Dynamic Observing and Tiling Strategies for the DESI Legacy Surveys

Wide-field imaging surveys typically aim to cover one or more contiguous areas of sky much larger than the footprint of the imaging camera. The Legacy Surveys represent a particularly extreme case where we have imaged a 16,000 deg² region using cameras that have fields of view of between 0.36 and 3.18 deg² (see Table 1). In addition, all of the camera focal planes are CCD mosaics that have gaps between individual CCDs. Hence, an efficient tiling pattern has to both cover the entire area with as few tiles as possible, and also cover all of the CCD gaps to some minimum depth driven by the science requirements.

Once the basic tiling strategy was identified, we defined a total of three independent tilings, with each tiling offset from the other two by some prescribed amount. Three tilings ensure that the footprint is almost entirely covered, while also minimizing the amount of area that does not have at least two images at any given position. Two-pass coverage is useful both to discriminate and mask any particle events or other detector-based anomalies, and to boost the signal-to-noise ratio (S/N) compared to a single pass. We used a Monte Carlo process of different offsets for the tiling sets for each camera in order to select the offsets that maximized three-pass coverage while minimizing one-pass coverage.

The detailed implementations for each camera are described in the following two subsections.

DECam has a roughly circular field of view of a_FoV = 3.18 deg² (Flaugher et al. 2015). To cover the entire sky, the ideal tiling would require $N=4\pi {(180/\pi )}^{2}/{a}_{\mathrm{FoV}}=12,973$ tiles (not accounting for CCD gaps or nonworking CCDs, see Table 1).

For defining the tiling for DECaLS, we adopted the approach of Hardin et al. (2012), who considered the general problem of covering a sphere uniformly with a fixed number of points. We selected the precomputed icosahedral arrangements of Hardin et al. (2012) with tiling N_tile that was close in number to but greater than N (i.e., the minimum number while still providing sufficient overlap with the neighboring tile). We investigated the icosahedral tilings with N_tile = [15,252, 15,392, 15,872, 16,002, 16,472, 16,752] and settled on N = 15,872 as providing the best solution with 99.98% and 98.01% of the sky having at least two and three exposures respectively, using a three-pass strategy.

Two of the three passes are copies of the first pass, offset by [ΔR.A., Δdecl.] of [0.2917, 0.0833] deg and [0.5861, 0.1333] deg respectively. This solution results in fractional coverage within the DESI footprint as shown in Table 2. Ideally, we would obtain three-image coverage of 100%, but this is not possible with a three-pass strategy given the gaps between the DECam CCDs. The resulting tiling for DECaLS is shown in Figure 1 along with the as-observed coverage statistics (which include pointing errors during the observations).

Zoom In Zoom Out Reset image size

The Mosaic3 Camera has an approximately square on-sky footprint with a field of view of 35.89' × 36.06' (Table 1; see also Dey et al. 2016). Given the smaller size and roughly square footprint, we settled on a tiling pattern that was aligned along rows of constant decl., with adjacent frames overlapping by 1.7' on all four sides. The resulting map has 122,765 tile centers in a single pass; the two other passes are offset by 11.7' and 23.5' in decl., respectively (or one-third and two-third of the field of view).

This choice of tiling ensures that 99.5% of the footprint is covered by at least three exposures (see Table 2). The tiling for MzLS is shown in Figure 2 along with the as-observed coverage statistics.

Zoom In Zoom Out Reset image size

Three passes, each constituting a complete tiling of the footprint as described in the previous section, were chosen to maximize the scientific uniformity and utility of the survey. In order to ensure that a given survey could be photometrically calibrated, we reserved the first tiling of the footprint (Pass 1) for times with photometric conditions when the seeing was good (i.e., <1.3''). We reserved the second tiling (Pass 2) for times with either photometric conditions or good seeing. We reserved the third tiling (Pass 3) for times when neither of these conditions were met, but were still deemed acceptable, i.e., seeing <2'', transparency >0.9, and sky brightness no more than 0.25 mag brighter than the nominal value for that band. This strategy was designed to ensure that every point within the survey footprint had at least one image that could be photometrically calibrated and at least one image that had good seeing. We observed three passes across the entire survey footprint to ensure the high completeness in two passes across every point in the footprint. During times when the weather was poor (i.e., worse than Pass 3 conditions), we still took data when possible, but these data did not contribute to the final catalogs.

