 21.465 | 21.430 | -0.029 | -0.004 | ... | 1.0 |
| F791W | I | (V-I) | 21.482 | 21.496 | 21.506 | 21.471 | -0.084 | 0.011 | 1.0 | ... |
| F814W | I | (U-I) | 21.573 | 21.586 | 21.596 | 21.561 | -0.018 | 0.002 | ... | ... |
| F814W | I | (B-I) | 21.593 | 21.606 | 21.616 | 21.581 | -0.031 | 0.007 | ... | ... |
| F814W | I | (V-I) | 21.597 | 21.610 | 21.620 | 21.585 | -0.062 | 0.025 | ... | ... |
| F814W | I | (R-I) | 21.597 | 21.610 | 21.620 | 21.585 | -0.112 | 0.084 | ... | ... |
| F850LP | I | (V-I) | 19.885 | 19.898 | 19.909 | 19.874 | 0.160 | 0.023 | ... | ... |
| F1042M | I | (V-I) | 16.072 | 16.085 | 16.095 | 16.060 | 0.350 | 0.022 | ... | ... |
| Filter | SMAG | SCOL | ZP(PC1) | ZP(WFC2) | ZP(WFC3) | ZP(WFC4) | T1 | T2 | Cmin | Cmax |
|---|---|---|---|---|---|---|---|---|---|---|
| F380W | B | (B-V) | 20.257 | 20.268 | 20.265 | 20.277 | -0.581 | 0.777 | ... | 0.5 |
| F380W | B | (B-V) | 20.609 | 20.620 | 20.617 | 20.629 | -0.943 | 0.103 | 0.5 | ... |
| F410M | B | (B-V) | 18.917 | 18.928 | 18.925 | 18.937 | -0.183 | -0.287 | ... | ... |
| F439W | B | (U-B) | 20.094 | 20.104 | 20.102 | 20.113 | -0.103 | -0.046 | ... | ... |
| F439W | B | (B-V) | 20.107 | 20.117 | 20.115 | 20.126 | 0.003 | -0.088 | ... | ... |
| F439W | B | (B-R) | 20.101 | 20.111 | 20.109 | 20.120 | 0.019 | -0.049 | ... | ... |
| F439W | B | (B-I) | 20.104 | 20.114 | 20.112 | 20.123 | 0.005 | -0.023 | ... | ... |
| F450W | B | (B-V) | 21.205 | 21.216 | 21.213 | 21.225 | 0.230 | -0.003 | ... | ... |
| F467M | B | (B-V) | 19.144 | 19.155 | 19.152 | 19.164 | 0.480 | -0.299 | ... | 0.5 |
| F467M | B | (B-V) | 19.095 | 19.106 | 19.103 | 19.115 | 0.432 | -0.002 | 0.5 | ... |
| F547M | V | (B-V) | 20.848 | 20.851 | 20.859 | 20.868 | 0.031 | -0.039 | ... | 1.0 |
| F547M | V | (B-V) | 20.800 | 20.803 | 20.811 | 20.820 | 0.056 | -0.016 | 1.0 | ... |
| F547M | V | (V-I) | 20.848 | 20.851 | 20.859 | 20.868 | 0.027 | -0.032 | ... | 1.1 |
| F547M | V | (V-I) | 20.800 | 20.803 | 20.811 | 20.820 | 0.049 | -0.013 | 1.1 | ... |
| F555W | V | (U-V) | 21.726 | 21.729 | 21.737 | 21.746 | -0.014 | 0.005 | ... | ... |
| F555W | V | (B-V) | 21.745 | 21.748 | 21.756 | 21.765 | -0.060 | 0.033 | ... | ... |
| F555W | V | (V-R) | 21.750 | 21.753 | 21.761 | 21.770 | -0.121 | 0.120 | ... | ... |
| F555W | V | (V-I) | 21.745 | 21.748 | 21.756 | 21.765 | -0.052 | 0.027 | ... | ... |
| F569W | V | (V-I) | 21.418 | 21.421 | 21.429 | 21.438 | 0.089 | -0.003 | ... | 2.0 |
| F569W | V | (V-I) | 21.750 | 21.753 | 21.761 | 21.770 | -0.125 | 0.022 | 2.0 | ... |
| F606W | V | (B-V) | 22.093 | 22.096 | 22.104 | 22.113 | 0.293 | 0.015 | ... | 1.7 |
| F606W | V | (B-V) | 22.883 | 22.886 | 22.894 | 22.903 | -0.284 | 0.081 | 1.7 | ... |
| F606W | V | (V-I) | 22.093 | 22.096 | 22.104 | 22.113 | 0.254 | 0.012 | ... | 2.0 |
| F606W | V | (V-I) | 22.883 | 22.886 | 22.894 | 22.903 | -0.247 | 0.065 | 2.0 | ... |
| F622W | R | (V-R) | 21.571 | 21.591 | 21.588 | 21.586 | -0.252 | -0.111 | ... | ... |
| F675W | R | (U-R) | 21.272 | 21.292 | 21.288 | 21.287 | 0.039 | -0.007 | ... | ... |
| F675W | R | (B-R) | 21.253 | 21.273 | 21.269 | 21.268 | 0.092 | -0.017 | ... | ... |
| F675W | R | (V-R) | 21.252 | 21.272 | 21.268 | 21.267 | 0.253 | -0.125 | ... | ... |
| F675W | R | (R-I) | 21.243 | 21.263 | 21.259 | 21.258 | 0.273 | -0.066 | ... | ... |
| F702W | R | (V-R) | 21.660 | 21.681 | 21.677 | 21.675 | 0.343 | -0.177 | ... | 0.6 |
| F702W | R | (V-R) | 21.538 | 21.559 | 21.555 | 21.553 | 0.486 | -0.079 | 0.6 | ... |
| F785LP | I | (V-I) | 19.892 | 19.901 | 19.898 | 19.901 | 0.091 | 0.020 | ... | ... |
| F791W | I | (V-I) | 20.689 | 20.698 | 20.696 | 20.698 | -0.029 | -0.004 | ... | 1.0 |
| F791W | I | (V-I) | 20.730 | 20.739 | 20.737 | 20.739 | -0.084 | 0.011 | 1.0 | ... |
| F814W | I | (U-I) | 20.821 | 20.830 | 20.827 | 20.829 | -0.018 | 0.002 | ... | ... |
| F814W | I | (B-I) | 20.841 | 20.850 | 20.847 | 20.849 | -0.031 | 0.007 | ... | ... |
| F814W | I | (V-I) | 20.845 | 20.854 | 20.851 | 20.853 | -0.062 | 0.025 | ... | ... |
| F814W | I | (R-I) | 20.845 | 20.854 | 20.851 | 20.853 | -0.112 | 0.084 | ... | ... |
| F850LP | I | (V-I) | 19.133 | 19.142 | 19.139 | 19.141 | 0.160 | 0.023 | ... | ... |
| F1042M | I | (V-I) | 15.320 | 15.329 | 15.326 | 15.328 | 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