Index: /trunk/doc/release.2015/systematics.20140411/systematics.tex =================================================================== --- /trunk/doc/release.2015/systematics.20140411/systematics.tex (revision 40119) +++ /trunk/doc/release.2015/systematics.20140411/systematics.tex (revision 40120) @@ -12,4 +12,5 @@ \RequirePackage{color} \RequirePackage{code} +\RequirePackage{pbox} \input{astro.sty} @@ -95,7 +96,7 @@ 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 +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 @@ -110,6 +111,4 @@ \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 @@ -176,12 +175,12 @@ 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 initially considered to be a sensitivity response which could be removed with a flat-field. As discussed in detail by -\cite{2014PASP..126..750P}, these Tree Rings are more correctly +\cite{2014PASP..126..750P}, these tree rings are more correctly interpretted as variations in the effective pixel area due to migration of the electrons pushed by lateral electric fields induced @@ -195,5 +194,5 @@ 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 +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 @@ -204,5 +203,5 @@ 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-like +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 @@ -222,5 +221,5 @@ 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{wainscoat.2015}. Under the +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 @@ -353,11 +352,11 @@ milliarcsecond for individual measurements of brighter stars. -\section{Tree-Ring-Like Patterns} +\section{Tree-Ring Patterns} \label{sec:tree.rings} \begin{table} -\caption{Systematic Trends : Stdev by filter\label{table:sigmas.by.filter}} % \tiny \begin{center} +\caption{Systematic Trends : Standard deviation by filter\label{table:sigmas.by.filter}} \begin{tabular}{|l|rrrrr|} \hline @@ -377,5 +376,5 @@ 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 +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 @@ -386,5 +385,5 @@ 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 +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 @@ -397,5 +396,5 @@ 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 @@ -412,5 +411,5 @@ type of measurement. To generate the photometry, astrometry, or second-moment plots, measurements were extracted from the PV0 DVO -database \citep{magnier.2017.calibration} for observations covering +database \citep{magnier2017.calibration} for observations covering the region ($\alpha$,$\delta$) = (90\degree\ -- 150\degree, -25\degree\ -- 10\degree). This region of the sky provides a fairly @@ -418,5 +417,5 @@ 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 ($|m_{psf} - +\citealt{magnier2017.analysis}) of likely stars ($|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 @@ -428,34 +427,33 @@ % PSF Magnitudes -\def\figwidth{2.75in} -\begin{figure*}[htbp] -\begin{center} -\parbox{\figwidth}{\includegraphics[width=\figwidth]{\picdir/dmag.g.\plotext}} -\parbox{\figwidth}{ -\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} -\includegraphics[width=\figwidth]{\picdir/dmag.i.\plotext} - -\includegraphics[width=\figwidth]{\picdir/dmag.z.\plotext} -\includegraphics[width=\figwidth]{\picdir/dmag.y.\plotext} +\def\figwidth{5.2in} +\def\jumpleft{-2.6in} +\def\capwidth{2.4in} +\begin{figure*}[htbp] +\begin{center} +\parbox[b]{\figwidth}{\includegraphics[width=\figwidth]{\picdir/dmag.\plotext}} +\hspace{\jumpleft} +\parbox[b]{\capwidth}{ +\caption{PSF Magnitude residuals by filter (\grizy). White boxes are + GPC1 cells which have been masked due to poor response. Superpixels + representing regions of $10\times10$ pixels are used to determine + the median deviation for measurements at the given chip pixel + location compared with the average photometry for the given + object.} \label{fig:psfmags.by.filter}} \end{center} \end{figure*} % Aperture Magnitudes -\def\figwidth{2.75in} -\begin{figure*}[htbp] -\begin{center} -\parbox{\figwidth}{\includegraphics[width=\figwidth]{\picdir/dapmag.g.\plotext}} -\parbox{\figwidth}{ -\caption{Aperture Magnitude residuals by Filter - } \label{fig:apmags.by.filter}} - -\includegraphics[width=\figwidth]{\picdir/dapmag.r.\plotext} -\includegraphics[width=\figwidth]{\picdir/dapmag.i.\plotext} - -\includegraphics[width=\figwidth]{\picdir/dapmag.z.\plotext} -\includegraphics[width=\figwidth]{\picdir/dapmag.y.\plotext} +\begin{figure*}[htbp] +\begin{center} +\parbox[b]{\figwidth}{\includegraphics[width=\figwidth]{\picdir/dapmag.