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Changeset 40562


Ignore:
Timestamp:
Dec 3, 2018, 5:47:07 AM (8 years ago)
Author:
eugene
Message:

added updated images; text mods from Dave Soderblom

Location:
trunk/doc/release.2015/ps1.detrend
Files:
23 added
2 edited
2 moved

Legend:

Unmodified
Added
Removed

  • trunk/doc/release.2015/ps1.detrend/Makefile

    r39866 r40562  
    11# $Id: Makefile,v 1.16 2006-01-16 01:11:40 eugene Exp $
    2 PDFLATEX = env TEXINPUTS=.:..:inputs:./inputs:LaTeX:$(TEXINPUTS): pdflatex
    3 BIBTEX   = env BIBINPUTS=.:..:inputs:../inputs BSTINPUTS=.:..:inputs:../inputs bibtex
     2
     3DO_PDFLATEX = 1
     4DO_BIBTEX = 1
    45
    56help:
    67        @echo "USAGE: make (target)"
    7         @echo "  targets:  all detrend"
     8        @echo "  targets:  all tgz pdf"
    89
    9 all: detrend.pdf
    10 
    11 DETREND = detrend.tex
    12 
    13 #       pics/Metadata.ps
    14 #       pics/earthrot.ps
    15 
    16 detrend.pdf: $(DETREND)
    17         rm -f detrend.aux detrend.bbl detrend.blg
    18         $(PDFLATEX) $<
    19         $(BIBTEX) detrend
    20         $(PDFLATEX) $<
    21         $(PDFLATEX) $<
    22         $(PDFLATEX) $<
    23 
    24 #detrend.ps: $(DETREND)
    25 
    26 include ../Makefile.Common
     10all: pdf tgz
     11tgz: detrend.tgz
     12pdf: detrend.pdf
    2713
    2814FILES = \
    … …  
    6349images/stack_3775944_expwt.jpg
    6450
    65 submission :
    66         tar --transform 's%inputs/%%' -zcf waters2017.tgz $(FILES)
     51include ../Makefile.Common
     52
     53# submission :
     54#       tar --transform 's%inputs/%%' -zcf waters2017.tgz $(FILES)

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

    r40559 r40562  
    136136(to create difference images), along with the resulting image products and their
    137137properties.
    138 \citet[][Paper I]{chambers2017} provides an overview of the Pan-STARRS System, the
     138\citet[][Paper I]{chambers2017} provide an overview of the Pan-STARRS System, the
    139139design and execution of the Surveys, the resulting image and catalog data
    140140products, a discussion of the overall data quality and basic
    … …  
    143143%Pan-STARRS Data Processing Stages
    144144\citet[][Paper II]{magnier2017.datasystem}
    145 describes how the various data processing stages are organized and
     145describe how the various data processing stages are organized and
    146146implemented
    147147in the Imaging Processing Pipeline (IPP), including details of the
    … …  
    154154%Pan-STARRS Pixel Analysis : Source Detection
    155155\citet[][Paper IV]{magnier2017.analysis}
    156 describes the details of the source detection and photometry, including
     156describe the details of the source detection and photometry, including
    157157point-spread-function and extended source fitting models, and the
    158158techniques for ``forced'' photometry measurements.
    … …  
    160160%Pan-STARRS Photometric and Astrometric Calibration
    161161\citet[][Paper V]{magnier2017.calibration}
    162 describes the final calibration process, and the resulting photometric and
     162describe the final calibration process, and the resulting photometric and
    163163astrometric quality.
    164164%Flewelling et al. 2017 (Paper VI)
    165165%Pan-STARRS 1 Database and Data Products
    166166\citet[][Paper VI]{flewelling2017}
    167 describes the details of the resulting catalog data and its organization
     167describe the details of the resulting catalog data and its organization
    168168in the Pan-STARRS database.
    169169%
    … …  
    171171\citet[][Paper VII]{huber2017}
    172172%Huber et al. 2017 (Paper VII)
    173 describes the Medium Deep Survey in detail, including the unique issues and
     173describe the Medium Deep Survey in detail, including the unique issues and
    174174data products specific to that survey. The Medium Deep Survey is not part
    175175of Data Release 1. (DR1)
    … …  
    188188view.
    189189
     190\note{DS notes fonts are not consistent for keywords, etc}
     191
     192\note{DS: captions need to be clear re: illustrated effect}
     193
    190194\note{need to define PV3 (and PV0-2) here.  see datasystem.tx}
    191195
    192196%The Processing Version 3 (PV3) reduction represents the third full
    193197DR1 contains the results of the third full reduction of the Pan-STARRS
    194 archival data.  The first two reductions were used internally for
    195 pipeline optimization and the development of the initial photometric
    196 and astrometric reference catalog \citep{magnier2017.calibration}.
    197 The products from these reductions were not publicly released, but
    198 have been used to produce a wide range of scientific papers from the
    199 Pan-STARRS 1 Science Consortium members.
     198archival data, idenfied as PV3.  Previous reductions \citep[PV0, PV1,
     199  PV2; see][]{magnier2017.datasystem}
     200were used internally for pipeline optimization and the development of
     201the initial photometric and astrometric reference catalog
     202\citep{magnier2017.calibration}.  The products from these reductions
     203were not publicly released, but have been used to produce a wide range
     204of scientific papers from the Pan-STARRS 1 Science Consortium members
     205\citep{chambers2017}.
    200206
    201207The Pan-STARRS image processing pipeline (IPP) is described elsewhere
    … …  
    232238are provided in \citet{magnier2017.analysis}.
    233239
    234 A limited version of same reduction procedure described above is also
     240A limited version of the same reduction procedure described above is also
    235241performed in real time on new exposures as they are observed by the
    236242telescope.  This process is automatic, with new exposures being
    … …  
    301307
    302308These corrections assume that the detector response is linear across
    303 the full range of values.  This assumption is not universally true for
    304 GPC1, and an additional set of detrending steps are required as a
     309the full dynamic range and that the pixels contain only signals coming
     310from the imaged portion of the sky, or from linear dark current
     311sources within the detector.  This assumption is not universally true
     312for GPC1, and an additional set of detrending steps are required as a
    305313result.  The first of these is the \IPPprog{burntool} correction,
    306314which removes the flux trails left by the incomplete transfer of
    307315charge along the readout columns.  These trails are generally only
    308316evident for the brightest stars, as only pixels that are at or beyond
    309 the saturation point of the detector leave residual charge.  More
    310 widespread is the non-linearity at the faint end of the pixel range.
