Index: trunk/doc/release.2015/systematics.20140411/diffusion.tex
===================================================================
--- trunk/doc/release.2015/systematics.20140411/diffusion.tex	(revision 40134)
+++ trunk/doc/release.2015/systematics.20140411/diffusion.tex	(revision 40135)
@@ -96,14 +96,14 @@
 $3\pi$ survey to characterize the behavior of the deep-depletion
 devices used in the Pan-STARRS\,1 Gigapixel Camera.  We have
-identified systematic spatial variations in the photometric behavior and
-stellar profiles which are similar to the so-called ``tree rings''
-identified in devices used by other wide-field cameras (DECam and
-Hypersuprime Camera).  The tree-ring features identified in these
-other cameras result from lateral electric fields which displace the
-electrons as they are transported in the silicon to the pixel
-location.  In contrast, we show that the photometric and morphological
-modifications observed in the GPC1 detectors are caused by variations
-in the vertical charge transportation rate and resulting charge
-diffusion variations.
+identified systematic spatial variations in the photometric
+measurements and stellar profiles which are similar in pattern to the
+so-called ``tree rings'' identified in devices used by other
+wide-field cameras (e.g., DECam and Hypersuprime Camera).  The
+tree-ring features identified in these other cameras result from
+lateral electric fields which displace the electrons as they are
+transported in the silicon to the pixel location.  In contrast, we
+show that the photometric and morphological modifications observed in
+the GPC1 detectors are caused by variations in the vertical charge
+transportation rate and resulting charge diffusion variations.
 \end{abstract}
 
@@ -125,7 +125,7 @@
 trap electrons, specifically those generated by absorbed photons.  The
 thick silicon substrate required illumination from the ``front'' side
-with the thin gate structures to allow the photons to reach the
+containing the thin gate structures to allow the photons to reach the
 depletion region and be detected.  These early CCDs had modest quantum
-efficiency as photons were easily absorbed by the several micron thick
+efficiency as photons were easily absorbed by the several-micron-thick
 gate structures.  For an excellent review of the history of CCD
 development, see \cite{1992ASPC...23....1J}.
@@ -137,10 +137,10 @@
 delicate device only \approx 10 - 20\micron\ thick, exposing the
 depletion region on the backside.  Photons entering the backside of
-the device are not blocked by the gate structures and thus more easily
-absorbed and detected.  Thinned backside-illuminated CCDs have high
-quantum efficiency to blue photons.  However, as the wavelength
+the device are not blocked by the gate structures and are thus more
+easily absorbed and detected.  Thinned backside-illuminated CCDs have
+high quantum efficiency to blue photons.  However, as the wavelength
 increases beyond \approx 800 nm, the silicon becomes more transparent
-to the photons, with a corresponding drop in quantum efficiency for
-red photons.  In addition, thin film interference between the entering
+to the photons with a corresponding drop in quantum efficiency for
+red photons.  In addition, thin-film interference between the entering
 photons and those reflecting off the front side of the CCD result in
 ``fringe'' patterns for redder photons.
@@ -167,6 +167,6 @@
 
 While these deep-depletion CCDs seem to be ideal, they do have
-features which can cause challenges for precise measurements.  As a
-result of the ``Brighter-Fatter Effect''
+features which can cause challenges for precise measurements.  For
+example, as a result of the ``Brighter-Fatter Effect''
 \citep{2014JInst...9C3048A,2015JInst..10C5032G}, the profile of bright
 stars are measured to be wider than the profiles of faint stars.  The
@@ -177,5 +177,5 @@
 The effects of lateral electric fields are likewise identified as the
 cause of the so-called ``tree rings'' observed in the flat-field,
-astrometry, and photometry response of thick deep depletion detectors
+astrometry, and photometry response of thick deep-depletion detectors
 \citep{2014PASP..126..750P}.  These tree-ring patterns have been noted
 in the flat-field response of deep depletion devices since their early
@@ -189,23 +189,24 @@
 silicon.  The changes in the effective area result in changes to the
 apparent flat-field response as well as the astrometric response of
-the detector.  More subtly, the flat-field response changes, since
-they do not reflect actual variations in sensitivity, can lead to
-systematic photometry errors for astronomical sources if the
-flat-field images are used in the standard fashion.
+the detector.  More subtly, the changes in the flat-field response,
+since they do not reflect actual variations in sensitivity, can lead
+to systematic photometry errors for astronomical sources if flat-field
+images are used in the standard fashion.
 
