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Changeset 39893


Ignore:
Timestamp:
Dec 18, 2016, 8:58:32 PM (10 years ago)
Author:
eugene
Message:

adding various plots

Location:
trunk/doc/release.2015/ps1.calibration
Files:
2 edited

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

    r39880 r39893  
    44# remember to set \pdfoutput at the top
    55
    6 DO_BIBTEX = 1
     6DO_BIBTEX = 0
    77# remember to change from \bibliography to \input{.bbl} at the bottom
    88
    … …  
    2020../inputs/apj.bst \
    2121../inputs/lib.bib \
     22pics/photflat.example.png \
     23pics/allsky.photom.sigma.png \
     24pics/KHexample.png \
     25pics/KHmap.png \
     26pics/dcr.r2.g.png \
     27pics/astroflat.gri.png \
     28pics/astroflat.zy.png \
     29pics/allsky.astrom.sigma.png \
     30pics/gaia.photom.png \
     31pics/gaia.astrom.png \
    2232calibration.tex
    2333

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

    r39880 r39893  
    6262K. W. Hodapp,\altaffilmark{\IfA}
    6363R. Jedicke,\altaffilmark{\IfA}
     64N. Kaiser,\altaffilmark{\IfA}
    6465R.-P. Kudritzki,\altaffilmark{\IfA}
    6566N. Metcalfe,\altaffilmark{\DUR}
    … …  
    6869% T. Grav,\altaffilmark{\IfA}
    6970% J. N. Heasley,\altaffilmark{\IfA}
    70 % N. Kaiser,\altaffilmark{\IfA}
    7171% G. A. Luppino,\altaffilmark{\IfA}
    7272% R. H. Lupton,\altaffilmark{\Princeton}
    … …  
    591591the data from the exposure are loaded into the DVO database.
    592592
     593\section{PV3 DVO Master Database}
     594
     595Data from the GPC1 chip images, the stack images, and the warp images
     596are loaded into DVO using the real-time analysis astrometric
     597calibration to guide the association of detections into objects.
     598After the full PV3 DVO database was constructed, including all of the
     599chip, stack, and warp detections, several external catalogs were
     600merged into the database.  First, the complete 2MASS PSC was loaded
     601into a stand-alone DVO database, which was then merged into the PV3
     602master database.  Next the DVO database of synthetic photometry in the
     603PS1 bands (see Section~\ref{sec:synthdb}) was merged in.  Next, the
     604full Tycho database was added, followed by the AllWISE database.
     605After the Gaia release in August 2016 \citep{2016AA...595A...2G}, we
     606generated a DVO database of the Gaia positional and photometric
     607information and merged that into the master DVO database.
     608
     609%% \note{need to describe the assignment of flags, etc, for the external data sources}.
     610
    593611\section{Photometry Calibration}
    594612
    … …  
    868886of responsibility. 
    869887
     888\begin{figure*}[htbp]
     889 \begin{center}
     890  \begin{minipage}{0.85\linewidth}
     891   \includegraphics[width=\textwidth,clip]{{pics/photflat.example}.png}
     892  \end{minipage}
     893  \hspace{-3.0in}
     894  \begin{minipage}{0.4\linewidth}
     895   \vspace{3.25in}
     896   \caption{\label{fig:photflat} High-resolution flat-field correction images for the 5 filters $grizy$.}
     897  \end{minipage}
     898 \end{center}
     899\end{figure*}
     900
    870901The iterations described above (calculate mean
    871902magnitudes, calculate zero points, calculate new measurements) are
    … …  
    900931back to all measurements in the database, updating the mean photometry
    901932as part of this process.  The calculations for this last step are
    902 performed in parallel on the DVO parition machines.
     933performed in parallel on the DVO partition machines.
    903934
    904935With the above software, we are able to perform the entire relphot
    … …  
    911942analysis.
