Index: trunk/doc/release.2015/systematics.20140411/systematics.tex =================================================================== --- trunk/doc/release.2015/systematics.20140411/systematics.tex (revision 40105) +++ trunk/doc/release.2015/systematics.20140411/systematics.tex (revision 40108) @@ -94,13 +94,13 @@ $3\pi$ survey to characterize the behavior of the deep-depletion devices used in the Pan-STARRS\,1 Gigapixel Camera. We have -identified systematic variations in the photometric behavior and -stellar profiles which are similar to the so-called tree rings +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 +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 range and resulting charge +in the vertical charge transportation rate and resulting charge diffusion variations. \end{abstract} @@ -110,4 +110,6 @@ \section{INTRODUCTION}\label{sec:intro} + +\note{KCC says: note what is unique to GPC1 vs other cameras} CCD detectors have evolved greatly since they were first introduced @@ -148,5 +150,5 @@ 1990s \citep{Holland.1996}, CCDs made from thick, high-resistivity ($ > 10 k\Omega$-cm) silicon were developed for astronomical instruments -in the early 2000s\citep{Holland.2003}. The high-resistivity of the +in the early 2000s \citep{Holland.2003}. The high-resistivity of the silicon allows for depletion regions of hundreds of microns in depth, compared to \approx 10\micron\ for the low-resistivity silicon. This @@ -158,8 +160,8 @@ to be absorbed, increasing quantum efficiency in the red. Because these thick, deep-depletion devices have near-unity quantum efficiency -across the whole a very wide spectral range, they have become the -design of choice for many modern, large-scale CCD cameras (e.g., -Pan-STARRS GPC1, \citealt{2009amos.confE..40T}; Subaru Hypersuprime -Camera, \citealt{2010SPIE.7735E..3FK}; Dark Energy Survey Camera, +across a very wide spectral range, they have become the design of +choice for many modern, large-scale CCD cameras (e.g., Pan-STARRS +GPC1, \citealt{2009amos.confE..40T}; Subaru Hypersuprime Camera, +\citealt{2010SPIE.7735E..3FK}; Dark Energy Survey Camera, \citealt{2015AJ....150..150F}). @@ -174,7 +176,7 @@ The effects of lateral electric fields are likewise identified as the -cause of the so-called ``Tree-Rings'' observed in the flat-field, +cause of the so-called ``Tree Rings'' observed in the flat-field, astrometry, and photometry response of thick deep depletion detectors -\citep{2014PASP..126..750P}. These tree-ring patterns have been noted +\citep{2014PASP..126..750P}. These Tree-Ring patterns have been noted in the flat-field response of deep depletion devices since their early testing \citep[see, e.g., Figure 2 in][]{2010SPIE.7735E..1RE} and were @@ -219,12 +221,13 @@ 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, the telescope has been operated by the Pan-STARRS New Science -Consortium (PSNSC). 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}. +2014, operations have been supported primarily by NASA's Near Earth +Object Observation program, see \cite{wainscoat.2015}. 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}. % 2004SPIE.5489..667H == PS1.optics @@ -310,5 +313,5 @@ the relatively small number of images available at the time. We have found that a single flat-field set can be used for all PS1 -observations to yield photometric consistency at the level of \approx +observations to yield photometric systematic errors at the level of \approx 2\%. PS1 benefits in this regard from the stability of having a single instrument which is rarely removed. @@ -319,5 +322,5 @@ aperture photometry performed using an aperture defined based on the image quality observed for a given chip. The aperture diameter is set -to be \approx 3.75 times the FWHM for the image. +to be 3.75 times the FWHM for the image. To improve the photometric systematic errors beyond the level achieved @@ -331,12 +334,13 @@ correction determined during the ubercal analysis \citep[see][]{2012ApJ...756..158S} consisted of an $8\times 8$ grid of -corrections for each GPC1 chip 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 systmatic uncertainties in the range 7 - 12 -millimagnitudes, depending on the filter \citep{2013ApJS..205...20M}. +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}. For all objects, positions are measured from the PSF model for the @@ -371,31 +375,31 @@ \end{table} -For many of the GPC1 OTA CCDs, we observe a pattern in the photometric -residuals which is similar in appearence to the Tree Rings described -in the Dark Energy Camera (DECam) by \cite{2014PASP..126..750P}. This -pattern consists of systematic deviations which are consistent in a -set of circular arcs centered on the corner of the CCD, as shown in -Figure~\ref{fig:psfmags.by.filter}. The details of the analysis used -to generate Figure~\ref{fig:psfmags.by.filter} are given below. For -now, we note that the GPC1 CCDs are constructed by dividing the -circular silicon wafer into 4 inscribed squares. Thus the corners of -the CCDs lie in the center of the silicon boule, just as the center of -the circular Tree Rings described by \cite{2014PASP..126..750P} match -the center of the boule from which they came. This gives the -impression that a similar mechanism is responsible for the pattern -observed in the