The information on this page is an update of that presented in Dolphin (2000), and is published in Dolphin (2009). The necessitation of the update is for a few reasons: The limitation of the new calibration equations is that they only consider cold (after April 1994) observations.

Contribution for 2002 HST Calibration Workshop proceedings available here.

Equations last updated May 13, 2009.

Previous equations:

WF4 Anomaly

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.

CTE Correction

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, calculate 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.

Zero Points relative to Holtzman et al. (1995)

 GAIN=7GAIN=14
FilterPC1WFC2WFC3WFC4PC1WFC2WFC3WFC4
F439W0.065 +/- 0.0080.067 +/- 0.0040.060 +/- 0.0040.073 +/- 0.0040.045 +/- 0.0020.065 +/- 0.0010.041 +/- 0.0010.063 +/- 0.002
F555W0.045 +/- 0.0030.044 +/- 0.0010.039 +/- 0.0020.048 +/- 0.0010.040 +/- 0.0020.034 +/- 0.0010.036 +/- 0.0010.051 +/- 0.002
F675W0.060 +/- 0.0070.061 +/- 0.0040.052 +/- 0.0040.070 +/- 0.0030.041 +/- 0.0020.054 +/- 0.0010.046 +/- 0.0010.047 +/- 0.003
F814W0.013 +/- 0.0020.036 +/- 0.0010.030 +/- 0.0010.032 +/- 0.0010.025 +/- 0.0010.036 +/- 0.0010.024 +/- 0.0010.030 +/- 0.001
note: add these values to Holtzman-calibrated magnitudes

Additional Offsets for Non-Standard Filters

FilterStd Filtoffset
F300WF336W-0.000 +/- 0.000
F380WF439W 0.077 +/- 0.003
F410MF439W 0.051 +/- 0.003
F450WF439W-0.007 +/- 0.003
F467MF439W-0.068 +/- 0.003
F547MF555W-0.004 +/- 0.002
F569WF555W-0.021 +/- 0.002
F606WF555W-0.017 +/- 0.002
F622WF675W-0.013 +/- 0.005
F702WF675W 0.006 +/- 0.003
F785LPF814W 0.007 +/- 0.003
F791WF814W-0.018 +/- 0.003
F850LPF814W 0.008 +/- 0.005
F1042MF814W 0.071 +/- 0.010
note: add these values plus the corresponding calibration from the standard filter table to Holtzman-calibrated magnitudes

WFPC2 Instrumental Magnitudes

GAIN=7 Zero Points for 1 DN/sec

FilterPC1WFC2WFC3WFC4
F380W21.000 +/- 0.00921.012 +/- 0.00521.012 +/- 0.00520.996 +/- 0.005
F410M19.360 +/- 0.00919.373 +/- 0.00619.373 +/- 0.00519.356 +/- 0.005
F439W20.874 +/- 0.00820.886 +/- 0.00420.886 +/- 0.00420.870 +/- 0.004
F450W21.970 +/- 0.00921.982 +/- 0.00521.982 +/- 0.00521.966 +/- 0.005
F467M19.895 +/- 0.00919.908 +/- 0.00619.908 +/- 0.00519.891 +/- 0.005
F547M21.618 +/- 0.00321.627 +/- 0.00221.630 +/- 0.00321.609 +/- 0.002
F555W22.508 +/- 0.00322.517 +/- 0.00122.520 +/- 0.00222.499 +/- 0.001
F569W22.181 +/- 0.00322.190 +/- 0.00222.193 +/- 0.00322.172 +/- 0.002
F606W22.850 +/- 0.00322.859 +/- 0.00222.862 +/- 0.00322.841 +/- 0.002
F622W22.329 +/- 0.00922.340 +/- 0.00622.338 +/- 0.00722.327 +/- 0.006
F675W22.033 +/- 0.00722.044 +/- 0.00422.042 +/- 0.00422.030 +/- 0.003
F702W22.432 +/- 0.00822.443 +/- 0.00422.442 +/- 0.00522.430 +/- 0.004
F785LP20.635 +/- 0.00320.668 +/- 0.00320.670 +/- 0.00320.642 +/- 0.003
F791W21.441 +/- 0.00421.473 +/- 0.00421.475 +/- 0.00421.447 +/- 0.004
F814W21.591 +/- 0.00221.624 +/- 0.00121.625 +/- 0.00121.598 +/- 0.001
F850LP19.899 +/- 0.00519.932 +/- 0.00519.934 +/- 0.00519.906 +/- 0.005
F1042M16.189 +/- 0.01016.222 +/- 0.01016.224 +/- 0.01016.196 +/- 0.010

