Index: trunk/doc/release.2015/systematics.20140411/systematics.tex =================================================================== --- trunk/doc/release.2015/systematics.20140411/systematics.tex (revision 40099) +++ trunk/doc/release.2015/systematics.20140411/systematics.tex (revision 40102) @@ -1,3 +1,4 @@ -\documentclass[iop,floatfix]{emulateapj} +% \documentclass[iop,floatfix]{emulateapj} +\documentclass[10pt,preprint]{aastex} % \pdfoutput=1 @@ -22,12 +23,12 @@ \def\plotext{ps} -\def\picdir{/home/eugene/chipresid.20140404} -%\def\picdir{/data/kukui.2/eugene/chipresid.20140404} +%\def\picdir{/home/eugene/chipresid.20140404} +\def\picdir{/data/kukui.2/eugene/chipresid.20140404} % Pick a terse version of the title here; -\shorttitle{Systematics in PS1} +\shorttitle{Charge Diffusion Variations in PS1} \shortauthors{E.A. Magnier et al} \begin{document} -\title{Systematic Effects in Pan-STARRS1 Photometry and Astrometry} +\title{Charge Diffusion Variations in Pan-STARRS\,1 CCDs} % this is a crude trick to get the order of affiliations right. These @@ -50,5 +51,5 @@ %PS Builder List % W.~S. Burgett,\altaffilmark{\IfA} -% K.~C. Chambers,\altaffilmark{\IfA} +K.~C. Chambers,\altaffilmark{\IfA} % L. Denneau,\altaffilmark{\IfA} % P. Draper,\altaffilmark{\DUR} @@ -85,14 +86,20 @@ \begin{abstract} -Lorem ipsum dolor sit amet, consectetur adipiscing elit. Vestibulum -bibendum nisi id tristique posuere. Duis eu mollis nulla. Maecenas est -turpis, mattis tempor urna vitae, placerat rhoncus sem. Lorem ipsum -dolor sit amet, consectetur adipiscing elit. Sed quis velit -nisl. Aliquam erat volutpat. Cras lacinia, nisl tristique auctor -molestie, dolor nulla rhoncus purus, ac accumsan nunc nunc ac -nibh. Maecenas vitae mollis mauris. Ut sollicitudin pulvinar purus, -eget luctus lorem tincidunt vitae. Vestibulum eu mattis neque. Nulla -in tortor id urna dapibus gravida a vel leo. - +Thick back-illuminated deep-depletion CCDs have superior quantum +efficiency over previous generations of thinned and traditional thick +CCDs. As a result, they are being used for major wide-field imaging +cameras in several projects. We use observations from the Pan-STARRS +$3\pi$ 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 in devices used by other wide-field cameras (DECam and +Hypersuprime Camera). The tree-ring features identified in these +other cameras result from lateral electric fields which displace the +electrons as they are transported in the silicon to the pixel +location. In contrast, we show that the photometric and morphological +modifications observed in the GPC1 detectors are caused by variations +in the vertical charge transportation range and resulting charge +diffusion variations. \end{abstract} @@ -102,17 +109,106 @@ \section{INTRODUCTION}\label{sec:intro} -\begin{verbatim} -* early CCDs were thick, but low resistivity Si had low cross-section to red photons -* thinning was used to improve the blue sensitivity, at the cost of further reducing the red sensitivity -* by the early 2000s, high-resistivity Si was used to make thick "deep-depletion" devices with good red and blue response. -* voltages? -* sky-scraper pixels -* Plazas et al and other effects -* -\end{verbatim} +CCD detectors have evolved greatly since they were first introduced +for astronomical imaging in the mid 1970s. In addition to the +well-known increases in the size of CCDs over the past 4 decades, CCD +architecture has gone through three major evolutionary stages. + +The first generation of CCDs used a silicon substrate a few hundred +microns thick on top of which gate structures were deposited to define +the pixels. A positive voltage applied to the gate layers would +create a shallow region (\approx 10 microns thick) in which the holes +were depleted. This ``depletion region'' acted as a potential well to +trap electrons, specifically those generated by absorbed photons. The +thick silicon substrate required illumination from the ``front'' side +with the thin gate structures to allow the photons to reach the +depletion region and be detected. These early CCDs had modest quantum +efficiency as photons were easily absorbed by the several micron thick +gate structures. For an excellent review of the history of CCD +development, see \cite{1992ASPC...23....1J}. + +Thinned, backside-illuminated CCDs such as the TI 3PCCD +\citep{1981SPIE..290....6B} were developed to address the quantum +efficiency limitations of the first generation thick CCDs. The +silicon