PS1 photometry and the DECam photometry, namely the -diffusive effects of lateral electric field variations in the -detectors. In the next section, we will make the case that the -patterns observed in the PS1 photometry residuals are {\em not} caused -by this mechanism, but are instead caused by variations in the {\em - vertical} electric field (the field direction perpendicular to the -CCD surface). +For many of the GPC1 OTA CCDs, we observe a spatial pattern in the +photometric residuals for each device which is similar in appearence +to the Tree Rings described in the Dark Energy Camera (DECam) by +\cite{2014PASP..126..750P}. This pattern consists of systematic +deviations which are consistent in a set of circular arcs centered on +the corner of the CCD, as shown in Figure~\ref{fig:psfmags.by.filter}. +The details of the analysis used to generate +Figure~\ref{fig:psfmags.by.filter} are given below. For now, we note +that the GPC1 CCDs are constructed by dividing the circular silicon +wafer into 4 inscribed squares. Thus the corners of the CCDs lie in +the center of the silicon boule, just as the center of the circular +Tree Rings described by \cite{2014PASP..126..750P} match the center of +the boule from which they came. This gives the impression that a +similar mechanism is responsible for the pattern observed in the PS1 +photometry and the DECam photometry, namely the diffusive effects of +lateral electric field variations in the detectors. In the next +section, we will make the case that the patterns observed in the PS1 +photometry residuals are {\em not} caused by this mechanism, but are +instead caused by variations in the {\em vertical} electric field (the +field direction perpendicular to the CCD surface). First, in this section, we will describe how we have measured the -presence or absence of these tree-ring patterns in 5 types of data. +presence or absence of these Tree-Ring patterns in 5 types of data. 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, +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 @@ -408,15 +412,16 @@ type of measurement. To generate the photometry, astrometry, or second-moment plots, measurements were extracted from the PV0 DVO -database for observations covering the region ($\alpha$,$\delta$) = -(90\degree\ -- 150\degree, -25\degree\ -- 10\degree). This region of -the sky provides a fairly high density of stars, but avoids the -Galactic Plane where confusion may potentially contaminate the -measurement. We limit the analysis to good measurements -(\ippmisc{PSF_QF} $>$ 0.85) of likely stars ($|m_{psf} - m_{aper}| < -0.2$). Only measurements with instrumental magnitude $< -8.0$ -($-2.5\log \mbox{cts sec}^{-1} < -8.0$) are included to ensure +database \citep{magnier.2017.calibration} for observations covering +the region ($\alpha$,$\delta$) = (90\degree\ -- 150\degree, +-25\degree\ -- 10\degree). This region of the sky provides a fairly +high density of stars, but avoids the Galactic Plane where confusion +may potentially contaminate the measurement. We limit the analysis to +good measurements (\ippmisc{PSF_QF} $>$ 0.85, see +\citealt{magnier.2017.analysis}) of likely stars ($|m_{psf} - +m_{aper}| < 0.2$). Only measurements with instrumental magnitude $< +-8.0$ ($-2.5\log \mbox{cts sec}^{-1} < -8.0$) are included to ensure reasonable signal-to-noise per measurement. We require at least 2 -measurements in a given filter and 5 measurements total for any star -included in the analysis. +measurements in a given filter and at least 5 measurements total for +any star included in the analysis. \subsection{Photometric Residuals} @@ -428,6 +433,6 @@ \parbox{\figwidth}{\includegraphics[width=\figwidth]{\picdir/dmag.g.\plotext}} \parbox{\figwidth}{ -\caption{PSF Magnitude residuals by Filter - } \label{fig:psfmags.by.filter}} +\caption{PSF Magnitude residuals by Filter. \note{expand colorscale + bars, make clearer labels} } \label{fig:psfmags.by.filter}} \includegraphics[width=\figwidth]{\picdir/dmag.r.\plotext} @@ -468,5 +473,5 @@ millimagnitudes for all 5 plots. -The tree-ring pattern is clearly visible for the four blue filters, +The Tree-Ring pattern is clearly visible for the four blue filters, but finging dominates the pattern for \yps. Small offsets of individual cells are also apparent for \zps. While the patterns are @@ -481,5 +486,5 @@ Figure~\ref{fig:apmags.by.filter} shows the equivalent measurement for aperture photometry instead of PSF photometry. The finging -pattern again dominates the plot for \yps, but the tree-rings are not +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 which is not observed in the PSF magnitudes. While the per-pixel @@ -518,15 +523,15 @@ Y| > 0.5$ arcsec before measuring the median values for each superpixel. We have determined the approximate center of the circular -tree-ring pattern as (-5,4960) for this particular chip. 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). +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). 