GAIN=14 Zero Points for 1 DN/sec

FilterPC1WFC2WFC3WFC4
F380W20.234 +/- 0.00420.255 +/- 0.00320.237 +/- 0.00320.258 +/- 0.003
F410M18.595 +/- 0.00418.616 +/- 0.00418.598 +/- 0.00418.618 +/- 0.004
F439W20.108 +/- 0.00220.129 +/- 0.00120.111 +/- 0.00120.132 +/- 0.002
F450W21.204 +/- 0.00421.225 +/- 0.00321.207 +/- 0.00321.228 +/- 0.004
F467M19.130 +/- 0.00419.151 +/- 0.00419.133 +/- 0.00419.153 +/- 0.004
F547M20.867 +/- 0.00320.863 +/- 0.00220.871 +/- 0.00220.884 +/- 0.002
F555W21.757 +/- 0.00221.753 +/- 0.00121.761 +/- 0.00121.774 +/- 0.002
F569W21.430 +/- 0.00321.426 +/- 0.00221.434 +/- 0.00221.447 +/- 0.003
F606W22.099 +/- 0.00322.095 +/- 0.00222.103 +/- 0.00222.116 +/- 0.002
F622W21.564 +/- 0.00621.579 +/- 0.00521.576 +/- 0.00521.576 +/- 0.006
F675W21.268 +/- 0.00221.282 +/- 0.00121.280 +/- 0.00121.279 +/- 0.003
F702W21.667 +/- 0.00421.682 +/- 0.00321.679 +/- 0.00321.679 +/- 0.004
F785LP19.902 +/- 0.00319.915 +/- 0.00319.908 +/- 0.00319.912 +/- 0.003
F791W20.707 +/- 0.00420.720 +/- 0.00420.713 +/- 0.00420.717 +/- 0.004
F814W20.857 +/- 0.00120.870 +/- 0.00120.863 +/- 0.00120.867 +/- 0.001
F850LP19.166 +/- 0.00519.179 +/- 0.00519.172 +/- 0.00519.176 +/- 0.005
F1042M15.456 +/- 0.01015.468 +/- 0.01015.462 +/- 0.01015.466 +/- 0.010

note: WFPC2mag = -2.5 log (DN/s) + ZP(FG) - CTE
ZP(FG) from above tables
CTE calculated from above equations

UBVRI Transformations

GAIN=7

FilterSMAGSCOLZP(PC1)ZP(WFC2)ZP(WFC3)ZP(WFC4)T1T2CminCmax
F380WB(B-V)21.02521.03721.03721.021-0.581 0.777...0.5
F380WB(B-V)21.37721.38921.38921.373-0.943 0.1030.5...
F410MB(B-V)19.67019.68319.68319.666-0.183-0.287......
F439WB(U-B)20.86120.87320.87320.857-0.103-0.046......
F439WB(B-V)20.87420.88620.88620.870 0.003-0.088......
F439WB(B-R)20.86820.88020.88020.864 0.019-0.049......
F439WB(B-I)20.87120.88320.88320.867 0.005-0.023......
F450WB(B-V)21.97221.98421.98421.968 0.230-0.003......
F467MB(B-V)19.90219.91519.91519.898 0.480-0.299...0.5
F467MB(B-V)19.85319.86619.86619.849 0.432-0.0020.5...
F547MV(B-V)21.61321.62221.62521.604 0.031-0.039...1.0
F547MV(B-V)21.56521.57421.57721.556 0.056-0.0161.0...
F547MV(V-I)21.61321.62221.62521.604 0.027-0.032...1.1
F547MV(V-I)21.56521.57421.57721.556 0.049-0.0131.1...
F555WV(U-V)22.48922.49822.50122.480-0.014 0.005......
F555WV(B-V)22.50822.51722.52022.499-0.060 0.033......
F555WV(V-R)22.51322.52222.52522.504-0.121 0.120......
F555WV(V-I)22.50822.51722.52022.499-0.052 0.027......
F569WV(V-I)22.17922.18822.19122.170 0.089-0.003...2.0
F569WV(V-I)22.51122.52022.52322.502-0.125 0.0222.0...
F606WV(B-V)22.85922.86822.87122.850 0.293 0.015...1.7
F606WV(B-V)23.64923.65823.66123.640-0.284 0.0811.7...
F606WV(V-I)22.85922.86822.87122.850 0.254 0.012...2.0
F606WV(V-I)23.64923.65823.66123.640-0.247 0.0652.0...
F622WR(V-R)22.34322.35422.35222.341-0.252-0.111......
F675WR(U-R)22.05322.06422.06222.050 0.039-0.007......
F675WR(B-R)22.03422.04522.04322.031 0.092-0.017......
F675WR(V-R)22.03322.04422.04222.030 0.253-0.125......
F675WR(R-I)22.02422.03522.03322.021 0.273-0.066......
F702WR(V-R)22.43722.44822.44722.435 0.343-0.177...0.6
F702WR(V-R)22.31522.32622.32522.313 0.486-0.0790.6...
F785LPI(V-I)20.63820.67120.67320.645 0.091 0.020......
F791WI(V-I)21.44121.47321.47521.447-0.029-0.004...1.0
F791WI(V-I)21.48221.51421.51621.488-0.084 0.0111.0...
F814WI(U-I)21.56721.60021.60121.574-0.018 0.002......
F814WI(B-I)21.58721.62021.62121.594-0.031 0.007......
F814WI(V-I)21.59121.62421.62521.598-0.062 0.025......
F814WI(R-I)21.59121.62421.62521.598-0.112 0.084......
F850LPI(V-I)19.88119.91419.91619.888 0.160 0.023......
F1042MI(V-I)16.13616.16916.17116.143 0.350 0.022......

