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9696$3\pi$ survey to characterize the behavior of the deep-depletion
9797devices used in the Pan-STARRS\,1 Gigapixel Camera.  We have
98 identified systematic spatial variations in the photometric behavior and
99 stellar profiles which are similar to the so-called tree rings''
100 identified in devices used by other wide-field cameras (DECam and
101 Hypersuprime Camera).  The tree-ring features identified in these
102 other cameras result from lateral electric fields which displace the
103 electrons as they are transported in the silicon to the pixel
104 location.  In contrast, we show that the photometric and morphological
105 modifications observed in the GPC1 detectors are caused by variations
106 in the vertical charge transportation rate and resulting charge
107 diffusion variations.
98identified systematic spatial variations in the photometric
99measurements and stellar profiles which are similar in pattern to the
100so-called tree rings'' identified in devices used by other
101wide-field cameras (e.g., DECam and Hypersuprime Camera).  The
102tree-ring features identified in these other cameras result from
103lateral electric fields which displace the electrons as they are
104transported in the silicon to the pixel location.  In contrast, we
105show that the photometric and morphological modifications observed in
106the GPC1 detectors are caused by variations in the vertical charge
107transportation rate and resulting charge diffusion variations.
108108\end{abstract}
109109

125125trap electrons, specifically those generated by absorbed photons.  The
126126thick silicon substrate required illumination from the front'' side
127 with the thin gate structures to allow the photons to reach the
127containing the thin gate structures to allow the photons to reach the
128128depletion region and be detected.  These early CCDs had modest quantum
129 efficiency as photons were easily absorbed by the several micron thick
129efficiency as photons were easily absorbed by the several-micron-thick
130130gate structures.  For an excellent review of the history of CCD
131131development, see \cite{1992ASPC...23....1J}.

137137delicate device only \approx 10 - 20\micron\ thick, exposing the
138138depletion region on the backside.  Photons entering the backside of
139 the device are not blocked by the gate structures and thus more easily
140 absorbed and detected.  Thinned backside-illuminated CCDs have high
141 quantum efficiency to blue photons.  However, as the wavelength
139the device are not blocked by the gate structures and are thus more
140easily absorbed and detected.  Thinned backside-illuminated CCDs have
141high quantum efficiency to blue photons.  However, as the wavelength
142142increases beyond \approx 800 nm, the silicon becomes more transparent
143 to the photons, with a corresponding drop in quantum efficiency for
144 red photons.  In addition, thin film interference between the entering
143to the photons with a corresponding drop in quantum efficiency for
144red photons.  In addition, thin-film interference between the entering
145145photons and those reflecting off the front side of the CCD result in
146146fringe'' patterns for redder photons.

167167
168168While these deep-depletion CCDs seem to be ideal, they do have
169 features which can cause challenges for precise measurements.  As a
170 result of the Brighter-Fatter Effect''
169features which can cause challenges for precise measurements.  For
170example, as a result of the Brighter-Fatter Effect''
171171\citep{2014JInst...9C3048A,2015JInst..10C5032G}, the profile of bright
172172stars are measured to be wider than the profiles of faint stars.  The

177177The effects of lateral electric fields are likewise identified as the
178178cause of the so-called tree rings'' observed in the flat-field,
179 astrometry, and photometry response of thick deep depletion detectors
179astrometry, and photometry response of thick deep-depletion detectors
180180\citep{2014PASP..126..750P}.  These tree-ring patterns have been noted
181181in the flat-field response of deep depletion devices since their early

