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Changeset 40306


Ignore:
Timestamp:
Dec 27, 2017, 2:12:32 PM (9 years ago)
Author:
eugene
Message:

finish mods; add referee response

Location:
trunk/doc/release.2015/systematics.20140411
Files:
3 added
2 edited

Legend:

Unmodified
Added
Removed

  • trunk/doc/release.2015/systematics.20140411/Makefile

    r40304 r40306  
    2121pics/radial_p1_r.pdf \
    2222pics/radial_p2_r.pdf \
    23 pics/radial_p3_r.pdf
     23pics/radial_p3_r.pdf \
     24pics/filter_trends.pdf
    2425
    2526OLD_PDFPICS = \

  • trunk/doc/release.2015/systematics.20140411/diffusion.tex

    r40305 r40306  
    2020
    2121\definecolor{light-gray}{gray}{0.50}
    22 \newcommand\oldtext[1]{\textbf{\color{light-gray}#1}}
     22% \newcommand\oldtext[1]{\textbf{\color{light-gray}#1}}
     23\newcommand\oldtext[1]{\ignorespaces}
    2324\newcommand\newtext[1]{\textbf{\color{blue}#1}}
    2425\newcommand\fixtext[1]{\textbf{\color{red}#1}}
    … …  
    376377\label{sec:tree.rings}
    377378
    378 \begin{table}
    379 % \tiny
    380 \begin{center}
    381 \caption{Systematic Trends : Standard deviation by filter\label{table:sigmas.by.filter}}
    382 \begin{tabular}{|l|rrrrr|}
    383 \hline
    384 {\bf Filter} & {\bf psf mags} & {\bf ap mags} & {\bf astrom} & {\bf smear} & {\bf flat} \\
    385              & mmags         & mmags          & mas          & pixels$^2$  & mmags \\
    386 \hline
    387 \gps & 11.8 & 13 & 8.0  & 0.169 &  3.0 \\
    388 \rps & 10.9 & 12 & 6.7  & 0.133 &  2.2 \\
    389 \ips &  8.5 & 10 & 6.0  & 0.069 &  1.7 \\
    390 \zps &  8.7 & 12 & 5.5  & 0.052 &  3.2 \\
    391 \yps & 16.5 & 26 & 6.8  & 0.059 & 15.3 \\
    392 \hline
    393 \end{tabular}
    394 \end{center}
    395 \end{table}
     379%% \begin{table}
     380%% % \tiny
     381%% \begin{center}
     382%% \caption{Systematic Trends : Standard deviation by filter\label{table:sigmas.by.filter}}
     383%% \begin{tabular}{|l|rrrrr|}
     384%% \hline
     385%% {\bf Filter} & {\bf psf mags} & {\bf ap mags} & {\bf astrom} & {\bf smear} & {\bf flat} \\
     386%%              & mmags         & mmags          & mas          & pixels$^2$  & mmags \\
     387%% \hline
     388%% \gps & 11.8 & 13 & 8.0  & 0.169 &  3.0 \\
     389%% \rps & 10.9 & 12 & 6.7  & 0.133 &  2.2 \\
     390%% \ips &  8.5 & 10 & 6.0  & 0.069 &  1.7 \\
     391%% \zps &  8.7 & 12 & 5.5  & 0.052 &  3.2 \\
     392%% \yps & 16.5 & 26 & 6.8  & 0.059 & 15.3 \\
     393%% \hline
     394%% \end{tabular}
     395%% \end{center}
     396%% \end{table}
    396397
    397398For many of the GPC1 OTA CCDs, we observe a spatial pattern in the
    … …  
    422423illustrate the effects in detail, but a similar set of effects are
    423424seen in many, if not all, of the GPC1 detectors with varying
    424 strengths.  \fixtext{First, we show the residual PSF photometry.  Second, we
     425strengths.  First, we show the residual PSF photometry.  Second, we
    425426show the residual aperture photometry.  Third, we show the astrometric
    426427residual patterns.  Fourth, we show the patterns observed in the
    427428flat-field images.  Finally, we show measurements derived from the
    428 second-moments of the stars.}
     429second-moments of the stars.
