The Photometric Performance and Calibration of the Hubble Space Telescope Advanced Camera for Surveys

Figure 2 shows a schematic of the WFC focal plane array and readout amplifiers. The WFC focal plane array consists of two mosaicked CCDs (WFC‐1 and WFC‐2). The imaging area of each of the two chips consists of 4096 columns, each containing 2048 pixels. Each pixel is 15 × 15 μm in size. The serial register, along one of the 4096 pixel edges of the device, is split in the middle so that the entire device can be read out through either one or both of the amplifiers that terminate each end of the serial register. There are 24 additional extended pixels (physical overscan) on each side of the serial readout register, just before each amplifier. The WFC raw data also contain a virtual overscan of 20 rows, obtained by overclocking after the readout of the last CCD row. In order to minimize the readout time and reduce the number of serial transfers, the default configuration is a 2 amp readout. Hence, each amplifier is used to read a single 2048 × 2048 quadrant. WFC‐1 uses amplifiers A and B, and WFC‐2 uses amplifiers C and D. The WFC detectors are operated in multi‐pinned phase (MPP) mode. MPP is used to hold the signal charge away from the surface Si‐Si0₂ interface, thus reducing the dark current rate, minimizing surface residual image effects, and providing better charge transfer efficiency. The WFC detectors are operated in MPP mode only during the integration and not during the readout. Ground testing demonstrated that this configuration allows a higher full‐well capacity and provides better cosmetics.

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The physical separation between the two CCDs is equivalent to 50 pixels, which corresponds to 25. The structure of the data and data products of the ACS calibration pipeline (CALACS; Hack & Greenfield 2000) is based on the previous HST instruments' file format and consists of multiextension FITS files that store science (SCI), data quality (DQ), and error (ERR) arrays. Since WFC data come from two CCD chips, they are treated as separate observations, with a specific SCI, DQ, and ERR array for each chip, and with both chips being stored in the same FITS file. Thus, the array SCI‐1 in the FITS extension [1] stores data from WFC‐2, and the SCI‐2 array in the FITS extension [4] stores WFC‐1 data. A more detailed description of the ACS file structure is available in ADHv4. At the end of the CALACS steps, when WFC data are drizzled to combine dithered¹² exposures and/or remove geometric distortion, both chips are included in a single FITS extension.

The imaging area of the HRC consists of 1024 columns, each with 1024 pixels 21 × 21 μm in size. This CCD has four output amplifiers, one at each end of the two serial registers. The array can therefore be divided into 512 × 512 quadrants to minimize the readout time. The default configuration is a single amplifier readout, namely amplifier C, which was selected for its lower read noise and better cosmetics. The HRC CCD is operated in MPP mode during integration time and readout. There are 19 additional extended pixels (physical overscan) on each side of the serial readout register. The HRC data also contain a virtual overscan; 20 rows on the top of the chip, obtained by overclocking the readout of the last CCD row. The structure of the HRC data is simple; a single HRC exposure comes from a single chip and has only three data extensions. One particularity of all HRC images is the presence of a finger‐like shadow departing from one edge of the image (Fig. 2). This is the shadow of a fixed occulting mask, called the "Fastie finger," a 08 wide, 5 ^'' long reflecting finger permanently located at the CCD entrance window. This mask, together with the two coronagraphic circular stops that can be flipped in and out of the light path, constitutes the coronographic capability of the HRC (Krist et al. 2003b).

3.1.1. WFC

3.1.2. HRC

Even after the bias‐level subtraction from the overscan, some structure remains in the bias frames. This structure includes real bias pattern and also some dark current. In every image, including the zero‐exposure time bias frames, dark counts accumulate for an additional time beyond the integration time, primarily in the time required to read out the detector. Since the WFC is operated in non‐MPP readout, the dark‐current rate during the readout is higher than during integration time. In order to remove this structure, a superbias is subtracted from each image. Bias frames are being taken as part of the ACS daily monitoring program for each supported gain state. Superbiases are created weekly by combining seven daily frames (Mutchler et al. 2004). There is some evidence for intermittent variations in the WFC bias structure at sub‐ADU levels. On a few occasions, some frames have shown bias jumps in one or more quadrants, running for several hundred rows. These effects occur at a few tenths of an ADU level, and they might appear in one or more quadrants simultaneously. The probable source is interference with the electronics by other activities on the spacecraft. At the moment, there is no automatic detection of bias jumps within the calibration pipeline. Although bias jumps at the sub‐ADU level are not important for most applications, they might exist in processed data, and we recommend a careful inspection of the data for their presence.

CALACS removes the dark current from each scientific frame by subtracting a superdark frame. Every day, four 1000 s long dark frames are acquired for both the WFC and the HRC. Every 2 weeks, all the daily darks are combined in order to derive an accurate average dark rate for pixels that do not vary. These include normal pixels and "hot" pixels; i.e., pixels that generate a dark current higher than the average. Permanent hot pixels are due to native silicon lattice imperfections or impurities. During on‐orbit operations, CCDs are exposed to radiation sources, such as protons and neutrons, that induce lattice damage and therefore generate hot pixels. As a consequence, the population of hot pixels changes on a daily basis. Therefore, the STScI calibration pipeline uses as a baseline a biweekly superdark that is updated with the hot pixel population of a specific day (Mutchler et al. 2004). For each science image, CALACS subtracts the appropriate superdark, which has been multiplied by the exposure time and divided by the gain. Any dark current accumulated during the readout time is automatically removed by the superbias subtraction.

Sirianni et al. (2004) analyzed the evolution of the hot pixel population in 2 yr of on‐orbit operation from WFC and HRC dark frames. The number of hot pixels increases linearly with time. Pixels with a dark current greater than 0.08 e⁻ pixel⁻¹ s⁻¹ are flagged has "hot" in the data quality array in the FITS file. For this threshold, Sirianni et al. (2004) report a daily rate of about 47 and 800 new hot pixels for the HRC and WFC, respectively. Most radiation‐induced hot pixels can be annealed by elevating the temperature of the CCD, thus allowing the reconstruction of the damaged lattice structure. An analysis of the effectiveness of the monthly annealing process in the first 2 yr of ACS operation shows that the annealing rate of new hot pixels with this threshold has been ∼82% and ∼86% for the WFC and HRC, respectively. Therefore, the population of permanent hot pixels is growing at a daily rate of about 6 and 140 new pixels for the HRC and WFC, respectively. Currently (2005 April), about 0.9% of the pixels of the WFC and the HRC CCDs are permanently classified as "hot." By comparison, cosmic rays typically impact 1.5%–3% of the pixels in a 1000 s exposure. Hot pixels could, for the most part, be eliminated by the superdark subtraction. However, since the dark current in hot pixels is dependent on the signal level (Janesick 2001), this process is not perfect. Moreover, there are indications that the noise in hot pixels is much higher than the normal shot noise (Riess 2002b). As a consequence, since the location of hot pixels is known from dark frames, they are flagged and discarded during image combinations. Careful planning of the observations, including a dithering strategy, will remove the impact of hot pixels on the science frame. See AIHv5 and ADHv4 for the best strategy for hot‐pixel removal.

Appropriate flat‐fielding normalizes the system illumination pattern, together with pixel‐to‐pixel nonuniformities, to generate accurate count rates that are independent of field position. Since in any WFC image each quadrant is read out independently, the ability to combine photometry from different chips/quadrants depends on the accuracy of the cross‐quadrant and cross‐chip normalization.

Intensive ground testing was devoted to the creation of laboratory flat fields to use for the reduction of on‐orbit data by simulating sky illumination of the CCDs. The Refractive Aberrated Simulator/Hubble Optical Mechanical Simulator (RAS/HOMS) was used to produce high–S/N flat fields that include both the low‐frequency (L‐flat) and the high‐frequency pixel‐to‐pixel (P‐flat) structure (Martel & Hartig 2001; Bohlin et al. 2001). The low‐order structure of the flats over the FOV is mostly due to the variations in the sensitivity of the CCD detectors. Thickness variations, nonuniform doping, or antireflection coating can result in a different response to incoming photons across the device area. Moreover, since the conversion of photons to electrons occurs at different depths within the CCD photosensitive silicon substrate, depending on the energy of the photons, the "cosmetics" of a flat field strongly depends on the wavelength (see AIHv5). Furthermore, since the filters are close to the focal plane, any variation in the filter transmission also contributes to the L‐flat structure. The HRC CCD shows a typical sensitivity variation from center to edge of ∼10%, while the large‐format WFC minimum to maximum sensitivity variation is ∼15%. To normalize to unity, the flats were normalized by the average number of counts in the central 1% (in area) of the image. In the case of the WFC frames, the WFC‐2 image was divided by the WFC‐1 central value, in order to preserve the overall sensitivity difference between the two CCDs across the gap that separates the two chips.

These "ground" flats contain information about the variation in CCD response and spatial structure in filter transmission, and were expected to differ from on‐orbit flats principally by the ratio of the real HST ACS illumination pattern and the RAS/HOMS illumination pattern. A comparison of the observed count rates for the same star in different positions across the chip, after flat fielding, provides an estimate of the residual errors of the flat field and of the accuracy of the chip‐to‐chip normalization. Early Servicing Mission Orbital Verification (SMOV) data, of both individual spectrophotometric standards and stellar fields, suggested the presence of a residual low‐frequency flat‐field structure. There are a variety of plausible approaches to calibrate and remove this effect. However, the easiest methods to implement are either improper or not practical. The internal ACS calibration lamps illuminate the back of the calibration door, which is placed in the light path when a calibration lamp is turned on. Hence, the photons arrive at the detector through a different light path from science observations, bypassing the OTA. This results in a significantly different illumination pattern for internal flats relative to a uniform "sky." So while internal flat‐field lamps exist, they are only used to monitor temporal variations. Bright Earth flats prove to be impractical, since they saturate in even the shortest exposures, except when the HRC or the two narrowband filters are employed. Even then, the resulting images are highly structured and streaky in appearance, due to terrestrial and atmospheric features passing through the field of view. The most obvious approach to correcting for a residual L‐flat structure is to use deep images of "empty" sky fields. However, the creation of sky flats with appropriate S/Ns requires a very large number of images in each filter, in addition to careful masking to remove galaxies, stars, and other sources. Such an effort is currently in progress.

