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Ignore:
Timestamp:
Aug 21, 2017, 6:14:59 PM (9 years ago)
Author:
eugene
Message:

update text and figures based on comments; sent to the consortium

Location:
trunk/doc/release.2015/systematics.20140411
Files:
7 added
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  • trunk/doc/release.2015/systematics.20140411/systematics.tex

    r40108 r40120  
    1212\RequirePackage{color}
    1313\RequirePackage{code}
     14\RequirePackage{pbox}
    1415\input{astro.sty}
    1516
    … …  
    9596devices used in the Pan-STARRS\,1 Gigapixel Camera.  We have
    9697identified systematic spatial variations in the photometric behavior and
    97 stellar profiles which are similar to the so-called Tree Rings
     98stellar profiles which are similar to the so-called ``tree rings''
    9899identified in devices used by other wide-field cameras (DECam and
    99 Hypersuprime Camera).  The Tree-Ring features identified in these
     100Hypersuprime Camera).  The tree-ring features identified in these
    100101other cameras result from lateral electric fields which displace the
    101102electrons as they are transported in the silicon to the pixel
    … …  
    110111
    111112\section{INTRODUCTION}\label{sec:intro}
    112 
    113 \note{KCC says: note what is unique to GPC1 vs other cameras}
    114113
    115114CCD detectors have evolved greatly since they were first introduced
    … …  
    176175
    177176The effects of lateral electric fields are likewise identified as the
    178 cause of the so-called ``Tree Rings'' observed in the flat-field,
     177cause of the so-called ``tree rings'' observed in the flat-field,
    179178astrometry, and photometry response of thick deep depletion detectors
    180 \citep{2014PASP..126..750P}.  These Tree-Ring patterns have been noted
     179\citep{2014PASP..126..750P}.  These tree-ring patterns have been noted
    181180in the flat-field response of deep depletion devices since their early
    182181testing \citep[see, e.g., Figure 2 in][]{2010SPIE.7735E..1RE} and were
    183182initially considered to be a sensitivity response which could be
    184183removed with a flat-field.  As discussed in detail by
    185 \cite{2014PASP..126..750P}, these Tree Rings are more correctly
     184\cite{2014PASP..126..750P}, these tree rings are more correctly
    186185interpretted as variations in the effective pixel area due to
    187186migration of the electrons pushed by lateral electric fields induced
    … …  
    195194
    196195In this paper, we examine the behavior of an apparently-similar kind
    197 of Tree Ring observed in the Pan-STARRS GPC1 CCDs.  Although we also
     196of tree ring observed in the Pan-STARRS GPC1 CCDs.  Although we also
    198197observe the pixel effective area changes caused by lateral electric
    199198fields as described by \cite{2014PASP..126..750P}, we show below a
    … …  
    204203profile fitting techniques.  In Section~\ref{sec:PS1}, we discuss the
    205204Pan-STARRS telescope, camera, and survey data used in this analysis.
    206 In Section~\ref{sec:tree.rings}, we present the Tree-Ring-like
     205In Section~\ref{sec:tree.rings}, we present the tree-ring
    207206patterns as observed in several different types of measurements:
    208207flat-field response, systematic photometry residuals, systematic
    … …  
    222221Consortium to perform a set of wide-field science surveys; since March
    2232222014, operations have been supported primarily by NASA's Near Earth
    224 Object Observation program, see \cite{wainscoat.2015}.  Under the
     223Object Observation program, see \cite{2015IAUGA..2251124W}.  Under the
    225224PS1SC, the largest survey, both in terms of area of the sky covered
    226225($3\pi$ steradians) and fraction of observing time (56\%), was the
    … …  
    353352milliarcsecond for individual measurements of brighter stars.
    354353
    355 \section{Tree-Ring-Like Patterns}
     354\section{Tree-Ring Patterns}
    356355\label{sec:tree.rings}
    357356
    358357\begin{table}
    359 \caption{Systematic Trends : Stdev by filter\label{table:sigmas.by.filter}}
    360358% \tiny
    361359\begin{center}
     360\caption{Systematic Trends : Standard deviation by filter\label{table:sigmas.by.filter}}
    362361\begin{tabular}{|l|rrrrr|}
    363362\hline
    … …  
    377376For many of the GPC1 OTA CCDs, we observe a spatial pattern in the
    378377photometric residuals for each device which is similar in appearence
    379 to the Tree Rings described in the Dark Energy Camera (DECam) by
     378to the tree rings described in the Dark Energy Camera (DECam) by
    380379\cite{2014PASP..126..750P}.  This pattern consists of systematic
    381380deviations which are consistent in a set of circular arcs centered on
    … …  
    386385wafer into 4 inscribed squares.  Thus the corners of the CCDs lie in
    387386the center of the silicon boule, just as the center of the circular
    388 Tree Rings described by \cite{2014PASP..126..750P} match the center of
     387tree rings described by \cite{2014PASP..126..750P} match the center of
    389388the boule from which they came.  This gives the impression that a
    390389similar mechanism is responsible for the pattern observed in the PS1
    … …  
    397396
    398397First, in this section, we will describe how we have measured the
    399 presence or absence of these Tree-Ring patterns in 5 types of data.
     398presence or absence of these tree-ring patterns in 5 types of data.
