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ACS Data Handbook 2011
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ACS Data Handbook > Chapter 5: ACS Data Analysis > 5.1 Photometry

5.1
5.1.1
We strongly recommend that, whenever practical, ACS photometric results be referred to a system based on its own filters. Transformation to other photometric systems is possible (see Sirianni et al., 2005, PASP) but such transformations have limited precision and strongly depend on the color range, surface gravity and metallicity of the stars considered.
Three magnitude systems, based on ACS filters are commonly used: VEGAMAG, STMAG and ABMAG. They are all based on the knowledge of the throughput for the entire system (OTA + ACS CAMERA + FILTER + DETECTOR). These synthetic systems are tied to observed standard stars.
VEGAMAG, a widely-used standard star-based system, is subject to systematic errors tied to the calibration of the standard star. In the last decades, it has become more common to use photometric systems such as ABMAG (Oke, J. B. 1964, ApJ 140, 689) or STMAG (Koorneef, J. et. al. 1986, in Highlights of Astronomy (IAU), Vol.7, ed. J.-P. Swings, 833) which are directly related to physical units. The choice between standard-based and flux-based systems is mostly a matter of personal preference. Any new determination of the absolute efficiency of the instrument results in revised magnitudes for these three systems.
VEGAMAG
The VEGAMAG system uses Vega (α Lyr) as the standard star. The spectrum of Vega used to define this system is a composite spectrum of empirical and synthetic spectra (Bohlin & Gilliland, 2004). The “Vega magnitude” of a star with flux F is
where Fvega is the calibrated spectrum of Vega in SYNPHOT. In the VEGAMAG system, by definition, Vega has zero magnitude at all wavelengths.
STMAG and ABMAG
These two similar photometric systems are flux-based. The conversion is chosen such 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, while in the ABMAG system, the flux density is expressed per unit frequency. The magnitude definitions are:
where Fν is expressed in erg cm-2 sec-1 Hz-1, and Fλ in erg cm-2 sec-1 Å-1. Another way to express these zeropoints is to say that an object with a constant Fν = 3.63 x 10-20 erg cm-2 sec-1 Hz-1 will have magnitude AB = 0 in every filter, and an object with Fλ = 3.63 x 10-9 erg cm-2 sec-1 Å-1 will have magnitude STMAG = 0 in every filter.
Zeropoints
By definition, the zeropoint of an instrument is the magnitude of an object that produces one count per second.
Each zeropoint refers to a count rate measured in a specific aperture. For point source photometry, it is not practical to measure counts in a very large aperture. Therefore, counts are measured in a small aperture, then an aperture correction is applied to transform the result to an “infinite” aperture. For ACS, all zeropoints refer to a nominal “infinite” aperture of radius 5".5.
By definition, the magnitude in the passband P in any of the ACS systems is given by:
ACSmag(P) = -2.5 log(total electrons/sec) + zeropoint
The choice of the zeropoint determines the magnitude system of ACSmag(P). There are several ways to determine the zeropoints:
Use SYNPHOT; you can renormalize a spectrum to 1 count/second in the appropriate ACS passband and specify an output zeropoint value based on a selected magnitude system (provided that the most updated throughput tables are included in your SYNPHOT distribution). For instance, the calcphot task can be used with a renormalized 10,000°K blackbody to calculate the photometric parameters for a passband, using the following syntax:
calcphot obsmode "rn(bb(10000),band(obsmode),1,counts)" form
where, in this example, “obsmode” is the passband, e.g. “acs,hrc,f555w” and “form” is the output magnitude system: “ABMAG,” “VEGAMAG,” or “STMAG.”
Use the header keywords; the simplest way to calculate the STMAG or ABMAG zeropoint for your data is to use the photometric keywords (listed below) in the SCI extension of ACS images:
-
PHOTFLAM is the inverse sensitivity (erg cm-2 sec-1 Å-1); it represents the flux of a source with constant Fλ which produces a count rate of 1 electron per second.
-
PHOTPLAM is the pivot wavelength.
-
PHOTZPT is the STMAG zeropoint, permanently set to -21.1.
The header keywords PHOTFLAM, PHOTZPT, and PHOTPLAM relate to the STMAG and ABMAG zeropoints through these 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) + 18.6921
Use a list of published zeropoints, available at the ACS Web page:
/hst/acs/analysis/zeropoints
Additional information about zeropoints are available at that Web page. Please note that WFC zeropoints for -81°C are still valid for post-SM4 data.
