Changeset 39920 for branches/czw_branch/20160809/doc/release.2015/ps1.calibration

Timestamp:

Jan 6, 2017, 11:15:00 AM (10 years ago)

Author:

eugene

Message:

merge changes from trunk (updates to the papers)

Location:

branches/czw_branch/20160809/doc/release.2015/ps1.calibration

Files:

• . (modified) (1 prop)
• Makefile (copied) (copied from trunk/doc/release.2015/ps1.calibration/Makefile )
• arxiv.metadata (copied) (copied from trunk/doc/release.2015/ps1.calibration/arxiv.metadata )
• calibration.tex (modified) (6 diffs)
• pics (copied) (copied from trunk/doc/release.2015/ps1.calibration/pics )

branches/czw_branch/20160809/doc/release.2015/ps1.calibration/calibration.tex

@@ -8 +8 @@
 %\documentclass[preprint2,longabstract]{aastex}
 \RequirePackage{color}
-% \input{astro.sty}
+\RequirePackage{code}
+\input{astro.sty}
 
 % online version may use color, but print version needs b/w
@@ -14 +15 @@
 %\def\plotmode{bw}
 
-%\def\plotext{pdf}
-\def\plotext{ps}
+\def\plotext{pdf}
+%\def\plotext{ps}
 
 %\def\picdir{/home/eugene/chipresid.20140404}
@@ -21 +22 @@
 
 % Pick a terse version of the title here;
-\shorttitle{Pixel Analysis in PS1}
+\shorttitle{PS1 Calibration}
 \shortauthors{E.A. Magnier et al}
 \begin{document}
-\title{Pan-STARRS Pixel Analysis : Source Detection \& Characterization}
+\title{Pan-STARRS Photometric and Astrometric Calibration}
 
 % this is a crude trick to get the order of affiliations right.  These
@@ -31 +32 @@
 % list and (2) re-order the list at the bottom (and comment-out as needed)
 \def\IfA{1}
-\def\CfA{2}
-\def\MPIA{3}
-\def\Princeton{3}
-\def\USNO{4}
-\def\JHU{1}
+\def\LBL{2}
+\def\Hubble{3}
+\def\ITC{4}
+\def\Harvard{5}
+\def\MPIA{6}
+\def\ARI{7}
+\def\Princeton{8}
+\def\DUR{9}
+\def\CfA{10}
 
 % This example has a first author from UH:
 \author{
-Eugene A. Magnier,\altaffilmark{\IfA}
-IPP Team,
-%PS Builder List
+Eugene. A. Magnier,\altaffilmark{\IfA}
+Edward. F. Schlafly,\altaffilmark{\LBL,\Hubble}
+Douglas P. Finkbeiner,\altaffilmark{\ITC,\Harvard}
+J.~L. Tonry,\altaffilmark{\IfA}
+B. Goldman,\altaffilmark{\MPIA}
+S. R\"oser,\altaffilmark{\ARI}
+E. Schilbach,\altaffilmark{\ARI}
+K.~C. Chambers,\altaffilmark{\IfA} 
+H.~A. Flewelling,\altaffilmark{\IfA}
+M. E. Huber,\altaffilmark{\IfA}
+P.~A. Price,\altaffilmark{\Princeton}
+W.~E. Sweeney,\altaffilmark{\IfA}
+C. Z. Waters,\altaffilmark{\IfA}
+% PS1 Builders
+L. Denneau,\altaffilmark{\IfA}
+P. Draper,\altaffilmark{\DUR}
+K. W. Hodapp,\altaffilmark{\IfA}
+R. Jedicke,\altaffilmark{\IfA}
+N. Kaiser,\altaffilmark{\IfA}
+R.-P. Kudritzki,\altaffilmark{\IfA}
+N. Metcalfe,\altaffilmark{\DUR}
+C.~W. Stubbs,\altaffilmark{\CfA}
 % W.~S. Burgett,\altaffilmark{\IfA}
-% K.~C. Chambers,\altaffilmark{\IfA} 
 % T. Grav,\altaffilmark{\IfA}
 % J. N. Heasley,\altaffilmark{\IfA}
-% K. W. Hodapp,\altaffilmark{\IfA}
-% R. Jedicke,\altaffilmark{\IfA}
-% H.~A. Flewelling,\altaffilmark{\IfA}
-% N. Kaiser,\altaffilmark{\IfA}
-% R.-P. Kudritzki,\altaffilmark{\IfA}
 % G. A. Luppino,\altaffilmark{\IfA}
 % R. H. Lupton,\altaffilmark{\Princeton}
@@ -56 +74 @@
 % J.~S. Morgan,\altaffilmark{\IfA}
 % P. M. Onaka,\altaffilmark{\IfA}
-% P.~A. Price,\altaffilmark{\Princeton}
-% W.~E. Sweeney,\altaffilmark{\IfA}
-% C.~W. Stubbs,\altaffilmark{\CfA}
-% J.~L. Tonry, \altaffilmark{\IfA}
-% R. J. Wainscoat,\altaffilmark{\IfA} and 
+R. J. Wainscoat\altaffilmark{\IfA}
 % M. F. Waterson,\altaffilmark{\IfA} 
 } % this bracket terminates author list
 
+\altaffiltext{\IfA}{Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu HI 96822}
+\altaffiltext{\LBL}{Lawrence Berkeley National Laboratory, One Cyclotron Road, Berkeley, CA 94720, USA}
+\altaffiltext{\Hubble}{Hubble Fellow}
+\altaffiltext{\ITC}{Institute for Theory and Computation, Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, MS-51, Cambridge, MA 02138 USA}
+\altaffiltext{\Harvard}{Department of Physics, Harvard University, Cambridge, MA 02138 USA}
+\altaffiltext{\MPIA}{Max Planck Institute for Astronomy, K\"onigstuhl 17, D-69117 Heidelberg, Germany}
+\altaffiltext{\ARI}{Astronomisches Rechen-Institut, Zentrum f\"ur Astronomie der Universit\"at Heidelberg, M\"ochhofstrasse 12-14, D-69120 Heidelberg, Germany}
+\altaffiltext{\Princeton}{Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA}
+\altaffiltext{\DUR}{Department of Physics, Durham University, South Road, Durham DH1 3LE, UK}
+\altaffiltext{\CfA}{Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138}
+
 % The ordering here should be sequential, matching the sequence in the list of authors:
-\altaffiltext{\IfA}{Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu HI 96822}
-% \altaffiltext{\CfA}{Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138}
-% \altaffiltext{\Princeton}{Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA}
 % \altaffiltext{\USNO}{US Naval Observatory, Flagstaff Station, Flagstaff, AZ 86001, USA}
 % \altaffiltext{\JHU}{Department of Physics and Astronomy, Johns Hopkins University, 3400 North Charles Street, Baltimore, MD 21218, USA}
-% \altaffiltext{\MPIA}{Max Planck Institute for Astronomy, K\"onigstuhl 17, D-69117 Heidelberg, Germany}
+
+% \altaffiltext{\Strassborg}{
+
 \begin{abstract}
 
-Lorem ipsum dolor sit amet, consectetur adipiscing elit. Vestibulum
-bibendum nisi id tristique posuere. Duis eu mollis nulla. Maecenas est
-turpis, mattis tempor urna vitae, placerat rhoncus sem. Lorem ipsum
-dolor sit amet, consectetur adipiscing elit. Sed quis velit
-nisl. Aliquam erat volutpat. Cras lacinia, nisl tristique auctor
-molestie, dolor nulla rhoncus purus, ac accumsan nunc nunc ac
-nibh. Maecenas vitae mollis mauris. Ut sollicitudin pulvinar purus,
-eget luctus lorem tincidunt vitae. Vestibulum eu mattis neque. Nulla
-in tortor id urna dapibus gravida a vel leo.
+The Pan-STARRS\,1 $3\pi$ survey has produced photometry and astrometry
+covering the \approx 30,000 square degrees $\delta > -30$\degrees.  
+This article describes the photometric and astrometric calibration of this survey.
 
