Space Telescope Science Institute
2010 WFPC2 Data Handbook
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WFPC2 Data Handbook > Chapter 5: WFPC2 Data Analysis > 5.1 Photometric Zeropoint

5.1 Photometric Zeropoint
The zeropoint of an instrument, by definition, is the magnitude of an object that produces one count (or data number, DN) per second. The magnitude of an arbitrary object producing DN counts in an observation of length EXPTIME is therefore:
m = -2.5 x log10(DN / EXPTIME) + ZEROPOINT
It is the setting of the zeropoint that determines the connection between observed counts and a standard photometric system (such as Cousins RI), or between counts and astrophysically interesting measurement units such as the flux incident on the telescope.
Zeropoints and Apertures
Historically, each zeropoint refers to a countrate measured in an infinite aperture. Since it’s almost never practical to measure counts in a very large aperture, a definition of zeropoint linked to a smaller aperture is often more convenient.
Holtzman et al. (1995b) published a list of zeropoints that refers to counts measured within a standard aperture of radius 0".5 for point source targets. The photometric calibrations defined by STScI and returned by SYNPHOT are for infinite apertures. In the case of WFPC2, the nominal infinite aperture is defined as having 1.096 times the flux in a 0".5 radius aperture. This is equivalent to setting the aperture correction between a 0".5 radius aperture and an infinite aperture to 0.1 magnitudes.
There are several photometric systems commonly used for WFPC2 data, often causing some confusion about the interpretation of the photometric zeropoint used, and the subsequent photometry results. Before continuing with the discussion, it is worthwhile to define these photometric systems more precisely.
The WFPC2 filters do not have exact counterparts in any standard filter sets. For example, while F555W and F814W are reasonable approximations of Johnson V and Cousins I respectively, neither match is exact, and the differences can amount to 0.1 magnitudes, clearly significant in precise photometric work. Other commonly used filters, such as F336W and F606W, have much poorer matches in the Johnson-Cousins system. We recommend that, whenever practical, WFPC2 photometric results be referred to a system based on its own filters.
It is possible to define “photometric transformations” which convert WFPC2 photometry to another photometric system (see Holtzman et al. [1995b] for some examples). However, such transformations have limited precision, and depend on the color range, metallicity, and surface gravity of the stars considered; they can easily have errors of 0.2 magnitudes or more, depending on the filter and on how much the spectral energy distribution differs from that of the objects on which the transformation is defined, which happens frequently for galaxies at high redshift.
There are several photometric systems defined for WFPC2 observations. Two of them, the WFPC2 Flight System1 and the WFPC2 Synthetic System1, have zeropoints tied to observed standards. A modified version of the WFPC2 Synthetic System was subsequently implemented in SYNPHOT as the VEGAMAG2 System.
In recent years, it has become increasingly common to use photometric systems in which the zeropoint is defined directly in terms of a reference flux in physical units. The STMAG system is a flux-based system similar to the AB system. Figure 5.1, taken from the SYNPHOT Users Manual, shows the relationship between Johnson V, STMAG, and AB MAG systems, superposed on the spectrum of Vega. Flux-based systems make the conversion of magnitudes to fluxes much simpler and cleaner, but have the side effect that any new determination of the absolute efficiency of the instrumental setup results in revised magnitudes. The choice between standard-based and flux-based systems is mostly a matter of personal preference.
Additional details about these systems are outlined below:
This system is defined such that:
stars of color zero in the Johnson-Cousins UBVRI system have color zero between any pair of WFPC2 standard photometric filters (F336W, F439W, F555W, F675W, F814W), and
This system was established by Holtzman et al. (1995b) by observing two globular cluster fields (ω Cen and NGC 6752) with HST and from the ground. The ground-based observations were taken with WFPC2 flight-spare filters and standard UBVRI filters. In practice, the system was defined by least-squares optimization of the transformation matrix. The observed stars near color zero were primarily white dwarfs, so the WFPC2 zeropoints defined in this system match the UBVRI zeropoints for stars with high surface gravity; the zeropoints for main sequence stars would differ by 0.02–0.05 magnitudes, depending on the filter
These zeropoints were determined such that the magnitude of Vega, when observed through the WFPC2 photometric filter set in a 0".5 aperture radius, is identical to the magnitude of Vega in their counterpart Johnson-Cousins filters. For the filters in the WFPC2 photometric filter set, F336W, F439W, F555W, F675W, and F814W, these magnitudes are 0.02, 0.02, 0.03, 0.039, and 0.035, respectively. The calculations were done via synthetic photometry.