    311 Some readout cells and some readout cell edge pixels experience a sag
    312 relative to linear at low illumination, such that faint pixels appear
    313 fainter than expected.  The correction to this requires amplifying the
    314 pixel values in these regions to match the expected model.
     317the saturation point of the detector leave residual charge.  A second
     318confounding effect is the non-linearity at the faint end of the pixel
     319range.  Some readout cells and some readout cell edge pixels
     320experience a sag relative to the linear trend at low illumination,
     321such that faint pixels appear fainter than expected.  The correction
     322to this requires amplifying the pixel values in these regions to match
     323the linear response.
    315324
    316325Large regions of some OTA cells experience significant charge transfer
    … …  
    326335field of view.
    327336
    328 For the PV3 processing, all detrending is done by the
    329 \IPPprog{ppImage} program.  This program applies the detrend
    330 corrections to the individual cells, and then an OTA-level mosaic is
    331 constructed for the signal image, the mask image, and the variance map
    332 image.  The single epoch photometry is done at this stage as well.
    333 The following subsections (\ref{sec:overscan} - \ref{sec:background})
    334 detail the detrending process used on GPC1 that are common to other
    335 detectors.  The GPC1 specific detrending steps are included after,
    336 explaining these additional steps that remove the instrument signature.
     337Within the IPP, all detrending is done by the \IPPprog{ppImage}
     338program.  This program applies the detrend corrections to the
     339individual cells, and then an OTA-level mosaic is constructed for the
     340signal image, the mask image, and the variance map image.  The single
     341epoch photometry is done at this stage as well.  The following
     342subsections (\ref{sec:overscan} - \ref{sec:background}) detail the
     343detrending process used on GPC1 that are common to other detectors.
     344The GPC1 specific detrending steps are included after, explaining
     345these additional steps that remove the instrument signature.
    337346
    338347\subsection{Overscan}
    … …  
    427436  \centering
    428437  \begin{minipage}{0.45\hsize}
    429     \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5677g0123o_M_OS_NL_XY23_b1.jpg}
     438    \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5677g0123o_M_OS_NL_XY23.png}
    430439  \end{minipage}%
    431440  \begin{minipage}{0.45\hsize}
    432     \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5677g0123o_to_DARK_XY23_b1.jpg}
     441    \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5677g0123o_to_DARK_XY23.png}
    433442  \end{minipage}
    434443  \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, removing the amplifier glows in the cell corners.}
    … …  
    482491  \centering
    483492  \begin{minipage}{0.45\hsize}
    484     \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5677g0123o_VIDEODARK_VDim_Rdark_XY22_b1.jpg}
     493    \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5677g0123o_VIDEODARK_VDim_Rdark_XY22.png}
    485494  \end{minipage}%
    486495  \begin{minipage}{0.45\hsize}
    487     \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5677g0123o_VIDEODARK_VDim_VDdark_XY22_b1.jpg}
     496    \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5677g0123o_VIDEODARK_VDim_VDdark_XY22.png}
    488497  \end{minipage}
    489498  \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.}
    … …  
    498507characteristics.  Instead, there is a gradient along the pixel rows,
    499508with the noise generally higher away from the read out amplifier
    500 (higher cell x pixel positions).  This is likely an effect of the
     509(higher cell $x$ pixel positions).  This is likely an effect of the
    501510row-by-row bias issue discussed below (Section~\ref{sec:pattern.row}).
    502511As a result of this increased noise, more sources are detected in the
    … …  
    526535dependent read noise.  By binning the number of false positives
    527536measured on the bias frames on the noisemap inputs using 20 pixel
    528 boxes in the cell x-axis, and comparing this to the number expected
     537boxes in the cell $x$-axis, and comparing this to the number expected
    529538from random Gaussian noise, we estimated the true read noise level.
    530539
    … …  
    574583
    575584In addition to this flat field applied to the individual images, the
    576 ubercal process used to calibrate the database of all detections
    577 \citep{2012ApJ...756..158S} constructs ``in catalog'' flat field
    578 corrections.  Although a single set of image flat fields was used for
    579 the entire PV3 survey, five separate ``seasons'' of database flat
    580 fields were needed to ensure proper calibration.  This indicates that
    581 the flat field response is not completely fixed in time.  More details
    582 on this process are contained in \citet{magnier2017.calibration}.
     585``ubercal'' analysis -- in which photometric data are used define
     586image zero points
     587\citep[][]{2012ApJ...756..158S,magnier2017.calibration} and in turn
     588used used to calibrate the database of all detections -- constructs
     589``in catalog'' flat field corrections.  Although a single set of image
     590flat fields was used for the PV3 processing of the entire $3\pi$
     591survey, five separate ``seasons'' of database flat fields were needed
     592to ensure proper calibration.  This indicates that the flat field
     593response is not completely fixed in time.  More details on this
     594process are contained in \citet{magnier2017.calibration}.
    583595
    584596\subsection{Fringe correction}
    … …  
    619631\begin{figure}
    620632  \centering
    621   \begin{minipage}{0.5\hsize}
    622     \includegraphics[width=1.5\hsize,angle=0,clip]{images/o5220g0025o_XY53_nofringe.png}
     633  \begin{minipage}{0.45\hsize}
     634    \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5220g0025o_nofringe_XY53.png}
    623635  \end{minipage}%
    624   \begin{minipage}{0.5\hsize}
    625     \includegraphics[width=1.5\hsize,angle=0,clip]{images/o5220g0025o_XY53_fringe.png}
     636  \begin{minipage}{0.45\hsize}
     637    \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5220g0025o_fringe_XY53.png}
    626638  \end{minipage}
    627639  \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.