 In this paper, we examine the behavior of an apparently-similar kind
-of tree ring observed in the Pan-STARRS GPC1 CCDs.  Although we also
-observe the pixel effective area changes caused by lateral electric
-fields as described by \cite{2014PASP..126..750P}, we show below a
-second effect which is more important in driving systematic photometry
+of tree-ring pattern observed in the Pan-STARRS\,1 Gigapixel Camera 1
+CCDs.  Although we also observe the changes in effective pixel area
+caused by lateral electric fields as described by
+\cite{2014PASP..126..750P}, we show below a second effect which is
+more important in these devices in driving systematic photometry
 errors.  We find that variations in charge diffusion, also resulting
 from changes in the silicon doping structures, affect both the
 observed stellar profiles as well as the photometry measured with
 profile fitting techniques.  In Section~\ref{sec:PS1}, we discuss the
-Pan-STARRS telescope, camera, and survey data used in this analysis.
-In Section~\ref{sec:tree.rings}, we present the tree-ring
-patterns as observed in several different types of measurements:
-flat-field response, systematic photometry residuals, systematic
-astrometric residuals, and stellar profile shape variations.  In
+Pan-STARRS\,1 telescope, camera, and survey data used in this analysis.
+In Section~\ref{sec:tree.rings}, we present the tree-ring patterns as
+observed in several different types of measurements: flat-field
+response, systematic photometric residuals, systematic astrometric
+residuals, and stellar profile shape variations.  In
 Section~\ref{sec:discussion}, we discuss the interpretation of
 patterns we observe and present a simple model to explain the observed
@@ -219,15 +220,15 @@
 Haleakala on the Hawaiian island of Maui, has been surveying the sky
 regularly since May 2010 \citep{chambers2017}.  From May 2010 through
-March 2014, PS1 was run under the aegis of the Pan-STARRS Science
-Consortium to perform a set of wide-field science surveys; since March
-2014, operations have been supported primarily by NASA's Near Earth
-Object Observation program, see \cite{2015IAUGA..2251124W}.  Under the
-PS1SC, the largest survey, both in terms of area of the sky covered
-($3\pi$ steradians) and fraction of observing time (56\%), was the
-\TPS\ in which the entire sky north of Declination $-30$\degrees\ was
-imaged up \approx 80 times over 4 years.  These observations were
-distributed over five filters, \grizy, and have been astrometrically
-and photometrically calibrated to good precision
-\citep{magnier2017.calibration}.
+March 2014, PS1 was run under the aegis of the Pan-STARRS\,1 Science
+Consortium (PS1SC) to perform a set of wide-field science surveys;
+since March 2014, operations have been supported primarily by NASA's
+Near Earth Object Observation program
+\citep[see][]{2015IAUGA..2251124W}.  Under the PS1SC, the largest
+survey, both in terms of area of the sky covered ($3\pi$ steradians)
+and fraction of observing time (56\%), was the \TPS\ in which the
+entire sky north of Declination $-30$\degrees\ was imaged \approx 80
+times over 4 years.  These observations were distributed over five
+filters, \grizy, and have been astrometrically and photometrically
+calibrated to good precision \citep{magnier2017.calibration}.
 
 % 2004SPIE.5489..667H == PS1.optics
@@ -237,5 +238,5 @@
 The wide-field PS1 telescope optics \citep{2004SPIE.5489..667H} image
 a 3.3 degree field of view on a 1.4 gigapixel camera
-\citep[GPC1][]{2009amos.confE..40T}, with low distortion and generally
+\citep[GPC1;][]{2009amos.confE..40T}, with low distortion and generally
 good image quality.  The median seeing for the \TPS\ data vary
 somewhat by filter: (\grizy) = (1.31, 1.19, 1.11, 1.07, 1.02)
@@ -244,12 +245,12 @@
 University of Hawaii's Institute for Astronomy operations on Maui.
 