    912943
     944\begin{figure}[htbp]
     945  \begin{center}
     946 \includegraphics[width=\hsize,clip]{{pics/allsky.photom.sigma}.png}
     947  \caption{\label{fig:allsky.photom.sigma} Consistency of photometry
     948    measurements across the sky.  Each panel shows a map of the
     949    standard deviation of photometry residuals for stars in each
     950    pixel.  The median value of the measure standard deviations across
     951    the sky is $(\sigma_g, \sigma_r, \sigma_i, \sigma_z, \sigma_y) =
     952    (14, 14, 15, 15, 18)$ millimags.  These values reflect the typical
     953    single-measurement errors for bright stars.}
     954  \end{center}
     955\end{figure}
     956
    913957%% \note{need to discuss the process of setting the final mean magnitudes}
     958
     959\subsubsection{Photometric Flat-field}
    914960
    915961For PV3, the relphot analysis was performed two times.  The first
    … …  
    927973and to set the average magnitudes.
    928974
     975Figure~\ref{fig:photflat} shows the high-resolution photometric
     976flat-field corrections applied to the measurements in the DVO
     977database.  These flat-fields make low-level corrections of up to
     978\approx 0.03 magnitudes.  Several features of interest are apparent in
     979these images. 
     980
     981First, at the center of the camera is an important structure caused by
     982the telescope optics which we call the ``tent''.  In this portion of
     983the focal plane, the image quality degrades very quickly.  The
     984photometry is systematically biased because the point spread function
     985model cannot follow the real changes in the PSF shape on these small
     986scales.  As is evident in the image, the effect is such that the flux
     987measured using a PSF model is systematically low, as expected if the
     988PSF model is too small. 
     989
     990The square outline surrounding the ``tent'' is due to the 2$\times$2
     991sampling per chip used for the Ubercal flat-field corrections.  The
     992imprint of the Ubercal flat-field is visible throughout this
     993high-resolution flat-field: in regions where the underlying flat-field
     994structure follows a smooth gradient across a chip, the Ubercal
     995flat-field partly corrects the structure, leaving behind a saw-tooth
     996residual.  The high-resolution flat-field corrects the residual
     997structures well.
     998
     999Especially notable in the bluer filters is a pattern of quarter
     1000circles centered on the corners of the chips.  These patterns are
     1001similar to the ``tree rings'' reported by the DES team and others
     1002(G. Berstein REF \& REFS).  The details of these tree rings are beyond
     1003the scope of this article, and will be explored in future work.
     1004Unlike the tree ring features discussed by these other authors, the
     1005features observed in the GPC1 photometry are not caused by an
     1006interaction of the flat-field with the effective pixel geometry.
     1007Instead, these photometric features are due to low-level changes in
     1008the PSF size which we attribute to variable charge diffusion (Magnier
     1009in prep).
     1010
     1011Other features include some poorly responding cells (e.g., in XY14)
     1012and effects at the edges of chips, possibly where the PSF model fails
     1013to follow the changes in the PSF.
     1014
     1015%% XXX : need to refer to system paper on the central tent?
     1016
    9291017%% \note{show the flat-field residual images, discuss the features?}. 
    9301018
    9311019For stacks and warps, the image calibrations were determined after the
    932 relative astrometry was performed on the individual chips.  Each stack
     1020relative photometry was performed on the individual chips.  Each stack
    9331021and each warp was tied via relative photometry to the average
    9341022magnitudes from the chip photometry.  In this case, no flat-field
    … …  
    9411029appropriate for a given warp.  This latter effect is one of several
    9421030which degrade the warp photometry compared to the chip photometry at
    943 the bright end. 
     1031the bright end.
     1032
     1033\subsection{Photometry Calibration Quality}
     1034
     1035Figure~\ref{fig:allsky.photom.sigma} shows the standard devitions of
     1036the mean residual photometry for bright stars as a function of
     1037position across the sky.  For each pixel in these images, we selected
     1038all objects with (14.5, 14.5, 14.5, 14.0, 13.0) $<$ ($g,r,i,z,y$) $<$
     1039(17, 17, 17, 16.5, 15.5), with at least 3 measurements in $i$-band (to
     1040reject artifacts detected in a pair of exposures from the same night),
     1041with \code{PSF_QF} $> 0.85$ (to reject excessively-masked objects),
     1042and with $mag_{\rm PSF} - mag_{rm Kron} < 0.1$ (to reject galaxies).
