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detrend.tex

Timestamp:

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

Author:

eugene

Message:

merge changes from trunk (updates to the papers)

File:

: 1 edited

branches/czw_branch/20160809/doc/release.2015/ps1.detrend/detrend.tex (modified) (28 diffs)

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

-              r39618
+              r39920
+\documentclass[12pt,preprint]{aastex}
 %\documentclass[iop,floatfix]{emulateapj}
 % \pdfoutput=1
+\pdfoutput=1
 % see latex.readme.txt for notes on using the PS1 template
+\documentclass[12pt,preprint]{aastex}
 %\documentclass[manuscript]{aastex}
 %\documentclass[preprint2]{aastex}
 %\documentclass[preprint2,longabstract]{aastex}
 \RequirePackage{color}
 \input{astro.sty}
 %\usepackage{subcaption}
+%\usepackage{natbib}
 % online version may use color, but print version needs b/w
 …
+}
 \newcommand{\erfcinv}{\mathop{\rm erfcinv}\nolimits}
+\newcommand{\ippprog}[1]{\textbf{\texttt{#1}}}
+\newcommand{\ippstage}[1]{\textsc{#1}}
+% CZW Moved to global input file.
+%\newcommand{\ippprog}[1]{\textbf{\texttt{#1}}}
+%\newcommand{\ippstage}[1]{\textsc{#1}}
 \newcommand{\asinh}{\mathop{\rm asinh}\nolimits}
 % Pick a terse version of the title here;
 …
 % 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\Princeton{2}
+\def\DUR{3}
+\def\STSCI{4}
+\def\Pitt{5}
+%\def\CfA{2}
+%\def\MPIA{3}
+%\def\USNO{4}
+%\def\JHU{1}
 % This example has a first author from UH:
 \author{
+C. Z. Waters,\altaffilmark{\IfA}
+IPP Team,
+C.~Z. Waters,\altaffilmark{\IfA}
+E.~A. Magnier,\altaffilmark{\IfA}
+P.~A. Price,\altaffilmark{\Princeton}
+K.~C. Chambers,\altaffilmark{\IfA}
+W.~S. Burgett,\altaffilmark{\IfA}
+P. Draper,\altaffilmark{\DUR}
+H.~A. Flewelling,\altaffilmark{\IfA}
+K. W. Hodapp,\altaffilmark{\IfA}
+M.~E. Huber,\altaffilmark{\IfA}
+R. Jedicke,\altaffilmark{\IfA}
+N. Kaiser,\altaffilmark{\IfA}
+R.-P. Kudritzki,\altaffilmark{\IfA}
+R.~H. Lupton,\altaffilmark{\Princeton}
+ N. Metcalfe,\altaffilmark{\DUR}
+A. Rest,\altaffilmark{\STSCI}
+W.~E. Sweeney,\altaffilmark{\IfA}
+J.~L. Tonry, \altaffilmark{\IfA}
+R.~J. Wainscoat,\altaffilmark{\IfA}
+W.~M. Wood-Vasey\altaffilmark{\Pitt}
+}
+%PS1 Builders
 %PS Builder List
+% W.~S. Burgett,\altaffilmark{\IfA}
+% K.~C. Chambers,\altaffilmark{\IfA}
 % L. Denneau,\altaffilmark{\IfA}
-% P. Draper,\altaffilmark{\DUR}
-% H.~A. Flewelling,\altaffilmark{\IfA}
 % T. Grav,\altaffilmark{\IfA}
 % J. N. Heasley,\altaffilmark{\IfA}
-% K. W. Hodapp,\altaffilmark{\IfA}
-% M. E. Huber,\altaffilmark{\IfA}
-% R. Jedicke,\altaffilmark{\IfA}
-% N. Kaiser,\altaffilmark{\IfA}
-% R.-P. Kudritzki,\altaffilmark{\IfA}
 % G. A. Luppino,\altaffilmark{\IfA}
-% R. H. Lupton,\altaffilmark{\Princeton}
-% E. A. Magnier,\altaffilmark{\IfA}
-% N. Metcalfe,\altaffilmark{\DUH}
 % D. G. Monet,\altaffilmark{\USNO}
 % J.~S. Morgan,\altaffilmark{\IfA}
 % P. M. Onaka,\altaffilmark{\IfA}
-% P.~A. Price,\altaffilmark{\Princeton}
 % C.~W. Stubbs,\altaffilmark{\CfA}
+% W.~E. Sweeney,\altaffilmark{\IfA}
+% J.~L. Tonry, \altaffilmark{\IfA}
+% R. J. Wainscoat,\altaffilmark{\IfA} and
+% C. Z. Waters,\altaffilmark{\IfA}
+} % this bracket terminates author list
+ % this bracket terminates author list
 % 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{\Princeton}{Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA}
+\altaffiltext{\STSCI}{Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA}
+\altaffiltext{\DUR}{Department of Physics, Durham University, South Road, Durham DH1 3LE, UK}
+\altaffiltext{\Pitt}{Pittsburgh Particle Physics, Astrophysics, and Cosmology Center (PITT PACC), Physics and Astronomy Department, University of Pittsburgh, Pittsburgh, PA 15260, 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}
 …
 \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-STARRS1 Science Consortium have carried out a set of imaging
+surveys using the 1.4 giga-pixel GPC1 camera on the PS1 telescope.  As
+this camera is composed of many individual electronic readouts, and
+covers a very large field of view, great care was taken to ensure that
+the many instrumental effects were corrected to produce the most
+uniform detector response possible.  We present the image detrending
+steps used as part of the processing of the data contained within the
+public release of the Pan-STARRS1 Data Release 1 (DR1).  In addition
+to the single image processing, the methods used to transform the
+,573 individual exposures into a common sky-oriented grid are
+discussed, as well as those used to produce both the image stack and
+difference combination products.
 \end{abstract}
 …
 \keywords{Surveys:\PSONE }
-%% http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?2007ASPC..364..153M&amp;data_type=PDF_HIGH&amp;whole_paper=YES&amp;type=PRINTER&amp;filetype=.pdf
 \section{Introduction and Survey Description}
+This is the third in a series of seven papers describing the Pan-STARRS1
+Surveys,
+the data reduction techniques and the resulting data products. This paper (Paper III)
+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.
+\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]{magnier2017a}
+describes how the various data processing stages are organized 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}
+%Magnier et al. 2017 (Paper IV)
+%Pan-STARRS Pixel Analysis : Source Detection
+\citet[][Paper IV]{magnier2017b}
+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]{magnier2017c}
+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 has already been described
+in detail in \cite{2012ApJ...750...99T}.
 …
 with the PS1 telescope on Haleakala Maui to image the sky north of
 $-30^\circ$ declination.  The GPC1 camera is composed of 60 orthogonal
 transfer array (OTA) devices, each of with is an $8\times{}8$ grid of
+transfer array (OTA) devices, each of which is an $8\times{}8$ grid of
 readout cells.  This parallelizes the readout process, reducing the
 overhead in each exposure.  However, as a consequence of this large
+number of individual detector readouts, there are a number of
+calibrations that need to be included to ensure the response is
+consistent across the entire field of view.
+The PV3 reduction represents the third full processing version of the
+Pan-STARRS archival data.  The first two reductions were used
+internally for pipeline optimization and the development of the
+initial photometric and astrometric reference catalog.  The products
+from these reductions were not publicly released, but have been used
+to produce a wide range of scientific papers from the Pan-STARRS 1
+Science Consortium members.
+number of individual detector readouts, many calibrations are needed
+to ensure the response is consistent across the entire field of view.
+The Processing Version 3 (PV3) reduction represents the third full
+reduction of the Pan-STARRS archival data.  The first two reductions
+were used internally for pipeline optimization and the development of
+the initial photometric and astrometric reference catalog \citep{magnier2017c}.  The
+products from these reductions were not publicly released, but have
+been used to produce a wide range of scientific papers from the
+Pan-STARRS 1 Science Consortium members.
 The Pan-STARRS image processing pipeline (IPP) is described elsewhere
 \citep{MagnierKaiserChambers2006}, but a short summary follows.  The
+\citep{magnier2017a}, but a short summary follows.  The
 archive of raw exposures is stored on disk, with a database storing
 the metadata of exposure parameters.  For the PV3 processing, large
 …
 This stage performs the image detrending (described below in section
 \ref{sec:detrending}), as well as the single epoch photometry
 \citep{MagnierXXY}, in parallel on the individual OTA device data.
+\citep{magnier2017b}, in parallel on the individual OTA device data.
 Following the \ippstage{chip} stage is the \ippstage{camera} stage, in
 which the astrometry and photometry for the entire exposure is
 calibrated against the reference catalog.  This stage also performs
+masking updates based on the now-known positions and brightnesses of
+stars that create dynamic features (see Section
+\ref{sec:dynamic_masks} below).  The \ippstage{warp} stage is the next
 to operate on the data, transforming the detector oriented
 \ippstage{chip} stage images into sky oriented images that have common
+tessellations and sky projections (Section \ref{sec:warping}).  When
+all \ippstage{warp} stage processing is done for the region of the
+sky, \ippstage{stack} processing is performed (Section
+\ref{sec:stacking}) to construct deeper, fully populated images from
+the set of \ippstage{warp} images that cover that region of the sky.
+Beyond the \ippstage{stack} stage, a series of additional stages are
+done that are more fully described in other papers.  Transient
+features are identified in the \ippstage{diff} stage, which takes
 input \ippstage{warp} and/or \ippstage{stack} data and performs image
 differencing \citep{HuberXXX}.  Further photometry is performed in the
+\ippstage{staticsky} and \ippstage{skycal} stages, which add extended
+source fitting to the point source photometry of objects detected in
 the \ippstage{stack} images, and calibrate the results against the
 reference catalog.  The \ippstage{fullforce} stage takes the catalog
+output of the \ippstage{skycal} stage, and uses the objects detected
+in that to perform forced photometry on the individual \ippstage{warp}
+stage images.  The details of these stages are provided in
 \citet{MagnierXXY}.
+calibrated by matching the detections against the reference catalog.
+This stage also performs masking updates based on the now-known
+positions and brightnesses of stars that create dynamic features (see
+Section \ref{sec:dynamic_masks} below).  The \ippstage{warp} stage is
+the next to operate on the data, transforming the detector oriented
+\ippstage{chip} stage images onto common sky oriented images that have
+fixed sky projections (Section \ref{sec:warping}).  When all
+\ippstage{warp} stage processing is done for the region of the sky,
+\ippstage{stack} processing is performed (Section \ref{sec:stacking})
+to construct deeper, fully populated images from the set of
+\ippstage{warp} images that cover that region of the sky.  Beyond the
+\ippstage{stack} stage, a series of additional stages are done that
+are more fully described in other papers.  Transient features are
+identified in the \ippstage{diff} stage, which takes input
+\ippstage{warp} and/or \ippstage{stack} data and performs image
+differencing (Section \ref{sec:diffs}).  Further photometry is
+performed in the \ippstage{staticsky} and \ippstage{skycal} stages,
+which add extended source fitting to the point source photometry of
+objects detected in the \ippstage{stack} images, and calibrate the
+results against the reference catalog.  The \ippstage{fullforce} stage
+takes the catalog output of the \ippstage{skycal} stage, and uses the
+objects detected in that to perform forced photometry on the
+individual \ippstage{warp} stage images.  The details of these stages
+are provided in \citet{magnier2017b}.
 The same reduction procedure described above is also performed in real
 …
 \ippstage{diff} stage.  This allows the ongoing solar system moving
 object search to identify candidates for follow up observations within
+hours of the initial set of observations \citep{WainscoatXXX}.
+\czwdraft{Should there be a discussion of any header keywords/OTA file formats?}
+Section \ref{sec:detrend construction} provides an overview of the
+detrend creation process for GPC1, with details of the application of
+those detrends to correct particular issues in Section
+\ref{sec:detrending}.  An analysis of the algorithms used to complete
+the \ippstage{warp} (section \ref{sec:warping}) and \ippstage{stack}
+(section \ref{sec:stacking}) stage transformations of the image data
+to from the detector frame to a common sky frame, and the co-adding of
+hours of the initial set of observations \citep{2015IAUGA..2251124W}.
+Section \ref{sec:detrending} provides an overview of the detrending
+process that corrects the instrumental signatures of GPC1, with
+details of the construction of those detrends in Section
+\ref{sec:detrend construction}.  An analysis of the algorithms used to
+complete the \ippstage{warp} (section \ref{sec:warping}),
+\ippstage{stack} (section \ref{sec:stacking}), and \ippstage{diff}
+(section \ref{sec:diffs}) stage transformations of the image data to
+from the detector frame to a common sky frame, and the co-adding of
 those common sky frame images continues after the list of detrend
 steps.  Finally, a discussion of the remaining issues and possible
 future improvements is presented in section \ref{sec:discussion}.
+\czwdraft{Is this a sufficient explanation?  Also, is this the right
+  place for it?}  Image products presented in figures have been
+mosaicked to arrange pixels in the following way.  Single cell images
+are arranged such that pixel $(1,1)$ is at the lower left corner.
+Images mosaicked to the OTA level have cell xy00 in the lower left
+corner, with cells xy10, xy20, etc. sequentially to the right, and
+cells xy01, xy02, etc. sequentially to the top of this cell.  Again,
+pixel $(1,1)$ of cell xy00 is located in the lower left corner of the
+image.  For mosaics of the full field of view, the OTAs are arranged
+as they see the sky.  The lower left corner is the empty location
+where OTA70 would exist.  Toward the right, the OTA labels decrease in
+$X$ label, with the empty OTA00 located in the lower right.  The OTA
+$Y$ labels increase upward in the mosaic.  The OTAs to the left of the
+midplane (OTA4Y-OTA7Y) are oriented with cell xy00 and pixel $(1,1)$
+to the lower left of their position.  Due to the electronic
+connections of the OTAs in the focal plane, the OTAs to the right of
+the midplane (OTA0Y-OTA3Y) oriented with cell xy00 and pixel $(1,1)$
+to the top right of their position, and have a negative parity to the
+mosaic in both x and y.
+% Discuss 2-phase/3-phase device differnces
+%\section{General Detrend Discussion}
+%\label{sec:detrending}
+Image products presented in figures have been
+mosaicked to arrange pixels as follows.  Single cell images are
+arranged such that pixel $(1,1)$ is at the lower left corner.  Images
+mosaicked to the OTA level have cell xy00 in the lower left corner,
+with cells xy10, xy20, etc. sequentially to the right, and cells xy01,
+xy02, etc. sequentially to the top of this cell.  Again, pixel $(1,1)$
+of cell xy00 is located in the lower left corner of the image.  For
+mosaicks of the full field of view, the OTAs are arranged as they see
+the sky.  The lower left corner is the empty location where OTA70
+would exist.  Toward the right, the OTA labels decrease in $X$ label,
+with the empty OTA00 located in the lower right.  The OTA $Y$ labels
+increase upward in the mosaic.  The OTAs to the left of the midplane
+(OTA4Y-OTA7Y) are oriented with cell xy00 and pixel $(1,1)$ to the
+lower left of their position.  Due to the electronic connections of
+the OTAs in the focal plane, the OTAs to the right of the midplane
+(OTA0Y-OTA3Y) are rotated 180 degrees, and are oriented with cell xy00
+and pixel $(1,1)$ to the top right of their position.
+\textit{Note: These papers are being placed on the 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
+.  Feedback and suggestions for additional information from early
+  users of the data products are welcome during the submission and
+  refereeing process.}
+\section{GPC1 Detrend Details}
+\label{sec:detrending}
+Ensuring a consistent and uniform detector response across the
+three-degree diameter field of view of the GPC1 camera is essential to
+a well calibrated survey.  Many standard image detrending steps are
+done for GPC1, with overscan subtraction removing the detector bias
+level, dark frame subtraction to remove temperature and exposure time
+dependent detector glows, and flat field correction to remove pixel to
+pixel response functions.  We also construct fringe correction for the
+reddest data in the \yps{} filter, to remove the interference patterns that
+arise in that filter due to the variations in the thickness of the
+detector surface.
+These corrections, however, assume that the detector response is
+linear across the full range of values.  This is not universally the
+case with GPC1, and this requires an additional set of detrending
+steps to remove these non-linear responses.  The first of these is the
+\ippprog{burntool} correction, which removes the persistence trails
+caused by the incomplete transfer of charge along the readout columns.
+This bright-end nonlinearity is generally only evident for the
+brightest stars, as only pixels that are at or beyond the saturation
+point of the detector have this issue.  More widespread is the
+non-linearity at the faint end of the pixel range.  Some readout cells
+and some readout cell edge pixels experience a sag relative to linear
+at low illumination, such that faint pixels appear fainter than
+expected.  The correction to this requires amplifying the pixel values
+in these regions to match the expected model.
+The final non-linear response issue has no good option for correction.
+Large regions of some OTA cells experience significant charge transfer
+issues, making them unusable for science observations.  These regions
+are therefore masked in processing, with these CTE regions making up
+the largest fraction of masked pixels on the detector.  Other regions
+are masked for other regions, such as static bad pixel features or
+temporary readout masking caused by issues in the camera electronics
+that make these regions unreliable.  These all contribute to the
+detector mask, which is augmented in each exposure for dynamic
+features that are masked based on the astronomical features within the
+field of view.
+For the PV3 processing, all detrending is done by the
+\ippprog{ppImage} program.  This program applies the detrends to the
+individual cells, and then an OTA level mosaic is constructed for the
+science image, the mask image, and the variance map image.  The single
+epoch photometry is done at this stage as well.  The following
+subsections (\ref{sec:burntool} - \ref{sec:background}) detail these
+detrending steps, presented in the order in which they are applied to
+the individual OTA image data.
+\subsection{Burntool / Persistence effect}
+\label{sec:burntool}
+Pixels that approach the saturation point on GPC1, which varies by
+readout with common values around 60000 DN, cause persistence problems
+on that and subsequent images.  During the read out process of an
+image with such a bright pixel, some of the charge associated with it
+is not fully shifted down the detector column toward the amplifier.
+As a result, this charge remains in the starting cell, and is
+partially collected in subsequent shifts, resulting in a ``burn
+trail'' that extends from the center of the bright source away from
+the amplifier (vertically along the pixel columns toward the top of
+the cell).
+This incomplete charge shifting in nearly full wells continues as each
+row is read out.  This results in a remnant charge being deposited in
+the pixels that the full well was shifted through.  In following
+exposures, this remnant charge leaks out, resulting in a trail that
+extends from the initial location of the bright source on the previous
+image towards the amplifier (vertically down along the pixel column).
+This remnant charge can remain on the detector for up to thirty
+minutes, requiring the locations of these ``burns'' be retained
+between exposures.
+Both of these types of persistence trails are measured and optionally
+repaired via the \ippprog{burntool} program.  This program does an
+initial scan of the images, and identifies objects with pixel values
+brighter than a conservative threshold of 30000 DN.  The trail from
+the peak of that object is fit with a one-dimensional power law in
+each pixel column above the threshold, based on empirical evidence
+that this is the functional form of this persistence effect.  This
+also matches the expectation that a constant fraction of charge is
+incompletely transferred at each shift beyond the persistence
+threshold.  Once this fit is done, the model can be subtracted from
+the image, and the location of the star is stored in a table along
+with the exposure PONTIME, which denotes the number of seconds since
+the detector was last powered on, and provides an internally consistent
+time scale.
+For subsequent exposures, the table associated with the previous image
+is read in, and after correcting trails from the stars on the new
+image, the positions of the bright stars from the table are used to
+check for remnant trails on the image.  These are fit and subtracted
+using a one-dimensional exponential model, again based on empirical
+studies.  If a significant model is found, then this location is
+retained in the image output table.  If not, the old burn is allowed
+to expire.
+The main concern with this method of correcting the persistence trails
+is that it is based on fits to the raw image data, which may have
+other signal sources not determined by the persistence effect.  The
+presence of other stars or artifacts along the path of the burn can
+result in a poor model to be fit, resulting in either an over- or
+under-subtraction of the persistence burn.  For this reason, the image
+mask is marked with a value indicating that this correction has been
+applied.  These pixels are not fully excluded, but they are marked as
+suspect, which allows them to be excluded from consideration in
+subsequent stages, such as image stacking.
+Another concern is that the cores of very bright stars are deformed by
+this process, as the burntool fitting subtracts flux
+from only one side of the star.  As most stars that result in burns already
+have saturated cores, they are already ignored for the purpose of
+PSF determination and are flagged as saturated by the photometry
+reduction.