substrate was removed using a chemical process, leaving a +delicate device only \approx 10 - 20\micron\ thick, exposing the +depletion region on the backside. Photons entering the backside of +the device are not blocked by the gate structures and thus more easily +absorbed and detected. Thinned backside-illuminated CCDs have high +quantum efficiency to blue photons. However, as the wavelength +increases beyond \approx 800 nm, the silicon becomes more transparent +to the photons, with a corresponding drop in quantum efficiency for +red photons. In addition, thin film interference between the entering +photons and those reflecting off the front side of the CCD result in +``fringe'' patterns for redder photons. + +Early generations of CCDs were made of low-resistivity (\approx 10 - +50 $\Omega$-cm) silicon. Following experiments beginning in the early +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 +silicon allows for depletion regions of hundreds of microns in depth, +compared to \approx 10\micron\ for the low-resistivity silicon. This +modification allows for a back-illuminated CCD with a relatively thick +silicon subtrate of 75 - 300\micron. Blue photons impinging on the +back of the device are absorbed near the back surface of the device +and are caried through the depletion region to the gates on the front +side. The thick silicon allows red photons to have a greater chance +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, +\citealt{2015AJ....150..150F}). + +While these deep-depletion CCDs seem to be ideal, they do have +features which can cause challenges for precise measurements. As a +result of the ``Brighter-Fatter Effect'' +\citep{2014JInst...9C3048A,2015JInst..10C5032G}, the profile of bright +stars are measured to be wider than the profiles of faint stars. The +accepted interpretation is that the electric fields produced by the +electrons accumulated from a star repel successive incoming electrons, +with the repulsion increasing the more electrons have accumulated. + +The effects of lateral electric fields are likewise identified as the +cause of the so-called ``Tree-Rings'' observed in the flat-field, +astrometry, and photometry response of thick deep depletion detectors +\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 +interpretted as variations in the effective pixel area due to +migration of the electrons pushed by lateral electric fields induced +by small changes in the doping used to set the resistivity of the +silicon. The changes in the effective area result in changes to the +apparent flat-field response as well as the astrometric response of +the detector. More subtly, the flat-field response changes, since +they do not reflect actual variations in sensitivity, can lead to +systematic photometry errors for astronomical sources if the +flat-field images are used in the standard fashion. + +In this paper, we examine the behavior of an apparently-similar kind +of Tree Ring observed in the Pan-STARRS GPC1 CCDs. Although we also +observe the pixel effective area changes caused by lateral electric +fields as described by \cite{2014PASP..126..750P}, we show below a +second effect which is more important in driving systematic photometry +errors. We find that variations in charge diffusion, also resulting +from changes in the silicon doping structures, affect both the +observed stellar profiles as well as the photometry measured with +profile fitting techniques. In Section~\ref{sec:PS1}, we discuss the +Pan-STARRS telescope, camera, and survey data used in this analysis. +In Section~\ref{sec:tree.rings}, we present the Tree-Ring-like +patterns as observed in several different types of measurements: +flat-field response, systematic photometry residuals, systematic +astrometric residuals, and stellar profile shape variations. In +Section~\ref{sec:discussion}, we discuss the interpretation of +patterns we observe and present a simple model to explain the observed +behavior. We conclude with a discussion of the implications of this +effect on astronomical measurements from deep depletion instruments \section{Pan-STARRS1} - -\note{tidy up this section} +\label{sec:PS1} The 1.8m Pan-STARRS\,1 telescope (PS1), located on the summit of @@ -121,12 +217,12 @@ 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 is operated by the Pan-STARRS New Science +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 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 the 4 years. These -observations were