     1043We then generated histograms of the difference between the average
     1044magnitude and the apparent magnitude in an individual image for each
     1045filter for all stars in a given pixel in the images.  From these
     1046residual histograms, we can then determine the median and the 68\%-ile
     1047range to calculate a robust standard deviation.  This represents the
     1048bright-end systematic error floor for a measurement from a single
     1049exposure.  The standard deviations are then plotted in
     1050Figure~\ref{fig:allsky.photom.sigma}. 
     1051
     1052The 5 panels in Figure~\ref{fig:allsky.photom.sigma} show several
     1053features.  The Galactic bulge is clearly seen in all five filters,
     1054with the impact strongest in the reddest bands.  We attribute this to
     1055the effects of crowding and contamination of the photometry by
     1056neighbors.  Large-scale, roughly square features \approx 10 degrees on
     1057a side in these images can be attributed to the vagaries of weather:
     1058these patches correspond to the observing chunks.  These images
     1059include both photometric and non-photometric exposures.  It seems
     1060plausible that the non-photometric images from relatively poor quality
     1061nights elevate the typical errors.  On small scales, there are
     1062circular patterns \approx 3 degrees in diameter corresponding to
     1063individual exposures; these represent residual flat-fields structures
     1064not corrected by our stellar flat-fielding.  The median of the
     1065standard deviations in the five filters are
     1066$(\sigma_g,\sigma_r,\sigma_i,\sigma_z,\sigma_y) = (14, 14, 15, 15,
     106718)$ millimagnitudes.
    9441068
    9451069%% \note{recommendation}
    … …  
    9491073\subsubsection{Iteratively Reweighted Least Squares Fitting (1D)}
    9501074
    951 \subsubsection{Seletion of Measurements}
     1075\subsubsection{Selection of Measurements}
    9521076
    9531077\subsubsection{Stack Photometry}
    … …  
    9571081\begin{figure*}[htbp]
    9581082  \begin{center}
    959  \includegraphics[width=0.48\hsize,clip]{{pics/DXT0.mean}.png}
    960  \includegraphics[width=0.48\hsize,clip]{{pics/DXT1.mean}.png}
    961  \includegraphics[width=0.48\hsize,clip]{{pics/DYT0.mean}.png}
    962  \includegraphics[width=0.48\hsize,clip]{{pics/DYT1.mean}.png}
    963   \caption{\label{fig:KHchip} Illustration of the Koppenh\"ofer Effect
     1083 \includegraphics[width=\hsize,clip]{{pics/KHexample}.png}
     1084  \caption{\label{fig:KHexample} Illustration of the Koppenh\"ofer Effect
    9641085    on chip XY04.  In each plot, the solid line shows the measured
    9651086    mean residual for stars detected on this chip as a function of the
    … …  
    9841105\end{figure}
    9851106
    986 \section{PV3 DVO Master Database}
    987 
    988 Data from the GPC1 chip images, the stack images, and the warp images
    989 are loaded into DVO using the real-time analysis astrometric
    990 calibration to guide the association of detections into objects.
    991 After the full PV3 DVO database was constructed, including all of the
    992 chip, stack, and warp detections, several external catalogs were
    993 merged into the database.  First, the complete 2MASS PSC was loaded
    994 into a stand-alone DVO database, which was then merged into the PV3
    995 master database.  Next the DVO database of synthetic photometry in
    996 the PS1 bands (see Section~\ref{sec:synthdb}) was merged in.  Next,
    997 the full Tycho database was added, followed by the AllWISE database.
    998 After the Gaia release in August 2016, we generated a DVO database of
    999 the Gaia positional and photometric information and merged that into
    1000 the master DVO database.
    1001 
    1002 %% \note{need to describe the assignment of flags, etc, for the external data sources}.
    1003 
    1004 \section{Astrometry Analysis}
     1107\section{Astrometry Calibration}
    10051108
    10061109Once the full PV3 dataset loaded into the master PV3 DVO database,
    … …  
    10811184form which can be applied to the database measurements.
