Index: /trunk/doc/release.2015/systematics.20140411/systematics.tex =================================================================== --- /trunk/doc/release.2015/systematics.20140411/systematics.tex (revision 37872) +++ /trunk/doc/release.2015/systematics.20140411/systematics.tex (revision 37872) @@ -0,0 +1,842 @@ +\documentclass[iop,floatfix]{emulateapj} +% \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} + +% online version may use color, but print version needs b/w +\def\plotmode{col} +%\def\plotmode{bw} + +%\def\plotext{pdf} +\def\plotext{ps} + +\def\picdir{/home/eugene/chipresid.20140404} +%\def\picdir{/data/pikake.2/eugene/chipresid.20140404} + +% Pick a terse version of the title here; +\shorttitle{Systematics in PS1} +\shortauthors{E.A. Magnier et al} +\begin{document} +\title{Systematic Effects in Pan-STARRS1 Photometry and Astrometry} + +% this is a crude trick to get the order of affiliations right. These +% names are used in the affiliations below. The user needs to (1) set +% the order and numbers to have the correct sequence in the author +% 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} + +% This example has a first author from UH: +\author{ +Eugene A. Magnier,\altaffilmark{\IfA} +J.~L. Tonry, \altaffilmark{\IfA} +D. Finkbeiner,\altaffilmark{\CfA} +E. Schlafly,\altaffilmark{\MPIA} +%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 + +% The ordering here should be sequential, matching the sequence in the list of authors: +\altaffiltext{\IfA}{Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu HI 96822} +\altaffiltext{\CfA}{Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138} +% \altaffiltext{\Princeton}{Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA} +% \altaffiltext{\USNO}{US Naval Observatory, Flagstaff Station, Flagstaff, AZ 86001, USA} +% \altaffiltext{\JHU}{Department of Physics and Astronomy, Johns Hopkins University, 3400 North Charles Street, Baltimore, MD 21218, USA} +\altaffiltext{\MPIA}{Max Planck Institute for Astronomy, K\"onigstuhl 17, D-69117 Heidelberg, Germany} +\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. + +\end{abstract} + +% insert additional keywords as appropriate: +\keywords{Surveys:\PSONE } + +\section{INTRODUCTION}\label{sec:intro} + +% discuss the science drivers +% summary concept of paper: +%% explore the systematic limitations of PS1 +%% connections between astrometric and photometric systematics + +\section{Pan-STARRS1} + +The Pan-STARRS\,1 telescope (PS1) has recently completed observations +for its first survey mission (REF). PS1 is 1.8m telescope located on +the summit of Haleakala on the Hawaiian island of Maui (REF). This +wide-field telescope images a 3.3 degree field of view on a 1.4 +gigapixel camera, with low distortion and generally good image quality +(median \approx \note{1.1 arcseconds} in all filters except for g, +with 1.3 arcseconds). Available filters are \gps,\rps,\ips with +bandpasses similar to the equivalent SDSS filters; \zps is somewhat +bluer than the SDSS $z$, while \yps is somewhat redder (see, REF, for +a complete specification). + +The first PS1 science survey mission began 2010 May and completed 31 +March 2014. The bulk of the observing time (56\%) goes to the +``3$\pi$ Survey'', in which the \approx 30,000 square degrees +observable from Hawaii (north of Dec = -30) were repeatedly observed +over the nearly 4 year survey period. The typical coverage at the end +of the survey is \approx 10 observations per filter per point on the +sky in the 3$\pi$ region. The repeated observations allows for good +characterization of systematic sources of uncertainty. + +The PS1 data will be released to the public in the Spring of 2015 via +the Mikulsky Archive to Space Telescopes (MAST) at the Space Telescope +Science Institute (STScI). + +\subsection{GigaPixel Camera\,1} + +The PS1 GigaPixel Camera\,1 (GPC1) was the largest astronomical camera +until HypersuprimeCam was completed. GPC1 is a mosaic camera +consisting of 60 detectors (``chips'') arranged in an 8x8 grid with +the 4 corners missing (FIGURE?). The detectors in this camera are +othogonal transfer array devices (REF), in which the single silicon +chip is sub-divided into a checkerboard of 64 sub-arrays (``cells''). +Each cell may be independently addressed and read, and the charge +accumulated in the pixels may be moved in either the $x$ or $y$ +directions (thus the term ``orthogonal transfer''). The full GPC1 +thus consists of a total of 3840 cells, each \note{608 x 610} pixels. + +\subsection{Data Processing} + +Images obtained from PS1 are written to a set of computers located in +the observatory dome (``pixel servers''), and notification