THE HST EXTREME DEEP FIELD (XDF): COMBINING ALL ACS AND WFC3/IR DATA ON THE HUDF REGION INTO THE DEEPEST FIELD EVER^*

Here we briefly discuss the HST observations that were used to create the XDF dataset. In its current form, the XDF includes over 10 years of ACS/WFC and 3 years of WFC3/IR observations taken from mid-2002 through the end of 2012. These observations include data from the original ACS optical HUDF program (HST PID 9978) and the WFC3/IR HUDF09 and HUDF12 programs (HST PID 11563 and 12498). A complete list of HST programs that contribute to the XDF dataset is given in Table 2.

In order to specifically determine which HST observations to include in the XDF dataset, we executed searches using the MAST HST archive. We constrained our search to include only HST ACS/WFC and WFC3/IR imaging observations within a 13 arcminute radius of the original HUDF coordinates (α = 03:32:39.0, δ = −27:47:29.0) while limiting the search to the HST filters F435W, F606W, F775W, F814W, F850LP, F105W, F125W, F140W, and F160W, and the exposure time to >100 s. Although there have been many other HST observations taken with legacy instruments (e.g., WFPC2 and NICMOS), we chose to use only imaging data from HST's current optical and near-IR instruments and only filters where a substantial investment of HST orbits had been contributed. Once we had determined the set of observations to include in the XDF dataset, we used the HST MAST archive or the Canadian Astronomy Data Centre HST archive to acquire these data.

Our search resulted in a total of 2963 HST exposures, 1972 in the optical filters of ACS/WFC and 991 exposures in the NIR with WFC3/IR. These images add up to a total exposure time of almost 2 Ms. This corresponds to about 21.7 days of actual open-shutter observing time (13.6 days in ACS and 8.1 days in WFC3/IR). To acquire this amount of data would have taken HST about 790 orbits or about 52 days of clock time.

As would be expected from looking at the distribution of exposures in Figure 2, the exposure times vary significantly across the image for the different filters. The total exposure times per filter are shown in Table 3, while exposure time maps per filter are presented in Figures 3 and 4.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

The ACS/WFC channel consists of two 4096 × 2048 pixel detectors at a scale of 005 pixel⁻¹ providing a 202'' × 202'' field of view. All ACS/WFC images used in the XDF dataset were processed through the most recent version of the ACS calibration pipeline calacs (2012.2). The standard calibration process includes bias subtraction, dark current correction, bad pixel masking, and flat-fielding. In addition to these calibration processes, images taken after HST Servicing Mission 4 (SM4) have been corrected for charge transfer efficiency (CTE) degradation (Anderson & Bedin 2010), bias shift, bias striping (Grogin et al. 2010), and amplifier crosstalk (Suchkov et al. 2010).

The XDF ACS/WFC dataset was processed by the data reduction pipeline APSIS (Blakeslee et al. 2003). The reduction process is quite similar to the process used by the MultiDrizzle software package (Koekemoer et al. 2003) where each image is passed through a full drizzle–blot–drizzle cycle. Images are background-subtracted and drizzled onto a common tangential plane pixel grid. These images are median-stacked and the median stack image is blotted back to each input image position and used as a template for cosmic-ray rejection. A cosmic-ray mask is generated for each image and combined with the data quality array. The final image mosaic is produced by drizzling all the input images onto a single image mosaic and combining them with inverse-variance weight maps that take into account all noise sources (readout, dark current, and background noise).

While APSIS is perfectly adequate for producing science quality images when combining datasets consisting of tens of images, the XDF dataset, with hundreds of images, required further processing.

3.2.1. ACS/WFC Image Registration

Since the pointing accuracy of HST is only good to within a few arcseconds, the world coordinate system (WCS) of each image must be refined in order to acquire precise registration across all images within the ACS/WFC dataset. APSIS performs the image registration process using software we developed called superalign (see the Appendix). Briefly, superalign takes as input both source positions from a reference catalog and source positions from catalogs generated for each image (after rectifying each catalog to remove the geometric distortion). Then superalign uses these positions to compute accurate shift and rotation corrections that are applied to each input image. The input reference catalog was generated from an image produced by combining the original HUDF F775W image with an astrometrically calibrated GOODS mosaic to provide accurate alignment both over and outside the HUDF area.