    429430
    430431For all effects discussed below, we are measuring the mean value of
    … …  
    458459\hspace{\jumpleft}
    459460\parbox[b]{\capwidth}{
    460 \caption{PSF Magnitude residuals by filter (\grizy).  White boxes are
     461\caption{PSF Magnitude residuals by filter (\grizy) for a single
     462  example GPC1 device (XY40).  White boxes are
    461463  GPC1 cells which have been masked due to poor response.  Superpixels
    462464  representing regions of $10\times10$ pixels are used to determine
    463465  the median deviation for measurements at the given chip pixel
    464466  location compared with the average photometry for the given
    465   object.} \label{fig:psfmags.by.filter}}
     467  object.  Fringing dominates the \yps-band signal, saturating the
     468  color scale to black or white in areas.} \label{fig:psfmags.by.filter}}
    466469\end{center}
    467470\end{figure*}
    … …  
    473476\hspace{\jumpleft}
    474477\parbox[b]{\capwidth}{
    475 \caption{Aperture Magnitude residuals by filter (\grizy).  White boxes
     478\caption{Aperture Magnitude residuals by filter (\grizy) for a single
     479  example GPC1 device (XY40).  White boxes
    476480  are GPC1 cells which have been masked due to poor response.
    477481  Superpixels representing regions of $10\times10$ pixels are used to
    478482  determine the median deviation for measurements at the given chip
    479483  pixel location compared with the average photometry for the given
    480   object.  } \label{fig:apmags.by.filter}}
     484  object.  Fringing dominates the \yps-band signal, saturating the
     485  color scale to black or white in areas.} \label{fig:apmags.by.filter}}
    481486\end{center}
    482487\end{figure*}
    … …  
    495500
    496501The tree-ring pattern is clearly visible for the four blue filters,
    497 but finging dominates the pattern for \yps.  Small offsets of
     502but fringing dominates the pattern for \yps.  Small offsets of
    498503individual cells are also apparent for \zps.  While the patterns are
    499504clear across the image, the signal-to-noise of the structures per
    500 pixel is not very strong in these images.  The per-pixel standard
     505pixel is not very strong in these images.  \oldtext{The per-pixel standard
    501506deviations of these plots are listed in
    502 Table~\ref{table:sigmas.by.filter}.  The per-pixel standard deviation
     507Table~1.}  The \oldtext{per-pixel} standard deviation \newtext{of the pixel values in the images (a measure of the noise in the absence of any systematic signal)}
    503508is comparable to the amplitude of the correlated structures, so we
    504509need to integrate along the radial structures to make stronger
    … …  
    506511
    507512Figure~\ref{fig:apmags.by.filter} shows the equivalent measurement for
    508 aperture photometry instead of PSF photometry.  The finging
    509 pattern again dominates the plot for \yps, but the tree rings are not
    510 seen in any of the filters.  A diagonal pattern is visible in \gps\
    511 which is not observed in the PSF magnitudes.  While the per-pixel
    512 scatter is somewhat (10\% to 20\%) higher for these aperture
    513 magnitudes than for the PSF magnitudes
    514 (Table~\ref{table:sigmas.by.filter}), a structure with the amplitude
     513aperture photometry instead of PSF photometry.  The fringing pattern
     514again dominates the plot for \yps, but the tree rings are not seen in
     515any of the filters.  A diagonal pattern is visible in \gps\ which is
     516not observed in the PSF magnitudes.  While the \newtext{standard
     517  deviation of the pixel values} \oldtext{per-pixel scatter} is
     518somewhat (10\% to 20\%) higher for these aperture magnitudes than for
     519the PSF magnitudes\oldtext{ (Table~1)}, a structure with the amplitude
    515520of the PSF magnitude tree-rings would certainly have been obvious.