    … …  
    710722  \tablewidth{0pc}
    711723  \tablecaption{GPC1 Mask Values}
    712   \tablehead{\colhead{Mask Name} & \colhead{Mask Value} & \colhead{Description}}
     724  \tablehead{\colhead{Mask Name} & \colhead{Mask Value} &
     725    \colhead{Description (static values listed in bold)}}
    713726  \startdata
    714   DETECTOR & 0x0001 & A detector defect is present. \\
    715   FLAT     & 0x0002 & The flat field model does not calibrate the pixel reliably. \\
    716   DARK     & 0x0004 & The dark model does not calibrate the pixel reliably. \\
    717   BLANK    & 0x0008 & The pixel does not contain valid data. \\
    718   CTE      & 0x0010 & The pixel has poor charge transfer efficiency. \\
     727  {\bf DETECTOR & 0x0001 & A detector defect is present.} \\
     728  {\bf FLAT     & 0x0002 & The flat field model does not calibrate the pixel reliably.} \\
     729  {\bf DARK     & 0x0004 & The dark model does not calibrate the pixel reliably.} \\
     730  {\bf BLANK    & 0x0008 & The pixel does not contain valid data.} \\
     731  {\bf CTE      & 0x0010 & The pixel has poor charge transfer efficiency.} \\
    719732  SAT      & 0x0020 & The pixel is saturated. \\
    720733  LOW      & 0x0040 & The pixel has a lower value than expected. \\
    721   SUSPECT  & 0x0080 & The pixel is suspected of being bad. \\
     734  SUSPECT  & 0x0080 & The pixel is suspected of being bad (overloaded with the BURNTOOL bit). \\
    722735  BURNTOOL & 0x0080 & The pixel contain an burntool repaired streak. \\
    723736  CR       & 0x0100 & A cosmic ray is present. \\
    … …  
    764777Table \ref{tab:crosstalk_rules} summarizes the list of known crosstalk
    765778rules, with an estimate of the magnitude difference between the source
    766 and ghost.  For all of the rules, any source cell $v$ within the specified
    767 column of cells on any of the OTAs in the specified column of OTAs $Y$
    768 can create a ghost in the same cell $v$ and OTA $Y$ in the target column of
    769 cells and OTAs.  In each of these cases, a source object with an
    770 instrumental magnitude brighter than -14.47 creates a ghost object
    771 many orders of magnitude fainter at the target location.  The cell
    772 (x,y) pixel coordinate is identical between source and ghost, as a
    773 result of the transfer occurring as the devices are read.  A circular
    774 mask is added to the ghost location with radius $R = 3.44 \left(-14.47
    775 - m_{source, instrumental}\right)$ pixels.  Any objects in the
    776 photometric catalog found at the location of the ghost mask have the
    777 GHOST mask bit set, marking the object as a likely ghost.  The
    778 majority of the crosstalk rules are bi-directional, with a source in
    779 either position creating a ghost at the corresponding crosstalk target
    780 position.  The two faintest rules are uni-directional, due to
    781 differences in the electronic path for the crosstalk.
    782 
    783 For the very brightest sources ($m_{instrumental} < -15$), there can
    784 be crosstalk ghosts between all columns of cells during the readout.
     779and ghost.  For all of the rules, any source cell $v$ within the
     780specified column of cells on any of the OTAs in the specified column
     781of OTAs $Y$ can create a ghost in the same cell $v$ and OTA $Y$ in the
     782target column of cells and OTAs.  This effect depends on the number of
     783electrons detected for the star, thus the size of the ghost scales
     784with the instrumental magnitude ($m_{inst} = -2.5 \log_{10} (ADU)$) of
     785the star.  In each of these cases, a source object with $m_{inst} <
     786-14.47$) (corresponding to $\rps \lesssim 14$ for the $3\pi$ survey)
     787creates a ghost object many orders of magnitude fainter at the target
     788location.  The cell ($x,y$) pixel coordinate is identical between
     789source and ghost, as a result of the transfer occurring as the devices
     790are read.  A circular mask is added to the ghost location with radius
     791$R = 3.44 \left(-14.47 - m_{inst,source}\right)$ pixels; only
     792positive radii are allowed.  Any objects in the photometric catalog
     793found at the location of the ghost mask have the GHOST mask bit set,
     794marking the object as a likely ghost.  The majority of the crosstalk
     795rules are bi-directional, with a source in either position creating a
     796ghost at the corresponding crosstalk target position.  The two
     797faintest rules are uni-directional, due to differences in the
     798electronic path for the crosstalk.
     799
     800For the very brightest sources ($m_{inst} < -15$), there can be
     801crosstalk ghosts between all columns of cells during the readout.
    785802These ``bleed'' ghosts were originally identified as ghosts of the
    786803saturation bleeds appearing in the neighboring cells, and as such, the
    … …  
    788805bottom of cells in all columns that are in the same row of cells as
    789806the bright source.  The width of this box is a function of the source
    790 magnitude, with $W = 5 * \left(-15 - m_{source, instrumental}\right)$
     807magnitude, with $W = 5 \times \left(-15 - m_{inst,source}\right)$
    791808pixels.
