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WFC3 Data Handbook > Chapter 9: WFC3 Data Analysis > 9.1 Photometry

 9.1 Photometry
9.1.1 Photometric Systems
The STMAG and ABMAG systems 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 Fλ. An object with Fλ = 3.63 x 10-9 erg cm-2 s-1 Å-1 will have STMAG=0 in every filter, where the STMAG zero point is 21.10.
 • STMAG = -2.5 log Fλ - 21.10
In the ABMAG system, the flux density is expressed per unit frequency, and the reference spectrum is flat in Fν. An object with Fν = 3.63 x 10-20 erg cm-2 s-1 Hz-1 will have magnitude ABMAG=0 in every filter, where the ABMAG zero point is 48.6.
 • ABMAG = -2.5 log Fν - 48.6
The relationship between ABMAG and STMAG is:
 • ABMAG = STMAG - 5 log (PHOTPLAM) + 18.692
where Fν is expressed in erg cm-2 s-1 Hz-1, Fλ in erg cm-2 s-1 Å-1, and PHOTPLAM is the bandpass pivot wavelength in angstroms.
Formally, the HST VEGAMAG system is defined by the absolute spectral energy distribution of Vega, such that Vega has VEGAMAG=0 at all wavelengths. Thus, the VEGAMAG magnitude of an object with flux F is
mvega= -2.5 log10 (Fobject/Fvega)

where Fvega is the CALSPEC observed flux density of Vega. For the equations that define the average flux, see Bohlin 2014. In the Johnson-Cousins magnitude system, the average value of six A0V stars sets the zero point values so that U-B=0 and B-V=0 ( Johnson & Morgan, 1953) and by extension V-R=0 and V-I =0 ( Cousins 1974). In this system Vega has the following magnitudes: U=0.03, B=0.03, V=0.03, R=0.07, I=0.10, J=-0.18, H=-0.03, K=0.13. The VEGAMAG system is convenient for many observers because of its long heritage; however, the ABMAG system is popular with large imaging surveys.
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), the ABMAG system in Oke (1964) and the STMAG system in Koorneef et al., 1986. 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 (see Sirianni et al., 2005, for a nice discussion).
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). For WFC3, this throughput measures the performance within a given bandpass taking into account the HST Optical Telescope Assembly (OTA), pick-off mirror, mirror reflectivity, filter throughput, transmission of the outer and 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 model atmosphere spectra, and therefore they will change whenever that calibration is improved.
The photometric zero point can be determined using several techniques. In pysynphot 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 pysynphot installation). This is described in the pysynphot examples, Section 9.1.10.  Similarly, the most updated STMAG and ABMAG zero points for WFC3 data can be computed using photometric keywords in the SCI extension(s) of the image header. Specifically, the keyword PHOTFLAM is the inverse sensitivity and represents the flux density (erg/cm2/sec/A) of a star that produces a response of one electron per second in this bandpass. The header keyword PHOTPLAM is the pivot wavelength of the filter. The header keywords PHOTFLAM and PHOTPLAM relate to the STMAG and ABMAG zero points through the formulae:

STMAG_ZPT = -2.5 Log (PHOTFLAM) - PHOTZPT = -2.5 Log (PHOTFLAM)- 21.10

ABMAG_ZPT = -2.5 Log (PHOTFLAM) - 21.10 - 5 Log (PHOTPLAM) + 18.692
The UVIS imaging channel consists of two separate e2v (now Teledyne e2v) CCDs mounted side by side. The two detectors (chips) have different quantum efficiencies at wavelengths < 3500 Å where UVIS2 is up to ~30% more sensitive than UVIS1. At longer wavelengths, the response of two detectors is similar to within 0.5%. Motivated by the different quantum efficiencies, evidence that the CCDs are aging differently, and the desire to improve the accuracy and precision of the photometry, the UVIS photometric calibration is now determined for each chip independently. New flat fields have been computed for all full-frame filters (excluding the QUAD filters and the grism), with low-frequency corrections for the in-flight sensitivity computed separately for each chip ( WFC3 ISR 2016-04, WFC3 ISR 2016-05). The 2016 reference files are now normalized to the median value of each chip, removing any correction for sensitivity offsets between chips from the flats (see Section 5.4.3). Instead, the chip sensitivity ratio is computed from calibration observations of white-dwarf standards measured on each chip in order to correct for any offsets in the quantum efficiency as a function of wavelength.
