The DECam Plane Survey: Optical Photometry of Two Billion Objects in the Southern Galactic Plane

DECaPS is designed to measure the fluxes of stars over a substantial fraction of the Milky Way disk. Specifically, the survey targeted a depth reaching below the main-sequence turn-off of a 10 Gyr, solar metallicity population at a distance of eight kiloparsecs. For unextinguished stars, this would correspond to a magnitude of 18.6 in r, but substantial extinction in the Galactic plane requires dramatically deeper observations. Extinction in the Galactic midplane varies greatly; much of the outer Galaxy has $E(B-V)\lt 1$ mag, but, especially in the inner Galaxy, extinction can become very high. Through $E(B-V)=1.5$ mag at 8 kpc, the target stars lie at 24.5, 22.3, 21.2, 20.6, and 20.3 mag (AB) in the grizY bands. DECam can reach these magnitudes at $5\sigma$ in less than 30 s exposures in the rizY bands. In the g band, much longer exposures are necessary to reach this depth due to extinction, but 96 s exposures were expected to reach a $5\sigma$ depth of 24.1 mag, corresponding to $E(B-V)=1.4$ mag. Because overheads between exposures with DECam are close to 30 s, it is wasteful to take exposures much shorter than 30 s; accordingly, we adopt a 96 s exposure time in g and 30 s in all other bands. Given the conditions actually obtained at the telescope, the survey reached typical 6σ depths of 23.7, 22.8, 22.3, 21.9, and 21.0 mag (AB) in grizY. The extra depth in the redder bands improves our distance reach in extinguished regions where g photometry, in particular, is not practical. The survey is slightly shallow in individual exposures in g, but three images are available of each part of the sky, allowing improved average photometry.

Figure 2 shows the 6σ depths obtained by DECaPS over all exposures taken by the program. The distributions of depths in each filter are tight. A few shallower exposures in each filter are attributable to cloudy weather. The i-band depth distribution is bimodal due to significantly darker skies in the second half of the DECaPS observations than in the first.

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The survey aims for coverage of the entire $| b| \lesssim 4^\circ$, $\delta \lt -30^\circ$ sky. A small fraction of the DECam focal plane is not available for imaging, primarily due to gaps between the CCDs. To address this problem, DECaPS adopts a three-pass dither strategy, where each part of the footprint is observed with three different exposures, slightly offset from one another. The survey uses the three-pass tiling strategy developed for the DECam Legacy Survey (DESI Collaboration et al. 2016a, 2016b).

This tiling scheme uniformly covers the sky with pointings separated by distances closely matched to the DECam field of view. The field centers of the three passes are slightly rotated relative to one another to dither the exposures around each tile center, filling in the gaps in the DECam focal plane.

The DECaLS tiling scheme happens to contain dithers primarily in the right-ascension direction around right ascensions of $90^\circ$ and $270^\circ$. This leads to a small amount of area without any DECaPS coverage within 10° of the Galactic center.

The DECaPS cadence aims to observe each part of the footprint in photometric conditions on three separate nights. Typically, these three nights fall in one observing run and occur subsequently, but the vagaries of the weather led to a few regions in which two passes were observed immediately after one another on a single night, and others in which repeat observations of the same field were taken about one year apart from one another.

This cadence was designed to enable an internal photometric calibration based on repeated observations of the same stars (e.g., Padmanabhan et al. 2008; Schlafly et al. 2012; Burke et al. 2017). Observing in different passes on different nights then both filled in the gaps in the footprint that would be left by a single pass, and provided the repeat observations needed to constrain the atmospheric throughput as a function of time.

We obtained 22 nights on the Blanco 4 m through the NOAO. The observing runs are described in Table 2. Observations were made in gr when the Moon was down and izY when the Moon was up. The longer exposure time in g meant that the survey needed roughly equal amounts of Moon-up and Moon-down time. The efficiency of the DECam system was excellent, enabling observations to keep up with the footprint as it crossed the meridian. The southern location of the footprint and telescope, combined with favorable scheduling, allowed the survey to obtain very low airmasses, with a mean airmass of 1.15 and a standard deviation of 0.10.

Table 3.  Photometric Calibration Performance

Filter	${\sigma }_{\mathrm{ZP}}$ (mmag)	${\sigma }_{\mathrm{bright}}$ (mmag)
g	10.3	7.6
r	10.2	6.9
i	8.6	6.7
z	9.4	6.4
Y	8.3	6.0

Note. The performance of the photometric calibration. The simple nightly zero-point and airmass term described the zero-points of individual images to better than about 1% (${\sigma }_{\mathrm{ZP}}$). Bright stars on each image agreed with the mean fluxes of those stars over all observations with a scatter of better than 8 mmag in each band (${\sigma }_{\mathrm{bright}}$).

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Owing to a slight imbalance in the amount of dark and bright time available in good conditions, r-band observations in 2017 January were taken with longer 50 s exposures when the Moon was up, and in 2017 April/May, some izY exposures were taken with the Moon down.

While analyzing CP images, we found a number of bad columns caused by charge traps in the CCDs. In the worst cases, these were very significant and could lead the DECaPS pipeline to detect hundreds of spurious sources along the bad columns. To identify these features, we high-pass filtered images by subtracting a 7 × 7 median filter. We then took the median value of each pixel in a stack of 100 high-pass filtered images to identify pixels that were consistently significantly high or low. This process identified 24,357 pixels that had not been identified as problematic by the CP and were consistently discrepant by more than eight counts. This is a vanishingly small fraction of the DECam focal plane ($\approx 0.005 \%$), but in low-density regions, these pixels could result in large numbers of spurious sources. This improved masking has since been incorporated directly into the CP.