This is a modified version of the WFPC2 synthetic system used in SYNPHOT. The zeropoints were defined by the magnitude of Vega being exactly zero in all filters and therefore differ from the synthetic zeropoints published by Holtzman et al. (1995b). VEGAMAG for a star of flux F is
VEGAMAG = -2.5 * log10(F/FVega)
where FVega is the calibrated spectrum of Vega in SYNPHOT constructed from observed and synthetic spectra (Bohlin & Gilliland, 2004, AJ). SYNPHOT zeropoints refer to the nominal infinite aperture (and therefore differ from the WFPC2 Synthetic System zeropoints by ~0.1 magnitudes).
This system, along with the AB System (Oke 1974), are the most commonly-used flux-based systems at UV and visible wavelengths. The STMAG system is based on a spectrum with constant flux density per unit wavelength. The AB system is based on a spectrum with constant flux density per unit frequency. (In other words, the reference spectrum flux density, fλ, and reference spectrum flux density, fν, for the STMAG and AB systems, respectively, are flat.) Their zeropoint values, 21.10 and 48.6, respectively, are set such that the magnitude of Vega is close to zero in mAB, mST, and Johnson V. The magnitudes can be expressed as
where fν is expressed in erg cm-2 s-1 Hz-1, and fλ in erg cm-2 s-1 ┼-1. Another way to express these zeropoints is to say that an object with fν = 3.63 x 10-20 erg cm-2 s-1 Hz-1 will have mAB = 0 in every filter, and an object with fλ = 3.63 x 10-9 erg cm-2 s-1 ┼-1 will have mST = 0 in every filter. For more information, please refer to the SYNPHOT User’s Guide.
Figure 5.1: Comparison of ABvv and STλ Systems
Standard photometric systems generally use the spectrum of Vega to define magnitude zero. The spectrophotometric magnitudes ABν and STλ refer instead to spectra of constant fν and fλ, respectively. Magnitude zero in both systems is defined to be the mean flux density of Vega in the Johnson V passband. Thus all three of the spectra shown here produce the same count rate in the Johnson V passband. The pivot wavelength of Johnson V is defined to be the crossing point of the ABν = 0 and STλ = 0 spectra. (Same as Figure 3.1 in the SYNPHOT Users Guide, version 5).
Several ways to determine the zeropoint, depending on the photometric system being used, are listed below. Note: adjustments to zeropoints, based on time-dependent UV contamination and QE changes are covered in Section 5.2.
Do it yourself: over the operational life of WFPC2, a substantial amount of effort has gone into obtaining accurate zeropoints for all of the filters used. Nonetheless, if good ground-based photometry is available for objects in your WFPC2 field, it can be used to determine a zeropoint for these observations. This approach may be particularly useful in converting magnitudes to a standard photometric system, provided all targets have similar spectral energy distribution; in this case, the conversions are likely to be more reliable than those determined by Holtzman et al. (1995b), which are only valid for stars within a limited range of color, metallicity, and surface gravity.
Use a summary list: lists of zeropoints have been published3 by Holtzman et al. (1995b), WFPC2 ISR 96-04, and WFPC2 ISR 97-10. A list of zeropoints derived from observations done in the final years of WFPC2 operation may be posted to the WFPC2 Web site in the near future. The Holtzman et al. (1995b) zeropoints essentially define the WFPC2 flight photometric system as discussed earlier; they are based on observations of ω Cen and NGC 6752 for the five main broad band colors (i.e., F336W, F439W, F555W, F675W, F814W), as well as synthetic photometry for most other filters. Transformations from the WFPC2 filter set to UBVRI are included, although these should be used with caution, as stated above. Holtzman et al. (1995b) also includes a cookbook section describing in detail how to do photometry with WFPC2. Zeropoints in WFPC2 ISRs 96-04, 97-10 and in Table 5.13are based on the VEGAMAG system and do not include new conversions to UBVRI.
Use the PHOTFLAM keyword in the header of your data: the zeropoint of your data in the STMAG system can be determined using the PHOTFLAM keyword in the header of your calibrated science image. PHOTFLAM is defined as the flux of a source with constant flux per unit wavelength (in erg s-1 cm-2 ┼-1) which produces a count rate of 1 DN per second for the observing mode specified in the keyword PHOTMODE. The PHOTFLAM value is generated by the STSDAS synthetic photometry package, synphot, which you may also find useful for a wide range of photometric and spectroscopic analyses. PHOTFLAM can be used to convert an exposure-normalized image from counts per second to flux units in erg s-1 cm-2 ┼-1 simply by multiplying the exposure-normalized image by the value of PHOTFLAM. For point-source photometry, STMAG magnitudes can be obtained by adding the STMAG zeropoint for an image’s observing mode to the measured instrumental magnitudes (after correction to an infinite aperture). The STMAG zeropoint is defined as
= -2.5 Log (PHOTFLAM) - 21.10
Table 5.1: Values, From 2002, of PHOTFLAM and Zeropoint in the VEGAMAG System3