+\begin{figure}
+  \centering
+  \begin{minipage}{0.45\hsize}
+    \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5677g0123o_XY11_bt_trail.png}
+%    \caption{(a)}
+%  \end{subfigure}%
+%  \begin{subfigure}[]{.45\hsize}
+  \end{minipage}%
+  \begin{minipage}{0.45\hsize}
+    \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5677g0124o_XY11_bt_trail.png}
+%    \caption{(b)}
+%  \end{subfigure}
+  \end{minipage}
+  \caption{Example of a profile cut along the y-axis through a bright star on exposure o5677g0123o OTA11 in cell xy60 (left panel) and on the subsequent exposure o5677g0124o (right panel).  In both figures, the green points show the image corrected with all appropriate detrending steps, but without burntool applied, illustrating the amplitude of the persistence trails.  The red points show the same data after the burntool correction, which reduces the impact of these features.  Both exposures are in the \gps{} filter with exposure times of 43s}
+\end{figure}
+\begin{figure}
+  \centering
+  \begin{minipage}{0.45\hsize}
+    \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5677g0123o_XY11_nobt.png}
+%    \caption{(a)}
+%  \end{subfigure}%
+%  \begin{subfigure}[]{.45\hsize}
+  \end{minipage}%
+  \begin{minipage}{0.45\hsize}
+    \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5677g0124o_XY11_nobt.png}
+%    \caption{(b)}
+%  \end{subfigure}
+  \end{minipage}
+  \begin{minipage}{0.45\hsize}
+    \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5677g0123o_XY11_bt.png}
+%    \caption{(a)}
+%  \end{subfigure}%
+%  \begin{subfigure}[]{.45\hsize}
+  \end{minipage}%
+  \begin{minipage}{0.45\hsize}
+    \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5677g0124o_XY11_bt.png}
+%    \caption{(b)}
+%  \end{subfigure}
+  \end{minipage}
+  \caption{Example of OTA11 cell xy60 on exposures o5677g0123o (left) and o5677g0124o (right).  The top panels show the image with all appropriate detrending steps, but without burntool, and the bottom show the same with burntool applied.  There is some slight over subtraction in fitting the initial trail, but the impact of the trail is greatly reduced in both exposures.}
+\end{figure}
+\subsection{Overscan}
+\label{sec:overscan}
+Each cell on GPC1 has an overscan region that covers the first 34
+columns of each row, and the last 10 rows of each column.  No light
+lands on these pixels, so the image region is trimmed to exclude them.
+Each row has an overscan value subtracted, calculated by finding the
+median value of that row's overscan pixels and then smoothing between
+rows with a three-row boxcar median.
+\subsection{Non-linearity Correction}
+\label{sec:nonlinearity}
+The pixels of GPC1 are not uniformly linear at all flux levels.  In
+particular, at low flux levels, some pixels have a tendency to sag
+relative to the expected linear value.  This effect is most pronounced
+along the edges of the detector cells, although some entire cells show
+evidence of this effect.
+To correct this sag, we studied the flux behavior of a series of flat
+frames for a ramp of exposure times with approximate logarithmically
+equal spacing between 0.01s and 57.04s.  As the exposure time
+increases, the flux on each pixel also increases in what is expected
+to be a linear manner.  Each of these flat exposures in this ramp is
+overscan corrected, and then the median is calculated for each cell,
+as well as for the rows and columns within ten pixels of the edge of
+the science region.  From these median values at each exposure time
+value, we can construct the expected trend by fitting a linear model,
+$f_{region} = G * t_{exp} + B$, to determine the gain, $G$, and the
+bias, $B$, for the region considered.  This fitting was limited to only
+the range of fluxes between 12000 and 38000 counts, as these ranges
+were found to match the linear model well.  This range avoids the
+non-linearity at low fluxes, as well as the possibility of high-flux
+non-linearity effects.
+We store the average flux measurement and deviation from the linear
+fit for each exposure time for all regions on all detector cells in
+the linearity detrend look up tables.  When this is applied to science
+data, these lookup tables are loaded, and a linear interpolation is
+performed to determine the correction needed for the flux in that
+pixel.  This look up is performed for both the row and column of each
+pixel, to allow the edge correction to be applied where applicable,
+and the full cell correction elsewhere.  The average of these two
+values is then applied to the pixel value, reducing the effects of
+pixel nonlinearity.
+This non-linearity effect appears to be stable in time for the
+majority of the detector pixels, with little evident change over the
+survey duration.  However, as the non-linearity is most pronounced at
+the edges of the detector cells, those are the regions where the
+correction is most likely to be incomplete.  Because of this fact,
+most pixels in the static mask with either the DARKMASK or FLATMASK
+bit set are found along these edges.  As the non-linearity correction
+is unable to reliably restore these pixels, they produce inconsistent
+values after the dark and flat have been applied, and are therefore
+rejected.
+\begin{figure}
+  \centering
+  \includegraphics[width=0.9\hsize,angle=0,clip]{images/linearity_XY27_xy16.png}
+  \caption{Example plot of the linearity correction as a fraction of observed flux for OTA27, cell xy16.}
+\end{figure}
+\subsection{Dark/Bias Subtraction}
+\label{sec:dark}
+The dark model we make for GPC1 considers each pixel individually,
+independent of any neighbors.  To construct this model, we fit a
+multi-dimensional model to the array of input pixels from a randomly
+selected set of 100-150 overscan and non-linearity corrected dark
+frames chosen from a given date range.  The model fits each pixel as a
+function of the exposure time $t_{exp}$ and the detector temperature
+$T_{chip}$ of the input images such that $\mathrm{dark} = a_0 + a_1
+t_{exp} + a_2 T_{chip} t_{exp} + a_3 T_{chip}^2 t_{exp}$.  This
+fitting uses two iterations to produce a clipped fit, rejecting at the
+$3\sigma$ level.  The final coefficients $a_i$ for the dark model are
+stored in the detrend image.  The constant $a_0$ term includes the
+residual bias signal after overscan subtraction, and as such, a
+separate bias subtraction is not necessary.
+Applying the dark model is simply a matter of calculating the response
+to the exposure time and detector temperature for the image to be
+corrected, and subtracting the resulting dark signal from the image.
+\subsubsection{Time evolution}
+The dark model is not consistently stable over the full survey, with
+significant drift over the course of multiple months.  Some of the
+changes in the dark can be attributed to changes in the voltage
+settings of the GPC1 controller electronics, but the majority seem to
+be the result of some unknown parameter.  We can separate the dark
+model history of GPC1 into three epochs.  The first epoch covers all
+data taken prior to 2010-01-23.  This epoch used a different header
+keyword for the detector temperature, making data from this epoch
+incompatible with later dark models.
+The second epoch covers data between 2010-01-23 and 2011-05-01, and is
+characterized by a largely stable but oscillatory dark solution.
+There are two modes that the dark model switches between apparently at
+random.  No clear cause has been established for the switching, but
+there are clear differences between the two modes that require the
+observation dates to be split to use the model that is most
+appropriate.
+The initial evidence of these two modes comes from the discovery of a
+slight gradient along the rows of certain cells.  This is a result of
+a drift in the bias level of the detector as it is read out.  An
+appropriate dark model should remove this gradient entirely.  For
+these two modes, the direction of this bias drift is different, so a
+single dark model generated from all dark images in the time range
+over corrects the positive-gradient mode, and under corrects the
+negative-gradient mode.  Upon identifying this two-mode behavior, and
+determining the dates each mode was dominant, two separate dark
+models were constructed from appropriate ``A'' and ``B'' mode dark
+frames.  Using the appropriate dark minimizes the effect of this bias
+gradient in the dark corrected data.
+The bias drift gradients of the mode switching can be visualized in
+Figure \ref{fig:dark switching}.  This figure shows the image profile
+along the x-pixel axis binned along the full y-axis of the first row
+of cells.  The raw data is shown, illustrating the positional
+dependence the dark signal has on the image values.  In addition,
+both the correct B-mode dark and incorrect A-mode dark have been
+applied to this image, showing that although both correct the bulk of
+the dark signal, using the incorrect mode creates larger intensity
+gradients.
+After 2011-05-01, the two-mode behavior of the dark disappears, and is
+replaced with a slow observation date dependent drift in the magnitude
+of the gradient.  This drift is sufficiently slow that we have modeled
+it using three observation date independent dark model for different
+date ranges.  These darks cover the range from 2011-05-01 to
+-08-01, 2011-08-01 to 2011-11-01, and 2011-11-01 and on.  The
+reason for this time evolution is unknown, but as it is correctable
+with a small number of dark models, this does not significantly impact
+detrending.
+\begin{figure}
+  \centering
+%  \begin{subfigure}[]{.45\hsize}
+  \begin{minipage}{0.45\hsize}
+    \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5677g0123o_M_OS_NL_XY23_b1.jpg}
+%    \caption{(a)}
+%  \end{subfigure}%
+%  \begin{subfigure}[]{.45\hsize}
+  \end{minipage}%
+  \begin{minipage}{0.45\hsize}
+    \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5677g0123o_to_DARK_XY23_b1.jpg}
+%    \caption{(b)}
+%  \end{subfigure}
+  \end{minipage}
+  \caption{An example of the dark model application to exposure o5677g0123o, OTA23 (2011-04-26, 43s \gps{} filter).  The left panel shows the image data mosaicked to the OTA level, and has had the static mask applied, the overscan subtracted, and the detector non-linearity corrected.  The right panel, shows the same exposure with the dark applied in addition to the processing shown on the left.}
+\end{figure}
+\begin{figure}
+  \centering
+  \includegraphics[width=0.9\hsize,angle=0,clip]{images/B_profile_ex.png}
+  \caption{Example showing a profile cut across exposure o5676g0195, OTA67 (2011-04-25, 43s \gps{} filter).  The entire first row of cells (xy00-xy07) have had a median calculated along each pixel column on the OTA mosaicked image.  Arbitrary offsets have been applied to shift the curves to not overlap.  The top curve (in purple) shows the initial raw profile, with no dark model applied.  The next curve (in green) shows the smoother profile after applying the correct B-mode dark model.  Applying the incorrect A-mode dark results in the blue curve, which shows a significant increase in gradients across the cells.  The orange curve shows the result of the PATTERN.CONTINUITY correction.  Although this creates a larger gradient across the mosaicked images, it decreases the cell-to-cell level changes.  The final yellow curve shows the final image profile after all detrending and background subtraction, and has not had an offset applied.  The bright source at the cell xy00 to xy01 transition is a result of a large optical ghost, which due to the area covered, increases the median level more than the field stars.}
+  \label{fig:dark switching}
+\end{figure}
+\subsubsection{Video Dark}
+\label{sec:video_darks}
+The dark signal is stronger in cell corners due to glow from the
+read-out amplifiers.  The standard dark model corrects this for most
+observations.  However, as mentioned above, when a cell is repeatedly
+read in video mode, the dark model for the OTA containing it changes.
+Surprisingly, added reads for the video cell do not amplify the
+amplifier glow, but rather decrease the dark signal in these regions.
+As a result, using the standard dark model on the data for these OTAs
+results in oversubtraction of the corner glow.
+Video darks have been constructed to eliminate the effect this
+observational change has on the final image quality.  This was done by
+running the standard dark construction process on a series of dark
+frames that have had the video signal enabled for some cells.  GPC1
+can only run video signals on a subset of the OTAs at a given time.
+This requires two passes to enable the video signal across the full
+set of OTAs that support video cells.  This is convenient for the
+process of creating darks, as those OTAs that do not have video
+signals enabled create standard dark models, while the video dark is
+created for those that do.
+This simultaneous construction of video and standard dark models is
+useful, as it provides the ability to isolate the response on the
+standard dark from the video signals.  Isolating this response is
+essential for attempting to create archival video darks.  We only have
+raw video dark frame data after 2012-05-16, when this problem was
+initially identified, so any data prior to that can not be directly
+corrected for the video dark signal.  Isolating the video signal
+response allows linear corrections to the pre-existing standard dark
+models for archival data.  Testing this shows that constructing a
+video dark for older data simply as $VD_{2009} = D_{2009} - D_{Modern}
++ VD_{Modern}$ produces a satisfactory result that does not
+over subtract the amplifier glow.  This is shown in figure
+\ref{fig:video_darks}, which shows video cells from before 2012-05-16,
+corrected with both the standard and video darks, with the early video
+dark constructed in such a manner.
+\begin{figure}
+  \centering
+%  \begin{subfigure}[]{.45\hsize}
+  \begin{minipage}{0.45\hsize}
+    \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5677g0123o_VIDEODARK_VDim_Rdark_XY22_b1.jpg}
+%    \caption{(a)}
+%  \end{subfigure}%
+%  \begin{subfigure}[]{.45\hsize}
+  \end{minipage}%
+  \begin{minipage}{0.45\hsize}
+    \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5677g0123o_VIDEODARK_VDim_VDdark_XY22_b1.jpg}
+%    \caption{(b)}
+%  \end{subfigure}
+  \end{minipage}
+  \caption{An example of the video dark model application to exposure o5677g0123o, OTA22 (2011-04-26, 43s \gps{} filter), which has a video cell located in cell xy16.  The left panel shows the image data mosaicked to the OTA level, and has had the static mask applied, the overscan subtracted, the detector non-linearity corrected, and a regular dark applied.  The right panel, shows the same exposure with a video dark applied instead of the standard dark.  The main impact of this change is the improved correction of the corner glows, which are over subtracted with the standard dark.}
+  \label{fig:video_darks}
+\end{figure}
+\subsection{Noisemap}
+\label{sec:noisemap}
+Based on a study of the positional dependence of all detected sources,
+we have discovered that the cells in GPC1 do not have uniform noise
+characteristics.  Instead, there is a gradient along the pixel rows,
+with the noise generally higher away from the read out amplifier
+(higher cell x pixel positions).  This is likely an effect of the
+row-by-row bias issue discussed below.  This gradient causes the read
+noise to increase as the row is read out.  As a result of this
+increased noise, more sources are detected in the higher noise regions
+when the read noise is assumed constant across the readout.  Read noise is the
+To
+mitigate this noise gradient, we constructed an initial set of
+noisemap images by measuring the median variance on bias frames.  The
+variance is calculated in boxes of 20x20 pixels, and then linearly
+interpolated to cover the full image.
+Unfortunately, due to correlations within this noise, the variance
+measured from the bias images does not fully remove the positional
+dependence of objects that are detected.  This simple noisemap
+underestimates the noise observed when the image is filtered during
+the object detection process.  This filtering convolves the background
+noise with a PSF, which has the effect of amplifying the correlated
+peaks in the noise.  This amplification can therefore boost background
+fluctuations above the threshold used to select real objects,
+contaminating the final object catalogs.
+In the detection process, we expect false positives at a rate equal to
+the one-tailed probability beyond the detection threshold.  For these
+tests, only detections measured at the $\sigma_{thresh} = 5\sigma$
+level are used, to match that used in the photometry on science data.
+This probability can be converted into a number of false number by
+considering a given area.  As the detections must be isolated to not
+be detected as an extended object, this area must be reduced by the
+area a given PSF occupies.  Combining this, we find that we expect a
+probability $P = 1 - \Phi_{normal}(5) = \frac{1}{2}
+\erfcinv\left(\frac{5}{\sqrt{2}}\right)$, and an area given $N$
+exposures of area $X\times Y$, $A = \frac{X \times Y \times
+  N}{A_{PSF}}$.  For a typical $1"$ seeing, $A_{PSF}$ is approximately
+pixels.  Using this model for the false positives, we found that
+the added read noise was insufficient to account for the observed
+false positive rate.  Inverting this relation, we can measure
+$\sigma_{obs}$, the true threshold level based on the number of false
+positives observed.  This $\sigma_{obs}$ is the combined to form a
+boost factor $B = \sigma_{thresh} / \sigma_{obs}$ that amplifies the
+  noisemap to match the observed false detection rate.
+The row-to-row variations that contribute to the extra noise are
+related to the dark model, and because of this, as the dark model
+changes, the effective noise also changes.  To ensure that the
+noisemap accurately matches the true noise level, we have created
+different noisemap models for the three major time ranges of the dark
+model.  We do not see any strong evidence that the noisemaps have the
+A/B modes visible in the dark, and so we do not generate different
+models for each individual dark model.  The additional pixel-to-pixel
+variance from this noisemap is added to the Poissonian variance to
+form the science variance image generated by the \ippstage{chip}
+processing.
+\subsection{Flat}
+Determining a flat field correction for GPC1 is a challenging
+endeavor, as the wide field of view makes it difficult to construct a
+uniformly illuminated image.  Using a dome screen is not possible, as
+the variations in illumination and screen rigidity create large
+scatter between different images that are not caused by the detector
+response function.  Because of this, we use sky flat images taken at
+twilight, which are more consistently illuminated than screen flats.
+We calculate the mean of these images to determine the initial flat
+model.
+From this starting skyflat model, we construct a photometric
+correction to remove the effect of the illumination differences over
+the detector surface.  This is done by dithering a series of science
+exposures with a given pointing.  By fully calibrating these exposures
+with the initial flat model, and then comparing the measured fluxes
+for the same star as a function of position on the detector, we can
+determine position dependent scaling factors.  From the set of scaling
+factors for the full catalog of stars observed in the dithered
+sequence, we can construct a model of the error in the initial flat
+model as a function of detector position.  Applying a correction that
+reduces the amplitude of these errors produces a flat field model that
+better represents the true detector response.
+In addition to this flat field applied to the individual images, the
+ubercal process used to calibrate the database of all detections
+\citep{2012ApJ...756..158S} constructs internal ``flat field'' corrections.
+Although a single set of image flat fields was used for the entire PV3
+survey, five separate ``seasons'' of database flat fields were needed
+to ensure proper calibration.  This indicates that the flat field
+response is not completely fixed in time.  More details on this
+process are contained in \citet{magnier2017c}.
+\subsection{Pattern correction}
+\label{sec:pattern}
+Due to detector specific issues that are not cleanly removed by the
+dark model, we have a set of ``pattern'' corrections that are applied
+to some selection of the OTAs in the camera.  This is done to reduce
+the effect that detector differences have on the measured astronomical
+signal that are not stable enough to be corrected with a static model.
+Because of this, the pattern corrections attempt to identify and
+correct the detector issues based on appropriate filtering the
+individual science exposures.
+The PATTERN.ROW correction is used to remove any remaining row-by-row
+bias variation, and the PATTERN.CONTINUITY correction attempts to
+ensure that the cells of a given OTA are consistent with the other
+cells on that OTA.
+\subsubsection{Pattern Row}
+%% Statistics so I have them written down somewhere
+%% chipProcessedImfile.bg/bg_stdev by filter for XY33 (a good chip)
+%% filter  bg_mean stdev median Qsig                              bg_stdev_mean stdev median Qsig
+%% g        36.37422026669   64.64175104057  32.693   6.10284     14.696938349131  78.80460307171  8.8401  0.5417843
+%% r       200.96143304525  471.87743546238 117.105  94.55608     33.854672792146  79.01642728089 13.4564  5.3771355
+%% i       447.00504994458  938.38517801037 286.810 154.71397     57.298335510188  99.38392923935 20.0217 24.2254723
+%% z       317.54933679054  390.38930252748 241.014 114.13316     48.359069000176  94.44452756094 17.9404  9.1535209
+%% y       371.09019536218  293.57439970375 288.481 133.38769     43.724342221691 135.04286534327 19.9029  7.5396461
+As discussed above in the dark and noisemap sections, certain
+detectors have significant bias offsets between adjacent rows, caused
+by noise in the camera control electronics.  The magnitude of these
+offsets increases as the distance from the readout amplifier
+increases, resulting in horizontal streaks that are more pronounced
+along the large x pixel edge of the cell.  As the level of the offset
+is apparently random between exposures, the dark correction cannot
+fully remove this structure from the images, and the noisemap value
+only indicates the level of the average variance added by these bias
+offsets.  Therefore, we apply the PATTERN.ROW correction in an attempt
+to mitigate the offsets and correct the image values.  To force the
+rows to agree, a second order clipped polynomial is fit to each row in
+the cell.  Four fit iterations are run, and pixels $2.5\sigma$ deviant
+are excluded from subsequent fits, to minimize the effect stars and
+other astronomical signals have.  This final trend is then subtracted
+from that row.  Simply doing this subtraction will also have the
+effect of removing the background sky level.  To prevent this, the
+constant and linear terms for each row are stored, and linear fits are
+made to these parameters as a function of row, perpendicular to the
+initial fits.  This produces a plane that is added back to the image
+to restore the background offset and any linear ramp that exists in
+the sky.
+These row-by-row variations have the largest impact on data taken in
+the \gps{} filter, as the read noise is the dominant noise source in
+that filter.  At longer wavelengths, the noise from the Poissonian
+variation in the sky level increases.  Although the PATTERN.ROW correction is still applied to data taken in the other filters,
+This correction was required on all cells on all OTAs prior to
+-12-01, at which point a modification of the camera electronics
+reduced the scale of the row-by-row offsets for the majority of the
+OTAs.  As a result, we only apply this correction to the cells where
+it is still necessary, as shown in Figure \ref{fig: pattern row
+  cells}.  A list of these cells is listed in Table
+\ref{tab:pattern_row_cells}.
+Although this correction does largely resolve the row-by-row offset
+issue in a satisfactory way, large and bright astronomical objects can
+bias the fit significantly.  This results in an oversubtraction of the
+offset near these objects.  As the offsets are calculated on the pixel
+rows, this oversubtraction is not uniform around the object, but is
+preferentially along the horizontal x axis of the object.  Most
+astronomical objects are not significantly distorted by this, with
+this only becoming on issue for only bright objects comparable to the
+size of the cell (598 pixels = 150").
