Index: /trunk/doc/release.2015/systematics.20140411/diffusion.tex
===================================================================
--- /trunk/doc/release.2015/systematics.20140411/diffusion.tex	(revision 40304)
+++ /trunk/doc/release.2015/systematics.20140411/diffusion.tex	(revision 40305)
@@ -19,7 +19,8 @@
 %\newcommand\newtext[1]{\textbf{\color{blue}#1}}
 
-\newcommand\oldtext[1]{\textbf{\color{lightgray}#1}
-\newcommand\newtext[1]{\textbf{\color{blue}#1}
-\newcommand\fixtext[1]{\textbf{\color{red}#1}
+\definecolor{light-gray}{gray}{0.50}
+\newcommand\oldtext[1]{\textbf{\color{light-gray}#1}}
+\newcommand\newtext[1]{\textbf{\color{blue}#1}}
+\newcommand\fixtext[1]{\textbf{\color{red}#1}}
 
 \usepackage[T1]{fontenc}% (2) specify encoding
@@ -514,4 +515,11 @@
 of the PSF magnitude tree-rings would certainly have been obvious.
 
+\newtext{Figure~\ref{fig:all.effects.rband} shows the complete set of
+  measured effects for the \rps\ filter.  In addition to the PSF and
+  aperture photometry, this figure shows the astrometric residuals,
+  the high-frequency flat-field structures, along with two
+  measurements derived from the second moments: the ``smear'' and the
+  ``shear'', discussed below.}
+
 \subsection{Astrometric Residuals}
 
@@ -533,5 +541,6 @@
 %% \end{figure*}
 
-Figure~\ref{fig:astrom.by.filter} shows a similar type of measurement
+\oldtext{Figure~3} \newtext{Figure~\ref{fig:all.effects.rband} (middle-left)}
+shows a similar type of measurement
 for astrometric residuals.  To generate this plot, we use the same
 selection of measurements for astrometry as for photometry.  In this
@@ -550,12 +559,12 @@
 : tangential component).
 
-Figure~\ref{fig:astrom.by.filter} shows the 2D patterns of $\delta R$
+\oldtext{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.  A tree-ring
+from -20 to +20 milliarcseconds for all 5 plots.}  A tree-ring
 pattern is visible for all five filters, with systematic structures
 following a circular pattern centered on the chip corner; the finging
-pattern is not apparent in the \yps\ astrometry.  The per-pixel
+pattern is not apparent in the \yps\ astrometry.  \oldtext{The per-pixel
 standard deviations of these plots are listed in
-Table~\ref{table:sigmas.by.filter}.  The signal-to-noise of these
+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.
@@ -579,5 +588,6 @@
 
 % 2012ApJ...750...99T = Tonry et al PS1 phot system
-Figure~\ref{fig:flats.by.filter} shows the high-spatial-frequency
+\oldtext{Figure~4} \newtext{Figure~\ref{fig:all.effects.rband} (middle-right)}
+shows the high-spatial-frequency
 structures in the flat-field images.  For this measurement, we have
 used a set of monochromatic flat-field images obtained with a tunable
@@ -597,6 +607,6 @@
 pixels associated with each superpixel.  
 
-Figure~\ref{fig:flats.by.filter} shows the superpixel images for the
-flat-fields in the five filters.  These flat-field images are
+\fixtext{Figure~\ref{fig:flats.by.filter} shows the superpixel images for the
+flat-fields in the five filters.}  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
@@ -699,5 +709,6 @@
 PSF ellipticity from the $e_1$ term.
 
-Figure~\ref{fig:smear.by.filter} shows the spatial trend of the smear,
+\oldtext{Figure~5} \newtext{Figure~\ref{fig:all.effects.rband} (lower-left)}
+shows the spatial trend of the smear,
 $e_0$.  The dynamic range of these images is -0.3 to +0.3 pixel$^2$. A
 tree-ring pattern is visible for all 5 filters, though \yps\ is
@@ -705,8 +716,10 @@
 spatial frequencies can also be seen.
 