On February 23, 2016, the WFC3 calibration pipeline was modified to support the chip-dependent calibration (calwf3 version 3.3 and greater, note: the version used to reduce a specific image is recorded in the CAL_VER header keyword). Two new header keywords PHTFLAM1 and PHTFLAM2 are populated with the inverse sensitivity values for UVIS1 and UVIS2, respectively. The PHOTFLAM keyword is populated with the value of PHTFLAM1 for backward compatibility with user software. A new keyword switch FLUXCORR (see Sections 3.2.13 and 3.4.3) scales UVIS2 to match UVIS1 by multiplying the UVIS2 science array by the inverse sensitivity ratio, PHTRATIO = PHTFLAM2/PHTFLAM1. After applying PHTRATIO, a point source should produce approximately the same number of electrons on UVIS1 and UVIS2 in calibrated (flt, flc) images corrected for distortion using the pixel area map (see Section 9.1.11), such that a single value of PHOTFLAM may be used for the full frame image. Subarray data obtained with UVIS2 are also scaled by the PHTRATIO. This ensures that objects have the same signal regardless of the chip on which they were observed.
The original 2009 photometric calibration was based on the average of two white dwarf standards GD153 and GRW + 70d5824 ( WFC3 ISR 2009-31) and used a smooth polynomial fit to correct for the increased on-orbit sensitivity with wavelength. By 2012, a larger cumulative set of calibration observations made it possible to replace the polynomial fits with more accurate filter-dependent corrections. These revised solutions were based on the average of three white dwarfs (GD153, GD71, G191B2B) plus the G-type star P330E. These were not documented in a formal ISR, but were posted to the WFC3 photometry web page and populated in the image headers. In 2016, the inverse sensitivity values were recomputed using only calibration observations of the three white dwarfs, obtained over a time period of six years and measured at multiple positions on the detector. The 2016 inverse sensitivity values are systematically ~3% smaller than the prior set of solutions across the full wavelength range of the UVIS detector and are a result of improvements in the photometric reduction. More detail on the improved reduction is available in WFC3 ISR 2016-01, ISR 2016-03 and ISR 2017-14Figures 9.1 shows the ratio of the inverse sensitivity values from 2016 to 2012 as a function of the filter pivot wavelength, where the mean ratio for both chips is ~0.97.
The systematic change in the new chip-dependent calibration brings the UVIS photometric system closer to ACS/WFC. This is illustrated in Figures 9.2, which plots the difference in magnitude (WFC3/UVIS - ACS/WFC) in the STMAG system for observations of NGC104 obtained in the F814W filter from programs 11452 and 10737 for WFC3 and ACS, respectively. With the prior (2012) UVIS calibration, relative photometry between the two detectors measured in a large 0.5” aperture radius (the standard for ACS photometry) shows a mean offset of 0.036 mag. This offset is reduced to 0.001 mag with the improved 2016 calibration.

The WFC3/UVIS photometric keyword values have historically been reported in the image header for the infinite aperture, with accompanying encircled energy tables to correct photometry performed at smaller apertures. For convenience, two sets of zero point tables have been provided to users, corresponding to both the infinite and the 10 pixel aperture ( WFC3 ISR 2009-31). In the 2016 release, two sets of tables were again computed, but the values populated in the image header changed convention to correspond to a 10 pixel aperture. This resulted in PHOTFLAM values which were ~10% larger than the 2012 values due primarily to the change in aperture. Based on feedback from the WFC3 user community and for consistency with other HST instruments, the chip-dependent inverse sensitivity values in the image header reverted back to the ‘infinite’ aperture as of June 15, 2017 (calfw3 version 3.4.1 onwards), which is defined at a radius of 6" (151 pixels). The revised 2017 photometric calibration is described in WFC3 ISR 2017-14 and is based on better polynomial fits to the wavelength-dependent components of the throughput response and improved models for the three white dwarf standards.  Current estimates of the photometric uncertainties are ~1.5% for broadband filters, ~2-3% for medium band, and 5-10% for narrow band filters.  Further discussion of the photometric errors is provided in Section 5.7.
