Overview of the DESI Legacy Imaging Surveys

Explorations of the universe begin with images. In the last few decades, systematic surveys of the sky across the electromagnetic spectrum have revolutionized the ways in which we study physical processes in known astronomical sources, identify new astrophysical sources and phenomena, and map our environs (e.g., see Djorgovski et al. 2013, for an excellent summary). The amazing bounty of wide-field imaging surveys at optical wavelengths has been recently demonstrated by the Sloan Digital Sky Survey (SDSS; York et al. 2000; Abazajian et al. 2009; Aihara et al. 2011), Pan-STARRS1 (PS1; Chambers et al. 2016), and the Dark Energy Survey (The Dark Energy Survey Collaboration 2005), all of which continue to advance our knowledge of the universe in multiple fields of astrophysics (e.g., Dark Energy Survey Collaboration et al. 2016).

In this paper we describe the DESI Legacy Imaging Surveys (hereafter the Legacy Surveys) aimed at mapping 14,000 deg² of the extragalactic sky in three optical bands (g, r and z). The very wide areal coverage and the need to finish the survey in less than 3 years necessitated the use of three different telescope platforms: the Blanco telescope at the Cerro Tololo Inter-American Observatory; the Mayall Telescope at the Kitt Peak National Observatory; and the University of Arizona Steward Observatory 2.3 m (90 inch) Bart Bok Telescope at Kitt Peak National Observatory. In addition, the Legacy Surveys source catalogs incorporate mid-infrared photometry for all optically detected sources from new image stacks of data from the Wide-field Infrared Survey Explorer satellite (Wright et al. 2010).

2.1. Imaging for the Dark Energy Spectroscopic Instrument Surveys

2.2. Complementing Existing Spectroscopy

Beyond the primary goal of providing DESI targets, the imaging survey described in this paper has more wide-ranging astrophysical motivations. The Sloan Digital Sky Survey (SDSS; e.g., Abazajian et al. 2009; Abolfathi et al. 2018) project has overwhelmingly demonstrated the power of combining wide-field imaging and spectroscopic surveys within the same footprint. The SDSS-I,II,III/BOSS surveys contain ∼2.8 million spectra, including 300,000 unique stars, 700,000 galaxies at z < 0.2, 500,000 galaxies at 0.2 < z <0.5, 1 million galaxies at z > 0.5, 100,000 QSOs at z < 2, and 200,000 QSOs at z > 2.⁷¹ The median extragalactic redshift of these samples is already z_med ≈ 0.5, and SDSS-IV/eBOSS (Dawson et al. 2016, 2014–2020) is currently adding another 600,000 galaxies at 0.6 < z < 1 (Prakash et al. 2016; Raichoor et al. 2017) and 500,000 new QSOs at z > 0.9 (Myers et al. 2015). Most of these data are already available publicly.

While most SDSS-I spectra targeted nearby galaxies (r < 17.77; i.e., 4–5 mag brighter than the imaging detection limit), BOSS (SDSS-III) targeted much fainter sources (galaxies to i = 19.9 and QSOs to g = 22), near the limits of the original SDSS imaging (Dawson et al. 2013); eBOSS (SDSS-IV) goes even fainter (see, e.g., Abolfathi et al. 2018). While adequate for the study of large-scale structure, the full science impact of these data is limited by the depth and quality of the existing imaging. The bulk of existing spectroscopic redshifts are in the northern sky and have poor overlap with most deep, wide-field imaging surveys (see Figure 1). The SDSS imaging data (which provided the spectroscopic targets) do not provide precise photometry, well-resolved size measurements, detailed morphologies, or environmental measures for the bulk of the faint galaxies targeted by the existing spectroscopy.

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The Legacy Surveys will greatly remedy this situation by imaging the entire BOSS footprint to magnitudes suitable for the study of the z > 0.5 universe (see Figure 1). Based on the magnitude distribution of galaxies in the zCOSMOS catalog (Lilly et al. 2007), imaging to the 5σ z-band depth of the Legacy Surveys will result in increasing the number of detected z > 0.5 galaxies (z > 1) galaxies by a factor of >15 (>200) over SDSS. Measuring g − r versus r − z colors cleanly isolates z > 0.5 galaxies. Optical photometry coupled with the WISE mid-infrared photometry can be used to measure stellar masses and AGN activity for such galaxies (see, e.g., Section 3 of DESI Collaboration et al. 2016a, and references therein) can be used to resolve morphologies and structural parameters for all SDSS spectroscopic galaxies. The combination of the image quality (median FWHM in the z band of ≈11) and depth of the Legacy Surveys can be used to measure improved morphologies and structural parameters for all SDSS spectroscopic galaxies.

Spectroscopy complements deep imaging; it provides robust redshifts; a crisp 3D view of large-scale structure; dynamical information through velocity dispersions; spectral diagnostics of stellar populations, star formation rates, and nuclear activity; and probes of the intergalactic medium through absorption line studies. The combination enables numerous astrophysical studies. For example:

• 1.  
  The Evolution of Galaxy Clusters: While SDSS has obtained redshifts of 1.5 million massive galaxies, often the central, brightest galaxies in groups and clusters, current imaging often cannot detect their satellites. The Legacy Surveys will significantly improve stellar mass models for these galaxies and enable a sensitive search for faint cluster members. Extrapolating from the SDSS Stripe 82 imaging (Rykoff et al. 2014, 2016), we expect to identify ∼75,000 clusters, nearly all of which will have spectroscopic redshifts available from SDSS. Spectroscopy provides three key benefits not available to photometric-only surveys: (1) calibration of cluster masses by stacked velocity dispersion measurements (e.g., Becker et al. 2007); (2) tests of general relativity by the comparison of the velocity field around clusters to the weak-lensing shear mass profile (e.g., Lam et al. 2012; Zu et al. 2014); and (3) calibration of cluster masses by detecting the weak-lensing magnification of the luminosity function of background galaxies and quasars (Coupon et al. 2013, 2015). Magnification-based methods have systematic uncertainties that are completely independent from the shape and photometric redshift systematics expected to dominate the error budget of imaging-only surveys like DES or LSST, thereby enabling a critical consistency test with these surveys.
• 2.  
  Galaxy Halos through Cosmic Time: The contents (and shapes) of galaxy dark matter halos can be revealed from the cross-correlation of spectroscopic and imaging maps (Eisenstein et al. 2005; Tal et al. 2013) and from galaxy-galaxy weak lensing (e.g., Mandelbaum et al. 2016). These methodologies benefit substantially from deeper imaging, with statistical errors on cross-correlations and lensing signals often scaling as ${N}_{\mathrm{gal}}^{-1/2}$. Higher precision is crucial: variations in clustering as a function of galaxy properties are often only of order 10%, so distinguishing between models requires percent-level clustering measurements. The z ≈ 22.8 AB mag 5σ depth of the Legacy Surveys imaging will increase the samples available to these methodologies by factors of >15 (based on comparisons to the zCOSMOS catalogs; Lilly et al. 2007). Cross-correlation studies use angular correlations to tie deep photometric catalogs to overlapping spectroscopic maps, measuring the mean environments and clustering of galaxies and AGN with great accuracy. SDSS has provided high-precision results at lower redshift using these techniques (e.g., measuring the mean environment of galaxies as a function of luminosity, color, and scale; Hogg et al. 2003; Eisenstein et al. 2005; Masjedi et al. 2006; Jiang et al. 2012) and interpreting this to constrain halo populations and merger rates (Zheng et al. 2009; Watson et al. 2012). The Legacy Surveys will extend this to far larger (>10–100×) spectroscopic and photometric samples at high redshift, measuring the satellite distributions around central galaxies as a function of redshift, luminosity, stellar mass, color, major axis orientation, velocity dispersion, [O ii] emission-line equivalent width, and so on. Cross-correlation also enables more robust clustering measurements around rare spectroscopic populations and the ability to calibrate galaxy redshift distributions from imaging data (Newman 2008; Myers et al. 2009; Ménard et al. 2013; Schmidt et al. 2013).
• 3.  
  The Evolution of Halo Gas: SDSS spectra have already yielded >50,000 Mg ii absorption line systems at 0.4 < z < 2.5 toward background QSOs (Zhu & Ménard 2013), and eBOSS will increase the number of sightlines to nearly a million. By cross-correlating 2000 absorbers at z ∼ 0.5 with SDSS photometric galaxies, Lan et al. (2014) extracted new relations between galaxy properties and their surrounding gas (e.g., their Figure 2(a)). The Legacy Surveys will dramatically improve this type of analysis by extending its reach from z ∼ 0.5 to z ∼ 2, sampling the full range of ∼100,000 identified absorbers. This will map the cosmic evolution of halo gas as a function of redshift, making it possible to understand its dependence on galaxy type, orientation, luminosity, star formation rate, environment, and so on.
• 4.  
  The Halo of the Milky Way: The SDSS, PS1 and DES imaging surveys have revolutionized the study of the Milky Way, finding numerous stellar halo streams (e.g., Newberg et al. 2002; Yanny et al. 2003; Grillmair 2009; Bernard et al. 2016; Shipp et al. 2018) and dwarf galaxies (Willman et al. 2005; Laevens et al. 2014; Bechtol et al. 2015; Drlica-Wagner et al. 2015). The Legacy Surveys will map at least twice as far out into the Galactic halo over 14,000 deg², increasing the volume of the MW explored by a factor of ∼5 relative to SDSS+Pan-STARRS. This will enable tests of predictions that stellar halo substructure dramatically increases with distance (Bell et al. 2008; Helmi et al. 2011). Our photometric parallax-based maps will extend to ∼40 kpc using main sequence stars (Jurić et al. 2008; Ivezić et al. 2008), ∼80 kpc using gr-selected main sequence turnoff stars (Bell et al. 2008), and ∼150 kpc using ugr-identified Blue Horizontal Branch (BHB) stars where u band is available (Ruhland et al. 2011). The deeper data on known streams (Odenkirchen et al. 2003; Carballo-Bello et al. 2018) will be used to test for the presence of "missing satellites" via their signatures in these streams (Carlberg 2009; Yoon et al. 2011). Imaging from the Legacy Surveys should be sufficient to discover 8–20 new dwarf galaxies. Each dwarf galaxy discovery immediately adds years of Fermi integration to the search for dark matter detection via gamma-rays (Albert et al. 2017). Finally, given the 10 yr time baseline between imaging from SDSS and the Legacy Surveys, proper motions should be measured to accuracies of a few milliarcsec per year for stars 2 mag fainter than the Gaia limits.