As much as possible, we scheduled z-band observations during bright time (i.e., when the Moon was above the horizon, or the Sun's altitude was between −10° and −15°) and reserved dark time for g and r. With these constraints on the Sun and Moon imposed, dark-time and bright-time observations were then planned independently.

In addition, at all times, we restricted observations to airmass ≤2.4 and to pointings that were separated from the Moon by at least 40°–50°, with the exact separation determined by the Moon's phase. We also avoided observing tiles within 1.2° of bright planets. We enforced minimum and maximum exposure times (see Table 3) to ensure that we did not exceed depth when observing conditions were excellent, and to prevent saturation when the sky was too bright and curtail long exposures in otherwise poor conditions.

The basic logic we adopted is as follows.

• 1.  
  Tag tiles with bad exposures as unobserved.
• 2.  
  Rank order by R.A. and split unobserved tiles by filter.
• 3.  
  Remove tiles that are too close to the median position of the Moon and planets (Mars–Neptune) over the night.
• 4.  
  Rank order the list of future observing nights, starting with the desired night, by local mean sidereal time (LMST) and then split each night into one-minute-spaced intervals in LMST.
• 5.  
  Split the LMST list into dark and bright time.
• 6.  
  For bright and dark time respectively, match the rank-ordered R.A. and LMST lists by minimizing the time difference between them.
• 7.  
  Retain LMSTs that are within 5° of each R.A.
• 8.  
  The annealing process: randomly swap the LMST of two tiles. Accept the new positions if the total airmass is reduced. Repeat 400 times.
• 9.  
  For DECaLS only: prioritize the tiles for building that night's plan. Observations are chosen preferentially at decl. near decl. = 0, with a penalty of 1/100.0 per deg away from the equator. Also prioritize selecting tiles near the last observation, with a penalty of 1/10.0 per deg for distances more than 2° away. Priorities are increased (doubled) for observations of tiles that have been previously observed in at least one other filter. Increase priority for observations of the same tile. This should preferentially schedule pairs of g + r exposures in dark time. Priorities set to zero for tiles within 1 .20° of Mars–Neptune.
• 10.  
  Build the plan for the night. Pass 1 is preferentially selecting Pass 1 tiles, then Pass 2, then Pass 3, then a repeat observation of an already-observed tile. Pass 2 is preferentially selecting Pass 2 tiles, then Pass 3, etc.
• 11.  
  Observations begin and end at 12° twilight for DECaLS and 10° for MzLS.
• 12.  
  The untangling process: reduce slews by splitting tiles into blocks (consecutive tiles having slews >5°) and then trying all permutations of the blocks. After this the tiles are split again, using blocks of eight consecutive tiles, and the best permutation is chosen.
• 13.  
  Create a list of reserve tiles for bright and dark time from the list of observed and unobserved tiles that are closest to transit and sufficiently far from the Moon and planets.
• 14.  
  Observe tiles at their assigned LMST.

Observing conditions at ground-based observatories change due to temporal and spatial changes in atmospheric transparency and stability, thermal imbalances between the telescope, dome and ambient environment, and the spatial location of celestial objects at the time during which they are observed.

In an ideal world, observing conditions can be monitored during each on-sky integration as it is in progress, and the total duration of the ongoing exposure can be modified in real time to ensure that the image being taken reaches the appropriate depth. This could be accomplished using, say, nondestructive reads to monitor the actual image data as it is being collected, or alternatively using some proxy to estimate the current conditions in the region (e.g., a guide or photometric camera co-located with the telescope and pointed at the same spot in the sky).

The hardware realities of the Mosaic3 and DECam instruments prevented us from implementing any real-time exposure control. However, we were able to implement the next best option: to analyze each image as soon as it was taken, estimate the image quality, transparency, resulting depth and telescope pointing offset, and then adjust our exposure time as soon as possible, typically with a lag of 1 or 2 images.