5.1.2
In order to reduce errors due to residual flat fielding errors and background variations, and to increase the signal-to-noise ratio, aperture photometry and PSF-fitting photometry are usually performed by measuring the flux within a small radius around the center of the source. (For a discussion on the optimal aperture size, see Sirianni et al., 2005, PASP). Therefore, a small aperture measurement needs to be adjusted to a “total count rate” by applying an aperture correction.
For point sources, ACS zeropoints (available in STMAG, ABMAG, and VEGAMAG) are applied to a measured magnitude that is aperture-corrected to a nominal “infinite” aperture of radius 5".5. For surface photometry, these zeropoints can be directly added to values in units of magnitude/arcsec2. In order to facilitate the conversion for point sources, Sirianni et al., 2005 provides corrections derived from the encircled energy profiles of an intermediate aperture (0".5 radius) to an infinite aperture—these corrections from the paper are reproduced in Tables Table 5.1 and Table 5.2. This correction is filter dependent and varies between ~0.09 and ~0.12 magnitudes for WFC and between ~0.09 and ~0.31 magnitudes for the HRC.
Table 5.1: Aperture Correction from 0".5 Aperture Radius to Infinite Aperture Radius in units of OBMAG (from Sirianni et al., 2005, PASP)
Sirianni et al. defined OBMAG as
OBMAG = -2.5 log (count rate, r <=0."5 [e-/s]) - Aperture Correction.
Users should determine the aperture correction between their own photometry and aperture photometry with a 0".5 radius aperture. This is usually done by measuring a few bright stars in an uncrowded region of the field of view using the measure aperture and the 0".5 radius aperture, and applying the difference between them to all photometric measurements. If such stars are not available, encircled energies have been tabulated by Sirianni et al., 2005. However, note that accurate aperture corrections are a function of time and location on the chip and also depend on the kernel used by Drizzle1; blind application of tabulated encircled energies, especially at small radii, should be avoided.
Aperture corrections for near-IR filters present further complications; all ACS CCD detectors suffer from scattered light at long wavelengths. These thinned backside-illuminated devices are relatively transparent to near-IR photons. The transmitted long wavelength light illuminates and scatters in the CCD header, a soda glass substrate. It is then reflected back from the header’s metallized rear surface and re-illuminates the CCDs front-side photosensitive surface (Sirianni et al. 1998, proc SPIE vol. 3555, 608, ed. S. D’Odorico). The fraction of the integrated light in the scattered light halo increases as a function of wavelength. As a consequence, the PSF becomes increasingly broad with increasing wavelengths. WFC CCDs incorporate a special anti-halation aluminum layer between the frontside of the CCD and its glass substrate. While this layer is effective at reducing the IR halo, it appears to give rise to a relatively strong scatter along one of the four diffraction spikes at wavelengths greater than 9000 Å (Hartig et al. 2003, proc SPIE vol. 4854, 532, ed. J. C. Blades, H. W. Siegmund), see Section 5.1.4 for more details.
The same mechanism responsible for the variation of the intensity and extension of the halo as a function of wavelength is also responsible for the variation of the shape of the PSF as a function of color of the source. As a consequence, in the same near-IR filter, the PSF for a red star is broader than the PSF of a blue star. Gilliland & Riess (2002 HST Calibration Workshop Proceedings, page 61). and Sirianni et al., 2005, PASP provide assessments of the scientific impact of these PSF artifacts in the red. The presence of the halo has the obvious effect of reducing the signal-to-noise and the limiting magnitude of the camera in the red. It also impacts the photometry in very crowded fields. The effects of the long wavelength halo should also be taken into account when performing morphological studies and performing surface photometry of extended objects (see Sirianni et al., 2005, PASP for more details).
The aperture correction for red objects should be determined using an isolated same-color star in the field of view, or using the effective wavelength versus aperture correction relation (Sirianni et al., 2005, PASP). If the object’s spectral energy distribution (SED) is available, an estimate of the aperture correction is also possible with SYNPHOT; a new parameter, “aper,” has been implemented to call the encircled energy tables in the OBSMODE synphot field for ACS. A typical OBSMODE for an aperture of 0".5 would read like “acs,wfc,f850lp,aper$0.5”. A comparison with the infinite aperture magnitude using the standard OBSMODEacs,wfc,f850lp” would give an estimate of the aperture correction to apply. Please refer to the SYNPHOT Handbook for more details.