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2.3. Photometry from the WISE Satellite

The footprint of the Legacy Surveys is designed to correspond to the DESI Survey footprint, which is defined to be the extragalactic sky above a Galactic latitude of b = 15° that can be observed spectroscopically from Kitt Peak (i.e., at decl. δ > −20°). These selections result in an ≈14,000 deg² area, which contains two contiguous regions: one in the North Galactic Cap (NGC) covering 9900 deg² and one in the South Galactic Cap (SGC) covering 4400 deg².

The basic criteria described result in a larger area in the NGC (A semester) relative to the SGC (B semester). However, we also need to conduct a uniform, wide-area extragalactic survey with fields that can be scheduled throughout the year, minimizing observations at high airmass (at low or high declinations) and in regions of high Galactic extinction or high stellar density. To minimize scheduling issues for DESI, the NGC portion of the footprint is trimmed to decl. δ > −82 and the SGC area extends southward to δ ≈ −133 in regions not covered by the Dark Energy Survey (DES; The Dark Energy Survey Collaboration 2005), and to δ ≈ −184 in the region covered by DES. These choices were informed by realistic simulations of the DESI survey, including a dynamic observing model similar to that described in Section 6.2.

Since the primary motivation is an extragalactic cosmological survey, additional cuts are imposed to remove those parts of the sky with the largest stellar density. For the survey regions closest to the Galactic center (i.e., −90° < l < +90°), only regions with Galactic latitude $| b| \gt 18^\circ$ are selected; in the Galactic anti-center, a less stringent criterion of $| b| \gt 14^\circ$ is imposed, allowing the survey to extend a bit closer to the Galactic plane.

Finally, the selected footprint is modified to both avoid small holes within the survey and to avoid largely disconnected regions that arise as a result of the E(B − V) cuts. For example, an "orphaned" area of 600 deg² in the northern part of the SGC has therefore been excluded from the DESI footprint.

The final footprint is shown in Figure 1. The DESI spectroscopic survey is expected to observe most or all this footprint, dependent upon the level of completion of the Legacy Surveys. The current coverage of the footprint is shown in Figure 2.

The four target classes that will be used as cosmological tracers by DESI can be selected using a combination of optical imaging data in the g, r, and z bands and mid-infrared imaging in the 3.4 and 4.6 μm WISE bands (see Appendix A for further details). DESI requires that the Legacy Surveys deliver 5σ detections of a "fiducial" g = 24.0, r = 23.4 and z = 22.5 AB mag galaxy with an exponential light profile of half-light radius r_half = 0.45 arcsec. DESI also requires the depth (and the resulting target selection) to be as uniform as possible across the survey footprint. Ideally, a cosmological survey would use the same imaging data to select all science and calibration targets. However, the ambitious footprint coupled with the short timeline for DESI and lack of very-wide-field imaging capabilities in the northern hemisphere necessitated using multiple platforms to cover the footprint.

Consequently, a combination of three telescopes is used to provide the optical imaging for the Legacy Surveys: the Blanco 4 m telescope at Cerro Tololo, the Bok 90 inch, and the Mayall 4 m telescope at Kitt Peak (see Table 1). The areas of the Legacy Surveys imaged using each of these telescopes are shown in Figure 1, and the next three subsections discuss these surveys and their current status in more detail. The status of the WISE data used in the Legacy Surveys catalogs is presented in Section 5.

DESI targeting requires uniformity in the imaging within each sub-footprint, and resorting to multiple platforms poses challenges. In order to minimize non-uniformity and cross-calibration issues, the overall footprint was divided into only three contiguous regions. Two of these three regions are being imaged using the Dark Energy Camera on the Blanco telescope, the instrument and telescope combination delivering the widest field of view (and therefore the fastest survey capability). The other region, which is in the NGC north of δ ≈ + 34°, is being imaged from Kitt Peak using the 90Prime Camera on the Bok telescope for the g and r bands, and the Mosaic-3 camera on the Mayall telescope for the z-band observations. The sub-footprints of these individual surveys overlap in the NGC (in an area of ≈300 deg²) in the decl. range +32° < δ < +34°, so that the color transformations between the different camera+telescope combinations can be calibrated to high precision and accuracy. An additional ≈100 deg² in SDSS Stripe 82 is also being imaged by all three surveys to aid the cross-calibration (see Table 2).

A fill factor of unity is not required for the DESI Key Project. As long as the detailed sky mask is well-characterized, the clustering analyses can make use of that mask with information loss proportional to this fractional loss of area. The DESI requirements are that the coverage to full depth in all three optical bands should exceed 90% of the footprint, and that 95% (98%) must be within 0.3 (0.6) magnitudes of full depth. The g, r, and z filter bandpasses used by the Legacy Surveys are shown in Figure 3. The observing nights allocated to each survey are shown in Table 3.

4.1. DECaLS: The Dark Energy Camera Legacy Survey

4.2. BASS: The Beijing–Arizona Sky Survey

The Beijing–Arizona Sky Survey (BASS; Zou et al. 2017b) is imaging the decl. ≥ +32° region of the DESI NGC footprint (≈5100 deg²) in the g and r optical bands. BASS uses the 90Prime camera (Williams et al. 2004) at the prime focus of the Bok 2.3 m telescope. The Bok Telescope, owned and operated by the University of Arizona, is located on Kitt Peak, adjacent to the Mayall Telescope. The 90Prime instrument is a prime focus 8k × 8k CCD imager, with four University of Arizona ITL 4k × 4k CCDs that have been thinned and UV optimized with peak QE of 95% at 4000 Å (see Williams et al. 2004, for details). These CCDs were installed in 2009 and have been operating routinely since then. 90Prime delivers a 112 field of view, with 045 pixels and 94% filling factor. The median FWHM of the DIQ at the telescope is 16 and 15 in the g and r bands, respectively. The throughput and performance in these bands were demonstrated with data in 2013 September.

BASS tiles the sky in three passes, similar to the DECaLS survey strategy. At least one of these passes is observed in photometric conditions (Pass 1) and seeing conditions better than 17. Observations in g band are restricted to dark time, when the moon is below the horizon. The typical individual exposure times are 100 s per band, with the requirement that three passes are needed to reach depth. As in the case of DECaLS, the exposure times are varied depending on the conditions, but limited between 50 and 250 s. We refer the reader to (Zou et al. 2017b) for further details.

Table 4.  Depths and Delivered Image Quality

Survey	Single-frame Depthsa						DIQd
Name	PSF Depthb			Galaxy Depthc			('')
	g	r	z	g	r	z	g	r	z
DECaLSe	23.95	23.54	22.50	23.72	23.27	22.22	1.29	1.18	1.11
BASSf	23.65	23.08		23.48	22.87		1.61	1.47
MzLSg			22.60			22.29			1.01

Notes.

^aIn AB mag. ^bMedian 5σ detection limit in AB mag for a point source in individual images. ^cMedian 5σ detection limit in AB mag for the fiducial DESI target (galaxy with an exponential disk profile with ${r}_{\mathrm{half}}=0\buildrel{\prime\prime}\over{.} 45$). ^dDelivered image quality, defined as the FWHM in arcseconds of the measured point-spread function. For comparison, the corresponding median FWHM for the SDSS imaging is $\approx 0.85\times {\mathrm{psfWidth}}_{\mathrm{SDSS}}=1.22$, 1.12, 1.10 arcsec in the g, r, and z bands, respectively (see https://www.sdss.org/dr14/imaging/other_info/#SeeingandSkyBrightness). ^eFrom Data Release 5. ^fFrom Data Release 6. ^gBased on all data obtained for the survey.

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BASS was awarded 56/100/100/90 nights in the 2015A/2016A/2017A/2018A semesters (PIs: Zhou Xu and Xiaohui Fan) to target 5500 deg² in the NGC and ≈100 deg² in the SGC.⁷⁴ These areas include ≈400 deg² of overlap with regions covered by other components of the Legacy Surveys (Table 2) in order to cross-calibrate photometry. Prior to the start of BASS, it was determined that the existing Bok g-band filter was well matched to the DECam g-band filter, but the existing Bok r-band filter had a significantly different bandpass. A new r-band filter was therefore acquired from Asahi in 2015 April and was used for subsequent BASS observations. The 90Prime camera has excellent response at blue wavelengths, and as a result the effective throughput as a function of wavelength for the g and r photometric bands in the BASS survey is different than that for the same bands in the DECaLS survey.

The BASS survey began observations in spring 2015. A number of instrument control software updates, new flexure maps, and new observing tools were implemented that greatly improved the pointing accuracy, focusing of the telescope, and observing efficiency. A total of 15% of the g-band tiles and 2% of the r-band tiles were observed in spring 2015. It was discovered that those data suffered from defective electronics in the readout system that introduced analog-to-digital conversion errors, gain variations, and non-linearities. The 90Prime CCD controller electronics were replaced in September 2015 followed by a recommissioning of the system in fall 2015.