-Figure~\ref{fig:shear.by.filter} shows the spatial trend of the shear,
+\oldtext{Figure~6} \newtext{Figure~\ref{fig:all.effects.rband} (lower-right)}
+shows the spatial trend of the shear,
 $e_2$.  This value is positive definite and is plotted with a color
 scale ranging from -0.02 to 0.22 pixel$^2$.  Overlayed on
-Figure~\ref{fig:shear.by.filter} is a set of vectors representing the
+\oldtext{Figure~6} \newtext{Figure~\ref{fig:all.effects.rband} (lower-right)}
+is a set of vectors representing the
 ellipse orientation as a function of postion.  The length of the
 vectors corresponds to the value of $e_2$.  The tree-ring structure is
@@ -729,5 +742,6 @@
   much higher frequencies than the previous two effects.  Aperture
   magnitude (upper-right) and shear residuals (lower-right) do not
-  show a strong signal consistent with either of the two patterns.} \label{fig:all.effects.rband}
+  show a strong signal consistent with either of the two patterns.}
+\label{fig:all.effects.rband}
 \end{center}
 \end{figure*}
@@ -778,9 +792,9 @@
 For a given type of measurement, 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
+term\oldtext{: Figure~8 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
+filters\oldtext{, as shown in Figure~9}.  Here, the
 \yps\ correlation with \gps\ is quite weak: the fringing pattern
 dominates the tree rings for PSF photometry.  The radial component of
@@ -792,10 +806,11 @@
 pattern.
 
-For all four types of 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.
+For all four types of measurements, the \oldtext{slope of the fitted
+  lines} \newtext{amplitudes relative to \gps} 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
@@ -849,5 +864,13 @@
 pattern between the different types of measurements.  Different models
 for the tree-ring structures make different predictions about the
-correlations between different effects.  Note the very different
+correlations between different effects.
+%
+\newtext{Figure~\ref{fig:effects.vs.radius} shows the radial run of the
+  four effects which show clear tree rings (in \rps).  Since the tree
+  rings are relatively narrow, this figure shows only the radial range
+  of 150 - 300 pixels to allow the reader to see the relationship
+  between structures in the different effects. }
+%
+Note the very different
 spatial structure between the different measurements in a given
 filter: the radial variations do not all follow the same patterns.
@@ -863,5 +886,5 @@
   signal for \gps\ (upper-left), \rps\ (upper-right), \ips\ (lower-left),
   \zps\ (lower-right).
-} \label{fig:smear.vs.psfmag}
+} \label{fig:effects.vs.radius}
 \end{center}
 \end{figure*}
@@ -876,5 +899,5 @@
   signal for \gps\ (upper-left), \rps\ (upper-right), \ips\ (lower-left),
   \zps\ (lower-right).
-} \label{fig:smear.vs.psfmag}
+} \label{fig:dsmear.and.astrom}
 \end{center}
 \end{figure*}
@@ -889,5 +912,5 @@
   signal for \gps\ (upper-left), \rps\ (upper-right), \ips\ (lower-left),
   \zps\ (lower-right).
-} \label{fig:smear.vs.psfmag}
+} \label{fig:dastrom.and.flat}
 \end{center}
 \end{figure*}
@@ -897,26 +920,36 @@
 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}.  
+larger fluxes).  \oldtext{These trends are shown in Figure 12.}
 
 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}).
+radial component of the astrometric residuals
+\newtext{Figure~\ref{fig:dsmear.and.astrom} shows the radial run of
+  $\frac{\partial (\sigma^2_{major} + \sigma^2_{minor})}{\partial radius}$
+  and $\delta R$ together to illustrate this relationship.}
+\oldtext{: $\frac{\partial(\sigma^2_{major} + \sigma^2_{minor})}{\partial radius} \sim \delta R$. (see Figure~13).}
 
 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 be completely certain that the
-flat-field is proportional to the derivative of the astrometry
-residual, rather than the astrometry residual being proportional to
-the derivative of the flat-field.  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
-residual values without a derivative.  We are convinced that we have
-the sense of the derivative correct by examination of specific
-features in each image.
+astrometric residual is correlated with the flat-field residual
+errors.
+\newtext{Figure~\ref{fig:dastrom.and.flat} shows the radial run of
+  $\frac{\partial \delta R}{\partial radius}$ and $\delta flat$ together
+  to illustrate this relationship.}
+\oldtext{: $\frac{\partial \delta R}{\partial radius} \sim \delta flat$ (see Figure~14).}
+
+This last relationship is somewhat weakly measured.  Because of the
+periodic nature of the tree rings, it is also difficult to be
+completely certain that the flat-field is proportional to the
+derivative of the astrometry residual, rather than the astrometry
+residual being proportional to the derivative of the flat-field.
+\newtext{Careful examination of Figures~\ref{fig:effects.vs.radius}
+  and \ref{fig:dastrom.and.flat} convince us that we have the sense of
+  the derivative correct.}
+%
+\oldtext{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 residual values without a
+  derivative.  We are convinced that we have the sense of the
+  derivative correct by examination of specific features in each
+  image.}
 