    792809
    … …  
    824841extra travel distance, the resulting source is out of focus and
    825842elongated along the radial direction of the camera focal plane. These
    826 optical ghosts can be modeled in the focal plane coordinates (L,M)
     843optical ghosts can be modeled in the focal plane coordinates ($L,M$)
    827844which has its origin at the center of the focal plane.  In this
    828 system, a bright object at location (L,M) on the focal plane creates a
     845system, a bright object at location ($L,M$) on the focal plane creates a
    829846reflection ghost on the opposite side of the optical axis near
    830 (-L,-M).  The exact location is fit as a third order polynomial in the
    831 focal plane L and M directions (as listed in Table
     847($-L,-M$).  The exact location is fit as a third order polynomial in the
     848focal plane $L$ and $M$ directions (as listed in Table
    832849\ref{tab:ghost_centers}).  An elliptical annulus mask is constructed
    833850at the expected ghost location, with the major and minor axes defined
    … …  
    842859  \tablewidth{0pc}
    843860  \tablecaption{Optical Ghost Center Transformations}
    844   \tablehead{\colhead{Polynomial Term}&\colhead{L center}&\colhead{M center}}
     861  \tablehead{\colhead{Polynomial Term}&\colhead{$L$ center}&\colhead{$M$ center}}
    845862  \startdata
    846863  $x^0 y^0$ & -1.215661e+02 &  2.422174e+01 \\
    … …  
    898915Prior to 2010-08-24, a reflective surface at the edge of the camera
    899916aperture was incompletely screened to light passing through the
    900 telescope.  Sources brighter than $m_{inst} = -21$ that fell on this
    901 reflective surface resulted in light being scattered across the
    902 detector surface in a long narrow glint.  This surface was physically
    903 masked on 2010-08-24, removing the possibility of glints in subsequent
    904 data, but images that were taken prior to this date have an advisory
    905 dynamic mask constructed when a reference source falls on the focal
    906 plane within one degree of the detector edge.  This mask is 150 pixels
    907 wide, with length $L = 2500 \left(-20 - m_{inst}\right)$ pixels.
    908 These glint masks are constructed by selecting sufficiently bright
    909 sources in the reference catalog that fall within rectangular regions
    910 around each edge of the GPC1 camera.  These regions are separated from
    911 the edge of the camera by 17 arcminutes, and extend outwards an
    912 additional degree.
     917telescope.  Sources brighter than $m_{inst} = -21$ ($\rps \lesssim
     9187.5$) that fell on this reflective surface resulted in light being
     919scattered across the detector surface in a long narrow glint.  This
     920surface was physically masked on 2010-08-24, removing the possibility
     921of glints in subsequent data, but images that were taken prior to this
     922date have an advisory dynamic mask constructed when a reference source
     923falls on the focal plane within one degree of the detector edge.  This
     924mask is 150 pixels wide, with length $L = 2500 \left(-20 -
     925m_{inst}\right)$ pixels.  These glint masks are constructed by
     926selecting sufficiently bright sources in the reference catalog that
     927fall within rectangular regions around each edge of the GPC1 camera.
     928These regions are separated from the edge of the camera by 17
     929arcminutes, and extend outwards an additional degree.
    913930
    914931\begin{figure}
    … …  
    924941Bright sources also form diffraction spikes that are dynamically
    925942masked.  These are filter independent, and are modeled as rectangles
    926 with length $L = 10^{0.096 * (7.35 - m_{instrumental})} - 200$ and
    927 width $W = 8 + (L - 200) * 0.01$, with negative values indicating no
     943with length $L = 10^{0.096 \times (7.35 - m_{inst})} - 200$ and
     944width $W = 8 + (L - 200) \times 0.01$, with negative values indicating no
    928945mask is constructed, as the source is likely too faint to produce the
    929946feature.  These spikes are dependent on the camera rotation, and are
    930 oriented based on the header keyword at $\theta = n * \frac{\pi}{2} -
     947oriented based on the header keyword at $\theta = n \times \frac{\pi}{2} -
    931948\mathrm{ROTANGLE} + 0.798$, for $n = {0,1,2,3}$.
    932949
    933950The cores of stars that are saturated are masked as well, with a
    934 circular mask radius $r = 10.15 * (-15 - m_{instrumental})$.  An
     951circular mask radius $r = 10.15 \times (-15 - m_{inst})$.  An
    935952example of a saturated star, with the masked regions for the
    936953diffraction spikes and core saturation highlighted, is shown in Figure
    … …  
    939956\begin{figure}
    940957  \centering
    941   \includegraphics[width=0.9\hsize,angle=0,clip]{images/o6802g0338o_XY51_b1.jpg}
     958  \includegraphics[width=0.9\hsize,angle=0,clip]{images/o6802g0338o_SATSTAR_XY51.png}
    942959  \caption{Example of saturated star, with diffraction spikes extending from the core on exposure o6802g0338o, OTA51 (2014-05-25, 45s \gps{} filter).}
    943960  \label{fig:saturated star}
    … …  
    10471064median of the pixel distribution, with the standard deviation of the
    10481065distribution set as the median of the $\sigma$ values calculated from
    1049 the $0.5 * (\sigma_{+1} - \sigma_{-1})$, $\sigma_{+0.5} -
    1050 \sigma_{-0.5}$, and $0.25 * (\sigma_{+2} - \sigma_{-2})$ differences.
     1066the $0.5 \times (\sigma_{+1} - \sigma_{-1})$, $\sigma_{+0.5} -
     1067\sigma_{-0.5}$, and $0.25 \times (\sigma_{+2} - \sigma_{-2})$ differences.
    10511068If this measured standard deviation is smaller than 3 times the bin
    10521069size, then all points more than 25 bins away from the calculated
    … …  
    10571074are found by interpolating the 5 bins around the expected bin as well,
    10581075and the count of the number of input values within this inner
    1059 50-percentile region, $N_{50}$ is calculated.
     107650-percentile region, $N_{50}$, is calculated.