BASS completed 40% of its expected coverage in 100 scheduled nights in the 2016A semester (January–July). BASS is expected to complete observations by 2019 March. As of 2018 December, the BASS project has undergone two data releases that are detailed in Zou et al. (2017a, 2018).

4.3. MzLS: The Mayall z-band Legacy Survey

The Legacy Surveys source catalogs include mid-infrared photometry from the WISE satellite for all optically detected sources. Mid-infrared imaging is critical to the DESI targeting algorithms for luminous red galaxies (LRGs) and quasars (QSOs). During its primary 7 month mission from 2010 January through 2010 August, WISE conducted an all-sky survey in four bands centered at 3.4, 4.6, 12, and 22 μm (known as W1, W2, W3 and W4; Wright et al. 2010; Cutri et al. 2012). Following its primary 4-band mission, WISE continued survey operations in the three bluest bands for 2 months, then the two bluest bands for an additional 4 months, resulting in a combined 13 month mission that completed in 2011 February. Through a mission extension referred to as NEOWISE-Reactivation (NEOWISE-R; Mainzer et al. 2014), NASA reactivated the satellite and resumed 2-band survey observations on 2013 December 13. NEOWISE-R observations remain ongoing. Annual NEOWISE-R data releases, each consisting of single-exposure (Level 1b) images and source extractions, have occurred on 2015 March 25, 2016 March 23, 2017 June 1 and 2018 April 19.

DESI target selection utilizes the two shortest-wavelength bands at 3.4 μm (W1) and 4.6 μm (W2). Photometry in these bands is measured using The Tractor algorithm (see Section 8), adopting source centroid and morphology parameters from the optical imaging, which has much better angular resolution than WISE. The Tractor measurements are based on custom stacks of WISE/NEOWISE exposures that are optimized for forced photometry and therefore preserve the native WISE resolution. These stacks are referred to as unWISE coadds (Lang 2014). DR1 made use of the Lang (2014) unWISE coadds based on the initial 13 month WISE data set, reaching 5σ limiting magnitudes of 20.0 and 19.3 AB mag in W1 and W2. Subsequent Legacy Surveys releases have used a series of updated, deeper unWISE coadd data sets featuring progressively more NEOWISE-R imaging (Meisner et al. 2017a, 2017b, see Table 6). DR7 incorporates all five years of publicly available WISE and NEOWISE-R imaging, including that from the fourth-year NEOWISE-R release. The final catalogs from the Legacy Surveys will push even deeper at 3–5 μm by leveraging the full WISE and NEOWISE-R data sets.

In addition to the mid-infrared photometry measured from the "full-depth" W1/W2 unWISE stacks (which are required for DESI targeting), the Legacy Surveys DR3–DR7 also include W1/W2 forced photometry light curves corresponding to all optically detected sources. These light curves are measured from time-resolved unWISE coadds similar to those described in Meisner et al. (2018a, 2018b). Such light curves provide variability information on all optically-detected sources, which can be used, among other things, for the DESI quasar selection, although this possibility has not yet been tested in detail. In DR7, the Legacy Surveys W1/W2 light curves typically have 10 coadded epochs per band, spanning a ≈7.5 year time baseline.

In this section, we briefly describe the observing strategy employed by the Legacy Surveys. For a more detailed description of the implementation and algorithms, we refer the reader to K. Burleigh et al. (2019, in preparation).

6.1. Survey Strategy

6.2. Dynamic Observing

All data from the Legacy Surveys are first processed at NOAO/Tucson through the NOAO Community Pipelines ("CPs"). Each instrument and telescope combination has its own CP that takes raw data as an input and provides detrended and calibrated data products. The NOAO Pipeline Scientist and architect is co-author F. Valdes, who is responsible for the development and continued operation of the CPs. The CPs include algorithms and code (from a variety of sources, the key ones being code developed by DES Data Management, the TERAPIX suite, and IRAF; Tody 1986; Bertin & Arnouts 1996; Bertin et al. 2002; Bertin 2011; Valdes et al. 2014), which are modified and packaged for the needs of the NOAO environment and characteristics of the different instruments. A common feature of all the CPs is the orchestration framework (The NOAO High Performance Pipeline System; Scott et al. 2007) that allows parallelized processing across the NOAO computing resources to handle the large volumes of data produced by NOAO observing programs.

The CPs provide instrumentally calibrated data products for observers, programs, and archival researchers. Instrumental calibrations include typical CCD corrections (e.g., bias subtraction and flat-fielding); astrometric calibration (e.g., mapping the distortions and providing a world coordinate system, or WCS); photometric characterization (e.g., magnitude zero-point calibration); and artifact identification, masking, and/or removal (e.g., removal of cross-talk and pupil ghosts, and identification and masking of cosmic rays). Data products delivered to the NOAO Science Archive include flux calibrated images (i.e., individual images with and without distortion corrections applied and image stacks), bad data masks, and weight maps.

The three cameras used by the Legacy Surveys (i.e., DECam, Mosaic-3, and 90Prime) each have their own CP. The basic steps of each CP are summarized in Table 5. Detailed technical descriptions of each CP are in preparation⁷⁸ (Valdes et al. 2014, describes an early version of DECam CP). The CP for the DECaLS data evolved from the Dark Energy Survey pipeline such that it has algorithms and code from several sources. The key sources are code developed by DES Data Management, the TERAPIX suite, and IRAF (Tody 1986; Bertin & Arnouts 1996; Bertin et al. 2002; Bertin 2011; Valdes et al. 2014). Some calibrations are not perfect, with the detection and masking of artifacts being only partially effective and background pattern subtraction around very large and bright sources being prime examples. In particular, the CP can result in unmasked spurious sources in the final catalogs. First, the thick, deep depletion LBNL CCDs employed in the DECam and Mosaic-3 cameras are excellent detectors of particle events (see Groom 2004, for a more detailed discussion), a fraction of which are inadequately masked by the current CP. Second, asteroids and other moving targets are not flagged by the CP and may appear as detected sources in the catalogs (at least through DR7).

The CP-calibrated individual images, bad pixel masks, and weight maps are transferred to the National Energy Research Scientific Computing Center (NERSC), where post-processing is done in order to improve the astrometric and photometric calibrations and create the source catalogs. Similarly, the WISE satellite data are transferred to NERSC as they become public, and new coadded stacks are constructed on an approximately yearly basis.

7.1. Astrometric Calibration

The NOAO CP reductions of all Legacy Survey imaging data derive a WCS, a function mapping pixel coordinates to celestial coordinates. The function (TPV: tangent plane projection with polynomial distortions⁷⁹ ) is determined for each CCD by least square fitting to the pixel centroids of detected sources with known coordinates in a reference catalog. For the astrometric solution, the pixel centroids of reference stars are computed using intensity weighted means using Source Extractor (Bertin & Arnouts 1996) in the DECam CP, and using the ACE package in IRAF (Tody 1986; Valdes 2001) in the Mosaic-3 and 90Prime CPs. The final source positions in the catalogs are computed using The Tractor, as described in Section 8.

The reference coordinates were from the 2MASS catalog (Skrutskie et al. 2006) for DECam data from 2013 and 2014; later DECam data and all Mosaic-3 and 90Prime data use the Gaia DR1 catalog (Gaia Collaboration et al. 2016b). Since the calibration procedure ties source positions in each exposure to celestial sources, it effectively includes calibration for the atmospheric distortions (at some mean color) and, in the case of the Bok 90Prime data, correction for distortions resulting from the focusing procedures.

While this procedure corrects the data for global distortions (the TPV solutions are continuous and smooth across an individual CCD), it does not correct for some small-scale effects. For example, the DECam and Mosaic-3 CCDs are known to have very small-scale distortions known as "tree rings" (Plazas et al. 2014), and the Mosaic-3 CCDs show a residual astrometric pattern from bonding stresses. Differential chromatic refraction is also not accounted for in the astrometric solutions (see, e.g., Bernstein et al. 2017 for an excellent discussion of all the issues affecting the DECam astrometry). These combined effects affect the astrometric accuracy on individual CCDs at the level of ≈10–30 mas and are currently not corrected in the post-processing catalog generation step.

In addition, the Mosaic-3 electronics occasionally read out with a missing starting column. The CP detects and corrects this; however, because the edges are masked anyway, this has no effect on the astrometry. Prior to MJD 57674 the readout electronics introduced a one-third pixel shift between amplifiers in the vertical transfer direction (corresponding to the east–west direction on the sky). Since this is a precise, discrete offset, the CP corrects this completely with no effect on the astrometry.

90Prime has charge transfer effects that affect centroid measurement and, in particular, introduce systematic opposing shifts between amplifiers in the serial transfer direction. This effect is evident as a discrete jump at the amplifier boundaries in the astrometric offset when comparing the astrometry of reference stars from the Gaia DR1 catalog with that measured from the Bok data using the best-fit smooth astrometric solution. The systematic offset between the two halves is ≈160 mas for CCD-1 and ≈70 mas for the other three CCDs. The CP applies a relative shift to the pixels from each amplifier so that the astrometric offset jump across the boundary is minimized. These corrections are applied to each exposure and they substantially reduce, but do not completely remove, this systematic effect. The residual difference does show small temporal variations (of order a few mas) from night-to-night; correcting for this residual would require a higher order correction to the astrometry (rather than just a zero-point offset at the boundary), which may result in changing the shape of the PSF.

