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trunk/doc/release.2015/systematics.20140411/systematics.tex
r40099 r40102 1 \documentclass[iop,floatfix]{emulateapj} 1 % \documentclass[iop,floatfix]{emulateapj} 2 \documentclass[10pt,preprint]{aastex} 2 3 % \pdfoutput=1 3 4 … … 22 23 \def\plotext{ps} 23 24 24 \def\picdir{/home/eugene/chipresid.20140404}25 %\def\picdir{/data/kukui.2/eugene/chipresid.20140404}25 %\def\picdir{/home/eugene/chipresid.20140404} 26 \def\picdir{/data/kukui.2/eugene/chipresid.20140404} 26 27 27 28 % Pick a terse version of the title here; 28 \shorttitle{ Systematics in PS1}29 \shorttitle{Charge Diffusion Variations in PS1} 29 30 \shortauthors{E.A. Magnier et al} 30 31 \begin{document} 31 \title{ Systematic Effects in Pan-STARRS1 Photometry and Astrometry}32 \title{Charge Diffusion Variations in Pan-STARRS\,1 CCDs} 32 33 33 34 % this is a crude trick to get the order of affiliations right. These … … 50 51 %PS Builder List 51 52 % W.~S. Burgett,\altaffilmark{\IfA} 52 %K.~C. Chambers,\altaffilmark{\IfA}53 K.~C. Chambers,\altaffilmark{\IfA} 53 54 % L. Denneau,\altaffilmark{\IfA} 54 55 % P. Draper,\altaffilmark{\DUR} … … 85 86 \begin{abstract} 86 87 87 Lorem ipsum dolor sit amet, consectetur adipiscing elit. Vestibulum 88 bibendum nisi id tristique posuere. Duis eu mollis nulla. Maecenas est 89 turpis, mattis tempor urna vitae, placerat rhoncus sem. Lorem ipsum 90 dolor sit amet, consectetur adipiscing elit. Sed quis velit 91 nisl. Aliquam erat volutpat. Cras lacinia, nisl tristique auctor 92 molestie, dolor nulla rhoncus purus, ac accumsan nunc nunc ac 93 nibh. Maecenas vitae mollis mauris. Ut sollicitudin pulvinar purus, 94 eget luctus lorem tincidunt vitae. Vestibulum eu mattis neque. Nulla 95 in tortor id urna dapibus gravida a vel leo. 96 88 Thick back-illuminated deep-depletion CCDs have superior quantum 89 efficiency over previous generations of thinned and traditional thick 90 CCDs. As a result, they are being used for major wide-field imaging 91 cameras in several projects. We use observations from the Pan-STARRS 92 $3\pi$ survey to characterize the behavior of the deep-depletion 93 devices used in the Pan-STARRS\,1 Gigapixel Camera. We have 94 identified systematic variations in the photometric behavior and 95 stellar profiles which are similar to the so-called tree rings 96 identified in devices used by other wide-field cameras (DECam and 97 Hypersuprime Camera). The tree-ring features identified in these 98 other cameras result from lateral electric fields which displace the 99 electrons as they are transported in the silicon to the pixel 100 location. In contrast, we show that the photometric and morphological 101 modifications observed in the GPC1 detectors are caused by variations 102 in the vertical charge transportation range and resulting charge 103 diffusion variations. 97 104 \end{abstract} 98 105 … … 102 109 \section{INTRODUCTION}\label{sec:intro} 103 110 104 \begin{verbatim} 105 * early CCDs were thick, but low resistivity Si had low cross-section to red photons 106 * thinning was used to improve the blue sensitivity, at the cost of further reducing the red sensitivity 107 * by the early 2000s, high-resistivity Si was used to make thick "deep-depletion" devices with good red and blue response. 108 * voltages? 109 * sky-scraper pixels 110 * Plazas et al and other effects 111 * 112 \end{verbatim} 111 CCD detectors have evolved greatly since they were first introduced 112 for astronomical imaging in the mid 1970s. In addition to the 113 well-known increases in the size of CCDs over the past 4 decades, CCD 114 architecture has gone through three major evolutionary stages. 115 116 The first generation of CCDs used a silicon substrate a few hundred 117 microns thick on top of which gate structures were deposited to define 118 the pixels. A positive voltage applied to the gate layers would 119 create a shallow region (\approx 10 microns thick) in which the holes 120 were depleted. This ``depletion region'' acted as a potential well to 121 trap electrons, specifically those generated by absorbed photons. The 122 thick silicon substrate required illumination from the ``front'' side 123 with the thin gate structures to allow the photons to reach the 124 depletion region and be detected. These early CCDs had modest quantum 125 efficiency as photons were easily absorbed by the several micron thick 126 gate structures. For an excellent review of the history of CCD 127 development, see \cite{1992ASPC...23....1J}. 