Values are for the gain 7 setting. The PHOTFLAM values for gain 14 can be obtained by multiplying by the gain ratio: 1.987 (PC1), 2.003 (WF2), 2.006 (WF3), and 1.955 (WF4) (values from Holtzman et al. 1995b). For the zeropoints, add -2.5 log (gain ratio), or -0.745, -0.754, -0.756, and -0.728, respectively. The above values should be applied to the counts referenced to a nominal “infinite aperture,” defined by an aperture correction of 0.10 mag with respect to the standard aperture with 0".5 radius. Note: these values are out of date and only approximate. See Footnote 3, page 88.

Most of the tables used by the synphot package were updated in August 1995 and May 1997; an additional update for QE variations and contamination was provided in 2009. With these updates, SYNPHOT now provides absolute photometric accuracy of 2% rms for broad-band and intermediate-width filters between F300W and F814W, and of about 5% in the UV. Narrow-band filters are calibrated using continuum sources, but checks on line sources indicate that their photometric accuracy is also determined to 5% or better (the limit appears to be in the quality of the ground-based spectrophotometry). Prior to the May 1997 update, some far UV and narrow-band filters were in error by 10% or more; additional details are provided in WFPC2 ISR 97-10.
The synphot package can also be used to determine the transformation between magnitudes in different filters, subject to the uncertainties related to how well the spectrum chosen to do the determination matches the spectrum of the actual source. The transformation is relatively simple using SYNPHOT, and the actual correction factors are small when converting from the WFPC2 photometric filter set to Johnson-Cousins magnitudes. A variety of spectral atlases are available on the Web and in SYNPHOT.
In the examples below, the synphot command calcphot is used to determine the difference in zeropoint between the F814W filter and the Cousins I band for a K0 III star on WF3 using the gain = 7 setting. The Bruzual stellar atlas is being used to provide the spectrum for the K0 III star (file crgridbz77$bz_54.fits).
(1) Determine the STMAG value for the F814W passband:
(2) Determine the VEGAMAG value in Cousins I passband
The correction for the KO III star is the difference between its STMAG and VEGAMAG values, which is 1.24 magnitudes.
Nearly all of this offset is due to the definition of STMAG; the F814W filter is a very close approximation to the Cousins I, and color terms between these filters are very small. This is evident in Figure 5.2, which was created using the following synphot commands:
The Johnson UBVRI throughput data in SYNPHOT are the U3, B2, and V synthetic passbands given in Buser and Kurucz (1978) and the R,I are from Johnson (1965), Table A1. The Cousins R,I throughputs are from Bessell (1983), Table AII, the Str÷mgren passbands from Matsushima (1969), and the Walraven bands are from Lub and Pel (1977), Table 6. For more details, please see the SYNPHOT User's Guide.
Note that the zeropoints listed by Holtzman et al. (1995b) differ systematically by 0.85 mag from the SYNPHOT zeropoints in WFPC2 ISR 97-10. Most of the difference, 0.75 mag, is due to the fact that the Holtzman zeropoints are given for gain 14, while the SYNPHOT zeropoints are reported for gain 7, which is generally used for science observations. An additional 0.1 mag is due to the aperture correction; the Holtzman zeropoint refers to an aperture of 0".5, while the SYNPHOT zeropoint refers to a nominal infinite aperture, defined as 0.10 mag brighter than the 0".5 aperture
Figure 5.2: Plot of Passbands "wfpc2,3,a2d7,f814w" (dotted plot) and Cousins I (solid plot)

Developed by the WFPC2 IDT and detailed in Holtzman et al.(1995b).

For additional details, see WFPC2 ISR 96-04 and the SYNPHOT User’s Guide.

Table 5.1 gives approximate values of PHOTFLAM and zeropoints in the VEGAMAG system as of 2002. Observers requiring accurate results are advised to use the PHOTFLAM values in their image headers, as those have the latest calibrations and updates. Alternatively, the latest version of SYNPHOT can be used to compute updated parameters (see the end of Section 3.5 for details about bandpar and URESP/PHOTFLAM).

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