is then +sent via a web service to the Image Processing Pipeline (IPP) +computers in Kihei. The IPP cluster retrieves images from the summit +pixel servers as they are available, though no summit hand-shaking +takes place. The summit computers have a buffer for data from several +days' of observing so that data is not lost if the link to Kihei is +down or the IPP computer cluster is offline. + +Raw images are saved on the IPP cluster and processed as needed. In +general, every science exposure is processed as soon as possible in a +stream called the ``nightly science processing''. As the survey has +proceeded and improvements have been made in the analysis software, +images have been reprocessed. To date (2015 Jan), there have been 2 +complete reprocesssing runs (identified PV1 and PV2), and a third +(PV3) is in progress. As the software has been improved, the nightly +science processing software has been updated to reflect those +improvements. The nightly science processing thus is heterogenous in +the analysis and algorithms used. The software for the PVx +reprocessing is more homogenous. + +Raw images are stored as multi-extension FITS images, with each cell +in a given chip stored as a separate image extension. The raw data are +generally stored with lossless compression applied to the pixel +arrays \note{CFITSIO REF}. The data for the 60 chips in a given +exposure are stored as separate FITS files. + +The data processing system performs a number of steps distributed +across a cluster of linux-based computers. The first stage (``chip +processing'') is performed on individual chip image files +independently in parallel. At this stage, the images are detrended, +including overscan, bias, dark, flat-field, and (for $y$-band) +fringing corrections. Areas of bad data (e.g., regions of poor charge +transfer efficiency or non-linear dark glows) are masked. Within the +IPP processing code, masked pixels are identified as non-zero values +in a separate 16-bit mask image, which is then carried as part of the +processed image data products. The chip analysis also generates a +variance image which is used along with the signal image to specify +the noise properities as a function of pixel. Details of the +chip-stage processing can be found in \note{Waters et al REF}. + +The chip-stage analysis also includes source detection and basic +characterization. After a sky background model is subtracted from the +image, individual sources are detected via cross-correlation with a +PSF model. Sources detected in the image are used to define the PSF +model. Simple aperture based measurements (total flux, 2nd and +higher-order moments, etc) are measured for all detections. An +estimate of the extendedness (non-PSF-nature) of the sources is used +to distinguish ``stellar'' detections from ``non-stellar'' detections. +Non-stellar detections above a minimum signal-to-noise \note{of 20} +are fitted with a galaxy surface brightness model, while remaining +sources are fitted with a PSF model, or a cluster of PSF models. The +end result of the chip-stage analysis is a collection of parameters +for each detection, including the positions ($X$, $Y$), PSF model +flux, aperture fluxes, 2nd moments. Details of the source analysis +and characterization can be found in \note{Magnier et al REF}. + +\section{Photometry Analysis} + +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. + +% refer back to refcat, ubercal, tonry +% discuss the PSF modeling +% what are the limitations of the current photometric precision + +\section{Astrometry Analysis} + +Astrometric calibration defines a transformation from the raw +instrumental positions (X,Y on a chip) to RA,DEC coordinates on the +sky. Astrometry calibration is performed at two separate stages in +the IPP analysis. First, every exposure is calibrated independently +during the processing by comparison to a reference catalog. This +astrometric analysis is performed as part of the second processing +stage, the ``camera'' analysis stage. The output from the chip stage +for all chips in an exposure are processed as a group in this +analysis. The initial guess for the astrometry comes from the +telescope coordinates provided in the image headers. + +The RA, DEC, and position angle of the telescope boresite are provided +as part of the image metadata. The telescope and camera systems also +provide WCS header keywords for each chip separately. However, in the +early stages of the telescope commissioning, these values were not +reliable. Thus, within the IPP, and model for the camera layout is +used so that the single triplet (RA,DEC,PA) can be used to predict the +astrometric calibration