 \begin{table}
@@ -987,14 +1020,16 @@
 
 First, if we consider the smear pattern
-(Figure~\ref{fig:smear.by.filter}), the measurement shows that the
-intrinsic sizes of the stellar images are varying in a radial sense
-between the different tree-ring regions.  Although images experience
-an average image quality (due to seeing and focus) across the chip
-which may vary substantially from exposure to exposure, stars landing
-in the different tree-ring regions are consistently somewhat
+\oldtext{(Figure~5)}\newtext{(Figure~\ref{fig:all.effects.rband}, lower-left)},
+the measurement shows that the intrinsic sizes of the stellar images
+are varying in a radial sense between the different tree-ring regions.
+Although images experience an average image quality \oldtext{(due to
+  seeing and focus)} across the chip which may vary substantially from
+exposure to exposure \newtext{(due to seeing and focus)}, stars
+landing in the different tree-ring regions are consistently somewhat
 larger or somewhat smaller than that average.
 
 Next, we can explain the correlation between the PSF photometry
-residuals and the observed smear (Figure~\ref{fig:smear.vs.psfmag}).
+residuals and the observed smear
+\newtext{(Figure~\ref{fig:effects.vs.radius})}\oldtext{(Figure~12)}.
 In the photometry analysis, we model the PSF allowing for some spatial
 variation in the shape.  However, we have a limited number of stars to
@@ -1004,52 +1039,56 @@
 interpolation between the $3 \times 3$ grid points.  Thus, the spatial
 scale on which we model PSF variations is much larger than the spatial
-scale on which PSF variations are actually occuring, as illustrated
-by the changes in the smear plot (Figure~\ref{fig:smear.by.filter}).
+scale on which PSF variations are actually occuring, as illustrated by
+the changes in the smear plot
+\oldtext{(Figure~5)}\newtext{(Figure~\ref{fig:all.effects.rband}, lower-left)}.
 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 true PSF is smaller, we overestimate the flux -- this
-type of offset is a typical effect when mis-estimating the PSF size.
-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\%, roughly consistent with the
-observed photometric deviation of about 5 to 10 millimags for this
-amount of smearing.
+Conversely, when the true PSF is smaller, we overestimate the flux --
+this type of offset is a typical effect when mis-estimating the PSF
+size.  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\%, roughly
+consistent with the observed photometric deviation of about 5 to 10
+millimags for this amount of smearing.
 
 The correlation between the flat-field structures and the radial
 derivative of the astrometric residual displacements in the radial
-direction (Figure~\ref{fig:dastrom.vs.flat}) 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 result in flat-field deviations because 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 this description of the tree rings, the flat-field
-deviations are $-1 \times \frac{\partial \delta R}{\partial r}$.  The
-best-fit slopes of our correlations are \approx 0.5, but the
-signal-to-noise is rather low.  A slope of -1 appears to be consistent
-with our measurements.
+direction
+\oldtext{(Figure~14)}\newtext{(Figure~\ref{fig:dastrom.and.flat})}
+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 result in
+flat-field deviations because 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 this description of the
+tree rings, the flat-field deviations are $-1 \times \frac{\partial
+  \delta R}{\partial r}$.  The best-fit slopes of our correlations are
+\approx 0.5, but the signal-to-noise is rather low.  A slope of -1
+appears to be consistent with our measurements.
 
 The fact that the PSF ellipticity changes are {\em not} correlated
-with the tree-ring structure (Figure~\ref{fig:shear.by.filter}) tells us
-that, unlike the case for DES, the effective plate-scale changes seen
-in the flat-field and astrometry signals are not 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 magnitude residuals.
-It is likely in our opinion that the plate-scale changes causing the
-flat-field and astrometry effects are affecting both the ellipticity
-and the aperture magnitudes, but the level of the effect is too small
-to see given the other systematic structures (in the shear plot) and
-the noise level (in the aperture magnitudes).
+with the tree-ring structure
+\oldtext{(Figure~6)}\newtext{(Figure~\ref{fig:all.effects.rband})}
+tells us that, unlike the case for DES, the effective plate-scale
+changes seen in the flat-field and astrometry signals are not 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
+magnitude residuals.  It is likely in our opinion that the plate-scale
+changes causing the flat-field and astrometry effects are affecting
+both the ellipticity and the aperture magnitudes, but the level of the
+effect is too small to see given the other systematic structures (in
+the shear plot) and the noise level (in the aperture magnitudes).
 
 Finally, the correlation between the smear structures and the
 astrometry residuals shows that these two effects are connected.
-Although the correlation is weak in Figure~\ref{fig:dsmear.vs.astrom},
+Although the correlation is weak in
+\oldtext{Figure~13} \newtext{Figure~\ref{fig:effects.vs.radius}},
 careful inspection of the location of these two tree ring patterns
 shows that the locations of the rings in the radial astrometric