The gain on amplifier B on DECam CCD S7 is unstable. However, the CCD is often well behaved, motivating preservation of this CCD if possible. Significantly discrepant gain, however, can lead to a large jump in sky level at the amplifier boundary, which the DECaPS pipeline sky algorithm does not track. The result can be large positive backgrounds that the pipeline will try to explain as a blend of a large number of stars.

To avoid this, on S7 only, the pipeline compares the 10 pixels on each side of the amp boundary with one another. A linear function of row number is robustly fit to the difference between pixels and their mirrored pixels across the amp boundary. The derived fit is then applied to all pixels in amplifier B on S7 to remove the jump in background level. This by no means fully accounts for potential problems on S7 (a multiplicative problem has been "corrected" with an additive offset), but it is adequate to prevent catastrophic failure and to enable downstream processing to identify and exclude S7 amplifier B. For precision photometry in the merged DECaPS catalogs, S7 amplifier B is always excluded.

The DECaPS pipeline attempts to explain all flux in images as coming from a smooth background (i.e., the sky) and stars. This fails badly in the presence of galaxies and nebulosity, which the pipeline attempts to shred into many stars. For the most part, it seems an adequate simplification to shred galaxies into stars in the DECaPS footprint: the vast majority of the sources are stars, and both the algorithmic challenge and computational complexity of modeling galaxies is not justified. Nebulosity is more problematic. A small fraction (∼0.1%) of the footprint features substantial diffuse emission, primarily in the form of Hα, O iii, and scattered light from dust. This nebulosity can contain substantial fine structure that is not compatible with the DECaPS smooth-sky model, leading the pipeline to try to explain the nebulosity as the sum of thousands of carefully distributed stars. We address this problem by automatically flagging regions with nebulosity and adopting stricter source-detection criteria in flagged regions (see Section 4.2 for details of the source detection).

Convolutional neural networks (CNNs) are ideally suited to the task of recognizing nebulosity in an image. CNNs have found wide use in image, signal, and natural language processing, among other fields (see LeCun et al. 2015 for an accessible introduction). CNNs process input in a way that respects locality (e.g., nearby pixels in an image are more closely related than more distant pixels) and translation invariance (e.g., a given object might appear anywhere in an image). CNNs work by first identifying features on small scales (by sliding different convolutional filters across the input), and then connecting these features on ever larger scales to build up a rich representation of the input. In a typical classification problem, where one has labeled training data, one first defines the overall structure of the CNN (the number of layers in the network, the number of convolutional filters to include in each layer, etc.). Then, one feeds training data into the network, compares the network output with the desired answer, and uses backpropagation to vary the weights in the network so that the residuals are reduced. After many training epochs, the network "learns" the convolutional filter weights that minimize the classification errors. CNNs have proven remarkably successful in solving image- and signal-processing problems that humans can intuitively solve by eye or by ear (e.g., facial recognition, speech recognition, or identifying cats in images). A human with little to no prior knowledge can be quickly trained to identify nebulosity in astronomical images, making CNNs an obvious approach to solving this problem.

We trained a CNN to identify 512 × 512-pixel regions of images containing significant nebulosity, selected from all filters. After identification, these regions were flagged by adding a bit to the CP data-quality images (Table 5). Downstream in the analysis pipeline, putative stars in these regions were required to satisfy a sharpness criterion and be relatively uncontaminated by light from any nearby stars; otherwise, the putative stars were eliminated from the model. This prevents the pipeline from trying to explain the flux in large nebulous regions with thousands of point sources, at the expense of reducing the pipeline's capability to model blended stars in these regions.

In order to provide training and validation data for our network, we hand-classified 512 × 512-pixel images. We sorted the images into four categories:

• 1.  
  NEBULOSITY—significant contamination by nebulosity.
• 2.  
  NEBULOSITY_LIGHT—faint nebulosity.
• 3.  
  NORMAL—no contamination.
• 4.  
  SKY_ERROR—spurious fluctuations in sky level injected by upstream DECam pipeline.

We arrived at a data set of 2000 images labeled NORMAL, 1775 images labeled NEBULOSITY, 1058 images labeled NEBULOSITY_LIGHT and 629 images labeled SKY_ERROR. We used 80% of the images to train the network, and the remaining 20% to validate the network. This is a relatively small number of training images with which to train a CNN. We therefore augmented our data set by flipping the images vertically and horizontally, but did not perform other augmentation techniques (such as arbitrary rotation) that might alter the noise properties of the images or remove valuable information (e.g., the orientation of diffraction spikes). We histogram-equalized⁹ the images before feeding them to the neural network. This prevents the dynamic range of the image from being used up by a single saturated star.

On the validation data set, our trained network achieved 90% completeness and 90% purity in its NEBULOSITY classifications, with a vanishingly small percentage of NORMAL images being misclassified as NEBULOSITY. Our final validation loss (a measure of the accuracy of the classifications) was similar to our training loss, indicating that our network does not suffer from overfitting.

We applied our trained CNN to each 512 × 512-pixel region of each survey image in order to flag areas with nebulosity. The neural network identified regions affected by significant nebulosity very accurately. A few corner cases were marked as nebulous, such as artifacts near extremely bright stars (brighter than 6th mag), or ghosts associated with these stars. These regions are extremely rare, and from the perspective of the catalog, it is appropriate to flag them as nebulous anyway: the smooth-sky plus stars modeling is likewise inadequate here.

A more technical description of our CNN is provided in the Appendix.

The resulting images after CP processing are an extremely clean description of the sky, with most instrumental signatures accurately removed. A few remaining problems impact a small fraction of the images, however.

First, in regions featuring very significant nebulosity (primarily η Carinae), the CP sky subtraction has difficulties and introduces artifacts into the images. Fortunately, these artifacts are spatially smooth and are absorbed into the DECaPS pipeline sky estimates, and so these artifacts are not expected to influence the source detection or photometry in DECaPS. They do, however, lead to unsightly regions in DECaPS images in these regions.