    516521
    … …  
    541546%% \end{figure*}
    542547
    543 \oldtext{Figure~3} \newtext{Figure~\ref{fig:all.effects.rband} (middle-left)}
    544 shows a similar type of measurement
    545 for astrometric residuals.  To generate this plot, we use the same
    546 selection of measurements for astrometry as for photometry.  In this
    547 case, we extract the residual in both the RA and DEC directions
     548\oldtext{Figure~3} \newtext{Figure~\ref{fig:all.effects.rband}
     549  (middle-left)} shows a similar type of measurement for astrometric
     550residuals \newtext{in \rps-band}.  To generate this plot, we use the
     551same selection of measurements for astrometry as for photometry.  In
     552this case, we extract the residual in both the RA and DEC directions
    548553($\delta RA = \overline{RA} - RA_i$, $\delta DEC = \overline{DEC} -
    549554DEC_i$) and rotate these values to the chip coordinate system ($\delta
    … …  
    557562offsets into $\delta R,\delta \theta$ measurements ($\delta R$ :
    558563radial component away from the center of the pattern, $\delta \theta$
    559 : tangential component).
    560 
    561 \oldtext{Figure~\ref{fig:astrom.by.filter} shows the 2D patterns of $\delta R$
    562 for each filter (\grizy).  The dynamic range of the color scale is
    563 from -20 to +20 milliarcseconds for all 5 plots.}  A tree-ring
    564 pattern is visible for all five filters, with systematic structures
    565 following a circular pattern centered on the chip corner; the finging
    566 pattern is not apparent in the \yps\ astrometry.  \oldtext{The per-pixel
    567 standard deviations of these plots are listed in
    568 Table~\ref{table:sigmas.by.filter}.}  The signal-to-noise of these
    569 structures is again somewhat weak, but the pattern is clearly visible
    570 in these figures.
     564: tangential component). \newtext{The dynamic range of the color scale
     565  is from -20 to +20 milliarcseconds for this plot.}
     566
     567\oldtext{Figure~\ref{fig:astrom.by.filter} shows the 2D patterns of
     568  $\delta R$ for each filter (\grizy).  The dynamic range of the color
     569  scale is from -20 to +20 milliarcseconds for all 5 plots.}  A
     570tree-ring pattern is visible for all five filters, with systematic
     571structures following a circular pattern centered on the chip corner;
     572the fringing pattern is not apparent in the \yps\ astrometry.
     573\oldtext{The per-pixel standard deviations of these plots are listed
     574  in Table~1.}  The signal-to-noise of these structures is again
     575somewhat weak, but the pattern is clearly visible in \oldtext{these figures} \newtext{Figure~\ref{fig:all.effects.rband} (middle-left)}.
    571576
    572577\subsection{Flat-field Structures}
     578
     579% All Effects in r-band
     580\begin{figure*}[htbp]
     581\begin{center}
     582\parbox[b]{\figwidth}{\includegraphics[width=5.0in]{\picdir/all_effects_r.\plotext}}
     583\caption{All 6 measured effects for \rps for a single
     584  example GPC1 device (XY40).  This figure illustrates the
     585  different spatial structure observed for each of the 6 patterns
     586  measured in this work.  The PSF magnitude (upper-left) and smear
     587  residuals (lower-left) have a very clear common tree-ring structure,
     588  while the astrometric residual (middle-left) and flat-field
     589  residuals (middle-right) have their own common tree-ring pattern with
     590  much higher frequencies than the previous two effects.  Aperture
     591  magnitude (upper-right) and shear residuals (lower-right) do not
     592  show a strong signal consistent with either of the two patterns.}
     593\label{fig:all.effects.rband}
     594\end{center}
     595\end{figure*}
    573596
    574597% flat-field residual
    … …  
    590613\oldtext{Figure~4} \newtext{Figure~\ref{fig:all.effects.rband} (middle-right)}
    591614shows the high-spatial-frequency
    592 structures in the flat-field images.  For this measurement, we have
     615structures in the \newtext{\rps-band} flat-field\oldtext{ images}.  For this measurement, we have
    593616used a set of monochromatic flat-field images obtained with a tunable
    594617laser.  The laser is used to illuminate our flat-field screen which is
    … …  
    607630pixels associated with each superpixel. 