+\begin{deluxetable}{lcccc}
+  \tablecolumns{3}
+  \tablewidth{0pc}
+  \tablecaption{Cells which have PATTERN.ROW correction applied}
+  \tablehead{\colhead{OTA} & \colhead{Cell columns} & \colhead{Additional cells}}
+  \startdata
+  OTA11 &  & xy02, xy03, xy04, xy07 \\
+  OTA14 &  & xy23 \\
+  OTA15 & 0 & \\
+  OTA27 & 0, 1, 2, 3, 7 & \\
+  OTA31 & 7 & \\
+  OTA32 & 3, 7 & \\
+  OTA45 & 3, 7 & \\
+  OTA47 & 0, 3, 5, 7 & \\
+  OTA57 & 0, 1, 2, 6, 7 & \\
+  OTA60 &  & xy55 \\
+  OTA74 & 2, 7 & \\
+  \enddata
+  \label{tab:pattern_row_cells}
+\end{deluxetable}
+\begin{figure}
+  \centering
+  \includegraphics[width=0.9\hsize,angle=0,clip]{images/pattern_row_edit.png}
+  \caption{Diagram illustrating in red which cells on GPC1 require the PATTERN.ROW correction to be applied.  The footprint of each OTA is outlined, and cell xy00 is marked with either a filled box or an outline.  The labeling of the non-existent corner OTAs is provided to orient the focal plane.}
+  \label{fig: pattern row cells}
+\end{figure}
+\begin{figure}
+  \centering
+  \begin{minipage}{0.45\hsize}
+    \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5379g0103o_XY57_nopat.png}
+%    \caption{(a)}
+%  \end{subfigure}%
+%  \begin{subfigure}[]{.45\hsize}
+  \end{minipage}%
+  \begin{minipage}{0.45\hsize}
+    \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5379g0103o_XY57_pat.png}
+%    \caption{(b)}
+%  \end{subfigure}
+  \end{minipage}
+  \caption{Example of the PATTERN.ROW correction on exposure o5379g0103o OTA57 cell xy00 (\ips{} filter 45s).  The left panel shows the cell with all appropriate detrending except the PATTERN.ROW, and the right shows the same cell with PATTERN.ROW applied.  The correction reduces the correlated noise on the right side, which is most distant from the read out amplifier.  There is a slight over subtraction along the rows near the bright star.}
+\end{figure}
+\subsubsection{Pattern Continuity}
+After previous attempts to ensure that adjacent cells on an OTA
+matched background levels were insufficient in many situations, we
+designed a replacement correction that would reduce the background
+distortion for large objects.  In addition, studies of the background
+level illustrated that the row-by-row bias can introduce small
+background gradient variations along the rows of the cells that is not
+stable enough to be completely fit by the dark model.  This common
+feature across the columns of cells results in a ``saw tooth'' pattern
+horizontally across an OTA, and as the background model fits a smooth
+sky level, this induces over and under subtraction at the cell
+boundaries.
+The PATTERN.CONTINUITY correction, attempts to match the edges of a
+cell to those of its neighbors.  For each cell, a thin box 10 pixels
+wide on each edge is extracted and the median value of unmasked values
+calculated for that box.  These median values are then used to
+construct a vector of differences $\Delta_i = \sum_{j} \mathrm{Edge}_{i} -
+\mathrm{Edge}_{j}$, along with a matrix of associations $A_{i,i'} = \sum_{j}
+\delta(i,j) \delta(j,i')$ denoting which cell boundaries are adjacent.
+By solving the system $A x = \Delta$, we find the set of offsets $x_i$
+to be applied to each cell to ensure the minimum differences between
+all cell edges and their neighbors.
+For OTAs that initially show the saw tooth pattern, the effect of this
+correction is to align the cells into a single ramp, at the expense of
+the absolute background level.  However, as we subtract off a smooth
+background model prior to doing photometry, these deviations from an
+absolute sky level are unimportant.  The fact that the final ramp is
+smoother than it would be otherwise also allows for the background
+subtracted image to more closely match the astronomical sky, without
+significant errors at cell boundaries.  An example of the effect of
+this correction on an image profile is shown in Figure \ref{fig:dark switching}.
+\subsection{Fringe correction}
+\label{sec:fringe}
+% det_id 296 is the fringe we use.
+Due to variations in the thickness of the detectors, we observe
+interference patterns at the infrared end of the filter set, as the
+wavelength of the light becomes comparable to the thickness of the
+detectors.  Visually inspecting the images shows that the fringing is
+most prevalent in the \yps{} filter images, with negligible fringing in the
+other bands.  As a result of this, we only apply a fringe correction
+to the \yps{} filter data.
+The fringe used for PV3 processing was constructed from a set of 20
+s science exposures.  These exposures are overscan subtracted, and
+corrected for non-linearity, and have the dark and flat models
+applied.  These images are smoothed with a Gaussian kernel with
+$\sigma = 2$ pixels to minimize pixel to pixel noise.  The fringe
+image data is then constructed by calculating the clipped mean of the
+input images with two iteration of clipping at the $3\sigma$ level.
+A course background model for each cell is constructed by calculating
+the median on a 3x3 grid (approximately 200x200 pixels each).  A set
+of 1000 randomly selected points are then selected on the fringe image
+for each cell, and a median calculated for this position in a 10x10
+pixel box, with the background level subtracted.  These sample
+locations provide scale points to allow the amplitude of the measured
+fringe to be compared to that found on science images.
+To apply the fringe, the same sample locations are measured on the
+science image to determine the relative strength of the fringing in
+that particular image.  A least squares fit between the fringe
+measurements and the corresponding measurements on the science image
+provides the scale factor multiplied to the fringe before it is
+subtracted from the science image.
+\begin{figure}
+  \centering
+  \begin{minipage}{0.5\hsize}
+    \includegraphics[width=1.5\hsize,angle=0,clip]{images/o5220g0025o_XY53_nofringe.png}
+  \end{minipage}%
+  \begin{minipage}{0.5\hsize}
+    \includegraphics[width=1.5\hsize,angle=0,clip]{images/o5220g0025o_XY53_fringe.png}
+  \end{minipage}
+  \caption{Example of the \yps{} filter fringe pattern on exposure o5220g0025o OTA53 (\yps{} filter 30s).  The left panel shows the OTA mosaic with all detrending except the fringe correction, while the right shows the same including the fringe correction.  Both images have been smoothed with a Gaussian with $\sigma = 3$ pixels to highlight the faint and large scale fringe patterns.
+}
+  \label{fig: fringe example}
+\end{figure}
+\subsection{Masking}
+\label{sec:masking}
+\subsubsection{Static Masks}
+\label{sec:static_masks}
+Due to the large size of the detector, it is expected that there
+are a number of pixel defects that do not have the detection
+sensitivity on par with their neighbors.  To remove these pixels, we
+have constructed a static mask that identifies the known defects.
+This mask is constructed in three phases.
+First, a CTEMASK is constructed to mask out regions in which the
+charge transfer efficiency is low compared to the rest of the
+detector.  Twenty-five of the sixty OTAs in GPC1 show some evidence of
+CTE issues, with this pattern appearing (to varying degrees) in
+roughly triangular patches on the OTA due to defects in the
+semiconductor manufacturing.  To generate the mask for these regions,
+a sample set of 26 evenly illuminated flat field images were measured
+to produce a map of the image variance in 20x20 pixel bins.  As the
+flat image is expected to illuminate the image uniformly, the expected
+variances in each bin should be Poissonian distributed with the flux
+level.  However, in regions with CTE issues, adjacent pixels are not
+independent, as the charge in those pixels is more free to spread.
+This reduces the pixel-to-pixel differences, resulting in a lower than
+expected variance.  All regions with variance less than half the
+average image level are added to the static CTEMASK.
+The next step of mask construction is to examine the flat and dark
+models, and exclude pixels that appear to be poorly corrected by these
+models.  The DARKMASK process looks for pixels that are more than
+$8\sigma$ discrepant in $10\%$ of the 100 input dark frame images
+after those images have had the dark model applied to them.  These
+pixels are assumed to be unstable with respect to the dark model, and
+have the DARK bit set in the static mask, indicating that they are
+unreliable in scientific observing.  Similarly, the FLATMASK process
+looks for pixels that are $3\sigma$ discrepant in the same fraction of
+input flat field images after both the dark and flat models have
+been applied.  Those pixels that do not follow the flat field model of
+the rest of image are assigned the FLAT mask bit in the static mask,
+removing the pixels that cannot be corrected to a linear response.
+The final step of mask construction is to examine the detector for
+bright columns and other static pixel issues.  This is first done by
+processing a set of 100 \ips{} filter science images in the same fashion as
+for the DARKMASK.  A median image is constructed from these inputs
+along with the per-pixel variance.  These images are used to identify
+pixels that have unexpectedly low variation between all inputs, as
+well as those that significantly deviate from the global median value.
+Once this initial set of bad pixels is identified, a $3\times{}3$
+pixel triangular kernel is convolved with the initial set, and any
+convolved pixel with value greater than 1 is assigned to the static
+mask.  This does an excellent job of removing the majority of the
+problem pixels.  A subsequent manual inspection allows human
+interaction to identify other inconsistent pixels including the
+vignetted regions around the edge of the detector.
+Figure \ref{fig:static mask} shows an example of the static mask for
+the full GPC1 field of view.  Table \ref{tab:mask_values} lists the
+bit mask values used for the different sources of masking.
+\begin{figure}
+  \centering
+  \includegraphics[width=0.9\hsize,angle=0,clip]{images/gpc1_mask_indexed.png}
+  \label{fig:static mask}
+  \caption{Image map of the GPC1 static mask.  The CTE regions are clearly visible as roughly triangular patches covering the corners of some OTAs.  Some entire cells are masked, including an entire column of cells on OTA14.  Calcite cells remove large areas from OTA17 AND OTA76.}
+\end{figure}
+\begin{deluxetable}{ccl}
+  \tablecolumns{3}
+  \tablewidth{0pc}
+  \tablecaption{GPC1 Mask Values}
+  \tablehead{\colhead{Mask Name} & \colhead{Mask Value} & \colhead{Description}}
+  \startdata
+  DETECTOR & 0x0001 & A detector defect is present. \\
+  FLAT     & 0x0002 & The flat field model does not calibrate the pixel reliably. \\
+  DARK     & 0x0004 & The dark model does not calibrate the pixel reliably. \\
+  BLANK    & 0x0008 & The pixel does not contain valid data. \\
+  CTE      & 0x0010 & The pixel has poor charge transfer efficiency. \\
+  SAT      & 0x0020 & The pixel is saturated. \\
+  LOW      & 0x0040 & The pixel has a lower value than expected. \\
+  SUSPECT  & 0x0080 & The pixel is suspected of being bad. \\
+  BURNTOOL & 0x0080 & The pixel contain an burntool repaired streak. \\
+  CR       & 0x0100 & A cosmic ray is present. \\
+  SPIKE    & 0x0200 & A diffraction spike is present. \\
+  GHOST    & 0x0400 & An optical ghost is present. \\
+  STREAK   & 0x0800 & A streak is present. \\
+  STARCORE & 0x1000 & A bright star core is present. \\
+  CONV.BAD & 0x2000 & The pixel is bad after convolution with a bad pixel. \\
+  CONV.POOR& 0x4000 & The pixel is poor after convolution with a bad pixel. \\
+  MARK     & 0x8000 & An internal flag for temporarily marking a pixel. \\
+  \enddata
+  \label{tab:mask_values}
+\end{deluxetable}
+\subsubsection{Dynamic masks}
+\label{sec:dynamic_masks}
+In addition to the static mask that removes the constant detector
+defects, we also generate a set of dynamic masks that change with the
+astronomical features in the image.  These masks are advisory in
+nature, and do not completely exclude the pixel from further
+processing consideration.  The first of these dynamic masks is the
+burntool advisory mask mentioned above.  These pixels are included for
+photometry, but are rejected more readily in the stacking and
+difference image construction, as they are more likely to have small
+deviations due to imperfections in the burntool correction.
+The remaining dynamic masks are not generated until the IPP
+\ippstage{camera} stage, at which point all object photometry is
+complete, and an astrometric solution is known for the exposure.  This
+added information provides the positions of bright sources based on
+the reference catalog, including those that fall slightly out of the
+detector field of view or within the inter chip gaps, where internal
+photometry may not identify them.  These bright sources are the origin
+for many of the image artifacts that the dynamic mask identifies and
+excludes.
+\subsubsubsection{Electronic crosstalk ghosts}
+\label{sec:crosstalk}
+Due to electrical crosstalk between the flex cables connecting the
+individual detector OTA devices, ghost objects can be created by the
+presence of a bright source at a different position on the camera.
+Table \ref{tab:crosstalk_rules} summarizes the list of known crosstalk
+rules, with an estimate of the magnitude difference between the source
+and ghost.  For all of the rules, any cell $v$ within the specified
+column of cells on any of the OTAs in the specified column of OTAs $Y$
+creates the ghost in the same $v$ and $Y$ in the target column of
+cells and OTAs.  In each of these cases, a source object with an
+instrumental magnitude brighter than -14.47 creates a ghost object
+many orders of magnitude fainter at the target location.  The cell
+(x,y) pixel coordinate is identical between source and ghost, as a
+result of the transfer occurring as the devices are read.  A circular
+mask is added to the ghost location with radius $R = 3.44 \left(-14.47
+- m_{source, instrumental}\right)$ pixels.  Any objects in the
+photometric catalog found at the location of the ghost mask have the
+GHOST mask bit set, marking the object as a likely ghost.  The
+majority of the crosstalk rules are bi-directional, with a source in
+either position creating a ghost at the corresponding crosstalk target
+position.  The two faintest rules are uni-directional, due to
+differences in the electronic path for the crosstalk.
+For the very brightest sources ($m_{instrumental} < -15$), there can
+be crosstalk ghosts between all columns of cells during the readout.
+These ``bleed'' ghosts were originally identified as ghosts of the
+saturation bleeds appearing in the neighboring cells, and as such, the
+masking for these objects puts a rectangular mask down from top to
+bottom of cells in all columns that are in the same row of cells as
+the bright source.  The width of this box is a function of the source
+magnitude, with $W = 5 * \left(-15 - m_{source, instrumental}\right)$
+pixels.
+\begin{deluxetable}{lllc}
+  \tablecolumns{4}
+  \tablewidth{0pc}
+  \tablecaption{GPC1 Crosstalk Rules}
+  \tablehead{\colhead{Type}&\colhead{Source OTA/Cell}&\colhead{Ghost OTA/Cell}&\colhead{$\Delta m$}}
+  \startdata
+  Inter-OTA & OTA2Y XY3v & OTA3Y XY3v & 6.16 \\
+            & OTA3Y XY3v & OTA2Y XY3v &      \\
+            & OTA4Y XY3v & OTA5Y XY3v &      \\
+            & OTA5Y XY3v & OTA4Y XY3v &      \\
+  Intra-OTA & OTA2Y XY5v & OTA2Y XY6v & 7.07 \\
+            & OTA2Y XY6v & OTA2Y XY5v &      \\
+            & OTA5Y XY5v & OTA5Y XY6v &      \\
+            & OTA5Y XY6v & OTA5Y XY5v &      \\
+  One-way   & OTA2Y XY7v & OTA3Y XY2v & 7.34 \\
+            & OTA5Y XY7v & OTA4Y XY2v &      \\
+  \enddata
+  \label{tab:crosstalk_rules}
+\end{deluxetable}
+\subsubsubsection{Optical ghosts}
+\label{sec:optical_ghosts}
+Due to imperfections in the anti-reflective coating on the optical
+surfaces of GPC1, bright sources can also result in large out of focus
+objects, particularly in the \gps{} filter data.  These objects are the
+result of light reflecting back off the surface of the detector,
+reflecting again off the lower surfaces of the optics (particularly
+the L1 corrector lens), and then back down onto the focal plane.  Due
+to the extra travel distance, the resulting source is out of focus and
+elongated along the radial direction of the camera focal plane. These
+optical ghosts can be modeled in the focal plane coordinates (L,M)
+which has its origin at the center of the focal plane.  In this
+system, a bright object at location (L,M) on the focal plane creates a
+reflection ghost on the opposite side of the optical axis at (-L,-M).
+The exact location is fit as a third order polynomial in the focal
+plane L and M directions (as listed in Table \ref{tab:ghost_centers}).
+An elliptical annulus mask is constructed at the expected ghost
+location, with the major and minor axes defined by linear functions of
+the ghost distance from the optical axis, and oriented with the
+ellipse major axis is along the radial direction (Table
+\ref{tab:ghost_radii}).  All stars brighter than a filter-dependent
+threshold (listed in Table \ref{tab:ghost_magnitudes}) have such masks
+constructed.
+\begin{deluxetable}{lcc}
+  \tablecolumns{3}
+  \tablewidth{0pc}
+  \tablecaption{Optical Ghost Center Transformations}
+  \tablehead{\colhead{Polynomial Term}&\colhead{L center}&\colhead{M center}}
+  \startdata
+  $x^0 y^0$ & -1.215661e+02 &  2.422174e+01 \\
+  $x^1 y^0$ &  1.321875e-02 &  4.170486e-04 \\
+  $x^2 y^0$ & -4.017026e-09 & -1.934260e-08 \\
+  $x^3 y^0$ &  1.148288e-10 & -1.173657e-12 \\
+  $x^0 y^1$ & -1.908074e-03 &  1.189352e-02 \\
+  $x^1 y^1$ &  8.479150e-08 & -9.256748e-08 \\
+  $x^2 y^1$ &  1.635732e-11 &  1.140772e-10 \\
+  $x^0 y^2$ &  2.625405e-08 &  8.123932e-08 \\
+  $x^1 y^2$ &  1.125586e-10 &  1.328378e-11 \\
+  $x^0 y^3$ &  2.912432e-12 &  1.170865e-10 \\
+  \enddata
+  \label{tab:ghost_centers}
+\end{deluxetable}
+\begin{deluxetable}{lcccc}
+  \tablecolumns{5}
+  \tablewidth{0pc}
+  \tablecaption{Optical Ghost Annulus Axis Length}
+  \tablehead{\colhead{Radial Order}&\colhead{Inner Major Axis}&\colhead{Inner Minor Axis}&    \colhead{Outer Major Axis}&\colhead{Outer Minor Axis}}
+  \startdata
+  $r^0$ & 3.926693e+01 & 5.287548e+01 & 7.928722e+01 & 1.314265e+02 \\
+  $r^1$ & 5.325759e-03 &-2.191669e-03 & 1.722181e-02 & -2.627153e-03 \\
+  \enddata
+  \label{tab:ghost_radii}
+\end{deluxetable}
+\begin{deluxetable}{lc}
+  \tablecolumns{2}
+  \tablewidth{0pc}
+  \tablecaption{Optical Ghost Magnitude Limits}
+  \tablehead{\colhead{Filter}&\colhead{$m_{inst}$}}
+  \startdata
+  \gps{} & -16.5 \\
+  \rps{} & -20.0 \\
+  \ips{} & -25.0 \\
+  \zps{} & -25.0 \\
+  \yps{} & -25.0 \\
+  \wps{} & -20.0 \\
+  \enddata
+  \label{tab:ghost_magnitudes}
+\end{deluxetable}
+\begin{figure}
+  \centering
+  \includegraphics[width=0.9\hsize,angle=0,clip]{images/full_fpa_ghosts.jpg}
+  \caption{Example of the full GPC1 field of view illustrating the sources and destinations of optical ghosts on exposure o5677g0123o (2011-04-26, 43s \gps{} filter).  The bright stars on OTA33 and OTA44 result in nearly circular ghosts on the opposite OTA.  In contrast, the trio of stars on OTA11 result in very elongated ghosts on OTA66.}
+\end{figure}
+\subsubsubsection{Optical glints}
+\label{sec:glints}
+Prior to 2010-08-24, a reflective surface at the edge of the camera
+aperture was incompletely screened to light passing through the
+telescope.  Sources brighter than $m_{inst} = -21$ that fell on this
+reflective surface resulted in light being scattered across the
+detector surface in a long narrow glint.  This surface was physically
+masked on 2010-08-24, removing the possibility of glints in subsequent
+data, but that taken prior have an advisory dynamic mask constructed
+when a reference source falls on the focal plane within one degree of
+the detector edge.  This mask is 150 pixels wide, with length $L =
+\left(-20 - m_{inst}\right)$ pixels.  These glint masks are
+constructed by selecting sufficiently bright sources in the reference
+catalog that fall within rectangular regions around each edge of the
+GPC1 camera.  These regions are separated from the edge of the camera
+by 17 arcminutes, and extend outwards an additional degree.
+\begin{figure}
+  \centering
+  \includegraphics[width=0.9\hsize,angle=0,clip]{images/glint_example_o5379g0103o.jpg}
+  \caption{Example of a glint on exposure o5379g0103o (2010-07-02, 45s \ips{} filter).  The source star out of the field of view creates a long reflection that extends through OTA73 and OTA63.}
+\end{figure}
+\subsubsubsection{Diffraction Spikes and Saturated Stars}
+\label{sec:diffraction_spikes}
+Bright sources also form diffraction spikes that are dynamically
+masked.  These are filter independent, and are modeled as rectangles
+with length $L = 10^{0.096 * (7.35 - m_{instrumental})} - 200$ and
+width $W = 8 + (L - 200) * 0.01$, with negative values indicating no
+mask is constructed, as the source is likely too faint to produce the
+feature.  These spikes are dependent on the camera rotation, and are
+oriented at $\theta = n * \frac{\pi}{2} - \mathrm{ROTANGLE} + 0.798$,
+based on the header keyword.
+The cores of stars that are saturated are masked as well, with a
+circular mask radius $r = 10.15 * (-15 - m_{instrumental})$.  An
+example of a saturated star, with the masked regions for the
+diffraction spikes and core saturation highlighted, is shown in Figure
+\ref{fig:saturated star}.
+\begin{figure}
+  \centering
+  \includegraphics[width=0.9\hsize,angle=0,clip]{images/o6802g0338o_XY51_b1.jpg}
+  \caption{Example of saturated star, with diffraction spikes extending from the core on exposure o6802g0338o, OTA51 (2014-05-25, 45s \gps{} filter).}
+  \label{fig:saturated star}
+\end{figure}
+\subsubsection{Masking Fraction}
+\label{sec:masking_fraction}
+For the full field of view that falls on the sixty OTAs, 14.7\% of all
+pixels are masked.  The large fraction of this masking is due to
+regions that fall within the vignetted region.  Defining the diameter
+of the unvignetted region to have be 3 degrees, and excluding pixels
+that fall beyond this point reduces the static masking fraction to
+.7\%.