Second, the CP has difficulties identifying cosmic rays in crowded regions. Moreover, cosmic rays that are identified are frequently only partially masked. This leads to occasional spurious sources in the DECaPS source catalogs. Fortunately, the relatively short DECaPS exposures and dense fields means that only a tiny number of sources are affected. Nevertheless, sources detected in only a single image, especially when partially masked (QF < 1, Table 4), are likely to be spurious.

Table 4.  Individual-image Catalog Fields

Name	Description
x	x coordinate (pix)
y	y coordinate (pix)
flux	instrumental flux (ADU)
dx	x uncertainty (pix)
dy	y uncertainty (pix)
dflux	flux uncertainty (ADU)
fluxlbs	local-background-subtracted flux (ADU)
dfluxlbs	fluxlbs uncertainty (ADU)
qf	PSF-weighted fraction of good pixels
rchi2	PSF-weighted fraction average ${\chi }^{2}$
fracflux	PSF-weighted fraction of flux from this source
flags	CP flag value at central pixel
fwhm	FWHM of PSF at source location (pix)
sky	sky at source location (ADU)
gain	gain at source location (e-/ADU)

Note. Fields in the DECaPS individual-image catalogs. A more complete description is available at the survey website. All fields are stored as 32-bit floating point numbers, except for x and y , which are stored as 64-bit floating point numbers, and flags , which is stored as a 32-bit integer.

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Bleed trails associated with very bright stars occasionally introduce crosstalk artifacts in images. In rare cases on DECam CCD N15, the crosstalk correction for extremely saturated parts of the bleed trail is incorrect and leads to dramatic oversubtraction of the crosstalk on the adjacent amplifier. This case introduces spurious sources in the DECaPS processing, because the only mechanism the DECaPS modeling has to address regions with substantial negative flux is to reduce the sky level. This can leave significant positive sky on the image everywhere away from the crosstalk artifact, corrupting the flux measurements of stars throughout the image and potentially introducing numerous spurious stars that attempt to explain the high background. Fortunately, we have only observed this effect on a few individual CCD frames of the 600,000 composing the survey.

Related effects occur whenever processing errors leave large negative fluxes in the images. Very bright stars saturate the serial register, leading to large artifacts in the images. These artifacts are usually masked by the CP, but in rare cases, they are not masked and result in spurious sources and contaminated fluxes.

In the initial smooth-sky subtraction, the median of each 20 × 20 pixel subregion of the residual image (image minus best-fit model image) is computed. The pipeline linearly interpolates between these median values to construct a smooth-sky image, which is subtracted from the residual image. This sky estimate will remove most nebulosity in addition to the sky, and will be biased high by any undetected sources in the image.

Next, sources are detected. The pipeline convolves the residual image times the CP inverse-variance image with the PSF to construct a significance image. This image gives the statistical significance of an isolated point source being present at each point in the image, neglecting covariance with any other sources. Following standard least-squares analysis for an image with varying noise, the significance image S_I is given by Equation (1),

$$\begin{eqnarray}s{({\boldsymbol{x}})}^{2} & = & \displaystyle \int d{\boldsymbol{u}}\,\sigma {({\boldsymbol{x}}+{\boldsymbol{u}})}^{-2}{P}^{2}({\boldsymbol{u}})\\ {S}_{I}({\boldsymbol{x}}) & = & \displaystyle \frac{\displaystyle \int d{\boldsymbol{u}}\,I({\boldsymbol{x}}+{\boldsymbol{u}})\,\sigma {({\boldsymbol{x}}+{\boldsymbol{u}})}^{-2}P({\boldsymbol{u}})}{s({\boldsymbol{x}})},\end{eqnarray} \tag{ 1 }$$

where ${\boldsymbol{x}}$ gives the pixel coordinates in the image, I is the residual image, σ is the CP statistical uncertainty image, and P is the PSF.

Peaks in S_I of greater than 5 are potential newly detected stars. This value corresponds to $5\sigma$ for isolated stars including only photon and detector noise, neglecting difficulties with blending. Accordingly, if peaks are too blended with stars in the current best-fit model image M, they are excluded. To assess this, the pipeline defines a "blending threshhold" B of 0.2 and constructs an analogous "model significance image," S_M, according to Equation (1), with the current model image taking the place of the residual image. Peaks are kept only if one of the following two conditions are satisfied:

• 1.  
  ${S}_{I}/{S}_{M}\gt 2B$: the ratio of the peak in the significance image to the model signifcance image is more than twice the blending threshhold, or
• 2.  
  $({S}_{I}/{S}_{M}\gt B){\rm{and}}\,(I/M\gt B)$: the same ratio is more than the blending threshhold, and the ratio of the image to the model (without smoothing to construct the significance image) is also more than the blending threshhold.

Initially, a criterion based only on I/M was desired, but since even isolated $5\sigma$ stars may have central pixels with negative fluxes due to noise, additional criteria based on the significance images were adopted.

In regions featuring substantial nebulosity, the above procedure identifies substructures in the nebulosity as stars. In order to prevent the pipeline from generating thousands of spurious sources in these regions, this procedure is altered in the roughly $0.1 \%$ of the footprint flagged as nebulous. First, the blending threshhold is increased to 100 (from 0.2) in these regions, effectively preventing the pipeline from finding any blended sources. Second, the sharpness of the peak in the significance image is compared with expectations from the PSF model. The drop in significance from the peak pixel to any neighboring pixel must be more than 70% of the expectation to be kept (or 50% if the central pixel is saturated). Otherwise, peaks are rejected as unlikely to be stars and not included in the image modeling in subsequent steps. This is the only special treatment the pipeline performs in regions with nebulosity. No attempt beyond the normal sky subtraction is made to improve the fluxes of stars in these regions.

