Index: trunk/doc/release.2015/systematics.20140411/systematics.tex
===================================================================
--- trunk/doc/release.2015/systematics.20140411/systematics.tex	(revision 40097)
+++ trunk/doc/release.2015/systematics.20140411/systematics.tex	(revision 40098)
@@ -22,6 +22,6 @@
 \def\plotext{ps}
 
-\def\picdir{/home/eugene/chipresid.20140404}
-%\def\picdir{/data/kukui.2/eugene/chipresid.20140404}
+%\def\picdir{/home/eugene/chipresid.20140404}
+\def\picdir{/data/kukui.2/eugene/chipresid.20140404}
 
 % Pick a terse version of the title here;
@@ -102,4 +102,6 @@
 \section{INTRODUCTION}\label{sec:intro}
 
+
+
 % discuss the science drivers
 % summary concept of paper:
@@ -316,5 +318,5 @@
 included in the analysis.
 
-\subsubsection{Photometric Residuals}
+\subsection{Photometric Residuals}
 
 % PSF Magnitudes
@@ -385,5 +387,5 @@
 of the PSF magnitude tree-rings would certainly have been obvious.
 
-\subsubsection{Astrometric Residuals}
+\subsection{Astrometric Residuals}
 
 % astrometry radial term
@@ -431,5 +433,5 @@
 in these figures.
 
-\subsubsection{Flat-field Structures}
+\subsection{Flat-field Structures}
 
 % flat-field residual
@@ -485,5 +487,5 @@
 similar to the aperture residuals is seen in \gps.
 
-\subsubsection{Second Moments}
+\subsection{Second Moments}
 
 % Smear Images
@@ -547,8 +549,21 @@
 combinations, inspired by discussions of lensing measurements \citep{1995ApJ...449..460K}:
 \begin{eqnarray}
-R^2 & = & \delta M_{xx} + \delta M_{yy} \\
-e_1 & = & \delta M_{xx} + \delta M_{yy} \\
-e_2 & = & 2 \delta M_{xy}
+e_0 & = & \delta M_{xx} + \delta M_{yy}  \\ 
+e_1 & = & \delta M_{xx} - \delta M_{yy}  \\
+e_2 & = & \sqrt{e_1^2 + 4 \delta M_{xy}}
 \end{eqnarray}
+For a 2D Gaussian profile with an elliptical contour, these values are
+related to the shape of the elliptical contour as follows:
+\begin{eqnarray}
+e_0 & = & \sigma^2_a  + \sigma^2_b \\
+e_1 & = & (\sigma^2_a  - \sigma^2_b) \cos (2 \theta) \\
+e_2 & = & \sigma^2_a  - \sigma^2_b 
+\end{eqnarray}
+Where $\sigma_a$ and $\sigma_b$ are the major and minor axis
+dimensions of the ellipse and $\theta$ is the position angle.  
+Thus, $e_0$ is a measurement of the change in the size of the stellar
+PSFs as a function of position in the detector (``smear''), $e_2$ is a measurement
+of the change in ellipticity of the stellar PSFs (``shear''), and we
+can determine the angle of the PSF ellipticity from the $e_1$ term.
 
 Figure~\ref{fig:smear.by.filter} shows the spatial trend of the {\em
@@ -574,5 +589,5 @@
 unrelated to the radial trend from the upper-left corner.
 
-\subsubsection{Correlations Between Tree-Ring-Like Patterns}
+\subsection{Correlations Between Tree-Ring-Like Patterns}
 
 \begin{table}