    400399For all of these examples, we use a single GPC1 CCD (XY40) to
    401400illustrate the effects in detail, but a similar set of effects are
    … …  
    412411type of measurement.  To generate the photometry, astrometry, or
    413412second-moment plots, measurements were extracted from the PV0 DVO
    414 database \citep{magnier.2017.calibration} for observations covering
     413database \citep{magnier2017.calibration} for observations covering
    415414the region ($\alpha$,$\delta$) = (90\degree\ -- 150\degree,
    416415-25\degree\ -- 10\degree).  This region of the sky provides a fairly
    … …  
    418417may potentially contaminate the measurement.  We limit the analysis to
    419418good measurements (\ippmisc{PSF_QF} $>$ 0.85, see
    420 \citealt{magnier.2017.analysis}) of likely stars ($|m_{psf} -
     419\citealt{magnier2017.analysis}) of likely stars ($|m_{psf} -
    421420m_{aper}| < 0.2$).  Only measurements with instrumental magnitude $<
    422421-8.0$ ($-2.5\log \mbox{cts sec}^{-1} < -8.0$) are included to ensure
    … …  
    428427
    429428% PSF Magnitudes
    430 \def\figwidth{2.75in}
    431 \begin{figure*}[htbp]
    432 \begin{center}
    433 \parbox{\figwidth}{\includegraphics[width=\figwidth]{\picdir/dmag.g.\plotext}}
    434 \parbox{\figwidth}{
    435 \caption{PSF Magnitude residuals by Filter.  \note{expand colorscale
    436     bars, make clearer labels} } \label{fig:psfmags.by.filter}}
    437 
    438 \includegraphics[width=\figwidth]{\picdir/dmag.r.\plotext}
    439 \includegraphics[width=\figwidth]{\picdir/dmag.i.\plotext}
    440 
    441 \includegraphics[width=\figwidth]{\picdir/dmag.z.\plotext}
    442 \includegraphics[width=\figwidth]{\picdir/dmag.y.\plotext}
     429\def\figwidth{5.2in}
     430\def\jumpleft{-2.6in}
     431\def\capwidth{2.4in}
     432\begin{figure*}[htbp]
     433\begin{center}
     434\parbox[b]{\figwidth}{\includegraphics[width=\figwidth]{\picdir/dmag.\plotext}}
     435\hspace{\jumpleft}
     436\parbox[b]{\capwidth}{
     437\caption{PSF Magnitude residuals by filter (\grizy).  White boxes are
     438  GPC1 cells which have been masked due to poor response.  Superpixels
     439  representing regions of $10\times10$ pixels are used to determine
     440  the median deviation for measurements at the given chip pixel
     441  location compared with the average photometry for the given
     442  object.} \label{fig:psfmags.by.filter}}
    443443\end{center}
    444444\end{figure*}
    445445
    446446% Aperture Magnitudes
    447 \def\figwidth{2.75in}
    448 \begin{figure*}[htbp]
    449 \begin{center}
    450 \parbox{\figwidth}{\includegraphics[width=\figwidth]{\picdir/dapmag.g.\plotext}}
    451 \parbox{\figwidth}{
    452 \caption{Aperture Magnitude residuals by Filter
    453  } \label{fig:apmags.by.filter}}
    454 
    455 \includegraphics[width=\figwidth]{\picdir/dapmag.r.\plotext}
    456 \includegraphics[width=\figwidth]{\picdir/dapmag.i.\plotext}
    457 
    458 \includegraphics[width=\figwidth]{\picdir/dapmag.z.\plotext}
    459 \includegraphics[width=\figwidth]{\picdir/dapmag.y.\plotext}
     447\begin{figure*}[htbp]
     448\begin{center}
     449\parbox[b]{\figwidth}{\includegraphics[width=\figwidth]{\picdir/dapmag.\plotext}}
     450\hspace{\jumpleft}
     451\parbox[b]{\capwidth}{
     452\caption{Aperture Magnitude residuals by filter (\grizy).  White boxes
     453  are GPC1 cells which have been masked due to poor response.
     454  Superpixels representing regions of $10\times10$ pixels are used to
     455  determine the median deviation for measurements at the given chip
     456  pixel location compared with the average photometry for the given
     457  object.  } \label{fig:apmags.by.filter}}
    460458\end{center}
    461459\end{figure*}
    … …  
    473471millimagnitudes for all 5 plots.