of each chip. This guess is generally good to +10s of pixels, and need only be accurate to \approx 1/2 of a chip for +the software to discover the true coordinates. + +The guess astrometry is used to select a set of likely reference stars +from the reference database. These stars are the cross-correlated +with the measured source positions to find the likely match between +stars in the reference catalog and detected sources in the image. + +Once a reliable match has been determined, astrometric transformations +are determined to match the raw (X,Y) coordinates of the detections to +sky coordinates of the corresponding reference stars. + +Within the IPP, two main classes of transformations may be used. For +single chips from non-mosaic cameras (or for the warp \& stack +skycells), the astrometry calibration consists of a projection from the +celestial sphere to a linearized coordinate system followed by a +transformation from the projection coordiante frame to the pixel +coordinate frame. The projection may be one of several possible +options (see Calabria et al REF), though in general the IPP uses the +SIN (or TAN) projection (define?). The transformation from the +projection coordiates to the pixel coordinate may use an afine +transformation or higher order polynomials (up to 3rd order). + +For chips from a mosaic camera, the astrometric transformation is +defined as a multi-level operation. As in single-chip astrometry, a +projection (SIN or TAN) is used to convert the spherical celestial +coordiates to a local linear system (the 'tanget plane' coorinate +system). There are then two level of cartesian transformations: a +first set of polynomials (up to 3rd order) are used to transform the +tangent plane coordinates to the ``focal plane'' coordinates. This, +relatively low-order, correction accounts for rotation of the camera +and basic optical distortion coming from the optics and the +atmosphere. A second transformation is used to convert the focal +plane coordinate to the pixel coordinates for each chip. For the +on-the-fly calibration, these +transformations may consist of a set of polynomials up +to 3rd order in X and/or Y (i.e, $x^i y^j$ where $i + j <= 3$) + +\note{add details on the transformation from focal-plane to tangent + plane: fit is done on the gradient}. + +The on-the-fly astrometric calibration determines the astrometric +transformation to an accuracy of at least 0.3 arcsec (chips with worse +astrometry are rejected). Data from these images may now be ingested +into our internal database software for astronomical objects, the +Desktop Virtual Observatory \citep[DVO,][]{PS1.IPP}. This database +software associates detections from images together based on their +positions in the sky to define astrnomical ``objects''. The database +includes metadata to describe the links between objects and their +multiple detections as well as metadata defining the images and their +astrometric transformations. + +After images have been ingested into the DVO software, calibration +improvements may be made within the database. A program called +``relastro'' is used to improve the astrometry iterative. In one +mode, relastro loops between improving the mean positions of objects +and using the improved mean positions to improve the astrometric +calibrations of the images. In normal usage, relastro is only allowed +to update the chip-to-focal plane transformations; it is not normally +used to improve the focal-plane to tangent plane transformations. +Also, within relastro, the transformation from chip-to-focal plane may +be represented using either the polynomials as above or with a linear +transformation plus bilinear interpolation of a grid of correction +cells. In the latter case, the grid may be sampled as finely as 6x6 +positions per chip. + +% precision demonstration +% koppenhoefer effect +% MISSING: DCR! + +\section{Systematic Residuals} + +\subsection{Camera-Scale Trends} + +\subsection{Tree-Rings : An Example Chip} + +\begin{table} +\caption{Systematic Trends : Stdev by filter\label{table:sigmas.by.filter}} +% \tiny +\begin{center} +\begin{tabular}{|l|rrrrr|} +\hline +{\bf Filter} & {\bf psf mags} & {\bf ap mags} & {\bf astrom} & {\bf smear} & {\bf flat} \\ + & mmags & mmags & mas & pixels$^2$ & mmags \\ +\hline +\gps & 11.8 & 13 & 8.0 & 0.169 & 3.0 \\ +\rps & 10.9 & 12 & 6.7 & 0.133 & 2.2 \\ +\ips & 8.5 & 10 & 6.0 & 0.069 & 1.7 \\ +\zps & 8.7 & 12 & 5.5 & 0.052 & 3.2 \\ +\yps & 16.5 & 26 & 6.8 & 0.059 & 15.3 \\ +\hline +\end{tabular} +\end{center} +\end{table} + +We observe a number of low-level effects in different types of +measurements which have a similar spatial structure on individual +chips. These structures have a circular pattern centered one corner +of the affected chips. \note{do all chips show all effects? is the + amplitude very different from chip to chip?