189189silicon.  The changes in the effective area result in changes to the
190190apparent flat-field response as well as the astrometric response of
191 the detector.  More subtly, the flat-field response changes, since
192 they do not reflect actual variations in sensitivity, can lead to
193 systematic photometry errors for astronomical sources if the
194 flat-field images are used in the standard fashion.
191the detector.  More subtly, the changes in the flat-field response,
192since they do not reflect actual variations in sensitivity, can lead
193to systematic photometry errors for astronomical sources if flat-field
194images are used in the standard fashion.
195195
196196In 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
198 observe the pixel effective area changes caused by lateral electric
199 fields as described by \cite{2014PASP..126..750P}, we show below a
200 second effect which is more important in driving systematic photometry
197of tree-ring pattern observed in the Pan-STARRS\,1 Gigapixel Camera 1
198CCDs.  Although we also observe the changes in effective pixel area
199caused by lateral electric fields as described by
200\cite{2014PASP..126..750P}, we show below a second effect which is
201more important in these devices in driving systematic photometry
201202errors.  We find that variations in charge diffusion, also resulting
202203from changes in the silicon doping structures, affect both the
203204observed stellar profiles as well as the photometry measured with
204205profile fitting techniques.  In Section~\ref{sec:PS1}, we discuss the
205 Pan-STARRS telescope, camera, and survey data used in this analysis.
206 In Section~\ref{sec:tree.rings}, we present the tree-ring
207 patterns as observed in several different types of measurements:
208 flat-field response, systematic photometry residuals, systematic
209 astrometric residuals, and stellar profile shape variations.  In
206Pan-STARRS\,1 telescope, camera, and survey data used in this analysis.
207In Section~\ref{sec:tree.rings}, we present the tree-ring patterns as
208observed in several different types of measurements: flat-field
209response, systematic photometric residuals, systematic astrometric
210residuals, and stellar profile shape variations.  In
210211Section~\ref{sec:discussion}, we discuss the interpretation of
211212patterns we observe and present a simple model to explain the observed

219220Haleakala on the Hawaiian island of Maui, has been surveying the sky
220221regularly since May 2010 \citep{chambers2017}.  From May 2010 through
221 March 2014, PS1 was run under the aegis of the Pan-STARRS Science
222 Consortium to perform a set of wide-field science surveys; since March
223 2014, operations have been supported primarily by NASA's Near Earth
224 Object Observation program, see \cite{2015IAUGA..2251124W}.  Under the
225 PS1SC, the largest survey, both in terms of area of the sky covered
226 ($3\pi$ steradians) and fraction of observing time (56\%), was the
227 \TPS\ in which the entire sky north of Declination $-30$\degrees\ was
228 imaged up \approx 80 times over 4 years.  These observations were
229 distributed over five filters, \grizy, and have been astrometrically
230 and photometrically calibrated to good precision
231 \citep{magnier2017.calibration}.
222March 2014, PS1 was run under the aegis of the Pan-STARRS\,1 Science
223Consortium (PS1SC) to perform a set of wide-field science surveys;
224since March 2014, operations have been supported primarily by NASA's
225Near Earth Object Observation program
226\citep[see][]{2015IAUGA..2251124W}.  Under the PS1SC, the largest
227survey, both in terms of area of the sky covered ($3\pi$ steradians)
228and fraction of observing time (56\%), was the \TPS\ in which the
229entire sky north of Declination $-30$\degrees\ was imaged \approx 80
230times over 4 years.  These observations were distributed over five
231filters, \grizy, and have been astrometrically and photometrically
232calibrated to good precision \citep{magnier2017.calibration}.
232233
233234% 2004SPIE.5489..667H == PS1.optics

237238The wide-field PS1 telescope optics \citep{2004SPIE.5489..667H} image
238239a 3.3 degree field of view on a 1.4 gigapixel camera
239 \citep[GPC1][]{2009amos.confE..40T}, with low distortion and generally
240\citep[GPC1;][]{2009amos.confE..40T}, with low distortion and generally
240241good image quality.  The median seeing for the \TPS\ data vary
241242somewhat by filter: (\grizy) = (1.31, 1.19, 1.11, 1.07, 1.02)

244245University of Hawaii's Institute for Astronomy operations on Maui.
245246
246 GPC1 \citep{2009amos.confE..40T}, currently the largest astronomical
247 camera in terms of number of pixels, consists of a mosaic of 60
248 edge-abutted $4800\times4800$ pixel detectors, with 10~$\mu$m pixels
249 subtending 0.258~arcsec. These CCID58 detectors, manufactured by
250 Lincoln Laboratory, are 75\micron-thick back-illuminated CCDs
251 \citep{2006amos.confE..47T,2008SPIE.7021E..05T}.  Initial performance
252 assessments are presented in \cite{2008SPIE.7014E..0DO}. The active,
253 usable pixels cover \approx 80\% of the FOV.
247GPC1, currently the largest astronomical camera in terms of number of
248pixels, consists of a mosaic of 60 edge-abutted $4800\times4800$ pixel
249detectors, with 10~$\mu$m pixels subtending 0.258~arcsec. These CCID58
250detectors, manufactured by Lincoln Laboratory, are 75\micron-thick
251back-illuminated CCDs \citep{2006amos.confE..47T,2008SPIE.7021E..05T}.
252Initial performance assessments are presented in
253\cite{2008SPIE.7014E..0DO}. The active, usable pixels cover \approx
25480\% of the FOV.
254255
255256\subsection{Data Processing and Calibration}