The chip-dependent calibration is implemented via a revised image photometry reference table (IMPHTTAB) which now contains two new extensions corresponding to the inverse sensitivity of each chip, PHTFLAM1 and PHTFLAM2 (see Section 3.2.12) for the infinite aperture.  The 2017 solutions are concordant with the current synthetic photometry tables available in the calibration reference data system ( CRDS), and these are described in detail in WFC3 ISR 2016-07. A history of critical IMPHTTAB reference file deliveries and corresponding versions of the calwf3 software is provided in Table 9.3 of Section 9.1.7.  Due to the change in aperture convention, the 2017 keyword values are now ~10% smaller than the 2016 values. Comparing the inverse sensitivity values at the same aperture, the 2017 values differ from 2016 by ~0.5% on average. The 2017 VEGAMAG zero points, on the other hand, changed by up to 0.1 mag in the UV compared to 2016, when they were calculated using the CALSPEC model for Vega. These are now calculated using Vega’s most recent CALSPEC STIS spectrum which differs by up to 10% at wavelengths shorter than 3000 Å. The latest calibration is described in WFC3 ISR 2017-14 and on the WFC3 main photometry webpage, which provides a link to the new UVIS tables for both the infinite and the 10 pixel aperture.
9.1.4 UV Photometry
On November 21, 2016, the team delivered a revised IMPHTTAB, which scales the PHTFLAM1 values by a factor reflecting the empirical count rate ratio of the calibration standards. These modified values of PHTFLAM1 are provided for the four UV filters (F218W, F225W, F275W and F200LP), such that the PHTRATIO values in the image headers match the observed count rate ratios for the white dwarfs. In these cases, the PHOTFLAM values should be used for photometry, and not the PHTFLAM1 values which have been modified to normalize the count rate ratio. For many applications, the difference for the two detectors is small compared to the photometric errors, so using a single PHOTFLAM value for the entire array is reasonable.
The QUAD filter calibration is unchanged from 2012 and still makes use of pre-flight flats that contain the UVIS flare (see Figure 5.4). Full-frame observations using a QUAD filter always have the 'FILTER' keyword populated with the filter element that corresponds to quadrant A, regardless of which filter was requested in the Phase II submission. Table 9.1 lists the four spectral elements associated with a single QUAD element, where the value of the filter keyword reported in the image header corresponds to amplifier A. Users can instead query the value of the “ASN_ID” keyword in their data to look for that association in MAST, where the database is populated with the correct ‘FILTER’ keyword. This discrepancy is due to different software systems creating the MAST database and populating the file header keywords. Observations with QUAD filters in subarray mode only cover a single quadrant (spectral element) and hence always have the correct filter keyword reported in their headers.
To avoid problems with using PHOTFLAM values from the wrong quadrant, all observations using QUAD filters have the PHOTCORR and FLUXCORR switches set to OMIT, so the photometric keywords are not populated in the image header during calwf3 processing. PHOTFLAM values thus have to be retrieved elsewhere, for example from Table 8 in WFC3 ISR 2017-14 or from the QUAD filter tables available on the WFC3 photometry website.
Table 9.1: The WFC3 UVIS channel contains five QUAD filters: each is a 2×2 mosaic of filter elements occupying a single filter slot, with each amplifier (quadrant) providing a different bandpass. Each image header FILTER keyword will be set to the amp A value for full-frame observations and set to the proper QUAD filter for subarray observations covering only one quadrant.
 Filter wheel Slot Amp A Amp B Amp C Amp D 11 4 FQ508N FQ674N FQ575N FQ672N 12 1 FQ437N FQ378N FQ232N FQ243N 12 2 FQ387N FQ492N FQ422M FQ436N 12 3 FQ889N FQ937N FQ906N FQ924N 12 4 FQ619N FQ750N FQ634N FQ727N
For the IR detector, the original 2009 photometric calibration was based on the average of the HST standards GD153 and P330E, a hot white dwarf and G-type star. As for UVIS, a smooth polynomial fit was used to correct for the increased on-orbit sensitivity with wavelength ( WFC3 ISR 2009-30).  By 2012, a larger cumulative set of calibration data allowed for more accurate filter-dependent corrections to the sensitivity with wavelength. The revised solutions were based on the average of three white dwarfs (GD153, GD71, G191B2B) plus P330E. While these solutions were not documented in a formal ISR, they are available from the WFC3 photometry webpage. Independent calibrations from the four standards agree to within ~1% in most filters, and the inverse sensitivity per filter, PHOTFLAM, is set to the average of the measurements.
The IR calibration is unchanged from 2012, and current estimates of the photometric uncertainties are ~2% for broadband filters and 5-10% for narrow band filters. Further discussion of the photometric errors is provided in Section 7.11. The IR photometry header keywords are populated by calwf3 using the IMPHTTAB reference file, which is described in Section 9.1.7.