At both the Mayall and Blanco telescopes, dynamic exposures were implemented using two (Python) software "bots"; both monitored the observing conditions and telescope pointing offsets, with one (copilot) providing a graphical view of the derived estimates and the other (decbot/mosbot in the cases of DECam/Mosaic3, respectively) writing the required scripts and interfacing with the instrument to modify the exposure time. These codes are all publicly available.¹⁶ We describe the individual pieces of this process below.

For each raw image, copilot measures the seeing, sky brightness, atmospheric transparency, and photometric zero-point. The bot extrapolates from the central 1000 × 1000 pixels of a single CCD or amplifier (CCD N4 for DECam and amplifier IM4 for Mosaic3) to infer statistics for the entire exposure. For the observers, copilot displays plots of seeing, sky brightness, transparency, and R.A. and decl. offsets. Figure 3 shows the summary plot from 2017 March 30.

Zoom In Zoom Out Reset image size

The combination of copilot and either mosbot or decbot performs on-the-fly image reductions, which we describe briefly below.

Detrending. The first step is to apply bias and gain, and then to estimate the sky level by sigma-clipping the central pixels. This provides a measure of the sky brightness m_sky, assuming the canonical zero-point for the given camera and filter.

Source detection. We correlate the image with a matched filter consisting of a 2D Gaussian with a FWHM of 5 pixels, and flagging pixels with ${\rm{S}}/{\rm{N}}\geqslant 20\,{\sigma }_{\mathrm{sky}}$. Aperture photometry is carried out for these (unresolved or star-like) sources using an aperture with a diameter of 7'' (constant pixel scale) and a sky annulus with a diameter of 14''–20'' (constant pixel scale). The source counts (${N}_{{\rm{e}}-}$) are then counts in the object aperture minus the mode of sky annulus times the area of the object aperture. The following restrictions were applied to ensure a clean sample of sources:

• 1.  
  ${N}_{{\rm{e}}-}\gt 0$;
• 2.  
  $12\lt {m}_{\mathrm{AB}}\lt 22$;
• 3.  
  at least 11'' (40 pixels) from CCD edges and any other sources;
• 4.  
  and no bad pixels within 5 pixels of the centroid.

Seeing quality determination. We estimate the seeing by fitting a circular 2D Gaussian to all sources with 20 < S/N < 100, where noise includes the Poisson noise from both the sky and the source, and only the FWHM is allowed to vary. The seeing we record is the median of the best-fit FWHM values.

On-the-fly photometric calibration. We compute photometric zero-points relative to the PS1 catalogs, and astrometric offsets from the Gaia DR1 catalogs (Gaia Collaboration et al. 2016a, 2016b). Note that we actually use a single PS1–Gaia catalog, created using a 3.5'' matching radius. There are occasional holes in the Gaia DR1 catalog in regions that contain plenty of bonafide PS1 stars, so our astrometry reverts to only using PS1 in such regions. We enforce the following constraints on the PS1–Gaia catalog:

• 1.  
  there can only be exactly one match between the catalogs;
• 2.  
  the PS1 catalog must not flag the source, in the g, r, and z bands as coming from a bad CCD region, containing bad pixels, or having NaN fluxes;
• 3.  
  and sources must have a star-like color in the range of $0.4\lt g-r\lt 2.7$, where g − r denotes the PS1 median point-spread function (PSF) magnitude color.

The instrumental zero-point is the difference between the PS1 magnitude of a source (${m}_{\mathrm{PS}1}$) and our measured aperture magnitude (${m}_{\mathrm{AB}}$), and the 2.5σ-clipped median for all sources in a CCD,

$$\begin{eqnarray}&&\mathrm{ZP}=\mathrm{Med}\left({m}_{\mathrm{PS}1}-{m}_{\mathrm{AB}}\right)+{\mathrm{ZP}}_{0},\end{eqnarray} \tag{ 1 }$$

where ${\mathrm{ZP}}_{0}$ is a band-dependent fiducial zero-point we obtained during nights with excellent conditions near the start of the DECaLS and MzLS observations. The relative atmospheric transparency, i.e., the fraction of light that penetrates Earth's atmosphere relative to a good night at the start of the survey, can then be computed from the zero-point

$$\begin{eqnarray}&&{T}_{\mathrm{rel}}={10}^{-0.4\left[{\mathrm{ZP}}_{0}-\mathrm{ZP}-{\text{}}K\left(X-1\right)\right]}\,,\end{eqnarray} \tag{ 2 }$$

where K is the atmospheric extinction coefficient and X is the airmass.