268269objects).  In addition, the \TPS\ dataset has been re-processed
269270several times with improved calibration and analysis techniques.  To
270 date (2017 July), 3 re-processings starting from raw pixel data have
271 been performed.  The labels PV0, PV1, PV2, PV3 are used identify the
272 nightly processing and successive re-processing versions.  PV3 has
271date (2017 September), 3 re-processings starting from raw pixel data
272have been performed.  The labels PV0, PV1, PV2, PV3 are used identify
273the nightly processing and successive re-processing versions.  PV3 has
273274been used for the public release of the Pan-STARRS \TPS\ data via the
274275{\it Barbara A. Mikulski Archive for Space Telescopes} (MAST) at the
275 Space Telescope Science Institute.\footnote{http//panstarrs.stci.edu}
276Space Telescope Science Institute.\footnote{http//panstarrs.stsci.edu}
277The process of the construction of this database and the schema
278details are discussed in detail by \cite{flewelling2017}.
276279
277280The data processing and calibration operations are discussed in detail

328331photometry is re-calibrated within the databasing system based on the
329332properties of the measured photometry.  The calibration process is
330 discussed by
331 \cite{2012ApJ...756..158S,2013ApJS..205...20M,magnier2017.calibration}.
332 As part of this process, several flat-field corrections have been
333 determined.  For the PV2 analysis discussed here, a flat-field
334 correction determined during the ubercal analysis
335 \citep[see][]{2012ApJ...756..158S} consisted of an $8\times 8$ grid of
336 corrections for each GPC1 chip, corresponding to a correction for each
337 OTA cell'' and filter for each of 4 seasons.  The boundaries of
338 those seasons are tentatively identified with modifications to the
339 baffle structures or the system optics.  The critical point here is
340 that the final effective flat-field image for the PV2 dataset is based
341 on a dome-flat at the highest resolution, with very low resolution
342 corrections based on photometry, resulting in photometric systematic
343 uncertainties in the range 7 - 12 millimagnitudes, depending on the
344 filter \citep{2013ApJS..205...20M}.
333discussed by \cite{2012ApJ...756..158S} and
334\cite{2013ApJS..205...20M,magnier2017.calibration}.  As part of this
335process, several flat-field corrections have been determined.  For the
336PV2 analysis discussed here, a flat-field correction determined during
337the ubercal analysis \citep[see][]{2012ApJ...756..158S} consisted of
338an $8\times 8$ grid of corrections for each GPC1 chip, corresponding
339to a correction for each OTA cell'' and filter for each of 4
340seasons.  The boundaries of those seasons are tentatively identified
341with modifications to the baffle structures or the system optics.  The
342critical point here is that the final effective flat-field image for
343the PV2 dataset is based on a dome-flat at the highest resolution,
344with very low resolution (hundreds of pixels) corrections based on
345photometry, resulting in photometric systematic uncertainties in the
346range 7 - 12 millimagnitudes, depending on the filter
347\citep{2013ApJS..205...20M}.
345348
346349For all objects, positions are measured from the PSF model for the

400403For all of these examples, we use a single GPC1 CCD (XY40) to
401404illustrate the effects in detail, but a similar set of effects are
402 seen in many of the GPC1 detectors.  First, we show the residual PSF
403 photometry.  Second, we show the residual aperture photometry.  Third,
404 we show the astrometric residual patterns.  Fourth, we show the
405 patterns observed in the flat-field images.  Finally, we show
406 measurements derived from the second-moments of the stars.
405seen in many, if not all, of the GPC1 detectors with varying
406strengths.  First, we show the residual PSF photometry.  Second, we
407show the residual aperture photometry.  Third, we show the astrometric
408residual patterns.  Fourth, we show the patterns observed in the
409flat-field images.  Finally, we show measurements derived from the
410second-moments of the stars.
407411
408412For all effects discussed below, we are measuring the mean value of