Color Correction
In some cases it may be necessary to compare ACS photometric results with existing datasets in different photometric systems (e.g., WFPC2, SDSS, or Johnson-Cousins). Since the ACS filters do not have exact counterparts in any other standard filter sets, 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 could be introduced. The transformations can be determined by using SYNPHOT, or by using the published transformation coefficients (Sirianni et al., 2005). In any case, users should not expect to preserve the 1% - 2% accuracy of ACS photometry on the transformed data.
5.1.3
When ACS images are flat-fielded by the calacs pipeline; the resultant flt.fits files are “flat” if the original sky intensity was also “flat.” However, there is still very significant geometric distortion remaining in these images. The pixel area on the sky varies across the field, and as a result, relative point source photometry measurements in the flt.fits images are incorrect.
One option is to drizzle the data; this will remove geometric distortion while keeping the sky flat. Therefore, both surface and point source relative photometry can be performed correctly on the resulting drz.fits files. The inverse sensitivity (in units of erg cm-2 sec-1 Å-1), given by the header keyword PHOTFLAM, can be used to compute the STMAG or ABMAG zeropoint, and to convert flux in electrons/seconds to absolute flux units:
STMAG_ZEROPOINT = -2.5 Log (PHOTFLAM) - PHOTZPT
ABMAG_ZEROPOINT = -2.5 Log (PHOTFLAM) - 21.10 - 5 Log (PHOTPLAM) + 18.6921
where,
STMAG_ZEROPOINT is the ST magnitude zeropoint for the observing configuration (given in the header keyword PHOTMODE).
PHOTFLAM2 is the mean flux density (in erg cm-2 sec-1 Å-1) that produces 1 count per second in the HST observing mode (PHOTMODE) used for the observation.
PHOTZPT2 is the ST magnitude zeropoint (= 21.10).
PHOTPLAM2 is the pivot wavelength.
Remember that for point source photometry, both these zeropoints should be applied to measurements corrected to the standard infinite aperture; for ACS, this is a radius of 5".5.
Additional information about zeropoints is available at the ACS Zeropoints Web page.
Users who wish to perform photometry directly on the distorted flt.fits files, rather than the drizzled (drz.fits) data products, will require a field-dependent correction to match their photometry with that obtained from drizzled data. Only then can the PHOTFLAM and PHOTPLAM values in the flt.fits images be used to obtain calibrated STMAG or ABMAG photometry. (Note: the corresponding drz.fits image has identical PHOTFLAM and PHOTPLAM values.)
The correction to the flt.fits images may be made by multiplying the measured flux in the flt.fits image by the pixel area at the corresponding position using a pixel area map (PAM), and then dividing by the exposure time. The easiest way to do it is to simply multiply the flt.fits image with its corresponding pixel area map.
DRZ_flux = FLT_flux * PAM / exposure time.
For example:
Both drz.fits and flt.fit images have units of electrons/seconds, and have the same PHOTFLAM values.
The PAM for the WFC is approximately unity at the center of the WFC2 chip, ~0.95 near the center of the WFC1 chip and ~1.12 near the center of the HRC. PAM images, which are very large, may be downloaded directly from this page:
/hst/acs/analysis/PAMS
Figure 5.1: Variation of the WFC and HRC Effective Pixel Area with Position in Detector Coordinates
Pixel Area Map Concept Illustration
To illustrate the concepts of extended source and point source photometry on flt.fits and drz.fits images, we consider a simple idealized example of a 3 x 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. Illustration of Geometric Distortion on a 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 ACS suffers from geometric distortion. As a consequence the pixel scale varies across the detector. The result is that the sky area coverage per pixel is not identical.:
The pixel area map (PAM), shown below, illustrates the differences in area for each pixel, represented by a fractional value, due to geometric distortion.
 
As a result, the raw data shows an apparent variation in surface brightness because some pixels detect flux from a larger sky area than others.