 \end{abstract}
@@ -88 +106 @@
 \keywords{Surveys:\PSONE }
 
+\section{Introduction}\label{sec:intro}
+
+This is the fifth in a series of seven papers describing the
+Pan-STARRS1 Surveys, the data reduction techiques and the resulting
+data products.  This paper (Paper V) describes the final calibration
+process, and the resulting photometric and astrometric quality.
+
+%Chambers et al. 2017 (Paper I)
+%The Pan-STARRS\,1 Surveys
+\citet[][Paper I]{chambers2017}
+provides an overview of the Pan-STARRS System, the design and
+execution of the Surveys, the resulting image and catalog data
+products, a discussion of the overall data quality and basic
+characteristics, and a brief summary of important results.
+
+%Magnier et al. 2017 (Paper II)
+%Pan-STARRS Data Processing Stages
+\citet[][Paper II]{magnier2017c}
+describes how the various data processing stages are organised and implemented
+in the Imaging Processing Pipeline (IPP), including details of the 
+the processing database which is a critical element in the IPP infrastructure . 
+
+%Waters et al. 2017 (Paper III) 
+%Pan-STARRS Pixel Processing : Detrending, Warping, Stacking
+\citet[][Paper III]{waters2017}
+describes the details of the pixel processing algorithms, including detrending, warping, and adding (to create stacked images) and subtracting (to create difference images) and resulting image products and their properties. 
+
+
+%Magnier et al. 2017 (Paper IV) 
+%Pan-STARRS Pixel Analysis : Source Detection 
+\citet[][Paper IV]{magnier2017a}
+describes the details of the source detection and photometry, including point-spread-function and extended source fitting models, and the techniques for ``forced" photometry measurements. 
+
+%Magnier et al. 2017 (Paper V) 
+%Pan-STARRS Photometric and Astrometric Calibration
+%\citet[][Paper V]{magnier2017b}
+%describes the final calibration process, and the resulting photometric and astrometric quality.  
+
+
+%Flewelling et al. 2017 (Paper VI)
+%Pan-STARRS 1 Database and Data Products
+\citet[][Paper VI]{flewelling2017}
+describes  the details of the resulting catalog data and its organization in the Pan-STARRS database. 
+%
+%
+\citet[][Paper VII]{huber2017}
+%Huber et al. 2017 (Paper VII)
+describes the Medium Deep Survey in detail, including the unique issues and data products specific to that survey. The Medium Deep Survey is not part of Data Release 1. (DR1) 
+
+%
+The Pan-STARRS1 filters and photometric system have already been
+described in detail in \cite{2012ApJ...750...99T}.
+
+{\color{red} {\em Note: These papers are being placed on arXiv.org to
+    provide crucial support information at the time of the public
+    release of Data Release 1 (DR1). We expect the arXiv versions to
+    be updated prior to submission to the Astrophysical Journal in
+    January 2017. Feedback and suggestions for additional information
+    from early users of the data products are welcome during the
+    submission and refereeing process.}}
+
+\section{Pan-STARRS\,1} 
+
+From May 2010 through March 2014, the Pan-STARRS Science Consortium
+used the 1.8m \PSONE\ telescope to perform a set of wide-field science
+surveys.  These surveys are designed to address a range of science
+goals included the search for hazardous asteroids, the study of the
+formation and architecture of the Milky Way galaxy, and the search for
+Type Ia supernovae to measure the history of the expansion of the
+universe.  
+
+The wide-field \PSONE\ telescope consists of a 1.8~meter diameter
+$f$/4.4 primary mirror with an 0.9~m secondary, producing a 3.3 degree
+field of view \citep{2004SPIE.5489..667H}.  The optical design yields
+low distortion and minimal vignetting even at the edges of the
+illuminated region.  The optics, in combination with the natural
+seeing, result in generally good image quality: the median image
+quality for the 3$\pi$ survey is FWHM = (1.31, 1.19, 1.11, 1.07, 1.02)
+arcseconds for (\grizy), with a floor of $\sim0.7$ arcseconds.  The
+\PSONE\ camera \citep{2009amos.confE..40T} is a mosaic of 60
+edge-abutted $4800\times4800$ pixel back-illuminated CCID58 Orthogonal
+Transfer Arrays manufactured by Lincoln Laboratory
+\citep{2006amos.confE..47T,2008SPIE.7021E..05T}.  The CCDs have
+10~$\mu$m pixels subtending 0.258~arcsec and are 70$\mu$m thick.  The
+detectors are read out using a StarGrasp CCD controller, with a
+readout time of 7 seconds for a full unbinned image
+\citep{2008SPIE.7014E..0DO}.  The active, usable pixels cover $\sim
+80$\% of the FOV.
+
+Nightly observations are conducted remotely from the Advanced
+Technology Research Center in Kula, the main facility of the
+University of Hawaii's Institute for Astronomy operations on Maui.
+During the \PSONE\ Science Survey, images obtained by the
+\PSONE\ system were stored first on computers at the summit, then
+copied with low latency via internet to the dedicated data analysis
+cluster located at the Maui High Performance Computer Center in Kihei,
+Maui.
+
+Images obtained by \PSONE\ are automatically processed in real time by
+the \PSONE\ Image Processing Pipeline \citep[IPP,][]{magnier2017a}.
+Real-time analysis goals are aimed at feeding the discovery pipelines
+of the asteroid search and supernova search teams.  The data obtained
+for the \PSONE\ Science Survey has also been used in three additional
+complete re-processing of the data: Processing Versions 1, 2, and 3
+(PV1, PV2, and PV3).  The real-time processing of the data is
+considered ``PV0''.  Except as otherwise noted, the PV3 analysis of
+the data is used for the purpose of this article.
+
+The data processing steps are described in detail by \cite{waters2017}
+and \cite{magnier2017a,magnier2017b}.  In summary, individual images
+are detrended: non-linearity and bias corrections are applied, a dark
+current model is subtracted and flat-field corrections are applied.
+The \yps-band images are also corrected for fringing: a master fringe
+pattern is scaled to match the observed fringing and subtracted.  Mask
+and variance image arrays are generated with the detrend analysis and
+carried forward at each stage of the IPP processing.  Source detection
+and photometry are performed for each chip independently.  As
+discussed below, preliminary astrometric and photometric calibrations
+are performed for all chips in a single exposure in a single analysis.
+
+Chip images are geometrically transformed based on the astrometric
+solution into a set of pre-defined pixel grids covering the sky,
+called skycells.  These transformed images are called the warp images.
+Sets of warps for a given part of the sky and in the same filter may
+be added together to generate deeper `stack' images.  PSF-matched
+difference images are generated from combinations of warps and stacks;
+the details of the difference images and their calibration are outside
+of the scope of this article.
+
+% Individual warp images are differenced during the nightly processing
+% to detect the fast moving asteroids.  Stacks are subtracted from
+% individual warps, and deep stacks are subtracted from stack generated
+% from images for a single night (nightly stacks).  
+
+Astronomical objects are detected and characterized in the stacks
+images.  The details of the analysis of the sources in the stack
+images are discussed in \cite{magnier2017b}, but in brief these include
+PSF photometry, along with a range of measurements driven by the goals
+of understanding the galaxies in the images.  Because of the
+significant mask fraction of the GPC1 focal plane, and the varying
+image quality both within and between exposures, the effective PSF of
+the PS1 stack images is highly variable.  The PSF varies significantly
+on scales as small as a few to tens of pixels, making accurate PSF
+modelling essentially infeasible.  The PSF photometry of sources in
+the stack images is thus degraded significantly compared to the
+quality of the photometry measured for the individual chip images.  
+
+To recover most of the photometric quality of the individual chip
+images, while also exploiting the depth afforded by the stacks, the
+PV3 analysis make use of forced photometry on the individual warp
+images.  PSF photometry is measured on the warp images for all sources
+which are detected in the stack images images.  The positions
+determined in the stack images are used in the warp images, but the
+PSF model is determined for each warp independently based on brighter
+stars in the warp image.  The only free parameter for each object is
+the flux, which may be insignificant or even negative for sources
+which are near the faint limit of the stack detections.  When the
+fluxes from the individual warp images are averaged, a reliable
+measurement of the faint source flux is determined.  The details of
+this analysis are described in detail in Magnier et al
+\cite{magnier2017b}.
+
+In this article, we discuss the photometric calibration of the
+individual exposures, the stacks, and the warp imags.  We also discuss
+the astrometric calibration of the individual exposures and the stack
+images.
+
+\section{Astrometric Models} 
+
+% \note{include projection math?}  
+% \note{reference discussion somewhere on cell vs chip}
+
+Three somewhat distinct astrometric models are employed within the IPP
+at different stages.  The simplest model is defined independently for
+each chip: a simple TAN projection as described by
+\cite{2002AA...395.1077C} is used to relate sky coordinates to a
+cartesian tangent-plane coordinate system.  A pair of low-order
+polynomials are used to relate the chip pixel coordinates to this
+tangent-plane coordinate system.  The transforming polynomials are of
+the form:
+\begin{eqnarray}
+P & = & \sum_{i,j} C^P_{i,j} X^i_{\rm chip} Y^j_{\rm chip} \\
+Q & = & \sum_{i,j} C^Q_{i,j} X^i_{\rm chip} Y^j_{\rm chip}
+\end{eqnarray}
+where $P,Q$ are the tangent plane coordinates, $X_{\rm chip}, Y_{\rm
+  chip}$ are the coordinates on the 60 GPC1 chips, and $C^P_{i,j}, C^Q_{i,j}$
+are the polynomial coefficients for each order.  In the \code{psastro}
+analysis, $i + j <= N_{\rm order}$ where the order of the fit, $N_{\rm
+  order}$, may be 1 to 3, under the restriction that sufficient stars
+are needed to constrain the order.  
+
+% \note{describe a bit better: this is automatically selected based on the number of stars}
+
+A second form of astrometry model which yields somewhat higher
+accuracy consists of a set of connected solutions for all chips in a
+single exposure.  This model also uses a TAN projection to relate the
+sky coordinates to a locally cartesian tangent plane coordinate system.
+A set of polynomials is then used to relate the tangent plane
+coordinates to a 'focal plane' coordinate system, $L,M$:
+\begin{eqnarray}
+P & = & \sum_{i,j} C^P_{i,j} L^i M^j \\
+Q & = & \sum_{i,j} C^Q_{i,j} L^i M^j
+\end{eqnarray}
+This set of polynomial accounts for effects such as optical distortion
+in the camera and distortions due to changing atmospheric refraction
+across the field of the camera.  Since these effects are smooth across
+the field of the camera, a single pair of polynomials can be used for
+each exposure.  Like in the chip analysis about, the \code{psastro}
+code restricts the exponents with the rule $i + j <= N_{\rm order}$
+where the order of the fit, $N_{\rm order}$, may be 1 to 3, under the
+restriction that sufficient stars are needed to constrain the order
+For each chip, a second set of polynomials describes the
+transformation from the chip coordinate systems to the focal
+coordinate system:
+\begin{eqnarray}
+L & = & \sum_{i,j} C^L_{i,j} X^i_{\rm chip} Y^j_{\rm chip} \\
+M & = & \sum_{i,j} C^M_{i,j} X^i_{\rm chip} Y^j_{\rm chip}
+\end{eqnarray}
+
+A third form of the astrometry model is used in the context of the
+calibration determined within the DVO database system.  We retain the
+two levels of transformations (chip $\rightarrow$ focal plane $\rightarrow$
+tangent plane), but the relationship between the chip and focal plane
+is represented with only the linear terms in the polynomial,
+supplemented by a course grid of displacements, $\delta L, \delta M$ sampled
+across the coordinate range
+of the chip.  This displacement grid may have a resolution of up to
+$6\times6$ samples across the chip.  The displacement for a specific
+chip coordinate value is determined via bilinear interpolation between
+the nearest sample points.  Thus, the chip to focal-plane
+transformation may be written as:
+\begin{eqnarray}
+  L & = & C^L_{0,0} + C^L_{1,0} X_{\rm chip} + C^L_{0,1} Y_{\rm chip} + \delta L(X_{\rm chip}, Y_{\rm chip}) \\
+  M & = & C^M_{0,0} + C^M_{1,0} X_{\rm chip} + C^M_{0,1} Y_{\rm chip} + \delta M(X_{\rm chip}, Y_{\rm chip}) 
+\end{eqnarray}
+
+{\bf WCS Keywords} When this polynomial representation is written to
+the output files, a set of WCS keywords are used to define the
+astrometric transformation elements.  It is necessary to transform the
+simply polynomials above into an alternate form:
+\begin{eqnarray}
+  P & = & \sum_{i,j} C^P_{i,j} (X_{\rm chip} - X_0)^i (Y_{\rm chip} - Y_0)^j \\
+  Q & = & \sum_{i,j} C^Q_{i,j} (X_{\rm chip} - X_0)^i (Y_{\rm chip} - Y_0)^j 
+\end{eqnarray}
+
+%% \note{need to complete this discussion of the WCS keywords, both
+%%   standard and non-standard, used to represent these polynomial
+%%   transformations}
+
+%% \begin{verbatim}
+%% Here is a list of the keywords 
+%% and the related terms from Eqns above:
+%% CTYPE1,2 : RA---WRP, DEC--WRP
+%% CTYPE1,2 : RA---DIS, DEC--DIS
+%% CRVAL1,2 : C^{L,M}_{0,0}
+%% CRPIX1,2 : X_0, Y_0
+%% PC001001 : C^{L}_{1,0}
+%% PC001002 : C^{L}_{0,1}
+%% PC002001 : C^{M}_{1,0}
+%% PC002002 : C^{M}_{0,1}
+%% PCA1XiYj : C^{L}_{i,j}
+%% PCA2XiYj : C^{M}_{i,j}
+%% \end{verbatim}
+
+\section{Real-time Calibration}
+
+\subsection{Overview}
+
+As images are processed by the data analysis system, every exposure is
+calibrated individually with respect to a photometric and astrometric
+database.  The goal of this calibration step is to generate a preliminary