distributed over five filters, \grizy, and have been -astrometrically and photometrically calibrated to good precision -\citep{magnier2017.calibration}. +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 @@ -138,18 +234,17 @@ \citep[GPC1][]{2009amos.confE..40T}, with low distortion and generally good image quality. The median seeing for the \TPS\ data vary -somewhat by filter, with (\grizy) = (XXXX). Routine observations are -conducted remotely from the Advanced Technology Research Center in -Kula, the main facility of the University of Hawaii's Institute for -Astronomy operations on Maui. - -GPC1 \citep{2009amos.confE..40T}, currently the largest astronomical camera in -terms of number of pixels, consists of a mosaic of 60 edge-abutted -$4800\times4800$ pixel detectors, with 10~$\mu$m pixels subtending -0.258~arcsec. These \note{OTA51} detectors, manufactured by Lincoln -Laboratory, are \note{75$\mu$m}-thick back-illuminated CCDs with a -readout time of 7 seconds for a full unbinned image. \note{details - about the voltages?} Initial performance assessments are presented -in \cite{2008SPIE.7014E..0DO}. The active, usable pixels cover $\sim 80$\% of the -FOV. +somewhat by filter: (\grizy) = (1.31, 1.19, 1.11, 1.07, 1.02) +arcseconds. Routine observations are conducted remotely from the +Advanced Technology Research Center in Kula, the main facility of the +University of Hawaii's Institute for Astronomy operations on Maui. + +GPC1 \citep{2009amos.confE..40T}, currently the largest astronomical +camera in terms of number of pixels, consists of a mosaic of 60 +edge-abutted $4800\times4800$ pixel detectors, with 10~$\mu$m pixels +subtending 0.258~arcsec. These CCID58 detectors, manufactured by +Lincoln Laboratory, are 75\micron-thick back-illuminated CCDs +\citep{Tonry.2006,Tonry.2008}. Initial performance assessments are +presented in \cite{2008SPIE.7014E..0DO}. The active, usable pixels +cover \approx 80\% of the FOV. \subsection{Data Processing and Calibration} @@ -161,16 +256,17 @@ Images obtained by PS1 are processed by the Pan-STARRS Image -Processing Pipeline (IPP; \citealp{PS1_IPP,magnier2017.datasystem}). All observations are processed -nightly, with results sent to groups within the science consortium -(i.e., PS1SC during the \TPS) performing short-term science projects -(e.g., searching for transient and moving objects). In addition, the -\TPS\ dataset has been re-processed several times with improved -calibration and analysis techniques. To date (2017 July), 3 -re-processings starting from raw pixel data have been performed. The -labels PV0, PV1, PV2, PV3 are used identify the nightly processing and -successive re-processing versions. PV3 has been used for the public -release of the Pan-STARRS \TPS\ data via the {\it Barbara A. Mikulski - Archive for Space Telescopes} (MAST) at the Space Telescope Science -Institute.\footnote{http//panstarrs.stci.edu} +Processing Pipeline (IPP; +\citealp{2006amos.confE..50M,magnier2017.datasystem}). All +observations are processed nightly, with results sent to groups within +the science consortium (i.e., PS1SC during the \TPS) performing +short-term science projects (e.g., searching for transient and moving +objects). In addition, the \TPS\ dataset has been re-processed +several times with improved calibration and analysis techniques. To +date (2017 July), 3 re-processings starting from raw pixel data have +been performed. The labels PV0, PV1, PV2, PV3 are used identify the +nightly processing and successive re-processing versions. PV3 has +been used for the public release of the Pan-STARRS \TPS\ data via the +{\it Barbara A. Mikulski Archive for Space Telescopes} (MAST) at the +Space Telescope Science Institute.\footnote{http//panstarrs.stci.edu} The data processing and calibration operations are discussed in detail @@ -207,20 +303,19 @@ factors which may make the flat-field image inconsistent with stellar photometry, e.g., SED, filter band-pass variations, etc -\citep[see][]{waters2017,2004PASP..116..449M,magnier.belgium}. This -correction was made on a relatively coarse grid across the focal plane -in order to accumulate sufficient statistics from the stars in the -relatively small number of images available at the time. We have +\citep[see][]{waters2017,2004PASP..116..449M,2007ASPC..364..153M}. +This correction was made on a relatively coarse grid across the focal +plane in order to accumulate sufficient statistics from the stars in +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 -2\% \note{use the ubercal flat stdev as a statistic}. PS1 benefits in -this regard from the stability of having a single instrument which is -rarely removed. +2\%. PS1 benefits in this regard from the stability of having a +single instrument which is rarely removed. Photometry of the PS1 images is performed using a point-spread-function (PSF) model as well as multiple kinds of -apertures \citep{magnier2017.analysis}. In this analysis, we -refer to aperture photometry performed using an aperture defined based -on the image quality observed for a given chip. The aperture diameter -is set to be \note{XXX} times the FWHM for the image. +apertures \citep{magnier2017.analysis}. In this analysis, we refer to +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 improve the photometric systematic errors beyond the level achieved @@ -228,17 +323,18 @@ photometry is re-calibrated within the databasing system based on the properties of the measured photometry. The calibration process is -discussed by \cite{2012ApJ...756..158S,2013ApJS..205...20M,magnier2017.calibration}. +discussed by +\cite{2012ApJ...756..158S,2013ApJS..205...20M,magnier2017.calibration}. As part of this process, several flat-field corrections have been determined. For the PV2 analysis discussed here, a flat-field correction determined during the ubercal analysis -\citep[see][]{2012ApJ...756..158S} consisted of an $8\times 8$ grid of corrections -for each GPC1 chip and filter for each of 4 seasons. The boundaries -of those seasons are \note{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 -calibration with roughly 1 millimag consistency for each measurement -\note{better number from ubercal?}. +\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}. For all objects, positions are measured from the PSF model for the @@ -252,4 +348,5 @@ \section{Tree-Ring-Like Patterns} +\label{sec:tree.rings} \begin{table} @@ -274,7 +371,7 @@ 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{plazas.2014}. 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 +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 @@ -282,13 +379,14 @@ 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{plazas.2014} 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 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). +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 @@ -296,10 +394,9 @@ 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 \note{many? most?} GPC1 detectors. First, we show the -residual PSF photometry. Second, we show the residual Aperture -photometry. Third, we show the astrometric residual patterns. -Fourth, we show the patterns observed in the flat-field images. -Finally, we show measurements derived from the second-moments of the -stars. +seen in many of the GPC1 detectors. First, we show the residual PSF +photometry. Second, we show the residual Aperture photometry. Third, +we show the astrometric residual patterns. Fourth, we show the +patterns observed in the flat-field images. Finally, we show +measurements derived from the second-moments of the stars. For all effects discussed below, we are measuring the mean value of @@ -308,5 +405,5 @@ represents the same range of true GPC1 XY40 pixels regardless of the type of measurement. To generate the photometry, astrometry, or -second-moment measurements were extracted from the \note{PV0} DVO +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 @@ -358,5 +455,5 @@ Figure~\ref{fig:psfmags.by.filter} shows the 2D patterns of PSF -photometric residuals. In this case, we select PSF magnitude +photometry residuals. In this case, we select PSF magnitude measurements for detections of stars which fall in the given superpixel. We subtract each measurement from the average magnitude @@ -378,5 +475,5 @@ is comparable to the amplitude of the correlated structures, so we need to integrate along the radial structures to make stronger -statements about these patterns. \note{hanging statement?