To optimize alignment within the ACS/WFC dataset, we split the images into two groups: a deep group with images from the original HUDF observations which were taken at a single position and two orientations and a shallow group made up of the remaining images, which were taken at a large variety of positions and orientations. These two groups are processed separately with superalign while using the same input reference catalog. The frame-by-frame alignment within our dataset is excellent as shown in Figure 5.

Zoom In Zoom Out Reset image size

3.2.2. ACS/WFC Final Mosaics

Our basic processing of the WFC3/IR images is based on the calwf3 pipeline as outlined below.

The WFC3 IR channel uses a 1024 × 1024 pixel detector with the outer 5 pixels on each side of the detector containing reference bias pixels yielding a final 1014 × 1014 pixel image at a scale of 0135 × 0121 pixel⁻¹ and a 131'' × 121'' field of view. All WFC/IR images are obtained in MULTIACCUM mode in which each image contains two short bias readouts followed by a number of non-destructive readouts as determined by the NSAMP parameter set in the Phase II proposal.

The standard calwf3 processing of a WFC3/IR image includes initializing the data quality array and flagging known bad pixels, subtracting the mean bias level computed from reference pixels surrounding the detector for each readout and then subtracting the zeroth (bias) read from each readout in order to remove any signal from external sources. It then proceeds by correcting for the non-linear detector response, subtracting the appropriate dark current reference image in each readout, computing photometric header keywords, and converting the units of the science and error data arrays to a count rate. This is followed by an "up-the-ramp" fitting in order to combine the data from each readout while identifying and flagging pixels suspected of cosmic-ray hits. The final step in the processing corrects for pixel-to-pixel and large-scale variations across the detector by dividing by the appropriate flat field image and then multiplying by the gain of the detector so the final units will be in electrons per seconds. This step produces the final calibrated image with the flt name extension.

3.3.1. Variable Background Correction

3.3.2. WFC3/IR Persistence Masking

The XDF WFC3/IR dataset was processed using tasks provided in the data reduction pipeline WFC3RED. For a general description of the WFC3RED pipeline, see Magee et al. 2011. The WFC3RED pipeline takes as input the pre-processed WFC3/IR flt images and an external reference image used for registration and performs background subtraction, image registration, creation of inverse-variance weight-maps (for drizzling), and generation of the final distortion-free image mosaics.

The background in WFC3/IR images can vary dramatically from image to image depending on the observational conditions and can contain features on various scales. The WFC3RED pipeline performs background subtraction by utilizing a two-pass background model. In each pass, a median filter is applied to the image and subtracted after aggressively masking sources. In the first pass, a large grid size (165 pixels) is used in order to remove any large-scale gradients. In the second, a smaller grid size (39 pixels) is used to remove smaller scale background features. In order to improve the pixel-by-pixel signal-to-noise ratio (S/N), and correct for any imperfections in the flats or darks, WFC3RED median-stacks all the background-subtracted images in each filter in the dataset to create super-median background images. These are subsequently subtracted from the individual images.

WFC3RED performs the image registration process in two steps. The first registration step is performed by superalign. While superalign accurately determines the shift and rotation correction to be applied to most of the WFC3/IR images, we find that for some images a small correction is needed.

As a second registration step, WFC3RED therefore uses MultiDrizzle to create distortion-free image stacks for each visit in the dataset and then cross-correlates the sources in each image stack with sources in the external reference image. Minor corrections to the shift and rotation are then applied to the WCS of each image in the visit to obtain an optimal registration.

Specifically, for the alignment of the XDF dataset, we used the original HUDF F775W image for registration, combined with astrometrically calibrated GOODS mosaics, to provide accurate alignment outside of the HUDF area. Thanks to our two-step alignment procedure, the registration of the XDF image to the HUDF is better than 1/10 of a pixel (i.e., <0003; see Section 4.2).