+Unfortunately, due to the design of the OTAs and readout cells, a
+non-negligible fraction of the field of view falls onto an area that
+does not have a detector pixel.  For a given OTA mosaicked to a
+$4846\times{}4868$ pixel image, the 64 $590\times{}598$ pixel readout
+cells cover 95.7\% of the OTA area, providing an additional 4.3\%
+masking in the unvignetted field of view due to the absence of a
+detector pixel.
+For the inter-chip gap area loss, we use two field of view
+calculations to estimate the masking fraction.  The reference field of
+view of GPC1 is 3 degrees, which at the nominal plate scale of 0.258
+arcseconds per pixel, translates to a 20930 FPA pixel radius.  Summing
+mask fractions from these three contributions within the unvignetted
+field of view results in an average of $\sim 20\%$ masking fraction
+across the field of view.  Dynamic masking adds an additional $2-3\%$
+on average, with advisory burntool masking contributing the largest
+single component.  Table \ref{tab:mask fraction} contains estimates of
+the mask fraction in the GPC1 detector footprint by the sources of the
+masking for the 3 degree field of view, as well as for a larger 3.25
+degree field of view that allows addition unvignetted regions in the
+corners to contribute.
+\begin{deluxetable}{lcc}
+  \tablecolumns{3}
+  \tablewidth{0pc}
+  \tablecaption{Mask Fraction by Mask Source}
+  \tablehead{\colhead{Mask Source}&\colhead{3 Degree FOV}&\colhead{3.25 Degree FOV}}
+  \startdata
+  No pixel        & 4.44\% & 9.47\% \\
+  Detector defect & 6.37\% & 7.91\% \\
+  CTE issue       & 2.62\% & 3.13\% \\
+  \enddata
+  \label{tab:mask fraction}
+\end{deluxetable}
+\subsection{Background subtraction}
+\label{sec:background}
+Once all other detrending is done, the pixels from each cell are
+mosaicked into the full $4846\times{}4868$ pixel OTA image.  A
+background model for the full OTA is then determined prior to the
+photometric analysis.  The mosaicked image is subdivided into
+$800\times{}800$ pixel segments that define each pixel of the
+background model, with the segments centered on the image center, and
+overlapping adjacent subdivisions by 400 pixels.  These overlaps help
+smooth the background model, as adjacent model pixels share input
+pixels.
+From each subdivision, 10000 random unmasked pixels are drawn.  In the
+case where the mask fraction is large (such as on OTAs near the edge
+of the field of view), and there are insufficient unmasked pixels to
+meet this criterion, all possible unmasked pixels are used instead.
+If this number is still small (less than 100 good pixels), the
+subdivision does not have a background model calculated, and instead,
+the value assigned to that model pixel is set as the average of the
+adjacent model pixels.  This allows up to eight neighboring background
+values to be used to patch these bad pixels.
+For the remaining subdivisions that have sufficient unmasked pixels
+for the background to be measured, the pixel values are used to
+calculate a set of robust statistics for the initial background guess.
+The minimum and maximum of the values are found, and checked to ensure
+that these are not the same value, which would indicate some problem
+with the input values.  The values are then inserted into a histogram
+with 1000 bins between the minimum and maximum values, and again
+checked for issues with the inputs by ensuring that the bin with the
+most input pixels does not contain more than half of the input values.
+In this case, the minimum and maximum do not constrain the true
+distribution of the input values well, and any values outside of the
+bins closest to the bin with the peak are masked for future
+consideration.  A cumulative distribution is then constructed from the
+histogram, which saves the computational cost of sorting all the input
+values.  The bins containing the 50-percentile point, as well as the
+.8\%, 84.1\% ($\pm 1 \sigma$), 30.8\%, 69.1\% ($\pm 0.5 \sigma$),
+.2\%, and 97.7\% ($\pm 2 \sigma$) points are identified in this
+cumulative histogram.  These bins, and the two bins to either side are
+then linearly interpolated to identify the pixel value corresponding
+to these points in the distribution.  The 50\% point is set as the
+median of the pixel distribution, with the standard deviation of the
+distribution set as the median of the $\sigma$ values calculated from
+the $0.5 * (\sigma_{+1} - \sigma_{-1})$, $\sigma_{+0.5} -
+\sigma_{-0.5}$, and $0.25 * (\sigma_{+2} - \sigma_{-2})$ differences.
+If this measured standard deviation is smaller than 3 times the bin
+size, then all points more than 25 bins away from the calculated
+median are masked, and the process is repeated until the bin size is
+sufficiently small to ensure that the distribution width is well
+sampled.  Once this iterative process converges, or 20 iterations are
+run, the 25- and 75-percentile values are found by interpolating the 5
+bins around the expected bin as well, and the count of the number of
+input values within this inner 50-percentile region, $N_{50}$ is
+calculated.
+These initial statistics are then used as the starting guesses for a
+second calculation of the background level that attempts to fit the
+distribution with a Gaussian.  All pixels that were masked in the
+initial calculation are unmasked, and a histogram is again constructed
+of the values, with a bin size set to $\sigma_{guess} / \left( N_{50} /
+\right)$.  With this bin size, we expect that a bin at $\pm 2
+\sigma$ will have approximately 50 input points, which gives a
+Poissonian signal to noise estimate around 7.  In the case where
+$N_{50}$ is small (due to a poorly populated input image), this bin
+size is fixed to be no larger than the guess of the standard
+deviation.  The endpoints of the histogram are clipped based on the
+input guesses, such that any input point with a value more than $5
+\sigma_{guess}$ away from the input mean are excluded from
+consideration.
+Two second order polynomial fits are then performed to the logarithm
+of the histogram counts set at the midpoint of each bin.  The first
+fit considers the ``lower half'' of the distribution, under the
+assumption that deviations from a normal distribution are caused by
+real astrophysical sources that will be brighter than the true
+background level.  From the bin with most pixel values, the lower
+bound is set by searching for the first bin from the peak that has
+fewer inputs than 25\% of the peak.  A similar search is performed for
+the upper bound, but with a criterion that the bin has fewer than 50\%
+of the peak.  On both sides of the peak, the bounds are adjusted to
+ensure that at least seven bins, equally distributed around the peak,
+are used.  The second fit is symmetric, fitting both sides of the
+distribution out to the point where the bin contains fewer than 15\%
+of the peak value.  The same seven-bin constraint is used for this
+fit.  The Gaussian mean and standard deviation are calculated from the
+polynomial coefficients, and the symmetric fit results are accepted
+unless the lower-half fit results in a smaller mean.  This process is
+repeated again if the calculated standard deviation is not larger than
+\% of the initial guess (suggesting an issue with the initial bin
+size).
+With this two-stage calculation performed across all subdivisions of
+the mosaicked OTA image, and missing model pixels filled with the
+average of their neighbors, the final background model is stored on
+disk as a $13\times{}13$ image with header entries listing the binning
+used.  The full scale background image is then constructed by
+bilinearly interpolating this binned model, and this is subtracted
+from the science image.  Each object in the photometric catalog has a
+SKY and SKY\_SIGMA value that is the evaluation of this model at the
+location of that object.
+Although this background modeling process works well for most of the
+sky, astronomical sources that are large compared to the
+$800\times{}800$ pixel subdivisions can bias the calculated background
+level high, resulting in an oversubtraction near that object.  The
+most common source that can cause this issue are large galaxies, which
+can have their own features modeled as being part of the background.
+For the specialized processing of M31, which covers an entire pointing
+of GPC1, the measured background was added back to the \ippstage{chip}
+stage images, but this special processing was not used for the large
+scale $3\Pi$ PV3 reduction.
 \section{GPC1 Detrend Construction}
 \label{sec:detrend construction}
+The detrends for GPC1 are all constructed in similar ways.  A series
+of appropriate exposures is selected from the database, and processed
+with the \ippprog{ppImage} program.  This program is used for the
+\ippstage{chip} stage processing as well, and is designed to do image
+processing.  The extent of this processing is dependent on the order
+in which the detrend is applied to science data.  In general, the
+input exposures to the detrend have all prior stages of detrend
+processing applied.  Table \ref{tab:detrend ppImage} summarizes stages
+applied for the detrends we construct.
+The various detrends for GPC1 are constructed in similar ways.  A
+series of appropriate exposures is selected from the database, and
+processed with the \ippprog{ppImage} program.  This program is used
+for the \ippstage{chip} stage processing as well, and is designed to
+do multiple image processing operations.  The extent of this
+processing is dependent on the order in which the detrend to be
+constructed is applied to science data.  In general, the input
+exposures to the detrend have all prior stages of detrend processing
+applied.  Table \ref{tab:detrend ppImage} summarizes stages applied
+for the detrends we construct.
 Once the input data has been prepared, the \ippprog{ppMerge} program
 …
 format of the detrend under construction, and after construction, are
 applied to the processed input data.  This creates a set of residual
 files that can be checked to determine if the newly created detrend
 works correctly.
 The process of detrend construction and testing can be iterated, with
+files that are checked to determine if the newly created detrend
+correctly removes the detector dependent signal.
+This process of detrend construction and testing can be iterated, with
 individual exposures excluded if they are found to be contaminating
 the output.  If the final detrend is considered sufficient, then the
+iterations are stopped and the detrend is finalized by selecting the
+date range to which it applies.  This allows subsequent science
+processing to select the detrends needed based on the observation
+date.  Table \ref{tab:detrend list} lists the set of detrends used in
 the PV3 processing.
+the output.  If the final detrend has sufficiently small residuals,
+then the iterations are stopped and the detrend is finalized by
+selecting the date range to which it applies.  This allows subsequent
+science processing to select the detrends needed based on the
+observation date.  Table \ref{tab:detrend list} lists the set of
+detrends used in the PV3 processing.
 \begin{deluxetable}{lcccc}
 …
             & 964  & 2010-09-01 00:00:00 & 2011-05-01 00:00:00 & \\
             & 965  & 2011-05-01 00:00:00 & & \\
+  FLAT      & 300  & 2009-12-09 00:00:00 & & g filter \\
+            & 301  & 2009-12-09 00:00:00 & & r filter \\
+            & 302  & 2009-12-09 00:00:00 & & i filter \\
+            & 303  & 2009-12-09 00:00:00 & & z filter \\
+            & 304  & 2009-12-09 00:00:00 & & y filter \\
+  FLAT      & 300  & 2009-12-09 00:00:00 & & \gps{} filter \\
+            & 301  & 2009-12-09 00:00:00 & & \rps{} filter \\
+            & 302  & 2009-12-09 00:00:00 & & \ips{} filter \\
+            & 303  & 2009-12-09 00:00:00 & & \zps{} filter \\
+            & 304  & 2009-12-09 00:00:00 & & \yps{} filter \\
+            & 305  & 2009-12-09 00:00:00 & & \wps{} filter \\
   FRINGE    & 296  & 2009-12-09 00:00:00 & & \\
   ASTROM    & 1064 & 2008-05-06 00:00:00 & & \\
 …
 \end{deluxetable}
-\section{GPC1 Detrend Details}
-\label{sec:detrending}
-Ensuring a consistent and uniform detector response across the
-three-degree diameter field of view of the GPC1 camera is essential to
-a well calibrated survey.  Many standard image detrending steps are
-done for GPC1, with overscan subtraction removing the detector bias
-level, dark frame subtraction to remove temperature and exposure time
-dependent detector glows, and flat field correction to remove pixel to
-pixel response functions.  We also construct fringe correction for the
-reddest data in the y filter, to remove the interference patterns that
-arise in that filter due to the variations in the thickness of the
-detector surface.
-These corrections, however, assume that the detector response is
-linear across the full range of values.  This is not universally the
-case with GPC1, and this requires an additional set of detrending
-steps to remove these non-linear responses.  The first of these is the
-\ippprog{burntool} correction, which removes the persistence trails
-caused by the incomplete transfer of charge along the readout columns.
-This bright-end nonlinearity is generally only evident for the
-brightest stars, as only pixels that are at or beyond the saturation
-point of the detector have this issue.  More widespread is the
-non-linearity at the faint end of the pixel range.  Some readout cells
-and some readout cell edge pixels experience a sag relative to linear
-at low illumination, such that faint pixels appear fainter than
-expected.  The correction to this requires amplifying the pixel values
-in these regions to match the expected model.
-The final non-linear response issue has no good option for correction.
-Large regions of some OTA cells experience charge transfer issues,
-making them unusable to be used for science observations.  These
-regions are therefore masked in processing, with these CTE regions
-making up the largest fraction of masked pixels on the detector.
-Other regions are masked for other regions, such as static bad pixel
-features or temporary readout masking caused by issues in the camera
-electronics that make these regions unreliable.  These all contribute
-to the detector mask, which is augmented in each exposure for dynamic
-features that are masked based on the astronomical features within the
-field of view.
-For the PV3 processing, all detrending is done by the
-\ippprog{ppImage} program.  This program applies the detrends to the
-individual cells, and then an OTA level mosaic is constructed for the
-science image, the mask image, and the variance map image.  The single
-epoch photometry is done at this stage as well.  The following
-subsections (\ref{sec:burntool} - \ref{sec:background}) detail these
-detrending steps, presented in the order in which they are applied to
-the individual OTA image data.
-\subsection{Burntool / Persistence effect}
-\label{sec:burntool}
-Pixels that approach the saturation point on GPC1, which varies by
-readout with common values around 60000 DN, cause persistence problems
-on that and subsequent images.  During the read out process of an
-image with such a bright pixel, some of the charge associated with it
-is not fully shifted down the detector column toward the amplifier.
-As a result, this charge remains in the starting cell, and is
-partially collected in subsequent shifts, resulting in a ``burn
-trail'' that extends from the center of the bright source away from
-the amplifier (vertically along the pixel columns toward the top of
-the cell).
-This incomplete charge shifting in nearly full wells continues as each
-row is read out.  This results in a remnant charge being deposited in
-the pixels that the full well was shifted through.  In following
-exposures, this remnant charge leaks out, resulting in a trail that
-extends from the initial location of the bright source on the previous
-image towards the amplifier (vertically down along the pixel column).
-This remnant charge can remain on the detector for up to thirty
-minutes, requiring the locations of these ``burns'' be retained
-between exposures.
-Both of these types of persistence trails are detected and optionally
-repaired via the \ippprog{burntool} program.  This program does an
-initial scan of the images, and identifies objects with pixel values
-brighter than a threshold of 30000 DN.  The trail from that star is
-fit with a one-dimensional power law in each pixel column above that
-threshold, based on empirical evidence that this is the functional
-form of this persistence effect.  This also matches the expectation
-that a constant fraction of charge is incompletely transferred at each
-shift beyond the persistence threshold.  Once this fit is done, the
-model can subtracted from the image, and the location of the star is
-stored in a table along with the exposure PONTIME, which denotes the
-number of seconds since the detector was last powered on and provides
-an internally consistent time scale.
-For subsequent exposures, the table associated with the previous image
-is read in, and after correcting trails from the stars on the new
-image, the positions of the bright stars from the table are used to
-check for remnant trails on the image.  These are fit and subtracted
-using a one-dimensional exponential model, again based on empirical
-studies.  If a significant model with is determined, then this
-location is retained in the image output table.  If not, the old burn
-is allowed to expire.
-An issue with this method of correcting the persistence trails is that
-it is based on fits to the raw image data, which may have other signal
-sources not determined by the persistence effect.  The presence of
-other stars or artifacts along the path of the burn can result in a
-poor model to be determined, resulting in either an over- or
-under-subtraction of the persistence burn.  For this reason, the image
-mask is marked with a value indicating that this correction has been
-applied.  These pixels are not fully excluded, but they are marked as
-suspect, which allows them to be excluded from consideration in
-subsequent stages, such as image stacking.
-Another concern is that the cores of very bright stars are deformed by
-this process, as the burntool fitting subtracts flux
-from only one side of the star.  As most stars that result in burns already
-have saturated cores, they are already ignored for the purpose of
-PSF determination and are flagged as saturated by the photometry
-reduction.
-\begin{figure}
-  \centering
-  \begin{minipage}{0.45\hsize}
-    \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5677g0123o_XY11_bt_trail.png}
-%    \caption{(a)}
-%  \end{subfigure}%
-%  \begin{subfigure}[]{.45\hsize}
-  \end{minipage}%
-  \begin{minipage}{0.45\hsize}
-    \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5677g0124o_XY11_bt_trail.png}
-%    \caption{(b)}
-%  \end{subfigure}
-  \end{minipage}
-  \caption{Example of a profile cut along the y-axis through a bright star on exposure o5677g0123o OTA11 in cell xy60 (left panel) and on the subsequent exposure o5677g0124o (right panel).  In both figures, the green points show the image corrected with all appropriate detrending steps, but without burntool applied, illustrating the amplitude of the persistence trails.  The red points show the same data after the burntool correction, which reduce the impact of these features.  Both exposures are in the g-filter with exposure times of 43s}
-\end{figure}
-\begin{figure}
-  \centering
-  \begin{minipage}{0.45\hsize}
-    \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5677g0123o_XY11_nobt.png}
-%    \caption{(a)}
-%  \end{subfigure}%
-%  \begin{subfigure}[]{.45\hsize}
-  \end{minipage}%
-  \begin{minipage}{0.45\hsize}
-    \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5677g0124o_XY11_nobt.png}
-%    \caption{(b)}
-%  \end{subfigure}
-  \end{minipage}
-  \begin{minipage}{0.45\hsize}
-    \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5677g0123o_XY11_bt.png}
-%    \caption{(a)}
-%  \end{subfigure}%
-%  \begin{subfigure}[]{.45\hsize}
-  \end{minipage}%
-  \begin{minipage}{0.45\hsize}
-    \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5677g0124o_XY11_bt.png}
-%    \caption{(b)}
-%  \end{subfigure}
-  \end{minipage}
-  \caption{Example of OTA11 cell xy60 on exposures o5677g0123o (left) and o5677g0124o (right).  The top panels show the image with all appropriate detrending steps, but with burntool, and the bottom show the same with burntool applied.  There is some slight over subtraction in fitting the initial trail, but the impact of the trail is greatly reduced in both exposures.}
-\end{figure}
-\subsection{Masking}
-\label{sec:masking}
-\subsubsection{Static Masks}
-\label{sec:static_masks}
-Due to the large size of the detector, it is expected that there
-are a number of pixel defects that do not have the detection
-sensitivity on par with their neighbors.  To remove these pixels, we
-have constructed a static mask that identifies the known defects.
-This mask is constructed in three phases.
-First, a CTEMASK is constructed to mask out regions in which the
-charge transfer efficiency is low compared to the rest of the
-detector.  Twenty-five of the sixty OTAs in GPC1 show some evidence of
-CTE issues, with this pattern showing up (to varying degrees) in
-roughly triangular patches on the OTA due to defects in the
-semiconductor manufacturing.  To generate the mask for these regions,
-a sample set of 26 evenly illuminated flat field images were measured
-to produce a map of the image variance in 20x20 pixel bins.  As the
-flat image is expected to illuminate the image uniformly, the expected
-variances in each bin should be Poissonian distributed with the flux
-level.  However, in regions with CTE issues, adjacent pixels are not
-independent, as the charge in those pixels is more free to spread.
-This reduces the pixel-to-pixel differences, resulting in a lower than
-expected variance.  All regions with variance less than half the
-average image level are added to the static CTEMASK.
-The next step of mask construction is to examine the flat and dark
-models, and exclude pixels that appear to be poorly corrected by these
-models.  The DARKMASK process looks for pixels that are more than
-$8\sigma$ discrepant in $10\%$ of the 100 input dark frame images
-after those images have had the dark model applied to them.  These
-pixels are assumed to be unstable with respect to the dark model, and
-have the DARK bit set in the static mask, indicating that they are
-unreliable in scientific observing.  Similarly, the FLATMASK process
-looks for pixels that are $3\sigma$ discrepant in the same fraction of
-input flat field images after both the dark and flat models have
-been applied.  Those pixels that do not follow the flat field model of
-the rest of image are assigned the FLAT mask bit in the static mask,
-removing the pixels that cannot be corrected to a linear response.
-The final step of mask construction is to examine the detector for
-bright columns and other static pixel issues.  This is first done by
-processing a set of 100 i filter science images in the same fashion as
-for the DARKMASK.  A median image is constructed from these inputs
-along with the per-pixel variance.  These images are used to identify
-pixels that have unexpectedly low variation between all inputs, as
-well as those that significantly deviate from the global median value.
-Once this initial set of bad pixels is identified, a $3\times{}3$
-pixel triangular kernel is convolved with the initial set, and any
-convolved pixel with value greater than 1 is assigned to the static
-mask.  This does an excellent job of removing the majority of the
-problem pixels.  A subsequent manual inspection allows human
-interaction to identify other inconsistent pixels including the
-vignetted regions around the edge of the detector.
-Figure \ref{fig:static mask} shows an example of the static mask for
-the full GPC1 field of view.  Table \ref{tab:mask_values} lists the
-bit mask values used for the different sources of masking.