Any stars found are added to the list of currently detected stars in the image. These new stars may influence the fluxes and positions of other stars, at least through their influence on the sky, as well as through blending. Crowdsource simultaneously solves for an overall sky level and the fluxes and positions of all of the currently identified stars using the linear least-squares routine LSQR. A source's image is not a linear function of its position. Accordingly, for use with the LSQR, we linearize the problem by approximating changes in the position of the source by the first term in the Taylor series expansion. Fitting an overall sky level allows the fit to partially account for the initially high sky estimate.

The positions estimated in Section 4.3 are linearized approximations to the positions, and are accurate only for small changes in the positions of the source. Better performance can be obtained by computing the sources' centroids, but this is challenging in a crowded field, where the flux of neighboring stars is blended with the flux of a target star. Crowdsource attempts to overcome this by using its new best-fit model of the image to eliminate contaminating neighboring stars from the centroid computation. The pipeline visits each source in turn, and subtracts its model of all other sources from the image. The source's centroid is then measured on the neighbor-subtracted image. These centroids are used as input positions in the next iteration.

Finally, the PSF model is improved. The PSF is modeled as an ideal-seeing PSF, convolved with an elliptical Moffat PSF (Moffat 1969) representing the current seeing, plus a 9 × 9 residual image in the core of the PSF. The parameters of the Moffat PSF and the value of each pixel of the 9 × 9 residual image are allowed to change linearly over each 1024 × 1024 subregion of a CCD. The pipeline takes the brightest 200 unsaturated sources in each subregion, which are chosen to be unmasked, relatively unblended, and to have positions that did not move by more than 1 pixel in the previous iteration. The images of these stars, after neighbors have been subtracted according to the best model so far, are used to fit the parameters of the PSF model for the next iteration.

A primary goal of the ideal-seeing PSF is to allow the pipeline to describe diffraction spikes and other features in the wings of the PSF. These features may not be constant over the focal plane, but treating them as constant is an improvement over neglecting them altogether. The ideal-seeing PSF is derived by averaging the PSF of many stars in the focal plane over all CCDs and several images on a night with very good seeing. This PSF is then deconvolved with a Moffat PSF using Richardson-Lucy deconvolution to obtain a PSF with better seeing than obtained on any night. The wings of the deconvolved PSF are then fit as the sum of six Moffat PSFs plus power-law diffraction spikes and horizontal and vertical features. The resulting noise-free model PSF wings are then blended with the central high S/N core of the deconvolved PSF to produce the final ideal-seeing PSF.

The crowdsource analysis can fail in a number of ways. Because crowdsource attempts to explain all flux in the image as due to stars and a smooth background, violations of this assumption and imperfections in the PSF can introduce spurious sources into the catalog.

By far the most common cause of spurious sources is very bright stars. The crowdsource PSF wings are based on a single ideal-seeing model PSF that is fixed for all images in each band. This ideal-seeing PSF is then convolved with a Moffat profile, whose parameters may vary linearly in each image. This limited allowed variation, however, is not adequate to describe all of the features in the wings of the PSF. For instance, the relative amount of flux in the different diffraction spikes varies over the focal plane and cannot be captured in the crowdsource model. Accordingly, some spurious sources are present near most bright stars (brighter than roughly 12th mag). Extremely bright stars, like α Cen, can produce thousands of spurious sources. Demanding that a source be detected in multiple filters, or at least detected multiple times, can significantly reduce the number of this kind of spurious source.

Bright stars are especially problematic in Y band because of the extremely long PSF features extending vertically and horizontally from the PSF center in Y band. The crowdsource PSF model describes these features accurately, but for sufficiently bright stars, they are highly significant even several hundred pixels from the star's center, beyond the range that the crowdsource PSF extends. Accordingly, very bright stars in Y band can lead to clusters of spurious sources 150 pixels away in the horizontal and vertical directions, where the PSF model ends and flux is left on the image. These sources will not be detected in any other bands, but will slightly contaminate the Y-band photometry in their vicinity.

Because the crowdsource PSF model is expected to be imperfect, no attempt is made to find sources too near existing, brighter sources. This means that many close blends are not identified. Blends are usually not deblended if the two stars involved are separated by less than one half FWHM, although the flux ratio of the blended sources also matters. More aggressive deblending is possible, but must be balanced against avoiding incorrect deblending of single sources due to PSF-misestimation.

In extremely dense regions like Baade's window, the crowdsource algorithm never completely converges. A very small fraction of faint but clearly significant sources are never identified, and extremely complicated blends of hundreds of stars are not fully worked out. It is not clear how much better one can do in these regions, however: they are extremely blended, and the derived model images account for most of the flux.

In dense regions, the sky tends to be overestimated. The algorithm may move stars to regions where the sky has been overestimated and assign them negative fluxes to improve the fit of the model image to the observations, introducing spurious sources into the catalog. These objects can lead to sources with fracflux outside the range 0–1; see Section 7.2.1. A more sophisticated sky estimation algorithm might eliminate these spurious sources. However, even in the densest regions, less than half a percent of sources have negative fluxes. These are also easily identified and are rarely badly blended with other sources.

For simplicity, the crowdsource pipeline adopts a fixed size, $5^{\prime\prime} \times 5^{\prime\prime}$ PSF stamp independent of the seeing of the image. In the worst seeing conditions, this PSF stamp size does not enable the pipeline to track flux far enough into the PSF wings. This can lead to spurious sources $2\buildrel{\prime\prime}\over{.} 5$ from true sources, but only in images with $\mathrm{FWHM}\gt 2^{\prime\prime}$, roughly 0.4% of all images. Most such spurious sources should be detected in only one of the three observations of each part of the sky, facilitating their rejection from scientific analyses.