    608631
    609 \fixtext{Figure~\ref{fig:flats.by.filter} shows the superpixel images for the
    610 flat-fields in the five filters.}  These flat-field images are
    611 displayed as fractional deviations relative to the median flat-field
     632\oldtext{Figure~\ref{fig:flats.by.filter} shows the superpixel images for the
     633flat-fields in the five filters. These flat-field images are} \newtext{The flat-field image is}
     634displayed as fractional deviations relative to the median of the flat-field
    612635image and can thus be compared to the magnitude residuals.  When
    613 flattening an image, these flat-fields would be divided into the flux
     636flattening an image, \oldtext{these flat-fields} \newtext{the flat-field image} would be divided into the flux
    614637of the raw image.  The residuals are thus defined in the sense that a
    615 positive feature in these flats which does {\em not} represent a real
     638positive feature in \oldtext{these flats} \newtext{the flat} which does {\em not} represent a real
    616639quantum efficiency deviation would induce a {\em reduction} in the
    617640measured flux in those pixels, and thus a {\em negative} deviation in
    618641$\delta m_{psf}$ as defined above.  The dynamic range of the color
    619 scale in these plots is -0.01 to +0.01.  The tree-ring pattern is
     642scale in \oldtext{these plots} \newtext{this plot} is -0.01 to +0.01.  The tree-ring pattern is
    620643strong in the (\gps,\rps,\ips) images, but nearly swamped by fringing
    621 in \zps, and completely lost to finging in \yps.  A diagonal banding
    622 pattern is also seen in \gps: this feature is thought to be due to
     644in \zps, and completely lost to fringing in \yps.  A diagonal banding
     645pattern is also seen in \gps and \rps: this feature is thought to be due to
    623646the lithography process used to generate the CCD.  A blob can also
    624647been seen covering 4 cells near the center of this chip; this is
    … …  
    633656analysis of the tree rings, we high-pass filter the superpixel image
    634657by subtracting a copy smoothed with a Gaussian of $\sigma = 3.0$
    635 superpixels.
     658superpixels.  \newtext{This smoothing kernel is large enough compared
     659  to the tree ring structures that they are not suppressed
     660  significantly.  Without this smoothing, features from the diagonal
     661  banding pattern remain in the \rps-band image and contaminate the
     662  tree-ring signal.}
    636663
    637664\subsection{Second Moments}
    … …  
    711738\oldtext{Figure~5} \newtext{Figure~\ref{fig:all.effects.rband} (lower-left)}
    712739shows the spatial trend of the smear,
    713 $e_0$.  The dynamic range of these images is -0.3 to +0.3 pixel$^2$. A
     740$e_0$.  The dynamic range of \oldtext{these images} \newtext{this image} is -0.3 to +0.3 pixel$^2$. A
    714741tree-ring pattern is visible for all 5 filters, though \yps\ is
    715742dominated by the fringing pattern.  Structures with relatively low
    … …  
    724751ellipse orientation as a function of postion.  The length of the
    725752vectors corresponds to the value of $e_2$.  The tree-ring structure is
    726 {\em not} apparent in this figure for any filter.  The spatial
     753{\em not} apparent in \oldtext{this figure} \newtext{the shear} for any filter.  The spatial
    727754variations are low-frequency and unrelated to the radial trend from
    728755the upper-left corner.
    729 
    730 \subsection{Correlations Between Tree-Ring Patterns}
    731756
    732757% All Effects in r-band
    733758\begin{figure*}[htbp]
    734759\begin{center}
    735 \parbox[b]{\figwidth}{\includegraphics[width=5.0in]{\picdir/all_effects_r.\plotext}}
    736 \caption{All 6 measured effects for \rps.  This figure illustrates the
    737   different spatial structure observed for each of the 6 patterns
    738   measured in this work.  The PSF magnitude (upper-left) and smear
    739   residuals (lower-left) have a very clear common tree-ring structure,
    740   while the astrometric residual (middle-left) and flat-field
