# 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, then, which determines the connection between observed counts and a standard photometric system (such as Cousins RI), and, in turn, between counts and astrophysically interesting measurements such as the flux incident on the telescope.

#### Zeropoints and Apertures

Each zeropoint refers to a count rate (DN/EXPTIME) measured in a specific way. The zeropoints published by Holtzman et al. (1995b) refer to counts measured in a standard aperture of 0.5" radius. The zeropoint derived from the `PHOTFLAM` header keyword, as well as in other STScI publications, refer-for historical continuity-to counts measured over an "infinite" aperture. Since it is not practical to measure counts in a very large aperture, we use a nominal infinite aperture, defined as having 1.096 times the flux in an aperture with 0.5" radius. This definition is equivalent to setting the aperture correction between a 0.5" radius aperture and an infinite aperture to exactly 0.10 mag.

### 5.1.1 Photometric Systems Used for WFPC2 Data

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 first fundamental difference between systems has to do with the filter set on which they are based. The WFPC2 filters do not have exact counterparts in the 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 mag, 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 these results to one of the standard systems; 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 easily can have errors of 0.2 mag 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.

Two photometric systems, based on WFPC2 filters, are the WFPC2 flight system, defined by the WFPC2 IDT and detailed in Holtzman et al. (1995b), and the synthetic system, also defined by the IDT and subsequently used in synphot as the VEGAMAG system. For more references, see Harris et al. (1993), Holtzman et al. (1995b), `WFPC2 ISR`` 96-04`, and the `Synphot User's Guide`.

The WFPC2 flight system is defined so that stars of color zero in the Johnson-Cousins UBVRI system have color zero between any pair of WFPC2 filters and have the same magnitude in V and F555W. This system was established by Holtzman et al. (1995b) by observing two globular cluster fields ( Cen and NGC 6752) with HST and from the ground, where the ground-based observations were taken both with WFPC2 flight-spare filters and with 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 mag, depending on the filter.

The zeropoints in the WFPC2 synthetic system, as defined in Holtzman et al. (1995b), are determined so that the magnitude of Vega, when observed through the appropriate WFPC2 filter, would be identical to the magnitude Vega has in the closest equivalent filter in the Johnson-Cousins system. For the filters in the 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 are done via synthetic photometry. In the synphot implementation, called the VEGAMAG system, the zeropoints are defined by the magnitude of Vega being exactly zero in all filters.

The above systems both tie the zeropoints to observed standards. 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. Such 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.

The prevalent flux-based systems at UV and visible wavelengths are the AB system (Oke 1974) and the STMAG system. Both define an equivalent flux density for a source, corresponding to the flux density of a source of predefined spectral shape that would produce the observed count rate, and convert this equivalent flux to a magnitude. The conversion is chosen so that the magnitude in V corresponds roughly to that in the Johnson system. In the STMAG system, the flux density is expressed per unit wavelength, and the reference spectrum is flat in f, while in the AB system, the flux density is expressed per unit frequency, and the reference spectrum is flat in f. The definitions are:

where f is expressed in erg cm-2 s-1 Hz-1, and f in erg cm-2 s-1 Å-1.

Another way to express these zeropoints is to say that an object with f = 3.63 10-20 erg cm-2 s-1 Hz-1 will have mAB=0 in every filter, and an object with f = 3.63 10-9 erg cm-2 s-1 Å-1 will have mST=0 in every filter. See also the discussion in the `Synphot User's Guide`.

### 5.1.2 Determining the Zeropoint

There are several ways to determine the zeropoint, partly according to which photometric system is desired:

1. 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.
2. Use a summary list: Lists of zeropoints have been published by Holtzman et al. (1995b), `WFPC2 ISR`` 96-04`, and `WFPC2 ISR`` 97-10` (also reported in table 5.1). The Holtzman et al. (1995b) zeropoints essentially define the WFPC2 flight photometric system; as discussed above, they are based on observations of 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. This paper is available from the STScI WWW or by sending e-mail to `help@stsci.edu`. The more recent compilations of zeropoints in `WFPC2 ISR`` 96-04` and `97-10` use new WFPC2 observations, are based on the VEGAMAG system, and do not include new conversions to UBVRI.
3. Use the PHOTFLAM keyword in the header of your data: The simplest way to determine the zeropoint of your data is to use the `PHOTFLAM` keyword in the header of your image. `PHOTFLAM` is the flux of a source with constant flux per unit wavelength (in erg s-1 cm-2 Å-1) which produces a count rate of 1 DN per second. This keyword is generated by the synthetic photometry package, synphot, which you may also find useful for a wide range of photometric and spectroscopic analyses. Using `PHOTFLAM`, it is easy to convert instrumental magnitude to flux density, and thus determine a magnitude in a flux-based system such as AB or STMAG (see section 5.1.1); the actual steps required are detailed below.
 Note that the zeropoints listed by Holtzman et al. (1995b) differ systematically by 0.85 mag from the synphot zeropoints in table 5.1. 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

The tables used by the synphot package were updated in August 1995 and May 1997. 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; more details are provided in `WFPC2 ISR`` 97-10`.