    10601077
    10611078These initial statistics are then used as the starting guesses for a
    … …  
    11911208  \centering
    11921209  \begin{minipage}{0.45\hsize}
    1193     \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5677g0123o_XY11_nobt.png}
     1210    \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5677g0123o_nbt_XY11.png}
    11941211  \end{minipage}%
    11951212  \begin{minipage}{0.45\hsize}
    1196     \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5677g0124o_XY11_nobt.png}
     1213    \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5677g0124o_nbt_XY11.png}
    11971214  \end{minipage}
    11981215  \begin{minipage}{0.45\hsize}
    1199     \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5677g0123o_XY11_bt.png}
     1216    \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5677g0123o_wbt_XY11.png}
    12001217  \end{minipage}%
    12011218  \begin{minipage}{0.45\hsize}
    1202     \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5677g0124o_XY11_bt.png}
     1219    \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5677g0124o_wbt_XY11.png}
    12031220  \end{minipage}
    12041221  \caption{Example of OTA11 cell xy50 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.}
    … …  
    12461263We store the average flux measurement and deviation from the linear
    12471264fit for each exposure time for each region on all detector cells in
    1248 the linearity detrend look up tables.  An example of this data is
    1249 shown in figure \ref{fig: nonlinearity}.  When this correction is
     1265the linearity detrend look-up tables.  An example of this data is
     1266shown in Figure~\ref{fig: nonlinearity}.  When this correction is
    12501267applied to science data, these lookup tables are loaded, and a linear
    12511268interpolation is performed to determine the correction needed for the
    … …  
    12701287  \centering
    12711288  \includegraphics[width=0.9\hsize,angle=0,clip]{images/linearity_XY27_xy16.png}
    1272   \caption{Example plot of the linearity correction as a fraction of observed flux for OTA27, cell xy16.}
     1289  \caption{Example of the linearity correction as a fraction of observed flux for OTA27, cell xy16.}
    12731290  \label{fig: nonlinearity}
    12741291\end{figure}
    … …  
    12931310offsets increases as the distance from the readout amplifier and
    12941311overscan region increases, resulting in horizontal streaks that are
    1295 more pronounced along the large x pixel edge of the cell.  As the
     1312more pronounced along the large $x$ pixel edge of the cell.  As the
    12961313level of the offset is apparently random between exposures, the dark
    12971314correction cannot fully remove this structure from the images, and the
    … …  
    12991316by these bias offsets.  Therefore, we apply the PATTERN.ROW correction
    13001317in an attempt to mitigate the offsets and correct the image values.
    1301 To force the rows to agree, a second order clipped polynomial is fit
    1302 to each row in the cell.  Four fit iterations are run, and pixels
    1303 $2.5\sigma$ deviant are excluded from subsequent fits, to minimize the
    1304 effect stars and other astronomical signals have.  This final trend is
    1305 then subtracted from that row.  Simply doing this subtraction will
    1306 also have the effect of removing the background sky level.  To prevent
     1318To force the rows to agree, a second order clipped polynomial is
     1319fitted to each row in the cell.  Four fit iterations are run and
     1320pixels $2.5\sigma$ deviant (chosen empirically) are excluded from
     1321subsequent fits in order to minimize the bias from stars and other
     1322astronomical sources in the pixels.  This final trend is then
     1323subtracted from that row.  Simply doing this subtraction will also
     1324have the effect of removing the background sky level.  To prevent
    13071325this, the constant and linear terms for each row are stored, and
    13081326linear fits are made to these parameters as a function of row,
    … …  
    13681386  \centering
    13691387  \begin{minipage}{0.45\hsize}
    1370     \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5379g0103o_XY57_nopat.png}
     1388    \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5379g0103o_npt_XY57.png}
    13711389  \end{minipage}%
    13721390  \begin{minipage}{0.45\hsize}
    1373     \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5379g0103o_XY57_pat.png}
     1391    \includegraphics[width=0.9\hsize,angle=0,clip]{images/o5379g0103o_wpt_XY57.png}
    13741392  \end{minipage}
    13751393  \caption{Example of the PATTERN.ROW correction on exposure o5379g0103o OTA57 cell xy01 (\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.}
    … …  
    13791397\subsubsection{Pattern Continuity}
    13801398
    1381 The background levels of cells on a single OTA do not always have the
    1382 same value.  Even with dark and flat corrections applied, adjacent
    1383 cells may not match.  In addition, studies of the background level
    1384 indicate that the row-by-row bias can introduce small background
    1385 gradient variations along the rows of the cells that are not stable.
    1386 This common feature across the columns of cells results in a ``saw
    1387 tooth'' pattern horizontally across an the mosaicked OTA, and as the
    1388 background model fits a smooth sky level, this induces over and under
    1389 subtraction at the cell boundaries.
     1399The background sky levels of cells on a single OTA do not always have
     1400the same value.  Despite having dark and flat corrections applied,
     1401adjacent cells may not match even for images of nominally empty sky.
     1402In addition, studies of the background level indicate that the
     1403row-by-row bias can introduce small background gradient variations
     1404along the rows of the cells that are not stable.  This common feature
     1405across the columns of cells results in a ``saw tooth'' pattern
     1406horizontally across an the mosaicked OTA, and as the background model
     1407fits a smooth sky level, this induces over- and under subtraction at
     1408the cell boundaries.
    13901409
    13911410The PATTERN.CONTINUITY correction, attempts to match the edges of a
    13921411cell to those of its neighbors.  For each cell, a thin box 10 pixels
    13931412wide running the full length of each edge is extracted and the median
    1394 value of unmasked values calculated for that box.  These median values
     1413of unmasked values is calculated for that box.  These median values
    13951414are then used to construct a vector of the sum of the differences
    13961415between that cell's edges and the corresponding edge on any adjacent
    … …  
    13981417constructed, with the diagonal containing the number of cells adjacent
    13991418to that cell, and the off-diagonal values being set to -1 for each
    1400 pair of adjacent cells.  The offsets needed for each chip, $x$ can
    1401 then be found by solving the system $A x = \Delta$. A cell with the
     1419pair of adjacent cells.  The offsets needed for each chip, $\zeta$ can
     1420then be found by solving the system $A \zeta = \Delta$. A cell with the
    14021421maximum number of neighbors, usually cell xy11, the first cell not on
    14031422the edge of the OTA, is used to constrain the system, ensuring that
    … …  
    14961515  \tablewidth{0pc}
    14971516  \tablecaption{PV3 Detrends}
    1498   \tablehead{\colhead{Detrend Type} & \colhead{Detrend ID} & \colhead{Start Date} & \colhead{End Date} & \colhead{Note} }
     1517  \tablehead{\colhead{Detrend Type} & \colhead{Detrend ID} &
     1518    \colhead{Start Date (UT)} & \colhead{End Date (UT)} & \colhead{Note} }
    14991519  \startdata
    15001520  LINEARITY & 421  & 2009-01-01 00:00:00 & & \\
    … …  
    15411561To provide a consistent and uniform set of coordinates for image
    15421562combination (including stacking and differences), the individual
    1543 mosaicked OTA images are projected onto a common pixel grids, called
     1563mosaicked OTA images are projected onto common pixel grids, called
    15441564tessellations.  A tessellation can contain any number of tangent plane
    15451565projections, with those designed for single pointing surveys using
    … …  
    15541574used for processing image data beyond the initial chip stage.  The
    15551575coordinate system used for these images matches the parity of the sky,
    1556 with north in the positive y direction and east to the negative x
     1576with north in the positive $y$ direction and east to the negative $x$
    15571577direction.