\plotext}} +\hspace{\jumpleft} +\parbox[b]{\capwidth}{ +\caption{Aperture Magnitude residuals by filter (\grizy). White boxes + are GPC1 cells which have been masked due to poor response. + Superpixels representing regions of $10\times10$ pixels are used to + determine the median deviation for measurements at the given chip + pixel location compared with the average photometry for the given + object. } \label{fig:apmags.by.filter}} \end{center} \end{figure*} @@ -473,10 +471,10 @@ 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 clear across the image, the signal-to-noise of the structures per pixel is not very strong in these images. The per-pixel standard -deviations of these plots is listed in +deviations of these plots are listed in Table~\ref{table:sigmas.by.filter}. The per-pixel standard deviation is comparable to the amplitude of the correlated structures, so we @@ -486,5 +484,5 @@ 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 @@ -497,17 +495,17 @@ % astrometry radial term -\def\figwidth{2.75in} -\begin{figure*}[htbp] -\begin{center} -\parbox{\figwidth}{\includegraphics[width=\figwidth]{\picdir/drad.g.\plotext}} -\parbox{\figwidth}{ -\caption{astrometric radial-direction residuals by Filter - } \label{fig:astrom.by.filter}} - -\includegraphics[width=\figwidth]{\picdir/drad.r.\plotext} -\includegraphics[width=\figwidth]{\picdir/drad.i.\plotext} - -\includegraphics[width=\figwidth]{\picdir/drad.z.\plotext} -\includegraphics[width=\figwidth]{\picdir/drad.y.\plotext} +\begin{figure*}[htbp] +\begin{center} +\parbox[b]{\figwidth}{\includegraphics[width=\figwidth]{\picdir/drad.\plotext}} +\hspace{\jumpleft} +\parbox[b]{\capwidth}{ +\caption{Astrometric residuals of the displacement in the radial + direction, relative to the chip coordinate -5,4960 (upper left + corner), by filter (\grizy). White boxes are GPC1 cells which have + been masked due to poor response. Superpixels representing regions + of $10\times10$ pixels are used to determine the median deviation + for measurements at the given chip pixel location compared with the + average astrometry for the given + object. } \label{fig:astrom.by.filter}} \end{center} \end{figure*} @@ -523,5 +521,5 @@ 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 based on the +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 @@ -531,9 +529,9 @@ 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 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 -standard deviations of these plots is listed in +standard deviations of these plots area 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 @@ -543,17 +541,15 @@ % flat-field residual -\def\figwidth{2.75in} -\begin{figure*}[htbp] -\begin{center} -\parbox{\figwidth}{\includegraphics[width=\figwidth]{\picdir/dflat.g.\plotext}} -\parbox{\figwidth}{ -\caption{Flat-field high-frequency structues by Filter - } \label{fig:flats.by.filter}} - -\includegraphics[width=\figwidth]{\picdir/dflat.r.\plotext} -\includegraphics[width=\figwidth]{\picdir/dflat.i.\plotext} - -\includegraphics[width=\figwidth]{\picdir/dflat.z.\plotext} -\includegraphics[width=\figwidth]{\picdir/dflat.y.\plotext} +\begin{figure*}[htbp] +\begin{center} +\parbox[b]{\figwidth}{\includegraphics[width=\figwidth]{\picdir/dflat.\plotext}} +\hspace{\jumpleft} +\parbox[b]{\capwidth}{ +\caption{Flat-field high-frequency structues, by filter (\grizy). + White boxes are GPC1 cells which have been masked due to poor + response. Flat-field images generated using a tunable laser have + been combined (see text); a smoothed version has been subtracted to + high-pass the response. Flat-field pixels are averaged for + $10\times10$ superpixels. } \label{fig:flats.by.filter}} \end{center} \end{figure*} @@ -576,11 +572,8 @@ 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 -structures in the flat-field images. These flat-field images are +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 displayed as fractional deviations relative to the median flat-field image and can thus be compared to the magnitude residuals. When @@ -591,48 +584,51 @@ 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 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} +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. + +In order to suppress the large-scale structures for a quantitative +analysis of the tree rings, we high-pass filter the superpixel image +by subtracting a copy smoothed with a Gaussian of $\sigma = 3.0$ +superpixels. \subsection{Second Moments} % Smear Images -\def\figwidth{2.75in} -\begin{figure*}[htbp] -\begin{center} -\parbox{\figwidth}{\includegraphics[width=\figwidth]{\picdir/smear.g.\plotext}} -\parbox{\figwidth}{ -\caption{Smear by filter - } \label{fig:smear.by.filter}} -% note that the caption wants to be vertically centered. I can push it up -% by padding the end with a big \vspace{1in} - -\includegraphics[width=\figwidth]{\picdir/smear.r.\plotext} -\includegraphics[width=\figwidth]{\picdir/smear.i.\plotext} - -\includegraphics[width=\figwidth]{\picdir/smear.z.