+astrometric calibration, to be used by the warping analysis to determine
+the geometric transformation of the pixels, and preliminary
+photometric transformation, to be used by the stacking analysis to
+ensure the warps are combined using consistent flux units.
+
+The program used for the real-time calibration, \code{psastro}, loads
+the measurements of the chip detections from their individual
+\code{cmf}-format files.  It uses the header information populated at
+the telescope to determine an initial astrometric calibration guess
+based on the position of the telescope boresite right ascension,
+declination and position angle as reported by the telescope \& camera
+subsystems.  Using the initial guess, \code{psastro} loads astrometric
+and photometric data from the reference database.  
+
+\subsection{Reference Catalogs}
+
+During the course of the PS1SC Survey, several reference databases
+have been used.  For the first 20 months of the survey, \code{psastro}
+used a reference catalog with synthetic PS1 \grizy\ photometry
+generated by the Pan-STARRS IPP team based on based combined
+photometry from Tycho (B, V), USNO (red, blue, IR), and 2MASS $J, H,
+K$.  The astrometry in the database was from 2MASS.  After 2012 May, a
+reference catalog generated from internal re-calibration of the PV0
+analysis of PS1 photometry and astrometry was used for the reference
+catalog.  
+
+% \note{discuss history of the different refcats?}  
+
+Coordinates and calibrated magnitudes of stars from the reference
+database are loaded by \code{pasastro}.  A model for the positions of
+the 60 chips in the focal plane is used to determine the expected
+astrometry for each chip based on the boresite coordinates and
+position angle reported by the header.  Reference stars are selected
+from the full field of view of the GPC1 camera, padded by an
+additional 25\% to ensure a match can be determined even in the
+presence of substantial errors in the boresite coordinates.  It is
+important to choose an appropriate set of reference stars: if too few
+are selected, the chance of finding a match between the reference and
+observed stars is diminished.  In addition, since stars are loaded in
+brightness order, a selection which is too small is likely to contain
+only stars which are saturated in the GPC1 images.  On the other hand,
+if too many reference stars are chosen, there is a higher chance of a
+false-positive match, especially as many of the reference stars may
+not be detected in the GPC1 image.  The seletion of the reference
+stars includes a limit on the brightest and fainted magnitude of the
+stars selected.
+
+The astrometric analysis is necessarily performed first; after the
+astrometry is determined, an automatic byproduct is a reliable match
+between reference and observed stars, allowing a comparison of the
+magnitudes to determine the photometric calibration.  
+
+The astrometric calibration is performed in two major stages: first,
+the chips are fitted independently with independent models for each
+chip.  This fit is sufficient to ensure a reliable match between
+reference stars and observed sources in the image.  Next, the set of
+chip calibrations are used to define the transformation between the
+focal plane coordinate system and the tangent plane coordinate
+system.  The chip-to-focal plane transformations are then determined
+under the single common focal plane to tangent plane transformation.  
+
+\subsection{Cross-Correlation Search}
+
+The first step of the analysis is to attempt to find the match between
+the reference stars and the detected objects.  \code{psastro} uses 2D
+cross correlation to search for the match.  The guess astrometry
+calibration is used to define a predicted set of $X^{\rm ref}_{\rm
+  chip}, Y^{\rm ref}_{\rm chip}$ values for the reference catalog
+stars.  For all possible pairs between the two lists, the values of
+\begin{eqnarray}
+\Delta X & = & X^{\rm ref}_{\rm chip} - X^{\rm obs}_{\rm chip}\\
+\Delta Y & = & Y^{\rm ref}_{\rm chip} - Y^{\rm obs}_{\rm chip}
+\end{eqnarray}
+are generated.  The collection of $\Delta X, \Delta Y$ values are
+collected in a 2D histogram with sampling of 50 pixels and the
+peak pixel is identified.  If the astrometry guess were perfect, this
+peak pixel would be expected to lie at (0,0) and contain all of the
+matched stars.  However, the astrometric guess may be wrong in
+several ways.  An error in the constant term above, $C^P_{0,0},
+C^Q_{0,0}$ shifts the peak to another pixel, from which $C^P_{0,0},
+C^Q_{0,0}$ can easily be determined.  An error in the plate scale or a
+rotation will smear out the peak pixel potentially across many pixels
+in the 2D histogram.  
+
+To find a good match in the face of plate scale and rotation errors,
+the cross correlation analysis above is performed for a series of
+trials in which the scale and rotation are perturbed from the nominal
+value by a small amount.  For each trial, the peak pixel is found and
+a figure of merit is measured.  The figure of merit is defined as
+$\frac{\sigma^2_x + \sigma^2_y}{N_p^4}$ where $\sigma^2_{x,y}$ are the
+second moment of $\Delta X,Y$ for the star pairs associated with the
+peak pixel, and $N_p$ is the number of star pairs in the peak.  This
+figure of merit is thus most sensitive to a narrow distribution with
+many matched pairs.  For the PS1 exposures, rotation offsets of (-1.0,
+-0.5, 0.0, 0.5, 1.0) degrees, and plate scales of (+1\%, 0, -1\%) of
+the nominal plate scale are tested.  The best match among these 15
+cross-correlation tests is selected and used to generate a better
+astrometry guess for the chip.
+
+%% \note{option to downweight based on photometric inconsistency : not used in PS1 analysis}
+
+\subsection{Chip Polynomial Fits}
+
+The astrometry solution from the cross correlation step above is again
+used to selected matches between the reference stars and observed
+stars in the image.  The matching radius starts off quite large, and a
+series of fits is performed to generate the transformation between
+chip and tangent plane coordinates.  Three clipping iterations are
+performed, with outliers $> 3 \sigma$ rejected on each pass, where
+here $\sigma$ is determined from the distribution of the residuals in
+each dimension (X,Y) independently.  After each fit cycle, the matches
+are redetermined using a smaller radius and the fit re-tried.  
+
+\subsection{Mosaic Astrometry Polynomial Fits}
+
+The astrometry solutions from the independent chip fits are used to
+generate a single model for the camera-wide distortion terms.  The
+goal is to determine the two stage fit (chip $\rightarrow$ focal plane
+$\rightarrow$ tangent plane).  There are a number of degenerate terms
+between these two levels of transformation, most obviously between the
+parameters which define the constant offset from chip to focal plane
+($C^{L,M}_{0,0}$) and those which define the offset from focal plane
+to tangent plane ($C^{P,Q}_{0,0}$).  We limit ($C^{P,Q}_{0,0}$) to be
+0,0 to remove this degeneracy.  
+
+The initial fit of the astrometry for each chip follows the distortion
+introduced by the camera: the apparent plate scale for each chip is
+the combination of the plate scale at the optical axis of the camera,
+modified by the local average distortion.  To isolate the effect of
+distortion, we choose a single common plate scale for the set of chips
+and re-define the chip $\rightarrow$ sky calibrations as a set of chip
+$\rightarrow$ focal plane transformation using that common pixel
+scale.  We can now compare the observed focal plane coordinates,
+derived from the chip coordinates, and the tangent plane coordiantes,
+derived from the projection of the reference coordinates.  One caveat
+is that the chip reference coordinates are also degenerate with the
+fitted distortion.  In order to avoid being sensitive to the exact
+positions of the chips at this stage, we measure the local gradient
+between the focal plane and tangent plane coordinate systems.  We then
+fit the gradient with a polynomial of order 1 less than the polynomial
+desired for the distortion fit.  The coefficients of the gradient fit
+are then used to determine the coefficients for the polynomials
+representing the distortion.  
+
+%% \note{write out the math of the gradients}
+
+Once the common distortion coming from the optics and atmosphere have
+been modeled, \code{psastro} determines polynomial transformations
+from the 60 chips to the focal plane coordinate system.  In this
+stage, 5 iterations of the chip fits are performed.  Before each
+iteration, the reference stars and detected objects are matched using
+the current best set of transformations.  These fits start with low
+order (1) and large matching radius.  As the iterations proceed, the
+radius is reduced and the order is allowed to increaes, up to 3rd
+order for the final iterations.  
+
+%% \note{quality of the fits as a result of this stage}.
+
+\subsection{Real-time Photometric Calibration}
+
+%% \note{define / describe the robust median}
+
+After the astrometric calibration has finished, the photometric
+calibration is performed by \code{psastro}.  When the reference stars
+are loaded, the apparent magnitude in the filter of interest is also
+loaded.  Stars for which the reference magnitude is brighter than
+(\grizy) = (19, 19, 18.5, 18.5, 17.5) are used to determine the zero
+points by comparison with the instrumental magnitudes.  For the PV3
+analysis, an outlier-rejecting median is used to measure the zero
+point. For early versions of the analysis, when the reference catalog
+used synthetic magnitudes, it was necessary to search for the blue
+edge of the distribution: the synthetic magnitude poorly predicted the
+magnitudes of stars in the presence of significant extinction or for
+the very red stars, making the blue edge somewhat more reliable.  Note
+that we do not include an airmass correction in this zero point
+analysis: the airmass correction is folded into the observed zero
+point.  The zero point may be measured separately for each chip or as
+a single value for the entire exposure; the latter option was used for
+the PV3 analysis.
+
+\subsection{Real-time outputs}
+
+The calibrations determined by \code{psastro} as saved as part of the
+header information in the output FITS tables.  A single
+multi-extension FITS table is written using the \code{smf} format.  In
+these files, the measurements from each chip are written as a separate
+FITS table.  A second FITS extension for each chip is used to store
+the header information from the original chip image.  The original
+chip header is modified so that the extension corresponds to an image
+with no pixels data: \code{NAXIS} is set to 0, even though
+\code{NAXIS1} and \code{NAXIS2} are retained with the original
+dimensions of the chip.  A pixel-less primary header unit (PHU) is
+generated with a summary of some of the important and common
+chip-level keywords (e.g., \code{DATE-OBS}).  The astrometric
+transformation information for each chip is saved in the corresponding
+header using standard (and some non-standard) WCS keywords.  For the
+two-level astrometric model, the PHU header carries the astrometric
+transformation related to the projection and the camera-wide
+distortions.  Photometric calibrations are written as a set of
+keywords to individual chip headers, and if the calibration is
+performed at the exposure-level, to the PHU.  The photometry
+calibration keywords are:
+\begin{itemize}
+\item \code{ZPT_REF} : the nominal zero point for this filter
+\item \code{ZPT_OBS} : the measured zero point for this chip /
+  exposure
+\item \code{ZPT_ERR} : the measured error on \code{ZPT_OBS}
+\item \code{ZPT_NREF} : the number of stars used to measure \code{ZPT_OBS}
+\item \code{ZPT_MIN} : minimum reference magnitude included in analysis
+\item \code{ZPT_MAX} : maximum reference magnitude included in analysis
+\end{itemize}
+The keyword \code{ZPT_OBS} is used to set the initial zero point when
+the data from the exposure are loaded into the DVO database.
+
+\section{PV3 DVO Master Database}
+
+Data from the GPC1 chip images, the stack images, and the warp images
+are loaded into DVO using the real-time analysis astrometric
+calibration to guide the association of detections into objects.
+After the full PV3 DVO database was constructed, including all of the
+chip, stack, and warp detections, several external catalogs were
+merged into the database.  First, the complete 2MASS PSC was loaded
+into a stand-alone DVO database, which was then merged into the PV3
+master database.  Next the DVO database of synthetic photometry in the
+PS1 bands (see Section~\ref{sec:synthdb}) was merged in.  Next, the
+full Tycho database was added, followed by the AllWISE database.
+After the Gaia release in August 2016 \citep{2016AA...595A...2G}, we
+generated a DVO database of the Gaia positional and photometric
+information and merged that into the master DVO database.
+
+%% \note{need to describe the assignment of flags, etc, for the external data sources}.
+
+\section{Photometry Calibration}
+
+\subsection{Ubercal Analysis}
+
+% \note{clean up and re-word the pieces below}
+
+The photometric calibration of the DVO database starts with the
+``ubercal'' analysis technique as described by
+\cite{2012ApJ...756..158S}.  This analysis is performed by the group
+at Harvard, loading data from the \code{smf} files into their instance
+of the Large Scale Database \citep[LSD,][]{2011AAS...21743319J}, a
+system similar to DVO used to manage the detections and determine the
+calibrations.
+
+Photometric nights are selected and all other exposures are ignored.
+Each night is allowed to have a single fitted zero point and a single
+fitted value for the airmass extinction coefficient per filter.  The
+zero points and extinction terms are determined as a least squares
+minimization process using the repeated measurements of the same stars
