Space Telescope Science Institute
WFC3 Data Handbook 2.1 May 2011
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WFC3 Data Handbook > Chapter 7: WFC3 Data Analysis > 7.2 Photometry

The WFC3 filters naturally define their own photometric system and users are encouraged to refer their photometric results to this native system. The magnitude of a given object observed in a WFC3 filter is therefore simply given in “instrumental magnitudes” as WFC3MAG = -2.5log (count rate [e s-1]). It is also often convenient to convert the measured brightness of a source into a common photometric system. Today, three of the most common systems in use in astronomy are VEGAMAG, STMAG, and ABMAG. Although convenient, transformation to these (as well as other) photometric systems always has a limited precision and is dependent on the color range, surface gravity, and metallicity of the source stars considered (e.g., see Sirianni et al., 2005, PASP, 117, 1049 for a nice discussion).
A detailed discussion of these three photometric systems within the context of HST observations is provided in Sirianni et al. (2005) as well as WFC3 ISR 2009-31. Further information on the VEGAMAG system is also provided in Bohlin & Gilliland (2004, AJ, 127, 3508), the ABMAG system in Oke (1964, ApJ, 140, 689) and the STMAG system in Koorneef et al. (1986, in Highlights of Astronomy IAU, Vol.7, ed. J.-P. Swings, 833).
Summarizing, the VEGAMAG system is defined such that the bright AOV star α-Lyrae (i.e., Vega) has a magnitude of 0 at all wavelengths. The system was/is convenient for ground-based observers as Vega is a bright star that can be easily observed in the northern hemisphere, and contains a smooth spectrum with few features. The VEGAMAG system is the default SYNPHOT magnitude system, and the magnitude of a star with flux f in this system is simply −2.5log (f/fVega), where fVega is the calibrated spectrum of Vega in SYNPHOT. As this system depends on the calibration of the standard star, it is also subject to errors and changes in that calibration. The STMAG and ABMAG systems are different in that they define an equivalent flux density for a source of predefined shape that would produce the observed count rate. In the STMAG system, the flux density is expressed per unit wavelength, and, in the ABMAG system, the flux density is express per unit frequency. The reference spectra are flat as a function of wavelength and frequency in each respective case. The definitions of the systems are:
STMAG = -2.5 Log fλ - 21.10 (where fλ is expressed in erg cm-2sec-1-1),
ABMAG = -2.5 Log fν - 48.60 (where fν is expressed in erg cm-2sec-1Hz-1)
The offsets in these equations, e.g., −21.10 and −48.60, are also frequently referred to as zero points. However, these are a part of the definition of the photometric system. For example, in the STMAG system, the zero point of −21.10 is set so an object with this brightness will have a flux density of 1 erg cm-2sec-1-1.
Photometric Zero Points
The photometric zero point of a telescope/instrument/filter combination is a convenient way to characterize the overall sensitivity of the system. By most definitions, the zero point represents the magnitude of a star-like object that produces one count per second within a given aperture (see Maiz Apellaniz 2007, ASP, 364, 227). For WFC3, this throughput will measure the final performance taking into account the HST Optical Telescope Assembly (OTA), pick-off mirror, mirror reflectivity, filter throughput, outer window, inner window, and the quantum efficiency (QE) of the detector. For HST instruments such as WFC3, the zero points depend on the absolute flux calibration of HST white dwarf spectra, and therefore they will change whenever that calibration is improved.
The photometric zero point can be determined using several techniques. In SYNPHOT, a user can renormalize a spectrum to 1 count/sec in the appropriate WFC3 bandpass and output the zero point in the selected magnitude system (assuming that updated throughput tables are included in the local SYNPHOT installation). These examples renormalize a 10,000 K blackbody for WFC3-UVIS in the F606W filter and WFC3-IR in the F110W filter, and output the zero point in the VEGAMAG system:
Similarly, the most updated STMAG and ABMAG zero points for WFC3 data can be retrieved from photometric keywords in the SCI extension. Specifically, the keyword PHOTFLAM is the inverse sensitivity (erg cm-2 sec-1 -1); it represents the flux density of a star that produces a response of one count per second in this band pass. The header keyword PHOTPLAM is the pivot wavelength. The header keywords PHOTFLAM and PHOTPLAM relate to the STMAG and ABMAG zeropoints through the formulae:
= -2.5 Log (PHOTFLAM) - 21.10
These zero points, as well as those in the VEGAMAG system, are all published in WFC3 ISR 2009-31 for WFC3-UVIS and WFC3 ISR 2009-30 for WFC3-IR and are also published on the WFC3 Web page:
Note: As of September 2010, the WFC3 photometric keywords and derived zero points are based on the ground flat field from TV3 testing. New photometric zero points will soon be calculated based on on-orbit flat fields and updated on the Web page.