The IR detector has a low-level count rate non-linearity at ~1% per dex over a range of 12 magnitudes (see Section 7.7). Since bright standard stars (11th magnitude) are used to calibrate the detector, this means that faint source photometry (at the sky count rate ~23rd magnitude) using the computed set of IR zero points will be systematically ~4.5% too faint ( WFC3 ISR 2010-07 and 2011-15). Additional calibration data has been obtained in Cycle 24 (programs 14868 and 14870) to further quantify and correct for this effect as a function of wavelength.
The version of calwf3 used to calibrate WFC3 data may be found in the image header keyword CAL_VER. The current IMPHTTAB reference file for the IR channel is listed in Table 9.2.
The UVIS chip-dependent calibration was implemented in calwf3 v3.3. This required a new 5-extension IMPHTTAB reference file to carry additional keywords reflecting the inverse sensitivity for each CCD chip, PHTFLAM1 and PHTFLAM2.  A history of this reference file is provided in Table 9.3, which highlights the change in the standard aperture used to define the inverse sensitivity values written to the image header.
If data from multiple-visits programs are retrieved from MAST at different times (e.g. after the execution of each visit), it may be possible to observe systematic differences due to changes in the reference files and/or software. In this case, users have two options: 1) re-retrieve all pertinent datasets for the given science program from MAST or 2) reprocess the RAW files offline with a self consistent version of calwf3 and reference files. For manual reprocessing instructions, see the examples in the, Section 3.5.
 Activation Date Reference File Standard aperture Description Documentation 2012 Nov 19 wbj1825si_imp.fits Infinite First active IMPHTTAB, 3 extension FITS file, Used with calwf3 v3.1; Based on data from 2009-2012, averaged for 3 WD's plus P330E 2012 Values on Website only
 Activation Date Reference File Standard aperture Description Documentation 2012 Dec 28 wbj1825si_imp.fits Infinite First active IMPHTTAB, 3 extension FITS file; Used with calwf3 v3.1; ‘Single Chip’ solution; Based on data from 2009-2012, averaged for 3 WD's plus P330E 2012 Values on Website only 2013 Jul 03 x5h1320fi_imp.fits Infinite Based on 2012 solutions for 3 WD's and P330E; corrected by <1% to remove flat field normalization 2012 Values on Website only 2016 Feb 23 zcv2057li_imp.fits 10 pixel Chip-dependent solution; 5 extension FITS file; Used with calwf3 v3.3+; Master DRZ per filter for 3 WD's observed from 2009-2015; Change is ~4% from 2012. ISR-2016-03 2016 Nov 21 0bi2206ti_imp.fits 10 pixel Same as zcv2057li_imp.fits except equalizes UV count-rate across chips for blue sources. Change is 2% in F225W and 1% in F218W, F275W ISR-2017-07 2017 J un 15 1681905hi_imp.fits Infinite Better polynomial fits to data and updated models, matches synphot tables delivered April 2016; Used with calwf3 v3.4.1; Change is ~0.5% from 2016 at the same standard aperture. ISR-2017-14
For UVIS data retrieved after June 15, 2017, this flowchart is useful for determining which set of inverse sensitivity keywords to use for photometry. The light gray box shows the final calwf3 processing steps in the wf32d module. The data products (*flt.fits, *flc.fits) obtained from MAST are created with FLUXCORR set to PERFORM in calwf3. For most filters, a single keyword (PHOTFLAM) may be used for both chips. For the UV filters F218W, F225W, F275W, F200LP, bandpass differences between the chips means that the count ratio may not be equal across the two chips. In order to combine the two chips to create the *drz.fits, *drc.fits data products, calwf3 multiplies the UVIS2 science array by PHTRATIO (the inverse sensitivity ratio) to equalize the count rate of the hot, blue white dwarf standards across the two chips. Hence, using a single PHOTFLAM value for both chips may lead to errors of up to 2% in these filters ( WFC3 ISR 2017-07). To achieve higher photometric accuracy in these four UV filters, users are advised to treat the two chips as independent detectors. This is achieved either by using an alternate set of keywords (bottom center) or by setting FLUXCORR to OMIT, reprocessing the *raw.fits data with calwf3, and using a third set of keywords (bottom right). Note that PHOTFLAM is always the correct value to use for UVIS1. For combining *flt.fits, *flc.fits products which span multiple epochs (orientations) with AstroDrizzle, the majority of users are advised to use the FLUXCORR-scaled data products and a single PHOTFLAM value for photometry.
