9.1.1 Photometric Systems

The WFC3 filters naturally define their own photometric system and users are encouraged to refer their photometric results to this native system. The natural instrumental magnitude of an object observed in a WFC3 filter is instrumental mag = -2.5 log (count rate), where the count rate is in units of electrons per second (e¯/sec). WFC3 supports the STMAG, ABMAG and VEGAMAG photometric systems and provides zero points for these, in addition to the filter-dependent instrument sensitivity, which converts the measured count rate (e¯/sec) to a mean flux density F_λ in units of erg cm^-2 s^-1 Å^-1 and F_ν in units of erg cm^-2 s^-1 Hz^-1.

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 F_λ. An object with F_λ = 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 F_λ - 21.10

In the ABMAG system, the flux density is expressed per unit frequency, and the reference spectrum is flat in F_ν. An object with F_ν = 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 F_ν - 48.6

The relationship between ABMAG and STMAG is:

• ABMAG = STMAG - 5 log (PHOTPLAM) + 18.692

where F_ν is expressed in erg cm^-2 s^-1 Hz^-1, F_λ 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:

• m_vega= -2.5 log10 (F_object/F_vega) 

where F_vega is the CALSPEC observed flux density of Vega. For the equations that define the average flux, see Bohlin 2014 and Bohlin et al. 2020. 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 (Sirianni et al. 2005).

9.1.2 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). For WFC3, this throughput measures the performance within a given bandpass taking into account the HST Optical Telescope Assembly (OTA), pick-off mirror, relay mirror reflectivities, filter throughput, transmission of the outer and inner detector package windows, 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 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). Similarly, the 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 cm^-2 s^-1 Å^-1 ) of a star that produces a response of one electron per second in this bandpass. The header keyword PHOTPLAM is the pivot wavelength in Angstroms, where pivot wavelength is a measure of the effective wavelength of a filter (Tokunaga & Vacca 2006). 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

9.1.3 UVIS Photometric Calibration

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 (WFC3 Instrument Handbook Figure 5.2 and WFC3 ISR 2016-03 Figure 1) . At longer wavelengths, the response of two detectors is similar to within 0.5%. Monitoring observations of multiple CALSPEC standards acquired over time show the sensitivity of the two detectors is slowly changing (WFC3 ISRs 2016-17, 2017-15, 2018-16, 2021-04). The count rate ratio of the two detectors also changes with time.

The absolute photometric calibration of the two UVIS detectors has evolved over the years, including: a single detector solution computed in 2009 and 2012, a chip-dependent calibration in 2016 and 2017, and more recently a time- and chip-dependent calibration in 2020.

In-flight Calibration in 2009 and 2012

The first in-flight photometric calibration (in 2009) was based on the average measurements of two white dwarf spectrophotometric standard stars (GD153 and GRW+70d5824; WFC3 ISR 2009-31). The total system throughput of both CCDs was found to be significantly better than expected from the Thermal Vacuum 3 (TV3) testing campaign, with efficiency gains of ∼10% at the blue and red ends of the UVIS wavelength range and ∼20% near the central wavelength 5500 Å (Figure 6 in WFC3 ISR 2009-31). A smooth polynomial fit across wavelength was used to correct for the observed increase in on-orbit sensitivity.

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 standard star P330E. The revised solutions were not documented in a formal ISR but were posted to the WFC3 photometry web page and populated in the image headers. The updated calibration made use of improved flat fields delivered in 2011 which removed a large internal reflection, known as the UVIS 'flare', and corrected for low-frequency spatial variations in the in-flight sensitivity measured from dithered star cluster observations (WFC3 ISR 2013-10).

Chip-Dependent Solutions

On February 23, 2016, a chip-dependent photometric calibration was implemented for the UVIS detector, and updated inverse sensitivity values were computed (WFC3 ISR 2016-03) and later updated with improved CALSPEC models (WFC3 ISR 2017-14). The inverse sensitivity values were recomputed using calibration observations of only the three white dwarfs (GD153, GD71, G191B2B), obtained over about six years and measured at multiple positions on the detector. The 2016 inverse sensitivity values were systematically ~3% smaller than the 2012 set of solutions across the full wavelength range of the UVIS detector and are a result of improvements in the photometric reduction procedure (WFC3 ISR 2016-03). This systematic change brings the UVIS photometric system closer to ACS/WFC system (WFC3 ISR 2018-02).