 
The geometrical area of each pixel is imprinted in the flat field, along with its photometric sensitivity. In this example, since we assumed that the quantum efficiency is unity everywhere, the flat field is the equivalent of the PAM:
 
ACS flat fields are designed to produce a flat image when the instrument is uniformly illuminated. This, however, means that pixels which are smaller than average on the sky are boosted, while pixels with relatively large areas are suppressed. Application of the PAM removes this effect—pixels now show the true relative illumination they receive from a uniform source. However, the image remains geometrically distorted. Thus when doing aperture photometry on the field, the user should take into account that aperture sizes defined in pixels are then not uniform in size across the field of view.
 
multidrizzle is run on the flt.fits image. The output image is free of geometric distortion and is photometrically accurate.
When drizzling a single image, the user may want to user the Lanczos kernel which provides the best image fidelity for the single image case. However, this kernel does not properly handle missing data, and causes ringing around cosmic rays, and thus should not be used for the combination of multiple images, where sections of the image lost to defects on one chip can be filled in by other chips.
For additional information about the inner workings of Multidrizzle, please refer to The Multidrizzle Handbook.
 
Example #2 Illustration of Geometric Distortion and 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 3 x 3 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, as shown in the fractional area values below.
 
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 needs to be taken into account. This can be done by multiplying the flt.fits 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, he or she needs to calculate a new aperture correction to the total flux of the star. The aperture corrections discussed in Section 5.1.2 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.fits image. This is particularly true for small radius apertures.
5.1.4
PSF Field Dependence
Point spread functions in the ACS cameras are more stable over the field of view than in any other HST camera, especially when compared to WFPC2. The PSF does vary slightly in both shape and width across the field to a degree that may affect photometric measurements. This effect is described in detail in ACS ISR 2003-06. The variations in the HRC are very small and probably negligible when using apertures greater than r = 1.5 pixels or using PSF fitting. However, the WFC PSF varies enough in shape and width that significant photometric errors may be introduced when using small apertures or fixed-width PSF fitting.
The WFC PSF width variation is mostly due to changes in CCD charge diffusion. Charge diffusion, and thus the resulting image blur, is greater in thicker regions of the detector (the WFC CCD thickness ranges from 12.6 to 17.1 microns, see Figure 5.2). At 500 nm, the PSF FWHM varies by 25% across the field. Because charge diffusion in backside-illuminated devices like the ACS CCDs decreases with wavelength, the blurring and variations in PSF width will increase towards shorter wavelengths. At 500 nm, photometric errors as much as 15% may result when using small (r < 1.5 pixel) apertures. At r = 4 pixels, the errors are reduced to < 1%. Significant errors may also be introduced when using fixed-width PSF fitting.
PSF shape also changes over the WFC field due to the combined effects of aberrations like astigmatism, coma, and defocus. Astigmatism noticeably elongates the PSF cores along the edges and in the corners of the field. This may potentially alter ellipticity measurements of the bright, compact cores of small galaxies at the field edges. Coma is largely stable over most of the field and is only significant in the upper left corner, and centroid errors of ~0.15 pixels may be expected there.
Observers may use TinyTim to predict the variations in the PSF over the field of view for their particular observation. TinyTim accounts for wavelength and field-dependent charge diffusion and aberrations, and can be found at:
http://www.stsci.edu/software/tinytim/
For point source relative astrometry, procedures for obtaining the best results are described in ACS ISR 2006-01.
Figure 5.2: WFC Chip Thickness (left) and PSF FWHM (right)
PSF Long Wavelength Artifacts
Long wavelength ( > 700 nm) photons can pass entirely through a CCD without being detected and enter the substrate on which the detector is mounted. In the case of the ACS CCDs, the photons can be scattered to large distances (many arcseconds) within the soda glass substrate before reentering the CCD and being detected. This creates a large, diffuse halo of light surrounding an object, called the “red halo.” This problem was largely solved in the WFC by applying a metal coating between the CCD and the mounting substrate that reflects photons back into the detector. Except at wavelengths longer than 900 nm (where the metal layer becomes transparent), the WFC PSF is unaffected by the red halo. The HRC CCD, however, does not have this fix and is significantly impacted by the effect.
The red halo begins to appear in the HRC at around 700 nm. It exponentially decreases in intensity with increasing radius from the source. The halo is featureless but slightly asymmetrical, with more light scattered towards the lower half of the image. By 1000 nm, it accounts for nearly 30% of the light from the source and dominates the wings of the PSF, washing out the diffraction structure. Because of its wavelength dependence, the red halo can result in different PSF light distributions within the same filter for red and blue objects. The red halo complicates photometry in red filters. In broadband filters like F814W and especially F850LP (in the WFC as well as the HRC), aperture corrections will depend on the color of the star, see Section 5.1.2. for more discussion of this. Also, in high-contrast imaging where the PSF of one star is subtracted from another (including coronagraphic imaging), color differences between the objects may lead to a significant residual over-or-under-subtracted halo.