    474472
    475 The Tree-Ring pattern is clearly visible for the four blue filters,
     473The tree-ring pattern is clearly visible for the four blue filters,
    476474but finging dominates the pattern for \yps.  Small offsets of
    477475individual cells are also apparent for \zps.  While the patterns are
    478476clear across the image, the signal-to-noise of the structures per
    479477pixel is not very strong in these images.  The per-pixel standard
    480 deviations of these plots is listed in
     478deviations of these plots are listed in
    481479Table~\ref{table:sigmas.by.filter}.  The per-pixel standard deviation
    482480is comparable to the amplitude of the correlated structures, so we
    … …  
    486484Figure~\ref{fig:apmags.by.filter} shows the equivalent measurement for
    487485aperture photometry instead of PSF photometry.  The finging
    488 pattern again dominates the plot for \yps, but the Tree Rings are not
     486pattern again dominates the plot for \yps, but the tree rings are not
    489487seen in any of the filters.  A diagonal pattern is visible in \gps
    490488which is not observed in the PSF magnitudes.  While the per-pixel
    … …  
    497495
    498496% astrometry radial term
    499 \def\figwidth{2.75in}
    500 \begin{figure*}[htbp]
    501 \begin{center}
    502 \parbox{\figwidth}{\includegraphics[width=\figwidth]{\picdir/drad.g.\plotext}}
    503 \parbox{\figwidth}{
    504 \caption{astrometric radial-direction residuals by Filter
    505  } \label{fig:astrom.by.filter}}
    506 
    507 \includegraphics[width=\figwidth]{\picdir/drad.r.\plotext}
    508 \includegraphics[width=\figwidth]{\picdir/drad.i.\plotext}
    509 
    510 \includegraphics[width=\figwidth]{\picdir/drad.z.\plotext}
    511 \includegraphics[width=\figwidth]{\picdir/drad.y.\plotext}
     497\begin{figure*}[htbp]
     498\begin{center}
     499\parbox[b]{\figwidth}{\includegraphics[width=\figwidth]{\picdir/drad.\plotext}}
     500\hspace{\jumpleft}
     501\parbox[b]{\capwidth}{
     502\caption{Astrometric residuals of the displacement in the radial
     503  direction, relative to the chip coordinate -5,4960 (upper left
     504  corner), by filter (\grizy).  White boxes are GPC1 cells which have
     505  been masked due to poor response.  Superpixels representing regions
     506  of $10\times10$ pixels are used to determine the median deviation
     507  for measurements at the given chip pixel location compared with the
     508  average astrometry for the given
     509  object. } \label{fig:astrom.by.filter}}
    512510\end{center}
    513511\end{figure*}
    … …  
    523521Y| > 0.5$ arcsec before measuring the median values for each
    524522superpixel.  We have determined the approximate center of the circular
    525 Tree-Ring pattern as (-5,4960) for this particular chip based on the
     523tree-ring pattern as (-5,4960) for this particular chip based on the
    526524pattern of the X astrometry displacements.  Using this coordinate as the center
    527525of the pattern, we have converted the $\delta X,\delta Y$ offsets into
    … …  
    531529Figure~\ref{fig:astrom.by.filter} shows the 2D patterns of $\delta R$
    532530for each filter (\grizy).  The dynamic range of the color scale is
    533 from -20 to +20 milliarcseconds for all 5 plots.  A Tree-Ring-like
     531from -20 to +20 milliarcseconds for all 5 plots.  A tree-ring
    534532pattern is visible for all five filters, with systematic structures
    535533following a circular pattern centered on the chip corner; the finging
    536534pattern is not apparent in the \yps\ astrometry.  The per-pixel
    537 standard deviations of these plots is listed in
     535standard deviations of these plots area listed in
    538536Table~\ref{table:sigmas.by.filter}.  The signal-to-noise of these
    539537structures is again somewhat weak, but the pattern is clearly visible
    … …  
    543541
    544542% flat-field residual
    545 \def\figwidth{2.75in}
    546 \begin{figure*}[htbp]
    547 \begin{center}
    548 \parbox{\figwidth}{\includegraphics[width=\figwidth]{\picdir/dflat.g.\plotext}}
    549 \parbox{\figwidth}{
    550 \caption{Flat-field high-frequency structues by Filter
    551  } \label{fig:flats.by.filter}}
    552 
    553 \includegraphics[width=\figwidth]{\picdir/dflat.r.\plotext}
    554 \includegraphics[width=\figwidth]{\picdir/dflat.i.\plotext}
    555 
    556 \includegraphics[width=\figwidth]{\picdir/dflat.z.\plotext}
    557 \includegraphics[width=\figwidth]{\picdir/dflat.y.\plotext}
     543\begin{figure*}[htbp]
     544\begin{center}
     545\parbox[b]{\figwidth}{\includegraphics[width=\figwidth]{\picdir/dflat.\plotext}}
     546\hspace{\jumpleft}
     547\parbox[b]{\capwidth}{
     548\caption{Flat-field high-frequency structues, by filter (\grizy).
     549  White boxes are GPC1 cells which have been masked due to poor
     550  response.  Flat-field images generated using a tunable laser have
     551  been combined (see text); a smoothed version has been subtracted to
     552  high-pass the response.  Flat-field pixels are averaged for
     553  $10\times10$ superpixels. } \label{fig:flats.by.filter}}
    558554\end{center}
    559555\end{figure*}
    … …  
    576572median value in the image by more than 4 standard deviations are
    577573masked.  We generate the superpixel image by averaging the unmasked
    578 pixels associated with each superpixel.  In order to suppress
    579 large-scale gradients in the flat-field response, we high-pass filter
    580 the superpixel image by subtracting a copy smoothed with a Gaussian of
    581 $\sigma = 3.0$.
    582 
    583 Figure~\ref{fig:flats.by.filter} shows the remaining high-frequency
    584 structures in the flat-field images.  These flat-field images are
     574pixels associated with each superpixel. 
     575
     576Figure~\ref{fig:flats.by.filter} shows the superpixel images for the
     577flat-fields in the five filters.  These flat-field images are
    585578displayed as fractional deviations relative to the median flat-field
    586579image and can thus be compared to the magnitude residuals.  When
    … …  
    591584measured flux in those pixels, and thus a {\em negative} deviation in
    592585$\delta m_{psf}$ as defined above.  The dynamic range of the color
    593 scale in these plots is -0.01 to +0.01.  The Tree-Ring-like pattern is
     586scale in these plots is -0.01 to +0.01.  The tree-ring pattern is
    594587strong in the (\gps,\rps,\ips) images, but nearly swamped by fringing
    595588in \zps, and completely lost to finging in \yps.  A diagonal banding
    596 similar to the aperture residuals is seen in \gps.