In the interim, a faster approach has been taken by the STScI ACS group. As described by Mack et al. (2002b), a moderately dense star field (NGC 104, in most cases) was observed at typically nine offset positions separated by hundreds of pixels, resulting in flux measurements of each star in nine largely separated positions. Since the entire field of view is well sampled by stars, the flux data are fitted to yield a low‐order (fourth order) polynomial L‐flat, as well as the flat‐field–corrected flux of each star. The resulting polynomial is combined with the high spatial frequency structure of the ground flats to make new "P+L" flats, as described by Mack et al. (2002a) and van der Marel (2003). While the original ground‐based P flat fields produced photometric errors of the order of ±5% from corner to corner. The new "P+L" flats yield a more uniform photometric response (within ∼1%) for a given star for any position in the field of view. As more data become available, improvements will be possible with the adoption of sky flats. Updates will be posted on the STScI Web page.

Finally, for the first 2 yr of operation, the ACS filter wheel movements were accurate to one motor step, which leads to an error that can exceed 1% in the flat fields over small regions. For seven filters on the WFC and six on the HRC with the worst blemishes, flat fields are available as a function of the filter wheel offset step (Bohlin et al. 2003). CALACS automatically selects the appropriate flat field corresponding to the offset step of each observation. On 2004 March the flight software was updated to make the filter wheel movements completely accurate.

As with any other HST instrument, the ACS is subject to cosmic rays and protons from the Earth's radiation belts. Cosmic rays usually generate significant quantities of electrons in more than one pixel. A first characterization of the cosmic rays in ACS images (Riess 2002a) shows that the fraction of pixels affected by cosmic rays varies between 1.5% and 3% during a 1000 s exposure for both the HRC and WFC. As a consequence, great care must be taken in planning and analyzing ACS observations to minimize the impact of cosmic rays on science images.

Cosmic‐ray rejection in ACS frames can be performed in CALACS with the task acsrej or with MultiDrizzle. ADHv4 describes in great detail the two different techniques. Small offsets, even of the order of a few tenths of a pixel between pairs of images, can lead to apparent changes near a bright target that swamp expected Poisson differences. If large enough, these offsets can cause an incorrect flagging and rejection of the center of stars, mistaking the peak of a star for a cosmic ray. This problem is particularly severe for undersampled images. Optimization of the cosmic‐ray removal process may require fine‐tuning of the image alignment process (Mack et al. 2002a).

By design, the ACS focal plane arrays are tilted with respect to incoming rays (20° for the WFC and 31° for the HRC). The result of this design is an image of the sky that is distorted in two different ways: (1) the pixels are elongated with a scale smaller along the radial direction of the OTA field of view than along the tangential direction, and (2) the pixel area varies across the detector.

The distortion affects astrometry and therefore the ability to register images taken at different pointings. Moreover, since the distortion causes pixels to have different effective areas as a function of their position, photometry and flat fielding are also affected. The geometrical area of each pixel is imprinted in the flat field, as well as the photometric sensitivity. PyDrizzle accounts for these effects, and the final geometric corrected output is photometrically and astrometrically corrected. If, however, flat‐fielded images are analyzed prior to the geometric correction with PyDrizzle, the effective area of each pixel must be accounted for when doing integrated photometry. The correct total flux can be recovered by multiplying the flat‐fielded images by the appropriate pixel area map. Once this correction has been applied and the image transformed in e⁻ s⁻¹, the same zero point as that applied to drizzled data products can be used to transform to absolute flux units.

The calibration of the geometric distortion in the ACS detectors has been discussed in detail by Meurer et al. (2002, 2003) and Anderson (2002). Dithered observations of the rich NGC 104 star cluster have been used to calibrate the distortion. A fourth‐order polynomial solution was found adequate for characterizing the distortion to an average rms accuracy of ≃0.05 and ≃0.03 pixels for the WFC and HRC, respectively, over the entire field of view of the two cameras. Although the main distortion characterization was performed using F475W data, the wavelength dependency of the solution has been checked with complementary observations in F775W (WFC and HRC) and F220W (HRC). A marginal increase in the rms in the redder filter was observed for the WFC, and little or no increase for the HRC. A more significant increase in the rms fit (up to 0.11 pixels) was observed in the UV HRC filter F220W, quite likely due to the elongation of 01 of the UV PSF. Similar elongation has also been observed in SBC PSFs and can be attributed to the optics of either the ACS HRC/SBC mirrors or the HST OTA (Hartig et al. 2003).

Until 2004 September, the geometric distortion was removed by PyDrizzle in CALACS, using the correction table provided by Meurer et al. (2002), which provides an adequate solution for most of the applications that require an accuracy of the order of 0.1 pixels. A more sophisticated solution that includes a wavelength dependency based on the Anderson (2002) and Anderson & King (2004) results was implemented in CALACS at the end of 2004 September as part of MultiDrizzle (Koekemoer et al. 2002). The coefficients of the fit of the geometric distortion, and the scripts to transform these coefficients into a pixel area map, are available on the STScI/ACS Web page.

Charge transfer is one of the basic steps of CCD operation. Electrons are transferred from the pixel where they are collected to the readout amplifier. During the transfer of charge from one pixel to the next, defects in the silicon can result in traps that remove small amounts of charge from the charge packet. The charge transfer efficiency (CTE) measures the effectiveness of the charge transfer in a CCD, and it is typically measured as the fraction of charge transferred per pixel transfer.

CTE degradation is well known to affect data from previous HST cameras, such as WFPC2 and STIS. Several detailed studies characterizing CTE degradation and the formulation of empirical‐correction formulae for WFPC2 and STIS have been published (Whitmore et al. 1999; Stetson 1998; Saha et al. 2000; Dolphin 2000b; Goudfrooij & Kimble 2002).

The total amount of charge lost increases with the number of pixel transfers. Therefore, even if ACS has a better CTE per pixel than WFPC2, the impact of CTE degradation is expected to be larger in ACS data, given the greater number of transfers (2048 for WFC and 1024 for HRC vs. 800 for WFPC2).

During on‐orbit operations, CCDs are subject to radiation damage that degrades their ability to transfer charges. CTE degradation can lead to photometric inaccuracy (the magnitude of an object will depend on the position on the chip), astrometric shifts (the shape of the PSF is altered), and a decrease in discovery (the brightness of an object is reduced, and deferred charges can increase the noise in the background). A comprehensive discussion of the type of radiation damage is beyond the scope of this document. Excellent review papers on the subject can be found in the literature (e.g., Janesick et al. 1991; Hopkinson 1991). The principal factor that influences the charge transfer is the presence of spurious potential pockets and defects in the silicon lattice structure. These defects, more generically called traps, act as trapping sites for the transient electrons: part of the electrons contained in the signal packet can be trapped, and if they are released quickly, they rejoin the main packet of charge, but if they fall out of the traps at a slower rate than they go into the traps, they are left behind. The net CTE loss depends on the trap constants, their relevant variables, and the number density of traps (see Cawley et al. 2001 for a detailed description of the trap characteristics).

In order to reduce the impact of CTE degradation, the ACS CCDs, by design, incorporate a minichannel—a narrow extra‐doped channel inside the buried channel. The higher potential, due to the extra doping, is designed to store and transfer small charge packets (< 7–10 × 10³ e⁻) entirely within the minichannel. The possibility of interaction between the charge packet and the traps in the buried channel is therefore minimized, resulting in a significant improvement of the CTE at these low signal levels.

A poor CTE has a strong impact on high‐precision photometry. One of the major manifestations of a severely degraded CTE is the presence of tails of charge apparently streaming out of stellar point sources, in a direction away from the serial register. These tails are due to the release of trapped charges on timescales slightly longer than the readout clocking rate. Not all trapped charges are released within a few milliseconds; some traps release the charges in much longer timescales and contribute to the background noise of that same exposure or a subsequent one. This complex mechanism of capture and release, which depends on numerous factors (such as temperature, signal size, readout rate, and background level), can result in nonlinearity across the device, reduced image quality, reduced sensitivity, and a loss in spatial resolution. The effect of poor CTE on extended sources has been examined by Riess (2000) by subtracting pairs of images of galaxies observed near and far from the output amplifier. As one would expect, the charge is lost primarily from the leading edge of the galaxy image (the one closer to the readout amplifier). The trailing edge does not suffer significant loss, because the traps it sees are filled. It actually might see an increase in signal, due to deferred charges. The resulting asymmetry of extended objects may not have negligible consequences for statistical measurements of galaxy morphology, position angle, axial ratio, and asymmetry concentration (e.g., such as required for weak gravitational lensing studies of field galaxies). The net loss to a measured galaxy magnitude has small dependence on the size of the aperture used; it is usually in good agreement with the photometric loss expected for point‐source photometry.

Several programs monitor the CTE performance of the CCDs in ACS. They are based either on calibration images taken with internal lamps (Sirianni et al. 2003, 2004; Mutchler & Sirianni 2005) or on the analysis of the cosmic‐ray tails in dark images (Riess 2002b). These tests can track variations in CTE on a timescale of a few weeks. Monitoring CTE degradation is fairly easy, but the calculation of a correction formula based on stellar photometry and on the number of parallel and serial transfers in the CCDs is more difficult. There are several aspects to take into account: background level, signal strength of the source, photometric technique, etc. A large amount of data is necessary to constrain all dependencies. Riess (2003) and Riess & Mack (2004) have presented correction formulae to correct photometric losses as a function of a source's position, flux, background, time, and aperture size in ACS CCDs.

Riess (2003) found that the observed photometric losses in the WFC (HRC) range from 0.0% ± 0.2% (∼1%) for bright stars (∼10⁵ e⁻) on a significant background (∼tens of e) to as much as 7%–10% (5%–6%) for faint stars (a few hundred e) and a faint background (<5 e⁻). The observed dependence of the parallel transfer CTE loss (YCTE) versus stellar flux suggests a power‐law relation that was utilized in the correction formula. Such a formula includes the dependence on the position, stellar flux, background level, and time of observation. At the moment, the correction formula does not include a dependence on the number of serial transfers. In general, the contribution of CTE degradation in the serial direction to the total charge loss is minimal, due to the faster readout clocking, as demonstrated by prelaunch testing. While internal calibration data already show a degradation even in the serial direction, it is still too weak to be detected with stellar photometry. Future observations will allow better constraints on the correction for CTE loss in both directions.