    10821185
    1083 \begin{figure}[htbp]
    1084   \begin{center}
    1085  \includegraphics[width=\hsize,clip]{{pics/pv3.v1.dmag_g.sigma}.png}
    1086  \includegraphics[width=\hsize,clip]{{pics/pv3.v1.dmag_r.sigma}.png}
    1087  \includegraphics[width=\hsize,clip]{{pics/pv3.v1.dmag_i.sigma}.png}
    1088  \includegraphics[width=\hsize,clip]{{pics/pv3.v1.dmag_z.sigma}.png}
    1089  \includegraphics[width=\hsize,clip]{{pics/pv3.v1.dmag_y.sigma}.png}
    1090   \caption{\label{fig:dmag.measure} Consistency of photometry
    1091     measurements across the sky.  Each panel shows a map of the
    1092     standard deviation of photometry residuals for stars in each pixel.}
    1093   \end{center}
    1094 \end{figure}
    1095 
    10961186\subsubsection{Differential Chromatic Refraction}
    10971187
    … …  
    11281218We represent the trend with a spline fitted to this dataset. 
    11291219
    1130 %% The DCR trend has an amplitude of \note{XXX - XXX} in the five filters. 
     1220\begin{figure}[htbp]
     1221  \begin{center}
     1222 \includegraphics[width=\hsize,clip]{{pics/dcr.r2.g}.png}
     1223  \caption{\label{fig:DCRexample} Example of the DCR trend in the
     1224    g-band.  {\bf top:} DCR trend in the parallactic direction {\bf
     1225      bottom:} DCR trend perpendicular to the parallactic angle.}
     1226  \end{center}
     1227\end{figure}
     1228
     1229The amplitude of the DCR trend in the five filters is $(g,r,i,z,y) =
     1230(0.010, 0.001, -0.003, -0.017, -0.021)$ arcsec airmass$^{-1}$
     1231magntiude$^{-1}$.  We saturate the DCR correction if the term $color
     1232TAN (\zeta)$ for a given measurement is outside a range where the
     1233DCR correction is well measured.  The maximum DCR correction applied
     1234to the five filters is $(g,r,i,z,y) = (0.019, 0.002, 0.003, 0.006,
     12350.008)$ arcseconds.
     1236
    11311237%% \note{write down the DCR formalae for reference}.
     1238
     1239\begin{figure*}[htbp]
     1240 \begin{center}
     1241 \includegraphics[width=0.85\textwidth,clip]{{pics/astroflat.gri}.png}
     1242 \caption{\label{fig:astroflat.gri} High-resolution astrometric flat-field correction images for $gri$.}
     1243 \end{center}
     1244\end{figure*}
     1245
     1246\begin{figure*}[htbp]
     1247 \begin{center}
     1248 \includegraphics[width=0.85\textwidth,clip]{{pics/astroflat.zy}.png}
     1249 \caption{\label{fig:astroflat.zy} High-resolution astrometric flat-field correction images for $zy$.}
     1250 \end{center}
     1251\end{figure*}
    11321252
    11331253\subsubsection{Astrometric Flat-field}
    … …  
    11401260astrometric flat using a sampling resolution of 40x40 pixels, matching
    11411261the photometric flat-field correction images.
    1142 Figure~\ref{fig:astroflat} shows the astrometric flat-field images for
    1143 the five filters \grizy\ in each of the two coordinate directions.
    1144 These plots show several types of features.
     1262Figures~\ref{fig:astroflat.gri} and \ref{fig:astroflat.zy} show the
     1263astrometric flat-field images for the five filters \grizy\ in each of
     1264the two coordinate directions.  These plots show several types of
     1265features.
    11451266
    11461267The dominant pattern in the astrometric residual is roughly a series
    … …  
    11741295of this is unclear, but likely caused by the astrometry model failing
    11751296to follow the underlying variations because of the need to extrapolate
    1176 to the edge pixels.  Finally, we also identify an interesting effect
     1297to the edge pixels.  Finally, we also mention an interesting effect
    11771298{\em not} visible at the resolution of these astrometric flat-field
    11781299images.  Fine structures are observed at the \approx 10 pixel scale
    11791300similar to the ``tree rings'' reported by the DES team and others
    1180 (G. Berstein REF \& REFS).  We explore these tree rings in detail in
     1301(G. Berstein REF \& REFS).  The details of these tree rings are beyond
     1302the scope of this article, and will be explored in future work.