9.1.8 Aperture Corrections
The response (inverse sensitivity) values for the two WFC3 channels are computed for an infinite aperture and for an aperture radius of 10 pixels. Initially the infinite aperture measurement was obtained by taking the counts (i.e., of a standard star) in a large 2" aperture and correcting to the infinite aperture using an encircled energy (EE) model (see WFC3 ISR 2009-37 and WFC3 ISR 2009-38). Currently, the UVIS detector uses filter-based encircled energy curves for aperture corrections (see Tables 6,7 in WFC3 ISR 2017-14).
The infinite aperture response value can be scaled to the equivalent aperture-based response using the encircled energy fractions, which are wavelength specific. For example, the measured flux in the UVIS F606W filter within a 10 pixel aperture is ~91% of the total flux and within a 50 pixel (2.0") aperture is ~98% of the total flux. For the IR detector, the flux in F140W within an aperture radius of 3 pixels is ~84% of the total flux and ~97% within an aperture radius of 2.0".
Pysynphot may be used to scale the total counts from an infinite aperture to a specific radius using the ‘aper’ keyword as part of the observing mode. This is shown in Example 1 of Section 9.1.10, eg. for the 10 pixel (0.3962”) aperture on UVIS1:.
 bp = pysynphot.ObsBandpass('wfc3,uvis1,f814w,aper#0.3962')
In order to reduce errors due to background variations and to optimize the signal-to-noise, aperture photometry and PSF-fitting photometry are often performed by measuring the flux within a small radius around the center of the source. However, small aperture measurements need to be adjusted to a “total count rate” by applying an aperture correction (in magnitude units) or an encircled energy fraction (in flux units). For example, when making use of the 0.3962” set of zero point tables, users should determine the offset between their own ‘small aperture’ photometry and aperture photometry within a 10 pixel 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, one can use the tabulated EE values (see the following paragraph). Alternately, one can use the new MAST PSF search tool to download PSFs extracted from WFC3 archival data for a similar detector position and focus as the observation of interest. Further information on the PSF search tool by selecting Collection WFC3 UVIS PSF at:
Model encircled energies have been tabulated in WFC3 ISR 2009-37 for IR and WFC3 ISR 2009-38 for UVIS. New chip-dependent, filter-based EE fractions have been computed for the UVIS detector and spliced to the 2009 in-flight models at r=35 pixels (~1.4"). These may be found in WFC3 ISR 2017-14 for radii between 3 and 10 pixels and on the WFC3 photometry web pages for radii up to 50 pixels (~2.0"). The 2017 filter-dependent EE values agree with the 2009 models to ~1% for most filters. However users should be reminded that accurate aperture corrections are a function of time and position on the detector. Blind application of tabulated encircled energies should be avoided for small apertures (i.e., r< 8 pixels for UVIS, r<3 pixels for IR) where the measured photometry (and the EE fraction) is strongly dependent on the telescope focus and orbital breathing (see WFC3 ISR 2013-11).
9.1.9 Color Corrections
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.
Transformation coefficients for different spectral types and astronomical sources have been published in WFC3 ISR 2014-16. The photometric transformation coefficients between Johnson-Cousins UBVI filters and WFC3-UVIS wide-band filters for a given object spectrum can also be found at https://colortool.stsci.edu. Users are encouraged to calculate their own transformation coefficients to specific photometric systems. Example 3 in Section 9.1.10 shows how to use pysynphot to compute these photometric transformations.
As described in Section 9.1.4, the UV filters show color terms of several percent such the count rate photometry of the same stars measured on different CCD chips shows offsets which vary with the color of the source.
9.1.10 Pysynphot Examples
The WFC3 synthetic throughput tables may be obtained from the Calibration Reference Data System (CRDS) at:
http://www.stsci.edu/hst/observatory/crds/throughput.html
To run the following examples, the user should define the local path to throughput tables before starting python using one of the two commands below. For users not at STScI, replace /grp/hst/cdbs/ with your local directory containing the CRDS reference files.