In the future, the effects of CTE degradation can be mitigated using the postflash capability included in the ACS. A relatively low amount of charge is added to the general background, thus mitigating the effects of CTE degradation. However, the addition of this charge will of course elevate the background contribution of the noise. Also, the HRC can be operated in 4 amp readout, thus reducing the maximum number of parallel transfers from 1024 to 512.

In general, PSF field‐dependent variations in the ACS cameras are less severe than in other HST cameras. Krist (2003a) performed a very detailed study of the WFC and HRC field‐dependent PSF variations due to optical and detector effects. Residual optical aberrations reduce the flux within the core of the PSF and redistribute it into the wings, degrading the encircled energy (EE). In the ACS WFC, PSF core width and ellipticity variations across the field are large enough to be a concern in the case of very small aperture photometry. Therefore, when performing PSF‐fitting photometry, it is more appropriate to assume a spatially variable PSF when computing a PSF model or when fitting stars to the PSF model itself. In the smaller FOV of the HRC, the PSF can essentially be regarded as constant.

The major cause of alterations of the FWHM across the FOV is the blurring caused by the detector charge diffusion. All ACS CCDs are thinned backside‐illuminated devices; therefore, the electrodes are on the rear face of the chip. Since the depth at which a photon is absorbed within the epitaxial layer is proportional to the wavelength, blue photons generate electrons at the top of the photosensitive layer. If the electric field is weak at the depth at which the electrons are generated, they may move and be collected into adjacent pixels. Charge diffusion is expected to be greater in the thicker regions of the CCD, and the largest variations in charge diffusion across the FOV are seen at the short wavelengths. Thickness variations in the ACS CCDs have been derived from fringe flat fields obtained during ground tests of the camera (Walsh et al. 2002, 2003). These results show that the CCD thickness varies between 12.6 and 17 μm in the WFC and 12.5 and 16.0 μm in the HRC.

Analytical modeling of the PSF in any FOV position for both ACS CCD cameras is possible with Tiny Tim.¹⁴ Krist (2003a) developed a specific blurring kernel to reproduce the amount of charge diffusion observed, and these corrections have been implemented in the latest release of his software.

Dithering is a well‐established technique for HST imaging, and has many advantages, such as improving the sampling of the PSF and mitigating the impact of hot pixels and detector blemishes (see ADHv4). The choice of a kernel for drizzling can change the shape of the core of the PSF. All our data were processed with the default linear kernel, but a different kernel is possible, depending on the data and scientific objectives. For example, if a square kernel is applied to a single image, with the parameters set to perform a bilinear interpolation, the output image will have strongly correlated noise, in addition to a degraded resolution. In all cases in which correlated noise is a major concern, a more different drizzle kernel should be considered. For example, the ACS Science Team pipeline (Blakeslee et al. 2003a) processes all Guaranteed Time Observer (GTO) data with the Lanczos3 kernel, which produces a sharper PSF core and a significant decrease in the apparent noise correlation in adjacent pixels.

In order to measure the EE profile (i.e., the fraction of total source counts as a function of the aperture radius), we used the very high S/N observation of the spectrophotometric standard stars used for the zero‐point determinations (see § 7). All stars are near the center of the chip. In the case of the WFC, the star was first centered in WFC‐1 and then in WFC‐2. In all cases, a couple of images have been taken for cosmic‐ray rejection. The images have been processed with CALACS, and the geometric distortion has been removed with PyDrizzle.

The PSF of any instrument extends essentially to infinity. The far‐field PSF can be measured only with very high S/N observations of isolated stars. Still, it is impossible to measure the flux beyond a certain radius without incurring systematic errors due to background determination, large‐scale flat‐field residual errors, nearby objects in the field, or detector edges. We have chosen to normalize the EE curves to the light at a 55 circular radius aperture. An analysis of PSFs of saturated and unsaturated stars in all filters shows that this aperture is a safe assumption for measuring the total flux within an "infinite" aperture. It is also the maximum radius allowed for most of the images with stars centered in the HRC FOV, due to the presence of the Fastie finger.

One of the most difficult tasks for the proper measurement of encircled energy at large apertures is the determination of the sky background. In order to minimize the impact of errors on the sky background determination, we used the following technique in all cases for which multiple observations were available. First, using the information in the DQ array, we masked out the defective pixels in the SCI. This allowed us to exclude bad pixels or pixels masked by aperture features (such as the Fastie finger in the HRC) when performing statistics on the sky and the photometry. Then for each observation and for each filter, we determined the mode sky level in the sky annulus (from 6 ^'' to 8 ^'' for the WFC and from 56 to 65 for the HRC) and used this value to derive the total counts inside the 55 radius aperture. Under the assumption that the flux of a standard is constant and that for a large aperture the major source of error should only be the Poisson noise, we calculated the median value of all determinations of total flux and calculated the appropriate sky level in each image that would be necessary to reproduce the median flux level. We then used the new sky level to perform the aperture photometry with DAOPHOT in a wide range of aperture radii.

The mean EE curves for different broadband filters are plotted as a function of aperture radius in Figure 3 for the WFC and Figure 4 for the HRC.

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All curves are normalized to the mean value at 55; however, in order to show in more detail the structure of the curves at smaller radii, only the values for the inner 3 ^'' are plotted. The EE values for the broadband filters are tabulated, along with errors, in Tables 3 and 4. In order to better sample the impact of the long‐wavelength halo in the near‐IR (see § 4.3), we also include the narrowband filter F892N, whose effective wavelength falls between F814W and F850LP. The errors in these tables are the standard deviations from the different observations.

There are some variations between different observations. The main one is a commanded focus change obtained by means of a movement (3.6 μm) of the HST secondary mirror on 2002 December 2. This focus change has slightly modified the PSF in all wavelengths, but the most significant variation is seen in HRC‐UV PSFs, which show a slightly sharper core. Normal thermally induced variations of the HST focus (breathing) may typically produce, within a single orbit, a displacement of the secondary mirror comparable to the one commanded in 2002 December. We therefore chose to average the EE profiles before and after the focus change, to create the mean EE curves. The larger errors at small‐aperture radii in the EE curves of the HRC/UV filters reflect this variation in the PSF. On the other hand, the average PSFs at the center of WFC‐1 and WFC‐2 are remarkably similar, and we decided to combine the two data sets to improve the statistics.

Running PyDrizzle with different kernels produces PSF profiles that are significantly different only in the core of the PSF (0–10 pixels). The aperture corrections calculated with the EE can be applied to the photometric data, regardless of the choice of kernel, for aperture radii larger than 10 pixels.

All ACS CCD detectors suffer from scattered light at long wavelengths. They are thinned backside‐illuminated CCDs and consequently are relatively transparent to the near‐IR–wavelength photons. A 16 μm–thinned CCD transmits ∼5% of 8000 Å photons and ∼85% of 1 μm photons. In the case of SITe CCDs, 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 metalized rear surface and re‐illuminates the CCD's front‐side photosensitive surface (Sirianni et al. 1998). The fraction of integrated light in the scattered light halo increases as a function of wavelength. The onset of the halos occurs at a wavelength of ∼7500 Å. The HRC CCD scatters the near‐IR light into a broad halo centered on the target; the intensity of the halo increases with the wavelength and reaches about 20% of the total energy at 1 μm (Fig. 5).

In order to rectify the long‐wavelength halo, the WFC CCDs incorporate a special antihalation aluminum layer between the front side of the CCD and its glass substrate (Sirianni et al. 1998). While this layer is effective at suppressing the IR halo, it appears to give rise to a relatively strong spike in the row direction toward the edge containing amplifiers A and C, as illustrated in Figure 5. This feature, probably due to scatter from the CCD channel stop structure, contains ∼20% of the PSF energy at 1 μm but is almost insignificant at 8000 Å (Hartig et al. 2003).

The EE profiles change naturally with the wavelength in any diffraction‐limited optical system. However, at the onset of the long‐wavelength halo, the PSF becomes broader than expected. Figures 3 and 4 show the variation of the EE profile for the standard stars as a function of the filter in the visible and near‐IR for the WFC and HRC, respectively. In the case of the WFC, the long‐wavelength halo is effectively suppressed by the antihalation aluminum layer; the EE profiles of all filters from F555W to F814W overlap nicely, and only the F850LP EE shows sign of broadening, with ∼2.3% less flux in a 05 radius aperture than in the same aperture in F814W. The effect of the scattered light is more severe for the HRC (Fig. 4), in which the broadening of the PSF is clearly visible at F775W and increases at longer wavelengths. With respect to the flux contained in a 05 radius aperture in the F625W filter, the HRC F775W, F814W, and F850LP PSFs respectively contain about 3.3%, 8.5%, and 16.9% less flux.

The same mechanism responsible for the variation of the intensity and extension of the halo as a function of the wavelength is also responsible for the variation of the shape of the PSF as a function of the color of the source. The spectral energy distribution (SED) of two stars with different colors is different within any given bandpass. If we take as an example the F850LP filter and we observe a hot star and a cold star that produce the same total counts in this filter, more long‐wavelength photons are collected from the red star than from the blue star (see Fig. 6). As a result, the number of photons transmitted by the F850LP filter that are scattered in the CCD substrate is larger for the red star than for the blue star. The PSF for the red star will therefore be broader than that of the blue star. The effective wavelength is a source‐dependent passband parameter that represents the mean wavelength of the detected photons and can be used to estimate shifts of the average wavelength due to source characteristics (e.g., temperature, reddening, and redshift); it is defined as¹⁵

where P(λ) is the dimensionless passband transmission curve and f_λ(λ) is the flux distribution of the object, usually in ergs cm⁻² s⁻¹ Å⁻¹. The term λ_eff can be used to estimate the impact of the light scattering on the aperture correction for any observation.

