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Dec 8, 2019, 12:14:51 PM (7 years ago)
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eugene
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updates based on referee comments

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  • trunk/doc/release.2015/ps1.calibration/calibration.tex

    r41191 r41197  
    11021102from the recalculated mean.
    11031103
    1104 Suspicious stars are also excluded from the analysis.  We exclude stars
    1105 with reduced $\chi^2$ values more than 20.0, or more than 2$\times$
    1106 the median, whichever is larger.  We also exclude stars with standard
     1104Suspicious \textadd{(e.g., variable or otherwise poorly measured)}
     1105stars are also excluded from the analysis.  We exclude stars with
     1106reduced $\chi^2$ values more than 20.0, or more than 2$\times$ the
     1107median, whichever is larger.  We also exclude stars with standard
    11071108deviation (of the measurements used for the mean) greater than 0.005
    11081109mags or 2$\times$ the median standard deviation, whichever is greater.
     
    11521153    \sigma_i^{-2})^2}
    11531154\end{equation}
    1154 
    1155 These rejections and the over-weighting of the Ubercal measurements
    1156 are admittedly ad hoc.  Since the goal at this stage is to tie the
    1157 non-Ubercal data to the Ubercal system, we
    11581155
    11591156The calculation of the relative photometry zero points is performed
     
    12731270For PV3, the relphot analysis was performed two times.  The first
    12741271analysis used only the flat-field corrections determined by the
    1275 ubercal analysis, with a resolution of 2x2 flat-field values for each
     1272ubercal analysis, with a resolution of $2 \times 2$ flat-field values for each
    12761273GPC1 chip (corresponding to \approx 2400 pixels), and 5 separate
    12771274flat-field 'seasons'.  However, we knew from prior studies that there
     
    15131510\subsubsection{Iteratively Reweighted Least Squares Fitting}
    15141511
    1515 With an automatic process applied to hundreds of millions of stars, it
     1512With an automatic process applied to hundreds of millions of objects, it
    15161513is important for the analysis to provide a measurement of the
    1517 photometry of each object which is robust against failures.  The
    1518 Pan-STARRS\,1 detections have a relatively high rate of non-Gaussian
    1519 outliers, partly because of the wide range of instrumental features
    1520 affecting the data (see Paper III).  \textmod{We have used Iteratively
    1521   Reweighted Least Squares (IRLS) fitting to reduce the sensitivity of
    1522   the fits to outlier measurements.} 
     1514photometry of each object which is robust against failures or other
     1515outliers.  \textadd{We would like to calculate an average magnitude
     1516  for each filter in the assumption that the flux of the star is
     1517  constant and all measurements are drawn from that population.
     1518  However, even after rejecting bad measurements based on the quality
     1519  information above, individual measurements may still be deviant.}
     1520The Pan-STARRS\,1 detections have a relatively high rate of
     1521non-Gaussian outliers, partly because of the wide range of
     1522instrumental features affecting the data (see Paper III).  \textmod{We
     1523  have used Iteratively Reweighted Least Squares (IRLS) fitting to
     1524  reduce the sensitivity of the fits to outlier measurements.}
    15231525
    15241526We have also used bootstrap resampling to determine confidence limits
     
    17871789for either DR1 or DR2.  An update to the database will define fields
    17881790for each object which encapsulate the information about the ``primary''
    1789 and ``best'' detections.
     1791and ``best'' detections.  Users should consult the help pages at MAST
     1792for further information.
    17901793
    17911794\subsubsection{Warp Photometry}
     
    18261829than PSF-like, the object bit flag \code{ID_OBJ_EXT} is raised.  If
    18271830more than half of the PS1 \ippstage{chip}-stage measurements within a
    1828 single filter are extended, then the per-filter bit flag
     1831single filter are extended, then the per-filter bit flags
    18291832\code{ID_SEC_OBJ_EXT} and \code{ID_SEC_OBJ_EXT_PSPS} are set.  The
    18301833latter bit is a duplicate bit defined because the high bit in a 32-bit
     
    18321835object which has any \ippstage{chip}-stage measurements for one of the
    18331836five filters has the per-filter bit flag \code{ID_SECF_HAS_PS1} set.
     1837\textadd{Since stack images are more sensitive than the individual exposures,
     1838faint sources which are detected in only the stacks will have the bit
     1839flag {\tt ID\_SECF\_HAS\_PS1\_STACK} set but not {\tt ID\_SECF\_HAS\_PS1}
     1840as the latter only refers to individual chip detections.}
    18341841
    18351842In addition, if the object has measurements from the 2MASS point
     