    597 
    598 \note{CZW asks about the blob in the flat-field response.  KCC asks
    599   about the brick-wall pattern.  discuss these and fringing so we can
    600   move on to the tree rings}
     589pattern is seen in \gps: this features is thought to be due to the
     590lithography process used to generate the CCD.  A blob can also been
     591seen covering 4 cells near the center of this chip; this is apparently
     592a deposit of some kind on the detector.  Both of the latter two
     593effects behave like quantum efficiency variations and are removed well
     594by standard flat-field techniques.  Note that a small amount of the
     595diagonal banding pattern remains in the aperture magnitude residuals
     596for \gps.  For the rest of this article, we ignore these features and
     597concentrate on the tree ring features.
     598
     599In order to suppress the large-scale structures for a quantitative
     600analysis of the tree rings, we high-pass filter the superpixel image
     601by subtracting a copy smoothed with a Gaussian of $\sigma = 3.0$
     602superpixels.
    601603
    602604\subsection{Second Moments}
    603605
    604606% Smear Images
    605 \def\figwidth{2.75in}
    606 \begin{figure*}[htbp]
    607 \begin{center}
    608 \parbox{\figwidth}{\includegraphics[width=\figwidth]{\picdir/smear.g.\plotext}}
    609 \parbox{\figwidth}{
    610 \caption{Smear by filter
    611  } \label{fig:smear.by.filter}}
    612 % note that the caption wants to be vertically centered.  I can push it up
    613 % by padding the end with a big \vspace{1in}
    614 
    615 \includegraphics[width=\figwidth]{\picdir/smear.r.\plotext}
    616 \includegraphics[width=\figwidth]{\picdir/smear.i.\plotext}
    617 
    618 \includegraphics[width=\figwidth]{\picdir/smear.z.\plotext}
    619 \includegraphics[width=\figwidth]{\picdir/smear.y.\plotext}
     607\begin{figure*}[htbp]
     608\begin{center}
     609\parbox[b]{\figwidth}{\includegraphics[width=\figwidth]{\picdir/smear.\plotext}}
     610\hspace{\jumpleft}
     611\parbox[b]{\capwidth}{
     612\caption{Average residual smear variations, by filter (\grizy).  White
     613  boxes are GPC1 cells which have been masked due to poor response.
     614  The residual smear ($\sigma^2_{\mbox{major}} + \sigma^2_{\mbox{minor}}$) has been
     615  determined after the after PSF second moments have been subtracted
     616  for each image; these values are averaged for each $10\times10$
     617  superpixels.  } \label{fig:smear.by.filter}}
    620618\end{center}
    621619\end{figure*}
    622620
    623621% Shear Images
    624 \def\figwidth{2.75in}
    625 \begin{figure*}[htbp]
    626 \begin{center}
    627 \parbox{\figwidth}{\includegraphics[width=\figwidth]{\picdir/shear.g.\plotext}}
    628 \parbox{\figwidth}{
    629 \caption{Shear by Filter
    630  } \label{fig:shear.by.filter}}
    631 
    632 \includegraphics[width=\figwidth]{\picdir/shear.r.\plotext}
    633 \includegraphics[width=\figwidth]{\picdir/shear.i.\plotext}
    634 
    635 \includegraphics[width=\figwidth]{\picdir/shear.z.\plotext}
    636 \includegraphics[width=\figwidth]{\picdir/shear.y.\plotext}
     622\begin{figure*}[htbp]
     623\begin{center}
     624\parbox[b]{\figwidth}{\includegraphics[width=\figwidth]{\picdir/shear.\plotext}}
     625\hspace{\jumpleft}
     626\parbox[b]{\capwidth}{
     627\caption{Average residual shear variations, by filter (\grizy).  White
     628  boxes are GPC1 cells which have been masked due to poor response.
     629  The residual shear ($\sigma^2_{\mbox{major}} - \sigma^2_{\mbox{minor}}$) has been
     630  determined after the after PSF second moments have been subtracted
     631  for each image; these values are averaged for each $10\times10$
     632  superpixels.  } \label{fig:shear.by.filter}}
    637633\end{center}
    638634\end{figure*}
    … …  
    683679  smear}.  This value corresponds to the increase or decrease in
    684680the circularly-symmetric component of the image size.  The dynamic
    685 range of these images is -0.3 to +0.3 pixel$^2$. A Tree-Ring-like
     681range of these images is -0.3 to +0.3 pixel$^2$. A tree-ring
    686682pattern is visible for all 5 filters, though \yps is dominated by the
    687683fringing pattern.  Structures with relatively low spatial frequencies
    … …  
    695691ellipse orientation as a function of postion.  The length of the
    696692vectors corresponds to the value of $\sigma^2_{major} -
    697 \sigma^2_{minor}$.  The Tree-Ring-like structure is {\em not} apparent
     693\sigma^2_{minor}$.  The tree-ring structure is {\em not} apparent
    698694in this figure for any filter.  The spatial variations are
    699695low-frequency and unrelated to the radial trend from the upper-left
    700696corner.