    15581578
    … …  
    15721592output pixel has a unique sampling position on the input image
    15731593(although it may be off the image frame and therefore not populated),
    1574 preventing gaps in the output image due to the spacing of the input
    1575 pixels.
     1594guaranteing that all output pixels are addressed, and thus preventing
     1595gaps in the output image due to the spacing of the input pixels.
    15761596
    15771597With the locally linear grid defined, Lanczos interpolation
    1578 \citep{lanczos1956applied} with filter size parameter $a = 3$ on the input
    1579 image is used to determine the values to assign to the output pixel
    1580 location.  This process is repeated for all grid boxes, for all input
    1581 images, and for each output image product: the science image, the
    1582 variance, and the mask.  The image values are scaled by the absolute
    1583 value of the Jacobian determinant of the transformation for each grid
    1584 box.  This corrects the pixel values for the possible change in pixel
    1585 area due to the transformation.  Similarly, the variance image is
    1586 scaled by the square of this value, again to correctly account for the
    1587 pixel area change.
     1598\citep{lanczos1956applied} with filter size parameter $a = 3$ on the
     1599input image is used to determine the values to assign to the output
     1600pixel location.  This interpolation kernel was chosen as a compromise
     1601between simple interpolations and higher-order Lanczos kernels, with
     1602the goal of limiting the smear in the output image while avoiding
     1603the high-frequency ringing generated by higher order kernels.  This
     1604process is repeated for all grid boxes, for all input images, and for
     1605each output image product: the science image, the variance, and the
     1606mask.  The image values are scaled by the absolute value of the
     1607Jacobian determinant of the transformation for each grid box.  This
     1608corrects the pixel values for the possible change in pixel area due to
     1609the transformation.  Similarly, the variance image is scaled by the
     1610square of this value, again to correctly account for the pixel area
     1611change.
    15881612
    15891613The interpolation constructs the output pixels from more than one
    … …  
    15991623to scale the position uncertainties based on the new orientation.
    16001624
    1601 The output image also contains header keywords SRC\_0000, SEC\_0000,
    1602 MPX\_0000, and MPY\_0000 that define the mappings from the warped
    1603 pixel space to the input image.  The SRC keyword lists the input OTA
    1604 name, and the SEC keyword lists the image section that the mapping
    1605 covers.  The MPX and MPY contain the back-transformation linearized
    1606 across the full chip.  These parameters are stored in a string listing
    1607 the reference position in the chip coordinate frame, the slope of the
    1608 relation in the warp x axis, and the slope of the relation in the warp
    1609 y axis.  From these keywords, any position in the warp can be mapped
    1610 back to the location in any of the input OTA images, with some
    1611 reduction in accuracy.
     1625The output image also contains header keywords SRC\_nnnn, SEC\_nnnn,
     1626MPX\_nnnn, and MPY\_nnnn that define the mappings from the warped
     1627pixel space to the input images.  The 'nnnn' for each keyword has the
     1628values 0000, 0001, etc., up to the number of input images.  The SRC
     1629keyword lists the input OTA name, and the SEC keyword lists the image
     1630section that the mapping covers.  The MPX and MPY contain the
     1631back-transformation linearized across the full chip.  These parameters
     1632are stored in a string listing the reference position in the chip
     1633coordinate frame, the slope of the relation in the warp $x$ axis, and
     1634the slope of the relation in the warp $y$ axis.  From these keywords,
     1635any position in the warp can be mapped back to the location in any of
     1636the input OTA images, with some reduction in accuracy.
    16121637
    16131638\begin{figure}
    16141639  \centering
    1615   \includegraphics[width=0.9\hsize,angle=0,clip]{images/warp_1046511_sci.jpg}
     1640  \includegraphics[width=0.9\hsize,angle=0,clip]{images/warp_2046019_sci.png}
    16161641  \caption{Example of the warp image for skycell skycell.2047.005
    16171642    centered at ($\alpha,\delta$) = (179.763, 32.1899) for exposure
    … …  
    16291654\begin{figure}
    16301655  \centering
    1631   \includegraphics[width=0.9\hsize,angle=0,clip]{images/warp_1046511_wt.jpg}
     1656  \includegraphics[width=0.9\hsize,angle=0,clip]{images/warp_2046019_var.png}
    16321657  \caption{Example of the warp variance image for skycell
    16331658    skycell.2047.005 of exposure o4985g0073o, the same as in Figure
    … …  
    16441669\begin{figure}
    16451670  \centering
    1646   \includegraphics[width=0.9\hsize,angle=0,clip]{images/warp_1046511_mask.jpg}
     1671  \includegraphics[width=0.9\hsize,angle=0,clip]{images/warp_2046019_mask.png}
    16471672  \caption{Example of the warp mask image for skycell skycell.2047.005
    16481673    of exposure o4985g0073o, the same as in Figure \ref{fig:warp
    … …  
    16751700prepare the inputs and stack the frames.