    18721879
    18731880\subsection{Photometry Calibration Quality}
     1881\label{sec:photcal}
    18741882
    18751883% /data/kukui.1/eugene/cal.paper.images.20190217/scatter.sh : allsky.scatter.photom
     
    18921900position across the sky.  For each pixel in these images, we selected
    18931901all objects with (14.5, 14.5, 14.5, 14.0, 13.0) $<$ ($g,r,i,z,y$) $<$
    1894 (17, 17, 17, 16.5, 15.5) magnitudes, with at least 3 measurements in $i$-band (to
     1902(17, 17, 17, 16.5, 15.5) \textadd{magnitudes}, with at least 3 measurements in $i$-band (to
    18951903reject artifacts detected in a pair of exposures from the same night),
    18961904with \code{PSF_QF} $> 0.85$ (to reject excessively-masked objects),
     
    1922193018)$ millimagnitudes.
    19231931
     1932% /data/ipp070.0/eugene/dr2.figs.20190205/
    19241933% /data/kukui.1/eugene/cal.paper.images.20190217/kronrepair.sh : full.figure
    19251934\begin{figure*}[htbp]
     
    19291938    PV3.4 photometry illustrating the impact of the issues identified
    19301939    in the PV3.3 stack and warp photometry.  All figures use \ips-band
    1931     photometry.  The left panels use data from PV3.3 while the right
     1940    photometry, \textadd{restricted to objects brighter than 17 magnitudes with
     1941    at least 10 chip measurements}.  The left panels use data from PV3.3 while the right
    19321942    use PV3.4.  The top row shows the mean difference between the
    19331943    average photometry from individual exposures (``chip'') and the
     
    20252035
    20262036First, the astrometric calibration has a larger number of systematic
    2027 effects which must be performed.  These consist of: 1) the
     2037effects which must be corrected.  These consist of: 1) the
    20282038Koppenh\"ofer Effect, 2) Differential Chromatic Refraction, 3) Static
    20292039deviations in the camera.  We discuss each of these in turn below.
     
    20462056shift of about one pixel.  This effect was only observed in 2-phase
    20472057OTA devices, with 22 / 30 of these suffering from this effect.  By
    2048 adjusting the summing well high voltage down from a default +7 V to
     2058adjusting the summing well high voltage down from a default +7V to
    20492059+5.5V on the 2-phase devices, the effect was prevented in exposures
    20502060after 2011-05-03.  However, this left 101,550 exposures (27\%) already
     
    20782088Differential Chromatic Refraction (DCR) affects astrometry because the
    20792089reference stars used to the calibrate the images are not the same
    2080 color (SED) as the rest of the stars in the image.  For a given star
     2090color as the rest of the stars in the image.  For a given star
    20812091of a color different from the reference stars, as exposures are taken
    2082 at higher airmass, the apparent position of the star will be biased
     2092at higher airmass, the apparent position of the star will be \textadd{shifted}
    20832093along the parallactic angle.  While it is possible to build a model
    20842094for the DCR impact based on the filter response functions and
     
    21122122stars used the calibrate a specific blue- or red-filter image,
    21132123respecitively, while $\zeta$ is the zenith distance.
    2114 Figure~\ref{fig:DCRexample} shows the DCR trend for the 5 filters
    2115 \grizy, as well as the measured displacement in the direction
     2124Figure~\ref{fig:DCRexample} shows the DCR trend for the \gps\ filter
     2125as an example, as well as the measured displacement in the direction
    21162126perpendicular to the parallactic angle.  We represent the trend with a
    21172127spline fitted to this dataset.
     