    701697
    702 \subsection{Correlations Between Tree-Ring-Like Patterns}
     698\subsection{Correlations Between Tree-Ring Patterns}
     699
     700% All Effects in r-band
     701\begin{figure*}[htbp]
     702\begin{center}
     703\parbox[b]{\figwidth}{\includegraphics[width=5.0in]{\picdir/all.effects.r.\plotext}}
     704\caption{All 6 measured effects for \rps.  This figure illustrates the
     705  different spatial structure observed for each of the 6 patterns
     706  measured in this work.  The PSF magnitude (upper-left) and smear
     707  residuals (lower-left) have a very clear common tree-ring structure,
     708  while the astrometric residual (middle-left) and flat-field
     709  residuals (middle-right) have their own common tree-ring pattern with
     710  much higher frequencies than the previous two effects.  Aperture
     711  magnitude (upper-right) and shear residuals (lower-right) do not
     712  show a strong signal consistent with either of the two patterns.} \label{fig:all.effects.rband}
     713\end{center}
     714\end{figure*}
    703715
    704716\begin{table}
     717% \tiny
     718\begin{center}
    705719\caption{Systematic Trends : Correlations by filter\label{table:correlation.by.filter}}
    706 \note{reconsider the column order}
    707 % \tiny
    708 \begin{center}
    709720\begin{tabular}{|l|rrrr|}
    710721\hline
    711 {\bf Filter} & {\bf psf mags} & {\bf smear} & {\bf astrom} & {\bf flat} \\
     722{\bf Filter} & {\bf smear} & {\bf psf mags} & {\bf astrom} & {\bf flat} \\
    712723\hline
    713724\gps & 1.00 & 1.00 &  1.00 & 1.00 \\
    714 \rps & 0.84 & 0.78 &  0.84 & 0.76 \\
    715 \ips & 0.50 & 0.40 &  0.66 & 0.64 \\
    716 \zps & 0.26 & 0.16 &  0.37 & 0.33 \\
     725\rps & 0.78 & 0.84 &  0.84 & 0.76 \\
     726\ips & 0.40 & 0.50 &  0.66 & 0.64 \\
     727\zps & 0.16 & 0.26 &  0.37 & 0.33 \\
    717728\yps & 0.10 & 0.10 &  0.25 & 0.30 \\
    718729\hline
    … …  
    721732\end{table}
    722733
    723 Tree-Ring-like patterns are clearly seen in 4 of the measurement types
     734Tree-ring patterns are clearly seen in 4 of the measurement types
    724735above: the PSF photometry, the astrometry, the flat-field, and the
    725736smear terms.  As discussed above, the signal-to-noise per pixel in the
    726737plots of the systematic trends is relatively low (\approx 1.0).  While
    727 the Tree-Ring-like patterns are apparent in many of these figures,
     738the tree-ring patterns are apparent in many of these figures,
    728739there are also some other systematic structures which may degrade the
    729740signal further.
    730741
    731 To quantatatively compare the Tree-Ring-like trends between
     742To quantatatively compare the tree-ring trends between
    732743filters and between the types of measurements, we need to measure the
    733 Tree-Ring structure explicitly and filter out the other effects if
     744tree-ring structure explicitly and filter out the other effects if
    734745possible.  To do this, we have applied a high-pass filter to all of
    735746the relevant images (PSF photometry residuals, astrometric residuals
    … …  
    743754chip.
    744755
    745 \note{include the arc on one of the figures?}
    746 
    747 \note{do plots of all filter pairs in a triangle?  is that interesting?}
     756% \note{include the arc on one of the figures?}
     757
     758% \note{do plots of all filter pairs in a triangle?  is that interesting?}
    748759
    749760For a given type of measurement, the systematic effect is strongly
    … …  
    755766filters, as shown in Figure~\ref{fig:psfmag.trends}.  Here, the
    756767\yps\ correlation with \gps\ is quite weak: the fringing pattern
    757 dominates the Tree Rings for PSF photometry.  The radial component of
     768dominates the tree rings for PSF photometry.  The radial component of
    758769the astrometric residual is also well correlated between filters, with
    759770no loss of correlation due to fringing in \yps. Finally, the
    … …  
    766777listed in Table~\ref{table:correlation.by.filter}.  There is a
    767778consistency in the trend from \gps, with the strongest systematic
    768 Tree-Ring effects to \yps, with the weakest effects.  Note that the
     779tree-ring effects to \yps, with the weakest effects.  Note that the
    769780second moment smear and astrometry terms have different relative
    770781strength in \yps\ compared with \gps.
    … …  
    775786\begin{center}
    776787\includegraphics[width=\figwidth]{\picdir/smear.trends.\plotext}
    777 \caption{Smear : correlation between filters \note{include trend slopes in plots?}
     788\caption{Correlation of the smear ($\sigma^2_{\mbox{major}} +
     789  \sigma^2_{\mbox{minor}}$) signal in \gps\ with the other 4 bands:
     790  \rps\ (upper-left),  \ips\ (upper-right), \zps\ (lower-left), \yps\ (lower-right).
    778791} \label{fig:smear.trends}
    779792\end{center}
    … …  
    785798\begin{center}
    786799\includegraphics[width=\figwidth]{\picdir/psfmag.trends.\plotext}
    787 \caption{PSF magnitude residuals : correlation between filters
     800\caption{Correlation of the PSF magnitude residuals ($\delta m_{psf}$)
     801  in \gps\ with the other 4 bands: \rps\ (upper-left), \ips\
     802  (upper-right), \zps\ (lower-left), \yps\ (lower-right).
    788803} \label{fig:psfmag.trends}
    789804\end{center}
    … …  
    795810\begin{center}
    796811\includegraphics[width=\figwidth]{\picdir/astrom.trends.\plotext}
    797 \caption{Astrometry residuals : correlation between filters
     812\caption{Correlation of the radial astrometric residual displacement ($\delta R$)
     813  in \gps\ with the other 4 bands: \rps\ (upper-left), \ips\
     814  (upper-right), \zps\ (lower-left), \yps\ (lower-right).