    16761701
     1702\note{need to point out that we are convolving to a matched PSF}
     1703
    16771704Once all files are ingested, the first step is to measure the size and
    16781705shapes of the input image PSFs.  We exclude images that have a PSF
    16791706FWHM greater than 10 pixels (2.5 arcseconds), as those images have the
    16801707seeing far worse than average, and would degrade the final output
    1681 stack.  For the PV3 $3\pi$ survey, this size represents a PSF larger
     1708stack.  For the PV3 processing of the $3\pi$ survey, this size represents a PSF larger
    16821709than the $97$th percentile in all filters.  A target PSF for the stack
    16831710is constructed by finding the maximum envelope of all input PSFs,
    … …  
    16931720airmass, image exposure time, and zeropoint.  All output stacks are
    16941721constructed to a target zeropoint of 25.0 in all filters, and to have
    1695 an airmass of 1.0.  The output exposure time is set to the sum of the
    1696 input exposure times, regardless of whether those inputs are rejected later
    1697 in the combination process.  We can determine the relative
     1722an airmass of 1.0.  The target zeropoint is arbitrary; 25.0 was chosen
     1723to be roughly consistent with the PS1 zero points, while still being a
     1724simple number.  The output exposure time is set to the sum of the
     1725input exposure times, {\em regardless of whether those inputs are rejected
     1726later in the combination process}.  We can determine the relative
    16981727transparency for each input image by comparing the magnitudes of
    16991728matched sources between the different images.  Each image then has a
    17001729normalization factor defined, equal to $\mathrm{norm}_{input} =
    17011730(ZP_\mathrm{input} - ZP_\mathrm{target}) -
    1702 \mathrm{transparency}_\mathrm{input} - 2.5 * \log_{10}
    1703 (t_\mathrm{target} / t_\mathrm{input}) - \mathrm{F}_\mathrm{airmass} *
     1731\mathrm{transparency}_\mathrm{input} - 2.5 \times \log_{10}
     1732(t_\mathrm{target} / t_\mathrm{input}) - \mathrm{F}_\mathrm{airmass} \times
    17041733(\mathrm{airmass}_\mathrm{input} - \mathrm{airmass}_\mathrm{target})$.
    17051734For the PV3 processing, the airmass factor
    … …  
    17151744the entire region of the sky imaged.  This further calibration is not
    17161745available at the time of stacking, and so there may be small residuals
    1717 in the transparency values as a result of this \citet{magnier2017.calibration}.
     1746in the transparency values as a result of this \citep{magnier2017.calibration}.
    17181747
    17191748With the flux normalization factors and target PSF chosen, the
    1720 convolution kernels can be calculated for each image.  ISIS kernels
    1721 \citep{1998ApJ...503..325A} are used with FWHM values of 1.5, 3.0, and 6.0
    1722 pixels and polynomial orders of 6, 4, and 2.  Regions around the
    1723 sources identified in the input images are extracted, convolved with
    1724 the kernel, and the residual with the target PSF used to update the
    1725 parameters of the kernel via least squares optimization.  Stamps that
    1726 significantly deviate are rejected, although the squared residual
    1727 difference will increase with increasing source flux.  To mitigate
    1728 this effect, a parabola is fit to the distribution of squared
    1729 residuals as a function of source flux.  Stamps that deviate from this
    1730 fit by more than $2.5\sigma$ are rejected, and not used on further
    1731 kernel fit iterations.  This process is repeated twice, and the final
    1732 convolution kernel is returned.
     1749convolution kernels can be calculated for each image.  To calculate
     1750the convolution kernels, we use the algorithm described by
     1751\cite{1998ApJ...503..325A} and \cite{2000.alard} to perform optimal
     1752image subtraction.  These `ISIS' kernels \citep[named after the
     1753  software package described by][]{1998ApJ...503..325A} are used with
     1754FWHM values of 1.5, 3.0, and 6.0 pixels and polynomial orders of 6, 4,
     1755and 2.  Regions around the sources identified in the input images are
     1756extracted, convolved with the kernel, and the residual with the target
     1757PSF used to update the parameters of the kernel via least squares
     1758optimization.  Stamps that significantly deviate are rejected,
     1759although the squared residual difference will increase with increasing
     1760source flux.  To mitigate this effect, a parabola is fit to the
     1761distribution of squared residuals as a function of source flux.
     1762Stamps that deviate from this fit by more than $2.5\sigma$ are
     1763rejected, and not used on further kernel fit iterations.  This process
     1764is repeated twice, and the final convolution kernel is returned.
    17331765
    17341766This convolution may change the image flux scaling, so the kernel is
    … …  
    17591791identify discrepant input values that should be excluded.
    17601792
     1793\note{clarify 'should' below, e.g., with a histogram}
     1794
    17611795If only a single input is available, the initial stack contains the
    17621796value from that single input.  If there are only two inputs, the
    … …  
    17701804
    17711805\begin{eqnarray}
    1772   \mathrm{Stack}_\mathrm{value} &=& \sum_i\left(\mathrm{value}_\mathrm{input} * W_\mathrm{input}\right) / \sum_\mathrm{inputs}\left(W_\mathrm{input}\right) \\
    1773   \mathrm{Stack}_\mathrm{exp weight} &=& \sum_i \left(\mathrm{exptime}_\mathrm{input} * W_\mathrm{input}\right) / \sum_\mathrm{inputs}\left(W_\mathrm{input}\right) \\
     1806  \mathrm{Stack}_\mathrm{value} &=& \sum_i\left(\mathrm{value}_\mathrm{input} \times W_\mathrm{input}\right) / \sum_\mathrm{inputs}\left(W_\mathrm{input}\right) \\
     1807  \mathrm{Stack}_\mathrm{exp weight} &=& \sum_i \left(\mathrm{exptime}_\mathrm{input} \times W_\mathrm{input}\right) / \sum_\mathrm{inputs}\left(W_\mathrm{input}\right) \\
    17741808\end{eqnarray}
    17751809
    … …  
    18051839attempt to identify outlier points.  Again, if only one input is