-GPC1 \citep{2009amos.confE..40T}, currently the largest astronomical
-camera in terms of number of pixels, consists of a mosaic of 60
-edge-abutted $4800\times4800$ pixel detectors, with 10~$\mu$m pixels
-subtending 0.258~arcsec. These CCID58 detectors, manufactured by
-Lincoln Laboratory, are 75\micron-thick back-illuminated CCDs
-\citep{2006amos.confE..47T,2008SPIE.7021E..05T}.  Initial performance
-assessments are presented in \cite{2008SPIE.7014E..0DO}. The active,
-usable pixels cover \approx 80\% of the FOV.
+GPC1, currently the largest astronomical camera in terms of number of
+pixels, consists of a mosaic of 60 edge-abutted $4800\times4800$ pixel
+detectors, with 10~$\mu$m pixels subtending 0.258~arcsec. These CCID58
+detectors, manufactured by Lincoln Laboratory, are 75\micron-thick
+back-illuminated CCDs \citep{2006amos.confE..47T,2008SPIE.7021E..05T}.
+Initial performance assessments are presented in
+\cite{2008SPIE.7014E..0DO}. The active, usable pixels cover \approx
+80\% of the FOV.
 
 \subsection{Data Processing and Calibration}
@@ -268,10 +269,12 @@
 objects).  In addition, the \TPS\ dataset has been re-processed
 several times with improved calibration and analysis techniques.  To
-date (2017 July), 3 re-processings starting from raw pixel data have
-been performed.  The labels PV0, PV1, PV2, PV3 are used identify the
-nightly processing and successive re-processing versions.  PV3 has
+date (2017 September), 3 re-processings starting from raw pixel data
+have been performed.  The labels PV0, PV1, PV2, PV3 are used identify
+the nightly processing and successive re-processing versions.  PV3 has
 been used for the public release of the Pan-STARRS \TPS\ data via the
 {\it Barbara A. Mikulski Archive for Space Telescopes} (MAST) at the
-Space Telescope Science Institute.\footnote{http//panstarrs.stci.edu}
+Space Telescope Science Institute.\footnote{http//panstarrs.stsci.edu}
+The process of the construction of this database and the schema
+details are discussed in detail by \cite{flewelling2017}.
 
 The data processing and calibration operations are discussed in detail
@@ -328,19 +331,19 @@
 photometry is re-calibrated within the databasing system based on the
 properties of the measured photometry.  The calibration process is
-discussed by
-\cite{2012ApJ...756..158S,2013ApJS..205...20M,magnier2017.calibration}.
-As part of this process, several flat-field corrections have been
-determined.  For the PV2 analysis discussed here, a flat-field
-correction determined during the ubercal analysis
-\citep[see][]{2012ApJ...756..158S} consisted of an $8\times 8$ grid of
-corrections for each GPC1 chip, corresponding to a correction for each
-OTA ``cell'' and filter for each of 4 seasons.  The boundaries of
-those seasons are tentatively identified with modifications to the
-baffle structures or the system optics.  The critical point here is
-that the final effective flat-field image for the PV2 dataset is based
-on a dome-flat at the highest resolution, with very low resolution
-corrections based on photometry, resulting in photometric systematic
-uncertainties in the range 7 - 12 millimagnitudes, depending on the
-filter \citep{2013ApJS..205...20M}.
+discussed by \cite{2012ApJ...756..158S} and
+\cite{2013ApJS..205...20M,magnier2017.calibration}.  As part of this
+process, several flat-field corrections have been determined.  For the
+PV2 analysis discussed here, a flat-field correction determined during
+the ubercal analysis \citep[see][]{2012ApJ...756..158S} consisted of
+an $8\times 8$ grid of corrections for each GPC1 chip, corresponding
+to a correction for each OTA ``cell'' and filter for each of 4
+seasons.  The boundaries of those seasons are tentatively identified
+with modifications to the baffle structures or the system optics.  The
+critical point here is that the final effective flat-field image for
+the PV2 dataset is based on a dome-flat at the highest resolution,
+with very low resolution (hundreds of pixels) corrections based on
+photometry, resulting in photometric systematic uncertainties in the
+range 7 - 12 millimagnitudes, depending on the filter
+\citep{2013ApJS..205...20M}.
 