128 129 Thinned, backside-illuminated CCDs such as the TI 3PCCD 130 \citep{1981SPIE..290....6B} were developed to address the quantum 131 efficiency limitations of the first generation thick CCDs. The 132 silicon substrate was removed using a chemical process, leaving a 133 delicate device only \approx 10 - 20\micron\ thick, exposing the 134 depletion region on the backside. Photons entering the backside of 135 the device are not blocked by the gate structures and thus more easily 136 absorbed and detected. Thinned backside-illuminated CCDs have high 137 quantum efficiency to blue photons. However, as the wavelength 138 increases beyond \approx 800 nm, the silicon becomes more transparent 139 to the photons, with a corresponding drop in quantum efficiency for 140 red photons. In addition, thin film interference between the entering 141 photons and those reflecting off the front side of the CCD result in 142 ``fringe'' patterns for redder photons. 143 144 Early generations of CCDs were made of low-resistivity (\approx 10 - 145 50 $\Omega$-cm) silicon. Following experiments beginning in the early 146 1990s \citep{Holland.1996}, CCDs made from thick, high-resistivity ($ 147 > 10 k\Omega$-cm) silicon were developed for astronomical instruments 148 in the early 2000s\citep{Holland.2003}. The high-resistivity of the 149 silicon allows for depletion regions of hundreds of microns in depth, 150 compared to \approx 10\micron\ for the low-resistivity silicon. This 151 modification allows for a back-illuminated CCD with a relatively thick 152 silicon subtrate of 75 - 300\micron. Blue photons impinging on the 153 back of the device are absorbed near the back surface of the device 154 and are caried through the depletion region to the gates on the front 155 side. The thick silicon allows red photons to have a greater chance 156 to be absorbed, increasing quantum efficiency in the red. Because 157 these thick, deep-depletion devices have near-unity quantum efficiency 158 across the whole a very wide spectral range, they have become the 159 design of choice for many modern, large-scale CCD cameras (e.g., 160 Pan-STARRS GPC1, \citealt{2009amos.confE..40T}; Subaru Hypersuprime 161 Camera, \citealt{2010SPIE.7735E..3FK}; Dark Energy Survey Camera, 162 \citealt{2015AJ....150..150F}). 163 164 While these deep-depletion CCDs seem to be ideal, they do have 165 features which can cause challenges for precise measurements. As a 166 result of the ``Brighter-Fatter Effect'' 167 \citep{2014JInst...9C3048A,2015JInst..10C5032G}, the profile of bright 168 stars are measured to be wider than the profiles of faint stars. The 169 accepted interpretation is that the electric fields produced by the 170 electrons accumulated from a star repel successive incoming electrons, 171 with the repulsion increasing the more electrons have accumulated. 172 173 The effects of lateral electric fields are likewise identified as the 174 cause of the so-called ``Tree-Rings'' observed in the flat-field, 175 astrometry, and photometry response of thick deep depletion detectors 176 \citep{2014PASP..126..750P}. These tree-ring patterns have been noted 177 in the flat-field response of deep depletion devices since their early 178 testing \citep[see, e.g., Figure 2 in][]{2010SPIE.7735E..1RE} and were 179 initially considered to be a sensitivity response which could be 180 removed with a flat-field. As discussed in detail by 181 \cite{2014PASP..126..750P}, these Tree Rings are more correctly 182 interpretted as variations in the effective pixel area due to 183 migration of the electrons pushed by lateral electric fields induced 184 by small changes in the doping used to set the resistivity of the 185 silicon. The changes in the effective area result in changes to the 186 apparent flat-field response as well as the astrometric response of 187 the detector. More subtly, the flat-field response changes, since 188 they do not reflect actual variations in sensitivity, can lead to 189 systematic photometry errors for astronomical sources if the 190 flat-field images are used in the standard fashion. 