8.1 Photometry

• Choose an appropriate aperture size.
• Measure the counts within the aperture.
• Measure the background flux outside the aperture.
• Assess the fraction of encircled signal within your aperture using an appropriate FOC point spread function (PSF).
• Convert counts to flux using the PHOTFLAM keyword and exposure time. You can easily do the first three steps with standard IRAF aperture photometry tasks, for example, the phot task in the noao.digiphot.apphot package. Below we describe how to work with FOC point spread functions, and the section on "Converting Counts to Flux or Magnitude" on page 3-15 shows how to use the PHOTFLAM keyword.

http://www.stsci.edu/ftp/instrument_news/FOC/

foc_tools.html#psfs

/instrument_news/FOC/Foc_tools/psfs/psf_files/f96/foc+costar

The on-line PSF files are in FITS format and have been normalized so that the total background-subtracted flux is 1.0. The total fluxes and backgrounds were measured in exactly the same way as the DQE curve. So, for example, if a particular choice of aperture size and background region returns the result of 0.5 when applied to a PSF file, then 50% of the flux is measured.

Another example may further clarify this procedure. The image x2330106p is a 596 second F220W image of a field in the globular cluster 47 Tucanae. The inverse sensitivity for this image, given by the keyword PHOTFLAM in the image header, is 2.017 x 10^-17. However, as pointed out in "Absolute Sensitivity Correction (WAVCORR)" on page 6-3, the PHOTFLAM values in data taken in the early part of the COSTAR-corrected era were incorrect in that they did not use the COSTAR element in the PHOTMODE string, and the DQE curve used was subsequently superseded by one made using on-orbit measurements. Using synphot to re-evaluate the PHOTFLAM for this mode gives 3.131 x 10^-17. Photometry done on a particular star using phot found a total of 631.52 counts with a particular choice of aperture parameters. Using the same choice of parameters on the F220W PSF gives 0.713, or 71.3% of the flux. Thus, the total flux from the star is 631.52 / 0.713 = 885.72 counts, and the total count rate is 885.72/596.0 = 1.486 counts/sec. The weighted mean flux from the star over the F220W+FOC+OTA+COSTAR passband is then 1.486 x 3.131 x 10^-17 = 4.65 x 10^-17 erg cm^-2 s^-1 Å^-1.

One troublesome feature of the FOC's nearly diffraction-limited PSF is that small aberrations can affect the photometry significantly, especially within small apertures. Users should be aware that small, unpredictable, time-dependent focus variations due to thermal effects in the OTA (breathing) can slightly defocus the FOC PSF. The effect on photometry is small for aperture radii larger than 0.1 arcseconds (a few percent at most), but the flux in the central pixel can vary by more than a factor of two from one exposure to the next, especially in the 2000 to 3000 Å range.

Unfortunately, there is no good method to determine the quality of the focus for a particular image, making it very difficult to model the effect of defocusing on the aperture correction for stellar images. The alternative is to increase the sizes of the error bars to account for this uncertainty in the photometric zero point.

Similarly, there is a small field dependence of the PSF, mainly a focus and astigmatism term. The magnitude of the effect is small over the 512 x 512 imaging format compared to, say, the variations due to breathing. However, again there is no way to model the effect since it presupposes knowledge of the focus of the image at the center of the field.

Overall, users are advised to use an aperture larger than 0.1" radius if accuracy in the zero-point is required to better than 5%. Otherwise, one must expect some uncertainty in the zero point due to aperture correction uncertainties.

As already mentioned in Chapter 4, all pre-COSTAR data are affected by the spherical aberration of the primary mirror. This aberration seriously degraded the FOC PSF, which featured a diffraction limited core (~70 milliarcseconds FWHM) containing 10-15% of the total light of the source, superimposed on a bright diffuse halo. Figure 8.1 shows the aberrated PSF of a spectrophotometric standard star taken with the f/96 and the F140M filter.

Figure 8.1: Pre-COSTAR Image of a Star Taken with f/96 Relay and F180M Filter

8.1.2 Photometric Accuracy

• Relative Photometry: The accuracy to which you can measure the relative fluxes of sources on the same FOC image is dominated by errors in the flatfielding and is expected theoretically to be of the order of 3-5% for sources that do not fall on recognizable image defects (see "Commonly Observed Features" on page 4-7). Empirical determinations of photometric accuracy show that repeatabilities of 3-4% are typical for isolated bright stars where crowding is not important and the total detected flux is more than about 3000 counts. However, tests of photometric accuracy in crowded fields suggest relative errors of about 5% for f/96 and 10% for f/48. Users should bear in mind that there are no systematic, detailed studies of relative photometry with the FOC, so these estimates of the rms repeatability are somewhat anecdotal.