-\begin{figure}
-  \centering
-  \includegraphics[width=0.9\hsize,angle=0,clip]{images/gpc1_mask_indexed.png}
-  \label{fig:static mask}
-  \caption{Image map of static mask. color coded based on mask reason?  It won't be visible at true pixel scale.}
-\end{figure}
-\begin{deluxetable}{ccl}
-  \tablecolumns{3}
-  \tablewidth{0pc}
-  \tablecaption{GPC1 Mask Values}
-  \tablehead{\colhead{Mask Name} & \colhead{Mask Value} & \colhead{Description}}
-  \startdata
-  DETECTOR & 0x0001 & A detector defect is present. \\
-  FLAT     & 0x0002 & The flat field model does not calibrate the pixel reliably. \\
-  DARK     & 0x0004 & The dark model does not calibrate the pixel reliably. \\
-  BLANK    & 0x0008 & The pixel does not contain valid data. \\
-  CTE      & 0x0010 & The pixel has poor charge transfer efficiency. \\
-  SAT      & 0x0020 & The pixel is saturated. \\
-  LOW      & 0x0040 & The pixel has a lower value than expected. \\
-  SUSPECT  & 0x0080 & The pixel is suspected of being bad. \\
-  BURNTOOL & 0x0080 & The pixel contain an burntool repaired streak. \\
-  CR       & 0x0100 & A cosmic ray is present. \\
-  SPIKE    & 0x0200 & A diffraction spike is present. \\
-  GHOST    & 0x0400 & An optical ghost is present. \\
-  STREAK   & 0x0800 & A streak is present. \\
-  STARCORE & 0x1000 & A bright star core is present. \\
-  CONV.BAD & 0x2000 & The pixel is bad after convolution with a bad pixel. \\
-  CONV.POOR& 0x4000 & The pixel is poor after convolution with a bad pixel. \\
-  MARK     & 0x8000 & An internal flag for temporarily marking a pixel. \\
-  \enddata
-  \label{tab:mask_values}
-\end{deluxetable}
-\subsubsection{Dynamic masks}
-\label{sec:dynamic_masks}
-In addition to the static mask that removes the constant detector
-level defects, we also generate a set of dynamic masks that change
-with the astronomical features in the image.  These masks are advisory
-in nature, and do not completely exclude the pixel from further
-processing consideration.  The first of these dynamic masks is the
-burntool advisory mask mentioned above.  These pixels are included for
-photometry, but are rejected more readily in the stacking and
-difference image construction, as they are more likely to have small
-deviations due to imperfections in the burntool correction.
-The remaining dynamic masks are not generated until the IPP \ippstage{camera}
-stage, at which point all object photometry is complete, and an
-astrometric solution is known for the exposure.  This added
-information provides the positions of bright sources based on the
-reference catalog, including those that fall slightly out of the
-detector field of view or within the inter chip gaps, where internal
-photometry may not have identified them.  These bright sources are the
-origin for many of the image artifacts that the dynamic mask
-identifies and excludes.
-\subsubsection{Electronic crosstalk ghosts}
-\label{sec:crosstalk}
-Due to electrical crosstalk between the flex cables connecting the
-individual detector OTA devices, ghost objects can be created due to
-the presence of a bright source at a different position on the camera.
-Table \ref{tab:crosstalk_rules} summarizes the list of known crosstalk
-rules, with an estimate of the magnitude difference between the source
-and ghost.  For all of the rules, any cell $v$ within the specified
-column of cells on any of the OTAs in the specified column of OTAs $Y$
-creates the ghost in the same $v$ and $Y$ in the target column of
-cells and OTAs.  In each of these cases, a source object brighter than
--14.47 instrumental magnitude creates a ghost object many orders of
-magnitude fainter at the target location.  The cell (x,y) pixel
-coordinate is identical between source and ghost, as a result of the
-transfer occurring as the devices are read.  A circular mask is added
-to the ghost location with radius $R = 3.44 \left(-14.47 - m_{source,
-  instrumental}\right)$ pixels.  Any objects in the photometric
-catalog found at the location of the ghost mask have the GHOST mask
-bit set, marking the object as a likely ghost.  The majority of the
-crosstalk rules are bi-directional, with a source in either position
-creating a ghost at the corresponding crosstalk target position.  The
-two faintest rules are uni-directional, due to differences in the
-electronic path for the crosstalk.
-For the very brightest sources ($m_{instrumental} < -15$), there can
-be crosstalk ghosts between all columns of cells during the readout.
-These ``bleed'' ghosts were originally identified as ghosts of the
-saturation bleeds appearing in the neighboring cells, and as such, the
-masking for these objects puts a rectangular mask down from top to
-bottom of cells in all columns that are in the same row of cells as
-the bright source.  The width of this box is a function of the source
-magnitude, with $W = 5 * \left(-15 - m_{source, instrumental}\right)$
-pixels.
-\begin{deluxetable}{lllc}
-  \tablecolumns{4}
-  \tablewidth{0pc}
-  \tablecaption{GPC1 Crosstalk Rules}
-  \tablehead{\colhead{Type}&\colhead{Source OTA/Cell}&\colhead{Ghost OTA/Cell}&\colhead{$\Delta m$}}
-  \startdata
-  Inter-OTA & OTA2Y XY3v & OTA3Y XY3v & 6.16 \\
-            & OTA3Y XY3v & OTA2Y XY3v &      \\
-            & OTA4Y XY3v & OTA5Y XY3v &      \\
-            & OTA5Y XY3v & OTA4Y XY3v &      \\
-  Intra-OTA & OTA2Y XY5v & OTA2Y XY6v & 7.07 \\
-            & OTA2Y XY6v & OTA2Y XY5v &      \\
-            & OTA5Y XY5v & OTA5Y XY6v &      \\
-            & OTA5Y XY6v & OTA5Y XY5v &      \\
-  One-way   & OTA2Y XY7v & OTA3Y XY2v & 7.34 \\
-            & OTA5Y XY7v & OTA4Y XY2v &      \\
-  \enddata
-  \label{tab:crosstalk_rules}
-\end{deluxetable}
-%% \begin{figure}
-%%   \centering
-%%   \caption{Figure of crosstalk ghost and bright star source.  Plot of cut across ghost to illustrate the flat-top shape.}
-%% \end{figure}
-\subsubsection{Optical ghosts}
-\label{sec:optical_ghosts}
-% http://arxiv.org/pdf/1207.2513v1.pdf
-Due to imperfections in the anti-reflective coating on the optical
-surfaces of GPC1, bright sources can also result in large out of focus
-objects, particularly in the g-filter data.  These objects are the
-result of light reflecting back off the surface of the detector,
-reflecting again off the lower surfaces of the optics (particularly
-the L1 corrector lens), and then back down onto the focal plane.  Due
-to the extra travel distance, the resulting source is out of focus and
-elongated along the radial direction of the camera focal plane. These
-optical ghosts can be modeled in the focal plane coordinates (L,M)
-which has its origin at the center of the focal plane.  In this
-system, a bright object at location (L,M) on the focal plane creates a
-reflection ghost on the opposite side of the optical axis at (-L,-M).
-The exact location is fit as a third order polynomial in the focal
-plane L and M directions (as listed in Table \ref{tab:ghost_centers}).
-An elliptical annulus mask is constructed at the expected ghost
-location, with the major and minor axes defined by linear functions of
-the ghost distance from the optical axis, and oriented with the
-ellipse major axis is along the radial direction (Table
-\ref{tab:ghost_radii}).  All stars brighter than a filter-dependent
-threshold (listed in Table \ref{tab:ghost_magnitudes}) have such masks
-constructed.
-\begin{deluxetable}{lcc}
-  \tablecolumns{3}
-  \tablewidth{0pc}
-  \tablecaption{Optical Ghost Center Transformations}
-  \tablehead{\colhead{Polynomial Term}&\colhead{L center}&\colhead{M center}}
-  \startdata
-  $x^0 y^0$ & -1.215661e+02 &  2.422174e+01 \\
-  $x^1 y^0$ &  1.321875e-02 &  4.170486e-04 \\
-  $x^2 y^0$ & -4.017026e-09 & -1.934260e-08 \\
-  $x^3 y^0$ &  1.148288e-10 & -1.173657e-12 \\
-  $x^0 y^1$ & -1.908074e-03 &  1.189352e-02 \\
-  $x^1 y^1$ &  8.479150e-08 & -9.256748e-08 \\
-  $x^2 y^1$ &  1.635732e-11 &  1.140772e-10 \\
-  $x^0 y^2$ &  2.625405e-08 &  8.123932e-08 \\
-  $x^1 y^2$ &  1.125586e-10 &  1.328378e-11 \\
-  $x^0 y^3$ &  2.912432e-12 &  1.170865e-10 \\
-  \enddata
-  \label{tab:ghost_centers}
-\end{deluxetable}
-\begin{deluxetable}{lcccc}
-  \tablecolumns{5}
-  \tablewidth{0pc}
-  \tablecaption{Optical Ghost Annulus Axis Length}
-  \tablehead{\colhead{Radial Order}&\colhead{Inner Major Axis}&\colhead{Inner Minor Axis}&    \colhead{Outer Major Axis}&\colhead{Outer Minor Axis}}
-  \startdata
-  $r^0$ & 3.926693e+01 & 5.287548e+01 & 7.928722e+01 & 1.314265e+02 \\
-  $r^1$ & 5.325759e-03 &-2.191669e-03 & 1.722181e-02 & -2.627153e-03 \\
-  \enddata
-  \label{tab:ghost_radii}
-\end{deluxetable}
-\begin{deluxetable}{lc}
-  \tablecolumns{2}
-  \tablewidth{0pc}
-  \tablecaption{Optical Ghost Magnitude Limits}
-  \tablehead{\colhead{Filter}&\colhead{$m_{inst}$}}
-  \startdata
-  g & -16.5 \\
-  r & -20.0 \\
-  i & -25.0 \\
-  z & -25.0 \\
-  y & -25.0 \\
-  w & -20.0 \\
-  \enddata
-  \label{tab:ghost_magnitudes}
-\end{deluxetable}
-\begin{figure}
-  \centering
-  \includegraphics[width=0.9\hsize,angle=0,clip]{images/full_fpa_ghosts.jpg}
-  \caption{Example of the full GPC1 field of view illustrating the sources and destinations of optical ghosts on exposure o5677g0123o (2011-04-26, 43s g-filter).  The bright stars on OTA33 and OTA44 result in nearly circular ghosts on the opposite OTA.  In contrast, the trio of stars on OTA11 result in very elongated ghosts on OTA66.}
-\end{figure}
-\subsubsection{Optical glints}
-\label{sec:glints}
-Prior to \czwdraft{DATE}, a reflective surface at the edge of the
-camera aperture was incompletely screened to light passing through the
-telescope.  Sources brighter than $m = -20$ that fell on this
-reflective surface resulted in light being scattered across the
-detector surface in a long narrow glint.  This surface was physically
-masked on \czwdraft{DATE}, removing the possibility of glints in
-subsequent data, but that taken prior have a dynamic mask constructed
-when a reference source falls on the focal plane within one degree of
-the detector edge.  This mask is 150 pixels wide, with length $L =
-\left(-20 - m_{inst}\right)$ pixels.  \czwdraft{Am I correct that
-  this is basically a one-degree edge around the detector?}
-%%
-%% GLINT_MAX_MAG                   F32 -21.0
-%% GLINT.REGION                    MULTI
-%% GLINT.REGION                    METADATA
-%%   REGION                        STR  [-38000:-24000,-20000:+20000]
-%%   GLINT.TYPE                    STR  LEFT
-%% END
-%% GLINT.REGION                    METADATA
-%%   REGION                        STR  [+24000:+38000,-20000:+20000]
-%%   GLINT.TYPE                    STR  RIGHT
-%% END
-%% GLINT.REGION                    METADATA
-%%   REGION                        STR  [-20000:+20000,+24000:+38000:]
-%%   GLINT.TYPE                    STR  TOP
-%% END
-%% GLINT.REGION                    METADATA
-%%   REGION                        STR  [-20000:+20000,-38000:-24000]
-%%   GLINT.TYPE                    STR  BOTTOM
-%% END
-\begin{figure}
-  \centering
-  \includegraphics[width=0.9\hsize,angle=0,clip]{images/glint_example_o5379g0103o.jpg}
-  \caption{Example of a glint on exposure o5379g0103o (2010-07-02, 45s i-filter).  The source star out of the field of view creates a long reflection that extends through OTA73 and OTA63.}
-\end{figure}
-\subsubsection{Diffraction Spikes and Saturated Stars}
-\label{sec:diffraction_spikes}
-Bright sources also form diffraction spikes that are dynamically
-masked.  These are filter independent, and are modeled as rectangles
-with length $L = 10^{0.096 * (7.35 - m_{instrumental})} - 200$ and
-width $W = 8 + (L - 200) * 0.01$, with negative values indicating no
-mask is constructed, as the source is likely too faint to produce the
-feature.  These spikes are dependent on the camera rotation, and are
-oriented at $\theta = n * \frac{\pi}{2} - \mathrm{ROTANGLE} + 0.798$,
-based on the header keyword.
-%\subsubsection{Saturated stars}
-%\label{sec:saturated_stars}
-The cores of stars that are saturated are masked as well, with a
-circular mask radius $r = 10.15 * (-15 - m_{instrumental})$.  An
-example of a saturated star, with the masked regions for the
-diffraction spikes and core saturation highlighted, is shown in Figure
-\ref{fig:saturated star}.
-\begin{figure}
-  \centering
-  \includegraphics[width=0.9\hsize,angle=0,clip]{images/o6802g0338o_XY51_b1.jpg}
-  \caption{Example of saturated star, with diffraction spikes extending from the core on exposure o6802g0338o, OTA51 (2014-05-25, 45s g-filter).}
-  \label{fig:saturated star}
-\end{figure}
-\subsubsection{Video Mask}
-\label{sec:video_masks}
-One aspect of the OTAs on GPC1 is that an individual cell can be read
-repeatedly while the other cells integrate, resulting in a video
-signal from that cell.  This data is used for telescope guiding
-purposes, and a single exposure is likely to have a number of these
-video cells active on different OTAs.  For the 3PI survey, the median
-exposure has 14 video cells being read, although this number ranges
-from less than five to more than thirty, depending on the stellar
-density and field pointing.  Reading these cells while integrating on
-the others changes the characteristic dark model (see Section
-\ref{sec:video_darks} below) experienced by the other cells on the
-OTA.  The observed effect of this is that the glow associated with the
-amplifiers in the corners of the cells is suppressed during the video
-readout, relative to the nominal glow.  The standard dark model
-oversubtracts this glow, resulting in dark regions in the corners of
-the cells on an OTA taking video data.  Before the nature of this
-issue was fully understood, these poorly constrained corners were
-masked with 25-pixel radius quarter circles, centered on the (0,0)
-pixel nearest the cell amplifier.  The other corners of the cell were
-masked with a 15-pixel radius quarter circle, as the amplifier
-creating the glow is associated with another cell, separated by the
-inter-cell spacing, diminishing the area affected.  Due to the large
-area that this masking would cover, the PV3 processing used a more
-robust video dark model to correct this problem, as described in
-section \ref{sec:video_darks} below.
-\subsubsection{Masking Fraction}
-\label{sec:masking_fraction}
-For the full field of view that falls on the sixty OTAs, 14.7\% of all
-pixels are masked.  The large fraction of this masking is due to
-regions that fall within the vignetted region.  Defining the diameter
-of the unvignetted region to be 3 degrees, and excluding pixels that
-fall beyond this point reduces the static masking fraction to 9.7\%.
-Unfortunately, due to the design of the OTAs and readout cells, a
-non-negligible fraction of the field of view falls onto an area that
-does not have a detector pixel.  For a given OTA mosaicked to a
-$4846\times{}4868$ pixel image, the 64 $590\times{}598$ pixel readout
-cells cover 95.7\% of the OTA area, providing an additional 4.3\%
-masking in the unvignetted field of view due to the absence of a
-detector pixel.
-For the inter-chip gap area loss, we use two field of view
-calculations to estimate the masking fraction.  The reference field of
-view of GPC1 is 3 degrees, which at the nominal plate scale of 0.258
-arcseconds per pixel, translates to a 20930 FPA pixel radius.
-%% mysql> select filter,AVG(camProcessedExp.maskfrac_ref_static), AVG(camProcessedExp.maskfrac_ref_dynamic), AVG(camProcessedExp.maskfrac_ref_advisory), AVG(camProcessedExp.maskfrac_max_static),AVG(camProcessedExp.maskfrac_max_dynamic),AVG(camProcessedExp.maskfrac_max_advisory) from camRun join camProcessedExp USING(cam_id) JOIN chipRun USING(chip_id) JOIN rawExp USING(exp_id) WHERE camRun.label = 'LAP.PV3.20140730.final' GROUP BY filter;
-%% +---------+------------------------------------------+-------------------------------------------+--------------------------------------------+------------------------------------------+-------------------------------------------+--------------------------------------------+
-%% | filter  | AVG(camProcessedExp.maskfrac_ref_static) | AVG(camProcessedExp.maskfrac_ref_dynamic) | AVG(camProcessedExp.maskfrac_ref_advisory) | AVG(camProcessedExp.maskfrac_max_static) | AVG(camProcessedExp.maskfrac_max_dynamic) | AVG(camProcessedExp.maskfrac_max_advisory) |
-%% +---------+------------------------------------------+-------------------------------------------+--------------------------------------------+------------------------------------------+-------------------------------------------+--------------------------------------------+
-%%             static              dynamic                advisory
-%% | g.00000 |   0.19642137972007 | 0.00010322263512709 |    0.026838445469766
-%%           |   0.20949461794863 |   9.89200027293e-05 |    0.026431927734548 |
-%% | r.00000 |   0.19675996201399 | 0.00025214447869606 |    0.032641054600788
-%%           |   0.20989768279138 | 0.00023994155711801 |    0.032178525485201 |
-%% | i.00000 |   0.19677587604327 | 0.00057470697316504 |    0.038096251937072
-%%           |   0.21003570722292 | 0.00053987093278142 |    0.037471018638997 |
-%% | z.00000 |    0.1974290315691 | 0.00024758901226967 |     0.03064123748973
-%%           |   0.21055007930696 | 0.00023452690039757 |    0.030144453360769 |
-%% | y.00000 |   0.19828990634315 | 0.00014523787521897 |    0.021984846417987
-%%           |   0.21130344126869 | 0.00013634812877977 |     0.02163070300815 |
-Summing mask fractions from these three contributions within the
-unvignetted field of view results in an average of $\sim 20\%$ masking
-fraction across the field of view.  Dynamic masking adds an additional
-$2-3\%$, with advisory burntool masking contributing the largest
-single component.
-\subsection{Overscan}
-\label{sec:overscan}
-Each cell on GPC1 has an overscan region that covers the first 34
-columns of each row, and the last 10 rows of each column.  No light
-lands on these pixels, so the image region is trimmed to exclude them.
-Each row has an overscan value subtracted, calculated by finding the
-median value of that row's overscan pixels and then smoothing between
-rows with a three-row boxcar median.
-\subsection{Non-linearity Correction}
-\label{sec:nonlinearity}
-% check notebook, 2010-07/08
-The pixels of GPC1 are not uniformly linear at all flux levels.  In
-particular, at low flux levels, some pixels have a tendency to sag
-relative to the expected linear value.  This effect is most pronounced
-along the edges of the detector cells, although some entire cells show
-evidence of this effect.
-To correct this sag, we studied the flux behavior of a series of flat
-frames for a ramp of exposure times with approximate logarithmically
-equal spacing between 0.01s and 57.04s.  As the exposure time
-increases, the flux on each pixel also increases in what is expected
-to be a linear manner.  Each of these flat exposures in this ramp is
-overscan corrected, and then the median is calculated for each cell,
-as well as for the rows and columns within ten pixels of the edge of
-the science region.  From these median values at each exposure time
-value, we can construct the expected trend by fitting a linear model,
-$f_{region} = G * t_{exp} + B$, to determine the gain, $G$, and the
-bias, $B$, for the region considered.  This fitting was limited to only
-the range of fluxes between 12000 and 38000 counts, as these ranges
-were found to match the linear model well.  This range avoids the
-non-linearity at low fluxes, as well as the possibility of high-flux
-non-linearity effects.
-We store the average flux measurement and deviation from the linear
-fit for each exposure time for all regions on all detector cells in
-the linearity detrend look up tables.  When this is applied to science
-data, these lookup tables are loaded, and a linear interpolation is
-performed to determine the correction needed for the flux in that
-pixel.  This look up is performed for both the row and column of each
-pixel, to allow the edge correction to be applied where applicable,
-and the full cell correction elsewhere.  The average of these two
-values is then applied to the pixel value, reducing the effects of
-pixel nonlinearity.
-This non-linearity effect appears to be stable in time for the
-majority of the detector pixels, with little evident change over the
-survey duration.  However, as the non-linearity is most pronounced at
-the edges of the detector cells, those are the regions where the
-correction is most likely to be incomplete.  Because of this fact,
-most pixels in the static mask with either the DARKMASK or FLATMASK
-bit set are found along these edges.  As the non-linearity correction
-is unable to reliably restore these pixels, they produce inconsistent
-values after the dark and flat have been applied, and are therefore
-rejected.