WFC3RED creates the final image mosaics for each filter by running MultiDrizzle in three passes. For the first pass, each filter dataset is processed using the full-drizzle–blot–drizzle cycle. Each individual image is drizzled to a separate undistorted image matching the same size, scale, and orientation as the external reference image (i.e., the HUDF image in the case of the XDF). These images are then stacked into a single image using the MultiDrizzle "median" algorithm.¹² The stacked median image is then blotted back to each of the input image (distorted) positions, rescaled by the exposure time, and used as a clean template for identifying cosmic-rays and bad pixels. A cosmic-ray/bad-pixel mask is created and the data quality array is updated for each image. Last, a combined drizzle image is produced for each filter by using the inverse-variance weight maps.

In order to remove any excess background emission in the final image mosaics, WFC3RED runs MultiDrizzle a second time. In this pass, only the blotting back process of MultiDrizzle is run, this time using a combined drizzle image from the first pass to create an image at each position. These images are then used to create a median stack of images in each filter masking out the sources apparent in the combined drizzle image (rather than just those apparent in the individual images). These super-median images are subtracted from each of the individual images.

In the last pass only, the final image combination step of MultiDrizzle is run. A final image mosaic is created for each filter, using inverse-variance weight-maps with a pixfrac¹³ of 0.8, a "square" kernel, and an output scale of 006 pixel⁻¹.

The WFC3/IR dataset involved a slightly smaller effort than that involved in processing the ACS/WFC dataset but is still comparable to it. Nearly 1000 exposures totaling ∼0.7 million seconds in the four wide WFC3/IR filters were processed to form the extremely deep near-infrared dataset for the XDF. The two primary components of the WFC3/IR data were from the HUDF09 and the HUDF12 programs, with additional contributions from the CDF-S CANDELS dataset.

While the two primary datasets were closely aligned, the CANDELS data was at different orientations and centers and added to the complexity of the task for the WFC3/IR data. Processing the WFC3/IR data has many challenges similar to those of the ACS, but the WFC3/IR data also bring some unique challenges to the table. The issues that required particular attention were the misflagging of pixels as cosmic rays, persistence effects, and dealing with dramatically varying backgrounds. Fortunately, the smaller WFC3/IR datasets (∼300 Gbyte) processed more rapidly (typically within a day) and so it was possible to evaluate the output of a processing run, derive a fix for a problem, and do another run with a reasonable turnaround of several days. Nonetheless, the total time to identify the data problems, refine the software, test and fully process the data, and iterate as needed, meant that the WFC3/IR data also took many months of effort.

The XDF data products are organized into sets of images by passband (ACS/WFC F435W, F606W, F775W, F814W, and F850LP; WFC3/IR F105W, F125W, F140W, and F160W) and image scale. We drizzled the data to two different scales 006 pixel⁻¹ and 003 pixel⁻¹. The ACS benefits from drizzling to a 003 pixel⁻¹ scale because of its smaller native pixels and the better point-spread function (PSF) at shorter wavelengths, and so we provide the ACS data at this scale. These 30 mas images are exactly aligned with the original HUDF ACS images, having the same pixel positions and WCS configuration.

For the WFC3/IR data, a 006 pixel⁻¹ scale is more appropriate. We provide matched ACS and WFC3/IR data at the 60 mas scale. Each 60 mas pixel⁻¹ image is approximately 5 k × 5 k pixels and each 30 mas pixel⁻¹ image is approximately 10 k × 10 k pixels. For each filter we provide both the science and inverse-variance weight image.

The full set of XDF data products are available through the MAST High Level Science Products archive at http://archive.stsci.edu/prepds/xdf/.

The overall 5σ depths of the XDF image are presented in Table 4. In Figure 6, we show the gains in exposure time of the XDF image relative to the original HUDF ACS images. Since many of the additional data were taken as parallel images (mostly as part of the HUDF09 program), the added exposure time is highly position-dependent. In particular, the HUDF09 parallel ACS observations do not cover the whole XDF image, resulting in maximal gains in exposure time over the eastern part of the image (left on the figures), and only a small increase in exposure time on the west (right).

Zoom In Zoom Out Reset image size

In order to quantify the (position-dependent) gain in the depth of the images, we selected 5000 random empty sky regions of the images and measured the flux variation in circular apertures of 035 diameter. This was done in both the XDF and the original HUDF images. The flux variations are converted into 5σ magnitude depths and are reported in Table 5. As can be seen, averaged over the whole field, the XDF images are 0.12–0.20 mag deeper than the original HUDF data.