} We use measurements +from chip XY40 to illustrate the spatial patterns and relationships +between the different effects. For all effects, we are measuring the +mean value of the effect in 10x10 pixel boxes. The resulting images +are all constructed so that a given superpixel represents the same +range of true GPC1 XY40 pixels. Measurements were extracted from the +``nightly science'' DVO database for observations covering the region +($\alpha$,$\delta$) = (90\degree\ -- 150\degree, -25\degree\ -- +10\degree). This region avoids the Galactic Plane where astrometric +outliers have been more common. We limit the analysis to good +measurements (PSF\_QF $>$ 0.85) of likely stars ($|m_{psf} - m_{aper}| +< 0.2$). Only measurements with instrumental magnitude $< -8.0$ +($-2.5\log \mbox{cts sec}^{-1} < -8.0$) are include to ensure +reasonable signal-to-noise per measurement. We require at least 2 +measurements in a given filter and 5 measurements total for any star +included in the analysis. + +The following four different measurements show tree-ring structures +(a) photometric residuals, (b) astrometric residuals, (c) a portion of +the flat-field structure, and (d) variations in the second-moment of +stars. In the following section, we show the spatial patterns for +these features and measure their intensity as a function of the +different filters. By comparing the spatial structures, we show that +these effects are directly related. We defer for now discussion of +any causes of the observed effects. + +\subsubsection{Photometric Residuals} + +% PSF Magnitudes +\def\figwidth{2.75in} +\begin{figure*}[htbp] +\begin{center} +\parbox{\figwidth}{\includegraphics[width=\figwidth]{\picdir/dmag.g.\plotext}} +\parbox{\figwidth}{ +\caption{PSF Magnitude residuals by Filter + } \label{fig:psfmags.by.filter}} + +\includegraphics[width=\figwidth]{\picdir/dmag.r.\plotext} +\includegraphics[width=\figwidth]{\picdir/dmag.i.\plotext} + +\includegraphics[width=\figwidth]{\picdir/dmag.z.\plotext} +\includegraphics[width=\figwidth]{\picdir/dmag.y.\plotext} +\end{center} +\end{figure*} + +% Aperture Magnitudes +\def\figwidth{2.75in} +\begin{figure*}[htbp] +\begin{center} +\parbox{\figwidth}{\includegraphics[width=\figwidth]{\picdir/dapmag.g.\plotext}} +\parbox{\figwidth}{ +\caption{Aperture Magnitude residuals by Filter + } \label{fig:apmags.by.filter}} + +\includegraphics[width=\figwidth]{\picdir/dapmag.r.\plotext} +\includegraphics[width=\figwidth]{\picdir/dapmag.i.\plotext} + +\includegraphics[width=\figwidth]{\picdir/dapmag.z.\plotext} +\includegraphics[width=\figwidth]{\picdir/dapmag.y.\plotext} +\end{center} +\end{figure*} + +The tree-ring structure is clearly seen in the PSF magnitude +residuals. In this case, we select PSF magnitude measurements for +detections which fall in the given superpixel. We subtract each +measurement from the average magnitude for the object in the selected +filter ($\delta m_{psf} = \overline{m}_{psf} - m_{psf}$) to determine the +residual magnitude, excluding as bad any measurement with $|\delta +m_{psf}| > 0.5$. For a given superpixel, we measure the median of the +$\delta m_{psf}$ distribution. Figure~\ref{fig:psfmags.by.filter} +shows the 2D patterns of $\delta m_{psf}$ for each filter (\grizy). +The dynamic range of the color scale is from -20 to +20 +millimagnitudes for all 5 plots. + +The tree-ring pattern is clearly visible for the four blue filters, +but finging dominates the pattern for \yps. Small offsets of +individual cells are also apparent for \zps. While the patterns are +clear across the image, the signal-to-noise of the structures per +pixel is not very strong in these images. The per-pixel standard +deviations of these plots is listed in +Table~\ref{table:sigmas.by.filter}. The per-pixel standard deviation +is comparable to the amplitude of the correlated structures, so we +need to integrate along the radial structures to make stronger +statements about these patterns. + +We have also performed the same measurement for aperture magnitudes, +using the same selections. The 2D patterns for the aperture +magnitudes is shown in Figure~\ref{fig:apmags.by.filter}. The finging +pattern again dominates the plot for \yps, but the tree-rings are not +seen in any of the filters. A diagonal pattern is visible in \gps +which is not observed in the PSF magnitudes. While the per-pixel +scatter is somewhat (10\% to 20\%) higher for these aperture +magnitudes than for the PSF magnitudes +(Table~\ref{table:sigmas.by.filter}), a structure with the amplitude +of the PSF magnitude tree-rings would certainly have been obvious. + +\subsubsection{Astrometric Residuals} + +% astrometry radial term +\def\figwidth{2.75in} +\begin{figure*}[htbp] +\begin{center} +\parbox{\figwidth}{\includegraphics[width=\figwidth]{\picdir/drad.g.