 For all objects, positions are measured from the PSF model for the
@@ -400,9 +403,10 @@
 For all of these examples, we use a single GPC1 CCD (XY40) to
 illustrate the effects in detail, but a similar set of effects are
-seen in many of the GPC1 detectors.  First, we show the residual PSF
-photometry.  Second, we show the residual aperture photometry.  Third,
-we show the astrometric residual patterns.  Fourth, we show the
-patterns observed in the flat-field images.  Finally, we show
-measurements derived from the second-moments of the stars.
+seen in many, if not all, of the GPC1 detectors with varying
+strengths.  First, we show the residual PSF photometry.  Second, we
+show the residual aperture photometry.  Third, we show the astrometric
+residual patterns.  Fourth, we show the patterns observed in the
+flat-field images.  Finally, we show measurements derived from the
+second-moments of the stars.
 
 For all effects discussed below, we are measuring the mean value of
@@ -486,5 +490,5 @@
 aperture photometry instead of PSF photometry.  The finging
 pattern again dominates the plot for \yps, but the tree rings are not
-seen in any of the filters.  A diagonal pattern is visible in \gps
+seen in any of the filters.  A diagonal pattern is visible in \gps\
 which is not observed in the PSF magnitudes.  While the per-pixel
 scatter is somewhat (10\% to 20\%) higher for these aperture
@@ -523,8 +527,9 @@
 superpixel.  We have determined the approximate center of the circular
 tree-ring pattern as (-5,4960) for this particular chip based on the
-pattern of the X astrometry displacements.  Using this coordinate as the center
-of the pattern, we have converted the $\delta X,\delta Y$ offsets into
-$\delta R,\delta \theta$ measurements ($\delta R$ : radial component
-away from the center, $\delta \theta$ : tangential component).
+pattern of the X astrometry displacements.  Using this coordinate as
+the center of the pattern, we have converted the $\delta X,\delta Y$
+offsets into $\delta R,\delta \theta$ measurements ($\delta R$ :
+radial component away from the center of the pattern, $\delta \theta$
+: tangential component).
 
 Figure~\ref{fig:astrom.by.filter} shows the 2D patterns of $\delta R$
@@ -534,5 +539,5 @@
 following a circular pattern centered on the chip corner; the finging
 pattern is not apparent in the \yps\ astrometry.  The per-pixel
-standard deviations of these plots area listed in
+standard deviations of these plots are listed in
 Table~\ref{table:sigmas.by.filter}.  The signal-to-noise of these
 structures is again somewhat weak, but the pattern is clearly visible
@@ -588,13 +593,13 @@
 strong in the (\gps,\rps,\ips) images, but nearly swamped by fringing
 in \zps, and completely lost to finging in \yps.  A diagonal banding
-pattern is seen in \gps: this features is thought to be due to the
-lithography process used to generate the CCD.  A blob can also been
-seen covering 4 cells near the center of this chip; this is apparently
-a deposit of some kind on the detector.  Both of the latter two
-effects behave like quantum efficiency variations and are removed well
-by standard flat-field techniques.  Note that a small amount of the
-diagonal banding pattern remains in the aperture magnitude residuals
-for \gps.  For the rest of this article, we ignore these features and
-concentrate on the tree ring features.
+pattern is also seen in \gps: this feature is thought to be due to
+the lithography process used to generate the CCD.  A blob can also
+been seen covering 4 cells near the center of this chip; this is
+apparently a deposit of some kind on the detector.  Both of the latter
+two effects behave like quantum efficiency variations and are removed
+well by standard flat-field techniques.  Note that a small amount of
+the diagonal banding pattern remains in the aperture magnitude
+residuals for \gps.  For the rest of this article, we ignore these
+features and concentrate on the tree-ring features.
 
 In order to suppress the large-scale structures for a quantitative
@@ -645,5 +650,5 @@
 $\sigma_{w}$.  (Note that, since the measured $\sigma$ of stellar
 objects is biased down by the weighting function, this is not quite
-the same as having $\sigma_{w} = 1.6$ times the true PSF $\sigma$, see
+the same as having $\sigma_{w} = 1.6$ times the true PSF $\sigma$; see
 discussion in \citealt{magnier2017.analysis}).  For each stellar
 detection, we extract the values $M_{xx,xy,yy} = \sum F_i w_i (x^2, x
@@ -677,23 +682,19 @@
 PSF ellipticity from the $e_1$ term.
 