} +statements about these patterns. Figure~\ref{fig:apmags.by.filter} shows the equivalent measurement for @@ -462,7 +559,7 @@ then observed by the PS1 telescope. These flat-field images were 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, -with \note{XXnm} band-pass. To enhance the signal-to-noise, we have -median-combined a set of 6 flats at the center of the corresponding filter. +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 @@ -535,5 +632,5 @@ multiple detections). The second moments are measured with a Gaussian weighting function, with the $\sigma_{w}$ scaled by the PSF size so -that the $\sigma$ measured for PSF stars is \approx 60\% of +that the $\sigma$ measured for PSF stars is \approx 65\% of $\sigma_{w}$. (Note that, since the measured $\sigma$ of stellar objects is biased down by the weighting function, this is not quite @@ -541,11 +638,10 @@ discussion in \citealt{magnier2017.analysis}). For each stellar detection, we extract the values $M_{xx,xy,yy} = \sum F_i w_i (x^2, x -y, y^2) / \sum F_i w_i$. For each exposure, we find the mean second -moments ($\bar{M_{xx,xy,yy}}$) for PSF objects on this chip (XY40) and -subtract that mean value 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 for each filter. - -\note{write out this math, check out psLibADD} +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 +determine the median of the residual second moments for each +superpixel, resulting in 3 images ($\delta M_{xx,xy,yy}$) for each +filter. Using the second moment images, we can construct certain interesting @@ -559,9 +655,9 @@ related to the shape of the elliptical contour as follows: \begin{eqnarray} -e_0 & = & \sigma^2_a + \sigma^2_b \\ -e_1 & = & (\sigma^2_a - \sigma^2_b) \cos (2 \theta) \\ -e_2 & = & \sigma^2_a - \sigma^2_b +e_0 & = & \sigma^2_{\mbox{major}} + \sigma^2_{\mbox{minor}} \\ +e_1 & = & (\sigma^2_{\mbox{major}} - \sigma^2_{\mbox{minor}}) \cos (2 \theta) \\ +e_2 & = & \sigma^2_{\mbox{major}} - \sigma^2_{\mbox{minor}} \end{eqnarray} -Where $\sigma_a$ and $\sigma_b$ are the major and minor axis +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 @@ -570,7 +666,6 @@ can determine the angle of the PSF ellipticity from the $e_1$ term. -Figure~\ref{fig:smear.by.filter} shows the spatial trend of the {\em - smear}, $\sigma^2_{major} + \sigma^2_{minor} = \delta M_{xx} + -\delta M_{yy}$. This value corresponds to the increase or decrease in +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 @@ -579,16 +674,15 @@ can also be seen. -We can also construct a measurement of the change in ellipticity -$\sigma^2_{major} - \sigma^2_{minor} = (M_{xx} - M_{yy})^2 + 4 -M_{xy}$. This value is plotted in Figure~\ref{fig:shear.by.filter}. -This value is positive definite and is plotted with a color scale -ranging from -0.02 to 0.22 pixel$^2$. We can also determine the -orientation of the corresponding ellipse. Overlayed on +Figure~\ref{fig:shear.by.filter} shows the spatial trend of $e_2$, the +{\em shear}. This value is positive definite and is plotted with a +color scale ranging from -0.02 to 0.22 pixel$^2$. We can also +determine the orientation of the corresponding ellipse. Overlayed on Figure~\ref{fig:shear.by.filter} is a set of vectors representing the ellipse orientation as a function of postion. The length of the vectors corresponds to the value of $\sigma^2_{major} - -\sigma^2_{minor}$. The tree-ring-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 corner. +\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 +corner. \subsection{Correlations Between Tree-Ring-Like Patterns} @@ -715,5 +809,5 @@ radial component of the astrometric residuals: $\frac{\partial (\sigma^2_{major} + \sigma^2_{minor})}{\partial radius} \sim \delta -R$ (see Figure~\ref{fig:dsmear.vs.astrom}. +R$ (see Figure~\ref{fig:dsmear.vs.astrom}). Finally, the radial derivative of the radial component of the @@ -730,5 +824,5 @@ residual values without a derivative. We are convinced that we have the sense of the derivative correct by examination of specific -features in each imaage (e.g., \note{give example}). +features in each imaage. \begin{table} @@ -781,9 +875,8 @@ \section{Discussion} +\label{sec:discussion} These trends help to illuminate the underlying causes of these different effects. - -\note{summarize what pure lateral electric fields would do} First, if we consider the smear pattern @@ -829,10 +922,5 @@ 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. \note{looks like a slope of 1.0 would not be excluded by these - plots} - -\note{I need to use the relationship between the astrometry and the - flat-field to calculate the amplitude of the lateral electric - fields.} +2, but otherwise exhibits the expected behavior. The fact that the PSF ellipticity changes are {\em not} correlated @@ -846,26 +934,78 @@ 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. + +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 $E_x$?