+from different nights to tie nights together.  Flat-field corrections
+are also determined as part of the minimization process.  In the
+original (PV1) ubercal analysis, \cite{2012ApJ...756..158S} determined
+flat-field corrections for $2\times 2$ sub-regions of each chip in the
+camera and four distinct time periods (``seasons'').  Later analysis
+(PV2) used an $8\times8$ grid of flat-field corrections to good
+effect.
+
+The ubercal analysis was re-run for PV3 by the Harvard group.  For the
+PV3 analysis, under the pressure of time to complete the analysis, we
+chose to use only a $2\times 2$ grid per chip as part of the ubercal
+fit and to leave higher frequency structures to the later analysis.  A
+5th flat-field season consisting of nearly the last 2 years of data
+was also included for PV3.  In retrospect, as we show below, the data
+from the latter part of the survey would probably benefit from
+additional flat-field seasons. 
+
+%% \note{something for PV4}.
+
+By excluding non-photometric data and only fitting 2 parameters for
+each night, the Ubercal solution is robust and rigid.  It is not
+subject to unexpected drift or sensitivity of the solution to the
+vagaries of the data set.  The Ubercal analysis is also especially
+aided by the inclusion of multiple Medium Deep field observations
+every night, helping to tie down overall variations of the system
+throughput and acting as internal standard star fields.  The resulting
+photometric system is shown by \cite{2012ApJ...756..158S} to have reliability
+across the survey region at the level of (8.0, 7.0, 9.0, 10.7, 12.4)
+millimags in (\grizy).  As we discuss below, this conclusion is
+reinforced by our external comparison.  
+
+%% \note{do I have a measurement
+%% of the bright end stability in PV3?  basically, what is the scatter
+%% per star as a function of position in the camera and magnitude?}
+
+The overall zero point for each filter is not naturally determined by
+the Ubercal analysis; an external constraint on the overall
+photometric system is required for each filter.
+\cite{2012ApJ...756..158S} used photometry of the MD09 Medium Deep
+field to match the photometry measured by \cite{2012ApJ...750...99T}
+on the reference photometric night of MJD 55744 (UT 02 July 2011).
+\cite{2014ApJ...795...45S} and \cite{2015ApJ...815..117S} have
+re-examined the photometry of Calspec standards %% XXX FIX: \citep{Bohlin.1996} as
+observed by PS1.  \cite{2014ApJ...795...45S} reject 2 of the 7 stars
+used by \cite{2012ApJ...750...99T} and add photometry of 5 additional
+stars.  \cite{2015ApJ...815..117S} further reject measurements of
+Calspec standards obtained close to the center of the camera field of
+view where the PSF size and shape changes very rapidly.  The result of
+this analysis modifies the over system zero points by 20 - 35
+millimags compared with the system determined by
+\cite{2012ApJ...756..158S}.
+
+%% \note{The calspec spectrophotometry values have also been re-examined
+%%   by REF; using these new measurements, \cite{2015ApJ...815..117S}
+%%   determine new zero points for the PS1 system, which we have applied
+%%   (see below).}
+
+% http://iopscience.iop.org/article/10.1088/0004-637X/815/2/117/pdf
+
+\subsection{Applying the Ubercal Zero Points : Setphot}
+
+The ubercal analysis above results in a table of zero points for all
+exposures considered to be photometric, along with a set of
+low-resolution flat-field corrections.  It is now necessary to use this
+information to determine zero points for the remaining exposures and
+to improve the resolution of the flat-field correction.  This analysis
+is done within the IPP DVO database system.
+
+The ubercal zero points and the flat-field correction data are loaded
+into the PV3 DVO database using the program \code{setphot}.  This
+program converts the reported zero point and flat field values to the
+DVO internal representation in which the zero point of each image is
+split into three main components:
+\[ 
+zp_{\rm total} = zp_{\rm nominal} + M_{cal} + K_{rm \lambda}(sec \zeta - 1)
+\]
+where $zp_{\rm nominal}$ and $K_{rm \lambda}$ are static values for
+each filter representing respectively the nominal zero point and the
+slope of the trend with respect to the airmass ($\zeta$) for each
+filter.  These static values are listed in Table~\ref{tab:zpts}.  When
+\code{setphot} was run, these static zero points have been adjusted by
+the Calspec offsets listed in Table~\ref{tab:zpts} based on the
+analysis of Calspec standards by \cite{2015ApJ...815..117S}.  These
+offsets bring the photometric system defined by the ubercal analysis
+into alignment with \cite{2015ApJ...815..117S}.  The value $M_{cal}$
+is the offset needed by each exposure to match the ubercal value, or
+to bring the non-ubercal exposures into agreement with the rest of the
+exposures, as discussed below.  The flat-field information is encoded
+in a table of flat-field offsets as a function of time, filter, and
+camera position.  Each image which is part of the ubercal subset is
+marked with a bit in the field \code{Image.flags}:
+\code{ID_IMAGE_PHOTOM_UBERCAL = 0x00000200}
+
+%% \note{give airmass formula for completeness?}.
+
+When \code{setphot} applies the ubercal information to the image
+tables, it also updates the individual measurements associated with
+those images.  In the DVO database schema, the normalized instrumental
+magnitude, $M_{\rm inst} = -2.5log_{10} (DN / sec) + 25.0$ are stored
+for each measurement.  The value of 25.0 is an arbitrary (but fixed)
+constant offset to place the instrumental magnitudes into
+approximately the correct range.  Associated with each measurement are
+two correction magnitudes: $M_{\rm cal}$ and $M_{\rm flat}$, along
+with the airmass for the measurement, calculated using the altitude of
+the individual detection as determined from the Right Ascension,
+Declination, the observatory latitude, and the sidereal time.  For a
+camera with the field of view of the PS1 GPC1, the airmass may vary
+significantly within the field of view, especially at low elevations.
+In the worst cases, at the celestial pole, the airmass range within a
+single exposure is XXX - XXX.  The complete calibrated (`relative')
+magnitude is determined from the stored database values as:
+\[
+M_{\rm rel} = M_{\rm inst} - 25.0 + zp_{\rm ref} + M_{\rm cal} + M_{\rm flat} + K_\lambda (sec \zeta - 1).
+\]
+The calibration offsets, $M_{\rm cal}$ and $M_{\rm flat}$, represent
+the per-exposure zero point correction and the slowly-changing
+flat-field correction respectively.  These two values are split so the
+flat-field corrections may be determined and applied independently
+from the time-resolved zero point variations.  Note that the above
+corrections are applied to each of the types of measurements stored in
+the database, PSF, Aperture, Kron.  The calibration math remains the
+same regardless of the kind of magnitude being measured.  Also note
+that for the moment, this discussion should only be considered as
+relevant to the chip measurements.  Below we discuss the implications
+for the stack and warp measurements.
+
+When the ubercal zero points and flat-field data are loaded,
+\code{setphot} updates the $M_{\rm cal}$ values for all measurements
+which have been derived from the ubercal images.  These measurements
+are also marked in the field \code{Measure.dbFlags} with the bit
+\code{ID_MEAS_PHOTOM_UBERCAL = 0x00008000}.  At this stage,
+\code{setphot} also updates the values of $M_{\rm flat}$ for all GPC1
+measurements in the appropriate filters.
+
+\subsection{Relphot Analysis}
+
+%% \note{how many exposures are not in ubercal?}
+
+Relative photometry is used to determine the zero points of the
+exposures which were not included in the ubercal analysis.  The
+relative photometry analysis has been described in the past by
+\cite{2013ApJS..205...20M}.  We review that analysis here, along with
+specific updates for PV3.
+
+As described above, the instrumental magnitude and the calibrated magnitude
+are related by arithmetic magnitude offsets which account for effects
+such as the instrumental variations and atmospheric attenuation.  
+\[
+M_{rel} = m_{inst} + ZP + M_{cal}
+\]
+
+From the collection of measurements, we can generate an average
+magnitude for a single star (or other object):
+\[ M_{ave} = \frac{\sum_i M_{rel,i} w_i}{\sum_i w_i} \]
+We find that the color difference of the different chips can be
+ignored, and set the value of $A$ to 0.0.
+Note that we only use a single mean airmass extinction term for all
+exposures -- the difference between the mean and the specific value
+for a given night is taken up as an additional element of the
+atmospheric attenuation.
+
+%% \note{color-color terms between chips?}
+
+We write a global $\chi^2$ equation which we attempt to minimize by
+finding the best mean magnitudes for all objects and the best
+$M_{\rm cal}$ offset for each exposure:
+\[ \chi^2 = \sum_{i,j} (m_{inst}[i,j] + ZP + K \zeta + M_{clouds}[i] - M_{ave}[j]) w_{i,j} / \sum_{i,j} w_{i,j} \]
+
+If everything were fitted at once and allowed to float, this system of
+equations would have $N_{exposures} + N_{stars} \sim 2 \times 10^5 + N
+\times 10^9$ unknowns.  We solve the system of equations by iteration,
+solving first for the best set of mean magnitudes in the assumption of
+zero clouds, then solving for the clouds implied by the differences
+from these mean magnitudes.  Even with 1-2 magnitudes of extinction,
+the offsets converge to the milli-magnitude level within 8 iterations.
+
+Only brighter, high quality measurements are used in the relative
+photometry analysis of the exposure zero points.  We use only the
+brighter objects, limiting the density to a maximum of 4000 objects
+per square degree (lower in areas where we have more observations).
+When limiting the density, we prefer objects which are brighter (but
+not saturated), and those with the most measurements (to ensure better
+coverage over the available images).
+
+There are a few classes of outliers which we need to be careful to
+detect and avoid.  First, any single measurement may be deviant for a
+number of reasons (e.g., it lands in a bad region of the detector,
+contamination by a diffraction spike or other optical artifact, etc).
+We attempt to exclude these poor measurements in advance by rejecting
+measurements which the photometric analysis has flagged the result as
+suspcious.  We reject detections which are excessively masked; these include
+detections which are too close to other bright objects, diffraction
+spikes, ghost images, or the detector edges.  However, these
+rejections do not catch all cases of bad measurements.
+
+%% \citep[\code{PSF_QF} $< 0.85$, see][]{magnier2017b}; 
+%% \note{refer to the PSPHOT bad and poor psphot bits?}  
+
+After the initial iterations, we also perform outlier rejections based
+on the consistency of the measurements.  For each star, we use a two
+pass outlier clipping process.  We first define a robust median and
+sigma from the inner 50\% of the measurements.  Measurements which are
+more than 5$\sigma$ from this median value are rejected, and the mean
+\& standard deviation (weighted by the inverse error) are
+recalculated.  We then reject detections which are more than 3$\sigma$
+from the recalculated mean.  
+
+Suspicious stars are also exclude from the analsis.  We exclude stars
+with reduced $\chi^2$ values more than 20.0, or more than 2$\times$
+the median, whichever is larger.  We also exclude stars with standard
+deviation (of the measurements used for the mean) greater than 0.005
+mags or 2$\times$ the median standard deviation, whichever is greater.
+
+%% \note{is this true?} 
+
+Similarly for images, we exclude those with more than 2 magnitudes of
+extinction or for which the deviation greater of the zero points per
+star are than 0.075 mags or 2$\times$ the median value, whichever is
+greater.  These cuts are somewhat conservative to limit us to only
+good measurements.  The images and stars rejected above are not used
+to calculate the system of zero points and mean magnitudes.  These
+cuts are updated several times as the iterations proceed.  After the
+iterations have completed, the images which have been reject are
+calibrated based on their overlaps with other images.
+
+We overweight the ubercal measurements in order to tie the relative
+photometry system to the ubercal zero points.  Ubercal images and
+measurements from those images are not allowed to float in the
+relative photometry analysis.  Detections from the Ubercal images are
+assigned weights of 10x their default (inverse-variance) weight.  The
+calculation of the formal error on the mean magnitudes propagates this
+additional weight, so that the errors on the Ubercal observations
+dominates where they are present. 
+
+% \note{do we drop this when calculating the final mean mags?}
+% \note{do I need to present the math?}
+\[ \mu = \frac{\sum m_i w_i \sigma_i^{-2}}{\sum w_i \sigma_i^{-2}} \]
+\[ \sigma_\mu = \frac{\sum w_i^2 \sigma_i^{-2}}{(\sum w_i \sigma_i^{-2})^2} \]
+
+The calculation of the relative photometry zero points is performed
+for the entire $3\pi$ data set in a single, highly parallelized
+analysis.  As discussed above, the measurement and object data in the
+DVO database are distributed across a large number of computers in the
+IPP cluster: for PV3, 100 parallel hosts are used.  These machines by
+design control data from a large number of unconnected small patches
+on the sky, with the goal of speeding queries for arbitrary chunks of
+the sky.  As a result, this parallelization is entirely inappropriate
+as the basis of the relative photometry analysis.  For the relative
+photometry calculation (and later for relative astrometry
+calculation), the sky is divided into a number of large, contiguous
+regions each bounded by lines of constant RA \& DEC, 73 regions in the
+case of the PV3 analysis.  A separate computer, called a ``region