\plotext}} +\parbox{\figwidth}{ +\caption{astrometric radial-direction residuals by Filter + } \label{fig:astrom.by.filter}} + +\includegraphics[width=\figwidth]{\picdir/drad.r.\plotext} +\includegraphics[width=\figwidth]{\picdir/drad.i.\plotext} + +\includegraphics[width=\figwidth]{\picdir/drad.z.\plotext} +\includegraphics[width=\figwidth]{\picdir/drad.y.\plotext} +\end{center} +\end{figure*} + +The tree-ring structure is also clearly seen in the astrometric +residuals. We use the same selection of measurements for astrometry +as for photometry. In this case, we extract the residual in both the +RA and DEC directions ($\delta RA = \overline{RA} - RA_i$, $\delta DEC += \overline{DEC} - DEC_i$) and rotate these values to the chip +coordinate system ($\delta X,\delta Y$). We again exclude as bad any +measurement with $|\delta X|$ or $|\delta Y| > 0.5$ arcsec before +measuring the median values for each superpixel. We have determined +the approximate center of the circular tree-ring pattern as (-5,4960) +for this particular chip. Using this coordinate as the center, we +have converted the $\delta X,\delta Y$ offsets into $\delta R,\delta +\theta$ measurements ($\delta R$ : radial component away from the +center, $\delta \theta$ : tangential component). + +Figure~\ref{fig:astrom.by.filter} shows the 2D patterns of $\delta R$ +for each filter (\grizy). The dynamic range of the color scale is +from -20 to +20 milliarcseconds for all 5 plots. The tree-ring +pattern is visible for all five filters; the finging pattern is not +apparent in the \yps\ astrometry. \note{low-frequency structures? did + that take off fringing?} The per-pixel standard deviations of these +plots is listed in Table~\ref{table:sigmas.by.filter}. The +signal-to-noise of these structures is again somewhat weak, but the +pattern is clearly visible in these figures. + +\subsubsection{Flat-field Structures} + +% flat-field residual +\def\figwidth{2.75in} +\begin{figure*}[htbp] +\begin{center} +\parbox{\figwidth}{\includegraphics[width=\figwidth]{\picdir/dflat.g.\plotext}} +\parbox{\figwidth}{ +\caption{Flat-field high-frequency structues by Filter + } \label{fig:flats.by.filter}} + +\includegraphics[width=\figwidth]{\picdir/dflat.r.\plotext} +\includegraphics[width=\figwidth]{\picdir/dflat.i.\plotext} + +\includegraphics[width=\figwidth]{\picdir/dflat.z.\plotext} +\includegraphics[width=\figwidth]{\picdir/dflat.y.\plotext} +\end{center} +\end{figure*} + +The tree-ring structure is also clearly seen in the flat-field +pattern. For this measurement, we have used a set of monochromatic +flat-field images obtained with a tunable laser. The laser is used to +illuminate our flat-field screen which is then observed by the PS1 +telescope. These flat-field images were obtained 2011 Feb 09 as part +of a campaign to study the PS1 system response (Tonry et al REF). +Flats were obtain in a set of 4nm steps, with XXnm band-pass. To +enhance the signal-to-noise, we have combined a set of 6 flats at the +center of the corresponding filter. \note{high-pass filtering}. + +Figure~\ref{fig:flats.by.filter} shows the remaining high-frequency +structures in the flat-field images. These flat-field images are +displayed as fractional deviations relative to the median flat-field +image and can thus be compared to the magnitude residuals. When +flattening an image, these flat-fields would be divided into the flux +of the raw image. The residuals are thus defined in the sense that a +positive feature in these flats which does {\em not} represent a real +quantum efficiency deviation would induce a {\em reduction} in the +measured flux in those pixels, and thus a {\em negative} deviation in +$\delta m_{psf}$ as defined above. The dynamic range of the color +scale in these plots is -0.01 to +0.01. The tree-ring pattern is +strong in the (\gps,\rps,\ips) images, but nearly swamped by fringing +in \zps, and completely lost to finging in \yps. A diagonal banding +similar to the aperture residuals is seen in \gps. + +\subsubsection{Second Moments} + +% Smear Images +\def\figwidth{2.75in} +\begin{figure*}[htbp] +\begin{center} +\parbox{\figwidth}{\includegraphics[width=\figwidth]{\picdir/smear.g.\plotext}} +\parbox{\figwidth}{ +\caption{Smear by filter + } \label{fig:smear.by.filter}} +% note that the caption wants to be vertically centered. I can push it up +% by padding the end with a big \vspace{1in} + +\includegraphics[width=\figwidth]{\picdir/smear.r.