In addition to the halo, two diffraction spike-like streaks can be seen in both HRC and WFC data beyond 1000 nm (including F850LP). In the WFC, one streak is aligned over the left diffraction spike (right spike in the HRC) while the other is seen above the right spike (below the left spike in the HRC). These seem to be due to scattering by the electrodes on the back sides of the detectors. They are about five times brighter than the diffraction spikes and result in a fractional decrease in encircled energy. They may also produce artifacts in sharp-edged extended sources.
Figure 5.3: CCD Scatter at Red Wavelengths.
WFC images of the standard star GD71 through filters F775W (9 sec., left), F850LP (24 sec., middle), and FR1016N at 996 nm (600 sec., right). The CCD scatter, undetected below ~800 nm, grows rapidly with longer wavelength. In addition to the asymmetrical, horizontal feature, a weaker diagonal streak also becomes apparent near 1 micron.
HRC and SBC UV PSFs
Below 3500 Å, the low- and mid-spatial frequency aberrations in HST result in highly asymmetric PSF cores surrounded by a considerable halo of scattered light extending 1 to 2 arcseconds from the star. The asymmetries may adversely affect PSF fitting photometry if idealized PSF profiles are assumed. Also, charge scattering within the SBC MAMA detector creates a prominent halo of light extending about 1" from the star that contains roughly 20% of the light. This washes out most of the diffraction structure in the SBC PSF wings.
5.1.5
ACS’s WFC and HRC cameras have CCD detectors that shift charge during readout and therefore suffer photometric losses due to imperfect charge transfer efficiency (CTE). Here we describe a method for correcting photometric measurements of point sources that are affected by imperfect CTE in the WFC and HRC.
Analysis results and CTE equations for WFC, described below, were determined from data up to 2006. However, initial evaluation of post-SM4 data show that CTE equations for WFC data continue to be valid within 1 σ.
Correction formulae were derived from matched sets of 47 Tucanae observations using a wide range of image positions, filters, and exposure times. Relative CTE losses were measured from images processed with multidrizzle using conventional aperture photometry with an aperture radius of 3 pixels (for WFC and HRC). Brightness of individual stars were tracked as a function of vertical (row) position. The correction formula can be used for aperture radii up to 5 pixels, but with a lower level of accuracy. See ACS ISR 2009-01 for more details on this issue and for comparisons with other photometric techniques.
The CTE correction method described above is presently the only one fully vetted by STScI. However, other groups have developed algorithms that perform “pixel-based” CTE correction methods (Massey et al. 2010, MNRAS 401, 371; Anderson & Bedin, 2010, PASP 122, 895) that not only correct point-source photometry, but also restores the original value of each pixel in extended sources. STScI is currently testing these methods and is working with the developers to improve the algorithms and implement them into the ACS calibration pipeline. Please check the ACS Web page for updates.
Figure 5.4 shows the impact of imperfect CTE on stellar photometry, measured in WFC images taken in September 2009. The panels represent two bins of integrated signals, 150 eto 300 e, and 1700 eto 4200 e, measured within an r = 3 pixel aperture. The sky level is measured within a 5 pixel-wide annulus located 15 pixels from the star. Stars surrounded by sky levels between 0 e and 1 e are plotted.
Figure 5.4: Effects of CTE Degradation on WFC Stellar Photometry, as of September 2009
This plot shows losses in aperture magnitudes for low (150 e-  300 e-) and moderate (1700 e-  4200 e-) stellar signals as a function of the number of parallel (ΔY) transfers during CCD readout. The data are obtained from short (30 sec.) narrow-band (F502N) WFC exposures of 47 Tuc, in September 2009. Positive and negative values of ΔY reflect the direction of parallel transfer. The dashed line is the best linear fit to the data. Open circles are rejected outliers.