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As noted earlier, the CP data is only the first part of the Legacy Surveys calibrations. Small residual mean offsets per CCD are applied to the CP astrometric zero-point calibrations using a reference catalog constructed from stars color-selected from the PS1 DR1 catalog (Chambers et al. 2016) with positions from the Gaia DR1 catalog (Gaia Collaboration et al. 2016b). For all releases prior to (and including) DR3 of the Legacy Surveys, astrometric and photometric calibration is based on comparisons to a subset of PS1 catalog sources with magnitudes <21.5 AB mag and colors $0.4\lt {(g-i)}_{\mathrm{PS}1}\,\lt 2.7$ AB mag. Starting with DR4 of the Legacy Surveys, PS1 positions of these sources were replaced with the Gaia DR1 catalog positions (i.e., post-DR3 astrometry is tied to Gaia). The astrometric residuals for bright stars relative to their Gaia DR1 catalog positions are shown in Figures 4–6. MzLS and DECaLS have rms scatters of ≈20 mas, with BASS showing slightly larger residuals. The residual scatter, outliers, and asymmetries visible in the distributions shown in Figures 4–6 are likely due to the following reasons: the higher-order and small-scale pixel-level distortions, which are larger in the thick, deep depletion CCDs in the Mosaic-3 and DECam cameras; (2) the lack of proper motions in the Gaia DR1 catalog, which exaggerates the scatter and causes outliers because of the difference in epoch between the two images; (3) the plots shown include all data, irrespective of observed image quality. Corrections for the offsets due to the higher order pixel-level distortions and modeling of stars with known proper motions will be incorporated into The Tractor modeling in future data releases.

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7.2. Photometric Calibration

The role of the CPs in photometric calibration is to remove any spatial variation in the photometric response of each CCD (i.e., to "flatten" each CCD) and to then estimate the conversion factor from analog digital units recorded by each CCD to photoelectrons. The CPs also provide the data quality masks and weight maps that are used for in the subsequent source detection and photometric calibration steps.

The Legacy Surveys are designed so that each part of the footprint is observed in photometric conditions at least once, and most of the footprint is observed in photometric conditions two or more times. Efforts to observe at the lowest possible airmasses and avoid the Moon drive an observing plan that features a rich set of overlaps between observations on different nights. Comparison of observations of the same stars on different nights and at different airmasses then enables determination of the system throughput and the transparency of the atmosphere for each photometric night of the survey. This procedure is the basis of the photometric calibration of the SDSS (Padmanabhan et al. 2008), as well as subsequent surveys like PS1 (Schlafly et al. 2012) and DES (Burke et al. 2018). Observations on nonphotometric nights will be calibrated by matching directly to overlapping observations taken on photometric nights.

The current photometric calibration for the Legacy Surveys (for all data releases through DR6) is, however, tied to the PS1 DR1 photometry through a set of color transformation equations. The magnitudes of PS1 DR1 catalog sources are first converted to the "native" system for each telescope+camera+filter, and the transformations are as follows:

$$\begin{eqnarray}\begin{array}{rcl}{g}_{\mathrm{DECaLS}} & = & {g}_{\mathrm{PS}1}+0.00062+0.03604{(g-i)}_{\mathrm{PS}1}\\ & & +\,0.01028(g-i{)}_{\mathrm{PS}1}^{2}-0.00613(g-i{)}_{\mathrm{PS}1}^{3}\end{array}\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}\begin{array}{rcl}{r}_{\mathrm{DECaLS}} & = & {r}_{\mathrm{PS}1}+0.00495-0.08435{(g-i)}_{\mathrm{PS}1}\\ & & +\,0.03222(g-i{)}_{\mathrm{PS}1}^{2}-0.01140(g-i{)}_{\mathrm{PS}1}^{3}\end{array}\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}\begin{array}{rcl}{z}_{\mathrm{DECaLS}} & = & {z}_{\mathrm{PS}1}+0.02583-0.07690{(g-i)}_{\mathrm{PS}1}\\ & & +\,0.02824(g-i{)}_{\mathrm{PS}1}^{2}-0.00898(g-i{)}_{\mathrm{PS}1}^{3}\end{array}\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}\begin{array}{rcl}{g}_{\mathrm{BASS}} & = & {g}_{\mathrm{PS}1}+0.00464+0.08672{(g-i)}_{\mathrm{PS}1}\\ & & -\,0.00668(g-i{)}_{\mathrm{PS}1}^{2}-0.00255(g-i{)}_{\mathrm{PS}1}^{3}\end{array}\end{eqnarray} \tag{ 4 }$$

$$\begin{eqnarray}\begin{array}{rcl}{r}_{\mathrm{BASS}} & = & {r}_{\mathrm{PS}1}+0.00110-0.06875{(g-i)}_{\mathrm{PS}1}\\ & & +\,0.02480(g-i{)}_{\mathrm{PS}1}^{2}-0.00855(g-i{)}_{\mathrm{PS}1}^{3}\end{array}\end{eqnarray} \tag{ 5 }$$

$$\begin{eqnarray}\begin{array}{rcl}{z}_{\mathrm{MzLS}} & = & {z}_{\mathrm{PS}1}+0.03664-0.11084{(g-i)}_{\mathrm{PS}1}\\ & & +\,0.04477(g-i{)}_{\mathrm{PS}1}^{2}-0.01223(g-i{)}_{\mathrm{PS}1}^{3}.\end{array}\end{eqnarray} \tag{ 6 }$$

These color transformations are measured empirically by comparing the Legacy Surveys and PS1 catalog data for stars with magnitudes <21.5 AB mag and colors $0\lt {(g-i)}_{\mathrm{PS}1}\lt 2.9$, and the absolute calibration is determined using the CALSPEC database⁸⁰ (see Bohlin et al. 2017, and references therein). The DECaLS transformations used herein are the same as those determined by Schlafly et al. (2018) for the DECaPS Galactic Plane Survey. The BASS and MzLS transformations were determined in a similar manner, using unresolved sources selected from PS1 DR1 with well-measured photometry (i.e., no flags) with colors in the range $0\lt {(g-i)}_{\mathrm{PS}1}\lt 2.9$. Constant terms in the calibration are intended to place the Legacy Surveys on the AB magnitude system (Oke & Gunn 1983), and were derived from comparison of the empirical transformations with synthetic transformations of calibrated Hubble Space Telescope standard stars, given the system throughputs of the DECam, BASS, and MzLS surveys. (The photometric transformations between the SDSS grz magnitudes and the Legacy Survey magnitudes are presented in Appendix B.)

We estimate a zero-point for each CCD independently, by (1) detecting sources on the pipeline-reduced data; measuring their instrumental magnitudes; (2) matching to the subset of PS1 DR1 catalog sources selected as calibrators; and then (3) comparing the instrumental magnitudes to the color-transformed PS1 DR1 magnitudes (i.e., as per Equations (1)–(6)). This procedure results in zero points for each CCD tied to the global PS1 calibration, but corrected to the "native" photometric frame for each individual survey.

In the future, we will migrate to an internal photometric calibration that will rely solely on data from each of the Legacy Surveys. The large network of repeat observations on different photometric nights enables the construction of a detailed description of the throughput of the various imaging systems used in the Legacy Surveys. We plan to not only measure overall system zero points and (gray) atmospheric transparency in each band on each night (see Padmanabhan et al. 2008), but also to determine how sensitivity varies within and among the different CCDs of each system as a function of time (see Schlafly et al. 2012, 2018). We can also determine and ameliorate systematic problems with aperture correction. Well-calibrated optical colors are now available from PS1 and Gaia, which will make it straightforward to remove systematic chromatic errors stemming from the different colors of stars and the varying effective throughput of the imaging system in different conditions (Li et al. 2016; Burke et al. 2018). The DECam Plane Survey, which used a similar three-pass strategy to DECaLS, obtained 6–8 mmag precision for bright stars (Schlafly et al. 2018), without accounting for color-dependent calibration terms; we anticipate similar photometric precision for the Legacy Surveys data.

All the source catalogs from the Legacy Surveys project are constructed using The Tractor. Co-author D. Lang has developed The Tractor⁸¹ as a forward-modeling approach to perform source extraction on pixel-level data. This algorithm is a statistically rigorous approach to fitting the differing PSF and pixel sampling of the different imaging data that compose the Legacy Surveys. This approach is particularly useful given the wide range in PSF shape and size exhibited by the Legacy Surveys data: the optical data have a typical PSF of ≈1 arcsec, and the WISE PSF FWHM is ≈6 arcsec in W1–W3 and ≈12 arcsec in W4.

For the Legacy Surveys, we have created a post-processing catalog generation pipeline called legacypipe,⁸² which wraps The Tractor, and which proceeds as follows. The Legacy Surveys footprint is analyzed in 025 × 025 regions called "bricks." We first identify all the CCDs that overlap a given brick, and each CCD is analyzed to estimate and subtract the sky. The initial sky estimate is computed by first subtracting a per-CCD median value of the unmasked pixels, then estimating a sliding median every 512 pixels on a box size of 1024 pixels, and fitting the result with a two-dimensional spline. This initial sky is biased by sources, but does remove slow variations in the sky background. Subtracting this initial sky model, we compute a five-pixel boxcar-smoothed image, detect and mask pixels above 3σ (in boxcar-smoothed sigmas) plus a three-pixel margin, and recompute the spline background estimate using the remaining unmasked pixels. This iteration results in a sky estimate less biased by sources in the image. The PSF for each CCD is then estimated on the sky-subtracted image using PSFEx (Bertin 2011), and each individual sky-subtracted CCD is convolved with its own PSF in order to facilitate source detection. We then create five separate stacks for the purpose of source detection: a weighted sum of all the (PSF-convolved) CCDs in a given band (resulting in three such stacks), a weighted sum of all three bands to optimize for a "flat" SED (i.e., zero AB mag color), and a weighted sum of all three bands to optimize for a "red" SED (i.e., with colors g − r =1 mag and $r-z=1$ mag). While these image stacks are weighted sums of the convolved images, the input images are not all convolved to a common PSF. Next, we detect sources on the three individual-band image stacks and the two grz image stacks using a simple thresholding algorithm, selecting sources above 6σ. This process identifies almost all sources in the images to faint magnitudes. The details of the entire legacypipe pipeline (and The Tractor) will be presented in a forthcoming paper (D. Lang et al. 2019, in preparation).