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-like +from -20 to +20 milliarcseconds for all 5 plots. A Tree-Ring-like pattern is visible for all five filters, with systematic structures -following a circular pattern centered on the chip corner.; the finging +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 is listed in @@ -562,15 +567,17 @@ obtained 2011 Feb 09 as part of a campaign to study the PS1 system response \citep{2012ApJ...750...99T}. Flats were obtain in a set of -4nm steps. To enhance the signal-to-noise, we have median-combined a -set of 6 flats at the center of the corresponding filter. - -In order to mask pixels which do not flatten well, we generate a -a copy of the image smoothed with a Gaussian kernel with -$\sigma = 1.5 pixels$. Any pixels in the smoothed image which deviate -from the median value in the image by more than 4 standard deviations -is masked. We generate the superpixel image by averaging the unmasked -pixels associated with each superpixel. We then high-pass filter the -superpixel image by subtracting a copy smoothed with a Gaussian of -$\sigma = 3.0$. +4nm steps sampling the spectral response curve of each filter. To +enhance the signal-to-noise, we have median-combined a set of 6 flats +at the wavelength center of the corresponding filter. + +In order to mask pixels which do not flatten well, we generate a copy +of the image smoothed with a Gaussian kernel with $\sigma = 1.5$ +pixels. Any pixels in the smoothed image which deviate from the +median value in the image by more than 4 standard deviations are +masked. We generate the superpixel image by averaging the unmasked +pixels associated with each superpixel. In order to suppress +large-scale gradients in the flat-field response, we high-pass filter +the superpixel image by subtracting a copy smoothed with a Gaussian of +$\sigma = 3.0$. Figure~\ref{fig:flats.by.filter} shows the remaining high-frequency @@ -584,8 +591,12 @@ measured flux in those pixels, and thus a {\em negative} deviation in $\delta m_{psf}$ as defined above. The dynamic range of the color -scale in these plots is -0.01 to +0.01. The tree-ring-like pattern is +scale in these plots is -0.01 to +0.01. The Tree-Ring-like pattern is strong in the (\gps,\rps,\ips) images, but nearly swamped by fringing in \zps, and completely lost to finging in \yps. A diagonal banding similar to the aperture residuals is seen in \gps. + +\note{CZW asks about the blob in the flat-field response. KCC asks + about the brick-wall pattern. discuss these and fringing so we can + move on to the tree rings} \subsection{Second Moments} @@ -641,6 +652,6 @@ detection, we extract the values $M_{xx,xy,yy} = \sum F_i w_i (x^2, x y, y^2) / \sum F_i w_i$. For each exposure, we find the median second -moments for PSF objects on this chip (XY40) and subtract that median -value from the instantaneous measurements of $M_{xx,xy,yy}$. We then +moments for PSF objects on this chip (XY40) and subtract those median +values from the instantaneous measurements of $M_{xx,xy,yy}$. We then determine the median of the residual second moments for each superpixel, resulting in 3 images ($\delta M_{xx,xy,yy}$) for each @@ -661,15 +672,16 @@ e_2 & = & \sigma^2_{\mbox{major}} - \sigma^2_{\mbox{minor}} \end{eqnarray} -Where $\sigma_{\mbox{major}}$ and $\sigma_{\mbox{minor}}$ 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. +Where $\sigma_{\mbox{major}}$ and $\sigma_{\mbox{minor}}$ 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 $e_0$, 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-like +range of these images is -0.3 to +0.3 pixel$^2$. A Tree-Ring-like pattern is visible for all 5 filters, though \yps is dominated by the fringing pattern. Structures with relatively low spatial frequencies @@ -683,5 +695,5 @@ 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-like structure is {\em not} apparent +\sigma^2_{minor}$. The Tree-Ring-like 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 @@ -692,4 +704,5 @@ \begin{table} \caption{Systematic Trends : Correlations by filter\label{table:correlation.by.filter}} +\note{reconsider the column order} % \tiny \begin{center} @@ -708,17 +721,17 @@ \end{table} -Tree-ring-like patterns are clearly seen in 4 of the measurement types +Tree-Ring-like patterns are clearly seen in 4 of the measurement types above: the PSF photometry, the astrometry, the flat-field, and the smear terms. As discussed above, the signal-to-noise per pixel in the plots of the systematic trends is relatively low (\approx 1.0). While -the tree-ring-like patterns are apparent in many of these figures, +the Tree-Ring-like patterns are apparent in many of these figures, there are also some other systematic structures which may degrade the signal further. -To quantatatively compare the tree-ring-like trends between +To quantatatively compare the Tree-Ring-like 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 +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 +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 @@ -730,4 +743,8 @@ chip. +\note{include the arc on one of the figures?} + +\note{do plots of all filter pairs in a triangle? is that interesting?} + For a given type of measurement, the systematic effect is strongly correlated between filters. The strongest correlation is the smear @@ -738,5 +755,5 @@ filters, as shown in Figure~\ref{fig:psfmag.trends}. Here, the \yps\ correlation with \gps\ is quite weak: the fringing pattern -dominates the tree-rings for PSF photometry. The radial component of +dominates the Tree Rings for PSF photometry. The radial component of the astrometric residual is also well correlated between filters, with no loss of correlation due to fringing in \yps. Finally, the @@ -749,5 +766,5 @@ 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 +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. @@ -758,5 +775,5 @@ \begin{center} \includegraphics[width=\figwidth]{\picdir/smear.trends.