\plotext} +\includegraphics[width=\figwidth]{\picdir/smear.i.\plotext} + +\includegraphics[width=\figwidth]{\picdir/smear.z.\plotext} +\includegraphics[width=\figwidth]{\picdir/smear.y.\plotext} +\end{center} +\end{figure*} + +% Shear Images +\def\figwidth{2.75in} +\begin{figure*}[htbp] +\begin{center} +\parbox{\figwidth}{\includegraphics[width=\figwidth]{\picdir/shear.g.\plotext}} +\parbox{\figwidth}{ +\caption{Shear by Filter + } \label{fig:shear.by.filter}} + +\includegraphics[width=\figwidth]{\picdir/shear.r.\plotext} +\includegraphics[width=\figwidth]{\picdir/shear.i.\plotext} + +\includegraphics[width=\figwidth]{\picdir/shear.z.\plotext} +\includegraphics[width=\figwidth]{\picdir/shear.y.\plotext} +\end{center} +\end{figure*} + +The tree-ring structure is also seen in the changes of the image size. +To measure this effect, we extract the second moments for all +detections, subject to the same selections as for the photometry and +astrometry residuals (good stars, multiple detections). The second +moments are measured with a Gaussian weighting function, with the +$\sigma_{w}$ scaled by the PSF size so that the $\sigma$ measured for +PSF stars is \approx 60\% of $\sigma_{w}$. (Note that, since the +measured $\sigma$ of stellar objects is biased down by the weighting +function, this is not quite the same as having $\sigma_{w} = 1.6$ +times the true PSF $\sigma$). For each detection, we measure +$M_{xx,xy,yy} = \sum F_i w_i (x^2, x y, y^2) / \sum F_i w_i$. For +each exposure, we find the mean second moments for PSF objects and +subtract that mean value from the instantaneous measurements of +$M_{xx,xy,yy}$. We then determine the median of the residual second +moments for each superpixel. + +Figure~\ref{fig:smear.by.filter} shows the spatial trend of the {\em + smear}, $\sigma^2_{major} + \sigma^2_{minor} = \delta M_{xx} + +\delta M_{yy}$. This value corresponds to the increase or decrease in +the circularly-symmetric component of the image size. The dynamic +range of these images is -0.3 to +0.3 pixel$^2$. The tree-ring pattern +is visible for all 5 filters, though \yps is dominated by the fringing +pattern. Structures with relatively low spatial frequencies can also +be seen. + +We can also construct a measurement of the change in ellipticity +$\sigma^2_{major} - \sigma^2_{minor} = (M_{xx} - M_{yy})^2 + 4 +M_{xy}$. This value is plotted in Figure~\ref{fig:shear.by.filter}. +This value is positive definite and is plotted with a color scale +ranging from -0.02 to 0.22 pixel$^2$. We can also determine the +orientation of the corresponding ellipse. Overlayed on +Figure~\ref{fig:shear.by.filter} is a set of vectors representing the +ellipse orientation as a function of postion. The length of the +vectors corresponds to the value of $\sigma^2_{major} - +\sigma^2_{minor}$. The tree-ring structure is not apparent in this +figure for any filter. The spatial variations are low-frequency and +unrelated to the radial trend from the upper-left corner. + +\subsubsection{Correlations Between Systematic Trends} + +\begin{table} +\caption{Systematic Trends : Correlations by filter\label{table:correlation.by.filter}} +% \tiny +\begin{center} +\begin{tabular}{|l|rrrr|} +\hline +{\bf Filter} & {\bf psf mags} & {\bf smear} & {\bf astrom} & {\bf flat} \\ +\hline +\gps & 1.00 & 1.00 & 1.00 & 1.00 \\ +\rps & 0.84 & 0.78 & 0.84 & 0.76 \\ +\ips & 0.50 & 0.40 & 0.66 & 0.64 \\ +\zps & 0.26 & 0.16 & 0.37 & 0.33 \\ +\yps & 0.10 & 0.10 & 0.25 & 0.30 \\ +\hline +\end{tabular} +\end{center} +\end{table} + +As discussed above, the signal-to-noise per pixel in the plots of the +systematic trends is relatively low (\approx 1.0). While the tree +rings are apparent in many of these figures, there are also +some other systematic structures which may degrade the signal +further. To quantatatively compare the tree-ring trends between +filters and between systematic effects, we need to measure the +tree-ring structure explicitly and filter out the other effects if +possible. To do this, we have applied a high-pass filter to all of +the relevant images (PSF Photometry residuals, Astrometric residuals +in the radial direction, flat-field residuals, and second moment smear +terms) to remove unrelated spatial structures. We have then measured +the median of the signal in radial bins centered on (-5,4960) across +an arc from $\phi$ = -20\degrees\ to -50\degrees (as measured relative +to the top row of the images. We have selected a small fraction of +the arc to minimize the error associated with the choice of the +pattern center and to avoid several bad cells near the bottom of the +chip. \note{draw the arcs?