GAIN=14

FilterSMAGSCOLZP(PC1)ZP(WFC2)ZP(WFC3)ZP(WFC4)T1T2CminCmax
F380WB(B-V)20.25920.28020.26220.283-0.581 0.777...0.5
F380WB(B-V)20.61120.63220.61420.635-0.943 0.1030.5...
F410MB(B-V)18.90518.92618.90818.928-0.183-0.287......
F439WB(U-B)20.09520.11620.09820.119-0.103-0.046......
F439WB(B-V)20.10820.12920.11120.132 0.003-0.088......
F439WB(B-R)20.10220.12320.10520.126 0.019-0.049......
F439WB(B-I)20.10520.12620.10820.129 0.005-0.023......
F450WB(B-V)21.20621.22721.20921.230 0.230-0.003......
F467MB(B-V)19.13719.15819.14019.160 0.480-0.299...0.5
F467MB(B-V)19.08819.10919.09119.111 0.432-0.0020.5...
F547MV(B-V)20.86220.85820.86620.879 0.031-0.039...1.0
F547MV(B-V)20.81420.81020.81820.831 0.056-0.0161.0...
F547MV(V-I)20.86220.85820.86620.879 0.027-0.032...1.1
F547MV(V-I)20.81420.81020.81820.831 0.049-0.0131.1...
F555WV(U-V)21.73821.73421.74221.755-0.014 0.005......
F555WV(B-V)21.75721.75321.76121.774-0.060 0.033......
F555WV(V-R)21.76221.75821.76621.779-0.121 0.120......
F555WV(V-I)21.75721.75321.76121.774-0.052 0.027......
F569WV(V-I)21.42821.42421.43221.445 0.089-0.003...2.0
F569WV(V-I)21.76021.75621.76421.777-0.125 0.0222.0...
F606WV(B-V)22.10822.10422.11222.125 0.293 0.015...1.7
F606WV(B-V)22.89822.89422.90222.915-0.284 0.0811.7...
F606WV(V-I)22.10822.10422.11222.125 0.254 0.012...2.0
F606WV(V-I)22.89822.89422.90222.915-0.247 0.0652.0...
F622WR(V-R)21.57821.59321.59021.590-0.252-0.111......
F675WR(U-R)21.28821.30221.30021.299 0.039-0.007......
F675WR(B-R)21.26921.28321.28121.280 0.092-0.017......
F675WR(V-R)21.26821.28221.28021.279 0.253-0.125......
F675WR(R-I)21.25921.27321.27121.270 0.273-0.066......
F702WR(V-R)21.67221.68721.68421.684 0.343-0.177...0.6
F702WR(V-R)21.55021.56521.56221.562 0.486-0.0790.6...
F785LPI(V-I)19.90519.91819.91119.915 0.091 0.020......
F791WI(V-I)20.70720.72020.71320.717-0.029-0.004...1.0
F791WI(V-I)20.74820.76120.75420.758-0.084 0.0111.0...
F814WI(U-I)20.83320.84620.83920.843-0.018 0.002......
F814WI(B-I)20.85320.86620.85920.863-0.031 0.007......
F814WI(V-I)20.85720.87020.86320.867-0.062 0.025......
F814WI(R-I)20.85720.87020.86320.867-0.112 0.084......
F850LPI(V-I)19.14819.16119.15419.158 0.160 0.023......
F1042MI(V-I)15.40315.41515.40915.413 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

References

"The Charge Transfer Efficiency and Calibration of WFPC2." Dolphin, 2000, A. E. PASP, 112, 1397

"WFPC2 Stellar Photometry with HSTphot." Dolphin, A. E. 2000, PASP, 112, 1383

"A Revised Characterization of the WFPC2 CTE Loss." Dolphin, A. E., PASP, 121, 655