Next, we detect sources on the individual-band image stacks and the two grz image stacks using a simple thresholding algorithm, selecting sources above 6σ. This process identifies almost all sources in the images to faint magnitudes. Each source is then modeled by The Tractor, which takes as input the NOAO pipeline-reduced individual images from multiple exposures in multiple bands, with different seeing in each. For each astronomical source, a source model is fit simultaneously to the pixel-level data of all images containing the source. The Tractor models each source using a small set of parametric light profiles: a delta function (for point sources); a de Vaucouleurs ${r}^{-1/4}$ law; an exponential disk; or a "composite" de Vaucouleurs plus exponential. The best-fit model is determined by convolving each model with the specific PSF for each individual exposure, fitting to each image, and minimizing the residuals for all images. The PSF for each optical image is constructed using PSFEx (Bertin 2011). We make the assumption that the model is the same across all the bands. Thus, if a source is determined to be a point source, it is modeled as a point source in every band and every exposure and its catalog photometry is based on this model. Alternatively, if the source is spatially extended, then the same light profile (an exponential disk, de Vaucouleurs, or combination) is consistently fit to all images in order to determine the best-fit source position, source shape parameters, and photometry.⁸³

The Tractor model fits are determined using only the optical grz data. The mid-infrared photometry for each optically-detected source is then determined by forcing the location and shape of the model, convolving with the WISE PSF and fitting to the WISE stacked image. This "forced photometry" approach allows us to deblend any confused WISE sources by using the higher-spatial-resolution optical data, but also limits the Legacy Surveys catalogs to only contain WISE photometry for sources that are detected at optical wavelengths. The procedure described produces object positions, fluxes, and colors that are consistently measured across the three Legacy Surveys.

Figure 7 shows examples of how The Tractor is being applied to the Legacy Surveys. The footprint of the Legacy Surveys is divided into "bricks" of size 025 × 025, and a model of the sky within each brick is computed using all CCDs that contribute data within that brick. The three sets of vertical panels show: the grz image data for a brick, the rendered The Tractor model, and the residual image (i.e., data − model). While most of the faint sources are well fit by the parametric models we used for the Legacy Surveys, more significant residuals are seen associated with very extended galaxies and the halos of bright, saturated stars.

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The Tractor and our source detection algorithms do result in the catalog containing a small fraction of spurious sources. These are primarily due to inadequately masked particle events or satellite trails,⁸⁴ single-exposure detections of transient sources (primarily asteroids⁸⁵ ), and sources identified in the extended scattered light halos or diffraction spikes associated with bright stars,⁸⁶ or in the diffuse emission associated with large galaxies.⁸⁷ In addition, spatially large, extended sources with complex morphologies (e.g., large galaxies⁸⁸ ) and crowded fields (e.g., globular clusters⁸⁹ and open star clusters⁹⁰ ) are poorly modeled by The Tractor. Finally, a small number of sources are missed by The Tractor catalog; these are primarily very low surface brightness diffuse sources⁹¹ or sources lying close to a (typically brighter) star or galaxy.⁹²

The "forced photometry" approach we use to measure the mid-infrared photometry from the WISE images allows us to detect fainter sources than a traditional approach while preserving the photometric reliability. For bright objects that were cleanly detected by WISE alone (and recorded in the AllWISE catalog), the pixel-level measurements are consistent with catalog-level measurements (see Figure 8, left panel). However, we are also able to measure the fluxes of significantly fainter objects, as well as study collections of objects that are blended in the WISE images but are resolved in the optical images. The increased level of source counts in the force-photometered data observed at bright WISE magnitudes (i.e., $W1\lesssim 16$ mag) in the right panel of Figure 8 is due to sources detected in the vicinity of bright stars or galaxies; ≈50% of these sources are real objects, and the remaining are spurious detections due to the halos or diffraction spikes around bright stars or the poorly modeled extended light of galaxies. All are located near other brighter targets, which is why they are compromised. We are currently working on improving the models for future data releases. Figure 9 compares a traditional optical-infrared color–color diagram, based on matching sources between catalogs at different wavelengths, to the photometry derived from our WISE forced photometry, which requires no such matching. This demonstrates how The Tractor greatly increases the access to mid-infrared photometry for targets fainter than the AllWISE catalog detection limits, albeit with increased scatter. We have verified the reliability of the forced photometry detections and measurements by comparing The Tractor catalog results with those from deep Spitzer data in the COSMOS field (i.e., the S-COSMOS catalog from Sanders et al. 2007). Defining reliability as the fraction of Spitzer sources recovered, we find that the reliability is ≥95% for sources with W1 or W2 signal-to-noise ratios of ≥5, corresponding to 21.3 and 20.4 AB mag, respectively. We have also compared the photometric measurements in our catalogs with those from S-COSMOS and find that they are in good agreement with the ≥5σ detections.

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The Tractor should improve target selection for all DESI target classes by allowing information from low signal-to-noise ratio measurements to be utilized. The Tractor is particularly important for targeting QSOs. Up to 15% of QSO spectra exhibit broad absorption lines that potentially reduce the measured flux in broadband imaging. In addition, high-redshift QSOs at z ≥ 5.0 (≥6.9) will drop out of the g band (g and r bands) completely (e.g., see Bañados et al. 2018). Finally, the 5σ optical limit at the extremes of DESI targeting corresponds to a <5σ limit in WISE for QSOs. The Tractor successfully differentiates between the QSOs that are detected in WISE and those that are not detected, whereas traditional "catalog-matching" approaches would not be successful.

The SDSS-IV/eBOSS (Dawson et al. 2016), which began observations in 2014 July, also utilized The Tractor and the WISE component of the Legacy Surveys to target LRGs (Prakash et al. 2016) and QSOs (Myers et al. 2015). For these eBOSS targets, The Tractor provided forced photometry based upon galaxy profiles measured by the SDSS imaging pipeline. Those profiles were convolved with the WISE PSF, and then a linear fit was performed on the full set of WISE imaging data. The result was a set of mid-infrared flux estimates for all SDSS objects, constructed so that the sum of flux-weighted profiles best matched the WISE images (Lang 2014; Lang et al. 2016b). The Legacy Surveys use the same fitting approach, using the deeper DECaLS, MzLS, and BASS optical images in place of the SDSS images.

The Tractor catalogs include source positions, fluxes, shape parameters, and morphological quantities that can be used to discriminate extended sources from point sources, together with errors on these quantities. The Tractor catalogs are vetted for DESI target selection using a series of image validation tests (as in, e.g., Appendix C).

The Legacy Surveys are being run as completely public projects. All raw optical imaging data are made available as soon as they are transferred from each telescope to the NOAO Science Archive.⁹³ The data transfer occurs within minutes for DECam and Mosaic-3 data, and by the following morning for 90Prime data. Pipeline-processed data are made public as soon as the reductions are completed, typically within a week of the observations. Finally, catalogs based on The Tractor and cross-matched data are released twice a year. All data (images, coadds, catalogs, and supplementary material) are available at the NOAO Science Archive and through the Legacy Surveys portal hosted at NERSC.⁹⁴ All the code used for creating the catalogs is publicly available.⁹⁵ In addition, the BASS data are independently processed and released by the BASS team (e.g., see Zou et al. 2017a, 2018, for details).

Tables 3 and 6 show the observing schedule at the Blanco, Bok, and Mayall telescopes and our data release milestones. The data releases provide required deliverables such as object catalogs, depth maps, and coadded images, models, and residuals (see Table 7; see http://legacysurvey.org for details regarding the data release contents).

As of 2018 December, the two most recent data releases are DR6 (containing all the MzLS and BASS data obtained through 2017 December 9 and 2017 June 25, respectively) and DR7 (containing all the DECaLS data obtained through 2018 March); see Table 6. Together, DR6+DR7 jointly cover nearly the entire DESI footprint and have significant overlap. The DR7 data release presents DECaLS data over ≈9766 deg² in g band, 9853 deg² in r band, and 10,610 deg² in z band, with 9298 deg² of coverage in all three bands. There are approximately 835 million unique sources in DR7 spread over 180,102 bricks. The DR6 data release presents MzLS+BASS data covering ≈4400 deg² in g band, 4400 deg² in r band, and 5300 deg² in z band, with ≈3900 deg² with three-band coverage. There are approximately 310 million unique sources in DR6 spread over 92,287 bricks. Approximately 7500 bricks overlap between DR6 and DR7, each containing more than 1000 objects.

Figures 10–12 show, respectively, the spatial distributions of the photometric residuals in the g, r, and z bands relative to the PS1 survey, the astrometric offsets relative to the Gaia DR1 catalog positions, and the best z-band image quality over the entire survey footprint. The three surveys provide nearly uniform coverage in photometry and astrometry, with rms scatter of <10 mmag and <5 mas for well-measured stars. Nevertheless, there remain systematic offsets between the subsurveys; these are particularly obvious at the boundary between the DECaLS and MzLS/BASS surveys, at decl. ≈ + 34° in the NGC. The astrometric offset results from a change in the way in which the Gaia positions were included in DR7: while the astrometric calibration in both DR6 and DR7 are tied to Gaia DR1, Gaia stars with proper motions in Gaia DR2 were modeled by The Tractor at the epoch of observation. Future Legacy Survey data releases will be consistently tied to the latest version of the Gaia catalog and self-consistently account for stars with well-measured proper motions.