} + +For a given trend, the systematic effect is strongly correlated +between filters. The strongest correlation is the smear term: +Figure~\ref{fig:smear.trends} shows the correlation of the smear +pattern between \gps\ and the other four filters. Even \yps\ is +strongly correlated with \gps\ despite the presence of the fringe +pattern. PSF photometric residuals are also correlated between +filters, as shown in Figure~\ref{fig:psfmag.trends}. Here, the +\yps\ correlation with \gps\ is quite weak: the fringing pattern +dominates the tree-rings for PSF photometry. The radial component of +the astrometric residual is also well correlated between filters, with +no loss of correlation due to fringing in \yps. Finally, the +flat-field residuals are generally correlated between filters, but +both \zps\ and \yps\ are affected by fringing. For \yps, the +correlation is completely washed out by the very strong fringing pattern. + +For all four measurements, the slope of the fitted lines are listed in +Table~\ref{table:correlation.by.filter}. There is a consistency in +the trend from \gps, with the strongest systematic tree-ring effects +to \yps, with the weakest effects. Note that the second moment smear +and astrometry terms have different relative strength in +\yps\ compared with \gps. + +% smear trends by filter +\def\figwidth{6.5in} +\begin{figure*}[htbp] +\begin{center} +\includegraphics[width=\figwidth]{\picdir/smear.trends.\plotext} +\caption{Smear : correlation between filters +} \label{fig:smear.trends} +\end{center} +\end{figure*} + +% psfmag trends by filter +\def\figwidth{6.5in} +\begin{figure*}[htbp] +\begin{center} +\includegraphics[width=\figwidth]{\picdir/psfmag.trends.\plotext} +\caption{PSF magnitude residuals : correlation between filters +} \label{fig:psfmag.trends} +\end{center} +\end{figure*} + +% astrom trends by filter +\def\figwidth{6.5in} +\begin{figure*}[htbp] +\begin{center} +\includegraphics[width=\figwidth]{\picdir/astrom.trends.\plotext} +\caption{Astrometry residuals : correlation between filters +} \label{fig:astrom.trends} +\end{center} +\end{figure*} + +% flat trends by filter +\def\figwidth{6.5in} +\begin{figure*}[htbp] +\begin{center} +\includegraphics[width=\figwidth]{\picdir/flat.trends.\plotext} +\caption{Flat-field rings : correlation between filters +} \label{fig:flat.trends} +\end{center} +\end{figure*} + +An important question is the relationship between the different types +of systematic effects. Different models for the tree-ring structures +will make different predictions about the correlations between +different effects. We find the following relationships hold. First, +the PSF magnitude residuals and the second-moment smear trends are +strongly anti-correlated: regions which have larger PSFs than the mean +tend to have smaller measured PSF fluxes than the mean (note that +$\delta m_{psf}$ is defined so that positive values correspond to +larger fluxes). These trends are shown in +Figure~\ref{fig:smear.vs.psfmag}. Second, the radial derivative of +the smear is anti-correlated with the radial component of the +astrometric residuals: $\frac{\partial (\sigma^2_{major} + + \sigma^2_{minor})}{\partial radius} \sim \delta R$ (see +Figure~\ref{fig:dsmear.vs.astrom}. Finally, the radial derivative of +the radial component of the astrometric residual is anti-correlated +with the flat-field residual errors: $\frac{\partial \delta + R}{\partial radius} \sim \delta flat$ (see +Figure~\ref{fig:dastrom.vs.flat}. This last relationship is somewhat +weakly measured. Because of the periodic nature of the tree rings, it +is also difficult to completely certain that the flat-field is +proportional to the derivative of the astrometry residual, and not the +other way around. The correlation is somewhat weaker for derivative +of the flat-field vs astrometry residual. The correlation is very +weak between the flat-field and the astrometry directly. We are +convinced that we have the sense of the derivative correct by the +details of specific features. + +\begin{table} +\caption{Systematic Trends : Correlations between trends\label{table:correlation.by.trend}} +% \tiny +\begin{center} +\begin{tabular}{|l|rrr|} +\hline +{\bf Filter} & {\bf psf mags} & {\bf $\grad$ smear} & {\bf $\grad$ astrom} \\ + & {\bf vs smear} & {\bf vs astrom} & {\bf vs flat} \\ +\hline +\gps & -0.056 & -0.060 & -0.47 \\ +\rps & -0.071 & -0.073 & -0.45 \\ +\ips & -0.077 & -0.095 & -0.45 \\ +\zps & -0.082 & -0.078 & -0.17 \\ +\hline +\end{tabular} +\end{center} +\end{table} + +% smear vs psfmag +\def\figwidth{6.5in} +\begin{figure*}[htbp] +\begin{center} +\includegraphics[width=\figwidth]{\picdir/smear.vs.psfmag.