    21312141 \includegraphics[width=\hsize,clip]{{\picdir/DCR.example}.\plotext}
    21322142  \caption{\label{fig:DCRexample} Example of the DCR trend in the
    2133     g-band.  {\bf top:} DCR trend in the parallactic direction {\bf
     2143    g-band, in which it is strongest.  {\bf top:} DCR trend in the parallactic direction {\bf
    21342144      bottom:} DCR trend perpendicular to the parallactic angle.}
    21352145  \end{center}
     
    21392149$(g,r,i,z,y) = (0.010, 0.001, -0.003, -0.017, -0.021)$ arcsec
    21402150airmass$^{-1}$ magnitude$^{-1}$.  We saturate the DCR correction if
    2141 the term $\left[gi_{\rm ref} - (g - i)\right] \tan \zeta$ or
    2142 $\left[zy_{\rm ref} - (z - y)\right] \tan \zeta$ for a given
     2151the term $\left[(g - i)_{\rm ref} - (g - i)\right] \tan \zeta$ or
     2152$\left[(z - y)_{\rm ref} - (z - y)\right] \tan \zeta$ for a given
    21432153measurement is outside of the range where the DCR correction is
    21442154measured.  The maximum DCR correction applied to the five filters is
     
    23402350In order to perform this analysis, we need estimated distances for
    23412351every reference star used in the analysis.  \cite{2014ApJ...783..114G}
    2342 performed SED fitting for 800M stars in the 3$\pi$ region using PV2
     2352performed spectral energy distribution (SED) fitting for 800M stars in the 3$\pi$ region using PV2
    23432353data.  The goal of this work was to determine the 3D structure of the
    23442354dust in the galaxy.  By fitting model SEDs to stars meeting a basic
     
    23542364and Solar motion parameters ($U_{\rm sol}, V_{\rm sol}, W_{\rm sol}$)
    23552365= (9.32, 11.18, 7.61) km sec$^{-1}$ as determined by
    2356 \cite{1997MNRAS.291..683F} using Hipparchus data.  Proper motions are
     2366\cite{1997MNRAS.291..683F} using Hipparcos data.  Proper motions are
    23572367determined from the following:
    23582368\begin{eqnarray}
     
    23662376is independent of distance while the reflex motion induced by the
    23672377solar motion decreases with increasing distance.  Also note that this
    2368 model assumes a flat rotation curve for objects in the thin disk.  Any
     2378model assumes a flat rotation curve for objects in the thin disk.  \textmod{Any
    23692379reference stars which are part of the halo population will have proper
    23702380motions which are not described by this model; the mostly random
    23712381nature of the halo motions should act to increase the noise in the
    2372 measurement, but should not introduce detectable motion biases.  Also,
    2373 if the distance modulus is not well determined, we can assume the
    2374 object is simply following the Galactic rotation curve and set a fixed
    2375 proper motion.  If we do not have a distance modulus from the Green et
    2376 al analysis, we assume a value of 500pc.
    2377 
    2378 \note{find the improvement by using 2MASS -- in the PS1 DRAVG pages}
     2382measurement.  We do not attempt to compensate for asymmetric drift in
     2383the populations with higher radial velocity dispersion.  This effect
     2384will introduce some bias in the azimuthal direction which our simple
     2385model cannot address.  For stars for which the distance modulus is not
     2386well determined, we assume the object is simply following the Galactic
     2387rotation curve and set a fixed proper motion.}  If we do not have a
     2388distance modulus from the Green et al analysis, we assume a value of
     2389500pc.  \textadd{We find that applying our Galactic rotatation model improves
     2390the systematic proper motion errors to some extent.  The standard
     2391deviation of the quasar proper motions (averaged on 12 arcminute
     2392superpixels across the sky) is reduced from $(\sigma_{\mu,\alpha},
     2393\sigma_{\mu,\delta}) = (4.6, 2.4)$ mas yr$^{-1}$ for the uncorrected
     2394analysis to $(\sigma_{\mu,\alpha}, \sigma_{\mu,\delta}) = (2.9, 2.0)$
     2395mas yr$^{-1}$ after correction for the Galactic rotation model.  The
     2396remaining quasar motions continue to show some systematics which may
     2397suggest the need to include a correction for the asymmetric drift.}
    23792398
    23802399For the initial PV3 analysis, we again used the 2MASS coordinates as
     
    23882407the Gaia DR1 coordinates.  The Gaia DR1 coordinates used a fixed 2015
    23892408epoch.  Coordinates were propagated from that epoch to the epoch for
    2390 each PS1 image as described above.
     2409each PS1 image as described above.  \textadd{In a future analysis, we will use
     2410the Gaia DR2 proper motions to tie the astrometric analysis to Gaia
     2411both in terms of the mean positions as well as the dynamical system.}
    23912412
    23922413\subsection{Object Astrometry}
     