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Despite efforts to keep the filter bandpasses as similar as possible for the Kitt Peak and Cerro Tololo surveys, there remain significant differences in the effective throughput as a function of wavelength between the different surveys, especially in the g and r photometric bands (see Figure 3). A direct comparison of the photometry for stellar sources observed by both sets yields the following color transformations (see Figure 13):

$$\begin{eqnarray}\begin{array}{rcl}{g}_{\mathrm{DR}6,\mathrm{BASS}} & = & {g}_{\mathrm{DR}7,\mathrm{DECaLS}}-0.039+0.038{(g-r)}_{\mathrm{DR}7}\\ & & +\,0.195(g-r{)}_{\mathrm{DR}7}^{2}-0.251(g-r{)}_{\mathrm{DR}7}^{3}\\ & & +\,0.092(g-r{)}_{\mathrm{DR}7}^{4}\end{array}\end{eqnarray} \tag{ 7 }$$

$$\begin{eqnarray}\begin{array}{rcl}{r}_{\mathrm{DR}6,\mathrm{BASS}} & = & {r}_{\mathrm{DR}7,\mathrm{DECaLS}}-0.004+0.035{(r-z)}_{\mathrm{DR}7}\\ & & -\,0.004(r-z{)}_{\mathrm{DR}7}^{2}\end{array}\end{eqnarray} \tag{ 8 }$$

$$\begin{eqnarray}&&{z}_{\mathrm{DR}6,\mathrm{MzLS}}={z}_{\mathrm{DR}7,\mathrm{DECaLS}}-0.050-0.008{(r-z)}_{\mathrm{DR}7}.\end{eqnarray} \tag{ 9 }$$

These color transformations are determined using unresolved objects (i.e., type "PSF" in both catalogs) with no masked pixels that are well detected (S/N ≥ 5) within the overlapping regions in both the DECaLS DR7 and BASS+MzLS DR6 catalogs (at $149.9\lt {\rm{R.A.}}\lt 220.1$, $31.9\lt {\rm{decl.}}\lt 33.6$). The polynomial least-squares fits were performed on samples restricted in magnitude and color: [15, 22] and $0\lt {(g-r)}_{\mathrm{DR}7}\,\lt 1.7$ in g band; and [15, 21.5] and $0\lt {(r-z)}_{\mathrm{DR}7}\lt 2.2$ in the r and z band. The photometry in the catalogs has not been corrected for these color transformations.

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The median photometric zero-point offsets between DR6 and DR7 are

$$\begin{eqnarray}&&\langle {g}_{\mathrm{DR}6,\mathrm{BASS}}-{g}_{\mathrm{DR}7,\mathrm{DECaLS}}\rangle =-0.028\,\mathrm{mag}\end{eqnarray} \tag{ 10 }$$

$$\begin{eqnarray}&&\langle {r}_{\mathrm{DR}6,\mathrm{BASS}}-{r}_{\mathrm{DR}7,\mathrm{DECaLS}}\rangle =-0.024\,\mathrm{mag}\end{eqnarray} \tag{ 11 }$$

$$\begin{eqnarray}&&\langle {z}_{\mathrm{DR}6,\mathrm{MzLS}}-{z}_{\mathrm{DR}7,\mathrm{DECaLS}}\rangle =0.057\,\mathrm{mag}.\end{eqnarray} \tag{ 12 }$$

These medians are computed for unresolved sources (i.e., type "PSF" in both catalogs) with magnitudes and colors in the range [16, 22] and $0\lt (g-r)\lt 1.7$ for g band, and [16, 22] and $0\lt (r-z)\lt 2.2$ in the r and z bands. Part of the zero-point offset is due to a change in the way in which the photometry was absolutely calibrated between DR6 and DR7. All data releases prior to DR7 fixed the absolute calibration such that the PS1 and Legacy Surveys magnitudes agreed for stars at a PS1 color of ${(g-i)}_{\mathrm{PS}1}=0$, whereas DR7 and all future releases place the Legacy Survey photometry on the AB magnitude scale, where small magnitude differences are expected at ${(g-i)}_{\mathrm{PS}1}=0$. This change resulted in offset differences of +0.009, −0.012, and +0.043 mag for the g, r, and z bands, respectively. In addition, some portion of the median offsets computed previously may be due to differences in the way the sky background is estimated in DR6 and DR7. We are currently working on the sky estimation algorithms, and these results may change before our final data release.

Figure 14 shows the grz-band source number counts derived from DR6 and DR7 of the Legacy Surveys. Figure 15 shows the grz-band depths for the DR6 and DR7 data. The DR6 imaging (from BASS and MzLS) is shallower than the DR7 imaging (from DECaLS), but still satisfies the DESI target selection requirements.

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Figure 16 shows the distributions, in grzW1 color–color planes, of sources from the Legacy Surveys DR7 differentiated by their morphological type. Sources best fit by PSF models are dominated by stars (as exemplified by the clearly visible stellar locus) but also contain compact galaxies and QSOs. The sources best fit by spatially extended models (EXP: exponential disks; and DEV: de Vaucouleurs ${r}^{1/4}$ profiles) trace the galaxy locus with minimal contamination from stars (since the star-galaxy separation is limited by the ground-based seeing).

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Figure 17 shows cutouts of a wide variety of astronomical sources imaged by the Legacy Surveys, to demonstrate the depth and image quality of the surveys. The large time baseline between the Legacy Surveys and SDSS also enables the detection of faint transients and the measurement of proper motions for faint stars (Figure 18 shows an example). The sensitivity of the Legacy Surveys data to low surface brightness structures has been exploited in the new version of Galaxy Zoo (https://blog.galaxyzoo.org/tag/decals/) and for finding faint tidal features associated with galaxies (e.g., Hood et al. 2018). In addition, the depth of the Legacy Surveys data has resulted in their use for selecting emission-line galaxy (DECaLS component; Raichoor et al. 2017) and QSO targets (WISE component Myers et al. 2015) for the SDSS-IV/eBOSS spectroscopic survey.

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All observations for the MzLS completed on 2018 February 12. Observing for BASS will continue through 2018 July. Observing for DECaLS is estimated to continue until 2019 March. The goal of the Legacy Surveys is to consolidate the data from all the subsidiary surveys into a final data release by 2019 June.

We have begun three wide-area optical imaging surveys that will cover a total area of 14,000 deg² in two contiguous portions and in three filters. These surveys are designed to provide targets for the DESI project, which will begin spectroscopic observations in 2019. The surveys include optical imaging data in three bands (g, r, and z band) from three ground-based telescopes (CTIO Blanco, KPNO Mayall, and Steward Bok 90") and will reach approximate 5σ depths of g = 24.0, r = 23.4, and z = 22.5 AB mag for faint galaxies. In addition, the data releases will contain mid-infrared photometry based on new, multi-epoch stacks of imaging data from the WISE satellite created by the unWISE project. The three surveys are the Dark Energy Camera Legacy Survey (DECaLS), the Mayall z-band Legacy Survey (MzLS), and the BASS; these surveys are jointly referred to as the Legacy Surveys.

We have implemented an automated observing strategy for all surveys, where observing conditions are monitored in near real time and exposure times are modified and target field selection is optimized on-the-fly to ensure that each individual observation reaches the required depth. This strategy ensures that the ground-based surveys produce data sets that are as uniform as possible. The data are pipeline processed using the NOAO Community Pipelines, and catalogs are then generated from the imaging data using an inference-based forward-modeling approach known as The Tractor, implemented at NERSC.

All the imaging data, source catalogs, and code from the Legacy Surveys are publicly available: the raw and pipeline-processed optical imaging data are made public as soon as they are available in the NOAO Archive and catalogs from the project are released approximately twice each year. There have been seven data releases thus far, which are described in detail in other papers. The imaging data are accessible from the Legacy Surveys website⁹⁶ and the NOAO Science Archive.⁹⁷ An image viewer (the Imagine sky viewer, at http://legacysurvey.org/viewer) is provided at the Legacy Surveys website that allows the user to examine the data, The Tractor models, and other supplementary data. A resource at the NOAO DataLab provides access to the catalogs through SQL queries or a Jupyter notebook interface.⁹⁸

The Legacy Surveys are nearing completion. We anticipate completing the surveys before the start of DESI spectroscopic observations in late 2019.

This paper presents observations obtained at Cerro Tololo Inter-American Observatory, National Optical Astronomy Observatory (NOAO Prop. ID: 2014B-0404; co-PIs: D. J. Schlegel and A. Dey), which is operated by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation. This paper also includes DECam observations obtained as part of other projects, namely the Dark Energy Survey (DES, NOAO Prop. ID: 2012B-0001); and 2012B-0003, 2012B-0416, 2012B-0506, 2012B-0569, 2012B-0617, 2012B-0621, 2012B-0624, 2012B-0625, 2012B-3003, 2012B-3011, 2012B-3012, 2012B-3016, 2012B-9993, 2012B-9999, 2013A-0327, 2013A-0360, 2013A-0386, 2013A-0400, 2013A-0455, 2013A-0529, 2013A-0609, 2013A-0610, 2013A-0611, 2013A-0613, 2013A-0614, 2013A-0618, 2013A-0704, 2013A-0716, 2013A-0717, 2013A-0719, 2013A-0723, 2013A-0724, 2013A-0737, 2013A-0739, 2013A-0741, 2013A-9999, 2013B-0325, 2013B-0438, 2013B-0440, 2013B-0453, 2013B-0502, 2013B-0531, 2013B-0612, 2013B-0613, 2013B-0615, 2013B-0616, 2013B-0617, 2014A-0073, 2014A-0191, 2014A-0239, 2014A-0255, 2014A-0256, 2014A-0270, 2014A-0306, 2014A-0313, 2014A-0321, 2014A-0327, 2014A-0339, 2014A-0348, 2014A-0386, 2014A-0390, 2014A-0412, 2014A-0415, 2014A-0429, 2014A-0496, 2014A-0608, 2014A-0610, 2014A-0611, 2014A-0613, 2014A-0620, 2014A-0621, 2014A-0622, 2014A-0623, 2014A-0624, 2014A-0632, 2014A-0640, 2014B-0146, 2014B-0244, 2014B-0608, 2014B-0610, 2014B-0614, 2015B-0187.