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In order to characterize the ACS throughput in the near‐IR and the PSF in the filters affected by the long‐wavelength halo, a set of intrinsically red stars have been observed with both the HRC and WFC (Gilliland & Riess 2002). We used these three stars with spectral types M, L, and T to calculate the near‐IR EE curves. For the M and T stars, flux‐calibrated spectra are available from the literature, whereas for the L dwarf a STIS spectrum has been acquired. Spectrophotometric data are used to get information on the wavelength distribution of the flux in the near‐IR filters (i.e., to calculate the effective wavelength). Gilliland & Riess (2002) compared the observed flux of the three standard stars within an aperture of 28 with the prediction of the ACS exposure time calculator and provided a provisional quantum efficiency correction in the near‐IR. We derived the EE profile from these stars using the same data, but as in the case of the EE of the standard stars, the curves have been normalized to the counts in a 55 radius aperture. Figures 7 and 8 show how the EE profile changes with spectral type in F850LP for the WFC and HRC, respectively. We did not include the curve for the T6.5 star in Figure 8, because it was impossible to obtain an accurate profile up to 55. It should be noted that although Figure 3 shows a broadening only for the WFC F850LP EE, this does not mean that only this filter can be affected by scattered light at long wavelengths. Those curves have been determined from the observations of two spectrophotometric standard stars, both hot white dwarfs. Although its effect is greatly reduced by the antihalation correction, light scattering also occurs when a very red object is imaged through the F775W and F814W WFC filters. From Figures 7 and 8 it is evident that for all filters affected by the long‐wavelength light scattering, the aperture correction will be different for objects with different colors (see § 4.5).

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The first assessment of the scientific impact of this PSF artifact in the near‐IR was made by Sirianni et al. (1998) and Gilliland & Riess (2002). The presence of an extended halo centered on the core of the target has the obvious effect of reducing the S/N and the limiting magnitude of the camera in the near‐IR. The halo can also have an impact on the photometry of very crowded fields. The effects of the long‐wavelength halo should also be taken into account when performing morphological studies. The apparent size of a resolved object in any near‐IR filter can increase with the intrinsic color of the source.

In general, the effects of the PSF red halo should also be considered in doing surface photometry of extended objects, as significant biases may occur. For example, Tonry et al. (1997, 2001) found that the (V - I) colors of their ground‐based survey galaxies measured with thinned SITe CCDs (such as used in the ACS) were too red by several hundredths of a magnitude or more. The bias was attributed to this fraction of the I‐band light of the standard stars being lost to the red halo. Since the galaxy photometry was measured over larger areas, they appeared too red with respect to the standards. Reobservation of the galaxies with thick CCDs was undertaken to ensure accurate photometry.

In the case of the ACS, we have calibrated the standard‐star photometry to an infinite radius, so the integrated colors of extended objects within very large apertures should be correct. However, a bias may still occur for measurements of small‐aperture colors or gradients, especially for the HRC. Michard (2002) has done experiments convolving model early‐type galaxies with empirical PSFs that included the CCD red halo. He found that the bias was large enough to reverse the sense of some (V - I) gradients; the effect on colors involving the z band would be even greater. Michard recommended convolving each image with the PSF from the other bandpass before attempting to measure galaxy color maps. Blakeslee et al. (2003b) took the opposite approach in measuring ACS/WFC (i - z) colors of faint early‐type galaxies within the galaxy effective radii. They deconvolved the images in each bandpass, using empirical WFC PSFs and an implementation of the CLEAN algorithm (Högbom 1974), which preserves total flux; the mean color correction for their sample was +0.05 mag, and twice this for the most compact galaxies. Thus, there are various approaches to the problem, but proper care is required to achieve accurate galaxy colors.

In order to reduce errors due to the residual flat‐fielding error and background variations, and to increase the S/N, the two most popular photometric techniques, aperture photometry and PSF‐fitting photometry, are usually performed by measuring the flux within a small radius around the center of the source. This measurement must be tied to the total count rates by applying an aperture correction. This correction could be the major source of systematic errors in the calibration of PSF fluxes.

For all the photometric calibration measurements, we decided to use an aperture of 55 radius. This allowed us to estimate the total flux of spectrophotometric standard stars and apply corrections to the response curve of the instrument (see § 6). Our zero points are based on such measurements, and therefore they refer to this fiducial aperture. However, such a large aperture can be used only for bright and isolated sources and is impractical for most science observations.

A definition of zero points linked to a smaller aperture is often more convenient. For example, WFPC2 zero points are historically defined in relation to the flux in an aperture of radius 05 (Holtzman et al. 1995a). Using a noninfinite zero point implies an additional correction to the zero point for surface photometry. This corresponds to the aperture correction from 05 to nominal infinity, which amounts to 0.1 mag for WFPC2, irrespective of filters (Holtzman et al. 1995a). But even a 05 aperture is impractical for point‐source photometry in a number of situations (photometry of crowded stellar fields, faint objects or targets with an uneven background), and smaller apertures need to be used, with the consequent need for aperture corrections. In all these circumstances, it is also impossible to measure the aperture correction from any smaller aperture radius to "infinity."

A WFPC2‐like approach for the zero‐point definition is less practical for ACS because, in both HRC and WFC, the aperture correction from 05 to "infinity" fluctuates from filter to filter, with variations up to 15%. In § 7 we therefore provide zero points for the fiducial aperture (55), which can be used directly for surface photometry. This choice is also dictated by the fact that the photometric calibration defined by STScI and returned by SYNPHOT traditionally refers to an "infinite" aperture, allowing a better conversion between point sources and extended sources.

As part of the ACS calibration we have determined the count rate conversion from an intermediate aperture to "infinity." In Table 5 we provide the aperture correction from 05 to "infinity" (AC05) derived from the EE profiles listed in Tables 3 and 4. The offset between photometry within a smaller aperture and photometry with a 05 radius aperture can be easily determined and added to the value listed in Table 5. This is usually done by measuring a few bright stars in an uncrowded region of the FOV and applying the offset to all photometric measurements. If we define the observed magnitude as

then for point‐source photometry, equation (1) becomes

where AC05 is listed in Table 5. The AC05 values are derived from the photometry of the two spectrophotometric standards stars used in this paper. They are both hydrogen white dwarfs and therefore are not suitable for deriving the aperture correction for stars with much redder colors (see § 4.5).

One problem that must be addressed is that the variation of the PSF as a function of position on the image may require the application of different aperture corrections for different regions of the FOV. Of course, how the photometry is carried out determines how seriously the results are affected by the space and temporal variations of the PSF. If the aperture used is large enough (about 05 in radius), then the aperture correction will be both small and fairly constant. When performing photometry in a small aperture, however, the assumption of a single aperture correction applied to all photometry in the entire chip may lead to large systematic errors. To minimize this effect, an empirical mapping of the aperture correction should be applied. An appropriate data set will eventually be available, but meanwhile it may be possible to compute a suite of PSF models using Tiny Tim. Unfortunately, the current version of Tiny Tim does not model the residual long‐wavelength halo in the WFC, and the HRC PSF models include only a rough estimate of the long‐wavelength scattered light.

Our determination of the EE profiles, and therefore of the aperture correction, is based on aperture photometry and on the measurement of the sky level within an annulus far from the object (from 6 ^'' to 8 ^'' for WFC and from 56 to 65 for HRC) in order to estimate the "true" sky level. If a smaller annulus is chosen, closer to the center of the object, the sky level will include more light from the wings of the stars, and therefore the sky‐subtracted counts will be lower. From the EE tabulated in this paper or from PSFs created with Tiny Tim and assuming a stable PSF, it is possible to calculate the correction to apply to a measurement with any choice of sky annulus to correct it for the true sky level.

Finally, we must stress that accurate aperture corrections are a function of time and location on the chip. A blind application of the data presented in this paper should be avoided, especially at small radii; and when using small apertures for the photometry, the aperture correction should be derived for each frame on which measurements are made. Avoiding this necessary step can introduce systematic errors in the photometry up to several percent. The tables provided here should be used to estimate approximate aperture corrections when it is otherwise impossible to determine such corrections directly from the image.

In order to assess when the broadening of the PSF due to the long‐wavelength halo should be taken into account and to estimate the aperture correction for red stars, we combined the information from the EE profiles of all the stars used for the characterization of the long‐wavelength light scattering. We first calculated the effective wavelength in all filters for each star.

The effective wavelength can change significantly within the same filter; for instance, in the WFC F850LP there is a difference of ∼760 Å between the effective wavelength of the hot white dwarfs and the cold T dwarf. Then we calculated the aperture correction from a few selected aperture radii to the nominal infinite aperture using the EE profile of each star. We finally correlated the aperture correction and the effective wavelength for each filter/aperture combination, as shown in Figures 9 and 10 for WFC and HRC, respectively, for a few selected apertures (3, 5, and 10 pixel radii, equivalent to 0125, 025, and 05 for WFC; and 3, 5, 10, and 20 pixel radius, equivalent to 0075, 0125, 025, and 050 for the HRC). The values for each star are represented with a different symbol. Not all the stars have a complete set of observations in all filters. For each star we display only the points relative to broadband and narrowband filters for which it was possible to determine an EE profile up to 55. For any choice of aperture radii, there is a fairly smooth variation of the aperture correction as a function of wavelength. For both the WFC and the HRC, the aperture correction is fairly uniform in the visible but increases in the blue and in the near‐IR. The increase of aperture correction in the blue is due to charge diffusion (see § 4.2), while the increase in the red is due to the long‐wavelength halo (see § 4.3). Naturally, the smaller the aperture, the stronger the variation in aperture correction with the effective wavelength. In Tables 6 and 7 we list the aperture correction to the fiducial aperture for a regular grid of effective wavelengths and several aperture radii obtained after interpolation of the plotted data.

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In order to use these tables, the effective wavelength for a specific observation needs to be calculated. If an empirical spectrum or a model of the SED of the object is available, the effective wavelength can be easily calculated for any filter, for example with the task CALCPHOT in SYNPHOT. Table 8 lists the effective wavelengths of a sample of stars of different spectral types in the near‐IR filters for WFC and HRC.