} + \section{Conclusion} -The tree rings are showing (at least?) two effects, though they must -be 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. - -In addition, there are radial plate-scale changes -correlated with the tree rings. These plate-scale changes introduce a -flat-field errors on the scale of \approx 1 millimagnitude and -astrometric errors in the scale of 2-3 milliarcseconds. The observed -relationship between the flat-field deviations and the radial -derivative of the astrometric deviations confirms that these two -measurements are caused by the same effect. - -There must be some common cause for both the smearing (charge -diffusion) and the radial plate-scale changes since the astrometric -deviations are correlated with the radial derivative of the smearing. +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. + +In addition, there are radial plate-scale changes correlated with the +tree rings. These plate-scale changes introduce a flat-field errors +on the scale of \approx 1 millimagnitude and astrometric errors in the +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 + 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 small-scale variations in the charge diffusion observed in these +% devices has not been reported for DECam, Hypersuprime Cam, or +% prototype LSST sensors. + +The small-scale variations in the charge diffusion observed in the +Pan-STARRS detectors represents a new type of systematic effect in +deep depletion devices. This feature, if present in other detectors, +could manifest in systematic errors in several ways. Like in the +Pan-STARRS analysis example, the charge diffusion variations result in +fine-structure in the observed stellar point-spread functions. For +very precise photometry or morphological analysis, it will be +necessary for the PSF models to account for the extra charge +diffusion. Unlike the non-uniform pixel-size effects, correction of +the PSF photometry cannot simply be performed as an average flat-field +correction on the measurements after they have been processed. +The additional smearing acts as a convolution with a Gaussian kernel +of fixed size for a given filter. The photometry bias is a function +of the fractional change of the PSF size. Thus, the introduced error +depends on the average PSF for the image in question: an image with +good image quality will suffer larger PSF model errors than an image +with poor image quality. To account for this effect in a rigorous +way, the analysis should use the measured diffusion variations to +modify the model PSFs as a function of position before they are used +for the image analysis. + +The charge diffusion variations may also have an impact on +spectroscopic measurements. Modern, precise spectroscopic +measurements rely on precise measurements of the stellar line +profiles. If such an analysis ignores variations in the charge +diffusion, the measured line widths may be systematically biased. + +This analysis points to the importance of careful instrumental +characterization, especially for those instruments which are used for +large-scale surveys with largely automatic data analysis systems and +stringent precision goals. \acknowledgments @@ -893,44 +1033,5 @@ \end{document} -Notes for paper re-work: - -* Paper focus is now only on the diffusion variations - * strip out the discussion of other systematic effects - * strip down the PS1 introduction discussion - -* tentative title: - Evidence for Small-Scale Charge-Diffusion Variations in Pan-STARRS CCDs - -* outline - - 1. introduction - * thick CCDs - * tree rings == transverse field effects (see Plazas et al) - * we see something else - - 4 model : diffusion variations due to E|| field variations - - 5 discussion (how to treat in calibration / analysis) - - 6 conclusions - -some possible refs to tree rings / charge diff: - -* http://adsabs.harvard.edu/abs/2016SPIE.9904E..2CW (Woods et al 2016; TESS) -* https://arxiv.org/pdf/1605.01001.pdf : plazas et al -* http://ieeexplore.ieee.org/document/1225293/?part=1 Altmannshofer et al 2003 (about thick Si) - -* plazas et al 2014 outline - - 1. intro: thick CCDs, transverse electric fields - 2. DES / DECam - - 2.1 flat-field tree rings (discussion of flat-field tree rings - starting from the premise that they know the answer). - - 3 impact on astrometry and photometry - - 4 improving calibrations given tree rings - - 5 summary and conclusions - +%% Some refs to be added as appropriate: +% Bernstein DEC astrometry : arxiv 1703.01679 +% Baumer et al arxiv 1706.07400 (Flat-fielding)