Two new header keywords, PHTFLAM1 and PHTFLAM2, were populated with the inverse sensitivity values for UVIS1 and UVIS2, respectively. For backward compatibility with existing user software, the original header keyword PHOTFLAM was populated with the value of PHTFLAM1. A new keyword switch FLUXCORR was added to scale UVIS2 to match UVIS1 by multiplying the UVIS2 science array by the inverse sensitivity ratio, PHTRATIO = PHTFLAM2/PHTFLAM1 (see Sections 3.2.13 and 3.4.3). 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). UVIS2 subarray data obtained are also scaled by the PHTRATIO, ensuring that sources have the same count rate in calibrated images, regardless of the chip on which they are observed. During the 2016 photometric calibration update, new flat fields were also 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). 

Time-Dependent Solutions

The 2016 chip-dependent calibration assumed a constant detector sensitivity with time. As more monitoring data were acquired, small sensitivity changes up to about 0.2% per year were found, depending on the filter and the detector (WFC3 ISR 2018-16, WFC3 ISR 2021-04). Over WFC3's on-orbit timespan to date (2009-2020), the change can amount to about 2%. Differences in the time-dependent sensitivity for UVIS1 and UVIS2, as well as small errors in the flat field between different amplifiers, resulted in count rate ratios across the two UVIS detectors differing by as much as 2% (WFC3 ISR-2018-08, WFC3 ISR 2021-04).

The models for the HST primary spectrophotometric standard white dwarfs (GD153, GD71 and G191B2B) provided by the CALSPEC calibration database were updated in March 2020 (Bohlin et al. 2020). Also, the Vega reference grey flux at 0.5556 μm, as reconciled with mid-IR absolute flux measures from the SPIRIT III instrument on MSX (Midcourse Space Experiment), increased by ~0.9%. The spectral energy distribution for Vega used in the new 2020 calibration is alpha_lyr_stis_010.fits. The standard white dwarf absolute fluxes are determined by the normalization of their modeled spectral energy distributions to their respective relative responses to Vega, using STIS precision spectrophotometry of all four stars along with the flux of Vega at 0.5556 μm (3.47x10^-9 erg cm^-2 s^-1 Hz^-1). This method provides the basis for HST's entire calibration system. With the adoption of the new models, the HST primary standard white dwarf absolute fluxes increased overall by ~2% for wavelengths in the range 0.15 - 0.4 μm, and ~1.5% in the range 0.4 - 1 μm, necessitating an update to the WFC3 inverse sensitivities. 

Major changes in the 2020 photometric calibration compared to the 2017 calibration can be summarized as follows.

1. The new photometric values are based on updated SEDs for the standard stars and a new reference flux for Vega (Bohlin et al. 2020).
2. Encircled energy values for a few filters were updated by correcting for the slow changes in sensitivity over time, then re-drizzling the standard star images and using the result to compute the new inverse sensitivities. 
3. Four additional years (2016-2019) of standard star photometry were included.
4. Data from an additional white dwarf spectrophotometric standard (GRW+70d5824) was included in the analysis.
5. Time-dependent corrections were applied to standard star photometry before deriving the inverse sensitivities. Furthermore, the standard star photometric measurements were weighted according to their photometric errors and the number of collected measurements.

Figure 9.1 shows an example of the time-dependent behavior of UVIS photometry over about 12 years, in this case for UVIS2 and the F814W filter.

The new time-dependent inverse sensitivities provide a photometric internal precision of < 0.5% for wide-, medium-, and narrow-band filters, with a significant improvement compared to the prior 2016-era values ( < 1% for wide-, < 2% for medium-, and < 5 - 10% for narrow-band filters). The 2020 photometric recalibration resulted in an updated correction for the inflight detector response, new aperture corrections, and new filter throughput tables for all filters delivered to CRDS. A new photometry table (IMPHTTAB) was also delivered ('51c1638pi_imp.fits', see Table 9.3) and all WFC3/UVIS archival data were reprocessed through the new version of the pipeline (calwf3 v3.5.2). The updated models can be downloaded from the CALSPEC webpage and used in synphot simulations.