WFC Parallel and Serial CTE
Figure 5.5 indicates that parallel CTE losses for WFC are strongly correlated with stellar signal. This has also been seen in WFPC2 and STIS data. This correlation suggests that charge traps may be present at varying depths of the silicon substrate of the CCDs. Larger charge packets (from brighter stars) lose more charge because they access deeper traps, but smaller charge packets (from fainter stars) lose a larger fraction of their signal. Figure 5.5 also shows a power-law relationship between CTE loss and stellar signal, which is utilized in the CTE correction formula.
Figure 5.5: Correlation between Parallel CTE Losses in WFC with Stellar Signal
Losses in WFC aperture magnitudes over 2,000 parallel transfers as a function of integrated stellar signal within a circular aperture of radius 3 pixels, measured in March 2006. The sky level surrounding all stars is ~3 e. The linear relationship in this log-log plot supports the power-law relation between Δmag and signal that is utilized in the CTE correction formulae.
Figure 5.6 shows the relationship between parallel CTE loss and background signal. Increased sky background can mitigate the CTE loss by filling traps in advance of the arrival of the stellar charge packet during readout. This phenomenon has also been seen in WFPC2 and STIS data. A power-law relation between loss in magnitude and sky background is also assumed in the CTE correction formula.
Figure 5.6: Relationship between Parallel CTE Loss and Background Signal
Losses in aperture magnitudes over 2048 parallel transfers for the WFC, as a function of sky background in March 2003. There is a weak correlation between reduced magnitude loss and higher background. To avoid any dependence on stellar flux, the plot reflects measurements associated with only those stars having aperture signals of ~1000 e.
Our parallel Y-CTE correction formula for WFC is
Y-CTE = 10A x SKYB x FLUXC x (Ytran/2000) x (MJD-52333) / 365
where
(Ytran/2000) reflects the linear relationship between CTE loss and the number of parallels transfers as seen in Figure 5.4. (Ytran is the number of parallel transfers.)
MJD (modified Julian date) is the date of the observation, found in the image header keyword EXPSTART. It’s used for factoring in the CTE linear degradation with time.
Table 5.2 contains the averaged best fit values of the parameters A, B, and C, and their uncertainties for a 3 pixel aperture radius. The parameters were determined by fitting data obtained from March 2003 to March 2006. The coefficients were derived separately for each epoch and then averaged using a weighted mean formula.
Table 5.2: Coefficients and Uncertainties for WFC Parallel CTE Correction within r = 3 Pixel Aperture
A(σ)
B(σ)
C(σ)
This CTE correction is applicable only to multidrizzled single exposure images. It is not meant for combined or averaged multidrizzled images.
To determine the CTE correction, expressed in magnitudes, for a multidrizzled single exposure image, users should:
1.
2.
Measure the integrated aperture signal and average sky value for the actual exposure time. (Note that multidrizzle images have units of e/sec.; therefore, multiply the measured flux in the multidrizzled image by its exposure time.)
3.
Ytran (Ytran = y coordinate for 1 < y< 2048, Ytran = 4096 - y for y > 2048).
4.
5.
Figure 5.7 shows the photometry of the 47 Tuc sample before and after application of the CTE correction (see ACS ISR 2009-01 for more information about the CTE correction equation).
Figure 5.7: Photometry of the 47 Tuc Sample Before and After CTE Correction
Magnitude losses before (top panel) and after (bottom panel) CTE correction, for a WFC image taken in September 2009 with F606W and a 40 sec exposure time. The average background level in the image is ~4 e. The dashed line is the best linear fit to the data. Open circles are rejected outliers.
As of 2009, we have seen no evidence of photometric losses in WFC, after the application of the Y-CTE equation, as shown in Figure 5.7.
Serial CTE decline, or charge losses that depend on the number of pixel transfers along the X-direction, continue to be negligible, as shown in Figure 5.8
Figure 5.8: CTE Losses as a Function of Number of Serial Transfers.
Losses in WFC aperture magnitudes for low (200 e-  500 e-) stellar signals as a function of the number of serial (ΔX) transfers during CCD readout. The data were taken in October 2009 using the F502N filter and a 30 sec. exposure time. Positive and negative values of ΔX reflect the direction of parallel transfer. The dashed line is the best linear fit to the data. Open circles are rejected outliers .
HRC Parallel and Serial CTE
A procedure similar to that described above for WFC was applied to HRC images of 47 Tuc. By utilizing three of the four readout amplifiers, two independent measurements of CTE losses for all combinations of filter, exposure time, and stellar signal were obtained.