486490aperture photometry instead of PSF photometry.  The finging
487491pattern again dominates the plot for \yps, but the tree rings are not
488 seen in any of the filters.  A diagonal pattern is visible in \gps
492seen in any of the filters.  A diagonal pattern is visible in \gps\
489493which is not observed in the PSF magnitudes.  While the per-pixel
490494scatter is somewhat (10\% to 20\%) higher for these aperture

523527superpixel.  We have determined the approximate center of the circular
524528tree-ring pattern as (-5,4960) for this particular chip based on the
525 pattern of the X astrometry displacements.  Using this coordinate as the center
526 of the pattern, we have converted the $\delta X,\delta Y$ offsets into
527 $\delta R,\delta \theta$ measurements ($\delta R$ : radial component
528 away from the center, $\delta \theta$ : tangential component).
529pattern of the X astrometry displacements.  Using this coordinate as
530the center of the pattern, we have converted the $\delta X,\delta Y$
531offsets into $\delta R,\delta \theta$ measurements ($\delta R$ :
532radial component away from the center of the pattern, $\delta \theta$
533: tangential component).
529534
530535Figure~\ref{fig:astrom.by.filter} shows the 2D patterns of $\delta R$

534539following a circular pattern centered on the chip corner; the finging
535540pattern is not apparent in the \yps\ astrometry.  The per-pixel
536 standard deviations of these plots area listed in
541standard deviations of these plots are listed in
537542Table~\ref{table:sigmas.by.filter}.  The signal-to-noise of these
538543structures is again somewhat weak, but the pattern is clearly visible

588593strong in the (\gps,\rps,\ips) images, but nearly swamped by fringing
589594in \zps, and completely lost to finging in \yps.  A diagonal banding
590 pattern is seen in \gps: this features is thought to be due to the
591 lithography process used to generate the CCD.  A blob can also been
592 seen covering 4 cells near the center of this chip; this is apparently
593 a deposit of some kind on the detector.  Both of the latter two
594 effects behave like quantum efficiency variations and are removed well
595 by standard flat-field techniques.  Note that a small amount of the
596 diagonal banding pattern remains in the aperture magnitude residuals
597 for \gps.  For the rest of this article, we ignore these features and
598 concentrate on the tree ring features.
595pattern is also seen in \gps: this feature is thought to be due to
596the lithography process used to generate the CCD.  A blob can also
597been seen covering 4 cells near the center of this chip; this is
598apparently a deposit of some kind on the detector.  Both of the latter
599two effects behave like quantum efficiency variations and are removed
600well by standard flat-field techniques.  Note that a small amount of
601the diagonal banding pattern remains in the aperture magnitude
602residuals for \gps.  For the rest of this article, we ignore these
603features and concentrate on the tree-ring features.
599604
600605In order to suppress the large-scale structures for a quantitative