The 2020 calibration now ties the inverse sensitivity values to a common reference epoch, i.e. MJD = 55008 (June 26, 2009) for all filters.  Values of the inverse sensitivities for both detectors at each observing epoch can be found in the image header. We also provide a tutorial in Section 9.5.2 for running synphot with the new filter curves in order to derive the inverse sensitivity, zeropoint values and throughput curves for any detector, observation epoch, filter or aperture. A second tutorial in Section 9.5.2 shows how to use the new time-dependent solutions to work with UVIS data obtained at different observation dates.

9.1.4 UV Filters

Photometric Calibration

One motivation of the chip-dependent calibration described above was to quantify and correct for bandpass differences, i.e. the response functions, between the two detectors in the UV.  Even when two systems (telescope + UVIS1 or UVIS2) use the same filter, the effective bandpasses can be dissimilar in the UV  (WFC3 ISR 2017-07, WFC3 ISR 2018-08, WFC3 ISR 2021-04).

Calibrated WFC3 data products (*flt.fits, *flc.fits) are combined in the pipeline using AstroDrizzle to create distortion-free data products (*drz.fits, *drc.fits) with the two CCD chips drizzled to the same output frame. AstroDrizzle assumes the images are in units of counts or count rate and not in the flux units used for photometry. This means that the same (hot white dwarf) star must have the same count rate on both chips for the drizzle software to properly combine dithered data in which the sources cross the chip boundary. Because of the different effective bandpasses in the UV, the measured count ratio between chips for the white dwarf standards does not equal the PHTRATIO value provided in the 2016 IMPHTTAB ('z*imp.fits') for several UV filters (see below). For example, the ratio of count rates between the two CCDs is about 2% higher in F225W filter than the ratio of the computed inverse sensitivity values.

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. (A similar approach was adopted for the UV filters in the October 2020 time-dependent IMPHTTAB.)  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.

For programs which require precise UV photometry, users are advised to treat the two chips as separate detectors and use the chip-dependent keyword values. For UVIS1, this means simply multiplying the measured count rate by PHOTFLAM. For UVIS2, the science array has already been scaled by PHTRATIO, so flux calibration may be achieved by dividing the measured count rate by PHTRATIO and then multiplying by PHTFLAM2, as reported in the image header. (Equivalently, this may be achieved simply by multiplying by PHTFLAM1.) Photometry may be computed directly from the calibrated data products (*flt.fits, *flc.fits) multiplied by the pixel area map to account for geometric distortion. Alternately, users can correct for variations in the pixel area by drizzling each chip separately prior to performing photometry. This makes it easier to keep track of which inverse sensitivity value to use with which detector pixels, of particular importance for observations obtained at different orientations or with large dithers.

A flowchart for determining which photometric keywords to use for UV photometry is provided in Figure 9.2. 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 drizzled (*drz.fits, *drc.fits) data products, calwf3 multiplies the UVIS2 science array by PHTRATIO (the inverse sensitivity ratio) to equalize 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 the 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 (*raw.fits) data with calwf3, and using a third set of keywords (bottom right).

Color terms

The UVIS1 and UVIS2 detectors have different quantum efficiencies in the ultra-violet (UV) regime (λ < 4,000 Å), where count rate ratios change as a function of spectral type. When calibrating photometry of stars cooler than T_eff ~ 30,000 K in the UV filters (e.g. when observing open and globular clusters, resolved local group galaxies, Galactic stellar populations), color term transformations must be applied to UVIS2 magnitudes. Sources of any spectral type observed only on a single UVIS detector will not require any magnitude offset.