The DECaPS pipeline aims to characterize all sources in individual images down to a point-source depth of 5σ. In practice, DECaPS achieved something closer to 6σ in typical images, owing to crosstalk between the sky subtraction routine and the source detection routine. Sky subtraction was performed by median-filtering the image in a 20 × 20 pixel region. Sources in this region will bias the sky high. Having been detected, the sources are subtracted and the sky is refit. This process is iterated several times, so the effect on the final fluxes is small. However, this means that once sources are detected at 5σ after an initial sky subtraction has been performed, they are later detected at apparently higher significance once the sky has been lowered. We could have eliminated this effect by using larger regions for the median filtering or considering a local background subtraction when defining the initial source significance, but both of these approaches also have downsides. Accordingly, the final survey does not quite reach 5σ.

The calibration model could be improved in several respects. It ignores "systematic chromatic errors" (Li et al. 2016), essentially neglecting the fact that changes in system throughput have a wavelength dependence. This causes stars to require different corrections into a "standard" system according to their spectra, but the DECaPS calibration performs the same correction for all objects. More physics-based analyses can readily accommodate these effects, and are already being performed for DECam (e.g., Burke et al. 2017).

The photometric calibration model is only able to predict the zero-point of a given exposure to within about 9 mmag (${\sigma }_{\mathrm{ZP}}$). While not bad, this is substantially worse than achieved by PS1, which had 3 mmag precision. Evidently, the simple single nightly system zero-point and airmass term provided a much better description of the zero-points in PS1 images than the similar model adopted for DECaPS. The dominant unmodeled source of variation in the zero-points of DECaPS images turns out to be the "aperture correction" of the crowded DECaPS photometry. If the pipeline PSF were perfectly accurate, then the measured PSF flux should equal the true flux on average. With an imperfect PSF, the measured PSF fluxes become systematically biased. The bias can be addressed by measuring aperture magnitudes for bright stars in very large apertures, and comparing them with the measured PSF fluxes of those stars. The difference is related to the aperture correction and can be applied to all PSF fluxes to correct them to total fluxes. This procedure is challenging in crowded fields, so DECaPS did not perform an aperture correction. Comparison of different PSF fitting routines indicates that the pipeline was too inflexible in fitting the PSF roughly $2^{\prime\prime}$ from the center of the PSF, leading to variation in the shape of the PSF at this radius to cause apparent ∼7 mmag variations in measured PSF flux—that would have been absorbed by the aperture correction, had one been made. Future reductions of the DECaPS imaging can improve on these results by using a more flexible PSF model, or alternatively, crowdsource could be adapted to compute an aperture correction on neighbor-subtracted images.

Other improvements on the DECaPS photometric calibration are possible. We neglect in this photometric calibration the "tree ring" pixel-area effects discussed in Plazas et al. (2014), which are expected to contribute a few mmag of photometric noise. Eliminating systematic chromatic errors is difficult without knowing the spectral energy distributions of the stars within the filter bandpasses, but upcoming Gaia low-resolution spectrophotometry will eliminate this problem for bright stars. By addressing these shortcomings, we expect that significantly better than 5 mmag photometry for typical stars is possible over large areas with DECam, even in crowded regions.

The absolute zero-point was obtained by reference to PS1, in combination with predicted colors in the DECam bands. The procedure is laid out in Scolnic et al. (2015): stellar energy distributions are taken from calibrated Hubble Space Telescope (HST) measurements and integrated over the PS1 and DECam filter bandpasses to predict the color differences between the surveys. Absolutely calibrated PS1 photometry is then transformed to absolutely calibrated DECam photometry using the derived color transformations for blue stars ($0.25\lt {g}_{\mathrm{PS}1}-{i}_{\mathrm{PS}1}\lt 1$) where the transformations are most accurate. The resulting absolutely calibrated, synthesized DECam photometry is then used to fix the absolute zero-points for DECaPS. Ultimately, this calibration derives from HST measurements from Bohlin (2014). A calibration field at $(\alpha ,\delta )=(100^\circ ,-27^\circ )$ is used to link the two surveys together.

The DECaPS absolute calibration is then no better than the PS1 absolute calibration. DECaPS adopted the original PS1 absolute calibration from Tonry et al. (2012) to remain consistent with the original PS1 photometry. The work of Scolnic et al. (2015) finds that this absolute calibration is somewhat offset from AB. To shift DECaPS to the absolute calibration of Scolnic et al. (2015), offsets of 0.020, 0.033, 0.024, 0.028, and 0.011 mag must be added to the DECaPS grizY magnitudes, respectively.

The accuracy of DECaPS photometry can be tested by comparison with PS1 over the limited area of overlap. The DECaPS survey extends slightly north of $\delta =-30^\circ$ toward the Galactic center and anticenter to enable this comparison, and also contains a few calibration fields off the plane above $\delta =-30^\circ$. The results of this comparison for the r band are shown in Figure 6. The first panel shows the comparison on a calibration field at $(l,b)=(236^\circ ,-14^\circ )$, the second panel shows the comparison at $(l,b)=(-115^\circ ,0^\circ )$, and the third panel shows the comparison at $(l,b)=(0^\circ ,0^\circ )$.

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The two surveys show good agreement in their photometry; the bright-end root mean square (rms) difference is 0.02 mag, and smallest in the unreddened calibration field. There is a modest trend in the photometry with magnitude in the anticentral field (0.03 mag over from 15th to 21st mag). The trend may be again connected to reddening (fainter stars are systematically more reddened), but we see the opposite trend, if any, in the most reddened Galactic center field. No two fields have quite the same overall zero-point; the DECam photometry becomes systematically brighter relative to the PS1 photometry in the more reddened fields. The Galactic center field is offset by −0.05 mag relative to the calibration field. We attribute this to the imperfect color transformations in the presence of reddening, and conclude that the calibration is more uniform than about 0.05 mag, although expectations from the internal repeatability suggest that the calibration should be significantly better than this. Other filters show qualitatively similar trends.