Overall, the measured photometric losses from imperfect CTE are much less accurate for the HRC data than for the WFC data because of the paucity of stars in HRC’s small field of view.
The adopted parallel (Y) CTE correction for HRC is
Y-CTE = 10A x SKYB x FLUXC x (Ytran/1000) x (MJD-52333) / 365
where the terms are defined in the same way as the WFC case. Table 5.3 contains the best fit values of the parameters A, B, and C and their uncertainties. Our calibration of HRC’s CTE is based on observations up to March 2006 (i.e., a few months before the ACS failure).
Table 5.3: Coefficients and Uncertainties for HRC Parallel CTE Correction Within r = 3 Pixel Aperture
A(σ)
B(σ)
C(σ)
The method to correct HRC data, which only applies to single-drizzled images, is similar to that for WFC. Users should:
1.
2.
Measure the integrated aperture signal and average sky value for the actual exposure time. (Note that multidrizzle images have units of e/sec.; therefore, multiply the measured flux in the multidrizzled image by its exposure time.)
3.
-
For readout amplifiers C and D, Ytran = y coordinate,
-
4.
5.
Users can determine which amplifier was used to read out their HRC images from the value in the image header keyword CCDAMP. Amplifier C was the standard default. There were no significant photometric losses in HRC images due to imperfect serial CTE. Additional information about CTE in the HRC is available in ACS ISR 2009-01.
CTE Trends and Evolution
The Y-CTE correction formulae include a linear time-dependence term which is bounded by the condition that photometric losses due to imperfect CTE were zero at launch (MJD = 52333). Future data will help refine the time-dependence, as well as the impact of the ACS temperature change in 2006, on the CTE photometric correction. However, we believe the linear time-dependence is well corroborated by other on-orbit data such as “Internal CTE Measurements” and measurements of deferred charge tails from cosmic ray events.
The Relationship Between Field-dependent Charge Diffusion and CTE
Because the WFC and HRC CCDs were thinned during the manufacturing process, there are large-scale variations in thicknesses of their pixels. Charge diffusion in CCDs depend on the pixel thickness (thicker pixels suffer greater diffusion), so the breadth of the PSF and, consequently, the corresponding aperture corrections are field-dependent (see Section 5.1.4). ACS ISR 2003-06 characterizes the spatial variation of charge diffusion as well as its impact on fixed aperture photometry. For intermediate and large apertures (r > 4 pixels), the spatial variation of photometry is less than 1%, but it becomes significant for small apertures (r < 3 pixels).
It is unnecessary to decouple the effects of imperfect CTE and charge diffusion on the field dependence of photometry. The CTE correction formulae account for both effects, as long as the user seeks to correct photometry to a “perfect CTE” in the aperture used to obtain measurements (e.g., the recommended aperture radius of 3 pixels). An aperture correction from the measuring aperture to a nominal “infinite” (5".5 radius) aperture is still necessary (see Section 5.1.2).
Internal CTE Measurements
CTE measurements from internal WFC and HRC calibration images have been obtained since the cameras were integrated into ACS. Extended Pixel Edge Response (EPER) and First Pixel Response (FPR) images are routinely collected to monitor the relative degradation of CTE over time. These images confirm a linear degradation, but are otherwise not applicable to the scientific calibration of ACS data. Results of the EPER and FPR tests were published in ACS ISR 2005-03 and routinely updated at
/hst/acs/performance/cte/
Pixel-based CTE Corrections
Anderson and Bedin (2010 PASP 122, 1035) have developed an empirical approach based on the profiles of warm pixels to characterize the effects of CTE losses for WFC. Their algorithm first develops a model that reproduces the observed trails and then inverts the model to convert the observed pixel values in an image into an estimate of the original pixel values. This algorithm is available for download as a stand-alone tool from the ACS Web site. The ACS-WFPC2 team is also working on implementing the CTE de-trailing software in the WFC calibration pipeline in the near future.
It is important to note that the results of the Anderson & Bedin correction on stellar fields are found to be in agreement with the photometric correction formula of Chiaberge et al. (ACS ISR 2009-01). Statistically significant deviations are observed only at low stellar fluxes (~300 e) and for background levels close to 0 e. Further testing and improvement of the pixel-based CTE correction code is currently underway at STScI. Please check the ACS CTE Web page for the latest updates.