If the SED of the object is totally unknown but observations with the same ACS camera in at least two filters exist, it is still possible to get an estimate of the effective wavelength. First the count rates of the target should be measured in both filters using the same aperture radii and in such a way that the instrumental color for the selected apertures can be calculated:

where flt1 and flt2 are the two filters and r is the radius of the aperture where both fluxes have been measured. Then a color_r versus effective wavelength relation can be created with SYNPHOT for any combination of filters and aperture radii using an atlas of synthetic spectra covering a large range of spectral types. Several spectral atlases are available in STSDAS, but any atlas can be used. Both effective wavelength and color_r can be computed with the routine CALCPHOT in SYNPHOT. In fact, a new keyword "aper" has been implemented to call for the encircled energy tables in the OBSMODE for ACS. This keyword allows one to estimate the flux of a star within a selected aperture and not just the total flux in an infinite aperture, which is the default for SYNPHOT.

As an example we show in Figure 11 the color_r versus effective wavelength relation for three near‐IR filters for the WFC using the color_r F814W–F850LP and an aperture of r = 05. In order to produce this plot, we ran CALCPHOT using the Bruzual, Perrson, Gunn, and Stryker (BPGS) stellar atlas¹⁶ available in STSDAS to calculate the effective wavelength and the synthetic color_r with r = 05. We also plot in Figure 11 the position of the five stars used for the EE study. This approach can be applied to any camera, color, and aperture. From plots of this type it is possible to estimate the effective wavelength of an object and get the aperture correction from any choice of aperture radius to the nominal "infinite" aperture from Tables 6 and 7.

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In order to better quantify the impact that the near‐IR scattered light has on ACS photometry, we present two cases in Appendix C, the first one for a high‐redshift galaxy and the second for point‐source photometry of an extremely red star.

The VEGAMAG system makes use of Vega (α Lyr) as the standard star. Calibrated empirical spectra are available covering the wavelength range from 3300 Å to 1.05 μm (Hayes 1985). Bohlin et al. (1990) have extended this spectral coverage down to 1150 Å using International Ultraviolet Explorer (IUE) spectra. Since its initial release, SYNPHOT adopted as reference the synthetic spectrum of Vega computed by Kurucz (1993) models with a normalization at V = +0.034 mag, assuming 3670 Jy for V = 0. Composite spectra of Vega have been constructed by assembling empirical and synthetic spectra (e.g., Colina et al. 1996). The most recent absolute calibration of Vega from the far‐UV to the IR is a composite spectrum with IUE data from 1140 to 1700 Å and HST STIS from 1700 to 4200 Å (Bohlin & Gilliland 2004). Longward of 4200 Å, the Kurucz¹⁹ model of Vega is used. The normalization has been done to the observed flux level of 3.46 × 10^-9 ergs cm⁻² s⁻¹ Å⁻¹ at 5556 Å, corresponding to V = 0.026. Since this new spectrum has been adopted as the Vega reference spectrum in SYNPHOT, we decided to use it to calculate the zero points for the ACS VEGAMAG system.

In the VEGAMAG system, by definition, Vega has magnitude 0 in all filters. Since the zero points in all VEGAMAG systems are tied to the observed Vega fluxes, their synthetic absolute magnitude may have systematic errors (probably up to 2%). Smaller errors, however, are expected in the colors. The values of the VEGAMAG Zpt(P) are listed in Tables 10 and 11 for both the WFC and HRC filters.

The STMAG magnitude system (Koorneef et al. 1986) is based on the definition of mean flux density per unit wavelength as

and the selection of a flat reference spectrum in f_λ, where f_λ is expressed in ergs s⁻¹ cm⁻² Å⁻¹. The magnitudes in the STMAG system are given by

The zero point K is defined by setting the magnitude of a source that has a flux density of 1 erg s⁻¹ cm⁻² Å⁻¹ to −21.10. Another way to express this zero point is to say that an object with a flux density of 3.631 × 10⁻⁹ ergs cm⁻² s⁻¹ Å⁻¹ will have magnitude STMAG = 0 in every filter.

Historically, the spectral flux density per unit wavelength that would generate 1 count s⁻¹ (within the nominal infinite aperture defined above) is stored in HST image headers as the keyword entry PHOTFLAM. Calling PHOTFLAM(P) the value of PHOTFLAM for the passband P, to directly convert count rates to average flux density

where the count rate is in e⁻ s⁻¹. The value of PHOTFLAM(P) can be derived directly by the passband function P(λ),

where A is the telescope collecting area in square centimeters. We list the value of PHOTFLAM(P) for all ACS filters in Tables 1 and 2. These values are also reported in the photometry keyword section in the header of the SCI extension of the calibrated ACS FITS file.

Thus, following the standard definition of any zero point, the STMAG zero point is

and the STMAG is therefore defined as

The STMAGZpt(P) are listed in Tables 10 and 11 for both WFC and HRC filters.

The ABMAG magnitude system is the analog of STMAG for a constant flux density per unit frequency f_ν (Oke 1964). The reference spectrum is flat in f_ν expressed in ergs s⁻¹ cm⁻² Hz⁻¹. The magnitudes in the ABMAG system are given by

The constant is chosen so that ABMAG matches the Johnson V magnitude for an object with a flat spectrum. Another way to express this zero point is to say that an object with a flux density of 3.631 × 10^-20 ergs cm⁻² s⁻¹ Hz⁻¹ will have magnitude ABMAG = 0 in every filter. There is a simple relation between the STMAG and the ABMAG due to their own definition (f_λ = f_νc/λ²) and the pivot wavelength definition,

Thus, STMAG can be converted into ABMAG as

where λ_p is in Å. This can also be rewritten as

therefore, the two flux‐based systems will give the same magnitude at λ = 5475.4 Å. This transformation provides an easy way to calculate the zero points in the ABMAG system starting from PHOTFLAM(P):

Equation (9) can therefore be rewritten as

ACS ABMAGZpt(P) are listed in Tables 10 and 11 for both WFC and HRC filters.

In the following sections we define SOURCE (S) as the photometric system of the observed data that we want to transform, and TARGET (T) as the photometric system after the transformation. Following this definition, SMAG is the magnitude in the SOURCE system, and TMAG and TCOL are the magnitude and color in the TARGET system. Since several photometric systems can be defined for each instrument, we need to clarify the default magnitude system used in the following transformations. In order to minimize the possible confusion and reduce the redundancy among different zero points, we only provide OBMAG‐to‐OBMAG (see eq. [1]) transformations, except for the transformation to the Landolt photometric system. The OBMAG‐to‐OBMAG transformations can be used to convert magnitudes to any photometric system by simply subtracting (adding) the corresponding zero points before (after) the transformation. We present an example in Appendix D.1.

The transformations have the following format:

where SMAG is the OBMAG in the source system, and TMAG and TCOL are the OBMAG magnitude and color (as difference of two OBMAGs) in the target system, and c0, c1, and c2 are the coefficients for the transformation. Please note that in the transformation equation the color term is in the TARGET system and not in the SOURCE system. The same approach was used by Holtzman et al. (1995a) for the transformations from WFCP2 to UBVRI, since this formalism carries several advantages, as discussed by Stetson (1992). Consequently, TCOL must be derived iteratively using ACS observations in two colors unless the target color is known.

The number of objects used for the observational transformations varies greatly depending on the area of the FOV, the photometric quality of the data, and the brightness of the stars. Photometric errors have been used as initial criteria to select stars for the transformations. Depending on the numbers of stars available, the error threshold was set between 0.02 and 0.06 mag. We divided the color range in equally sized bins and calculated the median and standard deviation for each bin. Outliers have been rejected based on the local median and standard deviation, using a σ‐clipping criterion. In transformation plots where observed stars are used, we show only representative points that are just local medians in any given color bin.

To estimate the uncertainties of the transformation parameters, we followed the approach employed by Holtzman et al. (1995a). For transformations derived from the observational data, we weighted stars equally and iterated the χ² minimization by adjusting the magnitude errors until χ² reached unity. In order to avoid overestimation of the uncertainty of synthetic stars, we measured the scatter from the fit and used this as a weight for the χ² minimization. This procedure not only prevents the fit from being partially weighted by a few bright stars, but also provides realistic errors that are not modeled by synthetic photometry.

In deriving the transformation between two photometric systems, the functional form of the transformation should be addressed. Although in principle a quadratic least‐squares fit is preferable, we found that for observational transformations, given the limited color range and limited statistics, a linear fit was more appropriate. In the case of observational transformations between the CCD cameras of the ACS that use the same filters, we also decided to perform a linear least‐squares fitting with iterative rejection. For all synthetic transformations we performed a quadratic least‐squares fitting.

A single set of coefficients does not always fit the data over the large color range of the stellar atlas. Sudden differences in the response curves can produce discontinuities in the color term dependencies and force us to limit the color range for which a set of coefficients can be used. When this happens, we divide the color range into two regions and provide separate coefficients for each segment.

Finally, the precision of the synthetic transformations depends on the accuracy of the total response function of the photometric passbands of ACS. As we discussed in § 6, a fairly significant revision of the prelaunch RQE has been necessary in order to reproduce the observed on‐orbit sensitivity. Although the derived RQE curves can now reproduce the count rates in all broadband filters with an accuracy better than 0.5%, it is possible that the shape of the total response of the bluest and reddest passbands is not a perfect representation of the real response curve. This could introduce systematic errors in the color transformations. In these cases (F435W and F850LP for the WFC, and F220W and F850LP for the HRC), we suggest using the observed transformations, if available.

The WFC and the HRC share all the visual and near‐IR filters of the ACS. The transformation between the two systems is therefore expected to be quite simple. However, the different optimization of the cameras (mirrors and CCDs) produces different total throughput curves, in particular in the blue and near‐IR (Fig. 13). Therefore, the transformation between filters in these wavelength regions could have a significant dependence on the color term.

For these "internal" transformations between the two CCD cameras, we used observations of two globular clusters, NGC 104 (programs 9018, 9656, and 9666) and NGC 2419 (program 9666). These globular clusters have very different metallicities ([Fe/H] ∼ -0.7 for NGC 104 and [Fe/H] ∼ -2.2 for NGC 2419), essentially spanning the whole metallicity distribution of the Galactic globular cluster system.