    798815} \label{fig:astrom.trends}
    799816\end{center}
    … …  
    805822\begin{center}
    806823\includegraphics[width=\figwidth]{\picdir/flat.trends.\plotext}
    807 \caption{Flat-field rings : correlation between filters
    808 } \label{fig:flat.trends}
    809 \end{center}
    810 \end{figure*}
    811 
    812 An important question is the relationship of the Tree-Ring-like
     824\caption{Correlation of the flat-field tree-ring structures in \gps\
     825  with the other 4 bands: \rps\ (upper-left), \ips\ (upper-right), \zps\
     826  (lower-left), \yps\ (lower-right).  } \label{fig:flat.trends}
     827\end{center}
     828\end{figure*}
     829
     830An important question is the relationship of the tree-ring
    813831pattern between the different types of measurements.  Different models
    814 for the Tree-Ring structures make different predictions about the
     832for the tree-ring structures make different predictions about the
    815833correlations between different effects.  Note the very different
    816834spatial structure between the different measurements in a given
    … …  
    846864
    847865\begin{table}
     866% \tiny
     867\begin{center}
    848868\caption{Systematic Trends : Correlations between trends\label{table:correlation.by.trend}}
    849 % \tiny
    850 \begin{center}
    851869\begin{tabular}{|l|rrr|}
    852870\hline
    … …  
    868886\begin{center}
    869887\includegraphics[width=\figwidth]{\picdir/smear.vs.psfmag.\plotext}
    870 \caption{Smear vs PSF mag residuals on the rings
     888\caption{Correlation of the PSF magnitude residuals ($\delta m_{PSF}$)
     889  with the smear ($\sigma^2_{\mbox{major}} + \sigma^2_{\mbox{minor}}$)
     890  signal for \gps\ (upper-left), \rps\ (upper-right), \ips\ (lower-left),
     891  \zps\ (lower-right).
    871892} \label{fig:smear.vs.psfmag}
    872893\end{center}
    … …  
    878899\begin{center}
    879900\includegraphics[width=\figwidth]{\picdir/dsmear.vs.astrom.\plotext}
    880 \caption{gradient of the Smear vs astrometry residuals on the rings
     901\caption{
     902Correlation of the radial astrometric residual displacement ($\delta
     903R$) with the derivative of the smear ($\partial
     904\sigma^2_{\mbox{major}} + \sigma^2_{\mbox{minor}}$) signal with
     905respect to the radial postion for \gps\ (upper-left), \rps\
     906(upper-right), \ips\ (lower-left), \zps\ (lower-right).
    881907} \label{fig:dsmear.vs.astrom}
    882908\end{center}
    … …  
    888914\begin{center}
    889915\includegraphics[width=\figwidth]{\picdir/dastrom.vs.flat.\plotext}
    890 \caption{gradient of the astrometry residuals vs flat-field rings
     916\caption{
     917Correlation of the derivative of the radial astrometric residual
     918displacement ($\delta R$) with respect to the radial position with the
     919flat-field tree-ring signal for \gps\ (upper-left), \rps\ (upper-right),
     920\ips\ (lower-left), \zps\ (lower-right).
    891921} \label{fig:dastrom.vs.flat}
    892922\end{center}
    … …  
    896926\label{sec:discussion}
    897927
    898 These trends help to illuminate the underlying causes of these
    899 different effects. 
     928These trends measured above (Section~\ref{sec:tree.rings}) help to
     929illuminate the underlying causes of these different effects.
    900930
    901931First, if we consider the smear pattern
    902932(Figure~\ref{fig:smear.by.filter}), the measurement shows that the
    903 intrinsic size of the stellar images is varying in a radial sense
    904 between the different Tree-Ring regions.  Although images experience
     933intrinsic sizes of the stellar images are varying in a radial sense
     934between the different tree-ring regions.  Although images experience
    905935an average image quality (due to seeing and focus) across the chip
    906936which may vary substantially from exposure to exposure, stars landing
    907 in the different Tree-Ring-like regions are consistently somewhat
     937in the different tree-ring regions are consistently somewhat
    908938larger or somewhat smaller than that average.
    909939
    910 Next, we can explain the relationship between the PSF photometry
    911 residuals and the observed smear: In the photometry analysis, we model
    912 the PSF, allowing for some spatial variation in the shape.  However,
    913 we have a limited number of stars to measure any spatial variation.
    914 Thus the 2D variation are sampled on a very coarse (e.g., $3 \times
    915 3$) grid for each chip: the PSF parameters may vary smoothly across
    916 the chip following the bilinear interpolation between the $3 \times 3$
    917 grid points.  Thus, the spatial scale on which we model PSF variations
    918 is much larger than the spatial scale on which PSF variations are
    919 apparently occuring, as illustrated by the changes in the smear plot.
     940Next, we can explain the correlation between the PSF photometry
     941residuals and the observed smear (Figure~\ref{fig:smear.vs.psfmag}).
     942In the photometry analysis, we model the PSF allowing for some spatial
     943variation in the shape.  However, we have a limited number of stars to
     944measure any spatial variation.  Thus the 2D variations are sampled on
     945a very coarse (e.g., $3 \times 3$) grid for each chip: the PSF
     946parameters may vary smoothly across the chip following the bilinear
     947interpolation between the $3 \times 3$ grid points.  Thus, the spatial
     948scale on which we model PSF variations is much larger than the spatial
     949scale on which PSF variations are actually occuring, as illustrated
     950by the changes in the smear plot (Figure~\ref{fig:smear.by.filter}).