191 192 In this paper, we examine the behavior of an apparently-similar kind 193 of Tree Ring observed in the Pan-STARRS GPC1 CCDs. Although we also 194 observe the pixel effective area changes caused by lateral electric 195 fields as described by \cite{2014PASP..126..750P}, we show below a 196 second effect which is more important in driving systematic photometry 197 errors. We find that variations in charge diffusion, also resulting 198 from changes in the silicon doping structures, affect both the 199 observed stellar profiles as well as the photometry measured with 200 profile fitting techniques. In Section~\ref{sec:PS1}, we discuss the 201 Pan-STARRS telescope, camera, and survey data used in this analysis. 202 In Section~\ref{sec:tree.rings}, we present the Tree-Ring-like 203 patterns as observed in several different types of measurements: 204 flat-field response, systematic photometry residuals, systematic 205 astrometric residuals, and stellar profile shape variations. In 206 Section~\ref{sec:discussion}, we discuss the interpretation of 207 patterns we observe and present a simple model to explain the observed 208 behavior. We conclude with a discussion of the implications of this 209 effect on astronomical measurements from deep depletion instruments 113 210 114 211 \section{Pan-STARRS1} 115 116 \note{tidy up this section} 212 \label{sec:PS1} 117 213 118 214 The 1.8m Pan-STARRS\,1 telescope (PS1), located on the summit of … … 121 217 March 2014, PS1 was run under the aegis of the Pan-STARRS Science 122 218 Consortium to perform a set of wide-field science surveys; since March 123 2014, the telescope isoperated by the Pan-STARRS New Science219 2014, the telescope has been operated by the Pan-STARRS New Science 124 220 Consortium (PSNSC). Under the PS1SC, the largest survey, both in 125 terms of area of the sky covered and fraction of observing time126 (56\%), was the \TPS\ in which the entire sky north of Declination 127 $-30$\degrees\ was imaged up \approx 80 times over the 4 years. These 128 observations were distributed over five filters, \grizy, and have been 129 a strometrically and photometrically calibrated to good precision130 \citep{magnier2017.calibration}.221 terms of area of the sky covered ($3\pi$ steradians) and fraction of 222 observing time (56\%), was the \TPS\ in which the entire sky north of 223 Declination $-30$\degrees\ was imaged up \approx 80 times over 4 224 years. These observations were distributed over five filters, \grizy, 225 and have been astrometrically and photometrically calibrated to good 226 precision \citep{magnier2017.calibration}. 131 227 132 228 % 2004SPIE.5489..667H == PS1.optics … … 138 234 \citep[GPC1][]{2009amos.confE..40T}, with low distortion and generally 139 235 good image quality. The median seeing for the \TPS\ data vary 140 somewhat by filter, with (\grizy) = (XXXX). Routine observations are 141 conducted remotely from the Advanced Technology Research Center in 142 Kula, the main facility of the University of Hawaii's Institute for 143 Astronomy operations on Maui. 144 145 GPC1 \citep{2009amos.confE..40T}, currently the largest astronomical camera in 146 terms of number of pixels, consists of a mosaic of 60 edge-abutted 147 $4800\times4800$ pixel detectors, with 10~$\mu$m pixels subtending 148 0.258~arcsec. These \note{OTA51} detectors, manufactured by Lincoln 149 Laboratory, are \note{75$\mu$m}-thick back-illuminated CCDs with a 150 readout time of 7 seconds for a full unbinned image. \note{details 151 about the voltages?