Example 1. Compute the UVIS inverse sensitivity values (and the equivalent STMAG, ABMAG, and VEGAMAG values) for F814W on UVIS1 in a 10-pixel (0.3962”) aperture, assuming a flat spectrum. The python code below shows how to reproduce the values in Tables 4 and 5 of WFC3 ISR 2017-04. The python code below replaces the following pyraf synphot command for computing the pivot wavelength and inverse sensitivity in a bandpass:

 # pyraf equivalent import pysynphot as S import numpy as np vega= S.FileSpectrum('/mydisk/myiref/alpha_lyr_stis_008.fits') bp = S.ObsBandpass('wfc3,uvis1,f814w,aper#0.3962') stmag = -21.1-2.5*np.log10(bp.unit_response()) abmag = -21.1-2.5*np.log10(bp.unit_response())-5*np.log10(bp.pivot())+18.692 vegauvis = S.Observation(vega,bp) vegamag= 2.5*np.log10(vegauvis.countrate()) print 'Obsmode=', bp print 'PivotWave=','{0:.2f}'.format(bp.pivot()) print 'Photflam=','{0:.6g}'.format(bp.unit_response()) print 'STMAG=','{0:.3f}'.format(stmag) print 'ABMAG=','{0:.3f}'.format(abmag) print 'VEGAMAG=','{0:.3f}'.format(vegamag)

 Obsmode= wfc3,uvis1,f814w,aper#0.3962 PivotWave= 8048.151 Photflam= 1.64279e-19 STMAG= 25.861 ABMAG= 25.025 VEGAMAG= 24.598
Example 2. Renormalize a 5,000 K blackbody for WFC3/IR in the F110W filter and output the zero point in the ABMAG system. The fourth line ‘spec.renorm’ renormalizes the blackbody spectrum to produce 1 count/sec in the Johnson V band. The python code below is the equivalent to the pyraf command:

 # pyraf equivalent import pysynphot as S import numpy as np bp = S.ObsBandpass('wfc3,ir,f110w') v_band = S.ObsBandpass('johnson,v') spec = S.BlackBody(5000) spec_renorm = spec.renorm(1,'counts',v_band) obs = S.Observation(spec_renorm,bp) print 'ABMAG=', '{0:.3f}'.format(obs.effstim('abmag')),'for Obsmode=',bp
Example 3. Find the color term for a 5000 K blackbody between the Cousins-I and WFC3/UVIS1 F814W bandpasses in the ABMAG system. (Since the Cousins-I bandpass does not have pre-defined binset, we use the binning from HST/WFC3 UVIS1 detector). The python code below is the equivalent to the pyraf command from Example 2 in WFC3 ISR 2014-16:

 # pyraf equivalent import pysynphot as S import numpy as np bp = S.ObsBandpass('wfc3,uvis1,f814w') i_band = S.ObsBandpass('i') spec = S.BlackBody(5000) obs_wfc3 = S.Observation(spec,bp) obs_i = S.Observation(spec,i_band,binset=obs_wfc3.binwave) color=obs_i.effstim('abmag') - obs_wfc3.effstim('abmag') print 'ABMAG(i)-ABMAG(UVIS1,F814W)= ','{0:.3f}'.format(color)
9.1.11 Pixel Area Maps
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 flat-fielding 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, while surface photometry measurements will be correct, 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 aperture photometry over the detector, most users will measure counts on distortion free images. The geometric distortion can be corrected using AstroDrizzle. The output of this processing will be a drz or drc 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:
 • achieve uniformity in the measured count rate of an object across the field,
 • match the output drizzled count rate.
This correction, in the form of an image, 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 x PAM, where the flt image has been converted to counts per second.
A contour plot of relative pixel size across the UVIS image, normalized to the central pixel, is shown in Figure 9.4. 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 9.5 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).
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.
AstroDrizzle 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.
Only by running AstroDrizzle 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 AstroDrizzle 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.
9.1.12 CTE
9.1.13 Red Leak
The design and manufacture of the UV filters was based on a careful balance of the achievable 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 9.4 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 effective temperature (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 effective temperature (Teff) of ~4000 K or cooler, necessitating appropriate corrections.