    920951When the true PSF is larger than the model PSF, our model fits
    921952systematically underestimate the amount of flux in a given object.
    922 Conversely, when the PSF is smaller, we overestimate the flux -- this
     953Conversely, when the true PSF is smaller, we overestimate the flux -- this
    923954type of offset is a typical effect when mis-estimating the PSF size.
    924955The slope of the trend depends on the mean typical seeing for the
    … …  
    930961amount of smearing.
    931962
    932 The relationship between the flat-field residual and the astrometric
    933 gradient is consistent with radial variations in the plate-scale.  The
    934 Tree-Rings observed by DES are completely attributed to effective
    935 plate scale changes.  Effective plate scale changes would result in
    936 flat-field deviations since the flat-field illumination is a source of
    937 constant surface brightness.  Pixels see a varying amount of flux
    938 depending on their effective area.  This changing plate scale also
    939 affects the astrometry since these variations occur on spatial scales
    940 much smaller than the astrometric model.  In such a model, the
    941 flat-field deviations are $-1 \times \frac{\partial Pos}{\partial R}$.
    942 The slope of our relationship is \approx 0.5 in normalized units.
    943 Thus the observed trends appear to be too weak by a factor of \approx
    944 2, but otherwise exhibits the expected behavior.
     963The correlation between the flat-field structures and the radial
     964derivative of the astrometric residual displacements in the radial
     965direction (Figure~\ref{fig:dastrom.vs.flat}) is consistent with radial
     966variations in the plate-scale.  The tree-rings observed by DES are
     967completely attributed to effective plate scale changes.  Effective
     968plate scale changes result in flat-field deviations because the
     969flat-field illumination is a source of constant surface brightness.
     970Pixels see a varying amount of flux depending on their effective area.
     971This changing plate scale also affects the astrometry since these
     972variations occur on spatial scales much smaller than the astrometric
     973model.  In this description of the tree rings, the flat-field
     974deviations are $-1 \times \frac{\partial \delta R}{\partial r}$.  The
     975best-fit slopes of our correlations are \approx 0.5, but the
     976signal-to-noise is rather low.  A slope of -1 appears to be consistent
     977with our measurements.
    945978
    946979The fact that the PSF ellipticity changes are {\em not} correlated
    947 with the Tree-Ring structure tells us that the effective plate-scale
    948 changes seen in the flat-field and astrometry signals are not the
    949 dominant cause of the PSF photometry errors.  Also, the fact that we
    950 do not measure significant aperture photometry errors correlated with
    951 the Tree Rings confirms this point.  The amplitude of the flat-field
    952 errors are 1-2 millimagnitudes, much smaller than the PSF photometry
    953 errors, and far below the pixel-to-pixel noise in the aperture
    954 magnitudes.
     980with the tree-ring structure (Figure~\ref{fig:shear.by.filter}) tells us
     981that, unlike the case for DES, the effective plate-scale changes seen
     982in the flat-field and astrometry signals are not the dominant cause of
     983the PSF photometry errors.  Also, the fact that we do not measure
     984significant aperture photometry errors correlated with the tree rings
     985confirms this point.  The amplitude of the flat-field errors are 1-2
     986millimagnitudes, much smaller than the PSF photometry errors, and far
     987below the pixel-to-pixel noise in the aperture magnitude residuals.
     988It is likely in our opinion that the plate-scale changes causing the
     989flat-field and astrometry effects is affecting both the ellipticity
     990and the aperture magnitudes, but the level of the effect is too small
     991to see given the other systematic structures (in the shear plot) and
     992the noise level (in the aperture magnitudes).
    955993
    956994Finally, the correlation between the smear structures and the
    957 astrometry residuals shows that these two effects are connected.  The
    958 underlying connection is the pattern of the resistivity variations.
    959 Regions with high (or low) resistivity show relatively high (or low)
    960 amounts of smear; astrometric deviations follow the gradient between
    961 these regions. 
     995astrometry residuals shows that these two effects are connected.
     996Although the correlation is weak in Figure~\ref{fig:dsmear.vs.astrom},
     997careful inspection of the location of the these two tree ring patterns
     998shows that the locations of the rings in the radial astrometric
     999residual images occurs at the boundaries between regions with
     1000substantially different values of the smear signal.
     1001
     1002We suggest that the underlying connection between all of these
     1003tree-ring effects is the pattern of the doping variations in the
     1004silicon.  As discussed by \cite{2014PASP..126..750P}, the tree-ring
     1005patterns seen by the DES team are caused by lateral electic fields in
     1006the detector silicon (in the plane of the CCD wafer) generated by
     1007variations in the space charges embedded in the silicon, in turn
     1008coming from low-level changes in the doping as the silicon boule is
     1009grown.  We conclude that the astrometric and flat-field variations
     1010seen in our detectors are caused by these same types of doping
     1011variations.  The changes in the smear (and thus the PSF magnitudes)
     1012are apparently also related to the doping variations.  The lateral
     1013electric fields which introduce the astrometry and flat-field
     1014variations occur at the boundary between regions with higher and lower
     1015space charges from the dopant.  Regions with high (or low) space
     1016charge density thus correspond to regions with relatively high (or
     1017low) amounts of smear; the astrometric deviations follow the gradient
     1018between these regions.
    9621019
    9631020We interpret the changes in the {\em smear} term as changes in the
    964 amount of charge diffusion.  The blue filters exhibit the strongest
    965 changes in the amount of smear.  These are also the filters for which
    966 the detected electrons have travelled the longest distance in the
    967 silicon, and are thus most affected by diffusion effects. 