} Initial performance assessments are presented 152 in \cite{2008SPIE.7014E..0DO}. The active, usable pixels cover $\sim 80$\% of the 153 FOV. 236 somewhat by filter: (\grizy) = (1.31, 1.19, 1.11, 1.07, 1.02) 237 arcseconds. Routine observations are conducted remotely from the 238 Advanced Technology Research Center in Kula, the main facility of the 239 University of Hawaii's Institute for Astronomy operations on Maui. 240 241 GPC1 \citep{2009amos.confE..40T}, currently the largest astronomical 242 camera in terms of number of pixels, consists of a mosaic of 60 243 edge-abutted $4800\times4800$ pixel detectors, with 10~$\mu$m pixels 244 subtending 0.258~arcsec. These CCID58 detectors, manufactured by 245 Lincoln Laboratory, are 75\micron-thick back-illuminated CCDs 246 \citep{Tonry.2006,Tonry.2008}. Initial performance assessments are 247 presented in \cite{2008SPIE.7014E..0DO}. The active, usable pixels 248 cover \approx 80\% of the FOV. 154 249 155 250 \subsection{Data Processing and Calibration} … … 161 256 162 257 Images obtained by PS1 are processed by the Pan-STARRS Image 163 Processing Pipeline (IPP; \citealp{PS1_IPP,magnier2017.datasystem}). All observations are processed 164 nightly, with results sent to groups within the science consortium 165 (i.e., PS1SC during the \TPS) performing short-term science projects 166 (e.g., searching for transient and moving objects). In addition, the 167 \TPS\ dataset has been re-processed several times with improved 168 calibration and analysis techniques. To date (2017 July), 3 169 re-processings starting from raw pixel data have been performed. The 170 labels PV0, PV1, PV2, PV3 are used identify the nightly processing and 171 successive re-processing versions. PV3 has been used for the public 172 release of the Pan-STARRS \TPS\ data via the {\it Barbara A. Mikulski 173 Archive for Space Telescopes} (MAST) at the Space Telescope Science 174 Institute.\footnote{http//panstarrs.stci.edu} 258 Processing Pipeline (IPP; 259 \citealp{2006amos.confE..50M,magnier2017.datasystem}). All 260 observations are processed nightly, with results sent to groups within 261 the science consortium (i.e., PS1SC during the \TPS) performing 262 short-term science projects (e.g., searching for transient and moving 263 objects). In addition, the \TPS\ dataset has been re-processed 264 several times with improved calibration and analysis techniques. To 265 date (2017 July), 3 re-processings starting from raw pixel data have 266 been performed. The labels PV0, PV1, PV2, PV3 are used identify the 267 nightly processing and successive re-processing versions. PV3 has 268 been used for the public release of the Pan-STARRS \TPS\ data via the 269 {\it Barbara A. Mikulski Archive for Space Telescopes} (MAST) at the 270 Space Telescope Science Institute.\footnote{http//panstarrs.stci.edu} 175 271 176 272 The data processing and calibration operations are discussed in detail … … 207 303 factors which may make the flat-field image inconsistent with stellar 208 304 photometry, e.g., SED, filter band-pass variations, etc 209 \citep[see][]{waters2017,2004PASP..116..449M, magnier.belgium}. This210 correction was made on a relatively coarse grid across the focal plane 211 in order to accumulate sufficient statistics from the stars in the 212 relatively small number of images available at the time. We have305 \citep[see][]{waters2017,2004PASP..116..449M,2007ASPC..364..153M}. 306 This correction was made on a relatively coarse grid across the focal 307 plane in order to accumulate sufficient statistics from the stars in 308 the relatively small number of images available at the time. We have 213 309 found that a single flat-field set can be used for all PS1 214 310 observations to yield photometric consistency at the level of \approx 215 2\% \note{use the ubercal flat stdev as a statistic}. PS1 benefits in 216 this regard from the stability of having a single instrument which is 217 rarely removed. 311 2\%. PS1 benefits in this regard from the stability of having a 312 single instrument which is rarely removed. 218 313 219 314 Photometry of the PS1 images is performed using a 220 315 point-spread-function (PSF) model as well as multiple kinds of 221 apertures \citep{magnier2017.analysis}. In this analysis, we 222 refer to aperture photometry performed using an aperture defined based 223 on the image quality observed for a given chip. The aperture diameter 224 is set to be \note{XXX}times the FWHM for the image.316 apertures \citep{magnier2017.analysis}. In this analysis, we refer to 317 aperture photometry performed using an aperture defined based on the 318 image quality observed for a given chip. The aperture diameter is set 319 to be \approx 3.75 times the FWHM for the image. 