    24062427\code{ID_MEAS_USED_OBJ}.  Some detections were identified as extreme
    24072428outliers if their position deviated from the mean object coordinate by
    2408 more than 2 arcseconds.  These detections were ignored and marked with
     2429more than 2 arcseconds.  \textadd{Such a large deviation can only occur when
     2430the in-database calibration is poor, for example near the edges of a
     2431chip.}  These detections were ignored and marked with
    24092432the bit flag \code{ID_MEAS_POOR_ASTROM}.
    24102433
     
    24182441\subsubsection{Iteratively Reweighted Least Squares Fitting}
    24192442
    2420 With an automatic process applied to hundreds of millions of stars, it
    2421 is important for the analysis to provide a measurement of the
    2422 astrometry of each object which is robust against failures.  The
    2423 Pan-STARRS\,1 detections have a relatively high rate of non-Gaussian
    2424 outliers, partly because of the high degree of structure in the
    2425 astrometric transformations introduced by the camera optics and the
    2426 atmosphere, and partly due to the high masked fraction and other
    2427 detector effects.  We have used a techinique called Iteratively
    2428 Reweighted Least Squares (IRLS) fitting to reduce the sensitivity of
    2429 the fits to outlier measurements.  We have also used bootstrap
    2430 resampling to determine confidence limits on our fits given the
    2431 observed collection of position measurements.
     2443\textmod{Just as with the photometric analysis, it is also important for the
     2444astrometric analysis to provide a measurement which is robust against
     2445failures.  In addition to the detector effects artifacts which affect
     2446astrometry, the astrometric measurments may have non-Gaussian outliers
     2447due to the high degree of structure in the astrometric transformations
     2448introduced by the camera optics and the atmosphere.  We have again
     2449used the IRLS technique to reduce the sensitivity of the fits to
     2450outlier measurements.}  We have also used bootstrap resampling to
     2451determine confidence limits on our fits given the observed collection
     2452of position measurements.
    24322453
    24332454We begin the astrometric analysis for each object by projecting the
     
    24742495weights.  New values for $\omega_\eta,\omega_\zeta$ are calculated,
    24752496and the fit is tried again.  On each iteration, the fitted parameters
    2476 are compared to the values from the previous iteration.  If they
     2497are compared to the values from the previous iteration.  If the
    24772498parameters have not changed significantly ($< 10^{-6}$) or if the
    24782499fractional change is less than some tolerance ($10^{-4}$), then
     
    24942515
    24952516Bootstrap-resampling analysis is used to assess the errors on the fit
    2496 parameters: A number of measurements equal to the number of unclipped
    2497 data points are randomly selected from the set of unclipped data
    2498 points, with replacement after each selection.  These data points are
    2499 then used to fit for the astrometric parameters, using ordinary least
    2500 squares fitting.  The parameters are recorded and the process re-run
    2501 300 times.  For each astrometric parameter, the error is determined as
    2502 half of the 68\% confidence range for the distribution of fitted
    2503 parameter values.
     2517parameters in a fashion similar to the photometry analysis: A number
     2518of measurements equal to the number of the remaining unclipped data
     2519points are randomly selected from the set of the remaining unclipped
     2520data points, with replacement after each selection.  These data points
     2521are then used to fit for the astrometric parameters, using ordinary
     2522least squares fitting.  The parameters are recorded and the process
     2523re-run 300 times.  For each astrometric parameter, the error is
     2524determined as half of the 68\% confidence range for the distribution
     2525of fitted parameter values.
    25042526
    25052527\subsubsection{Object Astrometry Flags}
     
    25112533fitted to parallax without proper motion as well.  If an object is
    25122534fitted for parallax, it is also fitted with a model including only
    2513 proper motion and only a mean position.  The chisq for all three fits
     2535proper motion and only a mean position.  The chi-square for all three fits
    25142536is saved.  Currently, the highest order fit allowed is saved in the
    25152537database, regardless of the significance of the improvement in adding
     
    26312653\sigma_\delta)$ is 16 milliarcseconds.
    26322654
    2633 The Galactic plane is clearly apparently in these images.  Like
     2655The Galactic plane is clearly apparent in these images.  Like
    26342656photometry, we attribute this to failure of the PSF fitting due to
    26352657crowding.  The celestial North pole regions have somewhat elevated
     
    27212743  Solar motion to correct the absolute proper motion (see
    27222744  Section~\ref{sec:galactic.rotation}).  We identify the resulting
    2723   database as PV3.1.  This database was used to generate the positions
     2745  database as PV3.2.  This database was used to generate the positions
    27242746  in the \ippdbtable{gaiaObject} table, which are exposed in the DR1
    27252747  release.
     