Another comparison between PS1 and DECaPS is shown in Figure 7, an i versus i − z color–magnitude diagram (CMD) in the PS1 and DECam bands. The superior depth and deblending of the DECaPS pipeline makes for a much more obvious bulge red clump at i = 21.5, $i-z=2.0;$ the DECaPS measurements clearly improve on the PS1 measurements in the small overlap region between the two surveys. On the other hand, a few blue sources around i = 22.0, $i-z=0.5$ are presumably largely spurious deblending errors in DECaPS; they are absent from the PS1 CMD, and can be largely eliminated by removing the most blended sources (fracflux, see Table 6).

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Table 6.  Merged Catalog Fields

Name	Description
ra	R.A. (deg)
dec	Decl. (deg)
posstdev	standard deviation in position (arcsec)
ra_ok	R.A. (ok detections only) (deg)
dec_ok	Decl. (ok detections only) (deg)
posstdev_ok	standard deviation (ok detections only) (arcsec)
ndet	number of detections
ndet_ok	number of ok detections
nmag	number of detections in each band
nmag_ok	number of okay detections in each band
mean	mean flux (units of 3631 Jy)
stdev	flux standard deviation (units of 3631 Jy)
err	uncertainty in mean flux (units of 3631 Jy)
median	median flux (units of 3631 Jy)
q25	$25\mathrm{th}$ percentile flux (units of 3631 Jy)
q75	$75\mathrm{th}$ percentile flux (units of 3631 Jy)
epochrange	MJD between first and last detections
epochrange_ok	MJD between first and last ok detections
epochmean	average MJD
epochmean_ok	average MJD (ok only)
maglimit	5σ magnitude limit of deepest image (ok only)
fracflux	average fractional flux in each band (ok only)

Note. Fields in the DECaPS merged catalogs. A more complete description is available at the survey website. Most fields are 32-bit floating point numbers, except for fields pertaining to epochs and positions, which are 64- bit floating point numbers. The fields describing the number of detections of sources are 16-bit integers.

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PS1 photometry is of qualitatively similar depth to DECaPS photometry. The PS1 filter bandpasses are moreover very similar to the DECaPS bandpasses. Accordingly, it is useful to have a set of color transformations to allow comparison between DECam grizY filters used in DECaPS and the PS1 grizy filters. To develop these color transformations and improve the stability of the photometric calibration, DECaPS observed a calibration field at $(\alpha ,\delta )=(100^\circ ,-27^\circ )$ on many different nights of the survey. This field has low reddening ($\approx 0.15$ mag $E(B-V)$) but is at low latitude ($b=-14^\circ$), meaning that it contains many stars suitable for deriving color transformations.

Color transformations between DECam and PS1 were fit with a cubic polynomial in the PS1 g − i color. The color transformations are given in Equation (2). Only point sources brighter than 19th mag in a nearby filter that was neither g, i, nor the filter of interest were used to determine the transformations. Furthermore, only stars with $0\lt {g}_{\mathrm{PS}1}-{i}_{\mathrm{PS}1}\lt 2.9$ were used; the color transformation outside this broad range requires more parameters and more stars to constrain. Figure 8 shows the derived color transformations. After color correction, the rms difference between DECaPS and PS1 photometry is about 0.015 mag.

$$\begin{eqnarray}c & = & {g}_{\mathrm{PS}1}-{i}_{\mathrm{PS}1}\\ {g}_{\mathrm{DECam}}-{g}_{\mathrm{PS}1} & = & 0.00062+0.03604c\\ & & +0.01028{c}^{2}-0.00613{c}^{3}\\ {r}_{\mathrm{DECam}}-{r}_{\mathrm{PS}1} & = & 0.00495-0.08435c\\ & & +0.03222{c}^{2}-0.01140{c}^{3}\\ {i}_{\mathrm{DECam}}-{i}_{\mathrm{PS}1} & = & 0.00904-0.04171c\\ & & +0.00566{c}^{2}-0.00829{c}^{3}\\ {z}_{\mathrm{DECam}}-{z}_{\mathrm{PS}1} & = & 0.02583-0.07690c\\ & & +0.02824{c}^{2}-0.00898{c}^{3}\\ {Y}_{\mathrm{DECam}}-{y}_{\mathrm{PS}1} & = & 0.02332-0.05992c\\ & & +0.02840{c}^{2}-0.00572{c}^{3}.\end{eqnarray} \tag{ 2 }$$

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The DECaPS footprint includes open clusters, globular clusters, nearby molecular clouds, distant molecular clouds, and regions with a wide range of stellar densities. Accordingly, CMDs from DECaPS show rich diversity.

To demonstrate the precision of the DECaPS photometry, Figure 9 shows the g, g − r CMD of stars within 003 of the center of NGC 2660, an approximately 1 Gyr old open cluster at a distance of 2.7 kpc (Sandrelli et al. 1999), together with a control annulus of equal area 01 from the cluster center. Reddening of the field stars in the region leads them to have a very similar CMD to that of NGC 2660, but nevertheless, the sharp NGC 2660 sequence clearly stands out from the background. A secondary sequence roughly 0.7 mag brighter than the primary sequence may indicate a substantial fraction of binaries (Sandrelli et al. 1999).

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The NGC 2660 CMD demonstrates the value of DECaPS photometry to constrain stellar populations in the Milky Way. However, typical CMDs in the footprint are much more complicated than that in the vicinity of NGC 2660. Figure 10 shows a selection of CMDs in different filters and Galactic longitudes from DECaPS.