The raw data have been processed through the CALACS pipeline at the STScI. For moderately crowded fields (∼6 ^' west of the core) of NGC 104, we simply performed 5 pixel radius aperture photometry using the IRAF APPHOT package. Because the NGC 104 data were originally acquired for the assessment of the geometric distortion and low‐frequency residuals in the flat field, each filter observation consists of multiple pointings offsets by large dithers. We decided to select only stars present in at least three pointings and to use the σ‐clipped averages of the magnitude in the multiple observations as an estimate of the brightness of the star.

The photometry of NGC 2419 required more complicated field‐dependent handling. Due to the larger distance of the cluster, a single pointing of WFC covers both the compact core and the moderately crowded outer regions. In the external regions of NGC 2419 we can safely perform 5 pixel radius aperture photometry. However, PSF‐fitting photometry is required for the crowded region of NGC 2419 common to the HRC and WFC. While the PSF of the HRC can be assumed to be nearly constant across the field, the PSF varies significantly across the WFC FOV (see § 4.2), thus preventing us from applying in the crowded area the PSF extracted from isolated stars in the external regions. We confirmed this fact by performing our initial PSF photometry assuming a spatially constant PSF; the result showed systematic errors up to ∼4%. Although in principle a PSF can be iteratively constructed even for an extremely crowded field, the task of achieving calibration‐quality photometry becomes prohibitively impractical if not impossible. An alternative is to use Tiny Tim (see footnote 14) to model the PSF on the crowded area. However, it is difficult to determine the time‐varying behavior of the PSF, mainly due to focus offset changes. Besides, most PSF photometry packages cannot readily make use of PSF images from Tiny Tim. We therefore decided to create position‐dependent PSF templates using the sparser observations of NGC 104. The PSFs were easily sampled from isolated stars over the entire field of view and then applied to the NGC 2419 field. In order to avoid effects due to PSF time variations, when possible we used the NGC 104 images that were closest to the date of the NGC 2419 observations. After checking the residuals in PSF‐subtracted images as well as various goodness‐of‐fit criteria, such as χ², best matching PSF templates were determined for each filter. This technique allowed us to remove any systematic effect on the photometry of the crowded regions.

Examining the NGC 104 and NGC 2419 data separately, one does not see strong evidence for a metallicity dependence in the transformation relations. Due to the different metallicities and distance moduli of the two clusters [(m - M) = 13.27 for NGC 104 (Zoccali et al. 2001) and (m - M) = 19.88 for NGC 2419 (Harris et al. 1997)] the range of colors that our selection criteria allow are not the same in both clusters. In particular, for NGC 2419 we used stars on the horizontal branch, the asymptotic giant branch, and on the red and subgiant branches. The NGC 104 data allow an extension to the red, since we can use main‐sequence stars at least 4 mag fainter than the turnoff point.

Figure 14 shows the observed color‐magnitude diagrams (CMDs) for the two clusters for the WFC and HRC. In order to look for metallicity effects, we must compare stars of similar colors in the two clusters. In most transformations, the data of the two clusters overlap only in a quite narrow color range spanning ≤0.6 mag. We therefore used the model atmospheres of Kurucz (1993) to investigate the metallicity dependency. We compared synthetic transformations using three different metallicities, [Fe/H] = 0, −0.5, and −2.0, and find that in the color range covered by the observational data, the systematic differences between the three metallicities are at most 0.3%. We therefore decided to combine the data for both clusters and also include the observations of the two spectrophotometric standards to determine the final transformations.

Even when combining all the observational data, the color range covered by all the stars (WDs+NGC 2419+NGC 104) were generally limited to 0.0<F435W - F555W<1.2 or −0.4<F555W - F814W<1.2 in the HRC VEGAMAG system; the transformation from observed stars cannot be assumed to be corrected for stars outside this color range. Synthetic transformations cover a larger color range and should be used instead.

We list the transformation coefficients to use in equation (12) for different combinations of most of the full‐sized filters in Tables 12 and 13 for the transformations from WFC to HRC and from HRC to WFC, respectively. The transformations between the primary filters from WFC to HRC are shown in Figure 15.

These figures show that the synthetic system matches the observations fairly well, usually within 1% for all stars within the range of colors in which our observations were made. There are, however, a few cases, F435W and F625W for example, where the discrepancy can rise up to a couple of percent for the reddest stars. In principle, one could argue that since the long‐wavelength light scattering is more severe in the HRC than in the WFC, an incorrect aperture correction could be the reason for this discrepancy. However, this is not the case, because these filters are not affected by this problem, which starts at λ>7000 Å. Also, the near‐IR filters, which suffer from extended PSF wings, and therefore could be more affected by aperture correction errors, do not show any systematic differences.

Although the BPGS atlas does not include stars with high surface gravities, but only main‐sequence stars and giants, the agreement with the two spectrophotometric white dwarfs does not show any systematics. This analysis suggests that we have a good understanding of the ACS synthetic system and that the derived transformations are accurate to 1%–2% or better in all filters. The synthetic curves can thus be used in place of the observational ones to produce transformations for objects with spectra different from the observed stars.

ACS filters differ significantly from the UBVRI bandpasses. The ACS filters are usually narrower, start at shorter wavelengths, and, apart from F814W, extend less to the red (see Fig. 13). As a consequence, the transformations between the two systems may be very sensitive to details in the underlying stellar spectrum and show strong dependencies on metallicity and surface gravity.

We compared ACS observations with ground‐based photometry of NGC 2419. In particular, we retrieved BVRI data from the Stetson Web page,²¹ and an independent BVRI data set was provided by Saha et al. (2005). The two NGC 2419 photometric control data sets are the same as recently used to examine the accuracy of the WFPC2 zero points (Heyer et al. 2002, 2004). The two observational CMDs from the two different sources are shown in Appendix D.2, Figure 20. In order to have a large number of common stars in the HRC and WFC FOV, ACS observations were centered in a region fairly close to the center of NGC 2419. As a consequence, the match with ground observations—centered in a more sparse region—resulted in only 30–60 stars, depending on the filter and camera.

We compare the two NGC 2419 control data sets and find a significant color term between them: red stars tend to be brighter in Stetson's (see footnote 19) than in Saha et al. (2005), with differences up to 3%–4% for stars with V - I>1.0 in the I band. Such differences, also discussed in Saha et al. (2005), could be due to different filter throughput curves, red‐leak control, and systematic effects in the transformation from the instrumental system to the standard system for the low surface gravity stars in NGC 2419.

For the synthetic UBVRI photometry, we first used the Landolt UBVRI filter set (i.e., Johnson UBV+Cousins RI) defined in SYNPHOT. In particular, the throughput data for the Johnson UBV bands are the U3, B2, and V synthetic bandpass data of Buser & Kurucz (1978), while the Cousins R and I throughputs are taken from Bessel (1983). However, we got poor agreement with the observed transformation using the B2 filter. We then tried using other B synthetic bandpasses and found a much better agreement when applying the B filter from the Harris set in use at KPNO and WIYN.²²

For both ACS cameras, we compared the observed transformations using the two NGC 2419 control data sets with the corresponding synthetic transformations. We obtained poor agreement with the I bands of Stetson's data set, with systematic offsets of the order of a few percent between the two curves. The observed R‐band transformation also shows some departures for the reddest stars. Finally, the V band shows a good match between observed and synthetic transformations. Using Saha's data set, we have significantly better results in V, R, and I available bands. The B band shows a similar agreement using either Stetson's or Saha's data set. The observed and synthetic transformation provide similar results for stars with B - V>0.5, whereas for bluer stars the discrepancy between the two transformations can be as high as 5%. Given the possible uncertainties in the shape of the blue side of the total response curve with the F435W filter, our bluest filter with WFC, we suggest using the observed transformations when this filter is involved.

We decided to use only the Saha photometric data set of NGC 2419 to calculate the coefficients for the observational transformations. However, in determining the new zero points for WFPC2, Heyer et al. (2002) find that Stetson's photometry produces values slightly closer to the historical zero points of WFPC2 than Saha's photometry. Unfortunately, no color term was taken into account.

We list the observational and synthetic transformation coefficients to use in equation (12) for different combinations of most filters in Appendix D.2, Tables 22 and 23, for WFC‐to‐BVRI and HRC‐to‐UBVRI, respectively. The transformations between primary filters are shown in Appendix D.2, Figures 21 and 22. An example of how to calculate the transformation is provided in Appendix D.1.

As expected, Figures 21 and 22 show large scatter in the synthetic transformation. The BPGS atlas includes stars with a wide range of surface gravity and possibly metallicity. We used the synthetic system to investigate dependencies of the main transformations on gravity and metallicity. For the gravity, we use the Bruzual Spectrum Synthesis Atlas (BZ77)²³ implemented in SYNPHOT. It provides solar‐metallicity spectra for main‐sequence stars (from spectral class O5 to M6), giant stars (from O8 to M6), and supergiants (from O9 to M1). For the metallicity dependence, we use the model atmosphere of Kurucz (1993). We selected models to cover the main sequence from O3 to M2 for the solar metallicity, and for [Fe/H] = + 0.5, −1.0, and −2.0. The results are shown in Appendix D.2, Figures 23 and 24, for the WFC and HRC, respectively. In both figures the column on the left shows the dependence on the surface gravity; filled circles represent data for a synthetic main sequence. The sequences of giant and supergiant stars are represented by gray stars and squares, respectively. The column on the right shows the dependence on the metallicity for main‐sequence stars: black dots show the solar metallicity, filled triangles are [Fe/H] = 0.5, gray filled stars are [Fe/H] = -1, and squares are [Fe/H] = -2.

These figures show that the dependency of the transformations on these quantities can be quite large. Gravity provides a large spread in short and long‐wavelength filters for stars around zero color and for low‐temperature stars. Metallicity causes more spread for redder stars. Significant departures from the relation derived from stellar spectra are expected for the transformation of nonstellar objects, especially for galaxies at high redshift.