DECaLS used data obtained with the Dark Energy Camera (DECam), which was constructed by the Dark Energy Survey (DES) collaboration. Funding for the DES Projects has been provided by the U.S. Department of Energy, the U.S. National Science Foundation, the Ministry of Science and Education of Spain, the Science and Technology Facilities Council of the United Kingdom, the Higher Education Funding Council for England, the National Center for Supercomputing Applications at the University of Illinois at Urbana-Champaign, the Kavli Institute of Cosmological Physics at the University of Chicago, the Center for Cosmology and Astro-Particle Physics at the Ohio State University, the Mitchell Institute for Fundamental Physics and Astronomy at Texas A&M University, Financiadora de Estudos e Projetos, Fundação Carlos Chagas Filho de Amparo, Financiadora de Estudos e Projetos, Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro, Conselho Nacional de Desenvolvimento Científico e Tecnológico and the Ministério da Ciência, Tecnologia e Inovacão, the Deutsche Forschungsgemeinschaft and the Collaborating Institutions in the Dark Energy Survey. The Collaborating Institutions are Argonne National Laboratory, the University of California at Santa Cruz, the University of Cambridge, Centro de Investigaciones Enérgeticas, Medioambientales y Tecnológicas-Madrid, the University of Chicago, University College London, the DES-Brazil Consortium, the University of Edinburgh, the Eidgenössische Technische Hochschule (ETH) Zürich, Fermi National Accelerator Laboratory, the University of Illinois at Urbana-Champaign, the Institut de Ciències de l'Espai (IEEC/CSIC), the Institut de Física d'Altes Energies, Lawrence Berkeley National Laboratory, the Ludwig-Maximilians Universität München and the associated Excellence Cluster Universe, the University of Michigan, the National Optical Astronomy Observatory, the University of Nottingham, the Ohio State University, the University of Pennsylvania, the University of Portsmouth, SLAC National Accelerator Laboratory, Stanford University, the University of Sussex, and Texas A&M University.

The Mayall z-band Legacy Survey (MzLS; NOAO Prop. ID no. 2016A-0453; PI: A. Dey) uses observations made with the Mosaic-3 camera at the Mayall 4 m telescope at Kitt Peak National Observatory, National Optical Astronomy Observatory, which is operated by the Association of Universities for Research in Astronomy (AURA) under cooperative agreement with the National Science Foundation. The authors are honored to be permitted to conduct astronomical research on Iolkam Du'ag (Kitt Peak), a mountain with particular significance to the Tohono O'odham.

The Beijing–Arizona Sky Survey (BASS; NOAO Proposal ID no. 2015A-0801; PIs: Zhou Xu and Xiaohui Fan) is a key project of the Telescope Access Program (TAP), which has been funded by the National Astronomical Observatories of China, the Chinese Academy of Sciences (the Strategic Priority Research Program "The Emergence of Cosmological Structures" Grant no. XDB09000000), and the Special Fund for Astronomy from the Ministry of Finance. The BASS is also supported by the External Cooperation Program of Chinese Academy of Sciences (Grant no. 114A11KYSB20160057), and Chinese National Natural Science Foundation (Grant no. 11433005). The Bok Telescope is located on Kitt Peak and operated by Steward Observatory, University of Arizona.

The Legacy Surveys imaging of the DESI footprint is supported by the Director, Office of Science, Office of High Energy Physics of the U.S. Department of Energy under Contract no. DE-AC02-05CH11231, by the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility under the same contract, and by the U.S. National Science Foundation, Division of Astronomical Sciences under Contract no. AST-0950945 to NOAO. Travel and other support for the DECaLS and MzLS projects are provided by the National Optical Astronomy Observatory, the Lawrence Berkeley National Laboratory, and the DESI Project.

This publication makes use of data from the Pan-STARRS1 Surveys (PS1) and the PS1 public science archive, which have been made possible through contributions by the Institute for Astronomy, the University of Hawaii, the Pan-STARRS Project Office, the Max Planck Society and its participating institutes, the Max Planck Institute for Astronomy, Heidelberg and the Max Planck Institute for Extraterrestrial Physics, Garching, Johns Hopkins University, Durham University, the University of Edinburgh, Queen's University Belfast, the Harvard-Smithsonian Center for Astrophysics, the Las Cumbres Observatory Global Telescope Network Incorporated, the National Central University of Taiwan, the Space Telescope Science Institute, the National Aeronautics and Space Administration under Grant no. NNX08AR22G issued through the Planetary Science Division of the NASA Science Mission Directorate, the National Science Foundation Grant no. AST-1238877, the University of Maryland, Eotvos Lorand University (ELTE), the Los Alamos National Laboratory, and the Gordon and Betty Moore Foundation.

This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement.

This publication makes use of data products from the Wide-field Infrared Survey Explorer (and its successor, the Near-Earth Object Wide-field Infrared Survey Explorer), which is a joint project of the University of California, Los Angeles, and the Jet Propulsion Laboratory/California Institute of Technology, funded by the National Aeronautics and Space Administration.

This research used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract no. DE-AC02-05CH11231.

The research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement no. 320964 (WDTracer).

J.M. gratefully acknowledges support from the National Science Foundation grant AST-1616414. A.D. thanks the Radcliffe Institute for Advanced Study for their generous support during the year these surveys were initiated. A.D., D.J.S., and D.L. thank the Aspen Center for Physics, which is supported by National Science Foundation grant PHY-1066293, for their hospitality and support during summer 2015, when this work was conducted.

Facilities: KPNO:Mayall (Mosaic-3) - , Steward:Bok (90Prime) - , CTIO:Blanco (DECam) - , WISE - Wide-field Infrared Survey Explorer, Gaia - .

Imaging data from the Legacy Surveys will be used to select targets for DESI. In this appendix, we describe the basic requirements that the DESI project's main cosmological survey imposes on imaging. There are five target classes for the DESI dark energy experiment: (1) Bright Galaxy Sample (BGS), (2) LRGs, (3) Emission-line Galaxies (ELGs), (4) quasars (QSOs) at z < 2.1, and (5) quasars at z > 2.1 for the measurement of the Lyα forest. The imaging surveys will also be used to select secondary targets such as other interesting object classes (rare objects, Milky Way stars, etc.), standard stars for spectrophotometric calibration, and locations for blank sky fibers.

In 2013, the DESI Project concluded that a three-band g/r/z optical imaging program complemented by WISE W1 and W2 photometry would be sufficient to select all target classes required for the DESI cosmology program. One optical band is sufficient to select the BGS, which is defined as a simple magnitude-limited sample. Two optical bands are necessary to select LRGs and quasars, as the WISE W1 infrared band provides adequate color information to clearly separate these targets from stars and other galaxies. Three optical bands are necessary to efficiently select the ELGs, as these galaxies are not well detected at the depth of the WISE data. Other imaging data (e.g., u band) may be used to further refine the selection of the high-redshift QSOs, which is the one target class that is not required (by DESI) to have a uniform selection if used for Lyα forest maps.

The requirements that DESI targeting imposes on the optical imaging are

• 1.  
  Imaging will be in three optical bands to a depth of at least g = 24.0, r = 23.4, and z = 22.5. The depths are defined as the optimal-extraction (forced-photometry) depths for a galaxy near the depth limits of DESI, where that galaxy is defined to be an exponential profile with a half-light radius of ${r}_{\mathrm{half}}=0.45$ arcsec. For such a profile, the effective number of pixels is well-approximated by ${N}_{\mathrm{eff}}={\left[{\left(4\pi {\sigma }^{2}\right)}^{(1/p)}+{\left(8.91{r}_{\mathrm{half}}^{2}\right)}^{(1/p)}\right]}^{p}$, where σ is the standard deviation for a Gaussian fit to the seeing, r_half is the half-light radius for an exponential-profile galaxy, and p = 1.15. In addition to the optical imaging, 4 years of WISE data in the W1 and W2 bands are assumed.
• 2.  
  Imaging will cover at least 14,000 deg² of the DESI footprint. This footprint is described in Section 3.
• 3.  
  The fill factor will be at least 90%. The areas with coverage to full depth in all 3 bands should exceed 90% of the footprint. The science loss is approximately proportional to this fractional loss of area.
• 4.  
  z-band image quality will be smaller than 1.5 arcsec FWHM. Many of the DESI galaxy targets appear small (less than 1 arcsec) and are near the limit at which they can be resolved as extended sources rather than point sources. Because of this, a morphological separation between extended sources and point sources will not be required for DESI galaxy targets. The primary driver for reasonably good image quality is to minimize blending between targets and other sources on the sky, especially in regions of high stellar density, such as near the Galactic plane. Reasonable image quality in at least one band will allow the identification of otherwise blended objects and the optimal extraction of their photometry in all bands. All of the DESI targets will be detected in z band, which is expected to have the best image quality; therefore an image quality requirement is specified in that one band.
• 5.  
  No regions larger than 3 deg in diameter will be covered by only nonphotometric observations. Photometric observations are defined as those obtained during nights demonstrated to have photometricity errors of 1% rms in g band and r band, or 2% rms in z band. Small regions, especially in CCD gaps on the imager focal planes, may be filled in with nonphotometric data and calibrated to neighboring photometric data.
• 6.  
  The random errors in astrometry will be less than 95 mas rms, and the systematic errors will be less than 30 mas. Astrometric errors impact the effective throughput of the DESI instrument for the spectroscopic survey. The systematics errors in the astrometry will be well-controlled by tying individual CCD images to Gaia (Gaia Collaboration et al. 2016a). The astrometric positions can take advantage of the signal in all filters.