We quantify the depth variations around the field seen in Figures 6 and 7 for one of the ACS filters, F606W. As expected, the eastern part of the image (left) shows much greater gains in depth than is average for the image. Due to the increases in exposure time, the eastern part is deeper by 0.25 mag in that filter compared to the HUDF image.

Zoom In Zoom Out Reset image size

While these gains may seem small (0.12–0.25 mag), it is worthwhile considering that to achieve these gains through a new imaging program would require between 100 and 240 orbits of new data, and so the effort expended on maximizing the return from existing datasets results in valuable and very cost-effective gains.

Note that the minimum gains are actually quite significant, averaging about 0.1 mag, even in the parts of the images which only got a very small increment in exposure time. The minimum gain in the redder filters is quite substantial, reaching 0.13 mag and 0.18 mag, while in the bluer filters it is 0.09 mag and 0.12 mag. This is mainly due to our subtraction of a sky image, which results in markedly smoother background compared to the original processing of the HUDF¹⁴ dataset. It is clear from the original HUDF images that the background is smoother in the bluer filters than it is in the redder filters and this is reflected in the gains that we see from the improved processing.

To exemplify the gains made, we provide a direct comparison in Figure 8 between the original HUDF and the XDF of a galaxy with low surface brightness structure.

Zoom In Zoom Out Reset image size

One important test when creating a new image of the HUDF is consistency with the previous data. We therefore created independent catalogs of both datasets for a detailed comparison. In particular, we used the publicly available images of the HUDF from MAST.

The weight maps provided by multidrizzle are inverse-variance maps. In order to use these as weight maps for source detection with SExtractor (Bertin & Arnouts 1996), we converted these images to rms maps using

$$\begin{equation*} \mathrm{{\rm rms}} = 1/\sqrt{\mathrm{WHT}}. \end{equation*}$$

All pixels where WHT = 0 are set to 1 in the rms map.

We then run SExtractor (v2.8.6) to detect sources and measure their positions (X/Y_IMAGE) and fluxes in circular apertures (MAG_APER) of 035 diameter. The source positions are compared in Figure 9, where we show that the alignment is better than 1/10 pixel. The median offsets are <3 mas, with a standard deviation of 10 mas.

Zoom In Zoom Out Reset image size

In Figure 10, we compare the F775W photometry in circular apertures between the XDF and the HUDF images (using identical magnitude zeropoints). The photometry is very consistent, being ≲ 1% in all cases except one. The only filter where the flux differences are larger than 1% is the F606W image. The exposure time gain in this filter is highest, and it is likely that the small changes in the ACS AB-magnitude zeropoint with time affect this filter most. In our reduction, we have not accounted for such drifts in the zeropoints over the last 10 years. If photometry to within better than 1% is required, this change must be accounted for. We plan to correct for this effect in a future release of the XDF images.

Zoom In Zoom Out Reset image size

There have been two previous releases of WFC3/IR images over the HUDF field. In particular, after the completion of the HUDF09 program (PI: Illingworth), our team released a reduction to MAST including the full 2 years worth of data totaling 111 orbits of WFC3/IR imaging in the three filters F105W, F125W, and F160W used in the HUDF09 observations.

Since then, another 128 orbits of WFC3/IR imaging were taken as part of the HUDF12 program (PI: Ellis). These images included additional F140W imaging and significantly increased the depth in the F105W filter image. A combination of WFC3/IR data from the HUDF09 and HUDF12 programs has been released to MAST by the HUDF12 team. The XDF image release includes our own reduction of these data together with all additional WFC3/IR data that have been taken over this field, and we drizzled these to an identical frame as the ACS imaging data for easy multi-wavelength analyses.

As we show in Figures 9 and 11, the WFC3/IR images of the XDF are in excellent agreement with the HUDF12 (and also the HUDF09) image release, both in terms of photometry and source positions. Aperture fluxes agree to within <0.3%, and the alignment of these 60 mas images is again better than 1/10 pixel (<4 mas).