     1303
     1304Unfortunately, we discovered a problem with the astrometric flat-field
     1305correction too late to be repaired for DR1.  As can be seen by
     1306inspection of Figures~\ref{fig:astroflat.gri} and
     1307\ref{fig:astroflat.zy}, there is significant pixel-to-pixel noise in
     1308the the astrometric flat-field images.  This pixel-to-pixel noise is
     1309caused by too few stars used in the measuremnt of the flat-field
     1310structure for the high-resolution sampling.  As a result, the
     1311astrometric flat-field correction reduces systematic structures on
     1312large spatial scales, but at the expense of degrading the quality of
     1313an individual measurement.  Only $i$-band has sufficient
     1314signal-to-noise per pixel to avoid significantly increasing the
     1315per-measurement position errors. 
     1316
     1317Figure~\ref{fig:allsky.astrom.sigma} shows the standard devitions of
     1318the mean residual astrometry in $(\alpha,\delta)$ for bright stars as
     1319a function of position across the sky.  For each pixel in these
     1320images, we selected all objects with $15 < i < 17$, with at least 3
     1321measurements in $i$-band (to reject artifacts detected in a pair of
     1322exposures from the same night), with \code{PSF_QF} $> 0.85$ (to reject
     1323excessively-masked objects), and with $mag_{\rm PSF} - mag_{rm Kron} <
     13240.1$ (to reject galaxies).  We then generated histograms of the
     1325difference between the object position predicted for the epoch of each
     1326measurement (based on the proper motion and parallax fit) and the
     1327observed position of that measurement, in both the Right Ascension and
     1328Declination directions (in linear arcseconds), for all stars in a
     1329given pixel in the images.  From these residual histograms, we can
     1330then determine the median and the 68\%-ile range to calculate a robust
     1331standard deviation.  This represents the bright-end systematic error
     1332floor for a measurement from a single exposure.  The standard
     1333deviations are then plotted in Figure~\ref{fig:allsky.photom.sigma}.
     1334The median value of the standard deviations across the sky is
     1335$(\sigma_\alpha, \sigma_\delta) = (22, 23)$ milliarcseconds.
     1336
     1337The Galactic plane is clearly apparently in these images.  Like
     1338photometry, we attribute this to failure of the PSF fitting due to
     1339crowding.  The celestial North pole regions have somewhat elevated
     1340errors in both R.A. and DEC.  This may be due to the larger typical
     1341seeing at these high airmass regions, but without further exploration
     1342this is interpretation uncertain.  Several features can be seen which
     1343appear to be an effect of the tie to the Gaia astrometry: the stripes
     1344near the center of the DEC image and the right side of the R.A. image.
     1345The mesh of circular outlines is due to the outer edge of the focal
     1346plane where the astrometric calibration is poorly determined.  As
     1347discussed above, the median values in the images are higher than
     1348expected based on our PV2 analysis of the astrometry: the median
     1349per-measurement error floor of \approx 22 mas is significantly worse
     1350than the \approx 17 mas value in that earlier analysis.  We attribute
     1351this degradation to the noise introduced by the astrometric
     1352flat-field.  This noise can likely be addressed before the DR2 release
     1353of the individual measurement data.
     1354
     1355\begin{figure}[htbp]
     1356  \begin{center}
     1357 \includegraphics[width=\hsize,clip]{{pics/allsky.astrom.sigma}.png}
     1358  \caption{\label{fig:allsky.astrom.sigma} Consistency of photometry
     1359    measurements across the sky.  Each panel shows a map of the
     1360    standard deviation of astrometry residuals for stars in each
     1361    pixel.  The median value of the standard deviations across the sky
     1362    is $(\sigma_\alpha, \sigma_\delta) = (22, 23)$ milliarcseconds.
     1363    These values reflect the typical single-measurement errors for
     1364    bright stars.  See discussion regarding the astrometric flat which
     1365    is likely responsible for these elevated value. }
     1366  \end{center}
     1367\end{figure}
     1368
     1369% plot of the astrometric error floor per filter?
    11811370
    11821371% \note{SECTION or REF?}.