For WFPC2, Holtzman et al. (1995, PASP, 107, 1065) measured photometric zero points in an intermediate-sized aperture of R = 0.5 arcseconds to alleviate uncertainties in the sky background for measurements made at larger apertures. These can include mapping the extended PSF wings, the digitized effects of the A/D converters, and CTE problems. Such an aperture is more convenient for typical point source photometry, however it cannot be used directly for surface photometry and will require a large correction. For ACS, Sirianni et al. (2005) use a much larger standard aperture of R = 5.5 arcseconds. Such an aperture is impractical for most point source photometry measurements, especially in crowded fields. However, Sirianni et al. (2005) point out that the ACS correction from a small to a large aperture varies strongly from filter to filter and the “infinite” aperture approach is the traditional SYNPHOT default and therefore a better conversion between point sources and extended sources will be enabled by this convention.
Both of the approaches above have advantages and, therefore, for WFC3, we compute zero points both for an infinite aperture and for R = 0.4 arcseconds (WFC3 ISR 2009-30 and WFC3 ISR 2009-31). Formally, the infinite aperture measurement was obtained by taking the counts (i.e., of a standard star) in a large 2 arcsecond aperture and correcting it a small amount based on a model (see WFC3 ISR 2009-37 and WFC3 ISR 2009-38). The infinite aperture value can also be scaled to the zero point in any aperture based on the enclosed energy fractions, which are provided on the same Web site listed above where the zero points are published. These corrections are wavelength specific. As an example on WFC3-UVIS, the measured flux in F606W within an aperture of radius 0.4 arcseconds (i.e., 10 pixels) is 91% of the total flux and the flux within 2.0 arcseconds is 98% of the total flux. For WFC3-IR, the flux in F140W within an aperture of 0.4 arcseconds (i.e., 3 pixels) is 84% of the total flux and the flux within 2.0 arcseconds is 97% of the total flux. Note, that an “aper” keyword can be used in SYNPHOT to scale the total counts from an infinite aperture to a specific radius, e.g.,:
Users should determine the offset between their own photometry and aperture photometry within a given radius aperture. This can be done by measuring a few bright stars in an uncrowded region of the field of view and applying the offset to all photometric measurements. If such stars are not available, encircled energies have been tabulated (WFC3 ISR 2009-37 and WFC3 ISR 2009-38). However users should be reminded that accurate aperture corrections are a function of time and location on the chip and also depend on the kernel used in Drizzle. They should avoid the blind application of tabulated encircled energies especially at small radii.
Color Correction
In some cases it may be desirable to compare WFC3 photometric results with existing datasets in different photometric systems (e.g., WFPC2, ACS, SDSS, 2MASS, Johnson-Cousins). Since the WFC3 filters do not have exact counterparts in any other “standard” filter set, the accuracy of these transformations is limited. Moreover if the transformations are applied to objects whose spectral type (e.g., color, metallicity, surface gravity) do not match the spectral type of the calibration observation, serious systematic effects can be introduced. For WFC3, at this time, these transformations can be determined by using SYNPHOT only. In the future, we will also publish transformation coefficients based on observations of star clusters observed in common with other photometric systems. In any case, users should not expect to preserve the 1% accuracy of WFC3 photometry on the transformed data.
The WFC3-UVIS CCDs and WFC3-IR detector contain pixels that vary in their area on the sky as a result of the geometric distortion. As a consequence of this, more light will fall on a larger pixel relative to a smaller pixel, leading to an overall gradient in an image of a smooth background. However, the flatfielding process in the HST CALWF3 pipeline is designed to produce images that have a flat background (e.g., sky), thereby suppressing counts (hereafter taken to be in units of electrons) in larger pixels relative to smaller pixels. Hence, the measured total brightness of sources on flt images will vary depending on the position of the object, and the areas of the pixels at that location.
To achieve uniform photometry over the detector, most users will measure counts on distortion free images. The geometric distortion can be corrected using multidrizzle. The output of this processing will be a drz image, which has a flat sky and contains pixels that are uniform in area (i.e., through proper corrections of the distortion and related pixel area variations). Therefore, photometry of any source in a drz image will yield the same count rate (electrons per second) irrespective of the position of the source on the image.
Photometry measured on an flt image therefore requires a field-dependent correction factor to:
This correction is reflected as an image and is called the Pixel Area Map (PAM), and comes from the derivatives of the geometric distortion polynomial. The size of the PAM image is the same as the flt image and each pixel value is set to the normalized area of that pixel. By multiplying the flt images by the PAM, users will recover the same count rate on flt images and drz images, and the same zero point will apply to both data products:
DRZ_flux = FLT_flux * PAM,
where the flt image has been converted to counts per second of exposure time.
A contour plot of relative pixel size across the UVIS image, normalized to the central pixel, is shown in Figure 7.1. The ratio of maximum to minimum pixel area over the detector is 1.074.
The variation of pixel area across the IR channel to be used for correction of point-source photometry from distortion-corrected images is shown in Figure 7.2. The maximum deviation from the central value is 4.1%.