    741   residuals (middle-right) have their own common tree-ring pattern with
    742   much higher frequencies than the previous two effects.  Aperture
    743   magnitude (upper-right) and shear residuals (lower-right) do not
    744   show a strong signal consistent with either of the two patterns.}
    745 \label{fig:all.effects.rband}
     760\parbox[b]{\figwidth}{\includegraphics[width=5.0in]{\picdir/filter_trends.\plotext}}
     761\caption{Amplitude of the 4 effects which follow the tree-rings as a
     762  function of filter, relative to the amplitude in the \gps-band.}
     763\label{fig:filter.trend}
    746764\end{center}
    747765\end{figure*}
    748766
    749 \begin{table}
    750 % \tiny
    751 \begin{center}
    752 \caption{Systematic Trends : Correlations by filter\label{table:correlation.by.filter}}
    753 \begin{tabular}{|l|rrrr|}
    754 \hline
    755 {\bf Filter} & {\bf smear} & {\bf psf mags} & {\bf astrom} & {\bf flat} \\
    756 \hline
    757 \gps & 1.00 & 1.00 &  1.00 & 1.00 \\
    758 \rps & 0.78 & 0.84 &  0.84 & 0.76 \\
    759 \ips & 0.40 & 0.50 &  0.66 & 0.64 \\
    760 \zps & 0.16 & 0.26 &  0.37 & 0.33 \\
    761 \yps & 0.10 & 0.10 &  0.25 & 0.30 \\
    762 \hline
    763 \end{tabular}
    764 \end{center}
    765 \end{table}
     767\subsection{Correlations Between Tree-Ring Patterns}
     768
     769%% \begin{table}
     770%% % \tiny
     771%% \begin{center}
     772%% \caption{\newtext{Amplitude of the four systematic trends in each filter
     773%%   relative to \gps.} \oldtext{Systematic Trends : Correlations by filter}\label{table:correlation.by.filter}}
     774%% \begin{tabular}{|l|rrrr|}
     775%% \hline
     776%% {\bf Filter} & {\bf smear} & {\bf psf mags} & {\bf astrom} & {\bf flat} \\
     777%% \hline
     778%% \gps & 1.00 & 1.00 &  1.00 & 1.00 \\
     779%% \rps & 0.78 & 0.84 &  0.84 & 0.76 \\
     780%% \ips & 0.40 & 0.50 &  0.66 & 0.64 \\
     781%% \zps & 0.16 & 0.26 &  0.37 & 0.33 \\
     782%% \yps & 0.10 & 0.10 &  0.25 & 0.30 \\
     783%% \hline
     784%% \end{tabular}
     785%% \end{center}
     786%% \end{table}
    766787
    767788Tree-ring patterns are clearly seen in 4 of the measurement types
    … …  
    807828
    808829For all four types of measurements, the \oldtext{slope of the fitted
    809   lines} \newtext{amplitudes relative to \gps} are listed in
    810 Table~\ref{table:correlation.by.filter}.  There is a consistency in
     830  lines} \newtext{amplitudes relative to \gps} are \oldtext{listed in
     831Table~2} \newtext{plotted in Figure~\ref{fig:filter.trend}}.  There is a consistency in
    811832the trend from \gps, with the strongest systematic tree-ring effects
    812833to \yps, with the weakest effects.  Note that the second moment smear
    … …  
    882903\begin{center}
    883904\includegraphics[width=\figwidth]{\picdir/radial_p1_r.\plotext}
    884 \caption{Correlation of the PSF magnitude residuals ($\delta m_{PSF}$)
    885   with the smear ($\sigma^2_{\mbox{major}} + \sigma^2_{\mbox{minor}}$)
    886   signal for \gps\ (upper-left), \rps\ (upper-right), \ips\ (lower-left),
    887   \zps\ (lower-right).
    888 } \label{fig:effects.vs.radius}
     905\caption{Radial run of the four tree-ring trends for \rps: smear
     906  ($\sigma^2_{\mbox{major}} + \sigma^2_{\mbox{minor}}$), PSF magnitude
     907  residuals ($\delta m_{PSF}$), flat-field, and astrometric residuals
     908  ($\delta R$).  } \label{fig:effects.vs.radius}
    889909\end{center}
    890910\end{figure*}
    … …  
    895915\begin{center}
    896916\includegraphics[width=\figwidth]{\picdir/radial_p2_r.\plotext}
    897 \caption{Correlation of the PSF magnitude residuals ($\delta m_{PSF}$)
    898   with the smear ($\sigma^2_{\mbox{major}} + \sigma^2_{\mbox{minor}}$)
    899   signal for \gps\ (upper-left), \rps\ (upper-right), \ips\ (lower-left),
    900   \zps\ (lower-right).
     917\caption{Radial run of the derivative of the smear ($\frac{\partial (\sigma^2_{major} + \sigma^2_{minor})}{\partial radius}$)
     918  and astrometric residuals ($\delta R$) for \rps.