\plotext} -\caption{Smear : correlation between filters +\caption{Smear : correlation between filters \note{include trend slopes in plots?} } \label{fig:smear.trends} \end{center} @@ -793,7 +810,7 @@ \end{figure*} -An important question is the relationship of the tree-ring-like +An important question is the relationship of the Tree-Ring-like pattern between the different types of measurements. Different models -for the tree-ring structures make different predictions about the +for the Tree-Ring structures make different predictions about the correlations between different effects. Note the very different spatial structure between the different measurements in a given @@ -817,6 +834,6 @@ 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 +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 @@ -885,8 +902,8 @@ (Figure~\ref{fig:smear.by.filter}), the measurement shows that the intrinsic size of the stellar images is varying in a radial sense -between the different tree-ring regions. Although images experience +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-like regions are consistently somewhat +in the different Tree-Ring-like regions are consistently somewhat larger or somewhat smaller than that average. @@ -895,24 +912,25 @@ the PSF, allowing for some spatial variation in the shape. However, we have a limited number of stars to measure any spatial variation. -Thus the 2D variation are sampled on a very coarse (e.g., 3x3) grid -for each chip: the PSF parameters may vary smoothly across the chip -following the bilinear interpolation between the 3x3 grid points. -Thus, the spatial scale on which we model PSF variations is much -larger than the spatial scale on which PSF variations are apparently -occuring, as illustrated by the changes in the smear plot. 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 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. +Thus the 2D variation are sampled on a very coarse (e.g., $3 \times +3$) grid for each chip: the PSF parameters may vary smoothly across +the chip following the bilinear 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 +apparently occuring, as illustrated by the changes in the smear plot. +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 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 relationship between the flat-field residual and the astrometric gradient is consistent with radial variations in the plate-scale. The -tree-rings observed by DES are completely attributed to effective +Tree-Rings observed by DES are completely attributed to effective plate scale changes. Effective plate scale changes would result in flat-field deviations since the flat-field illumination is a source of @@ -927,9 +945,9 @@ The fact that the PSF ellipticity changes are {\em not} correlated -with the tree ring structure tells us that the effective plate-scale -changes seen in the flat-field and astrometry signals are not also the +with the Tree-Ring structure tells us that 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 +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 @@ -953,9 +971,9 @@ \section{Conclusion} -The tree rings observed in the Pan-STARRS GPC1 data show (at least) +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 which the are also correlated with the tree ring +with the Tree-Ring pattern. These PSF size changes drive errors in +the PSF photometry which the are also correlated with the Tree-Ring pattern on the scale of a few millimagnitudes. These PSF size changes are consistent with changes in the charge diffusion, which also @@ -963,5 +981,5 @@ In addition, there are radial plate-scale changes correlated with the -tree rings. These plate-scale changes introduce a flat-field errors +Tree Rings. These plate-scale changes introduce a flat-field errors on the scale of \approx 1 millimagnitude and astrometric errors in the scale of 2-3 milliarcseconds. The observed relationship between the @@ -970,8 +988,11 @@ in][]{2014PASP..126..750P}. -The vertical diffusion variations and the lateral charge migration are -both driven by the same variations in the doping structures. This -point is clear from the spatial correlation of the gradient in the -smear variations and the astrometric variations. +The spatial correlation of the gradient in the smear variations and +the astrometric variations imply that both of these two types of tree +ring effects are related, even though they manifest through different +mechanisms. We suspect that the variations in both the vertical charge +diffusion and the lateral charge migration are driven by changes +in the electric field structures in the silicon due to the same +variations in the doping structures in the silicon. % The small-scale variations in the charge diffusion observed in these @@ -1029,4 +1050,6 @@ Lorand University (ELTE) and the Los Alamos National Laboratory. +\note{add NASA ops grant(s)} + \bibliographystyle{apj} \bibliography{lib}{}