-%% exptime n_included/det_id = 372
-%% clearly this isn't the one used, as 3-12 spans three data points, poorly.x
-%% 0.01 2
-%% 0.14 2
-%% 0.27 2
-%% 0.49 2
-%% 0.72 2
-%% 1.06 2
-%% 1.41 2
-%% 2.02 2
-%% 2.63 2
-%% 3.94 2
-%% 5.25 2
-%% 8.74 2
-%% 13.09 2
-%% 17.4 2
-%% 20.86 2
-%% 24.3 2
-%% 27.78 2
-%% 31.24 2
-%% 34.65 2
-%% 38.12 2
-%% 42.41 2
-%% 46.69 2
-%% 51.89 2
-%% 57.04 2
-%http://svn.pan-starrs.ifa.hawaii.edu/trac/ipp/wiki/DetectorLinearity_AllEdges
-%http://svn.pan-starrs.ifa.hawaii.edu/trac/ipp/wiki/DetectorLinearityArchive
-\begin{figure}
-  \centering
-  \includegraphics[width=0.9\hsize,angle=0,clip]{images/linearity_XY27_xy16.png}
-  \caption{Example plot of the linearity correction as a fraction of observed flux for OTA27, cell xy16.}
-\end{figure}
-\subsection{Dark/Bias Subtraction}
-\label{sec:dark}
-% http://svn.pan-starrs.ifa.hawaii.edu/trac/ipp/wiki/Background_Dark_Model
-The dark model we make for GPC1 considers each pixel individually,
-independent of any neighbors.  To create the dark model, we fit an
-multi-dimensional model to the array of input pixels from a randomly
-selected set of 100-150 overscan and non-linearity corrected dark
-frames chosen from a given date range.  The model fits each pixel as a
-function of the exposure time $t_{exp}$ and the detector temperature
-$T_{chip}$ of the input images such that $\mathrm{dark} = a_0 + a_1
-t_{exp} + a_2 T_{chip} t_{exp} + a_3 T_{chip}^2 t_{exp}$.  This
-fitting uses two iterations to produce a clipped fit, rejecting at the
-$3\sigma$ level.  The final coefficients $a_i$ for the dark model are
-stored in the detrend image.  The constant $a_0$ term includes the
-residual bias signal after overscan subtraction, and as such, a
-separate bias subtraction is not necessary.
-Applying the dark model is simply a matter of calculating the response
-to the exposure time and detector temperature for the image to be
-corrected, and subtracting the resulting dark signal from the image.
-\subsubsection{Time evolution}
-The dark model is not consistently stable over the full survey, with
-significant drift over the course of multiple months.  Some of the
-changes in the dark can be attributed to changes in the voltage
-settings of the GPC1 controller electronics, but the majority seem to
-be the result of some unknown parameter.  We can separate the dark
-model history of GPC1 into three epochs.  The first epoch covers all
-data taken prior to 2010-01-23.  This epoch used a different header
-keyword for the detector temperature, making data from this epoch
-incompatible with later dark models.
-The second epoch covers data between 2010-01-23 and 2011-05-01, and is
-characterized by a largely stable but oscillatory dark solution.
-There are two modes that the dark model switches between apparently at
-random.  No clear cause has been established for the switching, but
-there are clear differences between the two modes that require the
-observation dates to be split to use the model that is most
-appropriate.
-The initial evidence of these two modes comes from the discovery of a
-slight gradient along the rows of certain cells.  This is a result of
-a drift in the bias level of the detector as it is read out.  An
-appropriate dark model should remove this gradient entirely.  For
-these two modes, the direction of this bias drift is different, so a
-single dark model generated from all dark images in the time range
-over corrects the positive-gradient mode, and under corrects the
-negative-gradient mode.  Upon identifying this two-mode behavior, and
-determining the dates each mode was dominant, two separate dark
-models were constructed from appropriate ``A'' and ``B'' mode dark
-frames.  Using the appropriate dark minimizes the effect of this bias
-gradient in the dark corrected data.
-The bias drift gradients of the mode switching can be visualized in
-Figure \ref{fig:dark switching}.  This figure shows image profile
-along the x-pixel axis binned along the full y-axis of dark corrected
-images for OTA67.  These images are from sequential days, and have
-been corrected with a dark model constructed from the full set of dark
-data within the second epoch.  The opposite sign of the slopes of
-these profiles indicates that the average dark model does not correct
-these dates sufficiently, due to the contradictory dark signals
-between the two modes. \czwdraft{this paragraph dependent on that figure.}
-After 2011-05-01, the two-mode behavior of the dark disappears, and is
-replaced with a slow observation date dependent drift in the magnitude
-of the gradient.  This drift is sufficiently slow that we have modeled
-it using three observation date independent dark model for different
-date ranges.  These darks cover the range from 2011-05-01 to
--08-01, 2011-08-01 to 2011-11-01, and 2011-11-01 and on.  The
-reason for this time evolution is unknown, but as it is correctable
-with a small number of dark models, this does not significantly impact
-detrending.
-\begin{figure}
-  \centering
-%  \begin{subfigure}[]{.45\hsize}
-  \begin{minipage}{0.45\hsize}
-    \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5677g0123o_M_OS_NL_XY23_b1.jpg}
-%    \caption{(a)}
-%  \end{subfigure}%
-%  \begin{subfigure}[]{.45\hsize}
-  \end{minipage}%
-  \begin{minipage}{0.45\hsize}
-    \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5677g0123o_to_DARK_XY23_b1.jpg}
-%    \caption{(b)}
-%  \end{subfigure}
-  \end{minipage}
-  \caption{An example of the dark model application to exposure o5677g0123o, OTA23 (2011-04-26, 43s g-filter).  The left panel shows the image data mosaicked to the OTA level, and has had the static mask applied, the overscan subtracted, and the detector non-linearity corrected.  The right panel, shows the same exposure with the dark applied in addition to the processing shown on the left.}
-\end{figure}
-\begin{figure}
-  \centering
-  \includegraphics[width=0.9\hsize,angle=0,clip]{images/B_profile_ex.png}
-  \caption{Example showing a profile cut across exposure o5676g0195, OTA67 (2011-04-25, 43s g-filter).  The entire first row of cells (xy00-xy07) have had a median calculated along each pixel column on the OTA mosaicked image.  Arbitrary offsets have been applied to shift the curves to not overlap.  The top curve (in purple) shows the initial raw profile, without no dark model applied.  The next curve (in green) shows the smoother profile after applying the correct B-mode dark model.  Applying the incorrect A-mode dark results in the blue curve, which shows a significant increase in gradients across the cells.  The orange curve shows the result of the PATTERN.CONTINUITY correction.  Although this creates a larger gradient across the mosaicked images, it decreases the cell-to-cell level changes.  The final yellow curve shows the final image profile after all detrending and background subtraction, and has not had an offset applied.  The bright source at the cell xy00 to xy01 transition is a result of a large optical ghost, which due to the area covered, increases the median level more than the field stars.}
-  \label{fig:dark switching}
-\end{figure}
-\subsubsection{Video Dark}
-\label{sec:video_darks}
-The dark signal is stronger in cell corners due to glow from the
-read-out amplifiers.  The standard dark model corrects this for most
-observations.  However, as mentioned above, when a cell is repeatedly
-read in video mode, the dark model for the OTA containing it changes.
-Surprisingly, added reads for the video cell do not amplify the
-amplifier glow, but rather decrease the dark signal in these regions.
-As a result, using the standard dark model on the data for these OTAs
-results in oversubtraction of the corner glow.
-Video darks have been constructed to eliminate the effect this
-observational change has on the final image quality.  This was done by
-running the standard dark construction process on a series of dark
-frames that have had the video signal enabled for some cells.  GPC1
-can only run video signals on a subset of the OTAs at a given time.
-This requires two passes to enable the video signal across the full
-set of OTAs that support video cells.  This is beneficial to the
-process of creating darks, as those OTAs that do not have video
-signals enabled create standard dark models, while the video dark is
-created for the other devices.
-This simultaneous construction of video and standard dark models is
-useful, as it provides the ability to isolate the response on the
-standard dark from the video signals.  Isolating this response is
-essential for attempting to create archival video darks.  We only have
-raw video dark frame data after 2012-05-16, when this problem was
-initially identified, so any data prior to that can not be directly
-corrected for the video dark signal.  Isolating the video signal
-response allows linear corrections to the pre-existing standard dark
-models for archival data.  Testing this shows that constructing a
-video dark for older data simply as $VD_{2009} = D_{2009} - D_{Modern}
-+ VD_{Modern}$ produces a satisfactory result that does not
-oversubtract the amplifier glow.  This is shown in figure
-\ref{fig:video_darks}, which shows video cells from before 2012-05-16,
-corrected with both the standard and video darks, with the early video
-dark constructed in such a manner.
-\begin{figure}
-  \centering
-%  \begin{subfigure}[]{.45\hsize}
-  \begin{minipage}{0.45\hsize}
-    \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5677g0123o_VIDEODARK_VDim_Rdark_XY22_b1.jpg}
-%    \caption{(a)}
-%  \end{subfigure}%
-%  \begin{subfigure}[]{.45\hsize}
-  \end{minipage}%
-  \begin{minipage}{0.45\hsize}
-    \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5677g0123o_VIDEODARK_VDim_VDdark_XY22_b1.jpg}
-%    \caption{(b)}
-%  \end{subfigure}
-  \end{minipage}
-  \caption{An example of the video dark model application to exposure o5677g0123o, OTA22 (2011-04-26, 43s g-filter), which has a video cell located in cell xy16.  The left panel shows the image data mosaicked to the OTA level, and has had the static mask applied, the overscan subtracted, the detector non-linearity corrected, and a regular dark applied.  The right panel, shows the same exposure with a video dark applied instead of the standard dark.  The main impact of this change is the improved correction of the corner glows, which are oversubtracted with the standard dark.}
-  \label{fig:video_darks}
-\end{figure}
-\subsection{Noisemap}
-\label{sec:noisemap}
-Based on a study of the positional dependence of all detected sources,
-we have discovered that the cells in GPC1 do not have uniform noise
-characteristics.  Instead, there is a gradient along the pixel rows,
-with the noise generally higher away from the read out amplifier
-(higher cell x pixel positions).  This is likely an effect of the
-row-by-row bias issue discussed below.  This gradient causes the read
-noise to increase as the row is read out.  As a result of this
-increased noise, more sources are detected in the higher noise regions
-when the read noise is assumed constant across the readout.  To
-mitigate this noise gradient, we constructed an initial set of
-noisemap images by measuring the median variance on bias frames.  The
-variance is calculated in boxes of 20x20 pixels, and then linearly
-interpolated to cover the full image.
-Unfortunately, due to correlations within this noise, the variance
-measured from the bias images does not fully remove the positional
-dependence of objects that are detected.  The reason for this is that
-this simple noisemap underestimates the noise observed when the image
-is filtered during the object detection process.  This filtering
-convolves the background noise with a PSF, which has the effect of
-amplifying the correlated peaks in the noise.  This amplification can
-therefore boost background fluctuations above the threshold used to
-select real objects, contaminating the final object catalogs.
-In the detection process, we expect false positives at a rate equal to
-the one-tailed probability beyond the detection threshold.  For these
-tests, only detections measured at the $\sigma_{thresh} = 5\sigma$
-level are used, to match that used in the photometry on science data.
-This probability can be converted into a number of false number by
-considering a given area.  As the detections must be isolated to not
-be detected as an extended object, this area must be reduced by the
-area a given PSF occupies.  Combining this, we find that we expect a
-probability $P = 1 - \Phi_{normal}(5) = \frac{1}{2}
-\erfcinv\left(\frac{5}{\sqrt{2}}\right)$, and an area given $N$
-exposures of area $X\times Y$, $A = \frac{X \times Y \times
-  N}{A_{PSF}}$.  For a typical $1"$ seeing, $A_{PSF}$ is approximately
-pixels.  Using this model for the false positives, we found that
-the added read noise was insufficient to account for the observed
-false positive rate.  Inverting this relation, we can measure
-$\sigma_{obs}$, the true threshold level based on the number of false
-positives observed.  This $\sigma_{obs}$ is the combined to form a
-boost factor $B = \sigma_{thresh} / \sigma_{obs}$ that amplifies the
-  noisemap to match the observed false detection rate.
-The row-to-row variations that contribute to the extra noise are
-related to the dark model, and because of this, as the dark model
-changes, the effective noise also changes.  To ensure that the
-noisemap accurately matches the true noise level, we have created
-different noisemap models for the three major time ranges of the dark
-model.  We do not see any strong evidence that the noisemaps have the
-A/B modes visible in the dark, and so we do not generate different
-models for each individual dark model.  The additional pixel-to-pixel
-variance from this noisemap is added to the Poissonian variance to
-form the science variance image generated by the \ippstage{chip}
-processing.
-\subsection{Flat}
-Determining a flat field correction for GPC1 is a challenging
-endeavor, as the wide field of view makes it difficult to construct a
-uniformly illuminated image.  Using a dome screen is not possible, as
-the variations in illumination and screen rigidity create large
-scatter between different images that are not caused by the detector
-response function.  Because of this, we use sky flat images taken at
-twilight, which are more consistently illuminated than screen flats.
-We calculate the mean of these images to determine the initial flat
-model.
-From this starting model, we construct a correction to remove the
-effect of the illumination differences over the detector surface.
-This is done by dithering a series of science exposures with a given
-pointing.  By fully calibrating these exposures with the initial flat
-model, and then comparing the measured fluxes for the same star as a
-function of position on the detector, we can determine position
-dependent scaling factors.  From the set of scaling factors for the
-full catalog of stars observed in the dithered sequence, we can
-construct a model of the error in the initial flat model as a function
-of detector position.  Applying a correction that reduces the
-amplitude of these errors produces a flat field model that better
-represents the true detector response.
-The flat model appears stable with time, although directly measuring
-this is as difficult as originally constructing the model.  However,
-due to the photometric consistency observed in the final catalog of
-GPC1 measurements \citep{MagnierXXX}, we can be confident that the
-flat model does not have a major time dependent component.
-\subsection{Pattern correction}
-\label{sec:pattern}
-Due to detector specific issues that are not cleanly removed by the
-dark model, we have a set of ``pattern'' corrections that are applied
-to some selection of the OTAs in the camera.  This is done to reduce
-the effect that detector differences that are not stable enough to be
-corrected with a global model have on the measured astronomical
-signal.  Because these are not stable features that can simply be
-averaged over a large number of inputs, the pattern corrections
-attempt to identify and correct the detector issues based on
-appropriate filtering the individual science exposures.
-The PATTERN.ROW correction is used to remove any remaining row-by-row
-bias variation, and the PATTERN.CELL and PATTERN.CONTINUITY
-corrections attempt to ensure that the cells of a given OTA are
-consistent with the other cells on that OTA.
-\subsubsection{Pattern Row}
-% http://svn.pan-starrs.ifa.hawaii.edu/trac/ipp/wiki/GPC1_Bias_Pattern_Study
-As discussed above in the dark and noisemap sections, certain
-detectors have significant row-by-row bias offsets, caused by noise in
-the camera control electronics.  The magnitude of these offsets
-increases as the distance from the readout amplifier increases,
-resulting in horizontal streaks that are more pronounced along the
-large x pixel edge of the cell.  As the level of the offset is
-apparently random between exposures, the dark correction cannot fully
-remove this structure from the images, and the noisemap value only
-indicates the level of the average variance added by these bias
-offsets.  Therefore, we apply the PATTERN.ROW correction in an attempt
-to mitigate the offsets and correct the image values.  To force the
-rows to agree, a second order clipped polynomial is fit to each row in
-the cell.  Four fit iterations are run, and pixels $2.5\sigma$ deviant
-are excluded from subsequent fits, to minimize the effect stars and
-other astronomical signals have.  The final trend is then subtracted
-from the image.  Simply doing this subtraction will also have the
-effect of removing the background sky level.  To prevent this, the
-constant and linear terms for each row are stored, and linear fits are
-made to these parameters as a function of row.  This produces a plane
-that is added back to the image to restore the background offset and
-any linear ramp that exists in the sky.
-This correction was required on all cells on all OTAs prior to
--12-01, at which point a modification of the camera electronics
-reduced the scale of the row-by-row offsets for the majority of the
-OTAs.  As a result, we only apply this correction to the cells where
-it is still necessary, as shown in Figure \ref{fig: pattern row
-  cells}.  A list of these cells is listed in Table
-\ref{tab:pattern_row_cells}.
-Although this correction does largely resolve the row-by-row offset
-issue in a satisfactory way, large and bright astronomical objects can
-bias the fit significantly.  This results in an oversubtraction of the
-offset near these objects.  As the offsets are calculated on the pixel
-rows, this oversubtraction is not uniform around the object, but is
-preferentially along the horizontal x axis of the object.  Most
-astronomical objects are not significantly distorted by this, with
-this only becoming on issue for only bright objects comparable to the
-size of the cell (598 pixels = 150").
-%% \czwdraft{keep this?}  This row-by-row offset is visible in similar
-%% camera designs, and has been removed by identifying the noise signal
-%% in the pixel data stream.  By taking the FFT of the pixels and a
-%% reference signal, the frequency of this noise can be isolated and
-%% removed, resulting in a much cleaner image.  However, GPC1 does not
-%% record the value of the reference signal, instead automatically
-%% subtracting it from the data values.  Without this comparison signal,
-%% we have been unable to reproduce this method, as there is no obvious
-%% FFT component visible.
-\begin{deluxetable}{lcccc}
-  \tablecolumns{3}
-  \tablewidth{0pc}
-  \tablecaption{Cells which have PATTERN.ROW correction applied}
-  \tablehead{\colhead{OTA} & \colhead{Cell columns} & \colhead{Additional cells}}
-  \startdata
-  OTA11 &  & xy02, xy03, xy04, xy07 \\
-  OTA14 &  & xy23 \\
-  OTA15 & 0 & \\
-  OTA27 & 0, 1, 2, 3, 7 & \\
-  OTA31 & 7 & \\
-  OTA32 & 3, 7 & \\
-  OTA45 & 3, 7 & \\
-  OTA47 & 0, 3, 5, 7 & \\
-  OTA57 & 0, 1, 2, 6, 7 & \\
-  OTA60 &  & xy55 \\
-  OTA74 & 2, 7 & \\
-  \enddata
-  \label{tab:pattern_row_cells}
-\end{deluxetable}
-\begin{figure}
-  \centering
-  \includegraphics[width=0.9\hsize,angle=0,clip]{images/pattern_row_edit.png}
-  \caption{Diagram illustrating in red which cells on GPC1 require the PATTERN.ROW correction to be applied.  The footprint of each OTA is outlined, and cell xy00 is marked with either a filled box or an outline.  The labeling of the non-existent corner OTAs is provided to orient the focal plane.}
-  \label{fig: pattern row cells}
-\end{figure}
-\begin{figure}
-  \centering
-  \begin{minipage}{0.45\hsize}
-    \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5379g0103o_XY57_nopat.png}
-%    \caption{(a)}
-%  \end{subfigure}%
-%  \begin{subfigure}[]{.45\hsize}
-  \end{minipage}%
-  \begin{minipage}{0.45\hsize}
-    \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5379g0103o_XY57_pat.png}
-%    \caption{(b)}
-%  \end{subfigure}
-  \end{minipage}
-  \caption{Example of the PATTERN.ROW correction on exposure o5379g0103o OTA57 cell xy00 (i-filter 45s).  The left panel shows the cell with all appropriate detrending except the PATTERN.ROW, and the right shows the same cell with PATTERN.ROW applied.  The correction reduces the correlated noise on the right side, which is most distant from the read out amplifier.  There is a slight over subtraction along the rows near the bright star. \czwdraft{which I can't seem to find proper ranges to highlight.}}
-\end{figure}
-\subsubsection{Pattern Cell}
-As the measured background level of a given cell may not exactly match
-that of its neighbors, fitting a smooth background model over the full
-OTA can result in over and under-subtraction of the sky level at the
-cell boundary discontinuities.  The PATTERN.CELL correction was an
-initial attempt to remove this effect on the worst cells, by forcing
-all the cells of an OTA to the same level.  Each cell had the median
-value measured, and then each cell had an offset added that shifts the
-cell to match the median of those medians.
-This correction is reasonable when the astronomical signal is smooth,
-with no objects that are large relative to the size of an individual
-cell.  However, the presence of large galaxies (or even bright stars)
-can bias the offsets for some cells from their neighbors.  Because of
-this issue, we no longer apply this correction to any data.
-\subsubsection{Pattern Continuity}
-As the PATTERN.CELL correction was insufficient in many situations, we
-designed a replacement correction that would reduce the background
-distortion for large objects.  In addition, studies of the background
-level illustrated that the row-by-row bias can introduce small
-background gradient variations along the rows of the cells that is not
-stable enough to be completely fit by the dark model.  This common
-feature across the columns of cells results in a ``saw tooth'' pattern
-horizontally across an OTA, and as the background model fits a smooth
-sky level, this induces over and under subtraction at the cell
-boundaries.  As the PATTERN.CELL was designed to correct changes only
-in the median value between cells, it could not adequately resolve
-this higher order issue.
-The replacement for PATTERN.CELL is the PATTERN.CONTINUITY correction,
-which attempts to match the edges of a cell to those of its neighbors.
-For each cell, a thin box 10 pixels wide on each edge is extracted and
-the median value of unmasked values calculated for that box.  These
-median values are then used to construct a vector of differences
-$\Delta_i = \sum_{j} Edge_{i} - Edge_{j}$, along with a matrix of
-associations $A_{i,i'} = \sum_{j} \delta(i,j) \delta(j,i')$ denoting
-which cell boundaries touch another.  By solving the system $A x =
-diff$, we find the set of offsets $x_i$ to be applied to each cell to
-ensure the minimum differences between all cell edges and their
-neighbors.
-For OTAs that initially show the saw tooth pattern, the effect of this
-correction is to align the cells into a single ramp, at the expense of
-the absolute background level.  However, as we subtract off a smooth
-background model prior to doing photometry, these deviations from an
-absolute sky level are unimportant.  The fact that the final ramp is
-smoother than it would be otherwise also allows for the background
-subtracted image to more closely match the astronomical sky, without
-significant errors at cell boundaries.  An example of the effect of
-this correction on an image profile is shown in Figure \ref{fig:dark switching}.
-%% \begin{figure}
-%%   \centering
-%%   \caption{Continuity example, with background issue.}
-%%   \label{fig: continuity example}
-%% \end{figure}
-\subsection{Fringe correction}
-\label{sec:fringe}
-% det_id 296 is the fringe we use.