The derived transformations from the ACS systems to UBVRI can be applied to main‐sequence and giant stars without introducing errors of more than a few percent. However, it should not be expected that the 1%–2% accuracy of ACS photometry will be preserved in the transformed data. Transformation to U, B, and I filters are highly dependent on the object spectral details, and Tables 22 and 23 should be used with extreme caution for objects different from those used to derive the relations. Therefore, whenever possible, we strongly recommend working with the ACS system.

Most ACS broadband filters have, at least nominally, a close match in the vast WFPC2 filter complement. However, the different response of the two instruments and specific filter designs create significant differences between the ACS and WFPC2, as shown in Figure 13.

Since the installation of WFPC2 on HST a decade ago, a large amount of WFPC2 data has become publicly available through the HST archives for calibration purposes. Now many characteristics of the instrument are well understood, although refinements are still in progress (Baggett et al. 2001; Casertano & Wiggs 2001; Whitmore & Heyer 2002; Dolphin 2000a).

In order to derive transformations between ACS and WFPC2, we retrieved WFPC2 observations of NGC 104 (programs 7465, 6114, 6660, and 6114) and NGC 2419 (programs 7268, 7630, and 9601) from the STScI archive. Accurate stellar photometry on WFPC2 images requires a careful treatment of the undersampling effect, of position‐dependent pixel size variations, and of the charge transfer efficiency (CTE) degradation. We found that HSTPHOT,²⁴ an automatic stellar photometry software specifically designed for WFPC2 data (Dolphin 2000b), accounts for all these issues with acceptable accuracy. The dependability of the package was tested by first performing PSF‐fitting photometry with IRAF DAOPHOT on a subsample of the data, applying aperture corrections measured from isolated stars in the same images, and CTE correction from Dolphin (2000a), and comparing the results with HSTPHOT results. Since the results from these two methods did not show any systematic difference, we decided to use HSTPHOT to automatically process all the WFPC2 observations.

We used the multiphot photometry feature of HSTPHOT instead of performing photometry on combined images. This method, although reducing the detectability of faint stars, increased the photometric accuracy for the bright stars that we used to estimate the transformation coefficients. Finally, the HSTPHOT output flight system magnitudes were converted into OBMAGs by subtracting flight‐system zero points (Dolphin 2000b). Figure 25 in Appendix D.3 shows the observed CMD for the two clusters.

There is a subtlety involved in the determination of OBMAG in the WFPC2 photometric system, because WFPC2 zero points are slightly different depending on the chip. We choose the WF3 chip as a basis for our OBMAG definition. For the synthetic transformation, we used the sensitivity curves for all WFPC2/WF3 components currently available in SYNPHOT (Bagget et al. 1997).

We list the observational and synthetic transformation coefficients to use in equation (12) for different combinations of most filters in Appendix D.2, Tables 24 and 25 for WFC‐to‐WFPC2 and HRC‐to‐WFPC2 conversions, respectively. The appropriate WFPC2/WF3 zero points for gain = 15 must be added when transforming the WFPC2 OBMAG into any WFPC2 photometric system. The transformations between primary filters are shown in Appendix D.3, Figures 26 and 27.

Many people have contributed to this work. ACS was engineered, built, and tested by a dedicated team at Ball Aerospace, Boulder, CO. We thank the entire ACS Investigation Definition Team and all personnel at GSFC who have supported ground calibration and prelaunch testing. Special thanks to the entire crew of STS‐109, who did a superb job during an extraordinarily demanding servicing mission.

Thanks to ACS personnel at STScI, the ACS photometric calibration group, and the ACS science team. They have prepared many of the calibration proposals and were always available to discuss results. Among these people, we specially appreciate the comments and work we received from Ralph Bohlin, Francesca Boffi, Nick Cross, David Golimowski, Inge Heyer, John Krist, Adam Riess, and Roeland van der Marel.

We are indebted to Abhiji Saha for providing unpublished magnitudes and data relating to the UBVRI system. We also thank Tom Brown, Stefano Casertano, Leo Girardi, Brad Whitmore, and Manuela Zoccali for their useful suggestions and insightful discussion.

The entire paper has been modelled after equivalent WFPC2 calibration papers by John Holtzman and collaborators. We are indebted to them for setting a benchmark in comprehensive calibration papers, making our job much easier.

M. S. is particularly grateful to the ACS IDT team and all personnel of the Johns Hopkins University Physics and Astronomy department for 5 years of pleasant and productive work. Finally, we are grateful to K. Anderson, S. Busching, A. Framarini, S. Barkhouser, and T. Allen for their invaluable contributions to the ACS project at JHU.

We have much appreciated the many useful suggestions and constructive criticism of Gordon Walker, the referee of this paper, whose valuable help has considerably improved the presentation of our work.

ACS was developed under NASA contract NAS 532865, and this research has been supported by NASA grant NAG5‐7697 and by equipment grant from Sun Microsystems, Inc. The Space Telescope Science Institute is operated by AURA Inc., under NASA contract NAS 526555.

• 1.  
  Retrieve the image(s) from the HST archive or proceed with the manual recalibration of the data, following the recipe given in ADHv4. Be sure to use the best reference files, usually available a few weeks after the data acquisition.
• 2.  
  After running CALACS on the association file, the main output is the flat‐field‐corrected FLT image and/or the geometric corrected DRZ image.

  • i.  
    If CR‐SPLIT observations are available, the FLT images are combined to produce a CRJ frame free of cosmic rays. We draw the reader's attention to the fact that the default settings for the CR rejection routine are quite conservative. If the images in the CR‐SPLIT pair do not show any significant offset (<0.05 pixel), the scalenoise parameter may be reduced a more efficient CR rejection (see § 3.5). However, in the case of undersampled images, one should verify that the peak of the PSF is not affected (i.e., truncated) by a more "aggressive" CR‐removal technique.
  • ii.  
    If instead the observation consisted of dithered images but without CR‐SPLIT, the resulting FLT images will still have cosmic rays, which are removed during the combination of the dithered observations. MultiDrizzle performs a better CR‐rejection on non–CR‐splitted observations than PyDrizzle.²⁵
• 3.  
  Perform photometry of objects in the field using any choice of photometry technique.

  • i.  
    If work is carried out on the FLT image instead of the distortion‐corrected DRZ file, it is necessary to multiply each SCI (and ERR) frame of the FLT file by the appropriate pixel area map file (see § 3.6). This operation will ensure that the total integrated flux of the star is conserved. We emphasize here that even after the application of the pixel area map, the PSF of the stars will be distorted, and the amount of distortion is position dependent. The encircled energy (EE) profiles published in this paper were calculated from nondistorted PSFs. As a consequence, the aperture correction that can be derived from the EE profile cannot be directly applied to nondrizzled images, at least for small‐radius apertures. The zero points published in this paper refer to an "infinite" aperture and can be used once the aperture correction to a "total" flux has been applied.
  • ii.  
    The units of the FLT and DRZ images are e⁻ and e⁻ s⁻¹, respectively. Many photometry packages for PSF fitting use an optimal weighting scheme that depends on the readout noise, gain, and the true counts in the pixels. As a consequence, in order to compute the weights correctly, the image should not be divided by the exposure time. Therefore, the DRZ image should be multiplied by the exposure time before running such packages. The total number of electrons, instead of the electron rate, is also needed in order to properly calculate the CTE correction. For the same reasons, the background sky should not be subtracted from the image.
  • iii.  
    When performing aperture or PSF fitting photometry, possible systematic errors due to the spatial variation of the PSF should be addressed. This is particularly important when the photometry is carried out using a small‐radius aperture (<5 pixels). For very small aperture (r < 2 pixels) the systematic variations in aperture correction can be as high as 10%–15%. An example of the analysis of the optimal aperture is provided in Appendix F.

  This step should give you a set of measurements in units of electrons or e⁻ s⁻¹ in your selected aperture for all your objects. The instrumental magnitude can be calculated as −2.5 × log(e × s⁻¹).
• 4.  
  Consider correcting the photometry for CTE degradation. Unless your data were acquired in the first semester of 2002, the effects of CTE degradation are probably present in your data. Check on the STScI ACS Web page for updates on the CTE degradation correction. There are several things to keep in mind when calculating the correction for CTE degradation in your image:

  • i.  
    The flux level and the background level to use in the formula are in electrons and not e⁻ s⁻¹. When working with DRZ images, it is necessary to multiply the measured value by the exposure time.
  • ii.  
    When applying the CTE correction to combined images, each of the combined images must have the same or very similar exposure times. The output of CALACS, when CR‐SPLIT or DRZ observations are available, is the sum of the combined images. In this case, if all the combined images have the same exposure time, the measured values in the equation, such as SKY and FLUX, should be divided by the number of images used to create the add‐combine image. Determining the CTE correction for a combined image created with unequal exposure times (for example, one long exposure and one short exposure) cannot easily be done.
  • iii.  
    In particular for WFC observations, the FOV is large enough that the background sky might present gradients. In general, the use of a constant sky value for the determination of CTE correction in different regions of the FOV is not recommended. This is particularly true for all filters where the PSF wings are broadened by the long‐wavelength halo. Depending on the brightness of the star, the signal in the PSF wings can enhance the "local" sky and reduce the amount of lost signal within the aperture where the flux is measured. In such instances a global sky value would overestimate the CTE correction.
• 5.  
  Apply the aperture correction to all photometric measurements to transform the instrumental magnitudes into OBMAG:

  • i.  
    For filters bluer than F775W, determine the offset between your photometry and aperture photometry with a 05 radius aperture. This is usually done by measuring a few bright isolated objects in the field. Apply this offset to all the photometric measurements. Use Table 5 to get the value of AC05 for each filter. Add AC05 to the instrumental magnitude or insert the count rate at r = 05 and the value of AC05 in equation (2) to get OBMAG.
  • ii.  
    For all near‐IR filters, if your object is a blue star proceed as in (i). For all other objects, you need to estimate the impact of the red halo: first estimate the effective wavelength of the observation using the recipe in § 4.5, SYNPHOT, or Table 8. Then calculate the aperture correction from a 05 aperture radius to infinity using the relation in Figures 9 and 10 and Tables 6 and 7 and compare the results with the values in Table 5. If the calculated aperture correction is similar, within a few tenths of a percent, to the corresponding value in Table 5, then the red halo has little or no impact on your observations and you should proceed as in (i). If, however, the difference is larger, then you should use the relation in Figures 9 and 10 and Tables 6 and 7 to directly calculate the aperture correction from your aperture radius to infinity.
• 6.  
  Apply the appropriate zero point from Tables 10 and 11 to transform OBMAG to any choice of magnitude system.
• 7.  
  If your observations were processed with CALACS before 2004 January 6, and the gain is different from the default setting (1 for WFC, 2 for HRC), use Table 9 to correct the photometry.
• 8.  
  The magnitude can be corrected for interstellar extinction using Tables 14 and 15. Given E(B − V), the extinction A(P) in the passband P is calculated by multiplying E(B − V) by the value in the table that correspond to the correct passband and spectral type.
• 9.  
  If you want to transform the data to a different photometric system, use equation (12) with the coefficients in § 8 that are appropriate for the source and target systems. You should apply the correction for interstellar extinction (see § 10) before applying the transformations.