+host'' is responsible for each of these regions: that computer is
+responsible for calculating the mean magnitudes of the objects which
+land within its region and for determining the exposure zero points
+for exposures for which the center of the exposure lands in the region
+of responsibility.  
+
+\begin{figure*}[htbp]
+ \begin{center}
+  \begin{minipage}{0.85\linewidth}
+   \includegraphics[width=\textwidth,clip]{{pics/photflat.example}.png}
+  \end{minipage}
+  \hspace{-3.0in}
+  \begin{minipage}{0.4\linewidth}
+   \vspace{3.25in}
+   \caption{\label{fig:photflat} High-resolution flat-field correction images for the 5 filters $grizy$.}
+  \end{minipage}
+ \end{center}
+\end{figure*}
+
+The iterations described above (calculate mean
+magnitudes, calculate zero points, calculate new measurements) are
+peformed on each of the 73 region hosts in parallel.  However, between
+certain iteration steps, the region hosts must share some information.
+After mean object magnitudes are calculated, the region hosts must
+share the object magnitudes for the objects which are observed by
+exposures controlled by neighboring region hosts.  After image
+calibrations have been determined by each region host, the image
+calibrations must be shared with the neighboring region hosts so
+measurement values associated with objects owned by a neighboring
+region host may be updated.
+
+The completely work flow of the all-sky relative photometry analysis
+starts with an instance of the program running on a master computer.
+This machine loads the image database table and assigns the images to
+the 73 region hosts.  A process is then launched on each of the region
+hosts which is responsible for managing the image calibration analysis
+on that host.  These processes in turn make an intial request of the
+photometry information (object and measurement) from the 100 parallel
+DVO partition machines.  In practice, the processes on the the region
+hosts are launched in series by the master process to avoid
+overloading the DVO partition machines with requests for photometry
+data from all region hosts at once.  Once all of the photometry has
+been loaded, the region hosts perform their iterations, sharing the
+data which they need to share with their neighbors and blocking while
+they wait for the data they need to receive from their neighbors.  The
+management of this stage is performed by communication between the
+region host.  At the end of the iterations, the regions hosts write out
+their final image calibrations.  The master machine then loads the
+full set of image calibrations and then applies these calibrations
+back to all measurements in the database, updating the mean photometry
+as part of this process.  The calculations for this last step are
+performed in parallel on the DVO partition machines.
+
+With the above software, we are able to perform the entire relphot
+analysis for the full 3$\pi$ region at once, avoiding any possible
+edge effects.  The region host machines have internal memory ranging
+from 96GB to 192GB.  Regions are drawn, and the maximum allowed
+density was chosen, to match the memory usage to the memory available
+on each machine.  A total of 9.8TB of RAM was available for the
+analysis, allowing for up to 6000 objects per square degree in the
+analysis.
+
+\begin{figure}[htbp]
+  \begin{center}
+ \includegraphics[width=\hsize,clip]{{pics/allsky.photom.sigma}.png}
+  \caption{\label{fig:allsky.photom.sigma} Consistency of photometry
+    measurements across the sky.  Each panel shows a map of the
+    standard deviation of photometry residuals for stars in each
+    pixel.  The median value of the measure standard deviations across
+    the sky is $(\sigma_g, \sigma_r, \sigma_i, \sigma_z, \sigma_y) =
+    (14, 14, 15, 15, 18)$ millimags.  These values reflect the typical
+    single-measurement errors for bright stars.}
+  \end{center}
+\end{figure}
+
+%% \note{need to discuss the process of setting the final mean magnitudes}
+
+\subsubsection{Photometric Flat-field}
+
+For PV3, the relphot analysis was performed two times.  The first
+analysis used only the flat-field corrections determined by the
+ubercal analysis, with a resolution of 2x2 flat-field values for each
+GPC1 chip (corresponding to \approx 2400 pixels), and 5 separate
+flat-field 'seasons'.  However, we knew from prior studies that there
+were significant flat-field structures on smaller scales.  We used the
+data in DVO after the initial relphot calibration to measure the
+flat-field residual with much finer resolution: 124 x 124 flat-field
+values for each GPC1 chip (40x40 pixels per point).  We then used
+\code{setphot} to apply this new flat-field correction, as well as the
+ubercal flat-field corrections, to the data in the database.  At this
+point, we re-ran the entire relphot analysis to determine zero points
+and to set the average magnitudes.
+
+Figure~\ref{fig:photflat} shows the high-resolution photometric
+flat-field corrections applied to the measurements in the DVO
+database.  These flat-fields make low-level corrections of up to
+\approx 0.03 magnitudes.  Several features of interest are apparent in
+these images.  
+
+First, at the center of the camera is an important structure caused by
+the telescope optics which we call the ``tent''.  In this portion of
+the focal plane, the image quality degrades very quickly.  The
+photometry is systematically biased because the point spread function
+model cannot follow the real changes in the PSF shape on these small
+scales.  As is evident in the image, the effect is such that the flux
+measured using a PSF model is systematically low, as expected if the
+PSF model is too small.  
+
+The square outline surrounding the ``tent'' is due to the 2$\times$2
+sampling per chip used for the Ubercal flat-field corrections.  The
+imprint of the Ubercal flat-field is visible throughout this
+high-resolution flat-field: in regions where the underlying flat-field
+structure follows a smooth gradient across a chip, the Ubercal
+flat-field partly corrects the structure, leaving behind a saw-tooth
+residual.  The high-resolution flat-field corrects the residual
+structures well.
+
+Especially notable in the bluer filters is a pattern of quarter
+circles centered on the corners of the chips.  These patterns are
+similar to the ``tree rings'' reported by the DES team and others
+(G. Berstein REF \& REFS).  The details of these tree rings are beyond
+the scope of this article, and will be explored in future work.
+Unlike the tree ring features discussed by these other authors, the
+features observed in the GPC1 photometry are not caused by an
+interaction of the flat-field with the effective pixel geometry.
+Instead, these photometric features are due to low-level changes in
+the PSF size which we attribute to variable charge diffusion (Magnier
+in prep).
+
+Other features include some poorly responding cells (e.g., in XY14)
+and effects at the edges of chips, possibly where the PSF model fails
+to follow the changes in the PSF.
+
+%% XXX : need to refer to system paper on the central tent?
+
+%% \note{show the flat-field residual images, discuss the features?}.  
+
+For stacks and warps, the image calibrations were determined after the
+relative photometry was performed on the individual chips.  Each stack
+and each warp was tied via relative photometry to the average
+magnitudes from the chip photometry.  In this case, no flat-field
+corrections were applied.  For the stacks, such a correction would not
+be possible after the stack has been generated because multiple chip
+coordinates contribute to each stack pixel coordinate.  For the warps,
+it is in principle possible to map back to the corresponding chip, but
+the information was not available in the DVO database, and thus it was
+not possible at this time to determine the flat-field correction
+appropriate for a given warp.  This latter effect is one of several
+which degrade the warp photometry compared to the chip photometry at
+the bright end.
+
+\subsection{Photometry Calibration Quality}
+
+Figure~\ref{fig:allsky.photom.sigma} shows the standard devitions of
+the mean residual photometry for bright stars as a function of
+position across the sky.  For each pixel in these images, we selected
+all objects with (14.5, 14.5, 14.5, 14.0, 13.0) $<$ ($g,r,i,z,y$) $<$
+(17, 17, 17, 16.5, 15.5), with at least 3 measurements in $i$-band (to
+reject artifacts detected in a pair of exposures from the same night),
+with \code{PSF_QF} $> 0.85$ (to reject excessively-masked objects),
+and with $mag_{\rm PSF} - mag_{rm Kron} < 0.1$ (to reject galaxies).
+We then generated histograms of the difference between the average
+magnitude and the apparent magnitude in an individual image for each
+filter for all stars in a given pixel in the images.  From these
+residual histograms, we can then determine the median and the 68\%-ile
+range to calculate a robust standard deviation.  This represents the
+bright-end systematic error floor for a measurement from a single
+exposure.  The standard deviations are then plotted in
+Figure~\ref{fig:allsky.photom.sigma}.  
+
+The 5 panels in Figure~\ref{fig:allsky.photom.sigma} show several
+features.  The Galactic bulge is clearly seen in all five filters,
+with the impact strongest in the reddest bands.  We attribute this to
+the effects of crowding and contamination of the photometry by
+neighbors.  Large-scale, roughly square features \approx 10 degrees on
+a side in these images can be attributed to the vagaries of weather:
+these patches correspond to the observing chunks.  These images
+include both photometric and non-photometric exposures.  It seems
+plausible that the non-photometric images from relatively poor quality
+nights elevate the typical errors.  On small scales, there are
+circular patterns \approx 3 degrees in diameter corresponding to
+individual exposures; these represent residual flat-fields structures
+not corrected by our stellar flat-fielding.  The median of the
+standard deviations in the five filters are
+$(\sigma_g,\sigma_r,\sigma_i,\sigma_z,\sigma_y) = (14, 14, 15, 15,
+18)$ millimagnitudes.
+
+%% \note{recommendation}
+
+\subsection{Calculation of Object Photometry}
+
+\subsubsection{Iteratively Reweighted Least Squares Fitting (1D)}
+
+\subsubsection{Selection of Measurements}
+
+\subsubsection{Stack Photometry}
+
+\subsubsection{Warp Photometry}
+
+\begin{figure*}[htbp]
+  \begin{center}
+ \includegraphics[width=\hsize,clip]{{pics/KHexample}.png}
+  \caption{\label{fig:KHexample} Illustration of the Koppenh\"ofer Effect
+    on chip XY04.  In each plot, the solid line shows the measured
+    mean residual for stars detected on this chip as a function of the
+    instrumental magnitude / FWHM$^2$.  {\bf top left} X-direction before correction.  
+{\bf top right} Y-direction before correction.  
+{\bf bottom left} X-direction after correction.  
+{\bf bottom right} Y-direction after correction.  }
+  \end{center}
+\end{figure*}
+
+\begin{figure}[htbp]
+  \begin{center}
+ \includegraphics[width=\hsize,clip]{{pics/KHmap}.png}
+  \caption{\label{fig:KHmap} Map of the amplitude of the
+    Koppenh\"ofer Effect on chips across the focal plane.  In the
+    affected chips, bright stars are up to 0.2 \note{arcsec} deviant
+    from their expected positions. {\bf bottom left} X-direction before
+    correction.  {\bf bottom right} Y-direction before correction.  {\bf
+      top left} X-direction after correction.  {\bf top right}
+    Y-direction after correction.  }
+  \end{center}
+\end{figure}
+
+\section{Astrometry Calibration}
+
+Once the full PV3 dataset loaded into the master PV3 DVO database,
+along with supporting databases, and the photometric calibrations were
+performed, relative astrometry could be performed on the database to
+improve the overall astrometric calibration.
+
+In many respects the relative astrometric analysis is similar to the
+relative photometric analysis: the repeated measurements of the same
+object in different images are used to determine a high quality
+average position for the object.  The new average positions are then
+used to determine improved astrometric calibrations for each of the
+images.  These improved calibrations are used to set the observed
+coordinates of the measurements from those images, which are in turn
+used to improve the average positions of the objects.  The whole
+process is repeated for several iterations.  Like the photometric
+analysis, the astrometric analysis is performed in a parallel fashion
+with the same concept that specific machines are responsible for
+exposures and objects which land within their regions of
+responsibility, defined on the basis of lines of constant RA and DEC.
+Between iteration steps, the astrometric calibrations are shared
+between the parallel machines as are the improved positions for
+objects controlled by one machine but detect in images controlled by
+another machine.  Like the photometric analysis, the entire sky is
+processed in one pass.  However, there are some important differences
+in the details.
+
+\subsection{Systematic Effects}
+
+First, the astrometric calibration has a larger number of systematic
+effects which must be performed.  These consist of: 1) the
+Koppenh\"offer Effect, 2) Differential Chromatic Refraction, 3) Static
+deviations in the camera.  We discuss each of these in turn below.
+
+\subsubsection{Koppenh\"offer Effect}
+
+The Koppenh\"offer Effect was first identified in February 2011 by
+Johannes Koppenh\"offer (MPE) as part of the effort to search for
+planet transists in the Stellar Transit Survey data.  He noticed that
+the astromety of bright stars and faint stars disagreed on overlapping
+chips at the boundary between the STS fields.  After some exploration,
+it was determined that the X coordinate of the brightest stars was
+offset from the expected location based on the faint stars for a
+subset of the GPC1 chips.  The essence of the effect was that a large