• Absolute Photometry: The absolute photometric calibration of FOC f/96 images was derived empirically by comparing observed and predicted count rates for the spectrophotometric standard stars HZ4 and BPM 16274 (see FOC ISR 085). The predicted count rates were calculated using synphot from the pre-servicing mission FOC DQE curve, modified to include ground measurements of the COSTAR reflectivity. The observed count rates were measured by summing the flux within an aperture of 70 pixels (1 arcsecond) radius, accounting for the background measured also at 1 arcsecond radius. Note that this procedure is different from the pre-COSTAR case, where a 3 arcsecond radius aperture was used. The measured relation between observed and expected measurements and wavelength was found to be linear, and this linear relation was used to modify the FOC DQE curve. The scatter of the observed and expected measurements using the corrected FOC DQE curve was approximately 8% rms.

  The absolute sensitivity of the f/48 camera has been calibrated only under conditions of very poor instrument performance (high background), so all f/48 fluxes must be considered much more uncertain. Typical uncertainties are of the order of +/- 30%.

  Users must also account for the error sources discussed in the previous chapter. In addition to the 10-20% scatter in the absolute calibration accuracy of the f/96 camera (and the considerably higher uncertainty in the f/48 fluxes), there are several effects that can systematically shift the photometric scale for FOC data and go uncorrected in pipeline processing. These error sources, which should be corrected if possible, include:

• Format dependence of the FOC sensitivities (see page 7-10).
• The effect of the source spectrum on the calculated flux (see page 7-15).
• Flatfielding inaccuracies (see page 7-5 and below)

• Because of the FOC's limited dynamic range, obtaining high signal-to-noise flatfields consumes large numbers of HST orbits. Therefore most flatfields have only a few hundred counts per pixel with a corresponding signal to noise of on the order of 5% per pixel from photon noise alone.
• Small drifts in geometric distortion will shift many of the fine scale scratches and blemishes so that they are no longer aligned with those in the flatfield, producing worse flatfielding results around such features.
• The intensity of scratches and blemishes varies considerably with wavelength in the UV. Because there is a UV flatfield at only one wavelength, its scratches and blemishes will be of the wrong depth for most other images.
• Pattern noise and many of the other fine defects in FOC images are not stable and will not be properly removed. The resulting accuracy of relative photometry is largely governed by the small scale defects, scan rate oscillations, the intrinsic error in the large scale flatfield, and changes in the flatfield that depend on wavelength. This last error is probably on the order of 2-4% rms (this and subsequent discussions of errors apply to the area of the photocathode more than about 100 pixels away from the edges and corners of the format). Given the intrinsic error in the large scale flatfields, the observer should not expect the net large scale accuracy to be better than 3-5%. Some recent checks on photometric consistency of stars in a crowded field have had actual errors closer to 7%.

  Errors due to scan rate variations may be as high as 10-20% (peak). Fortunately these errors are usually confined to the first 100 pixels or so of the scan line. Fine scale features such as reseau marks, scratches, blemishes, and video defects can result in much higher errors for the affected pixels. The best data-analysis advice regarding these problems is to avoid placing targets near these defects in the first place! It is possible to flatfield out scratches and blemishes with the appropriate registration of the flatfield with the science image. To obtain the UV flatfield, contact the STScI help desk (help@stsci.edu). You should keep in mind, however, that no simple offset is likely to register the flatfield with the science image everywhere in the image. Such efforts are easier if you need to correct scratches and blemishes only in a limited area. Furthermore, if the effective wavelength of the target in the science image is much different from that of the flatfield, the scratches and blemishes may not have the same intensity and may not be flatfielded properly.

  Pattern noise can produce fluctuations as large as 10% in some pixels (for f/96). Fortunately, most analysis techniques average over at least a few pixels, and because the spatial frequencies of these patterns are high, integration over a sizeable aperture reduces their effect significantly. However, they can seriously affect certain image restoration techniques.