\plotext} +\caption{Smear vs PSF mag residuals on the rings +} \label{fig:smear.vs.psfmag} +\end{center} +\end{figure*} + +% dsmear vs astrom +\def\figwidth{6.5in} +\begin{figure*}[htbp] +\begin{center} +\includegraphics[width=\figwidth]{\picdir/dsmear.vs.astrom.\plotext} +\caption{gradient of the Smear vs astrometry residuals on the rings +} \label{fig:dsmear.vs.astrom} +\end{center} +\end{figure*} + +% dastrom vs flat +\def\figwidth{6.5in} +\begin{figure*}[htbp] +\begin{center} +\includegraphics[width=\figwidth]{\picdir/dastrom.vs.flat.\plotext} +\caption{gradient of the astrometry residuals vs flat-field rings +} \label{fig:dastrom.vs.flat} +\end{center} +\end{figure*} + +\section{Discussion} + +These trends help to illuminate the underlying causes of these +different effects. First, we can easily explain the relationship +between the PSF photometry residuals and the observed smear. In the +photometry analysis, we model the PSF allowing for some spatial +variation in the shape. However, we limit the 2D variation to a 3x3 +grid for each chip: the PSF parameters may vary smoothly across the +chip following the bilinear interpolation between the 3x3 grid points. +Thus, the spatial scale on which we model PSF variations is much +larger than the spatial scale on which PSF variations are apparently +occuring. When the true PSF is larger than the model PSF, our model +fits systematically underestimate the amount of flux in a given +object. Conversely, when the PSF is smaller, we overestimate the +flux. The slope of the trend depends on the mean typical seeing for +the given filter. For example, the \gps\ seeing is typically +1.3\arcsec, corresponding to a Gaussian $\sigma$ of 2.15 pixels. A +smearing of $\sigma^2_{major} + \sigma^2_{minor} = 0.1$ pixels$^2$ +would increase the size by about 0.02 pixels, or 1\%, so roughly +consistent with the observed photometric deviation of about 5 to 10 +millimags for this amount of smearing. \note{model the 2D effect more + explicitly}. + +Second, the relationship between the flat-field residual and the +astrometric gradient is consistent with radial variations in the +plate-scale. The tree-rings observed by DES are completely attributed +to effective plate scale changes. Effective plate scale changes would +result in flat-field deviations since the flat-field illumination is a +source of constant surface brightness. Pixels see a varying amount of +flux depending on their effective area. This changing plate scale +also affects the astrometry since these variations occur on spatial +scales much smaller than the astrometric model. In such a model, the +flat-field deviations are $-1 \times \frac{\partial Pos}{\partial R}$. +The slope of our relationship is \approx 0.5 in normalized units. +Thus the observed trends appear to be too weak by a factor of \approx +2. \note{looks like a slope of 1.0 would not be excluded by these + plots} + +The fact that the PSF ellipticity changes are {\em not} correlated +with the tree ring structure tells us that the effective plate-scale +changes seen in the flat-field and astrometry signals are not also the +dominant cause of the PSF photometry errors. Also, the fact that we +do not measure significant aperture photometry errors correlated with +the tree rings confirms this point. The amplitude of the flat-field +errors are 1-2 millimagnitudes, much smaller than the PSF photometry +errors, and far below the pixel-to-pixel noise in the aperture +magnitudes. + +\section{Conclusion} + +The tree rings are showing (at least?) two effects, though they must +be related. First, the images are experiencing circularly-symmetric +changes in the PSF size correlated with the tree-ring pattern. These +PSF size changes drive errors in the PSF photometry which the are also +correlated with the tree ring pattern on the scale of a few +millimagnitudes. These PSF size changes are consistent with changes +in the charge diffusion, which also introduces a circularly symmetric +smearing. + +In addition, there are radial plate-scale changes +correlated with the tree rings. These plate-scale changes introduce a +flat-field errors on the scale of \approx 1 millimagnitude and +astrometric errors in the scale of 2-3 milliarcseconds. The observed +relationship between the flat-field deviations and the radial +derivative of the astrometric deviations confirms that these two +measurements are caused by the same effect. + +There must be some common cause for both the smearing (charge +diffusion) and the radial plate-scale changes since the astrometric +deviations are correlated with the radial derivative of the smearing. + +\end{document}