5.1.6
HRC
When designing a UV filter, a high suppression of off-band transmission, particularly in the red, had to be traded with overall in-band transmission. The very high blue quantum efficiency of the HRC, compared to WFPC2, made it possible to obtain an overall red leak suppression comparable to that of the WFPC2 while using much higher transmission filters. The ratio of in-band versus total flux, determined using in-flight calibration observations, is given in Table 5.4 for the UV and blue HRC filters, where the cutoff point between in-band and out-of-band flux is defined as the filter’s 1% transmission points (See ACS ISR 2007-03 for more details). We report the percentage of in-band flux for seven stellar spectral types, elliptical galaxies spectrum (Ell. G), a reddened (0.61 < E(B-V) < 0.70) starburst galaxy (SB), and four different power-law spectral slopes .
Clearly, red leaks are not a problem for F330W, F435W, and F475W and are important for F250W and F220W. In particular, accurate UV photometry of objects with the spectrum of an M star will require correction for the red leak in F250W and will be essentially impossible in F220W. For the latter filter, a red leak correction will also be necessary for K and G types.
Table 5.4: In-band Flux as a Percentage of the Total Flux
α=-1
α=0
α=1
α=2
SBC
The visible light rejection of the SBC is excellent, but users should be aware that stars of solar type or later will have a significant fraction of the detected flux coming from outside the nominal bandpass of the detector. Details are given below in Table 5.5.
Table 5.5: Visible-Light Rejection of the SBC F115LP Imaging Mode
Percentage of all Detected Photons which have
λ<1800Å
Percentage of all Detected Photons which have
λ<3000Å
5.1.7
In an ongoing calibration effort, the star cluster NGC 6681 has been observed since the launch of ACS to monitor the UV performance of the HRC and SBC detectors.
Results for the SBC detector have been obtained using repeated measurements of ~50 stars in the same cluster to provide an estimate of the UV contamination in addition to the accuracy of the existing flat fields (see ACS ISR 2005-13). The uniformity of the detector response must be corrected prior to investigating any temporal loss in sensitivity. (See Section 4.4.2 for a discussion of the SBC L-flat corrections.)
Absolute UV sensitivity in the SBC just after launch appeared to decline linearly for the first ~1.6 years in orbit and then leveled off. Following the methodology for applying the STIS time-dependent sensitivity corrections (STIS ISR 2004-04), this SBC data have been fit using line segments. Because the sensitivity losses moderate after ~1.6 years in all five SBC filters, this was chosen as the break point for the two line segments. The slope of the first line segment gives the sensitivity loss and is summarized in Table 5.6 (in percent per year).
A decline in UV sensitivity of ~2%  4% per year was found for the SBC detector during this time. This result agrees with the sensitivity loss derived for the STIS FUV MAMA with the G140L filter for the first 5 years in orbit, where a 2% to 3% loss was observed. In the last two years before its failure3 prior to SM4, the rate of the STIS MAMA sensitivity loss slowed significantly compared to the previous 5 years. Similarly, after 1.6 years the ACS SBC loss rate has been consistent with zero.
Over time both the HRC and the SBC have a constant sensitivity within 1% (except the SBC filter F165LP which is within 2%). The three HRC filters F220W, F250W and F330W, do not change sensitivity by more than 1%. Presently, for the SBC the only conclusion is that any change in sensitivity is less than 2% because the precision of the current analysis is limited by the lack of an accurate L-flat field for the SBC.
The sensitivities of the WFC filters over the ACS lifetime are currently being investigated.
Table 5.6: UV Sensitivity Loss for the SBC Detector for the First 1.6 Years in Orbit
The UV sensitivity decreases linearly with time during this period and then levels off after 1.6 years, indicating no further loss.
Pivot Wavelength (Å)

1
The final PSF depends slightly on the kernel and pixel scale used to create the output image. This is because the final image is a convolution of the optical/electronic PSF with the final pixel scale and drizzle.pixfrac values. The effect on the PSF is small when the pixfrac and pixel scale values are small, and when the measuring aperture is just a few original pixels in radius.

2
Header keyword in calibrated images (flt.fits and drz.fits).

3
STIS ceased science operations in August 2004 due to a power supply failure within its Side-2 electronics (which had powered the instrument since May 2001 after the failure of the Side-1 electronics). In May 2009, during SM4, repairs to the electronics fully restored STIS operation.


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