Table 5.1 provides lists of the current values for `PHOTFLAM`. Please note that the headers of images processed before May 1997 contain older values of `PHOTFLAM`; the up-to-date values can be obtained by reprocessing the image (i.e., re-requesting the data via OTFR), from the table, or more directly by using the bandpar task in synphot (see Creation of Photometry Keywords in section 3.3.2: for an example). Note that to use bandpar, the synphot version must be up-to-date.1 Furthermore, when using bandpar, it is also possible to directly incorporate the contamination correction (see Contamination in section 5.2.1.

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 WWW` as well as via synphot.

Table 5.1: Current Values of PHOTFLAM and Zeropoint in the VEGAMAG system.
Filter1 PC WF2 WF3 WF4
New photflam Vega ZP New photflam Vega ZP New photflam Vega ZP New photflam Vega ZP
f122m 8.088e-15 13.768 7.381e-15 13.868 8.204e-15 13.752 8.003e-15 13.778
f160bw 5.212e-15 14.985 4.563e-15 15.126 5.418e-15 14.946 5.133e-15 15.002
f170w 1.551e-15 16.335 1.398e-15 16.454 1.578e-15 16.313 1.531e-15 16.350
f185w 2.063e-15 16.025 1.872e-15 16.132 2.083e-15 16.014 2.036e-15 16.040
f218w 1.071e-15 16.557 9.887e-16 16.646 1.069e-15 16.558 1.059e-15 16.570
f255w 5.736e-16 17.019 5.414e-16 17.082 5.640e-16 17.037 5.681e-16 17.029
f300w 6.137e-17 19.406 5.891e-17 19.451 5.985e-17 19.433 6.097e-17 19.413
f336w 5.613e-17 19.429 5.445e-17 19.462 5.451e-17 19.460 5.590e-17 19.433
f343n 8.285e-15 13.990 8.052e-15 14.021 8.040e-15 14.023 8.255e-15 13.994
f375n 2.860e-15 15.204 2.796e-15 15.229 2.772e-15 15.238 2.855e-15 15.206
f380w 2.558e-17 20.939 2.508e-17 20.959 2.481e-17 20.972 2.558e-17 20.938
f390n 6.764e-16 17.503 6.630e-16 17.524 6.553e-16 17.537 6.759e-16 17.504
f410m 1.031e-16 19.635 1.013e-16 19.654 9.990e-17 19.669 1.031e-16 19.634
f437n 7.400e-16 17.266 7.276e-16 17.284 7.188e-16 17.297 7.416e-16 17.263
f439w 2.945e-17 20.884 2.895e-17 20.903 2.860e-17 20.916 2.951e-17 20.882
f450w 9.022e-18 21.987 8.856e-18 22.007 8.797e-18 22.016 9.053e-18 21.984
f467m 5.763e-17 19.985 5.660e-17 20.004 5.621e-17 20.012 5.786e-17 19.980
f469n 5.340e-16 17.547 5.244e-16 17.566 5.211e-16 17.573 5.362e-16 17.542
f487n 3.945e-16 17.356 3.871e-16 17.377 3.858e-16 17.380 3.964e-16 17.351
f502n 3.005e-16 17.965 2.947e-16 17.987 2.944e-16 17.988 3.022e-16 17.959
f547m 7.691e-18 21.662 7.502e-18 21.689 7.595e-18 21.676 7.747e-18 21.654
f555w 3.483e-18 22.545 3.396e-18 22.571 3.439e-18 22.561 3.507e-18 22.538
f569w 4.150e-18 22.241 4.040e-18 22.269 4.108e-18 22.253 4.181e-18 22.233
f588n 6.125e-17 19.172 5.949e-17 19.204 6.083e-17 19.179 6.175e-17 19.163
f606w 1.900e-18 22.887 1.842e-18 22.919 1.888e-18 22.896 1.914e-18 22.880
f622w 2.789e-18 22.363 2.700e-18 22.397 2.778e-18 22.368 2.811e-18 22.354
f631n 9.148e-17 18.514 8.848e-17 18.550 9.129e-17 18.516 9.223e-17 18.505
f656n 1.461e-16 17.564 1.410e-16 17.603 1.461e-16 17.564 1.473e-16 17.556
f658n 1.036e-16 18.115 9.992e-17 18.154 1.036e-16 18.115 1.044e-16 18.107
f673n 5.999e-17 18.753 5.785e-17 18.793 6.003e-17 18.753 6.043e-17 18.745
f675w 2.899e-18 22.042 2.797e-18 22.080 2.898e-18 22.042 2.919e-18 22.034
f702w 1.872e-18 22.428 1.809e-18 22.466 1.867e-18 22.431 1.883e-18 22.422
f785lp 4.727e-18 20.688 4.737e-18 20.692 4.492e-18 20.738 4.666e-18 20.701
f791w 2.960e-18 21.498 2.883e-18 21.529 2.913e-18 21.512 2.956e-18 21.498
f814w 2.508e-18 21.639 2.458e-18 21.665 2.449e-18 21.659 2.498e-18 21.641
f850lp 8.357e-18 19.943 8.533e-18 19.924 7.771e-18 20.018 8.194e-18 19.964
f953n 2.333e-16 16.076 2.448e-16 16.024 2.107e-16 16.186 2.268e-16 16.107
f1042m 1.985e-16 16.148 2.228e-16 16.024 1.683e-16 16.326 1.897e-16 16.197
 1 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.