-Figure~\ref{fig:smear.by.filter} shows the spatial trend of $e_0$, the {\em
-  smear}.  This value corresponds to the increase or decrease in
-the circularly-symmetric component of the image size.  The dynamic
-range of these images is -0.3 to +0.3 pixel$^2$. A tree-ring
-pattern is visible for all 5 filters, though \yps is dominated by the
-fringing pattern.  Structures with relatively low spatial frequencies
-can also be seen.
-
-Figure~\ref{fig:shear.by.filter} shows the spatial trend of $e_2$, the
-{\em shear}.  This value is positive definite and is plotted with a
-color scale ranging from -0.02 to 0.22 pixel$^2$.  We can also
-determine the orientation of the corresponding ellipse.  Overlayed on
+Figure~\ref{fig:smear.by.filter} 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
+dominated by the fringing pattern.  Structures with relatively low
+spatial frequencies can also be seen.
+
+Figure~\ref{fig:shear.by.filter} 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
 ellipse orientation as a function of postion.  The length of the
-vectors corresponds to the value of $\sigma^2_{major} -
-\sigma^2_{minor}$.  The tree-ring structure is {\em not} apparent
-in this figure for any filter.  The spatial variations are
-low-frequency and unrelated to the radial trend from the upper-left
-corner.
+vectors corresponds to the value of $e_2$.  The tree-ring structure is
+{\em not} apparent in this figure for any filter.  The spatial
+variations are low-frequency and unrelated to the radial trend from
+the upper-left corner.
 
 \subsection{Correlations Between Tree-Ring Patterns}
@@ -741,17 +742,16 @@
 signal further.
 
-To quantatatively compare the tree-ring trends between
-filters and between the types of measurements, we need to measure the
-tree-ring structure explicitly and filter out the other effects if
-possible.  To do this, we have applied a high-pass filter to all of
-the relevant images (PSF photometry residuals, astrometric residuals
-in the radial direction, flat-field residuals, and second moment smear
-terms) to remove unrelated spatial structures.  We have then measured
-the median of the signal in radial bins centered on (-5,4960) across
-an arc from $\phi$ = -20\degrees\ to -50\degrees (as measured relative
-to the top row of the images.  We have selected a small fraction of
-the arc to minimize the error associated with the choice of the
-pattern center and to avoid several bad cells near the bottom of the
-chip.
+To quantitatively compare the tree-ring trends between filters and
+between the types of measurements, we need to measure the tree-ring
+structure explicitly and filter out the other effects if possible.  To
+do this, we have applied a high-pass filter to all of the relevant
+images (PSF photometry residuals, astrometric residuals in the radial
+direction, flat-field residuals, and second moment smear terms) to
+remove unrelated spatial structures.  We have then measured the median
+of the signal in radial bins centered on (-5,4960) across an arc from
+$\phi$ = -20\degrees\ to -50\degrees (as measured relative to the top
+row of the images).  We have selected a small fraction of the arc to
+minimize the error associated with the choice of the pattern center
+and to avoid several bad cells near the bottom of the chip.
 
 % \note{include the arc on one of the figures?}
@@ -852,7 +852,7 @@
 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
+(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
@@ -862,5 +862,5 @@
 residual values without a derivative.  We are convinced that we have
 the sense of the derivative correct by examination of specific
-features in each imaage.
+features in each image.
 
 \begin{table}
@@ -988,5 +988,5 @@
 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 is affecting both the ellipticity
+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
@@ -996,5 +996,5 @@
 astrometry residuals shows that these two effects are connected.
 Although the correlation is weak in Figure~\ref{fig:dsmear.vs.astrom},
-careful inspection of the location of the these two tree ring patterns
+careful inspection of the location of these two tree ring patterns
 shows that the locations of the rings in the radial astrometric
 residual images occurs at the boundaries between regions with
@@ -1019,32 +1019,31 @@
 between these regions.
 