Depth and exposure factor estimates. The 5σ AB magnitude depth, with Galactic extinction ${AE}(B-V)$ removed, is

$$\begin{eqnarray}&&{m}_{\mathrm{depth}}=-2.5{\mathrm{log}}_{10}\left(\displaystyle \frac{5{\sigma }_{\mathrm{sky},\mathrm{eff}}}{{t}_{\exp }}\right)+\mathrm{ZP}-{AE}(B-V),\end{eqnarray} \tag{ 3 }$$

where ${\sigma }_{\mathrm{sky},\mathrm{eff}}$ is the square root of sky counts from a region having the size of the source,

$$\begin{eqnarray}&&{\sigma }_{\mathrm{sky},\mathrm{eff}}=\sqrt{{\sigma }_{\mathrm{sky}}^{2}{N}_{\mathrm{eff}}},\end{eqnarray} \tag{ 4 }$$

where ${N}_{\mathrm{eff}}$ is the noise equivalent area, i.e., the effective number of pixels of an astrophysical source on the CCD, given by

$$\begin{eqnarray}&&{N}_{\mathrm{eff}}={\left(\sum _{i}{v}_{i}\right)}^{2}/\sum _{i}{v}_{i}^{2},\end{eqnarray} \tag{ 5 }$$

where v_i is the pixelized PSF centered on the source. If the source is an extended object, then v_i is the value of the PSF convolved with the object's surface brightness profile. For speed of computation, copilot uses an approximation for ${N}_{\mathrm{eff}}$ instead:

$$\begin{eqnarray}&&{\hat{N}}_{\mathrm{eff}}\approx 4\pi {\sigma }_{\mathrm{see}}^{2}+8.91{r}_{\mathrm{half}}^{2}+{P}_{\mathrm{sc}}^{2}/12,\end{eqnarray} \tag{ 6 }$$

where ${r}_{\mathrm{half}}=0.4^{\prime\prime}$ for extended sources and ${r}_{\mathrm{half}}=0^{\prime\prime}$ for point-sources, and ${P}_{\mathrm{sc}}$ is the plate scale. This approximation is based on the assumption that the seeing is Gaussian, which results in slightly underpredicting the true value of ${N}_{\mathrm{eff}}$ since the seeing profile has larger wings. In fact, this approximation systematically underestimates the true ${N}_{\mathrm{eff}}$ by 20%–40%, but we have found that a linear model ($A{\hat{N}}_{\mathrm{eff}}+B$) for each camera and point-source/extended source pair agrees well with the true ${N}_{\mathrm{eff}}$.

Combining Equations (2)–(4), we obtain the exposure time scaling factor relative to its value under nominal conditions, i.e., $E(B-V)=0$, ${T}_{\mathrm{rel}}=1$, and X = 1,

$$\begin{eqnarray}\begin{array}{rcl}\displaystyle \frac{{t}_{\exp }}{{t}_{\exp ,0}} & = & \displaystyle \frac{{N}_{\mathrm{eff}}}{{N}_{\mathrm{eff},0}}\displaystyle \frac{1}{{T}_{\mathrm{rel}}^{2}}\\ & & \times \,{10}^{0.8\left[{\text{}}K\left(X-1\right)+{AE}(B-V)\right]-0.4\left[{m}_{\mathrm{sky}}-{m}_{\mathrm{sky},0}\right]},\end{array}\end{eqnarray} \tag{ 7 }$$

where ${N}_{\mathrm{eff},0}$ is obtained using Equation (6) with the nominal seeing ${\sigma }_{\mathrm{see}}=1.3^{\prime\prime}$. This estimate for the corrected exposure time (rounded up to the nearest integer) is used to set the duration of the upcoming exposure. Finally, copilot compares the depth, estimated from detected PS1 stars, attained by a given image to the desired depth, which is defined as detecting the canonical 0.45'' exponential disk galaxy at S/N = 5, by computing the median ${m}_{\mathrm{depth}}$ of all detected sources. The success factor of the observation is presented as the exposure factor, ${R}_{\mathrm{expfac}}\equiv {t}_{\mathrm{observed}}/{t}_{\mathrm{desired}}$, i.e., the ratio between the actual exposure time used for the image and the exposure time that would have been needed to reach depth. The exposure factor is reported on the graph that is visible to the observer.