    901919} \label{fig:dsmear.and.astrom}
    902920\end{center}
    … …  
    908926\begin{center}
    909927\includegraphics[width=\figwidth]{\picdir/radial_p3_r.\plotext}
    910 \caption{Correlation of the PSF magnitude residuals ($\delta m_{PSF}$)
    911   with the smear ($\sigma^2_{\mbox{major}} + \sigma^2_{\mbox{minor}}$)
    912   signal for \gps\ (upper-left), \rps\ (upper-right), \ips\ (lower-left),
    913   \zps\ (lower-right).
    914 } \label{fig:dastrom.and.flat}
     928\caption{Radial run of
     929 the derivative of the astrometric residuals ($\frac{\partial \delta
     930   R}{\partial radius}$) and the flat-field for \rps.} \label{fig:dastrom.and.flat}
    915931\end{center}
    916932\end{figure*}
    … …  
    931947Finally, the radial derivative of the radial component of the
    932948astrometric residual is correlated with the flat-field residual
    933 errors.
    934 \newtext{Figure~\ref{fig:dastrom.and.flat} shows the radial run of
    935   $\frac{\partial \delta R}{\partial radius}$ and $\delta flat$ together
    936   to illustrate this relationship.}
    937 \oldtext{: $\frac{\partial \delta R}{\partial radius} \sim \delta flat$ (see Figure~14).}
     949errors.  \newtext{Figure~\ref{fig:dastrom.and.flat} shows the radial
     950  run of $\frac{\partial \delta R}{\partial radius}$ and the
     951  flat-field together to illustrate this relationship.}  \oldtext{:
     952  $\frac{\partial \delta R}{\partial radius} \sim \delta flat$ (see
     953  Figure~14).}
    938954
    939955This last relationship is somewhat weakly measured.  Because of the
    … …  
    953969  image.}
    954970
    955 \begin{table}
    956 % \tiny
    957 \begin{center}
    958 \caption{Systematic Trends : Correlations between trends\label{table:correlation.by.trend}}
    959 \begin{tabular}{|l|rrr|}
    960 \hline
    961 {\bf Filter} & {\bf psf mags} & {\bf $\grad$ smear} & {\bf $\grad$ astrom} \\
    962              & {\bf vs smear} & {\bf vs astrom}     & {\bf vs flat}        \\
    963 \hline
    964 \gps & -0.056 & -0.060 & -0.47  \\
    965 \rps & -0.071 & -0.073 & -0.45  \\
    966 \ips & -0.077 & -0.095 & -0.45  \\
    967 \zps & -0.082 & -0.078 & -0.17  \\
    968 \hline
    969 \end{tabular}
    970 \end{center}
    971 \end{table}
     971%% \begin{table}
     972%% % \tiny
     973%% \begin{center}
     974%% \caption{Systematic Trends : Correlations between trends\label{table:correlation.by.trend}}
     975%% \begin{tabular}{|l|rrr|}
     976%% \hline
     977%% {\bf Filter} & {\bf psf mags} & {\bf $\grad$ smear} & {\bf $\grad$ astrom} \\
     978%%              & {\bf vs smear} & {\bf vs astrom}     & {\bf vs flat}        \\
     979%% \hline
     980%% \gps & -0.056 & -0.060 & -0.47  \\
     981%% \rps & -0.071 & -0.073 & -0.45  \\
     982%% \ips & -0.077 & -0.095 & -0.45  \\
     983%% \zps & -0.082 & -0.078 & -0.17  \\
     984%% \hline
     985%% \end{tabular}
     986%% \end{center}
     987%% \end{table}
    972988
    973989% smear vs psfmag
    … …  
    10591075\oldtext{(Figure~14)}\newtext{(Figure~\ref{fig:dastrom.and.flat})}
    10601076is consistent with radial variations in the plate-scale.  The
    1061 tree-rings observed by DES are completely attributed to effective
     1077tree-rings observed in DECam are completely attributed to effective
    10621078plate scale changes.  Effective plate scale changes result in
    10631079flat-field deviations because the flat-field illumination is a source
    … …  
    10661082affects the astrometry since these variations occur on spatial scales
    10671083much smaller than the astrometric model.  In this description of the
    1068 tree rings, the flat-field deviations are $-1 \times \frac{\partial
     1084tree rings, the flat-field deviations are \newtext{proportional to $\frac{\partial
     1085\delta R}{\partial r}$, as observed in Figure~\ref{fig:dastrom.and.flat}.}
     1086\oldtext{$-1 \times \frac{\partial
    10691087  \delta R}{\partial r}$.  The best-fit slopes of our correlations are
    10701088\approx 0.5, but the signal-to-noise is rather low.  A slope of -1
    1071 appears to be consistent with our measurements.