645650$\sigma_{w}$.  (Note that, since the measured $\sigma$ of stellar
646651objects is biased down by the weighting function, this is not quite
647 the same as having $\sigma_{w} = 1.6$ times the true PSF $\sigma$, see
652the same as having $\sigma_{w} = 1.6$ times the true PSF $\sigma$; see
648653discussion in \citealt{magnier2017.analysis}).  For each stellar
649654detection, we extract the values $M_{xx,xy,yy} = \sum F_i w_i (x^2, x 677682PSF ellipticity from the$e_1$term. 678683 679 Figure~\ref{fig:smear.by.filter} shows the spatial trend of$e_0$, the {\em 680 smear}. This value corresponds to the increase or decrease in 681 the circularly-symmetric component of the image size. The dynamic 682 range of these images is -0.3 to +0.3 pixel$^2$. A tree-ring 683 pattern is visible for all 5 filters, though \yps is dominated by the 684 fringing pattern. Structures with relatively low spatial frequencies 685 can also be seen. 686 687 Figure~\ref{fig:shear.by.filter} shows the spatial trend of$e_2$, the 688 {\em shear}. This value is positive definite and is plotted with a 689 color scale ranging from -0.02 to 0.22 pixel$^2$. We can also 690 determine the orientation of the corresponding ellipse. Overlayed on 684Figure~\ref{fig:smear.by.filter} shows the spatial trend of the smear, 685$e_0$. The dynamic range of these images is -0.3 to +0.3 pixel$^2$. A 686tree-ring pattern is visible for all 5 filters, though \yps\ is 687dominated by the fringing pattern. Structures with relatively low 688spatial frequencies can also be seen. 689 690Figure~\ref{fig:shear.by.filter} shows the spatial trend of the shear, 691$e_2$. This value is positive definite and is plotted with a color 692scale ranging from -0.02 to 0.22 pixel$^2$. Overlayed on 691693Figure~\ref{fig:shear.by.filter} is a set of vectors representing the 692694ellipse orientation as a function of postion. The length of the 693 vectors corresponds to the value of$\sigma^2_{major} -
694 \sigma^2_{minor}$. The tree-ring structure is {\em not} apparent 695 in this figure for any filter. The spatial variations are 696 low-frequency and unrelated to the radial trend from the upper-left 697 corner. 695vectors corresponds to the value of$e_2$. The tree-ring structure is 696{\em not} apparent in this figure for any filter. The spatial 697variations are low-frequency and unrelated to the radial trend from 698the upper-left corner. 698699 699700\subsection{Correlations Between Tree-Ring Patterns} 741742signal further. 742743 743 To quantatatively compare the tree-ring trends between 744 filters and between the types of measurements, we need to measure the 745 tree-ring structure explicitly and filter out the other effects if 746 possible. To do this, we have applied a high-pass filter to all of 747 the relevant images (PSF photometry residuals, astrometric residuals 748 in the radial direction, flat-field residuals, and second moment smear 749 terms) to remove unrelated spatial structures. We have then measured 750 the median of the signal in radial bins centered on (-5,4960) across 751 an arc from$\phi$= -20\degrees\ to -50\degrees (as measured relative 752 to the top row of the images. We have selected a small fraction of 753 the arc to minimize the error associated with the choice of the 754 pattern center and to avoid several bad cells near the bottom of the 755 chip. 744To quantitatively compare the tree-ring trends between filters and 745between the types of measurements, we need to measure the tree-ring 746structure explicitly and filter out the other effects if possible. To 747do this, we have applied a high-pass filter to all of the relevant 748images (PSF photometry residuals, astrometric residuals in the radial 749direction, flat-field residuals, and second moment smear terms) to 750remove unrelated spatial structures. We have then measured the median 751of the signal in radial bins centered on (-5,4960) across an arc from 752$\phi$= -20\degrees\ to -50\degrees (as measured relative to the top 753row of the images). We have selected a small fraction of the arc to 754minimize the error associated with the choice of the pattern center 755and to avoid several bad cells near the bottom of the chip. 756756 757757% \note{include the arc on one of the figures?} 852852astrometric residual is anti-correlated with the flat-field residual 853853errors:$\frac{\partial \delta R}{\partial radius} \sim \delta flat$854 (see Figure~\ref{fig:dastrom.vs.flat}. This last relationship is 855 somewhat weakly measured. Because of the periodic nature of the Tree 856 Rings, it is also difficult to be completely certain that the 854(see Figure~\ref{fig:dastrom.vs.flat}). This last relationship is 855somewhat weakly measured. Because of the periodic nature of the tree 856rings, it is also difficult to be completely certain that the 857857flat-field is proportional to the derivative of the astrometry 858858residual, rather than the astrometry residual being proportional to 862862residual values without a derivative. We are convinced that we have 863863the sense of the derivative correct by examination of specific 864 features in each imaage. 864features in each image. 865865 866866\begin{table} 988988below the pixel-to-pixel noise in the aperture magnitude residuals. 989989It is likely in our opinion that the plate-scale changes causing the 990 flat-field and astrometry effects is affecting both the ellipticity 990flat-field and astrometry effects are affecting both the ellipticity 991991and the aperture magnitudes, but the level of the effect is too small 992992to see given the other systematic structures (in the shear plot) and 996996astrometry residuals shows that these two effects are connected. 