\plotext} -\includegraphics[width=\figwidth]{\picdir/smear.y.\plotext} +\begin{figure*}[htbp] +\begin{center} +\parbox[b]{\figwidth}{\includegraphics[width=\figwidth]{\picdir/smear.\plotext}} +\hspace{\jumpleft} +\parbox[b]{\capwidth}{ +\caption{Average residual smear variations, by filter (\grizy). White + boxes are GPC1 cells which have been masked due to poor response. + The residual smear ($\sigma^2_{\mbox{major}} + \sigma^2_{\mbox{minor}}$) has been + determined after the after PSF second moments have been subtracted + for each image; these values are averaged for each $10\times10$ + superpixels. } \label{fig:smear.by.filter}} \end{center} \end{figure*} % Shear Images -\def\figwidth{2.75in} -\begin{figure*}[htbp] -\begin{center} -\parbox{\figwidth}{\includegraphics[width=\figwidth]{\picdir/shear.g.\plotext}} -\parbox{\figwidth}{ -\caption{Shear by Filter - } \label{fig:shear.by.filter}} - -\includegraphics[width=\figwidth]{\picdir/shear.r.\plotext} -\includegraphics[width=\figwidth]{\picdir/shear.i.\plotext} - -\includegraphics[width=\figwidth]{\picdir/shear.z.\plotext} -\includegraphics[width=\figwidth]{\picdir/shear.y.\plotext} +\begin{figure*}[htbp] +\begin{center} +\parbox[b]{\figwidth}{\includegraphics[width=\figwidth]{\picdir/shear.\plotext}} +\hspace{\jumpleft} +\parbox[b]{\capwidth}{ +\caption{Average residual shear variations, by filter (\grizy). White + boxes are GPC1 cells which have been masked due to poor response. + The residual shear ($\sigma^2_{\mbox{major}} - \sigma^2_{\mbox{minor}}$) has been + determined after the after PSF second moments have been subtracted + for each image; these values are averaged for each $10\times10$ + superpixels. } \label{fig:shear.by.filter}} \end{center} \end{figure*} @@ -683,5 +679,5 @@ 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 pattern is visible for all 5 filters, though \yps is dominated by the fringing pattern. Structures with relatively low spatial frequencies @@ -695,24 +691,39 @@ 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 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-Like Patterns} +\subsection{Correlations Between Tree-Ring Patterns} + +% All Effects in r-band +\begin{figure*}[htbp] +\begin{center} +\parbox[b]{\figwidth}{\includegraphics[width=5.0in]{\picdir/all.effects.r.\plotext}} +\caption{All 6 measured effects for \rps. This figure illustrates the + different spatial structure observed for each of the 6 patterns + measured in this work. The PSF magnitude (upper-left) and smear + residuals (lower-left) have a very clear common tree-ring structure, + while the astrometric residual (middle-left) and flat-field + residuals (middle-right) have their own common tree-ring pattern with + 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} +\end{center} +\end{figure*} \begin{table} +% \tiny +\begin{center} \caption{Systematic Trends : Correlations by filter\label{table:correlation.by.filter}} -\note{reconsider the column order} -% \tiny -\begin{center} \begin{tabular}{|l|rrrr|} \hline -{\bf Filter} & {\bf psf mags} & {\bf smear} & {\bf astrom} & {\bf flat} \\ +{\bf Filter} & {\bf smear} & {\bf psf mags} & {\bf astrom} & {\bf flat} \\ \hline \gps & 1.00 & 1.00 & 1.00 & 1.00 \\ -\rps & 0.84 & 0.78 & 0.84 & 0.76 \\ -\ips & 0.50 & 0.40 & 0.66 & 0.64 \\ -\zps & 0.26 & 0.16 & 0.37 & 0.33 \\ +\rps & 0.78 & 0.84 & 0.84 & 0.76 \\ +\ips & 0.40 & 0.50 & 0.66 & 0.64 \\ +\zps & 0.16 & 0.26 & 0.37 & 0.33 \\ \yps & 0.10 & 0.10 & 0.25 & 0.30 \\ \hline @@ -721,15 +732,15 @@ \end{table} -Tree-Ring-like patterns are clearly seen in 4 of the measurement types +Tree-ring 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 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 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 @@ -743,7 +754,7 @@ chip. -\note{include the arc on one of the figures?} - -\note{do plots of all filter pairs in a triangle? is that interesting?} +% \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 @@ -755,5 +766,5 @@ 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 @@ -766,5 +777,5 @@ 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. @@ -775,5 +786,7 @@ \begin{center} \includegraphics[width=\figwidth]{\picdir/smear.trends.\plotext} -\caption{Smear : correlation between filters \note{include trend slopes in plots?} +\caption{Correlation of the smear ($\sigma^2_{\mbox{major}} + + \sigma^2_{\mbox{minor}}$) signal in \gps\ with the other 4 bands: + \rps\ (upper-left), \ips\ (upper-right), \zps\ (lower-left), \yps\ (lower-right). } \label{fig:smear.trends} \end{center} @@ -785,5 +798,7 @@ \begin{center} \includegraphics[width=\figwidth]{\picdir/psfmag.trends.