+charge packet could be drawn prematurely over an intervening negative
+serial phase into the summing well, and this leakage was
+proportionately worse for brighter stars.  The brighter the star, the
+more the charge packet was pushed ahead on the serial register.  The
+amplitude of the effect was at most $0\farcs{}25$, corresponding to a
+shift of about one pixel.  This effect was only observed in 2-phase
+OTA devices, with 22 / 30 of these suffering from this effect.  By
+adjusting the summing well high voltage down from a default +7 V to
++5.5V on the 2-phase devices, the effect was prevented in exposures
+after 2011-05-03.  However, this left 101,550 exposures (27\%) already
+contaminated by the effect.
+% This uses PV3 3-pi exposures:
+% group           N(<2011-05-03)    N(total)  %
+% PV3-3pi         101550            375573    24.47
+% exptype=OBJECT  229272            936879    27.04
+% ALL             322922            1163377   27.76
+
+% \note{was there is significant difference using a surface brightness version?}  
+
+We measured the Koppenh\"offer Effect by accumulating the residual
+astrometry statistics for stars in the database.  For each chip, we
+measured the mean X and Y displacements of the astrometric residuals
+as function of the instrumental magnitude of the star divided by the
+FWHM$^2$.  We measured the trend for all chips in a
+number of different time ranges and found the effect to be quite
+stable, in the period where it was present.  The effect only appeared
+in the serial direction.  Figure~\ref{fig:koppenhoefer} shows the KE
+trend for a typical affected chip both before and after the
+correction.  For the PV3 dataset, we re-measured the KE trends using
+stars in the Galactic pole regions after an initial relative
+astrometry calibration pass: the Galactic pole is necessary because
+the real-time astrometric calibration relies largely on the fainter
+stars which are not affected by the KE.  The trend is then stored in a
+form which can be applied to the database measurements.
+
+\subsubsection{Differential Chromatic Refraction}
+
+Differential Chromatic Refraction (DCR) affects astrometry because the
+reference stars used the calibrate the images are not the same color
+(SED) as the rest of the stars in the image.  For a given star of a
+color different from the reference stars, as exposures are taken at
+higher airmass, the apparent position of the star will be biased along
+the parallactic angle.  While it is possible to build a model for the
+DCR impact based on the filter response functions and atmospheric
+refraction, we have instead elected to use an empirical correction for
+the DCR present in the PV3 database.  We have measured the DCR trend
+using the astrometric residuals of millions of stars after performing
+an initial relative astrometry calibration.  We define a blue DCR
+color ($g-i$) to be used when correcting the filters \gps,\rps,\ips, and a red
+DCR color ($z - y$) to be used when correcting the filters $zy$.  In
+the process of performing the relative astrometry calibration, we
+record the median red and blue colors of the reference stars used to
+measure the astrometry calibration for each image.  As we determine
+the astrometry parameters for each object in the database, we record
+the median red and blue reference star colors for all images used to
+determine the astrometry for a given object.  For each star in the
+database, we know both the color of the star and the typical color of
+the reference stars used to calibrate the astrometry for that star.  
+
+We measure the mean deviation of the residuals in the parallactic
+angle direction and the direction perpendicular to the parallactic
+angle.  For each filter, we determine the DCR trend as a function of
+the difference between the star color and the reference star color,
+using the red or blue color approriate to the particular filter, times
+the tangent of the zenith distance.  Figure~\ref{fig:DCR} shows the
+DCR trend for the 5 filters \grizy, as well as the measured
+displacement in the direction perpendicular to the parallactic angle.
+We represent the trend with a spline fitted to this dataset.  
+
+\begin{figure}[htbp]
+  \begin{center}
+ \includegraphics[width=\hsize,clip]{{pics/dcr.r2.g}.png}
+  \caption{\label{fig:DCRexample} Example of the DCR trend in the
+    g-band.  {\bf top:} DCR trend in the parallactic direction {\bf
+      bottom:} DCR trend perpendicular to the parallactic angle.}
+  \end{center}
+\end{figure}
+
+The amplitude of the DCR trend in the five filters is $(g,r,i,z,y) =
+(0.010, 0.001, -0.003, -0.017, -0.021)$ arcsec airmass$^{-1}$
+magntiude$^{-1}$.  We saturate the DCR correction if the term $color
+TAN (\zeta)$ for a given measurement is outside a range where the
+DCR correction is well measured.  The maximum DCR correction applied
+to the five filters is $(g,r,i,z,y) = (0.019, 0.002, 0.003, 0.006,
+0.008)$ arcseconds.
+
+%% \note{write down the DCR formalae for reference}.
+
+\begin{figure*}[htbp]
+ \begin{center}
+ \includegraphics[width=0.85\textwidth,clip]{{pics/astroflat.gri}.png}
+ \caption{\label{fig:astroflat.gri} High-resolution astrometric flat-field correction images for $gri$.}
+ \end{center}
+\end{figure*}
+
+\begin{figure*}[htbp]
+ \begin{center}
+ \includegraphics[width=0.85\textwidth,clip]{{pics/astroflat.zy}.png}
+ \caption{\label{fig:astroflat.zy} High-resolution astrometric flat-field correction images for $zy$.}
+ \end{center}
+\end{figure*}
+
+\subsubsection{Astrometric Flat-field}
+
+After correction for both KE and DCR, we observe persistent residual
+astrometric deviations which depend on the position in the camera.  We
+construct an astrometric ``flat-field'' response by determining the
+mean residual displacement in the X and Y (chip) directions as a
+function of position in the focal plane.  We have measured the
+astrometric flat using a sampling resolution of 40x40 pixels, matching
+the photometric flat-field correction images.
+Figures~\ref{fig:astroflat.gri} and \ref{fig:astroflat.zy} show the
+astrometric flat-field images for the five filters \grizy\ in each of
+the two coordinate directions.  These plots show several types of
+features.
+
+The dominant pattern in the astrometric residual is roughly a series
+of concentric rings. The pattern is similar to the pattern of the
+focal surface residuals measured by (REF), which also has a concentric
+series of rings with similar spacing.  The ``tent'' in the center of
+the focal surface reflected in these astrometry residual plots.  Our
+interpretation of the structure is that the deviations of the focal
+plane from the ideal focal surface introduces small-scale PSF changes,
+presumably coupled to the optical aberrations, which result in small
+changes in the centroid of the object relative to the PSF model at
+that location.  Since the PSF model shape parameters are only able to
+vary at the level of a 6x6 grid per chips, the finer structures are
+not included in the PSF model.  The PV2 analysis shows the ring
+structure more clearly, with a pattern much more closely following the
+focal surface deviations.  In the PV2 analysis, the PSF model used at
+most a 3x3 grid per chip to follow the shape variations, so any
+changes caused by the optical aberrations would be less well modeled in
+the PV2 analysis, as we observe.
+
+A second pattern which is weakly seen in several chips consists of
+consistent displacements in the X (serial) direction for certain
+cells.  This effect can be seen most clearly in chips XY45 and XY46.
+In the PV2 analysis, this pattern is also more clearly seen.  In this
+case, the fact that the astrometric model used polynomials with a
+maximum of 3rd order per chip means the deviation of individual cells
+cannot be followed by the astrometric model.  
+
+A third effect is seen at the edge of the chips, where there appears
+to be a tendency for the residual to follow the chip edge.  The origin
+of this is unclear, but likely caused by the astrometry model failing
+to follow the underlying variations because of the need to extrapolate
+to the edge pixels.  Finally, we also mention an interesting effect
+{\em not} visible at the resolution of these astrometric flat-field
+images.  Fine structures are observed at the \approx 10 pixel scale
+similar to the ``tree rings'' reported by the DES team and others
+(G. Berstein REF \& REFS).  The details of these tree rings are beyond
+the scope of this article, and will be explored in future work.
+
+Unfortunately, we discovered a problem with the astrometric flat-field
+correction too late to be repaired for DR1.  As can be seen by
+inspection of Figures~\ref{fig:astroflat.gri} and
+\ref{fig:astroflat.zy}, there is significant pixel-to-pixel noise in
+the the astrometric flat-field images.  This pixel-to-pixel noise is
+caused by too few stars used in the measuremnt of the flat-field
+structure for the high-resolution sampling.  As a result, the
+astrometric flat-field correction reduces systematic structures on
+large spatial scales, but at the expense of degrading the quality of
+an individual measurement.  Only $i$-band has sufficient
+signal-to-noise per pixel to avoid significantly increasing the
+per-measurement position errors.  
+
+Figure~\ref{fig:allsky.astrom.sigma} shows the standard devitions of
+the mean residual astrometry in $(\alpha,\delta)$ for bright stars as
+a function of position across the sky.  For each pixel in these
+images, we selected all objects with $15 < i < 17$, with at least 3
+measurements in $i$-band (to reject artifacts detected in a pair of
+exposures from the same night), with \code{PSF_QF} $> 0.85$ (to reject
+excessively-masked objects), and with $mag_{\rm PSF} - mag_{rm Kron} <
+0.1$ (to reject galaxies).  We then generated histograms of the
+difference between the object position predicted for the epoch of each
+measurement (based on the proper motion and parallax fit) and the
+observed position of that measurement, in both the Right Ascension and
+Declination directions (in linear arcseconds), for all stars in a
+given pixel in the images.  From these residual histograms, we can
+then determine the median and the 68\%-ile range to calculate a robust
+standard deviation.  This represents the bright-end systematic error
+floor for a measurement from a single exposure.  The standard
+deviations are then plotted in Figure~\ref{fig:allsky.photom.sigma}.
+The median value of the standard deviations across the sky is
+$(\sigma_\alpha, \sigma_\delta) = (22, 23)$ milliarcseconds.
+
+The Galactic plane is clearly apparently in these images.  Like
+photometry, we attribute this to failure of the PSF fitting due to
+crowding.  The celestial North pole regions have somewhat elevated
+errors in both R.A. and DEC.  This may be due to the larger typical
+seeing at these high airmass regions, but without further exploration
+this is interpretation uncertain.  Several features can be seen which
+appear to be an effect of the tie to the Gaia astrometry: the stripes
+near the center of the DEC image and the right side of the R.A. image.
+The mesh of circular outlines is due to the outer edge of the focal
+plane where the astrometric calibration is poorly determined.  As
+discussed above, the median values in the images are higher than
+expected based on our PV2 analysis of the astrometry: the median
+per-measurement error floor of \approx 22 mas is significantly worse
+than the \approx 17 mas value in that earlier analysis.  We attribute
+this degradation to the noise introduced by the astrometric
+flat-field.  This noise can likely be addressed before the DR2 release
+of the individual measurement data.
+
+\begin{figure}[htbp]
+  \begin{center}
+ \includegraphics[width=\hsize,clip]{{pics/allsky.astrom.sigma}.png}
+  \caption{\label{fig:allsky.astrom.sigma} Consistency of photometry
+    measurements across the sky.  Each panel shows a map of the
+    standard deviation of astrometry residuals for stars in each
+    pixel.  The median value of the standard deviations across the sky
+    is $(\sigma_\alpha, \sigma_\delta) = (22, 23)$ milliarcseconds.
+    These values reflect the typical single-measurement errors for
+    bright stars.  See discussion regarding the astrometric flat which
+    is likely responsible for these elevated value. }
+  \end{center}
+\end{figure}
+
+% plot of the astrometric error floor per filter?
+
+% \note{SECTION or REF?}.
+
+After the initial analysis to measure the KE corrections, DCR
+corrections, and astrometric flat-field corrections, we applied these
+corrections to the entire database.  Within the schema of the
+database, each measurement has the raw chip coordinates
+(\code{Measure.Xccd,Yccd}) as well as the offset for that object based on each of
+these three corrections: \code{Measure.XoffKH,YoffKH,
+  Measure.XoffDCR,YoffDCR, Measure.XoffCAM,YoffCAM}.  The offsets are
+calculated for each measurement based on the observed instrumental
+chip magnitudes and FWHM for the Koppenhoffer Effect, on the average
+chip colors and the altitude \& azimuth of each measurement for the
+DCR correction, and on the chip coordinates for the astrometric
+flat-field corrections.  The corrections are combined and applied to
+the raw chip coordinates and saved back in the database in the fields
+\code{Measure.Xfix,Yfix}.  At this point, we are ready to run the
+full astrometric calibration. 
+
+\subsection{Galactic Rotation and Solar Motion}
+
+The initial analysis of the PV2 astrometry used the 2MASS positions as
+an inertial constraint: the 2MASS coordiates were included in the
+calculation of the mean positions for the objects in the database,
+with weight corresponding to the reported astrometric errors.  In this
+analysis, the object positions used to determine the calibrations of
+the image parameters ignored proper motion and parallax.  After the
+image calibrations were determined, then individual objects were