225 320 226 321 To improve the photometric systematic errors beyond the level achieved … … 228 323 photometry is re-calibrated within the databasing system based on the 229 324 properties of the measured photometry. The calibration process is 230 discussed by \cite{2012ApJ...756..158S,2013ApJS..205...20M,magnier2017.calibration}. 325 discussed by 326 \cite{2012ApJ...756..158S,2013ApJS..205...20M,magnier2017.calibration}. 231 327 As part of this process, several flat-field corrections have been 232 328 determined. For the PV2 analysis discussed here, a flat-field 233 329 correction determined during the ubercal analysis 234 \citep[see][]{2012ApJ...756..158S} consisted of an $8\times 8$ grid of corrections235 for each GPC1 chip and filter for each of 4 seasons. The boundaries 236 of those seasons are \note{tentatively} identified with modifications 237 to the baffle structures or the system optics. The critical point 238 here is that the final effective flat-field image for the PV2 dataset 239 is based on a dome-flat at the highest resolution, with very low 240 resolution corrections based on photometry, resulting in photometric 241 calibration with roughly 1 millimag consistency for each measurement 242 \note{better number from ubercal?}.330 \citep[see][]{2012ApJ...756..158S} consisted of an $8\times 8$ grid of 331 corrections for each GPC1 chip and filter for each of 4 seasons. The 332 boundaries of those seasons are tentatively identified with 333 modifications to the baffle structures or the system optics. The 334 critical point here is that the final effective flat-field image for 335 the PV2 dataset is based on a dome-flat at the highest resolution, 336 with very low resolution corrections based on photometry, resulting in 337 photometric systmatic uncertainties in the range 7 - 12 338 millimagnitudes, depending on the filter \citep{2013ApJS..205...20M}. 243 339 244 340 For all objects, positions are measured from the PSF model for the … … 252 348 253 349 \section{Tree-Ring-Like Patterns} 350 \label{sec:tree.rings} 254 351 255 352 \begin{table} … … 274 371 For many of the GPC1 OTA CCDs, we observe a pattern in the photometric 275 372 residuals which is similar in appearence to the Tree Rings described 276 in the Dark Energy Camera (DECam) by \cite{ plazas.2014}. This pattern277 consists of systematic deviations which are consistent in a set of 278 circular arcs centered on the corner of the CCD, as shown in373 in the Dark Energy Camera (DECam) by \cite{2014PASP..126..750P}. This 374 pattern consists of systematic deviations which are consistent in a 375 set of circular arcs centered on the corner of the CCD, as shown in 279 376 Figure~\ref{fig:psfmags.by.filter}. The details of the analysis used 280 377 to generate Figure~\ref{fig:psfmags.by.filter} are given below. For … … 282 379 circular silicon wafer into 4 inscribed squares. Thus the corners of 283 380 the CCDs lie in the center of the silicon boule, just as the center of 284 the circular Tree Rings described by \cite{plazas.2014} match the 285 center of the boule from which they came. This gives the impression 286 that a similar mechanism is responsible for the pattern observed in 287 the PS1 photometry and the DECam photometry, namely the diffusive 288 effects of lateral electric field variations in the detectors. In the 289 next section, we will make the case that the patterns observed in the 290 PS1 residuals are {\em not} caused by this mechanism, but are instead 291 caused by variations in the {\em vertical} electric field (the field 292 direction perpendicular to the CCD surface). 381 the circular Tree Rings described by \cite{2014PASP..126..750P} match 382 the center of the boule from which they came. This gives the 383 impression that a similar mechanism is responsible for the pattern 384 observed in the PS1 photometry and the DECam photometry, namely the 385 diffusive effects of lateral electric field variations in the 386 detectors. In the next section, we will make the case that the 387 patterns observed in the PS1 photometry residuals are {\em not} caused 388 by this mechanism, but are instead caused by variations in the {\em 389 vertical} electric field (the field direction perpendicular to the 390 CCD surface). 