-\czwdraft{This is still a mess}
-Due to variations in the thickness of the detectors, we observe
-interference patterns at the infrared end of the filter set, as the
-wavelength of the light becomes comparable to the thickness of these
-variations.  Visually inspecting the images shows that the fringing is
-most prevalent in the y-filter images, with negligible fringing in
-other bands.  As a result of this, we only apply a fringe correction
-to the y filter data.
-The fringe used for PV3 processing was constructed from a set of 20
-s science exposures.  These exposures are overscan subtracted, and
-corrected for non-linearity, and have the dark and flat models
-applied.  These images are smoothed with a Gaussian of $\sigma = 2$
-pixels to minimize pixel to pixel noise.  The fringe image data is
-then constructed by calculating the clipped mean of the input images
-with two iteration of clipping at the $3\sigma$ level.
-A course background model is constructed by calculating the median on
-a 3x3 grid (200x200 pixels each).  A set of 1000 randomly selected
-points are selected on \czwdraft{the final image} in each cell, and
-median calculated for this position in a 10x10 pixel box, and the
-background level subtracted.  These sample locations provide scale
-points to allow the amplitude of the measured fringe to be compared to
-that found on science images.
-To apply the fringe, the same sample locations are measured on science
-image to determine the relative strength of the fringing in that
-particular image.  A least squares fit between the fringe measurements
-and the corresponding measurements on the science provides the scale
-factor multiplied by the fringe before it is subtracted from the
-science image.
-\begin{figure}
-  \centering
-  \begin{minipage}{0.5\hsize}
-    \includegraphics[width=1.0\hsize,angle=0,clip]{images/o5220g0025o_XY53_nofringe.png}
-%    \caption{(a)}
-%  \end{subfigure}%
-%  \begin{subfigure}[]{.45\hsize}
-  \end{minipage}%
-  \begin{minipage}{0.5\hsize}
-    \includegraphics[width=1.0\hsize,angle=0,clip]{images/o5220g0025o_XY53_fringe.png}
-%    \caption{(b)}
-%  \end{subfigure}
-  \end{minipage}
-  \caption{Example of the y-filter fringe pattern on exposure o5220g0025o OTA53 (y-filter 30s).  The left panel shows the OTA mosaic with all detrending except the fringe correction, while the right shows the same including the fringe correction.  Both images have been smoothed with a Gaussian with $\sigma = 3$ pixels to highlight the faint and large scale fringe patterns. \czwdraft{See if there's a way to have mana produce images larger than the screen size.}}
-  \label{fig: fringe example}
-\end{figure}
-\subsection{Background subtraction}
-\label{sec:background}
-Once all other detrending is done, the pixels from each cell are
-mosaicked into the full $4846\times{}4868$ pixel OTA image.  A
-background model for the full OTA is then determined prior to the
-photometric analysis.  The mosaicked image is binned into
-$800\times{}800$ pixel bins, centered on the image center, and
-overlapping by a factor of 2 in both axes.  These bins have 10000
-random samples drawn, and a binned cumulative distribution function is
-generated.  These bins are interpolated to find the best mean value at
-the $50\%$ level, as well as the distribution $\sigma$ by estimating
-from the $32\%$ and $68\%$ levels.  Repeating this across all bins
-results in a $13\times{}13$ grid of background bins, which are
-bilinearly interpolated to generate the background model to subtract.
-Each object in the photometric catalog has a SKY and SKY\_SIGMA value
-based on this model as well.
-%% * Magic
-%% * Warping
-%%   * warping kernel
-%%   * linear-by-pieces
-%%   * Covariance
-%%   * def of skycells?
-%% * Stacking
-%%   * pixel combination rules
-%%   * pixel rejections
-%%   * convolution for matching (success and failure)
-%% * Difference Image analysis
 \section{Warping}
 \label{sec:warping}
 …
 projected onto a common set of tangent plane projected regions called
 projection cells.  These projection cells are $4\times{}4$ degree
 fields spaced onto set of centers that fully cover the sky.  They are
+fields spaced onto a set of centers that fully cover the sky.  They are
 arranged into rings of constant declination, and allowed to overlap as
 $|\delta|$ increases.  Each projection cell is further subdivided into
 $10\times{}10$ sky cells with fixed $0.25"$ resolution pixels, with
+$10\times{}10$ sky cells with fixed $0.25"$ resolution pixels, and
 constant overlap regions between adjacent skycells of $60"$.  These
 skycells are the main image unit used for processing image data beyond
 …
 name, and the SEC keyword lists the image section corresponding to the
 locally linear grid box.  The MPX and MPY contain the transformation
+parameters for the locally linear grid.  \czwdraft{Is this accurate?}
+% Read all images and astrometry
+% Check which input images overlap with output image. => 8007 when the inputs don't overlap.
+% Loop over each image.
+% Append detections from input into output detection list.
+% Determine transform back from warp pixels to source image.
+%% 2nd order polynomial in both x and y for this transformation. and save to header
+% Break warp image into 128x128pixel locally linear areas
+% Mask non finite pixels as saturated.
+% Define Lanczos-3 interpolation over the input image.
+% Iterate over warp pixel space (on each locally linear grid) and map interpolated input pixel positions onto warp.
+% Warp pixel space is defined as center based, so that's where the intpolation point comes from.
+% Covariance calculated based on the interpolation kernel at the center of the ll grid.
+% image = interp_image * jacobian
+% var   = interp_var * jacobian**2
+% mask  = interp_mask
+% jacobian = abs(mapXx * mapYy - mapYx * mapXy)
+% I don't understand that jacobian.
+%
+parameters for the locally linear grid.  These parameters are stored
+in a string listing the reference position in the chip coordinate
+frame, the slope of the relation in the warp x axis, and the slope of
+the relation in the warp y axis.  From these keywords, any position in
+the warp can be mapped back to the location in any of the input OTA
+images.
+\begin{figure}
+  \centering
+  \includegraphics[width=0.9\hsize,angle=0,clip]{images/warp_1046511_sci.jpg}
+  \caption{Example of the warp image for skycell skycell.2047.005
+    centered at ($\alpha,\delta$) = (179.763, 32.1899) for exposure
+    o4985g0073o, (2009-06-03, 30s \zps{} filter).  The data from six
+    OTAs contribute to this image, although they are all truncated by
+    the skycell boundaries.  This skycell image is aligned such that
+    north points to the top of the image, and east to the left.  The
+    contributing OTAs are from the right half of the detector, with
+    OTA24 contributing the most pixels, and originally have the
+    positive y axis pointing to the southwest in this warped image,
+    with the positive x axis to the northwest.}
+  \label{fig:warp image}
+\end{figure}
+\begin{figure}
+  \centering
+  \includegraphics[width=0.9\hsize,angle=0,clip]{images/warp_1046511_wt.jpg}
+  \caption{Example of the warp variance image for skycell
+    skycell.2047.005 of exposure o4985g0073o, the same as in Figure
+    \ref{fig:warp image}.  This variance map retains information about
+    the higher flux levels that were found in burntool corrected
+    persistence trails, which appear here as streaks along the
+    original OTA y axis.  The amplifier glows that are corrected in
+    the dark model are also more visible in the corners of the cells
+    in OTA24.  As both of these effects are corrected in the science
+    image, there are no significant features visible there.}
+  \label{fig:warp variance}
+\end{figure}
+\begin{figure}
+  \centering
+  \includegraphics[width=0.9\hsize,angle=0,clip]{images/warp_1046511_mask.jpg}
+  \caption{Example of the warp mask image for skycell skycell.2047.005
+    of exposure o4985g0073o, the same as in Figure \ref{fig:warp
+      image}.  This mask image shows the many small defects removed
+    from the image, along with larger advisory trails on corrected
+    burntool trails.  The saturated cores of the bright stars are also
+    masked, along with the diffraction spikes found on these stars.
+    In addition OTA24 shows the precautionary crosstalk bleed masks
+    for the two brightest stars applied to all cells within the same
+    row.}
+\end{figure}
 \section{Stacking}
 …
 Once individual exposures have been warped onto a common projection
 system, they can then be combined pixel-by-pixel regardless of their
 original orientation.  Creating a stacked image by coadding the
 individual warps increases the signal to noise which allows objects
 fainter than can be found on the individual inputs to be detected.
 Creating this stack also allows a complete image to be constructed
+that does not have regions masked due to the gaps between cells and
+OTAs.  This provides a fully populated static sky image that can
 be used for subtraction to find transient sources.
+original orientation.  Creating a stacked image by co-adding the
+individual warps increases the signal to noise, allowing for the
+detection of objects that would not be sufficiently significant to be measured from a single image.
+Creating this stack also allows a complete image to be
+constructed that does not have regions masked due to the gaps between
+cells and OTAs.  This fully populated static sky image can also be
+used as a template for subtraction to find transient sources.
 The stacked image is comprised of all warp frames for a given skycell
 …
 Once all files are ingested, the first step is to measure the size and
 shapes of the input image PSFs.  We exclude images that have a PSF
 FWHM greater than 10 pixels, as those images have the seeing far worse
+than average, and would degrade the final output stack.  For the PV3
 survey, this size represents a PSF larger than $97$th percentile in
+all filters.  A target PSF for the stack is constructed by finding the
+maximum envelope of all input PSFs, which sets the target PSF to the
+largest value among the input PSFs for a given position from the peak.
+This PSF is then circularized to ensure azimuthal symmetry, which
+prevents any of the input images from being deconvolved when matched
 to the target.
 The input images also need to have their flux normalized to prevent
+FWHM greater than 10 pixels (2.5 arcseconds), as those images have the
+seeing far worse than average, and would degrade the final output
+stack.  For the PV3 $3\Pi$ survey, this size represents a PSF larger
+than the $97$th percentile in all filters.  A target PSF for the stack
+is constructed by finding the maximum envelope of all input PSFs,
+which sets the target PSF to the largest value among the input PSFs
+for a given position from the peak.  This PSF is then circularized to
+ensure azimuthal symmetry, which prevents deconvolution of any of the
+input images when matched to the target.
+The input images also need to have their fluxes normalized to prevent
 differences in seeing and sky transparency from causing discrepancies
+during pixel rejection.  From the calibrated input catalogs, we have
+the instrumental magnitudes of all sources, along with the airmass,
+image exposure time, and zeropoint.  All output stacks are calibrated
+to a zeropoint of 25.0 in all filters, and to have an airmass of 1.0.
+The output exposure time is set to the sum of the input exposure
+times.  We can determine the relative transparency for each input
+image by comparing the magnitudes of matched sources between the
+different images.  Each image then has a normalization factor defined,
+equal to $norm_{i} = (ZP_{i} - ZP_{target}) - transparency_{i} - 2.5 *
+\log_{10} (t_{target} / t_{i}) - airmassTerm * (airmass_{i} -
+airmass_{target})$.  \czwdraft{ZP.AIRMASS is zero for all filters.
+  Does this simply mean that we assume any airmass differences are
+  folded into the transparency differences?  This would simplify this
+  discussion quite a bit if that's the case, as we can just say that
+  and skip all the extra airmass terms.}
+% PREPARE
+% load sources
+% load psfs
+% determine target as envelope of input psfs
+% FWHM clipping at 10
+% measure seeing
+% -         // M_app = m_inst + zp + c1 * airmass + 2.5log(t) - transparency
+%         // EAM : the discussion here was not quite right (or at least sloppy).  Here is a replacement explanation:
+%        // For any star, the observed instrumental magnitude on an image and the apparent magnitude are related by:
+%        // M_app = m_inst + zp + c1 * airmass + 2.5log(t) - transparency
+%        // NOTE the sign of 'transparency'  this must agree with the definition in pmSourceMatch.c. see, eg, line 457 where
+%        // transparency = m_inst + zp + c1 * airmass + 2.5log(t) - M_app
+%        // we want to adjust the input images to be in a consistent flux system so that the
+%        // final stack can be generated with a specific target zero point.  Any adjustment to
+%        // the flux scale of the image must be made in coordination with the resulting
+%        // zeropoint, exposure time, and airmass such that the above relationship yields the
+%        // same apparent magnitude for a given star:
+%        // m_inst_i : instrumental mags on input image (in)
+%        // m_inst_o : instrumental mags on re-normalized image (out)
+%        // m_inst_o + zp_o + c1 * airmass_o + 2.5log(t_o) - trans_o = m_inst_i + zp_i + c1 * airmass_i + 2.5log(t_i) - trans_i
+%        // m_inst_o = m_inst_i + (zp_i - zp_o) + c1 * (airmass_i - airmass_o) + 2.5log(t_i) - 2.5log(t_o) - trans_i + trans_o
+%        // zp_i, airmass_i, t_i, trans_i : reported or measured for input image
+%        // zp_o      = zpTarget      (from recipe)
+%        // airmass_o = airmassTarget (from recipe)
+%        // t_o       = sumExpTime    [sum of input exposure times: once images are scale to this time, they can be avereaged]
+%        // trans_o   = 0.0           [obviously!]
+%        // we have 2 cases: (a) all reported ZPs are good or (b) some are bad:
+%        // (a) FPA.ZP = zp_i + c1 * airmass_i
+%        //  --> zp[i] = zp_i + c1 * airmass_i + 2.5log(exptime_i)
+%        // (b)  zp[i] = c1 * airmass_i + 2.5log(exptime_i)
+%        // NOTE: in case (b), the current code is equating the TARGET zp with the NOMINAL zp, which is wrong.
+%        // m_inst_o - m_inst_i = zp[i] - zpTarget - c1 * airmassTarget - 2.5log(sumExpTime) - trans_i
+during pixel rejection.  From the reference catalog calibrated input
+catalogs, we have the instrumental magnitudes of all sources, along
+with the airmass, image exposure time, and zeropoint.  All output
+stacks are calibrated to a zeropoint of 25.0 in all filters, and to
+have an airmass of 1.0.  The output exposure time is set to the sum of
+the input exposure times, regardless of if those inputs are rejected
+later in the combination process.  We can determine the relative
+transparency for each input image by comparing the magnitudes of
+matched sources between the different images.  Each image then has a
+normalization factor defined, equal to $\mathrm{norm}_{input} = (ZP_\mathrm{input}
+- ZP_\mathrm{target}) - \mathrm{transparency}_\mathrm{input} - 2.5 *
+\log_{10} (t_\mathrm{target} / t_\mathrm{input}) -
+\mathrm{F}_\mathrm{airmass} * (\mathrm{airmass}_\mathrm{input} -
+\mathrm{airmass}_\mathrm{target})$.  For the PV3 processing, the
+airmass factor $\mathrm{F}_\mathrm{airmass}$ was set to zero, such
+that all flux differences from differing exposure airmasses are
+assumed to be included in the zeropoint and transparency values.
+The zeropoint calibration performed here uses the calibration of the
+individual input exposures against the reference catalog.  Upon the
+conclusion of the survey, the entire set of detection catalogs is
+further re-calibrated in the ``ubercal'' process \citep{2012ApJ...756..158S}.
+This produces a more consistent calibration of each exposure across
+the entire region of the sky imaged.  This further calibration is not
+available at the time of stacking, and so there may be small residuals
+in the transparency values as a result of this \citet{magnier2017c}.
 With the flux normalization factors and target PSF chosen, the
 convolution kernels can be calculated for each image.  ISIS kernels
+are used with FWHM values of 1.5, 3.0, and 6.0 pixels and polynomial
+orders of 6, 4, and 2.  \czwdraft{Skipping this bit because I'm not
+  completely sure I understand it.}  The image is then scaled by the
+normalization as $renorm = 10^{-0.4 * norm_{image}} /
+norm_{convolution}$, and the variance by the square of that value.
+% MATCH
+% match to target PSF.
+% use ISIS kernels to do matching/convolution
+% Input sources used for psf matching.
+% @ISIS.WIDTHS    F32     1.5  3.0  6.0   # Gaussian kernel FWHM values
+% @ISIS.ORDERS    S32     6    4    2     # Polynomial orders for ISIS kernels
+\citep{1998ApJ...503..325A} are used with FWHM values of 1.5, 3.0, and 6.0
+pixels and polynomial orders of 6, 4, and 2.  Regions around the
+sources identified in the input images are extracted, convolved with
+the kernel, and the residual with the target PSF used to update the
+parameters of the kernel via least squares optimization.  Stamps that
+significantly deviate are rejected, but as the squared residual
+difference will increase with increasing source flux.  To mitigate
+this effect, a parabola is fit to the distribution of squared
+residuals as a function of source flux.  Stamps that deviate from this
+fit by more than $2.5\sigma$ are rejected, and not used on further
+kernel fit iterations.  This process is repeated twice, and the final
+convolution kernel is returned.
+This convolution may change the image flux scaling, so a normalization
+factor is used to correct this.  This normalization factor is equal to
+the ratio of $10^{-0.4 \mathrm{norm}_{input}}$ to the sum of the
+kernel.  The image is multiplied by this factor, and the variance by
+the square of it, scaling all inputs to the common zeropoint.
 Once the convolution kernels are defined for each image, they are used
 to convolve the image to match the target PSF.  Any input image that
+has a $\chi^2$ value greater than 4.0$\sigma$ larger than the median
+value is rejected from the stack.  Each image also has a weight
+assigned, based on the image variance after convolution.  For a given
+image, the weight is equal to $W^{-1} = \langle Variance(x,y) \rangle
+* f_{covariance}$, where the angle brackets denote a robust median of
+the variance image, and the covariance factor $f_{covariance}$ is the
+peak value of the covariance matrix of the convolution.
+% CONVOLVE
+% Normalization to match target zeropoint/exptime
+% Reject images with bad match chi^2 values.  MATCH.REJ * rms + median threshold.
+% Additional variance from the convolution chi^2
+% Calculate image weights based on variance: W_i = 1 / (ROBUST_MEDIAN(variance_image_i) * CovarianceFactor)
+% CovarianceFactor = covariance->kernel[0][0]
+has a kernel match $\chi^2$ value greater than 4.0$\sigma$ larger than
+the median value is rejected from the stack.  Each image also has a
+weight assigned, based on the image variance after convolution.  A
+full image weight is then calculated for each input, with the weight,
+$W_\mathrm{input}$ is equal to the inverse of the median of the image
+variance multiplied by the peak of the image covariance (due to the
+warping process).
 Following the convolution, an initial stack is constructed.  For a
 …
 \begin{eqnarray}
   S_{value} &=& \sum_i\left(value_{i} * W_i\right) / \sum_i\left(W_i\right) \\
   S_{exp weight} &=& \sum_i \left(exptime_i * W_i\right) / \sum_i\left(W_i\right) \\
+  \mathrm{Stack}_\mathrm{value} &=& \sum_i\left(\mathrm{value}_\mathrm{input} * W_\mathrm{input}\right) / \sum_\mathrm{inputs}\left(W_\mathrm{input}\right) \\
+  \mathrm{Stack}_\mathrm{exp weight} &=& \sum_i \left(\mathrm{exptime}_\mathrm{input} * W_\mathrm{input}\right) / \sum_\mathrm{inputs}\left(W_\mathrm{input}\right) \\
 \end{eqnarray}
 …
 \begin{eqnarray}
   S_{variance} &=& 1 / \sum_i \left( 1 / variance_i \right)
+  \mathrm{Stack}_\mathrm{variance} &=& 1 / \sum_i \left( 1 / \sigma^2_\mathrm{input} \right)
 \end{eqnarray}
 The output mask value is taken to be zero (no masked bits), unless
 there were no valid inputs, in which case the BLANK mask bit is set.
-% INITIAL COMBINE
-% Calculate weighted mean of input images
-% mu = sum_i(f_i * W_i) / sum_i(W_i)
-% sigma = 1 / sum_i(1 / W_i)
-% nu = sum_i(m_i)
-%     // We're not using the input pixel variances to generate a weighted average for the pixel flux (because
-%    // that introduces systematic biases), so the variance of the output pixel value should simply be:
-%    //     simga^2 = sum(weight_i^2 * sigma_i^2) / (sum(weight_i))^2
-%    // This reduces, when the weights are all identically unity, to:
-%    //     variance_combination = sum(variance_i) / N^2
-%    // and if the variances are all equal:
-%    //     variance_combination = variance_individual / N
-%    // which makes sense --- the standard deviation of the combination is reduced by a factor of sqrt(N).
-% sumValueWeight = sum_i(values * weights)
-% sumWeight = sum_i(weights)
-% sumVarianceWeight == sum( 1 / variances)
-% sumExp  = sum_i(exptimes)
-% sumExpWeight = sum_i(exptims * weights)
-% mean = sumValueWeight / sumWeight
-% var  = 1 / sumVarianceWeight
-% exp = sumExp
-% expWeight = sumExpWeight
-% EXCEPT: if N = 1, accept it.  if N = 2, take average.
-%     if (!pmStackCombine(outRO, NULL, stack, maskBad, maskSuspect, maskBlank, kernelSize, iter,
-%                        combineRej, combineSys, combineDiscard, useVariance, safe, nminpix, false)) {
-%bool pmStackCombine(
-%    pmReadout *combined,                // output stacked readout
-%    pmReadout *expmaps,                 // output exposure map information
-%    psArray *input,                     // input exposures
-%    psImageMaskType badMaskBits,        // treat these bits as 'bad'
-%    psImageMaskType suspectMaskBits,    // treat these bits as 'suspect'
-%    psImageMaskType blankMaskBits,      // use this mask value for pixels missing input data (distinguish between Ninput = 0 and Ngood = 0?)
-%    int kernelSize,
-%    float iter,             0.5
-%    float rej,              4.0
-%    float sys,              0.1
-%    float olympic,          0.2
-%    bool useVariance,
-%    bool safe,
-%    int nminpix,
-%    bool rejection)
-%{
-% combineExtract
-%% pixels with mask values as suspect are appended to suspect pixel list.
-% combinePixels
-%% As described above.