• 1.  
  Retrieve the image(s) from the HST archive or proceed with the manual recalibration of the data, following the recipe given in ADHv4. Be sure to use the best reference files, usually available a few weeks after the data acquisition.
• 2.  
  After running CALACS on the association file, the main output is the flat‐field–corrected FLT image and/or the geometrically corrected DRZ image (see point 2 in Appendix B.1).
• 3.  
  Perform photometry of objects in the field using any choice of photometry technique (see point 3 in Appendix B.1). This step should give you a set of measurements in units of electrons or e⁻ s⁻¹ in your selected aperture for all your objects. The instrumental magnitude can be calculated as −2.5 × log(e × s⁻¹).
• 4.  
  Consider correcting the photometry for CTE degradation. Unless your data were acquired in the first semester of 2002, due to the large number of transfers, the effects of CTE degradation are probably present in your data. Check on the STScI ACS Web page for updates on the CTE degradation correction (see point 4 in Appendix B.1).
• 5.  
  Apply the aperture corrections to transform the instrumental magnitudes into OBMAG: these will of course in general be different for extended objects and for stars, so the corrections given in the tables should not be applied blindly. However, for barely resolved galaxies, the aperture corrections may be similar to the stellar ones if the apertures are at least several pixels in radius. If high accuracy is required, consider simulating galaxy profiles and convolving them with the PSFs of the appropriate bandpasses to determine the amount of light lost through the adopted aperture. If one is only interested in galaxy colors for a given aperture, and the PSFs of the two bandpasses are nearly identical, this step is unnecessary; however, for colors involving the near‐IR filters, particularly F850LP, there will in general be more light lost through the redder filter. In this case, one can determine the size of the differential aperture correction for the two bands by convolving galaxy models with the respective PSFs or else deconvolving the images and measuring the color change for the given aperture.
• 6.  
  Apply the appropriate zero point from Tables 10 and 11 to transform OBMAG to any choice of magnitude system.
• 7.  
  If your observations were processed with CALACS before 2004 January 6, and the gain is different from the default setting (1 for WFC, 2 for HRC), use Table 9 to correct the photometry.
• 8.  
  The magnitude can be corrected for interstellar extinction using Tables 14 and 15. Given E(B − V), the extinction A(P) in the passband P is calculated by multiplying E(B − V) by the value in the table that correspond to the correct passband and spectral type.
• 9.  
  If you want to transform the data to a different photometric system, see Appendix E. You should apply the correction for interstellar extinction (see § 10) before applying the transformations.

• 1.  
  Retrieve the image(s) from the HST archive or proceed with the manual recalibration of the data, following the recipe given in ADHv4. Be sure to use the best reference files, usually available a few weeks after the data acquisition.
• 2.  
  After running CALACS on the association file, the main output is the flat‐field–corrected FLT image and/or the geometrically corrected DRZ image (see point 2 in Appendix B.1).
• 3.  
  Measure the surface brightness in units of e s⁻¹ pixel⁻¹. If one is interested in absolute surface photometry within a single bandpass, we recommend using the distortion‐corrected (DRZ) image and converting from flux per pixel to flux per arcsec² via the output pixel scale used in the drizzling process. The FLT images may also be used, and since the pixel area variation has been divided out by applying the flat field, it is not necessary to apply the pixel area map. However, in this case, the appropriate factor to use in the conversion from pixel area to arcsec² depends on the mean pixel scale over the detector region used in normalization of the flat fields. Of course, if one is only interested in surface colors, this factor cancels out (since the flat fields for different bandpasses were normalized in the same way), and the colors can be determined simply from the flux per pixel in the two bands.
• 4.  
  The effect of the PSF red halo should also be considered in doing surface photometry of extended objects in near‐IR filters (see discussion in § 4.3).
• 5.  
  Convert the count rate into OBMAG arcsec⁻² using the appropriate pixel scale.
• 6.  
  Apply the appropriate zero point from Tables 10 and 11 to transform OBMAG arcsec⁻² to a surface brightness in your choice of magnitude system.
• 7.  
  If your observations were processed with CALACS before 2004 January 6, and the gain was different from the default setting, use Table 9 to correct the photometry.
• 8.  
  If you want to transform the data to a different photometric system, use equation (12) with the coefficients in § 8 that are appropriate for the source and target systems. For the color conversion of galaxies use the instructions in Appendix E. You should apply the correction for interstellar extinction before applying the transformations.

The red "halo" can affect both the magnitude and the color of a galaxy. The most commonly used software for performing photometry of galaxies is SExtractor (Bertin & Arnouts 1996), which provides several measurements of the magnitude. The most commonly used for faint galaxy photometry is MAG_AUTO, an aperture magnitude measured within an elliptical aperture adapted to the shape of the object and with a width scaled n times the isophotal radius. Other common choices are MAG_ISO, an isophotal magnitude that measures the integrated light above a certain threshold, and MAG_APER, a circular aperture. MAG_AUTO is the best choice for estimating total magnitudes, but even for filters not affected by long‐wavelength light scattering it excludes a significant amount of the light (Benítez et al. 2004). In order to accurately measure the color of galaxies, it is quite common to adopt a single aperture defined by a detection image²⁶ and selecting MAG_ISO or MAG_APER. If all filters have similar PSFs, then the magnitude measurements in all filters will be affected by the same systematic errors that cancel out when subtracting the magnitudes to calculate the colors. If the PSFs are different, then an aperture correction ought to be applied to the magnitudes in each filter.

For this simulation we use a model of a SB2 galaxy at redshift z = 5.8 normalized to a magnitude ABMAG = 26.0 in the F850LP filter. The color of this galaxy is F775W - F850LP = 1.65 (1.71) in ABMAG WFC (HRC) system. Using the data of the characterization of the long‐wavelength light scattering and SYNPHOT, we estimate that the effective wavelength λ_eff and the fraction of the total light enclosed in a 03 aperture radius at the calculated λ_eff (see Table 16). If we remove the AB zero points and scale the total counts for the EE for an aperture of 03 radius, we obtain the OBMAG presented in Table 17.

At this point there are two options: treat the measured counts as total counts, or decide to apply an aperture correction. The aperture correction can be calculated from different sources, from stars in the FOV, from the tabulated EE for the standard stars, using SYNPHOT, or calculating the effective wavelength and Tables 6 and 7. In Table 18 we report the different cases and show the different results.

For this example we simulate observations of an L3.5 star with magnitude VEGAMAG = 22.00 in the WFC F775W filter. The color of this star is F775W - F850LP = 1.84 (1.99) in VEGAMAG WFC (HRC) system. For this example we perform photometry in a 02 (4 pixels) radius aperture for WFC, and a 01 (4 pixels) radius aperture for HRC. Using the observed spectra of the L3.5 star 2M0036+18 and SYNPHOT, we estimate the effective wavelength λ_eff of the observations and the fraction of the total light enclosed in the selected aperture radius (Table 19). If we remove the VEGAMAG zero points and scale the total counts for the EE and an aperture of 4 pixels radius, we obtain the instrumental magnitude given in Table 20.

At this point it is important to address the issue of the aperture correction. The aperture correction can be calculated from different sources, from stars in the FOV, from the tabulated EE for the standard stars, using SYNPHOT, or calculating the effective wavelength and using Tables 6 and 7. In Table 21 we report the different cases and show the different results.

Here we present, as an example, a transformation between the HRC and the WFC photometric systems. Suppose we observed the globular cluster NGC 2419 with ACS/HRC in F555W and F814W and have stored the photometric tables in the ABMAG HRC photometric system. We want to compare this result with previous WFC observations of the same cluster in the VEGAMAG system. This is the procedure that we need to follow, step by step:

• 1.  
  Transform the HRC ABMAG photometry to OBMAG.This is simply done by subtracting the ABMAG zero points (Table 11) from our data set:

  

  
• 2.  
  Compute the first estimate of TCOL. This is the less critical step and can be done by simply assuming

  

  

  

  
• 3.  
  Transform F555W_HRC,OBMAG to F555W_WFC,OBMAG. From Table 13, we select the coefficients in the "synthetic" column for SMAG = F555W, TMAG = F555W, and TCOL = F555W - F814W and use them in equation (12):

  
• 4.  
  Transform F814W_{HRC, OBMAG} to F814W_{WFC, OBMAG}. We proceed similarly to step 3 for the F555W but in the "synthetic " column for SMAG = F814W, TMAG = F814W, and TCOL = F555W - F814W there are two sets of coefficients depending on the value of TCOL:for TCOL< -0.2,

  

  and for TCOL> -0.2,

  
• 5.  
  Now we have better estimate of F555W_WFC,OBMAG and F814W_WFC,OBMAG from steps (2) and (3). Obviously, TCOL should be updated:

  
• 6.  
  Repeat steps 3 trough 5 until convergence is reached. Usually not more than 10 iterations are needed.
• 7.  
  Convert F555W_WFC,OBMAG and F814W_WFC,OBMAG into VEGAMAG by adding the zero points from Table 10:

  

  

In Figure 19 we show the comparison between the HRC‐to‐WFC transformed magnitude and the WFC photometry, overplotting the transformed magnitudes in the observed WFC CMD and plotting the differences in magnitude in the two filters as a function of the color.