An inference modeling approach will be used for measuring the photometry in all bands from the optical and WISE imaging data. The DESI requirements for the imaging reductions are

• 1.  
  The model photometry will use the same model in all bands. The model photometry uses the same model in all bands to minimize systematic errors in the flux ratios (i.e., colors) of galaxies, which is critical for all target selection algorithms.
• 2.  
  Systematic errors due to PSF mis-estimation will be controlled to better than 1%.
• 3.  
  Systematic errors due to galaxy model mis-estimation will be controlled to better than 1%. A simple χ² fit would suffer from biases in the galaxy photometry due to the models not matching the actual morphology of individual galaxies, and this would be S/N-dependent.
• 4.  
  Depth maps will be computed in each band at all locations. The effective depth will be computed as a map for each filter. This is a function of the sky brightness, image quality, and sky transparency of all of the contributing images. In detail on small scales, it would include the features seen from bad columns on the CCD and increased noise near other sources on the sky.
• 5.  
  The ability will be provided to Monte Carlo simulated objects through the imaging pipeline. This requirement implies access to all of the calibrated image frames, the versioned code used to construct the final targeting catalogs, and the ability to run this code. This Monte Carlo ability will be used to map the effects of bright stars and other source contamination problems, which can both produce spurious targets and remove actual targets by blending them with other sources.

We compared the SDSS and Legacy Surveys photometry in two regions using the "sweeps" files, which contain matched SDSS and Legacy Survey sources and are included as part of the DR6 and DR7 Legacy Survey releases. For the SDSS-DR6 comparison, we used the region 230° ≤ R.A. ≤ 240° and 20 ≤ decl. ≤ 25; for the SDSS-DR7 comparison, we used the region 160° ≤ R.A. ≤ 170° and 20 ≤ decl. ≤ 25. The photometric transformations were then computed by fitting polynomials to the SDSS-Legacy Survey magnitude differences in the g, r, and z bands as a function of the SDSS $(g-i)$ color. The fits were done in the color range $-0.25\,\leqslant {(g-i)}_{\mathrm{SDSS}}\leqslant 3.5$ and restricted to bright stars (i.e., i ≤ 19). The resulting transformations are

$$\begin{eqnarray}\begin{array}{rcl}{g}_{\mathrm{DR}6,\mathrm{BASS}} & \approx & {g}_{\mathrm{SDSS}}-0.0125-0.0535{(g-i)}_{\mathrm{SDSS}}\\ & & +\,0.0162(g-i{)}_{\mathrm{SDSS}}^{2}-0.0047(g-i{)}_{\mathrm{SDSS}}^{3}\end{array}\end{eqnarray} \tag{ 13 }$$

$$\begin{eqnarray}\begin{array}{rcl}{r}_{\mathrm{DR}6,\mathrm{BASS}} & \approx & {r}_{\mathrm{SDSS}}-0.0215-0.0683{(g-i)}_{\mathrm{SDSS}}\\ & & +\,0.0265(g-i{)}_{\mathrm{SDSS}}^{2}-0.0084(g-i{)}_{\mathrm{SDSS}}^{3}\end{array}\end{eqnarray} \tag{ 14 }$$

$$\begin{eqnarray}\begin{array}{rcl}{z}_{\mathrm{DR}6,\mathrm{MzLS}} & \approx & {z}_{\mathrm{SDSS}}-0.0293-0.0387{(g-i)}_{\mathrm{SDSS}}\\ & & +\,0.0123(g-i{)}_{\mathrm{SDSS}}^{2}-0.0034(g-i{)}_{\mathrm{SDSS}}^{3}\end{array}\end{eqnarray} \tag{ 15 }$$

$$\begin{eqnarray}\begin{array}{rcl}{g}_{\mathrm{DR}7,\mathrm{DECaLS}} & \approx & {g}_{\mathrm{SDSS}}+0.0244-0.1183{(g-i)}_{\mathrm{SDSS}}\\ & & +\,0.0322(g-i{)}_{\mathrm{SDSS}}^{2}-0.0066(g-i{)}_{\mathrm{SDSS}}^{3}\end{array}\end{eqnarray} \tag{ 16 }$$

$$\begin{eqnarray}\begin{array}{rcl}{r}_{\mathrm{DR}7,\mathrm{DECaLS}} & \approx & {r}_{\mathrm{SDSS}}-0.0005-0.0868{(g-i)}_{\mathrm{SDSS}}\\ & & +\,0.0287(g-i{)}_{\mathrm{SDSS}}^{2}-0.0092(g-i{)}_{\mathrm{SDSS}}^{3}\end{array}\end{eqnarray} \tag{ 17 }$$

$$\begin{eqnarray}\begin{array}{rcl}{z}_{\mathrm{DR}7,\mathrm{DECaLS}} & \approx & {z}_{\mathrm{SDSS}}+0.0228-0.0229{(g-i)}_{\mathrm{SDSS}}\\ & & +\,0.0049(g-i{)}_{\mathrm{SDSS}}^{2}-0.0019(g-i{)}_{\mathrm{SDSS}}^{3}.\end{array}\end{eqnarray} \tag{ 18 }$$

The typical root-mean-square photometric scatter around these transformation relations is σ ≈ 30 mmag. These transformations are not valid for stars bluer or redder than the color range of the fit.

We have compared data from DR1 of the Subaru Hyper-SuprimeCam (HSC) surveys (Aihara et al. 2018)⁹⁹ with data from the Legacy Surveys in two regions: (1) 2445 ≤ R.A. ≤2465, 43° ≤ decl. ≤ 44°; and (2) 315 ≤ R.A. ≤ 36°, −6° ≤decl. ≤ −45. The first region corresponds to the "HECTOMAP" region in the HSC survey and is covered by the Legacy Surveys DR6 data. The second region corresponds to the XMM-LSS region in the HSC survey and is covered by the Legacy Surveys DR7 data. Selecting Legacy Survey sources of type "PSF" detected with a signal-to-noise ratio ≥5, we compared the HSC photometry to the DR6 and DR7 data and derived the following transformations:

$$\begin{eqnarray}&&{g}_{\mathrm{DR}6,\mathrm{BASS}}\approx {g}_{\mathrm{HSC}}-0.003+0.029{(g-r)}_{\mathrm{HSC}}\end{eqnarray} \tag{ 19 }$$

$$\begin{eqnarray}\begin{array}{rcl}{r}_{\mathrm{DR}6,\mathrm{BASS}} & \approx & {r}_{\mathrm{HSC}}+0.003-0.130{(r-z)}_{\mathrm{HSC}}\\ & & +\,0.053(r-z{)}_{\mathrm{HSC}}^{2}-0.013(r-z{)}_{\mathrm{HSC}}^{3}\end{array}\end{eqnarray} \tag{ 20 }$$

$$\begin{eqnarray}\begin{array}{rcl}{z}_{\mathrm{DR}6,\mathrm{MzLS}} & \approx & {z}_{\mathrm{HSC}}-0.011-0.076{(r-z)}_{\mathrm{HSC}}\\ & & +\,0.003(r-z{)}_{\mathrm{HSC}}^{2}\end{array}\end{eqnarray} \tag{ 21 }$$

$$\begin{eqnarray}&&{g}_{\mathrm{DR}7,\mathrm{DECaLS}}\approx {g}_{\mathrm{HSC}}+0.003-0.014{(g-r)}_{\mathrm{HSC}}\end{eqnarray} \tag{ 22 }$$

$$\begin{eqnarray}\begin{array}{rcl}{r}_{\mathrm{DR}7,\mathrm{DECaLS}} & \approx & {r}_{\mathrm{HSC}}-0.011-0.154{(r-z)}_{\mathrm{HSC}}\\ & & +\,0.055(r-z{)}_{\mathrm{HSC}}^{2}-0.013(r-z{)}_{\mathrm{HSC}}^{3}\end{array}\end{eqnarray} \tag{ 23 }$$

$$\begin{eqnarray}\begin{array}{rcl}{z}_{\mathrm{DR}7,\mathrm{DECaLS}} & \approx & {z}_{\mathrm{HSC}}-0.024-0.098{(r-z)}_{\mathrm{HSC}}\\ & & +\,0.004(r-z{)}_{\mathrm{HSC}}^{2}.\end{array}\end{eqnarray} \tag{ 24 }$$

The 50% completeness limits (measured relative to HSC) in [g, r, z] are [25.26, 24.84, 24.29] AB mag in DR7 and [24.535, 24.235, 23.336] AB mag in DR6, respectively. Of the 95,241 DR6 sources in region (1), 3506 (3.7%) have no matches in the HSC catalog. A total of 713 of these are bright sources (g ≤ 17, r ≤ 18, z ≤ 17) and are likely saturated in the HSC data; 1,431 are fainter than the 80% completeness limits. We examined 100 DR6 sources with magnitudes 20 < g < 22 that are missing in the HSC catalogs and found that 83 are fake sources: 33 due to particle events; 22 due to increased noise in, for example, regions near CCD edges; and 28 are fake sources created by The Tractor in the extended halos of bright (typically saturated) stars or galaxies. The remaining are real sources that have been split into multiple sources due to their complexity or mis-centered (due to low signal-to-noise data) in the DR6 catalog, or are low surface brightness sources not present in the HSC catalog. Despite these issues, the DR6 catalog reliability is higher than PS1 at faint magnitudes.