The upper panel of Figure 9.3 shows the synthetic ST magnitude difference, UVIS1 – UVIS2, for a sample of CALSPEC stars of varying spectral type (the white dwarfs (WDs) include G191B2B, GD71 and GD153), as computed for the three UV filters F218W, F225W, and F275W. Note that cool red sources such as the G-type star P330E measured on UVIS2 have a magnitude offset relative to UVIS1 up to ~0.08 mag when observed with the F225W filter while F-type stars such as HD160617 have a magnitude offset of ~0.04 mag.

The lower panel of Figure 9.3 shows the ST magnitude difference for the F225W and F275W filters for ω Cen Extreme Horizontal Branch (EHB), Horizontal Branch (HB), Main Sequence (MS), and Red-Giant Branch (RGB) stars measured on different detectors and amplifiers, A (UVIS1) and C (UVIS2). WFC3 observations of ω Cen validate the results of synthetic photometry: red stars (RGBs) observed on UVIS2 have a magnitude offset up to 0.08 mag relative to UVIS1.

Lookup tables with color term transformations are provided in WFC3 ISR-2018-08. The corrections may be applied to UVIS2 magnitudes when observing with the three UV filters F218W, F225W, and F275W. The inverse sensitivity ratio, PHTRATIO, is derived using photometry of the CALSPEC white dwarfs and is valid for hot stars, T_eff > 30,000 K. For cooler stars, when observing with UV filters, PHTRATIO is not equal to the ratio of the two detectors' count rates but changes with the stellar spectral type. Thus photometry for cooler stars measured on UVIS2 will require a magnitude offset depending on their color, temperature or spectral type. Before applying the offset to magnitudes measured on UVIS2, photometry must first be calibrated using the UVIS1 inverse sensitivities:

STMAG_ZPT(UVIS1) = -21.1 -2.5 x log(PHOTFLAM) 
STMAG_ZPT(UVIS2) = -21.1 -2.5 x log(PHOTFLAM) + Delta (Mag)

where the Delta (Mag) = Mag(UVIS1 – UVIS2) correction is listed in lookup tables in WFC3 ISR-2018-08.

Calibration of the Narrow-Band Filters for Emission-Line Objects

WFC3 has several narrow-band filters which are often used to study emission-line objects like planetary nebulae and HII regions. To derive the emission-line fluxes in such cases, one must correct the observed flux for signal arising from contaminating lines and the underlying continuum. A detailed method to carry out this correction is described in Appendix A of O’Dell et al. (2013).

9.1.5 UVIS Quad Filter Photometry

New inverse sensitivities for the 20 UVIS quad filters have been computed using the updated 2020 CALSPEC models for the HST flux standard stars as well as the updated reference fluxes of Vega (WFC3 ISR 2021-04). The new values do not include any time-dependent correction since insufficient observations were available to reliably measure any changes over time. Aside from the new models, the quad filter photometric calibration is unchanged from 2012 and still makes use of pre-flight flats that contain the UVIS flare (see Figure 5.4). 

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. A subarray observation with a quad filter only covers a single detector quadrant and hence, the science data will have the correct filter keyword reported in their headers. As there is only a single filter keyword in the science image headers, full-frame quad observations always have the keyword (FILTER) populated with the quad element that corresponds to quadrant A, regardless of which quad 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 the image header and search for that association in MAST, where the archive database is populated with the correct ‘FILTER’ keyword. This discrepancy is due to different software systems creating the MAST database and populating the science image header keywords.

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. As a result, the photometric keywords are not populated in the image header during calwf3 processing. The PHOTFLAM values thus have to be retrieved elsewhere, for example from Table 7 in WFC3 ISR 2021-04 or from the quad filter tables on the photometry website.

Table 9.1:  Detector quadrant (amp) imaging locations for the WFC3 quad filters. 

9.1.6 IR Photometric Calibration

For the IR detector, the initial on-orbit photometric calibration (in 2009) was based on the average of two HST spectrophotometric standards (GD153 and P330E, a hot white dwarf and G-type star, respectively). Following the same procedure adapted for UVIS, a smooth polynomial fit was used to correct for the increase in on-orbit sensitivity with wavelength relative to pre-launch ground tests (WFC3 ISR 2009-30). By 2012, a larger cumulative set of calibration data allowed for more accurate filter-dependent corrections to the sensitivity and the revised solutions were based on the average of three white dwarfs (GD153, GD71, G191B2B) plus the G-type star (P330E). While these 2012-era 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. 