 Teff (K) F218W F225W F275W F300X F336W 1000 1 1 1 1 1 2000 9.9E-01 9.9E-01 8.4E-01 5.5E-01 3.0E-02 3000 6.0E-01 2.7E-01 3.0E-02 8.9E-02 8.4E-04 4000 1.1E-01 1.8E-02 3.1E-03 3.3E-02 1.4E-04 5000 2.7E-02 3.2E-03 8.6E-04 1.7E-02 4.5E-05 6000 9.9E-03 1.0E-03 3.8E-04 1.0E-02 2.2E-05 7000 4.9E-03 4.6E-04 2.2E-04 7.3E-03 1.3E-05 8000 2.8E-03 2.5E-04 1.5E-04 5.5E-03 9.0E-06 9000 1.9E-03 1.6E-04 1.1E-04 4.4E-03 6.8E-06 10000 1.3E-03 1.1E-04 8.6E-05 3.7E-03 5.4E-06 11000 1.0E-03 8.6E-05 7.1E-05 3.2E-03 4.5E-06 12000 8.3E-04 6.9E-05 6.0E-05 2.8E-03 3.9E-06 13000 6.9E-04 5.7E-05 5.3E-05 2.6E-03 3.5E-06 14000 5.9E-04 4.8E-05 4.8E-05 2.3E-03 3.1E-06 15000 5.1E-04 4.2E-05 4.3E-05 2.2E-03 2.9E-06 20000 3.3E-04 2.6E-05 3.2E-05 1.7E-03 2.2E-06 30000 2.1E-04 1.7E-05 2.4E-05 1.3E-03 1.7E-06 40000 1.8E-04 1.4E-05 2.1E-05 1.2E-03 1.5E-06 50000 1.6E-04 1.3E-05 2.0E-05 1.1E-03 1.4E-06
9.1.14 UV Contamination
The UVIS detector is regularly monitored for contamination effects. These are related to volatile molecules that can progressively accumulate on either the detector itself or on other optical surfaces, and can cause a decline of sensitivity. When present, contamination is expected to manifest as a wavelength-dependent decline in the photometric throughput, strongest in the bluest filters. Historically, this monitoring has been done via observations of the spectrophotometric white dwarf standard GRW+70d5824 (GRW+70) in several key filters from 200 nm to 600 nm, with red filters acting as a control ( WFC3 ISR 2014-20). Recently, several major updates have been made to the UVIS contamination monitoring program, including the transition to a second white dwarf standard star, GD153, in late-2015 ( WFC3 ISR 2017-15), and additional monitoring data using scan-mode observations ( WFC3 ISR 2017-21).
Figure 9.7 shows the cumulative flux losses in units of percent loss per year as function of wavelength, based on linear fits to GRW+70 photometric measurements in a subset of blue filters (F218W, F225W, F275W, F336W, F438W) and in two control filters (F606W and F814W).  These are also reported in Table 9.5 along with the estimated uncertainties.
A small, steady decline in count rate is found for most filters but no evidence of contamination. These declines range from 0.01% to 0.3% per year and are stronger in longer wavelength filters, the opposite of the signature for contamination. Similar temporal changes are found for both standards, and the long-term trends in throughput agree with previous trends derived in 2014. For F606W, this amounts to a total decline of ~2.4% over eight years from 2009-2017. Work is underway to derive time-dependent corrections to the inverse sensitivity (zero point) values reported in the image header via the image photometry table (IMPHTTAB) reference file.
Table 9.5: The percent loss in flux per year, Fluxamp, for the white dwarf standard GRW+70d5824 observed in the A and C amplifiers, where Stddevamp is the estimated uncertainty.
 Filter FluxA FluxC F218W -0.001 0.014 +0.017 0.020 F225W +0.024 0.022 +0.021 0.020 F275W -0.058 0.017 +0.026 0.023 F336W -0.016 0.023 +0.008 0.027 F390M -0.196 0.049 -0.006 0.048 F438W -0.193 0.020 -0.179 0.032 F467M -0.248 0.061 -0.120 0.050 F547M -0.283 0.038 -0.141 0.038 F555W -0.214 0.057 -0.175 0.043 F606W -0.312 0.018 -0.249 0.021 F814W -0.170 0.023 -0.110 0.022 F850LP -0.173 0.124 -0.165 0.046 F218W -0.001 0.014 +0.017 0.020
Figure 9.6: Flux loss (percent) for GRW+70d5824 in the F606W filter measured in UVIS1 and UVIS2 based on observations from 2009 to 2016. Observations marked with 'X' were data taken in amplifiers B and D and were not included in the linear fit due to the limited date range. The symbols ‘m’ and σ annotated on the plot represent the slope (percent loss per year) and the total scatter in the data over the full MJD date range. See Table 9.5 for losses in other UVIS filters.

WFC3 Data Handbook > Chapter 9: WFC3 Data Analysis > 9.1 Photometry