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Each row of Figure 10 shows the stars in a one-degree radius beam in the Galactic plane ($b=0^\circ$) at different Galactic longitudes, stepping out in 30° increments from $l=0^\circ$ to $l=-120^\circ$. Each diagram shows a strong sequence of blue stars that are reddened as one proceeds to fainter magnitudes: FGK main-sequence stars in the presence of increasing extinction along the line of sight. The Galactic center field (top row) additionally features a fainter, redder sequence, coming from red clump stars in the Galactic bulge. Finally, there is a redder sequence visible at all magnitudes in the inner galaxy fields (top three rows), produced by the red clump in the Galactic disk. These sequences are marked in the Galactic center i versus i − z CMD. The blue main-sequence, bulge red clump, and disk red clump features are marked with offset solid, dashed, and dotted red lines, respectively. The outer Galaxy fields show relatively unreddened nearby stars (e.g., the unreddened M-dwarf sequence with $g-r=1.5$ mag at $l=-90^\circ$), on top of fainter, redder populations.

The CMDs in Figure 10 show stars in 1° radius beams. Within these regions, the reddening varies dramatically, complicating interpretation of the diagrams. For instance, despite the prominent bulge red clump sequence in the top row of Figure 10, bulge red clump stars are not detected directly at $(l,b)=(0^\circ ,0^\circ );$ most of the stars in this sequence come from the edge of the 1° field.

The internal consistency obtained in the DECaPS photometric calibration (Section 5) suggests that spatial systematic variations in the photometric calibration over the footprint should be no larger than 0.01 mag in size. This estimate can be tested by measuring the consistency of stellar colors over the DECaPS footprint (e.g., High et al. 2009; Schlafly et al. 2010). Unfortunately, because the DECaPS footprint features very large extinction, the typical colors of stars are completely dominated by reddening. Nevertheless, Figure 11 shows the median r − i color of stars with Y-band magnitudes brighter than 18 over the footprint. White to black spans 0.2–2.5 mag.

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The figure is clearly dominated by extinction in the Galactic plane. Well-known molecular clouds like the Vela Molecular Ridge around $l=-90^\circ$ and the Pipe Nebula at $(l,b)=(1^\circ ,4^\circ )$ are apparent. In the very inner Galaxy ($| l| \lt 5^\circ$), the median r − i color of stars becomes steadily redder as $b\to 0^\circ$, until $b\sim 1^\circ$, where the r − i color suddenly becomes more blue. This occurs because behind dense molecular clouds, only few stars are detected, leading the median-colored star to become a star in the foreground of those molecular clouds, rather than a star in their background. No clear signs of photometric errors due to the photometric calibration are present in Figure 11, but given the wide range of colors shown and the large variations in color due to dust reddening, this test does not strongly constrain the quality of the photometric calibration.

Precise astrometry was not a major objective of DECaPS. The crowdsource pipeline computes best-fit x and y positions for the sources it detects, and transforms these into celestial coordinates using the CP-computed World Coordinate System (WCS) with no additional steps or calibration.

This is a simple but problematic approach. The original CP WCS may have a different notion for the "center" of a source than the crowdsource pipeline. Ultimately, both pipelines attempt to use the centroids of the PSF as the center, but the centroid may have varying definitions depending on how much weight is put on flux far out in the wings of the PSF. This is a small effect, but it would motivate directly calibrating the crowdsource positions to external catalogs rather than using a separate set of centroids in the calibration.

Additionally, the CP WCS calibration changed over the course of DECaPS. Starting with CP version 4, WCSs were computed using Gaia as the astrometric reference catalog, while before that point, 2MASS was used. This is unfortunate for DECaPS, because it means that the astrometry from the first part of the survey is slightly inconsistent with the last part of the survey. Still, the 2MASS and Gaia astrometry are very similar, and DECaPS only requires that the astrometry be similar enough to one another so that most stars can be merged with an association distance of 05. However, other applications of the DECaPS observations, such as the construction of coadded stacks, may require greater fidelity.

Figure 12 shows the comparison between DECaPS and Gaia astrometry for stars brighter than 19th mag in r. The mean difference in position between the DECaPS stars in each part of the sky is shown; white to black is 0''–05. Typical values are 01 in the part of the footprint that was primarily observed using CP versions earlier than 4, while the CP 4-only fraction of the footprint shows much lower residuals. This level of difference between DECaPS and Gaia is unproblematic from a DECaPS perspective; the astrometry is much better than the 05 necessary to merge the catalogs from the individual images.

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The crowdsource pipeline iteratively identifies new sources after having subtracted models of other sources, later fitting the positions and fluxes of both newly identified and preexisting sources simultaneously. In the presence of an imperfect PSF and noise, this procedure can generate large numbers of spurious sources, for instance, around very bright stars (Section 4.6).

Even away from bright stars and without noise, in very dense regions, the heuristics crowdsource uses to avoid overfitting (Section 4.2) prevents the pipeline from finding the true solution, instead forcing it to find an approximate description that may include stars with fluxes and positions very different from those of the actual stars in the image. The prevalence of such spurious sources can be estimated using simulated images.

Images of the densest areas in the footprint are simulated using the observed PSFs from specific DECam CCDs. The simulation uses a luminosity function that is chosen to match the bright end of the observed luminosity function in dense Galactic bulge fields. 10⁵ sources are injected into a 1000 × 1000 pixel region with a spatially varying PSF taken from the crowdsource model of one of the DECaPS images. Crowdsource then analyzes these images with the PSF from another part of the same CCD—a PSF that is not exactly right, but is similar to the correct PSF. These tests are perfomed using a PSF with better-than-average seeing (07) as well as worse-than-average seeing (13). No noise is added to the images. The no-noise limit is appropriate because here the focus is on the densest regions, where the pipeline does not approach the $5\sigma$ photon-noise significance limit, and is instead limited by deblending heuristics and PSF systematics.