In October 2020, an updated set of inverse sensitivities was calculated and delivered, using the same data from the 2012 calibration plus 8 additional years of monitoring for the same four CALSPEC standards plus GRW+70d5824 (WFC3 ISR 2020-10). The 2020 photometric calibration also includes updates to the flat field reference files described in Section 7.8.3 as well as updates to the CALSPEC models. These new model spectra changed the flux of the stars (and thus the resulting zero points) by approximately 1% in the IR (Bohlin et al. (2020); Section 9.1.3).

Current estimates of the IR photometric uncertainties are ~2% for broad-band 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 exhibits a low-level count rate non-linearity (CRNL) 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 (about 23rd magnitude) using the computed set of IR zero points will be systematically ~4.5% too faint and require manual correction (WFC3 ISR 2010-07 and WFC3 ISR 2011-15). Additional calibration data were obtained in 2016-2017 (programs 14868 and 14870) to further quantify and correct for this effect as a function of wavelength. The results are presented in WFC3 ISR 2019-01 show the CRNL to be 0.0077 +/-0.0008 mag/dex, characterized over 16 magnitudes with no apparent wavelength dependence.

Measurements of standard stars acquired via staring mode do not show obvious evidence of any time dependence (WFC3 ISR 2020-10). However, issues with photometric repeatability as described in section Section 7.11 make detection of small sensitivity changes difficult to confirm. Independent studies of Omega Centauri in F160W (WFC3 ISR 2020-05) and the standard stars observed with the grisms (Bohlin and Deustua (2019)) show small declines in sensitivity over ~12 years, about 0.1-0.3% per year, while measurements of M35 via spatial scanning over ~5 years show an order of magnitude less effect (about 0.02% per year; WFC3 ISR 2021-05).  Further investigations are underway to better characterize the evolution of the IR detector sensitivity.

9.1.7 Image Photometry Reference Table

After December 2012, the HST calibration pipeline software (HSTCAL) no longer invokes synphot to calculate the photometric keyword values on-the-fly. Instead it uses an image photometry lookup table (IMPHTTAB) for each WFC3 channel which contains the values for PHOTFLAM (the inverse sensitivity), PHOTPLAM (the filter pivot wavelength), and PHOTBW (the filter bandwidth). The WFC3 data reduction pipeline calwf3 v3.1.6 was implemented at that time to support the change.  The version of calwf3 used to calibrate WFC3 data may be found in the image header keyword CAL_VER. The IMPHTTAB reference file for the IR channel is listed in Table 9.2 and includes the latest 2020 IR calibration.

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. The use of “Infinite” standard aperture ensures that the inverse sensitivity value is equally valid for point sources as well as extended sources. The UVIS time-dependent calibration was implemented in calwf3 v3.5.2, and the IMPHTTAB now contains additional columns to specify the inverse sensitivity as a function of date for each CCD chip.

If data from multiple-visits programs are retrieved from MAST at different times (e.g. after the execution of each visit), there may be 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 Section 3.5.

Table 9.2: The IMPHTTAB reference file used to populate the IR photometry keywords in the image header.

Table 9.3: The IMPHTTAB reference file used to populate the UVIS photometry keywords in the image header.

9.1.8 Aperture Corrections


The inverse sensitivity (response) values for the two WFC3 channels are computed using an aperture radius of 10 pixels (UVIS) and 3 pixels (IR) and then corrected to infinite aperture using the encircled energy. 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 (WFC3 ISR 2009-37, WFC3 ISR 2009-38). The IR EE was derived from deep exposures in F098M and F160W and extrapolated to other wavelengths using an optical model.  A similar approach was taken for the UVIS EE which was based on deep exposures in F275W and F621M. 