    27862808  \begin{center}
    27872809  \includegraphics[width=\hsize,clip]{{\picdir/gaia.photom.v1}.\plotext}
    2788   \caption{\label{fig:gaia.photom} Comparison with Gaia DR1
    2789     photometry. {\bf Left} Mean of PS1 - Gaia DR1, {\bf Right} Standard
    2790     deviation of PS1 - Gaia DR1.  For pixels with $|b| > 30$ and $\delta >
    2791     -30$, the standard deviation of the PS1 - Gaia DR1 mean values is 6.9
    2792     millimagnitudes, while the median of the standard deviations is 12.4
    2793     millimagnitudes.  The former is a statement about the consistency
    2794     of the Gaia DR1 and Pan-STARRS\,1 photometry, while the latter
    2795     reflects the combined bright-end errors for both systems.  }
     2810  \caption{\label{fig:gaia.photom} Comparison with Gaia DR1 photometry
     2811    (see Section~\ref{sec:gaia.tie} for sample selection). {\bf Left}
     2812    Mean of PS1 - Gaia DR1, {\bf Right} Standard deviation of PS1 -
     2813    Gaia DR1.  For pixels with $|b| > 30$ and $\delta > -30$, the
     2814    standard deviation of the PS1 - Gaia DR1 mean values is 6.9
     2815    millimagnitudes, while the median of the standard deviations is
     2816    12.4 millimagnitudes.  The former is a statement about the
     2817    consistency of the Gaia DR1 and Pan-STARRS\,1 photometry, while
     2818    the latter reflects the combined bright-end errors for both
     2819    systems.  }
    27962820  \end{center}
    27972821\end{figure*}
     
    28692893signal to noise in Gaia; they were also apparent in the plots of the
    28702894statisics of the per-exposure measurement residuals
    2871 (Figure~\ref{fig:allsky.astrom.sigma}.  The standard deviations of the
     2895(Figure~\ref{fig:allsky.astrom.sigma}).  The standard deviations of the
    28722896median differences are ($\sigma_\alpha, \sigma_\delta) = (4.8, 3.1)$
    28732897milliarcseconds.
     
    29322956\begin{figure*}[htbp]
    29332957  \begin{center}
    2934   \includegraphics[width=\hsize,clip]{{\picdir/A4}.pdf}
     2958  \includegraphics[width=0.95\hsize,clip]{{\picdir/A4}.pdf}
    29352959  \caption{\label{fig:pole.bad.histogram} Histogram of the fraction of bad groups for each skycell (red line).}
    29362960  \end{center}
     
    29492973based on a comparison between stack and mean object photometry.  In the
    29502974presence of modest registration errors, mean object photometry would
    2951 not be affected, as individual detection woulds have the correct
     2975not be affected, as individual detection would have the correct
    29522976signal, and averaging their flux in catalog space would yield the
    29532977correct total magnitude.  On the other hand, imperfect stacking would
     
    29602984in poor stack photometry for the affected skycells.
    29612985
    2962 Further investigaion revealed that the cause of these failures was an
     2986Further investigation revealed that the cause of these failures was an
    29632987error in the internal reference catalog used for the PV3 analysis (see
    29642988Section~\ref{sec:synthdb}).  This reference catalog used PS1
     
    29943018We first used the PV3 mean astrometry and photometry to define a new
    29953019reference catalog in the assumption that the bulk of the failures
    2996 would be eliminated by the astrometric recalibration.  We reprocesed a
     3020would be eliminated by the astrometric recalibration.  We reprocessed a
    29973021section of the polar cap data using this PV3-based reference catalog
    2998 and re-ran the astrometric registration test was repeated on the
     3022and re-ran the astrometric registration test on the
    29993023reprocessed exposures.  The reprocessing greatly ameliorated the
    30003024registration issue, as shown in Figure~\ref{fig:pole.bad.histogram}.
     