     1089appears to be consistent with our measurements.}
    10721090
    10731091The fact that the PSF ellipticity changes are {\em not} correlated
    10741092with the tree-ring structure
    10751093\oldtext{(Figure~6)}\newtext{(Figure~\ref{fig:all.effects.rband})}
    1076 tells us that, unlike the case for DES, the effective plate-scale
     1094tells us that, unlike the case for DECam, the effective plate-scale
    10771095changes seen in the flat-field and astrometry signals are not the
    10781096dominant cause of the PSF photometry errors.  Also, the fact that we
    … …  
    10991117tree-ring effects is the pattern of the doping variations in the
    11001118silicon.  As discussed by \cite{2014PASP..126..750P}, the tree-ring
    1101 patterns seen by the DES team are caused by lateral electic fields in
     1119patterns seen by the DECam team are caused by lateral electic fields in
    11021120the detector silicon (in the plane of the CCD wafer) generated by
    11031121variations in the space charges embedded in the silicon, in turn
    … …  
    11381156by \cite{Holland.2003}, the charge diffusion is related to the space
    11391157charge density by $\sigma \sim \rho^{-\frac{1}{2}}$ (their equation
    1140 6).  Regions with high space charge densities increase the migration
    1141 speed of the photoelectrons and reduce the amount of charge diffusion
    1142 smearing; and vice versa for regions of low space-charge densities.
     11586).  Regions with high space charge densities increase the electric
     1159field in the depletion region for a fixed voltage, and thus increase
     1160the migration speed of the photoelectrons, reducing the amount of
     1161charge diffusion smearing; and vice versa for regions of low
     1162space-charge densities.
    11431163
    11441164In summary, the variations in the space-charge density caused by
    … …  
    11491169photoelectrons, resulting in astrometric and flat-field deviations.
    11501170
    1151 The DES team did not detect these charge diffusion variations.  In
     1171The DECam team did not detect these charge diffusion variations.  In
    11521172that case, the amplitude of the photometric effects due to the lateral
    11531173field are dominant; these include both the modification of the
    … …  
    12081228diffusion.  Unlike the non-uniform pixel-size effects, correction of
    12091229the PSF photometry cannot simply be performed as an average flat-field
    1210 correction on the measurements after they have been processed. 
    1211 The additional smearing acts as a convolution with a Gaussian kernel
    1212 of fixed size for a given filter.  The photometry bias is a function
    1213 of the fractional change of the PSF size.  Thus, the introduced error
     1230correction on the measurements after they have been processed.  The
     1231additional smearing acts as a convolution with a Gaussian kernel of
     1232fixed size for a given filter.  The photometry bias is a function of
     1233the fractional change of the PSF size.  Thus, the introduced error
    12141234depends on the average PSF for the image in question: an image with
    12151235good image quality will suffer larger PSF model errors than an image
    … …  
    12181238modify the model PSFs as a function of position before they are used
    12191239for the image analysis.
     1240
     1241The PV3 analysis of the Pan-STARRS $3\pi$ dataset applied an average
     1242correction to the photometry and astrometry for each exposure as a
     1243function of camera position with fine-enough resolution to follow
     1244these tree-ring effects.  However, since the photometry was only
     1245corrected with an average flat-field-like correction, the full impact
     1246of the smearing on the PSF photometry is not corrected.  The remaining
     1247systematic structure will tend to average out with many observations
     1248in which the stars land on different portions of the detector.  A
     1249future re-processing will be required to completely correct for this
     1250effect.
    12201251
    12211252The charge diffusion variations may also have an impact on
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