Currently, the UVIS detector uses filter-based EE curves for aperture corrections (see Tables 6 & 7 in WFC3 ISR 2017-14 and the equivalent Tables 13-17 in WFC3 ISR 2016-03). The infinite aperture response value can be scaled to the equivalent aperture-based response using the EE fractions, which are wavelength specific. For example, the measured UVIS1 flux in the F606W filter within a 10 pixel radius aperture is ~91% of the total flux and within a 50 pixel (2.0") radius 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". 

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 EE fraction (in flux units). Users should determine the offset between their own 'small aperture' photometry and aperture photometry within a slightly larger radius, beyond which the EE does not change due to orbital breathing or detector position (as described in the next paragraph). 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 MAST PSF search tool to download PSFs extracted from WFC3 archival data for a similar detector position and focus as the observation of interest. The WFC3 observed PSF database can be accessed by choosing the 'Select a collection' to 'WFC3 PSF' on the MAST Portal interface (for details, see WFC3 ISR 2021-12). There are a total of about 23 million UVIS PSFs and 5 million IR PSFs in all the WFC3 images taken prior to January 2020, and all of these observed PSFs are available through the MAST Portal interface. In order to download appropriate PSFs, the user can first use the HST focus model (the "Annual Summary" provides the model focus values at 5-minute intervals) to estimate the focus value at the time of the observation. Then, the WFC3 PSF database can be searched for PSFs observed under similar focus, detector position, etc. as described in WFC3 ISR 2021-12. 

Model EEs have been tabulated for IR (WFC3 ISR 2009-37) and UVIS (WFC3 ISR 2009-38). 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 (WFC3 ISR 2013-11).

New EE corrections were calculated in 2020 for two UVIS filters, F275W and F814W, by correcting for time-dependent sensitivity changes of the detector before stacking the images. Values derived for UVIS1 and UVIS2 now show improved agreement with each other and with the 2009 EE values. Following these results, EE values for the other UV filters were also changed by ~1%. The EE at wavelengths greater than 7,500 Å were changed by ~0.5% to be in close agreement with the F814W values. Figure 9.4 shows the updated EE values at r=10 pixels (0.3962") as a function of wavelength and compares to prior calibration.

9.1.9 Color Corrections

In some cases it may be desirable to compare WFC3 photometric results with 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 (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 computed.  A new WFC3 notebook tutorial has been developed to assist users with these computations and is described in Section 9.5.2.

As described in Section 9.1.4.2, 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 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, a larger pixel collects more photons relative to a smaller pixel, leading to an overall gradient in an image of an intrinsically uniform background. However, the flat-fielding process in the HST calwf3 pipeline is designed to correct for that gradient and produce images that have a flat background. As a result, while surface photometry measurements on flat-fielded science data (flt) will be correct, the measured total brightness of sources will vary depending on the position of the object i.e. the areas of the pixels underlying the source.

To achieve uniform aperture photometry of point sources over the detector, observers can either use flt images after applying a pixel area map (PAM) correction or use distortion-free images (drz). The AstroDrizzle software corrects for distortion, yielding images (drz, drc) which have a flat sky and contain pixels that are uniform in area (i.e., corrected for distortion and related pixel area variations). Therefore, photometry of any source in an AstroDrizzle (drz, drc) image will yield the same count rate irrespective of the position of the source on the image. Photometry measured on a calibration pipeline image (flt) requires a field-dependent correction factor to achieve uniformity in the measured count rate of an object across the field.

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 calibrated (flt) image and each pixel value is set to the normalized area of that pixel. By multiplying the calibrated (flt) images by the PAM, users will recover the same count rate on both types of images (flt and drz,drc) and the same zero point will apply to both data products: drz = flt * PAM, where the (flt) image has been converted to counts per second.

A contour plot of the relative pixel size across the UVIS image, normalized to the central pixel, is shown in the left panel of Figure 9.5; the ratio of maximum to minimum pixel area is 1.074. The variation of pixel area across the IR channel is shown in the right panel of 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, which also discusses a unique choice for normalizing the WFC3 PAMs that differs from previous instruments. This approach ensures that the PAMs do not artificially scale the flux in FLT images by large amounts. Instead, 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 (WFC3 ISR 2010-08).