\plotext} -\caption{PSF magnitude residuals : correlation between filters +\caption{Correlation of the PSF magnitude residuals ($\delta m_{psf}$) + in \gps\ with the other 4 bands: \rps\ (upper-left), \ips\ + (upper-right), \zps\ (lower-left), \yps\ (lower-right). } \label{fig:psfmag.trends} \end{center} @@ -795,5 +810,7 @@ \begin{center} \includegraphics[width=\figwidth]{\picdir/astrom.trends.\plotext} -\caption{Astrometry residuals : correlation between filters +\caption{Correlation of the radial astrometric residual displacement ($\delta R$) + in \gps\ with the other 4 bands: \rps\ (upper-left), \ips\ + (upper-right), \zps\ (lower-left), \yps\ (lower-right). } \label{fig:astrom.trends} \end{center} @@ -805,12 +822,13 @@ \begin{center} \includegraphics[width=\figwidth]{\picdir/flat.trends.\plotext} -\caption{Flat-field rings : correlation between filters -} \label{fig:flat.trends} -\end{center} -\end{figure*} - -An important question is the relationship of the Tree-Ring-like +\caption{Correlation of the flat-field tree-ring structures in \gps\ + with the other 4 bands: \rps\ (upper-left), \ips\ (upper-right), \zps\ + (lower-left), \yps\ (lower-right). } \label{fig:flat.trends} +\end{center} +\end{figure*} + +An important question is the relationship of the tree-ring pattern between the different types of measurements. Different models -for the Tree-Ring structures make different predictions about the +for the tree-ring structures make different predictions about the correlations between different effects. Note the very different spatial structure between the different measurements in a given @@ -846,7 +864,7 @@ \begin{table} +% \tiny +\begin{center} \caption{Systematic Trends : Correlations between trends\label{table:correlation.by.trend}} -% \tiny -\begin{center} \begin{tabular}{|l|rrr|} \hline @@ -868,5 +886,8 @@ \begin{center} \includegraphics[width=\figwidth]{\picdir/smear.vs.psfmag.\plotext} -\caption{Smear vs PSF mag residuals on the rings +\caption{Correlation of the PSF magnitude residuals ($\delta m_{PSF}$) + with the smear ($\sigma^2_{\mbox{major}} + \sigma^2_{\mbox{minor}}$) + signal for \gps\ (upper-left), \rps\ (upper-right), \ips\ (lower-left), + \zps\ (lower-right). } \label{fig:smear.vs.psfmag} \end{center} @@ -878,5 +899,10 @@ \begin{center} \includegraphics[width=\figwidth]{\picdir/dsmear.vs.astrom.\plotext} -\caption{gradient of the Smear vs astrometry residuals on the rings +\caption{ +Correlation of the radial astrometric residual displacement ($\delta +R$) with the derivative of the smear ($\partial +\sigma^2_{\mbox{major}} + \sigma^2_{\mbox{minor}}$) signal with +respect to the radial postion for \gps\ (upper-left), \rps\ +(upper-right), \ips\ (lower-left), \zps\ (lower-right). } \label{fig:dsmear.vs.astrom} \end{center} @@ -888,5 +914,9 @@ \begin{center} \includegraphics[width=\figwidth]{\picdir/dastrom.vs.flat.\plotext} -\caption{gradient of the astrometry residuals vs flat-field rings +\caption{ +Correlation of the derivative of the radial astrometric residual +displacement ($\delta R$) with respect to the radial position with the +flat-field tree-ring signal for \gps\ (upper-left), \rps\ (upper-right), +\ips\ (lower-left), \zps\ (lower-right). } \label{fig:dastrom.vs.flat} \end{center} @@ -896,29 +926,30 @@ \label{sec:discussion} -These trends help to illuminate the underlying causes of these -different effects. +These trends measured above (Section~\ref{sec:tree.rings}) help to +illuminate the underlying causes of these different effects. First, if we consider the smear pattern (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 +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-like regions are consistently somewhat +in the different tree-ring regions are consistently somewhat larger or somewhat smaller than that average. -Next, we can explain the relationship between the PSF photometry -residuals and the observed smear: 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 measure any spatial variation. -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. +Next, we can explain the correlation between the PSF photometry +residuals and the observed smear (Figure~\ref{fig:smear.vs.psfmag}). +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 +measure any spatial variation. Thus the 2D variations 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 actually occuring, as illustrated +by the changes in the smear plot (Figure~\ref{fig:smear.by.filter}). 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 +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 @@ -930,60 +961,132 @@ 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 -plate scale changes. Effective plate scale changes would result in -flat-field deviations since 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 such a model, the -flat-field deviations are $-1 \times \frac{\partial Pos}{\partial R}$. -The slope of our relationship is \approx 0.5 in normalized units. -Thus the observed trends appear to be too weak by a factor of \approx -2, but otherwise exhibits the expected behavior. +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. 