    968 
    969 \note{add more quantitative discussion of the variations in $E_y$ vs $E_x$?}
     1021amount of charge diffusion as the photoelectrons travel to the bottom
     1022of the pixel well.  The blue filters exhibit the strongest changes in
     1023the amount of smear.  These are also the filters for which the
     1024detected electrons have travelled the longest distance in the silicon,
     1025and are thus most affected by diffusion effects.  Charge diffusion (as
     1026opposed to the charge drift caused by the lateral electric fields)
     1027results in a Gaussian smearing of the stellar profile: as the
     1028photoelectrons migrate from the site where they were generated by the
     1029incoming photon to the bottom of the pixel well, they follow a random
     1030walk in the plane of the detector.  The longer the electrons take to
     1031make the journey down to the bottom of the pixel, the further they are
     1032able to wander from their creation coordinate in the detector.
     1033Following the discussion in \cite{Holland.2003}, the amount of charge
     1034diffusion is thus related to the velocity of the electrons in the
     1035direction of the optical axis: $\sigma \sim \sqrt{2Dt}$ where $\sigma$
     1036is the size of the smearing kernel, $t$ is the time required for the
     1037electrons to traverse the thickness of the silicon wafer, and $D$ is
     1038the diffusion coefficient.  The velocity of the photoelectron, and
     1039thus the time to traverse the silicon, is related to the vertical
     1040electric fields in the silicon, which are caused by a combination of
     1041the applied voltages and the distribution of the space charges from
     1042the dopant.  As shown by \cite{Holland.2003}, the charge diffusion is
     1043related to the space charge density by $\sigma \sim
     1044\rho^{-\frac{1}{2}}$ (their equation 6).  Regions with high space
     1045charge densities increase the migration speed of the photoelectrons
     1046and reduce the amount of charge diffusion smearing; and vice versa for
     1047regions of low space-charge densities.
     1048
     1049In summary, the variations in the space-charge density caused by
     1050variations in the dopant result in regions of higher and lower charge
     1051diffusion, and in turn regions with PSF photometry systematic
     1052residuals.  The lateral gradients in the space-charge density induce
     1053lateral electric fields which in turn cause lateral motions of the
     1054photoelectrons, resulting in astrometric and flat-field deviations.
     1055
     1056The DES team did not detect these charge diffusion variations.  In
     1057that case, the amplitude of the photometric effects due to the lateral
     1058field are dominant; these include both the modification of the
     1059flat-field as well as PSF fitting errors due to the changing PSF sizes
     1060introduced by the varying effective pixels sizes.  If the smearing
     1061effect reported here were as large for DES compared with the lateral
     1062PSF size changes as they are for GPC1, then the reported PSF
     1063photometry residuals for would have had very different
     1064characteristics.  We conclude that, for DES, the lateral effects are
     1065much larger than the diffusion variations, compared with GPC1.  The
     1066relative amplitude of these two effects depends on the details of the
     1067applied voltages, the amplitude of the space-charge density variations
     1068compared with the typical space-charge density, and the detector
     1069thicknesses.  It is beyond the scope of this article to model these
     1070effects in detail.
     1071
     1072% http://adsabs.harvard.edu/abs/2006NIMPA.568...41K
    9701073
    9711074\section{Conclusion}
    9721075
    973 The Tree Rings observed in the Pan-STARRS GPC1 data show (at least)
     1076The tree rings observed in the Pan-STARRS GPC1 data show (at least)
    9741077two effects, though they are related.  First, the images are
    9751078experiencing circularly-symmetric changes in the PSF size correlated
    976 with the Tree-Ring pattern.  These PSF size changes drive errors in
    977 the PSF photometry which the are also correlated with the Tree-Ring
    978 pattern on the scale of a few millimagnitudes.  These PSF size changes
    979 are consistent with changes in the charge diffusion, which also
    980 introduces a circularly symmetric smearing.
     1079with the tree-ring pattern.  These PSF size changes drive errors in
     1080the PSF photometry on the scale of a few millimagnitudes, are also
     1081correlated with the tree-ring pattern.  These PSF size changes are
     1082consistent with changes in the charge diffusion, which also introduces
     1083a circularly symmetric smearing.
    9811084
    9821085In addition, there are radial plate-scale changes correlated with the
    983 Tree Rings.  These plate-scale changes introduce a flat-field errors
     1086tree rings.  These plate-scale changes introduce a flat-field errors
    9841087on the scale of \approx 1 millimagnitude and astrometric errors in the
    9851088scale of 2-3 milliarcseconds.  The observed relationship between the
    9861089flat-field deviations and the radial derivative of the astrometric
    987 deviations confirms this interpretation \citep[see discussion
     1090deviations confirms this interpretation \citep[see also discussion
    9881091  in][]{2014PASP..126..750P}.
    9891092
    … …  
    9911094the astrometric variations imply that both of these two types of tree
    9921095ring effects are related, even though they manifest through different
    993 mechanisms.  We suspect that the variations in both the vertical charge
     1096mechanisms.  We conclude that the variations in both the vertical charge
    9941097diffusion and the lateral charge migration are driven by changes
    9951098in the electric field structures in the silicon due to the same
    … …  
    10501153Lorand University (ELTE) and the Los Alamos National Laboratory.
    10511154
    1052 \note{add NASA ops grant(s)}
     1155\note{Ken: please add NASA ops grants}
    10531156
    10541157\bibliographystyle{apj}
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