 Due to the various non-astronomical ghosts that can occur on GPC1, and
 …
 warp-warp difference images to be constructed to identify transient
 detections, higher pixel values that come from sources like optical
 ghosts depend on the telescope pointing will come in pairs as well.
+ghosts that depend on the telescope pointing will come in pairs as well.
 The higher pixel value contaminants are also potentially problematic
 as they may appear to be real sources, prompting photometry to be
 …
 to reject higher pixel values than lower pixel values.
 Following this initial combination, a ``testing'' loop iterates in an
+Following the initial combination, a ``testing'' loop iterates in an
 attempt to identify outlier points.  Again, if only one input is
 available, that input is accepted.  If there are two inputs, $A$ and
+$B$, then a check is made to see if $(0.5 * (value_A - value_B))^2 >
+rej^2 * (variance_A + variance_B + (sys * value_A)^2 + (sys *
+value_B)^2)$, where $rej$ is the number of sigma deviant a point needs
+to be to be excluded, set to 4.0 for the PV3 processing, and $sys$ is
+an estimate of the systematic error, taken to be 0.1.
+$B$, then a check is made to see if $(0.5 * (\mathrm{value}_A -
+\mathrm{value}_B))^2 > 16 * (\sigma^2_A + \sigma^2_B
++ (0.1 * \mathrm{value}_A)^2 + (0.1 * \mathrm{value}_B)^2)$, such that
+the deviation of the inputs from their mean position is greater than
+four times the sum of their measured uncertainties and a 10\%
+systematic error term.  If this is the case, neither input is trusted,
+and both are flagged for rejection
 If the number of inputs is larger than 6, then a Gaussian mixture
 …
 input values are passed to an Olympic weighted mean calculation.  We
 reject $20\%$ of the number of inputs through this process.  The
+number of bad inputs is set to $N_{bad} = 0.2 * N_{input} + 0.5$, with
+the 0.5 term ensuring at least one input is rejected.  This number is
+further separated into the number of low values to exclude $N_{low} =
+N_{bad} / 2$, which will default to zero if there are few inputs, and
+$N_{high} = N_{input} + N_{low} - N_{bad}$.  After sorting the input
+values to determine which values fall into the low and high groups,
+the remaining input values are used in a weighted mean using the image
+weights above.
+number of bad inputs is set to $N_\mathrm{bad} = 0.2 *
+N_\mathrm{input} + 0.5$, with the 0.5 term ensuring at least one input
+is rejected.  This number is further separated into the number of low
+values to exclude $N_\mathrm{low} = N_\mathrm{bad} / 2$, which will
+default to zero if there are few inputs, and $N_\mathrm{high} =
+N_\mathrm{input} + N_\mathrm{low} - N_\mathrm{bad}$.  After sorting
+the input values to determine which values fall into the low and high
+groups, the remaining input values are used in a weighted mean using
+the image weights above.
 A systematic variance term is necessary to correctly scale how
 …
 \begin{eqnarray}
   limit_{mixture model} &=& 4^2 * (variance_i + \sigma_{MM}^2) \\
   limit_{default} &=& 4^2 * (variance_i + (0.1 * value_i)^2)
+  \mathrm{limit}_\mathrm{mixture\ model} &=& 4^2 * (\sigma^2_\mathrm{input} + \sigma_\mathrm{mixture\ model}^2) \\
+  \mathrm{limit}_\mathrm{default} &=& 4^2 * (\sigma^2_\mathrm{input} + (0.1 * \mathrm{value}_\mathrm{input})^2)
 \end{eqnarray}
 Each input pixel is then compared against this limit, and the most
+discrepant pixel that has $(value_i - mean)^2$ exceeding this limit is
+identified.  If there are suspect pixels in the set those pixels are
+marked for rejection, otherwise this worst pixel is marked for
+rejection.  Following this, the combine and test loop is repeated for
+until no more pixels are rejected, up to a maximum number of
+iterations equal to $50\%$ of the number of inputs.
+% combineTest
+%% if (Ninput > 6) { use KMM }
+%% KMM:
+%% Calculate KMMmu KMMsigma KMMpi KMMPunimodal
+%% SumWeights = sum(pixelWeights)
+%% SysVar = KMMSigma**2 OR (sys * pixelData[i])**2
+%% pixelLimts[i] = rej**2 * (pixelVariances[i] + sysVar)
+% Iterate 0.5 * Ninput times (at least once)
+%% Ninput = 1 => accept
+%% Ninput = 2 => if (0.5 * (A - B))**2 > rej**2 * (pixelVariance[A] + pixelVariance[B] + (sys * A)**2 + (sys * B)**2)
+%%               then if (suspect) mark reject else mark inspect
+%% Else       => if (useKMM and Punimodal < 0.05) median = KMMmean
+%%            => else median = combinationWeightedOlympic{}
+%%            => if (pixelData - median)**2 > pixelLimits[i] then find single worst deviant pixel value
+%% then       => if suspect (mark reject) else (mark reject worst deviant pixel value)
+%% combinationWeightedOlympic =>
+%% numBad = frac * Ninput + 0.5
+%% low = numBad / 2, high = low + numGood - numBad
+%% sort(values) =>
+%% if (i > low && i <= high) { sumValues = sum_i(values * weights); sumWeight = sum_i(weights)
+%% return (sumValues / sumWeight)
+% obtain lists of inspect and reject pixels.
+% normalize:?
+%            float normalise = powf(10.0, -0.4 * norm->data.F32[i]); // Normalisation
+%            psBinaryOp(ro->image, ro->image, ``*'', psScalarAlloc(normalise, PS_TYPE_F32));
+%            psBinaryOp(ro->variance, ro->variance, ``*'', psScalarAlloc(PS_SQR(normalise), PS_TYPE_F32));
+discrepant pixel that has $(\mathrm{value}_\mathrm{input} -
+\mathrm{mean})^2$ exceeding this limit is identified.  If there are
+suspect pixels in the set, those pixels are marked for rejection,
+otherwise this worst pixel is marked for rejection.  Following this,
+the combine and test loop is repeated for until no more pixels are
+rejected, up to a maximum number of iterations equal to $50\%$ of the
+number of inputs.
 With the initial list of rejected pixels generated, a rejection mask
+is made by constructing an empty image that has the rejected pixels
+set to a value of 1.0.  This image is then convolved with a 5 pixel
+FWHM zeroth-order ISIS kernel.  Any pixels that are above the threshold of
+.5 after this mask convolution are marked as bad and will be rejected in the final combination.
+If more than 10\% of all pixels from an input image are rejected, then
+that entire image is rejected as well.
+% PIXEL REJECTION
+% Construct 15-pixel wide ISIS kernel with 5 pixel FWHM 0-order.
+% Construct image of pixels to inspect and convolve with kernel (normalize out kernel power)
+% Determine pixels are bad if they're larger than THRESHOLD.MASK = 0.5.
+% If more than IMAGE.REJ = 0.1 fraction of pixels are rejected, the entire image is rejected.
+\czwdraft{I'm not entirely sure why we do what appears to be a similar
+  operation twice.  It also seems odd that this is in the CombineFinal
+  step, and not in the Reject step.}  Finally, the rejected pixels are
+allowed to grow to include pixels that are neighbors to many rejected
+pixels.  The ISIS kernel used in the previous step is used to
+is made for the input warp by constructing an empty image that has the
+rejected pixels from that input set to a value of 1.0.  This image is
+then convolved with a 5 pixel FWHM zeroth-order ISIS kernel.  Any
+pixels that are above the threshold of 0.5 after this mask convolution
+are marked as bad and will be rejected in the final combination.  If
+more than 10\% of all pixels from an input image are rejected, then
+the entire image is rejected as it likely has some systematic issue.
+Finally, a second pass at rejecting pixels is conducted, by growing the
+current list to include pixels that are neighbors to many rejected
+pixels.  The ISIS kernel used in the previous step is again used to
 determine the largest square box that contains under the limit of
+$0.25 * \sum_{x,y} kernel^2$.  This box is then convolved with the
+rejected pixel mask to reject their neighbors.  This final list of
+rejected pixels is passed to the final combination, which creates the
+final stack values from the weighted mean of the non-rejected pixels.
+Six total images are constructed for this final stack: the image, its
+variance, a mask, a map of the exposure time per pixel, that exposure
+time map weighted by the input image weight, and a map of the number
+of inputs per pixel.
+% FINAL COMBINE
+% Grow rejected pixels
+%% set threshold of (POOR.FRACTION = 0.25) * sum(kernel)**2
+%% Choose the largest square box that contains just under that threshold.
+%% Convolve that box with the rejected pixels to grow them.
+% Run combination pass again, but without doing rejection, simply applying the rejection lists already calculated.
+% ::
+%      if (!ppStackCombineFinal(stack, options->convCovars, options, config, false, true, true, true)) {
+% iter = 0
+% combineRej = NAN
+% combineSys = NAN
+% combineDiscard = NAN
+%    if (!pmStackCombine(outRO, expRO, stack, maskBad, maskSuspect, maskBlank, 0, iter, combineRej,
+%                        combineSys, combineDiscard, useVariance, safe, nminpix, rejected)) {
+$0.25 * \sum_{x,y} kernel^2$.  This square box is then convolved with
+the rejected pixel mask to reject the neighboring pixels.  This final
+list of rejected pixels is passed to the final combination, which
+creates the final stack values from the weighted mean of the
+non-rejected pixels.  Six total images are constructed for this final
+stack: the image, its variance, a mask, a map of the exposure time per
+pixel, that exposure time map weighted by the input image weight, and
+a map of the number of inputs per pixel.
 These convolved stack products are not retained, as the convolution
 …
 across the image, as the different PSF widths of the input images
 print through in the different regions to which they have contributed.
-% UNCONVOLVED IMAGE
-%         if (!ppStackCombineFinal(stack, options->origCovars, options, config, false, true, false, true)) {
-% no grow
-% only retain unconvolved products.
 %% Asinh compression
 …
 data values must first be made positive, which then sets the highest
 quantization sampling near the lowest values in the image.  Following
 techniques used by SDSS \citep{sdss}, we have instead opted to use the
+techniques used by SDSS \citep{2000AJ....120.1579Y}, we have instead opted to use the
 inverse hyperbolic sine function to transform the data.  The domain of
 this function allows any input value to be converted.  In addition,
 …
 / \alpha) - \exp(-C / \alpha)\right)$.
+\begin{figure}
+  \centering
+  \includegraphics[width=0.9\hsize,angle=0,clip]{images/stack_3775944_sci.jpg}
+  \caption{Example of the stack image for skycell skycell.2047.005
+    centered at ($\alpha,\delta$) = (179.763, 32.1899) in the \zps{}
+    filter, stack\_id 3775944.  This stack includes 25 input images,
+    including o4985g0073o the warp image in Figure \ref{fig:warp
+      image}, and has a combined exposure time of 870s.  Combining
+    such a large number of input images removes the inter-cell and
+    inter-chip gaps, providing a fully populated image.  In addition,
+    the combined signal allows many more faint objects to be found
+    than were visible on the single frame warp image.}
+  \label{fig:stack image}
+\end{figure}
+\begin{figure}
+  \centering
+  \includegraphics[width=0.9\hsize,angle=0,clip]{images/stack_3775944_mask.jpg}
+  \caption{Example of the stack mask image for skycell
+    skycell.2047.005 centered at ($\alpha,\delta$) = (179.763,
+.1899) in the \zps{} filter, stack\_id 3775944.  The entire
+    frame is largely unmasked after combining inputs, with the only
+    remaining masks falling on the cores of bright stars, and in small
+    regions around the brightest objects where the overlapping of
+    diffraction spike masks have removed all inputs.}
+  \label{fig:stack mask image}
+\end{figure}
+\begin{figure}
+  \centering
+  \includegraphics[width=0.9\hsize,angle=0,clip]{images/stack_3775944_wt.jpg}
+  \caption{Example of the stack variance image for skycell
+    skycell.2047.005 centered at ($\alpha,\delta$) = (179.763,
+.1899) in the \zps{} filter, stack\_id 3775944.  The variance
+    map for this stack is reasonably smooth, with the mottled pattern
+    from the inter-chip and inter-cell gaps printing through.  Some
+    regions with higher variance are found where the number of inputs
+    is lower.}
+  \label{fig:stack wt image}
+\end{figure}
+\begin{figure}
+  \centering
+  \includegraphics[width=0.9\hsize,angle=0,clip]{images/stack_3775944_num.jpg}
+  \caption{Example of the stack number image for skycell
+    skycell.2047.005 centered at ($\alpha,\delta$) = (179.763,
+.1899) in the \zps{} filter, stack\_id 3775944.  This map shows
+    the number of inputs contributing to each pixel of the output
+    stack.  Again, the pattern of the inter-chip and inter-cell gaps
+    is visible, along with the mask pattern of regions with CTE
+    problems (visible in the upper right corner). }
+  \label{fig:stack num image}
+\end{figure}
+\begin{figure}
+  \centering
+  \includegraphics[width=0.9\hsize,angle=0,clip]{images/stack_3775944_exp.jpg}
+  \caption{Example of the stack exposure time image for skycell
+    skycell.2047.005 centered at ($\alpha,\delta$) = (179.763,
+.1899) in the \zps{} filter, stack\_id 3775944.  As all input
+    warps had the same 30s exposure time, this map essentially
+    recreates the number map, with units of seconds of exposure
+    instead of number of inputs contributing to a given pixel.}
+  \label{fig:stack exp image}
+\end{figure}
+\begin{figure}
+  \centering
+  \includegraphics[width=0.9\hsize,angle=0,clip]{images/stack_3775944_expwt.jpg}
+  \caption{Example of the stack weighted exposure image for skycell
+    skycell.2047.005 centered at ($\alpha,\delta$) = (179.763,
+.1899) in the \zps{} filter, stack\_id 3775944.  This map shows
+    the weighted average exposure time, as described in the text.  It
+    is similar to the simple exposure time map, but shows how some
+    input exposures have their contributions weighted down due to the
+    observed larger image variances.}
+  \label{fig:stack exp wtimage}
+\end{figure}
+\section{Difference Images}
+\label{sec:diffs}
+Constructing difference images is essentially the same as that used in
+the stacking process.  An image is chosen as a template, another image
+as the input, and after matching sources to determine the scaling and
+transparency, convolution kernels are defined that are used to
+convolve one or both of the images to a target PSF.  The images are
+then subtracted, and as they should now share a common PSF, static
+sources are largely subtracted (completely in an ideal case), whereas
+sources that are not static between the two images leave a significant
+remnant.  More information on the difference image construction is
+contained in \citet{price2017}.  The follow section contains a
+overview of the difference image construction used for the data in
+DR2.
+The images used to construct difference images can be either
+individual warp skycell frames or stacked images, with support for
+either to be used as the template or input.  In general, for
+differences using stacks, the deepest stack (or the only stack in the
+case of a warp-stack difference) is used as the template.  The PV3
+processing used warp-stack differences of all input warps against the
+stack that was constructed from those inputs.  The same ISIS kernels
+as were used in the stack image combination were again used to match
+the stack PSF to the input warp PSF.  After convolution of the image
+products, the difference is constructed for both the positive (warp
+minus stack) and inverse (stack minus warp) to allow for the
+photometry of the difference image to detect sources that both rise
+and fall relative to the stack.  Note that the convolution process
+grows the mask fraction of pixels relative to the warp (the largest
+source of masked pixels in these warp stack differences).  Any pixel
+that after convolution has any contribution from a masked pixel is
+masked as well, ensuring only fully unmasked pixels are used.
+For warp-warp differences, such as those used for the ongoing Solar
+System moving object search in nightly observations \citep{2013PASP..125..357D}, the
+warp that was taken first is used as the template.  As there is less
+certainty in which of the two input images will have better seeing, a
+``dual'' convolution method is used.  Both inputs are convolved to a
+target PSF that is not identical to either input.  This intermediate
+target is essential for the case in which the PSFs of the two inputs
+have been distorted in orthogonal directions.  Simply convolving one
+to match the other would require some degree of deconvolution along
+one axis.  As this convolution method by necessity uses more free
+parameters, the ISIS kernels used are chosen to be simpler than those
+used in the warp-stack differences.  The ISIS widths are kept the same
+(1.5, 3.0, 6.0 pixel FWHMs), but each Gaussian kernel is constrained
+to only use a second-order polynomial.  As with the warp-stack
+differences, the mask fraction grows between the input warp and the
+final difference image due to the convolution.  For the warp-warp
+differences, each image mask grows based on the appropriate
+convolution kernel, so the final usable image area is highly dependent
+on ensuring that the telescope pointings are as close to identical as
+possible.  The observing strategy to enable this is discussed in more
+detail in \citet{chambers2017}.
 \section{Discussion}
 \label{sec:discussion}
+\czwdraft{Although the detrending and image combination algorithms
+  work well to produce a consistent and calibrated images, having the
+  full PV3 data set allows issues to be identified and solutions
+  created for future improvements to the IPP pipeline.  In addition,
+  the existence of the final calibrated catalog can be used to look
+  for issues that appear dependent on focal plane position.}
+Although the detrending and image combination algorithms work well to
+produce a consistent and calibrated images, having the full PV3 data
+set allows issues to be identified and solutions created for future
+improvements to the IPP pipeline.  In addition, the existence of the
+final calibrated catalog can be used to look for issues that appear
+dependent on focal plane position.
 An obvious way to make use of the PV3 catalog is to do a statistical
 …
 There is some evidence that we have not fully identified all of these
 crosstalk rules, based on a study of PV3 images.  For example,
+extremely bright stars \czwdraft{exp o5677g0123o has this rule, find a
+  magnitude} may be able to create crosstalk ghosts between the second
+extremely bright stars may be able to create crosstalk ghosts between the second
 cell column of OTA01 and OTA21, with possibly fainter ghosts appearing
 on OTA11.  Despite the symmetry observed in the main ghost rules,
 …
 The fringe model used currently is based on only a limited number of
+days of data \czwdraft{one, I believe}.  This means that the model
+calculated may not be fully sensitive to the exact spectrum of the
+sky.  This may make the model quality differ based on the date and
+local time of observation.  There is some evidence that the fringe
+model does fit some dates better than others, and so improving this by
+expanding the number of input exposures may improve a wider range of
+dates.
+% o5818g0349o is a good example of bad fringe correction.
+days of data.  This means that the model calculated may not be fully
+sensitive to the exact spectrum of the sky.  This may make the model
+quality differ based on the date and local time of observation.  There
+is some evidence that the fringe model does fit some dates better than
+others, and so improving this by expanding the number of input
+exposures may improve a wider range of dates.
 Finally, a large number of issues arise due to the row-to-row bias
 …
+\czwdraft{I need a good concluding thing to say, so it doesn't end with, ``we should do better next time.''}
+The Pan-STARRS1 Surveys (PS1) have been
+made possible through contributions by the Institute for Astronomy, the
+University of Hawaii, the Pan-STARRS Project Office, the Max-Planck
+Society and its participating institutes, the Max Planck Institute for
+Astronomy, Heidelberg and the Max Planck Institute for Extraterrestrial
+Physics, Garching, The Johns Hopkins University, Durham University,
+the University of Edinburgh, the 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, and the National
+Aeronautics and Space Administration under Grant No. NNX08AR22G issued
+through the Planetary Science Division of the NASA Science Mission
+Directorate, the National Science Foundation Grant No. AST-1238877,
+the University of Maryland, Eotvos Lorand University (ELTE),
+and the Los Alamos National Laboratory.
+\section{Conclusion}
+The Pan-STARRS1 PV3 processing has reduced an unprecedented volume of
+image data, and has produced a catalog for the $3\Pi$ Survey
+containing hundreds of billions of individual measurements of
+three billion astronomical objects.  Accurately calibrating
+and detrending is essential to ensuring the quality of these results.
+The detrending process detailed here produces consistent data, despite
+the many individual detectors and their individual response functions.
+From these individual exposures, we are able to construct images on
+common projections and orientations, further removing the particulars
+of any single exposure.  Furthermore, by created stacked images, we
+can determine an estimate of the true static sky, providing a deep
+data set that is ideal for use as a template for image differences.
+The Pan-STARRS1 Surveys (PS1) have been made possible through
+contributions by the Institute for Astronomy, the University of
+Hawaii, the Pan-STARRS Project Office, the Max-Planck Society and its
+participating institutes, the Max Planck Institute for Astronomy,
+Heidelberg and the Max Planck Institute for Extraterrestrial Physics,
+Garching, The Johns Hopkins University, Durham University, the
+University of Edinburgh, the 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,
+and the National Aeronautics and Space Administration under Grant
+No. NNX08AR22G issued through the Planetary Science Division of the
+NASA Science Mission Directorate, the National Science Foundation
+Grant No. AST-1238877, the University of Maryland, Eotvos Lorand
+University (ELTE), and the Los Alamos National Laboratory.
+\bibliography{lib}{}
+\bibliographystyle{apj}
 …
-% http://svn.pan-starrs.ifa.hawaii.edu/trac/ipp/wiki/GPC1_Detrend_Documentation
-% http://svn.pan-starrs.ifa.hawaii.edu/trac/ipp/wiki/GPC1_Detrend_Documentation#Currentdetrends
-% http://svn.pan-starrs.ifa.hawaii.edu/trac/ipp/wiki/stacking_coverage.20130307
-% http://svn.pan-starrs.ifa.hawaii.edu/trac/ipp/wiki/staticsky.20120706_excess_detections
-% http://svn.pan-starrs.ifa.hawaii.edu/trac/ipp/wiki/Stack_Rejection_Discussion
-% http://svn.pan-starrs.ifa.hawaii.edu/trac/ipp/wiki/Stack_Algorithm

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