    30163040
    30173041We consider skycells with more than 10\% bad groups to have been
    3018 adversely affected by this problem.  Uses of DR2 should be aware that
    3019 the affected skycells have poor astrometry and effective image
     3042adversely affected by this problem.  Users of DR2 should be aware that
     3043the affected stack skycells have poor astrometry and effective image
    30203044quality.  However, as these images may be useful to the community,
    30213045they are available from the MAST cutout server.  Users who attempt to
    30223046download these problem skycells will see a warning message and should
    3023 avoid using the skycell images for quantitative measurements without
     3047only use the skycell images for quantitative measurements with
    30243048extreme caution.  Since stack measurements from these skycells are
    30253049significantly damaged, the DR2 release has set the measured stack
     
    30293053\section{Conclusion}
    30303054
    3031 The Pan-STARRS Data Release 2 provides astromtry and photometry of
     3055The Pan-STARRS Data Release 2 provides astrometry and photometry of
    30323056roughly 3 billion astronomical objects across the $3\pi$ survey
    30333057region.  The photometry system has been shown to be reliable across
     
    30473071community.
    30483072
    3049 \note{need to add discussion of SDSS, DES, LSST, Gaia}
     3073\textadd{The past three decades have seen the digital release of a series of
     3074large-scale optical and near-IR astronomical surveys with generally
     3075steady improvements in quality.  The trend begins in the mid 1990s
     3076with the digitized photographic plate surveys such as USNO-B
     3077\cite{2003AJ....125..984M} and SuperCOSMOS \cite{2001MNRAS.326.1295H}
     3078which have photometric errors of roughly 300 millimags and astrometric
     3079errors of roughly 200 milliarcseconds.  The Hipparcos \& Tycho
     3080catalogs released in the mid 1990s have much smaller astrometric
     3081errors (roughly 0.6 milliarcseconds) but substantially limited depth
     3082($V < 11.5$) compared to the ground-based work
     3083\citep{1997AA...323L..57H}.}
     3084
     3085\textadd{The first generation of sky surveys using digital detectors, including
     3086SDSS \citep{2001ASPC..238..269L} and 2MASS
     3087\citep{2006AJ....131.1163S}, brought a substantial leap in the quality
     3088of both photometry and astrometry along with improvements in the depth
     3089and wavelength coverage.  Glossing over the details of how exactly to
     3090determine the accuracy of the SDSS and 2MASS photometry, it is clear
     3091that the photometric accuracy of those surveys are in the vicinity of
     309210 - 20 millimagnitudes for all filters, more than an order of
     3093magnitude improvement over the photographic plate surveys.  The
     3094astrometric accuracy of these two surveys (roughly 50 - 80
     3095milliarcseconds) is also a large improvement.}
     3096
     3097\textadd{The Pan-STARRS $3\pi$ Survey public release represents an important
     3098step in the ongoing progress towards covering the sky with
     3099well-characterized measurements.  The nearly coincident data releases
     3100from Gaia \citep{2016AA...595A...4L,2018AA...616A...1G} complement the
     3101PS1 releases greatly.  In the south, the Dark Energy Survey has
     3102produced its first public data release covering roughly 5000 square
     3103degrees of the sky \citep{2018ApJS..239...18A} with reported
     3104photometric precision of better than 10 millimagnitudes.}
     3105
     3106\textadd{The next decade will see further advances in survey breadth and depth
     3107along with further improvements in calibration quality.  Over the next
     31082-3 years, the Ultraviolet Near-Infrared Optical Northern Sky (UNIONS)
     3109Survey collaboration (a meta-collaboration of the Pan-STARRS and
     3110Canada-France Imaging Survey, or CFIS, collaborations) is expected to
     3111release deep photometry in the {\it ugriz} bands for roughly 5000
     3112square degrees of the northern hemisphere with agressive photometric
     3113precision goals.  This collaboration is in part motivated to support
     3114the Euclid satellite mission, which requires deep 8-band photometry to
     3115measure photometric redshifts, but only provides the {\it JHK} bands.
     3116The Large Synoptic Survey Telescope is also expected to produce
     3117high-precision photometry and astrometry to great depths over a very
     3118large portion of the sky available from the southern hemisphere.}