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 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 -magnitudes. +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 is 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. The -underlying connection is the pattern of the resistivity variations. -Regions with high (or low) resistivity show relatively high (or low) -amounts of smear; astrometric deviations follow the gradient between -these regions. +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 +shows that the locations of the rings in the radial astrometric +residual images occurs at the boundaries between regions with +substantially different values of the smear signal. + +We suggest that the underlying connection between all of these +tree-ring effects is the pattern of the doping variations in the +silicon. As discussed by \cite{2014PASP..126..750P}, the tree-ring +patterns seen by the DES team are caused by lateral electic fields in +the detector silicon (in the plane of the CCD wafer) generated by +variations in the space charges embedded in the silicon, in turn +coming from low-level changes in the doping as the silicon boule is +grown. We conclude that the astrometric and flat-field variations +seen in our detectors are caused by these same types of doping +variations. The changes in the smear (and thus the PSF magnitudes) +are apparently also related to the doping variations. The lateral +electric fields which introduce the astrometry and flat-field +variations occur at the boundary between regions with higher and lower +space charges from the dopant. Regions with high (or low) space +charge density thus correspond to regions with relatively high (or +low) amounts of smear; the astrometric deviations follow the gradient +between these regions. We interpret the changes in the {\em smear} term as changes in the -amount of charge diffusion. 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. - -\note{add more quantitative discussion of the variations in $E_y$ vs $E_x$?} +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 +variations in the dopant result in regions of higher and lower charge +diffusion, and in turn regions with PSF photometry systematic +residuals. The lateral gradients in the space-charge density induce +lateral electric fields which in turn cause lateral motions of the +photoelectrons, resulting in astrometric and flat-field deviations. + +The DES team did not detect these charge diffusion variations. In +that case, the amplitude of the photometric effects due to the lateral +field are dominant; these include both the modification of the +flat-field as well as PSF fitting errors due to the changing PSF sizes +introduced by the varying effective pixels sizes. If the smearing +effect reported here were as large for DES compared with the lateral +PSF size changes as they are for GPC1, then the reported PSF +photometry residuals for would have had very different +characteristics. We conclude that, for DES, the lateral effects are +much larger than the diffusion variations, compared with GPC1. The +relative amplitude of these two effects depends on the details of the +applied voltages, the amplitude of the space-charge density variations +compared with the typical space-charge density, and the detector +thicknesses. It is beyond the scope of this article to model these +effects in detail. + +% http://adsabs.harvard.edu/abs/2006NIMPA.568...41K \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 -pattern on the scale of a few millimagnitudes. These PSF size changes -are consistent with changes in the charge diffusion, which also -introduces a circularly symmetric smearing. +with the tree-ring pattern. These PSF size changes drive errors in +the PSF photometry on the scale of a few millimagnitudes, are also +correlated with the tree-ring pattern. These PSF size changes are +consistent with changes in the charge diffusion, which also introduces +a circularly symmetric smearing. 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 flat-field deviations and the radial derivative of the astrometric -deviations confirms this interpretation \citep[see discussion +deviations confirms this interpretation \citep[see also discussion in][]{2014PASP..126..750P}. @@ -991,5 +1094,5 @@ 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 +mechanisms. We conclude 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 @@ -1050,5 +1153,5 @@ Lorand University (ELTE) and the Los Alamos National Laboratory. -\note{add NASA ops grant(s)} +\note{Ken: please add NASA ops grants} \bibliographystyle{apj}