A detailed description of the WFC3 UVIS and IR PAMs is provided in WFC3 ISR 2010-08. This description also discusses a unique choice for normalizing the WFC3 PAMs that differs from previous instruments. This choice ensures that the PAMs do not artificially scale the flt flux by large amounts. Rather, the PAMs simply serve to provide a relative correction of the counts based on the size of pixels as compared to the size of a reference pixel near the center of the detectors (see detailed description in the ISR).
Figure 7.1: Variation of the effective pixel area with position on the UVIS detector. Darker shading indicates pixels with smaller area. Contours are drawn at 1% increments.
Figure 7.2: Variation of the effective pixel area with position on the IR detector. Darker shading indicates pixels with smaller area. Contours are drawn at 2% increments.
PAM Concept Illustration
To illustrate the concepts of extended source and point source photometry on FLT and drz images we consider a simple idealized example of a 3x3 pixel section of the detector. We assume that the bias and dark corrections are zero and that the quantum efficiency is unity everywhere.
Example #1 Constant Surface Brightness Object
Let’s suppose we are observing an extended object with a surface brightness of 2 e/pixel in the undistorted case. With no geometric distortion the image is:
In reality WFC3 suffers from geometric distortion and as a consequence pixels are not square and the pixel area varies across the detector
Let’s suppose the pixel area map (PAM) is:
As a result in the raw data there is an apparent variation in surface brightness.
The geometrical area of each pixel is imprinted in the flat field as well as the photometric sensitivity. In this example, since we assumed that the quantum efficiency is unity everywhere, the flat field is just the equivalent of the PAM:
WFC3 flat fields are designed to level out a uniformly illuminated source and not to conserve total integrated counts, so after the flat-field correction the FLT image has the correct surface brightness and can be used to perform surface photometry. However the image morphology is distorted.
MultiDrizzle can be run on the FLT image. The result is that each pixel is free of geometric distortion and is photometrically accurate.
Example #2 Integrated photometry of a point source
Now let’s suppose we are observing a point source and that all the flux is included in the 3x3 grid. Let the counts distribution be:
The total counts are 100. Due to the geometric distortion, the PSF as seen in the raw image is distorted. The total counts are conserved, but they are redistributed on the CCD.
After the flat-field correction, however, the total counts are no longer conserved:
In this example the counts now add up to 99.08, instead of 100.
In order to perform integrated photometry the pixel area variation need to be taken into account. this can be done by multiplying the FLT image by the PAM or by running MultiDrizzle.
Only by running MultiDrizzle can the geometric distortion be removed, but both approaches correctly recover the count total as 100. Users should be cautioned that this is just an idealized example. In reality the PSF of the star extends to a much bigger radius. If the user decides to work on the flat-fielded image after correcting by the pixel area map, they need to calculate a new aperture correction to the total flux of the star. The aperture corrections discussed in Section 7.2.2 are only for MultiDrizzle output images. In most cases the aperture correction for distorted images will be quite different from the same star measured in the drz image. This is particularly true for small radius apertures.
To date, all CCDs flown in the harsh radiation environment of HST suffer degradation of their charge transfer efficiency (CTE). The effect of CTE degradation is to reduce the apparent brightness of sources, requiring the application of photometric corrections to restore measured integrated counts to their “true” value.
On-orbit data taken with the WFC3 UVIS detector shows evidence for CTE degradation (see Section 5.6.2.) There are calibration proposals in the next cycle to study both hardware and software CTE mitigation techniques.
The design and manufacture of the UV filters was based on a careful balance of the in- and out-of-band transmissions: in general, higher in-band transmission results in poorer suppression of out-of-band transmission, and vice versa. The WFC3 filters represent an attempt to achieve an optimum result, maximizing the in-band transmission while keeping the out-of-band transmission as low as possible in order to minimize red leaks.
Table 7.1 below summarizes the red-leak levels for the WFC3 UV filters. The table lists the fraction of the total signal that is due to flux longward of 400 nm, as a function of effective temperature. This was calculated by convolving a blackbody of the given Teff with the system throughput in the listed filter. As can be seen from the table, red leaks should not be an issue for observations of any objects taken with F275W or F336W. The other UV filters have some red leaks, whose importance depends on stellar temperature. The red leaks in F218W and F300X, for example, exceed ~1% for objects cooler than ~6000 K, while in F225W the red leak reaches ~1% for objects with even cooler temperatures. The most extreme red leaks arise from F218W and F225W observations of objects with Teff of ~4000 K or cooler, necessitating appropriate corrections.
Table 7.1: Fraction of flux longward of 400 nm as a function of effective temperature.
Teff (K)
We have been monitoring the detectors for UV contamination since launch via two calibration proposals observing a standard star in the blue filters. Thus far we have seen no evidence of contamination. The monitoring program will be continued in cycle 19.

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