+fitted for proper motion and possibly parallax, as discussed in detail
+below. 
+
+Using the PV2 analysis of the astrometry calibration, we discovered
+large-scale systematic trends in the reported proper motions of
+background quasars.  This motion had an amplitude of 10 - 15
+milliarcseconds per year and clear trends with Galactic longitude.  We
+also observed systematic errors of the mean positions with respect to
+the ICRF milliarcsecond radio quasar positions, with an amplitude of
+\approx 60 milliarcseconds, again with trends associated with Galactic
+longitude.  Since the 2MASS data were believed to have minimal average
+deviations relative to the ICRF quasars, this latter seemed to be a
+real effect.  
+
+We realized that both the proper motion and the mean position biases
+could be caused by a single common effect: the proper motion of the
+stars used as reference stars between the 2MASS epoch (\approx 2000)
+and PS1 epoch (\approx 2012).  Since we are fitting the image
+calibrations without fitting for the proper motions of the stars, we
+are in essencence forcing those stars to have proper motions of 0.0.
+The background quasars would then be observed to have proper motions
+corresponding to the proper motions of the reference stars, but in the
+opposite direction.  We demonstrated that the observed quasar proper
+motions agreed well with the distribution expected if the median
+distance to our reference stars was \approx 500 pc.  
+
+For PV3, we desired to address this bias by including our knowledge
+about the distances to the reference stars and the expected typical
+proper motions for stars at those distances.  With some constraint on
+the distance to each star, we can determine the expected proper motion
+based on a model of the Galactic rotation and solar motions.  We can
+then calculate the mean positions for the objects keeping the assumed
+proper motion fixed.  When calibrating a specific image, the reference
+star mean position is then translated to the expected position at the
+epoch of that image.  The image calibration is then performed relative
+to these predicted postions.  This process naturally accounts for the
+proper motion of the reference stars.  In order to make the
+calibrations consistent with the observed coordinates of an external
+inertial reference, we perform the iterative fits using the technique
+as described, but assign very high weights in the initial iterations
+to the inertial reference, and reduce the weights as the astrometric
+calibration iterations proceed.
+
+In order to perform this analysis, we need estimated distances for
+every reference star used in the analysis.  Green et al (REF)
+performed SED fitting for 800M stars in the 3$\pi$ region using PV2
+data.  The goal of this work was to determine the 3D structure of the
+dust in the galaxy.  By fitting model SEDs to stars meeting a basic
+data quality cut, they determined the best spectral type, and thus
+$T_{\rm eff}$, absolute $r$-band magnitude, distance modulus, and
+extinction $A_V$ (the desired output and used to determine the dust
+extinction as a function of distance throughout the galaxy).  We use
+the distance modulus determined in this analysis to predict the proper
+motions.
+
+To convert the distances to proper motions, we use the Galactic
+rotation parameters ($A,B$) = (14.82,-12.37) km sec$^{-1}$ pc$^{-1}$
+and Solar motion parameters ($U_{\rm sol}, V_{\rm sol}, W_{\rm sol}$)
+= (9.32, 11.18, 7.61) km sec$^{-1}$ as determined by Feast \&
+Whitelock (REF) using Hipparchos data.  Proper motions are determined
+from the following:
+\begin{eqnarray}
+\mu^{\rm gal}_{l} & = & (A \cos (2 l) + B) \cos (b) \\
+\mu^{\rm gal}_{b} & = & \frac{-A \sin (2 l) \sin (2 b)}{2} \\
+\mu^{\rm sol}_{l} & = & \frac{U \sin(l) - V \cos(l)}{d} \\
+\mu^{\rm sol}_{b} & = & \frac{(U \cos(l) + V \sin(l)) \sin(b) - W \cos(b)}{d}
+\end{eqnarray}
+where $d$ is the distance and $l,b$ are the Galactic coordintes of the
+star. Note that the proper motion induced by
+%% \note{some reference for this?}  
+the Galactic rotation is independent of distance while the reflex
+motion induced by the solar motion decreases with increasing
+distance.  Also note that this model assumes a flat rotation curve for
+objects in the thin disk; any reference stars which are part of 
+the halo population will have proper motions which are not 
+described by this model; the mostly random nature of the halo motions
+should act to increase the noise in the measurement, but should not
+introduce detectable motion biases.  Also, if the distance modulus is
+not well determined, we can assume the object is simply following the
+Galactic rotation curve and set a fixed proper motion.  If we do not
+have a distance modulus from the Green et al analysis, we assume a
+value of 500pc.  
+
+%% \note{plots to show how well this worked for PV3 pre Gaia}
+
+\subsection{Gaia Constraint}
+
+After the full relative astrometry analysis was performed for the PV3
+database, the Gaia Data Release 1 became available
+\citep{2016A&A...595A...2G, 2016A&A...595A...4L}.  This afforded us
+the opportunity to constrain the astrometry on the basis of the Gaia
+observations.  Gaia DR1 objects which are bright enough to have proper
+motion and parallax solutions are in general saturated in the PS1
+observations.  Thus, we are limited to using the Gaia mean positions
+reported for the fainter stars.  We extracted all Gaia sources not
+marked as a duplicate from the Gaia archive and generated a DVO
+database from this dataset.  We then merged the Gaia DVO into the PV3
+master DVO database.  We re-ran the complete relative astrometry
+analysis using Gaia as an additional measurement.  We applied the
+analysis described above, applying the estimated distances to
+determine preliminary proper motions.  The Gaia mean epoch is reported
+as 2015.0, so all Gaia measurements were assigned this epoch.  We
+wanted to ensure the Gaia measurements dominated the astrometric
+solutions, so we made the weight very high for the Gaia points:
+1000$\times$ the nominal weight in the initial fits (to lock down the
+reference frame), decreasing to 100$\times$ the nominal weight for the
+last fits.  We also retained the 2MASS measurements in the analysis,
+but gave them somewhat lower weights than Gaia: while the 2MASS data
+does not have the accuracy of Gaia, the coverage is known to be quite
+complete, while the Gaia DR1 has clear gaps and holes.  Having 2MASS,
+even at a lower weight, helps to tile over those gaps.
+
+%% \note{Figures showing the Gaia residuals}
+
+\begin{figure*}[htbp]
+  \begin{center}
+  \includegraphics[width=\hsize,clip]{{pics/gaia.photom}.png}
+  \caption{\label{fig:gaia.photom} Comparison with Gaia
+    photometry. {\bf Left} Mean of PS1 - Gaia, {\bf Right} Standard
+    deviation of PS1 - Gaia.  For pixels with $|b| > 30$ and $\delta >
+    -30$, the standard deviation of the PS1 - Gaia mean values is 7
+    millimagnitudes, while the median of the standard deviations is 12
+    millimagnitudes.  The former is a statement about the consistency
+    of the Gaia and Pan-STARRS\,1 photometry, while the latter
+    reflects the combined bright-end errors for both systems.  }
+  \end{center}
+\end{figure*}
+
+Figure~\ref{fig:gaia.photom} shows a comparison between the Pan-STARRS
+photometry in $g,r,i$ and the Gaia photometry in the $G$-band.  To
+compare the PS1 photometry to the very broadband Gaia G filter, we
+have determined a transformation based on a 3rd order polynomial fit
+to $g-r$ and $g-i$ colors.  This transformation reproduces Gaia
+photometry reasonably well for stars which are not too red.  For a
+comparison, we have seleted all PS1 stars with Gaia measurements
+meeting the following criteria: $14 < i < 19$, with at least 10 total
+measurements, within a modest color range $0.2 < g - r < 0.9$.  We
+also restricted to objects with $i_{\rm PSF} - i_{\rm Kron} < 0.1$,
+using the average $i$ magnitudes determined from the individual
+exposures.  
+
+For Figure~\ref{fig:gaia.photom}, we calculate the difference between
+the estimated $G$-band magnitude based on PS1 $g,r,i$ photometry and
+the $G$-band photometry reported by Gaia.  For each pixel, we
+determine the histogram of these differences and calculate the median
+and the 68\%-ile range.  In Figure~\ref{fig:gaia.photom}, these
+values are plotted as a color scale.  
+
+The Galactic plane is clearly poorly matched between the two
+photometry systems.  This may in part be due to the difficulty of
+predicting $G$-band magnitudes for stars which are significantly
+extincted: the $G$-band includes significant flux from the PS1
+$z$-band which was not used in our transformation.  Many other large
+scale feature in the median differences have structures similar to the
+Gaia scanning pattern (large arcs and long parallel lines.  There are
+also structures related to the PS1 exposure footprint.  These show up
+as a mottling on the \approx 3 degree scale (e.g., lower right below
+the Galactic plane).  The amplitude of the residual structures is
+fairly modest.  The standard devition of the median difference values
+is 7 millimagnitudes.  This number gives an indication of the overall
+photometric consistency of both Gaia and PS1 and implies that the
+systematic error floor for each survey is less than 7 millimags.
+
+% set Gr = -0.090 + gr*gi*0.229 + gi*(-0.207+gi*(gi*0.015 - 0.250)) + gr*(0.491+gr*(-0.021*gr - 0.052)) 
+
+%\[
+%G - r = -0.09 + 0.229(g-r)(g-r) + (g-i)((
+
+\begin{figure*}[htbp]
+  \begin{center}
+  \includegraphics[width=\hsize,clip]{{pics/gaia.astrom}.png}
+  \caption{\label{fig:gaia.astrom} Comparison with Gaia
+    astrometry. {\bf Left} Mean of PS1 - Gaia, {\bf Right} Standard
+    deviation of PS1 - Gaia.  The median value of the standard
+    deviations is $(\sigma_\alpha, \sigma_\delta) = (4, 3)$
+    milliarcseconds. }
+  \end{center}
+\end{figure*}
+
+Figure~\ref{fig:gaia.astrom} shows a comparison between the Pan-STARRS
+mean astrometry positions in $\alpha,\delta$ and the Gaia astrometry.
+For this comparison, we have seleted all PS1 stars with Gaia
+measurements with $14 < i < 19$ and with at least 10 total
+measurements.  For Figure~\ref{fig:gaia.astrom}, we calculate the
+difference between the position predicted by PS1 at the Gaia epoch
+(using the proper motion and parallax fit) and the position reported
+by Gaia.  For each pixel, we determine the histogram of these
+differences in the R.A\. and DEC directions, and calculate the median
+and the 68\%-ile range.  In Figure~\ref{fig:gaia.astrom}, these
+values are plotted as a color scale.
+
+There is good consistency between the PS1 and Gaia astrometry.  There
+are patterns from the Galactic plane (though not very strongly at the
+bulge).  There are also clear features due to the PS1 exposure
+footprint (ring structure on \approx 3 degree scales).  In the plots
+of the scatter, there are patterns which are related to the Gaia
+scanning rule.  These are presumably regions with relatively low
+signal to noise in Gaia; they were also apparent in the plots of the
+statisics of the per-exposure measurement residuals
+(Figure~\ref{fig:allsky.astrom.sigma}.  The standard deviations of the
+median differences are ($\sigma_\alpha, \sigma_\delta) = (4, 3)$
+milliarcseconds.
+
+\subsection{Calculation of Object Astrometry}
+
+\subsubsection{Iteratively Reweighted Least Squares Fitting}
+
+\subsubsection{Seletion of Measurements}
+
+\section{Discussion}
+
+\section{Conclusion}
+
+\acknowledgments
+
+The Pan-STARRS1 Surveys (PS1) have been made possible through
+contributions of the Institute for Astronomy, the University of
+Hawaii, the Pan-STARRS Project Office, the Max-Planck Society and its
+participating institutes, the Max Planck Institute for Astronomy,
+Heidelberg and the Max Planck Institute for Extraterrestrial Physics,
+Garching, The Johns Hopkins University, Durham University, the
+University of Edinburgh, Queen's University Belfast, the
+Harvard-Smithsonian Center for Astrophysics, the Las Cumbres
+Observatory Global Telescope Network Incorporated, the National
+Central University of Taiwan, the Space Telescope Science Institute,
+the National Aeronautics and Space Administration under Grant
+No. NNX08AR22G issued through the Planetary Science Division of the
+NASA Science Mission Directorate, the National Science Foundation
+under Grant No. AST-1238877, the University of Maryland, and Eotvos
+Lorand University (ELTE) and the Los Alamos National Laboratory.
+
+\bibliographystyle{apj}
+%\bibliography{lib}{}
+\input{calibration.bbl}
+
+\end{document}
+
 \begin{verbatim}
-Intro
- Pan-STARRS background
- Scope: Source Detection \& Characterization, Galaxy modeling
- Requirements / Goals
- Comparable programs
- PSPhot
-
-Figures which might be interesting:
-
-* kron vs psf star-galaxy separation
-* lensing parameters for star-galaxy separation?
-* color-color locus plots
-* density of stars on the sky vs mag?
-* density of galaxies on the sky
-* good objects vs garbage?
-* bright-end astrometry residuals
-* bright-end photometry residuals
-* photometry residuals vs camera
-
-in patches, measure dlogN/dmag slope and roll-off (scale?)
-
-chip vs warp vs stack photometry across the sky
-
-color-color plots: g-r,r-i r-i,i-z (the stats from photladder paper)
-
-number of stars @ 20.5
-
-** do these plots in parallel : 
+ Plots:
+* illustration of the astrometric models (schematic)
+* astrometry cross-correlation example?
+* zero point history, including / excluding ubercal? (from Eddie)
+* applied flat-field images [FITS -> png]
+* Koppenhoffer plots [from presentations]
+* DCR plots [exist]
+* astrometric flat fields [FITS -> png]
+* PV3 vs Gaia [exit]
+* PV3 quasar motions [** need to extract **]
+* bright-end astrometry residuals [running cdhist code, but is the density too low?]
+* bright-end photometry residuals [running cdhist code, but is the density too low?]
+
+* careful discussion of calibration wrt scolnic et al
 