     3119
     3120\textadd{From our experience with the Pan-STARRS survey, and the results of the
     3121comparisons between surveys, a few lessons stand out.}
     3122
     3123\textadd{First, systematic errors come in many forms and dominate the
     3124calibration precision.  Internal or relative examination of the data
     3125can reveal important and unexpected effects such as the Koppenh\"ofer
     3126and vertical diffusion effects we identified in the Pan-STARRS
     3127devices.}
     3128
     3129\textadd{Second, cross-comparisons between independent datasets are critical to
     3130reveal the limitations.  This lesson has appeared several times in our
     3131intestigations, in the comparison between Pan-STARRS and Gaia above,
     3132between Pan-STARRS and SDSS \citep{2016ApJ...822...66F}, and in the
     3133comparison between Pan-STARRS and 2MASS \citep{2013ApJS..205...20M}.
     3134The cross-comparison can be used to explicitly constrain the
     3135calibration on one survey based on another, as was done by
     3136\cite{2016ApJ...822...66F} for the SDSS Hypercalibration solution.
     3137Alternatively, the cross-comparison can be used to identified issues
     3138which may be solved by improved internal analysis.  }
     3139
     3140\textadd{The third lesson we have learned is that there is no substitute for
     3141photometric conditions.  The cross-comparison of photometry between
     3142Pan-STARRS and Gaia suggests that the current Pan-STARRS calibration
     3143is limited in part by the excessive contribution of non-photometric
     3144observations.  This can be seen in the elevated scatter in patches
     3145which correspond to single observing blocks (see
     3146Figure~\ref{fig:allsky.photom.sigma} and discussion in
     3147Section~\ref{sec:photcal}).  A future re-analysis of the Pan-STARRS
     3148dataset will attempt to further limit the impact of the
     3149non-photometric data on the photometric calibration.  The other
     3150critical improvement will be to include more data from the continuing
     3151observations to ensure every patch of the sky is covered with
     3152photometric observations.}
     3153
     3154\textadd{Finally, while the systematics are still probably the limiting factor
     3155for the average calibration, for individual measurements of objects,
     3156we believe our current limitations come from a few specific factors.
     3157First, the quality of the aperture corrections, especially in the
     3158ability of the software to avoid extremely deviant results on occasion
     3159appears to be one of the main drivers of bad photometry measurements
     3160for brighter stars.  Second, the quality of the background sky model
     3161currently appears to be the limitation for the faint sources.
     3162Finally, improvements to the PSF model, especially including
     3163color-dependent and non-linear effects such as the brighter-fatter effect
     3164\citep{2014JInst...9C3048A,2015JInst..10C5032G} will probably be
     3165necessary to push the limits of photometric and astrometric accuracy.  }
     3166
     3167\textadd{While there is clearly still room for improvement, the Pan-STARRS
     3168$3\pi$ Survey DR1 and DR2 photometry will be a critical resource for
     3169many years.  We are confident that, in addition to the many science
     3170discoveries enabled by the large and accurate photometry, the
     3171high-quality photometry provided here will save observers countless
     3172hours of telescope time by obviating, or at least greatly reducing,
     3173the need to observe standard stars on a regular basis.}
     3174
     3175%%  USNO-A,B : 0.2 arcsec, 0.3 mag, R ~ 21
     3176%%    https://arxiv.org/pdf/astro-ph/0210694.pdf
     3177%%    https://ui.adsabs.harvard.edu/abs/2003AJ....125..984M/abstract
     3178%%  SuperCOSMOS : 0.2 arcsec, 0.3 mag
     3179%%    http://www-wfau.roe.ac.uk/sss/intro.html
     3180%%    https://ui.adsabs.harvard.edu/abs/2001MNRAS.326.1295H/abstract
     3181%%    https://ui.adsabs.harvard.edu/abs/2001MNRAS.326.1315H/abstract
     3182%%  Hipparcos : XX mas, 0.XX mag
     3183%%    https://ui.adsabs.harvard.edu/abs/1997A%26A...323..620K/abstract
     3184%%    https://ui.adsabs.harvard.edu/abs/1997A%26A...323L..57H/abstract
     3185
     3186% \note{need to add discussion of SDSS, DES, LSST, Gaia}
    30503187
    30513188\acknowledgments
     
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     3274% /data/kukui.1/eugene/cal.paper.images.20190217/kronrepair.sh : full.figure
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