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28.1 Photometric Zero Point

The zero point 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.

Zero Points and Apertures

Each zero point 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 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 0.5" radius and infinite aperture to exactly 0.10 mag.

28.1.1 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 of the photometry results themselves. Before continuing with the discussion of the photometry, 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" to convert these photometry results to one of the standard systems; see Holtzman et al. (1995b) for some examples. However, such transformations have limited precision, depend on the color range, metallicity, and surface gravity of the stars considered, and can easily 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; this 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, in Cen and in NGC 6752, with HST and from the ground; 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 stars near color zero which were observed are 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 be off 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 zero points 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.

28.1.2 Determining the Zero Point

There are several ways to determine the zero point, 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 on HST. Nonetheless, if good ground-based photometry is available for objects in your HST 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 28.1). 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 previous Section); 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 28.1. 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 28.1 lists the new values for PHOTFLAM. Please note that the headers of images processed before May 1997 contain out-of-date values of PHOTFLAM; the up-to-date values can be obtained by reprocessing the image, from the table, or more directly, by using the bandpar task in synphot-as long as the synphot version is up to date.1 When using bandpar, it is also possible to incorporate the contamination correction (see "Contamination" on page 28-6) directly into the value of PHOTFLAM.

The synphot package can be used to determine the transformation between magnitudes in different filters, subject to the uncertainties related to how well the spectrum chosen to determine the transformation 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. 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$bz_54 stmag
Mode = band(wfpc2,3,a2d7,f814W)
Pivot Equiv Gaussian
Wavelength FWHM
7982.044 1507.155 band(wfpc2,3,a2d7,f814W)
Spectrum: crgridbz77$bz_54
VZERO STMAG Mode: band(wfpc2,3,a2d7,f814W)
0. -15.1045
Comparing this result with:

calcphot "band(cousins,I)" crgridbz77$bz_54 vegamag
Mode = band(cousins,I)
Pivot Equiv Gaussian
Wavelength FWHM
7891.153 898.879 band(cousins,I)
Spectrum: crgridbz77$bz_54
VZERO VEGAMAG Mode: band(cousins,I)
0. -16.3327
shows that for a star of this color, the correction is 1.3 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). More details on the use of synphot can be found in the Synphot User's Guide.


Current Values of PHOTFLAM and Zeropoint in 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.



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1 For instructions on how to retrieve STSDAS synphot tables, see "Getting the Synphot Database" on page A-15.

stevens@stsci.edu
Copyright © 1997, Association of Universities for Research in Astronomy. All rights reserved. Last updated: 07/01/98 10:56:16