997997Although the correlation is weak in Figure~\ref{fig:dsmear.vs.astrom}, 998 careful inspection of the location of the these two tree ring patterns 998careful inspection of the location of these two tree ring patterns 999999shows that the locations of the rings in the radial astrometric 10001000residual images occurs at the boundaries between regions with 10191019between these regions. 10201020 1021 We interpret the changes in the {\em smear} term as changes in the 1022 amount of charge diffusion as the photoelectrons travel to the bottom 1023 of the pixel well. The blue filters exhibit the strongest changes in 1024 the amount of smear. These are also the filters for which the 1025 detected electrons have travelled the longest distance in the silicon, 1026 and are thus most affected by diffusion effects. Charge diffusion (as 1027 opposed to the charge drift caused by the lateral electric fields) 1028 results in a Gaussian smearing of the stellar profile: as the 1029 photoelectrons migrate from the site where they were generated by the 1030 incoming photon to the bottom of the pixel well, they follow a random 1031 walk in the plane of the detector. The longer the electrons take to 1032 make the journey down to the bottom of the pixel, the further they are 1033 able to wander from their creation coordinate in the detector. 1034 Following the discussion in \cite{Holland.2003}, the amount of charge 1035 diffusion is thus related to the velocity of the electrons in the 1036 direction of the optical axis:$\sigma \sim \sqrt{2Dt}$where$\sigma$1037 is the size of the smearing kernel,$t$is the time required for the 1038 electrons to traverse the thickness of the silicon wafer, and$D$is 1039 the diffusion coefficient. The velocity of the photoelectron, and 1040 thus the time to traverse the silicon, is related to the vertical 1041 electric fields in the silicon, which are caused by a combination of 1042 the applied voltages and the distribution of the space charges from 1043 the dopant. As shown by \cite{Holland.2003}, the charge diffusion is 1044 related to the space charge density by$\sigma \sim
1045 \rho^{-\frac{1}{2}}$(their equation 6). Regions with high space 1046 charge densities increase the migration speed of the photoelectrons 1047 and reduce the amount of charge diffusion smearing; and vice versa for 1048 regions of low space-charge densities. 1021We interpret the changes in the smear term as changes in the amount of 1022charge diffusion as the photoelectrons travel to the bottom of the 1023pixel well. The blue filters exhibit the strongest changes in the 1024amount of smear. These are also the filters for which the detected 1025electrons have travelled the longest distance in the silicon, and are 1026thus most affected by diffusion effects. Charge diffusion (as opposed 1027to the charge drift caused by the lateral electric fields) results in 1028a Gaussian smearing of the stellar profile: as the photoelectrons 1029migrate from the site where they were generated by the incoming photon 1030to the bottom of the pixel well, they follow a random walk in the 1031plane of the detector. The longer the electrons take to make the 1032journey down to the bottom of the pixel, the further they are able to 1033wander from their creation coordinate in the detector. Following the 1034discussion in \cite{Holland.2003}, the amount of charge diffusion is 1035thus related to the velocity of the electrons in the direction of the 1036optical axis:$\sigma \sim \sqrt{2Dt}$where$\sigma$is the size of 1037the smearing kernel,$t$is the time required for the electrons to 1038traverse the thickness of the silicon wafer, and$D$is the diffusion 1039coefficient. The velocity of the photoelectron, and thus the time to 1040traverse the silicon, is related to the vertical electric fields in 1041the silicon, which are caused by a combination of the applied voltages 1042and the distribution of the space charges from the dopant. As shown 1043by \cite{Holland.2003}, the charge diffusion is related to the space 1044charge density by$\sigma \sim \rho^{-\frac{1}{2}}\$ (their equation
10456).  Regions with high space charge densities increase the migration
1046speed of the photoelectrons and reduce the amount of charge diffusion
1047smearing; and vice versa for regions of low space-charge densities.
10491048
10501049In summary, the variations in the space-charge density caused by

10751074\section{Conclusion}
10761075
1077 The tree rings observed in the Pan-STARRS GPC1 data show (at least)
1078 two effects, though they are related.  First, the images are
1079 experiencing circularly-symmetric changes in the PSF size correlated
1080 with the tree-ring pattern.  These PSF size changes drive errors in
1081 the PSF photometry on the scale of a few millimagnitudes, are also
1076The tree rings observed in the Pan-STARRS GPC1 data show two different
1077effects, though they are related.  First, the images are experiencing
1078circularly-symmetric changes in the PSF size correlated with the
1079tree-ring pattern.  These PSF size changes drive errors in the PSF
1080photometry on the scale of a few millimagnitudes, and are also
10821081correlated with the tree-ring pattern.  These PSF size changes are
10831082consistent with changes in the charge diffusion, which also introduces

10851084