    … …  
    12951484
    12961485After the full relative astrometry analysis was performed for the PV3
    1297 database, the Gaia Data Release 1 became available.  This afforded us
     1486database, the Gaia Data Release 1 became available
     1487\citep{2016A&A...595A...2G, 2016A&A...595A...4L}.  This afforded us
    12981488the opportunity to constrain the astrometry on the basis of the Gaia
    12991489observations.  Gaia DR1 objects which are bright enough to have proper
    … …  
    13201510%% \note{Figures showing the Gaia residuals}
    13211511
     1512\begin{figure*}[htbp]
     1513  \begin{center}
     1514  \includegraphics[width=\hsize,clip]{{pics/gaia.photom}.png}
     1515  \caption{\label{fig:gaia.photom} Comparison with Gaia
     1516    photometry. {\bf Left} Mean of PS1 - Gaia, {\bf Right} Standard
     1517    deviation of PS1 - Gaia.  For pixels with $|b| > 30$ and $\delta >
     1518    -30$, the standard deviation of the PS1 - Gaia mean values is 7
     1519    millimagnitudes, while the median of the standard deviations is 12
     1520    millimagnitudes.  The former is a statement about the consistency
     1521    of the Gaia and Pan-STARRS\,1 photometry, while the latter
     1522    reflects the combined bright-end errors for both systems.  }
     1523  \end{center}
     1524\end{figure*}
     1525
     1526Figure~\ref{fig:gaia.photom} shows a comparison between the Pan-STARRS
     1527photometry in $g,r,i$ and the Gaia photometry in the $G$-band.  To
     1528compare the PS1 photometry to the very broadband Gaia G filter, we
     1529have determined a transformation based on a 3rd order polynomial fit
     1530to $g-r$ and $g-i$ colors.  This transformation reproduces Gaia
     1531photometry reasonably well for stars which are not too red.  For a
     1532comparison, we have seleted all PS1 stars with Gaia measurements
     1533meeting the following criteria: $14 < i < 19$, with at least 10 total
     1534measurements, within a modest color range $0.2 < g - r < 0.9$.  We
     1535also restricted to objects with $i_{\rm PSF} - i_{\rm Kron} < 0.1$,
     1536using the average $i$ magnitudes determined from the individual
     1537exposures. 
     1538
     1539For Figure~\ref{fig:gaia.photom}, we calculate the difference between
     1540the estimated $G$-band magnitude based on PS1 $g,r,i$ photometry and
     1541the $G$-band photometry reported by Gaia.  For each pixel, we
     1542determine the histogram of these differences and calculate the median
     1543and the 68\%-ile range.  In Figure~\ref{fig:gaia.photom}, these
     1544values are plotted as a color scale. 
     1545
     1546The Galactic plane is clearly poorly matched between the two
     1547photometry systems.  This may in part be due to the difficulty of
     1548predicting $G$-band magnitudes for stars which are significantly
     1549extincted: the $G$-band includes significant flux from the PS1
     1550$z$-band which was not used in our transformation.  Many other large
     1551scale feature in the median differences have structures similar to the
     1552Gaia scanning pattern (large arcs and long parallel lines.  There are
     1553also structures related to the PS1 exposure footprint.  These show up
     1554as a mottling on the \approx 3 degree scale (e.g., lower right below
     1555the Galactic plane).  The amplitude of the residual structures is
     1556fairly modest.  The standard devition of the median difference values
     1557is 7 millimagnitudes.  This number gives an indication of the overall
     1558photometric consistency of both Gaia and PS1 and implies that the
     1559systematic error floor for each survey is less than 7 millimags.
     1560
     1561% set Gr = -0.090 + gr*gi*0.229 + gi*(-0.207+gi*(gi*0.015 - 0.250)) + gr*(0.491+gr*(-0.021*gr - 0.052))
     1562
     1563%\[
     1564%G - r = -0.09 + 0.229(g-r)(g-r) + (g-i)((
     1565
     1566\begin{figure*}[htbp]
     1567  \begin{center}
     1568  \includegraphics[width=\hsize,clip]{{pics/gaia.astrom}.png}
     1569  \caption{\label{fig:gaia.astrom} Comparison with Gaia
     1570    astrometry. {\bf Left} Mean of PS1 - Gaia, {\bf Right} Standard
     1571    deviation of PS1 - Gaia.  The median value of the standard
     1572    deviations is $(\sigma_\alpha, \sigma_\delta) = (4, 3)$
     1573    milliarcseconds. }
     1574  \end{center}
     1575\end{figure*}
     1576
     1577Figure~\ref{fig:gaia.astrom} shows a comparison between the Pan-STARRS
     1578mean astrometry positions in $\alpha,\delta$ and the Gaia astrometry.