For example, the following commands can be used to determine the difference in zeropoint between F814W filter and the Cousins I band for a K0III star on WF3 using the gain=7 setting:
 sy> calcphot "band(wfpc2,3,a2d7,f814W)" crgridbz77\$bz_54 stmag

where the Bruzual stellar atlas is being used to provide the spectrum for the K0 III star (`file = crgridbz77\$bz_54`). The output is:
 sy> calcphot "band(wfpc2,3,a2d7,f814W)" crgridbz77\$bz_54 stmagMode = band(wfpc2,3,a2d7,f814W) Pivot Equiv Gaussian Wavelength FWHM 7982.044 1507.155 band(wfpc2,3,a2d7,f814W)Spectrum: crgridbz77\$bz_54 VZERO STMAG Mode: band(wfpc2,3,a2d7,f814W) 0. -15.1045

Comparing this result with:
 calcphot "band(cousins,I)" crgridbz77\$bz_54 vegamagMode = band(cousins,I)    Pivot     Equiv Gaussian  Wavelength       FWHM   7891.153      898.879     band(cousins,I)  Spectrum: crgridbz77\$bz_54    VZERO        VEGAMAG     Mode: band(cousins,I)      0.        -16.3327

shows that for a star of this color, the correction is 1.2 magnitudes (note that nearly all of this offset is due to the definition of STMAG; the F814W filter is a very close approximation to the Johnson-Cousins I, and color terms between these filters are very small). 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 Stromgren 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`. The tables below provide representative zeropoint transformations; typical uncertainties are ~5% (worse for U). A larger variety of spectra are available in the `atlases on the WWW` as well as in synphot.

Table 5.2: Rough Zeropoint Transformations for Johnson UBVRI
Spectral Type Atlas File Name U-F336W B-F439W V-F555W R-F675W I-F814W
O5V
bz_1
0.51
0.66
0.03
-0.69
-1.17
B0V
bz_5
0.45
0.66
0.03
-0.70
-1.18
B1V
bpgs_5
0.43
0.67
0.03
-0.69
-1.19
A0V
bpgs_14
-0.11
0.66
0.01
-0.70
-1.27
A0V
bz_13
-0.08
0.66
-0.00
-0.70
-1.27
F2V
bz_19
-0.02
0.61
-0.02
-0.71
-1.33
F6V
bpgs_33
0.00
0.61
-0.01
-0.71
-1.32
G0V
bpgs_36
0.04
0.58
-0.02
-0.70
-1.34
G0V
bz_24
0.00
0.57
-0.03
-0.72
-1.35
K0V
bz_28
-0.06
0.52
-0.03
-0.72
-1.36
K7V
bpgs_64
-0.00
0.42
-0.01
-0.79
-1.47
M0V
bpgs_66
-0.05
0.38
-0.02
-0.89
-1.56
M0V
bz_32
0.01
0.41
-0.02
-0.80
-1.52
M6V
bz_35
0.12
0.27
-0.05
-1.08
-1.69

Table 5.3: Rough Zeropoint Transformations For Cousins RI
Spectral Type Atlas File Name R-F675W I-F814W
O5V
bz_1
-0.73
-1.28
B0V
bz_5
-0.72
-1.28
B1V
bpgs_5
-0.72
-1.28
A0V
bpgs_14
-0.70
-1.26
A0V
bz_13
-0.70
-1.26
F2V
bz_19
-0.65
-1.27
F6V
bpgs_33
-0.64
-1.28
G0V
bpgs_36
-0.62
-1.27
G0V
bz_24
-0.62
-1.27
K0V
bz_28
-0.61
-1.27
K7V
bpgs_64
-0.57
-1.27
M0V
bpgs_66
-0.57
-1.28
M0V
bz_32
-0.57
-1.26
M6V
bz_35
-0.59
-1.23

The spectra in the preceding tables were taken from the `Bruzual library `(BZ77) and the `Bruzual-Persson-Gunn-Stryker atlas` (BPGS).

1 For instructions on how to retrieve STSDAS synphot tables, see appendix section A.3.2.

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