Zoom In Zoom Out Reset image size

The total number of sources in a field, or equivalently, the surface density of sources, has routinely been used as a gauge to quantify how faint a field reaches. The original Hubble Deep Field North (Williams et al. 1996) revealed some ∼2000–3000 sources within a small 5.7 arcmin² area (depending on whether the catalog was based on the V₆₀₆-band image alone or the V₆₀₆ + I₈₁₄ image). The HUDF in 2004 (Beckwith et al. 2006) significantly extended the depth available over the HDF-North, famously finding some 10,144 sources in a ∼11 arcmin² area or twice the number of sources per unit area as was revealed in the original Hubble Deep Field North image.

With the availability of our even deeper XDF exposure over the HUDF region, we can revisit this issue of source counts and the surface density of sources on the sky to very faint limits. Weighting the individual images according to the inverse-variance assuming a flat f_ν spectrum for sources, we constructed catalogs for the XDF using first only the optical ACS data over the ∼11 arcmin² full area with the HUDF region and second using the optical+near-IR data over the ∼4.7 arcmin² footprint originally defined by the HUDF09 program (see outlines in Figures 3 and 4).

Over the full ∼11 arcmin² area which made up the original HUDF release, our SExtractor catalogs reveal some 14,140 sources on the coadded B₄₃₅ + V₆₀₆ + i₇₇₅ + I₈₁₄ + z₈₅₀ image with a S/N >5 (Kron (1980) apertures, with Kron parameters of 1.6 and 2.5). The smaller ∼4.7 arcmin² area over which ultra-deep WFC3/IR imaging is available contains about 7121 galaxies above the same 5σ significance level, using as the detection image the coadded B₄₃₅ + V₆₀₆ + i₇₇₅ + I₈₁₄ + z₈₅₀ + Y₁₀₅ + J₁₂₅ + JH₁₄₀ + H₁₆₀ image.

The gains in depth in the optical lead to an ∼40% increase in the total number of sources over the ∼11 arcmin² HUDF area and an equivalent increase in the source surface density. Over the HUDF09 area where ultra-deep near-IR imaging data are available, we achieve even greater ⩾50% gains in source surface density as one might expect given the much greater depth of the collective optical+near-IR data set.

R.J.B. developed superalign, a short C code, to determine the internal shifts and rotations for an arbitrary number of (overlapping) contiguous images from a set of (distortion free) catalogs. It requires good initial guesses for the shifts and rotations (within 2.5 arcsec and 0.5 deg of the true solution, respectively), and thus is ideal for use with HST data where these quantities are only approximately known. This code was originally developed for use with the ACS GTO pipeline APSIS and offers several useful advantages relative to other image registration packages.

• 1.  
  It does not require that all images be contiguous with a single reference image. This allows one to construct arbitrarily large mosaics out of individual images.
• 2.  
  Input catalogs can include substantial (>80%) contamination from cosmic rays.

The algorithm that superalign uses to align large sets of exposures has a tree-like structure.

• 1.  
  First, superalign groups the exposures in terms of those that substantially overlap.
• 2.  
  Second, group by group (pointing by pointing), superalign iteratively aligns all the exposures. As it finds alignments that work between exposures within a group, it constructs an increasingly complete list of the probable stars. Candidate stars that appear in a statistically significant number of exposures are added to the complete list, while candidate stars that do not are classified as CRs.
• 3.  
  After generating a complete list of all the stars from each group, superalign begins building up a mosaic of stars starting at the central group and iteratively accreting nearby groups (to produce an ever larger list of stars). As each group is accreted, the relative position/rotation of all the groups added up to that point (within the ever growing mosaic) is re-optimized to minimize the overall error.

To determine the alignment between two individual catalogs, superalign uses a variation on the similar triangle method (Groth 1986). However, instead of attempting to find similar triangles in both images, superalign looks for similar bi-directional vectors (object pairs with the same separation and the same relative orientation). After finding similar vectors, superalign uses these vectors to determine a candidate transformation from one catalog onto another. Each transformation is given a score based upon how well it maps objects from one catalog onto the other. The transformation with the highest score is then adopted as the starting point in one final refinement step, where we perturb the coefficients in this transformation using a Markov Chain Monte Carlo process in an attempt to further improve the accuracy of the alignment.