Figure 9.5: (Left) 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.

(Right) Variation of the effective pixel area 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 images (flt, drz) we consider a simple idealized example of a 3 × 3 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

Assume an extended object has a surface brightness of 2 e¯/pixel in the undistorted case. Without any geometric distortion the image is shown in Figure 9.6 as the 'Actual Scene on the sky. With geometric distortion, the pixels are not square and the pixel area varies across the detector, as shown in the 'Detector pixel layout on the sky', with a corresponding pixel area map (PAM) in the top-right panel.

As a result of the distortion, there will be an apparent variation in surface brightness in the raw image (no flat applied). The geometric 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 science image (FLT) 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 flat fielded image (FLT); the resulting image (DRZ) will have pixels free of geometric distortion.

Example #2 Photometry of a point source

Assume we are observing a point source and that all the flux is included in the 3 × 3 grid with the count distribution as shown in the left panel of Figure 9.7. The total counts are 100. Due to geometric distortion, the PSF as seen in the raw image is distorted, i.e. the total counts are conserved but they are redistributed on the CCD. The flat-field correction, however, does not conserve the total counts since the counts now add up to 99.08, instead of 100. For accurate integrated photometry on flat fielded WFC3 images, the pixel area variation must be taken into account. This can be done by multiplying the science image (FLT) by the PAM or by running AstroDrizzle and performing the photometry on the DRZ image.

Only by running AstroDrizzle can the geometric distortion be removed, but both approaches (using either drz,drc or flt x PAM) will correctly recover integrated 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 flt x PAM image, they should calculate a new aperture correction to the total flux of the star as the aperture corrections discussed in Section 9.1.8 are only for drizzled output images (drz, drc). In most cases, the aperture correction for distorted flt images will be quite different from the same star measured in a drz image, particularly for small radius apertures.

9.1.11 CTE

To date, all CCDs flown in the harsh radiation environment of HST suffer degradation of their charge transfer efficiency (CTE). The effect of this degradation is to reduce the apparent brightness of sources, requiring the application of corrections to restore measured integrated counts to their true value. On-orbit data taken with the WFC3 UVIS detector shows evidence for CTE degradation over time (see Section 6.3), and this may be accounted for using either a pixel-based correction model (Section 6.4) or an empirical correction (Section 6.5).

9.1.12 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, calculated by convolving a blackbody of the given effective temperature (T_eff) 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 (T_eff) of ~4000 K or cooler, necessitating appropriate corrections.

Table 9.4: Fraction of flux longward of 400 nm as a function of effective temperature.

9.1.13 UV Contamination

The UVIS detector is regularly monitored for contamination effects i.e. a decline of sensitivity which could be due to volatile molecules accumulating on either the detector itself or on other optical surfaces. When present, contamination is expected to manifest as a wavelength-dependent decline in the photometric throughput, i.e. with the strongest effect present in the bluest filters. Historically, this monitoring has been done via observations of the spectrophotometric white dwarf standard GRW+70d5824 in several key filters from 200 nm to 600 nm, with red filters acting as a control (WFC3 ISR 2011-18, WFC3 ISR 2014-20). In late 2015, a second white dwarf standard star, GD153, was added to the monitoring program (WFC3 ISR 2017-15). In addition, scanning-mode observations of two standard stars were added to improve the precision of relative photometry over time (WFC3 ISR 2017-21, WFC3 ISR 2021-04).

A small, steady decline in count rate is found for most filters but no evidence of contamination. These declines range from 0.1% to 0.2% per year and are similar in strength in both the UV and longer-wavelength filters, contrary to the expectation for contamination. Similar temporal changes are found for all flux standards, and the long-term trends in throughput agree with previous trends derived in WFC3 ISR 2017-15, WFC3 ISR 2018-16, and WFC3 ISR 2021-04.  New time-dependent inverse sensitivity (PHOTFLAM) values are described in Section 9.1.3 and are recorded in the image headers by calwf3 using the image photometry table (IMPHTTAB) reference file.