 \end{verbatim}
 
-\section{INTRODUCTION}\label{sec:intro}
-
-\section{Pan-STARRS1}
-
-\section{Photometry Analysis}
-
-\section{Astrometry Analysis}
-
-\section{Systematic Residuals}
-
-\subsection{Camera-Scale Trends}
-
-\section{Discussion}
-
-\section{Conclusion}
-
-\end{document}
+List of Figures and their sources:
+
+* KH example & map:
+  * kukui:/data/kukui.3/eugene/pv3.stats.20161202
+    * kh.data.20151203.v1/spline.final.fits : spline fits to the KH data
+    * kh.data.20151203.v1.fits : densify images of residuals per chip : (dX,dY) & (T0, T1) = (pre fix, post fix)
+    * mana.sh : kh.example - plot of XY04
+    * mana.sh : khmap (needs cleanup)
+  * ipp094:/data/ipp094.0/eugene/pv3.cam.20150607/astrom.corrections : extractions and original scripts to make spline, etc
+
+* DCR plots:
+  * need to rebuild density plots (density images used to make splines are poor for plots)
+  * old examples:
+    * /data/kukui.3/eugene/dcr.20141205
+      * dcr.r2.g.png
+  * spline fits (DCR.example)
+    * g : dP/dQ =  0.010, dPmax =  0.019
+    * r : dP/dQ =  0.001, dPmax =  0.002
+    * i : dP/dQ = -0.003, dPmax = -0.003
+    * z : dP/dQ = -0.017, dPmax = -0.006
+    * y : dP/dQ = -0.021, dPmax = -0.008
+
+* astroflats:
+  * kukui:/data/kukui.3/eugene/pv3.cam.20150607
+    * plots.sh : 
+  * photflat.20151127.fix.fits was made in:
+    * kukui:/data/kukui.3/eugene/setphot.20151213
+
+* Gaia comparisons:
+  * ipp094:/data/ipp094.0/eugene/pv3.stats.20161022
+  * kukui:/data/kukui.3/eugene/pv3.stats.20161022
+  
+* photom & astrom residuals:
+  kukui:/data/kukui.3/eugene/pv3.stats.20161202/maps.measure
+