    18061840available, that input is accepted.  If there are two inputs, $A$ and
    1807 $B$, then a check is made to see if $(0.5 * (\mathrm{value}_A -
    1808 \mathrm{value}_B))^2 > 16 * (\sigma^2_A + \sigma^2_B
    1809 + (0.1 * \mathrm{value}_A)^2 + (0.1 * \mathrm{value}_B)^2)$, such that
     1841$B$, then a check is made to see if $(0.5 \times (\mathrm{value}_A -
     1842\mathrm{value}_B))^2 > 16 \times (\sigma^2_A + \sigma^2_B
     1843+ (0.1 \times \mathrm{value}_A)^2 + (0.1 \times \mathrm{value}_B)^2)$, such that
    18101844the deviation of the inputs from their mean position is greater than
    18111845four times the sum of their measured uncertainties and a 10\%
    … …  
    18241858distribution is likely to be unimodal), or if there are insufficient
    18251859inputs for this mixture model analysis, the input values are passed to
    1826 an Olympic weighted mean calculation.  We reject $20\%$ of the number
     1860an Olympic \note{define} weighted mean calculation.  We reject $20\%$ of the number
    18271861of inputs through this process.  The number of bad inputs is set to
    1828 $N_\mathrm{bad} = 0.2 * N_\mathrm{input} + 0.5$, with the 0.5 term
     1862$N_\mathrm{bad} = 0.2 \times N_\mathrm{input} + 0.5$, with the 0.5 term
    18291863ensuring at least one input is rejected.  This number is further
    18301864separated into the number of low values to exclude, $N_\mathrm{low} =
    … …  
    18431877
    18441878\begin{eqnarray}
    1845   \mathrm{limit}_\mathrm{mixture\ model} &=& 4^2 * (\sigma^2_\mathrm{input} + \sigma_\mathrm{mixture\ model}^2) \\
    1846   \mathrm{limit}_\mathrm{default} &=& 4^2 * (\sigma^2_\mathrm{input} + (0.1 * \mathrm{value}_\mathrm{input})^2)
     1879  \mathrm{limit}_\mathrm{mixture\ model} &=& 4^2 \times (\sigma^2_\mathrm{input} + \sigma_\mathrm{mixture\ model}^2) \\
     1880  \mathrm{limit}_\mathrm{default} &=& 4^2 \times (\sigma^2_\mathrm{input} + (0.1 \times \mathrm{value}_\mathrm{input})^2)
    18471881\end{eqnarray}
    18481882
    … …  
    18691903pixels.  The ISIS kernel used in the previous step is again used to
    18701904determine the largest square box that does not exceed the limit of
    1871 $0.25 * \sum_{x,y} kernel^2$.  This square box is then convolved with
     1905$0.25 \times \sum_{x,y} kernel^2$.  This square box is then convolved with
    18721906the rejected pixel mask to reject the neighboring pixels.  This final
    18731907list of rejected pixels is passed to the final combination, which
    … …  
    19241958\begin{figure}
    19251959  \centering
    1926   \includegraphics[width=0.9\hsize,angle=0,clip]{images/stack_3775944_sci.jpg}
     1960  \includegraphics[width=0.9\hsize,angle=0,clip]{images/stack_3956997_sci.png}
    19271961  \caption{Example of the stack image for skycell skycell.2047.005
    19281962    centered at ($\alpha,\delta$) = (179.763, 32.1899) in the \zps{}
    … …  
    19401974\begin{figure}
    19411975  \centering
    1942   \includegraphics[width=0.9\hsize,angle=0,clip]{images/stack_3775944_mask.jpg}
     1976  \includegraphics[width=0.9\hsize,angle=0,clip]{images/stack_3956997_mask.png}
    19431977  \caption{Example of the stack mask image for skycell
    19441978    skycell.2047.005 centered at ($\alpha,\delta$) = (179.763,
    … …  
    19541988\begin{figure}
    19551989  \centering
    1956   \includegraphics[width=0.9\hsize,angle=0,clip]{images/stack_3775944_wt.jpg}
     1990  \includegraphics[width=0.9\hsize,angle=0,clip]{images/stack_3956997_var.png}
    19571991  \caption{Example of the stack variance image for skycell
    19581992    skycell.2047.005 centered at ($\alpha,\delta$) = (179.763,
    … …  
    19682002\begin{figure}
    19692003  \centering
    1970   \includegraphics[width=0.9\hsize,angle=0,clip]{images/stack_3775944_num.jpg}
     2004  \includegraphics[width=0.9\hsize,angle=0,clip]{images/stack_3956997_num.png}
    19712005  \caption{Example of the stack number image for skycell
    19722006    skycell.2047.005 centered at ($\alpha,\delta$) = (179.763,
    … …  
    19822016\begin{figure}
    19832017  \centering
    1984   \includegraphics[width=0.9\hsize,angle=0,clip]{images/stack_3775944_exp.jpg}
     2018  \includegraphics[width=0.9\hsize,angle=0,clip]{images/stack_3956997_exp.png}
    19852019  \caption{Example of the stack exposure time image for skycell
    19862020    skycell.2047.005 centered at ($\alpha,\delta$) = (179.763,
    … …  
    19952029\begin{figure}
    19962030  \centering
    1997   \includegraphics[width=0.9\hsize,angle=0,clip]{images/stack_3775944_expwt.jpg}
     2031  \includegraphics[width=0.9\hsize,angle=0,clip]{images/stack_3956997_expwt.png}
    19982032  \caption{Example of the stack weighted exposure image for skycell
    19992033    skycell.2047.005 centered at ($\alpha,\delta$) = (179.763,
    … …  
    20712105
    20722106Although the detrending and image combination algorithms work well to
    2073 produce a consistent and calibrated images, having the full PV3 data
    2074 set allows issues to be identified and solutions created for future
    2075 improvements to the IPP pipeline.  In addition, the existence of the
    2076 final calibrated catalog can be used to look for issues that appear
    2077 dependent on focal plane position.
     2107produce consistent and calibrated images, having the PV3 processing of
     2108the full $3\pi$ data set allows issues to be identified and solutions
     2109created for future improvements to the IPP pipeline.  In addition, the
     2110existence of the final calibrated catalog can be used to look for
     2111issues that appear dependent on focal plane position.
    20782112
    20792113One obvious way to make use of the PV3 catalog is to do a statistical
    … …  
    21712205University (ELTE), and the Los Alamos National Laboratory.
    21722206
     2207\note{ApJ, etc latex macros have an extra comma}
     2208
    21732209\bibliography{lib}{}
    21742210\bibliographystyle{apj}
    … …  
    21762212
    21772213\end{document}
    2178 
    2179 
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