-We interpret the changes in the {\em smear} term as changes in the
-amount of charge diffusion as the photoelectrons travel to the bottom
-of the pixel well.  The blue filters exhibit the strongest changes in
-the amount of smear.  These are also the filters for which the
-detected electrons have travelled the longest distance in the silicon,
-and are thus most affected by diffusion effects.  Charge diffusion (as
-opposed to the charge drift caused by the lateral electric fields)
-results in a Gaussian smearing of the stellar profile: as the
-photoelectrons migrate from the site where they were generated by the
-incoming photon to the bottom of the pixel well, they follow a random
-walk in the plane of the detector.  The longer the electrons take to
-make the journey down to the bottom of the pixel, the further they are
-able to wander from their creation coordinate in the detector.
-Following the discussion in \cite{Holland.2003}, the amount of charge
-diffusion is thus related to the velocity of the electrons in the
-direction of the optical axis: $\sigma \sim \sqrt{2Dt}$ where $\sigma$
-is the size of the smearing kernel, $t$ is the time required for the
-electrons to traverse the thickness of the silicon wafer, and $D$ is
-the diffusion coefficient.  The velocity of the photoelectron, and
-thus the time to traverse the silicon, is related to the vertical
-electric fields in the silicon, which are caused by a combination of
-the applied voltages and the distribution of the space charges from
-the dopant.  As shown by \cite{Holland.2003}, the charge diffusion is
-related to the space charge density by $\sigma \sim
-\rho^{-\frac{1}{2}}$ (their equation 6).  Regions with high space
-charge densities increase the migration speed of the photoelectrons
-and reduce the amount of charge diffusion smearing; and vice versa for
-regions of low space-charge densities. 
+We interpret the changes in the smear term as changes in the amount of
+charge diffusion as the photoelectrons travel to the bottom of the
+pixel well.  The blue filters exhibit the strongest changes in the
+amount of smear.  These are also the filters for which the detected
+electrons have travelled the longest distance in the silicon, and are
+thus most affected by diffusion effects.  Charge diffusion (as opposed
+to the charge drift caused by the lateral electric fields) results in
+a Gaussian smearing of the stellar profile: as the photoelectrons
+migrate from the site where they were generated by the incoming photon
+to the bottom of the pixel well, they follow a random walk in the
+plane of the detector.  The longer the electrons take to make the
+journey down to the bottom of the pixel, the further they are able to
+wander from their creation coordinate in the detector.  Following the
+discussion in \cite{Holland.2003}, the amount of charge diffusion is
+thus related to the velocity of the electrons in the direction of the
+optical axis: $\sigma \sim \sqrt{2Dt}$ where $\sigma$ is the size of
+the smearing kernel, $t$ is the time required for the electrons to
+traverse the thickness of the silicon wafer, and $D$ is the diffusion
+coefficient.  The velocity of the photoelectron, and thus the time to
+traverse the silicon, is related to the vertical electric fields in
+the silicon, which are caused by a combination of the applied voltages
+and the distribution of the space charges from the dopant.  As shown
+by \cite{Holland.2003}, the charge diffusion is related to the space
+charge density by $\sigma \sim \rho^{-\frac{1}{2}}$ (their equation
+6).  Regions with high space charge densities increase the migration
+speed of the photoelectrons and reduce the amount of charge diffusion
+smearing; and vice versa for regions of low space-charge densities.
 
 In summary, the variations in the space-charge density caused by
@@ -1075,9 +1074,9 @@
 \section{Conclusion}
 
-The tree rings observed in the Pan-STARRS GPC1 data show (at least)
-two effects, though they are related.  First, the images are
-experiencing circularly-symmetric changes in the PSF size correlated
-with the tree-ring pattern.  These PSF size changes drive errors in
-the PSF photometry on the scale of a few millimagnitudes, are also
+The tree rings observed in the Pan-STARRS GPC1 data show two different
+effects, though they are related.  First, the images are experiencing
+circularly-symmetric changes in the PSF size correlated with the
+tree-ring pattern.  These PSF size changes drive errors in the PSF
+photometry on the scale of a few millimagnitudes, and are also
 correlated with the tree-ring pattern.  These PSF size changes are
 consistent with changes in the charge diffusion, which also introduces
@@ -1085,6 +1084,6 @@
 
 In addition, there are radial plate-scale changes correlated with the
-tree rings.  These plate-scale changes introduce a flat-field errors
-on the scale of \approx 1 millimagnitude and astrometric errors in the
+tree rings.  These plate-scale changes introduce flat-field errors on
+the scale of \approx 1 millimagnitude and astrometric errors on the
 scale of 2-3 milliarcseconds.  The observed relationship between the
 flat-field deviations and the radial derivative of the astrometric
@@ -1154,5 +1153,5 @@
 Lorand University (ELTE) and the Los Alamos National Laboratory.
 
-\note{Ken: please add NASA ops grants}
+% \note{Ken: please add NASA ops grants}
 
 \bibliographystyle{apj}