Figure 4 shows the comparison between the obsbot depth estimate and the one determined by the offline pipeline. The two are well correlated but is tighter for Mosaic than DECam. obsbot tends to slightly overestimate the depth, especially for DECam, but this is a small effect and had no adverse effect for the overall depth of the surveys.

Zoom In Zoom Out Reset image size

For each on-sky exposure that is written to disk, mosbot analyzes a single CCD amplifier to (a) determine the sky level, (b) detect sources and measure the FWHM, (c) match them to sources from the PanSTARRS1 catalog, (d) derive the zero-point of the image, (e) compare this zero-point to the fiducial zero-point to determine the transparency, and (f) derive the attained depth of the image. In addition, mosbot determines the airmass and Galactic extinction of the next pointing, predicts the band-dependent seeing based on an empirical relationship, and calculates the needed exposure time to reach depth using Equation (7).

mosbot only corrects the exposure time for upcoming observations; the pointing offset of the telescope (which is computed and displayed by both mosbot and copilot) has to be corrected by the night-time observer, and is done while the exposure is reading out.

At the start of the DECaLS survey, nightly observations began with nominal exposure times that the observers modified on hour timescales as conditions changed. On 2015 February 25, we started using copilot and decbot. Similarly to mosbot for MzLS, decbot uses the most recent raw image on the disk to predict the exposure time needed to reach the depth at the next pointing. Tiles with the earliest LMST are added to the queue while all tiles with LMST in the past are ignored.

While decbot and mosbot can also choose the pass number based on the derived conditions, the observers could force a pass in conditions that were at the limit between passes. This could be used to avoid large slews as the surveys progressed, which might have resulted in larger overheads and uneven completion rates in different passes.

With DECam, the slewing to the next pointing is simultaneous with reading out the CCD. On average, slewing is faster (about 30 s for less than 5°) than read out, so the next exposure usually begins before the image is built, compressed, and written to the disk. Only after the image is written can obsbot analyze the image and copilot provide an update to the exposure time. The observing software cannot change the exposure time once the exposure begins, so the exposure time would only be updated for the subsequent exposure.

As in the case of MzLS, decbot only corrects the exposure time for upcoming observations; the pointing offset of the telescope has to be corrected by the night-time observer by temporarily pausing the exposure queue.

Dynamic exposure times allow the observations to compensate, ideally in real time, for the variable conditions to ensure that each image reaches depth. This is demonstrated in Figure 5, which shows the reverse cumulative distributions of the exposure factors for the Pass 1, 2, and 3 images in two cases: the actual MzLS and DECaLS images obtained under the dynamic exposure time operations, and what would have resulted if we had used our fiducial exposure time (see Table 3). In the case of the actual observations, we have restricted our selection to frames with exposure times between the minimum and maximum times allowed. In the case of the MzLS observations, the exposure time was corrected with a typical lag time corresponding to one frame; for DECaLS, this was two frames, due to the structure of the queuing software. Even so, the dynamic observation results in dramatic gains, especially in the cases of the Pass 2 and 3 observations which are obtained under nonphotometric and/or poor seeing conditions. In the case of the fixed exposure times, we would have had to reobserve a larger number of the shallow fields, resulting in extra on-sky observing time and extra overheads (primarily due to telescope slews, dome rotations, and CCD readouts). In addition to saving time by not underexposing, dynamic observing can save time by not exposing for longer than is necessary. This can be seen from Figure 6 which shows the relative depths of MzLS and DECaLS exposures using our dynamic exposure strategy versus what we would have achieved with fixed exposure times, either averaged over the whole survey or adjusted every night. The distributions for lags of 1–2 exposures is much narrower around the prescribed depth than for the two fixed exposure time scenarios, especially in the case of the z band, for which there are long tails at high relative magnitudes.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size