For these tests, the true source catalog is known, so the number of spurious sources can be assessed. A catalog source is considered correct if it lies within one half FWHM of a true source with flux within a factor of two of the catalog flux. Any source not satisfying this condition is considered spurious. With this definition, the simulations find that roughly 12% of sources are spurious in the densest regions, for both good seeing and poor seeing images. This fraction is unchanged when the true PSF is replaced with a modestly different PSF from a different part of the same CCD; it stems from the deblending heuristics not allowing the pipeline to fully deblend sources, and not from PSF errors. The completeness rate is much higher for the good seeing image than the poor seeing image: roughly 28,000 sources are detected in the good seeing image, while 12,000 are detected in the poor seeing image.

These tests give a general sense for the rate of spurious sources in dense regions in the DECaPS individual epoch catalogs (see Section 7.2.1). In some ways, the tests underestimate the spurious source prevalence: they assume an absence of artifacts or nebulosity, that the noise model is known, and that the PSF has smooth wings. In other ways, the tests will overestimate the spurious detection prevalence: because they have zero noise, every bit of positive residual flux corresponds to a much greater than $5\sigma$ source. This forces the pipeline to deblend even the faintest, most blended sources, where the spurious source rate is highest, subject only to the deblending heuristics of Section 4.2. We defer to future work a more complete analysis of how the crowdsource pipeline behaves in different conditions.

DECaPS also includes band-merged catalogs, where an attempt is made to link together detections in different images of the same objects (Section 7.2.2). Linking detections together into objects can be challenging in dense regions where depth is determined largely by image quality. The number of spurious sources in band-merged catalogs depends on the variation in image qualities of the full set of images taken in a given part of the sky.

DECaPS images have been imported into the DECam Legacy Survey viewer (DESI Collaboration et al. 2016a, 2016b). Zero-points from the photometric calibration (see Section 5) are applied to each image, and a single constant sky per CCD is removed, according to the median sky estimate of the crowdsource analysis. Images are then projected onto a common frame and coadded with inverse-variance weighting to produce stacks. Stacks in the g, r, and z bands are then combined to produced color images and are made available online in a zoomable and pannable viewer. Figure 13 shows an example image from the viewer.

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Dramatic dust clouds are evident in the top half of the image, where nearly all stars are extremely red due to foreground extinction. A reflection nebula around one bright star lights up a large region with relatively blue reflected light. Several foreground stars are immediately identifiable from their bright, white colors, as compared with the red background stars. The greenish continuum emission at the bottom of the image is Hα and reflected light.

In order to preserve many of these continuum features in the viewer, a single background value is subtracted from each DECam CCD before coaddition. This well preserves features with spatial scales much smaller than a CCD, but corrupts structures with a larger spatial scale. Accordingly, some of the brightest and largest objects in the sky become corrupted in their display in the viewer. For instance, near α Centauri and η Carinae, the per-CCD sky subtraction removes a significant amount of flux from the objects themselves and leads to a multicolored checkerboard pattern around them in the viewer. A more advanced sky-subtraction routine that matches the sky in overlapping images would solve this problem. However, since this problem only affects a small number of very bright objects and since stellar photometry is not affected, this issue has not been addressed.

The viewer contains analogous stacks for the crowdsource model images, and the resulting residual images. These allow for rapid comparison between the data and the model, to assess the reliability of the modeling in any region of the sky. In general, the model is an excellent description of the data.

DECaPS provides catalogs from individual images analyzed by crowdsource as well as derived, band-merged catalogs giving average photometry in each band for each object.

7.2.1. Individual-image Catalogs

Catalogs generated by crowdsource for each individual DECaPS image are available from the DECaPS website. These catalogs contain the position of each source, its flux, and the associated uncertainties. These uncertainties are those that would be obtained for isolated stars given photon and detector noise and a perfect model, and they therefore underestimate the true uncertainties. A few other entries assess the reliability of the detection, giving the ${\chi }^{2}$ of the detection, and any flags at the location of the central pixel of this source in the CP data-quality image. A "quality factor" is also computed; it is the PSF-weighted fraction of pixels that have non-zero weight. A detection centered on the edge of a detector would have a quality factor of 0.5, while a good detection has a quality factor close to 1.

Blending is assessed via fracflux,

$$\begin{eqnarray}&&{\mathtt{fracflux}}=\displaystyle \frac{\int d{\boldsymbol{u}}\,N(u)P(u)({\sigma }^{-2}(u)\gt 0)}{\int d{\boldsymbol{u}}\,I(u)P(u)({\sigma }^{-2}(u)\gt 0)},\end{eqnarray} \tag{ 3 }$$

where P is the PSF and ${\sigma }^{-2}$ is the CP inverse-variance image (0 for problematic pixels like saturated pixels). In this equation, N is a $5^{\prime\prime} \times 5^{\prime\prime}$ postage stamp centered on the star, after subtracting the best-fit model of all other stars, and I is the same image without subtracting other stars. The value of fracflux usually ranges from 0 for very blended objects to 1 for isolated objects. Spurious sources with negative fluxes can lead to other values in rare cases (see Section 4.6).

Additional fields give further metadata: the FWHM of the PSF at the location of each source, and the value of the sky and gain. These fields, and short descriptions, are provided in Table 4. A total of slightly over 20 billion records are included in the individual-image catalogs.

The catalogs contain flux estimates and "local-background-subtracted" flux estimates, where an additional constant background was left free to vary around each source. To compute these fluxes, each star is considered one by one, and the best model of all of the other stars is subtracted. The $5^{\prime\prime} \times 5^{\prime\prime}$ region containing the now isolated star is fit with a two-parameter model: a flux, and a constant background. The resulting flux is recorded as the local-background-subtracted flux. In general, there is little difference between the default fluxes and the local-background-subtracted fluxes. This is expected because the usual sky subtraction operates on a 52 scale, very similar to the scale of the background subtraction performed here. The primary difference is that the sky subtraction here is simultaneously fit and constant over the region. Nevertheless, given the similarity between the local-background-subtracted and the ordinary fluxes, significant differences between the two can be used to indicate problems with the photometry.

7.2.2. Merged Catalogs