     1579For this comparison, we have seleted all PS1 stars with Gaia
     1580measurements with $14 < i < 19$ and with at least 10 total
     1581measurements.  For Figure~\ref{fig:gaia.astrom}, we calculate the
     1582difference between the position predicted by PS1 at the Gaia epoch
     1583(using the proper motion and parallax fit) and the position reported
     1584by Gaia.  For each pixel, we determine the histogram of these
     1585differences in the R.A\. and DEC directions, and calculate the median
     1586and the 68\%-ile range.  In Figure~\ref{fig:gaia.astrom}, these
     1587values are plotted as a color scale.
     1588
     1589There is good consistency between the PS1 and Gaia astrometry.  There
     1590are patterns from the Galactic plane (though not very strongly at the
     1591bulge).  There are also clear features due to the PS1 exposure
     1592footprint (ring structure on \approx 3 degree scales).  In the plots
     1593of the scatter, there are patterns which are related to the Gaia
     1594scanning rule.  These are presumably regions with relatively low
     1595signal to noise in Gaia; they were also apparent in the plots of the
     1596statisics of the per-exposure measurement residuals
     1597(Figure~\ref{fig:allsky.astrom.sigma}.  The standard deviations of the
     1598median differences are ($\sigma_\alpha, \sigma_\delta) = (4, 3)$
     1599milliarcseconds.
     1600
    13221601\subsection{Calculation of Object Astrometry}
    13231602
    … …  
    13491628
    13501629\bibliographystyle{apj}
    1351 \bibliography{lib}{}
    1352 %\input{calibration.bbl}
     1630%\bibliography{lib}{}
     1631\input{calibration.bbl}
    13531632
    13541633\end{document}
    … …  
    13721651\end{verbatim}
    13731652
     1653List of Figures and their sources:
     1654
     1655* KH example & map:
     1656  * kukui:/data/kukui.3/eugene/pv3.stats.20161202
     1657    * kh.data.20151203.v1/spline.final.fits : spline fits to the KH data
     1658    * kh.data.20151203.v1.fits : densify images of residuals per chip : (dX,dY) & (T0, T1) = (pre fix, post fix)
     1659    * mana.sh : kh.example - plot of XY04
     1660    * mana.sh : khmap (needs cleanup)
     1661  * ipp094:/data/ipp094.0/eugene/pv3.cam.20150607/astrom.corrections : extractions and original scripts to make spline, etc
     1662
     1663* DCR plots:
     1664  * need to rebuild density plots (density images used to make splines are poor for plots)
     1665  * old examples:
     1666    * /data/kukui.3/eugene/dcr.20141205
     1667      * dcr.r2.g.png
     1668  * spline fits (DCR.example)
     1669    * g : dP/dQ =  0.010, dPmax =  0.019
     1670    * r : dP/dQ =  0.001, dPmax =  0.002
     1671    * i : dP/dQ = -0.003, dPmax = -0.003
     1672    * z : dP/dQ = -0.017, dPmax = -0.006
     1673    * y : dP/dQ = -0.021, dPmax = -0.008
     1674
     1675* astroflats:
     1676  * kukui:/data/kukui.3/eugene/pv3.cam.20150607
     1677    * plots.sh :
     1678  * photflat.20151127.fix.fits was made in:
     1679    * kukui:/data/kukui.3/eugene/setphot.20151213
     1680
     1681* Gaia comparisons:
     1682  * ipp094:/data/ipp094.0/eugene/pv3.stats.20161022
     1683  * kukui:/data/kukui.3/eugene/pv3.stats.20161022
     1684 
     1685* photom & astrom residuals:
     1686  kukui:/data/kukui.3/eugene/pv3.stats.20161202/maps.measure
     1687
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