293 391 294 392 First, in this section, we will describe how we have measured the … … 296 394 For all of these examples, we use a single GPC1 CCD (XY40) to 297 395 illustrate the effects in detail, but a similar set of effects are 298 seen in \note{many? most?} GPC1 detectors. First, we show the 299 residual PSF photometry. Second, we show the residual Aperture 300 photometry. Third, we show the astrometric residual patterns. 301 Fourth, we show the patterns observed in the flat-field images. 302 Finally, we show measurements derived from the second-moments of the 303 stars. 396 seen in many of the GPC1 detectors. First, we show the residual PSF 397 photometry. Second, we show the residual Aperture photometry. Third, 398 we show the astrometric residual patterns. Fourth, we show the 399 patterns observed in the flat-field images. Finally, we show 400 measurements derived from the second-moments of the stars. 304 401 305 402 For all effects discussed below, we are measuring the mean value of … … 308 405 represents the same range of true GPC1 XY40 pixels regardless of the 309 406 type of measurement. To generate the photometry, astrometry, or 310 second-moment measurements were extracted from the \note{PV0}DVO407 second-moment plots, measurements were extracted from the PV0 DVO 311 408 database for observations covering the region ($\alpha$,$\delta$) = 312 409 (90\degree\ -- 150\degree, -25\degree\ -- 10\degree). This region of … … 358 455 359 456 Figure~\ref{fig:psfmags.by.filter} shows the 2D patterns of PSF 360 photometr icresiduals. In this case, we select PSF magnitude457 photometry residuals. In this case, we select PSF magnitude 361 458 measurements for detections of stars which fall in the given 362 459 superpixel. We subtract each measurement from the average magnitude … … 378 475 is comparable to the amplitude of the correlated structures, so we 379 476 need to integrate along the radial structures to make stronger 380 statements about these patterns. \note{hanging statement?}477 statements about these patterns. 381 478 382 479 Figure~\ref{fig:apmags.by.filter} shows the equivalent measurement for … … 462 559 then observed by the PS1 telescope. These flat-field images were 463 560 obtained 2011 Feb 09 as part of a campaign to study the PS1 system 464 response \citep{2012ApJ...750...99T}. Flats were obtain in a set of 4nm steps,465 with \note{XXnm} band-pass. To enhance the signal-to-noise, we have 466 median-combined aset of 6 flats at the center of the corresponding filter.561 response \citep{2012ApJ...750...99T}. Flats were obtain in a set of 562 4nm steps. To enhance the signal-to-noise, we have median-combined a 563 set of 6 flats at the center of the corresponding filter. 467 564 468 565 In order to mask pixels which do not flatten well, we generate a … … 535 632 multiple detections). The second moments are measured with a Gaussian 536 633 weighting function, with the $\sigma_{w}$ scaled by the PSF size so 537 that the $\sigma$ measured for PSF stars is \approx 6 0\% of634 that the $\sigma$ measured for PSF stars is \approx 65\% of 538 635 $\sigma_{w}$. (Note that, since the measured $\sigma$ of stellar 539 636 objects is biased down by the weighting function, this is not quite … … 541 638 discussion in \citealt{magnier2017.analysis}). For each stellar 542 639 detection, we extract the values $M_{xx,xy,yy} = \sum F_i w_i (x^2, x 543 y, y^2) / \sum F_i w_i$. For each exposure, we find the mean second 544 moments ($\bar{M_{xx,xy,yy}}$) for PSF objects on this chip (XY40) and 545 subtract that mean value from the instantaneous measurements of 546 $M_{xx,xy,yy}$. We then determine the median of the residual second 547 moments for each superpixel, resulting in 3 images for each filter. 548 549 \note{write out this math, check out psLibADD} 640 y, y^2) / \sum F_i w_i$. For each exposure, we find the median second 641 moments for PSF objects on this chip (XY40) and subtract that median 642 value from the instantaneous measurements of $M_{xx,xy,yy}$. We then 643 determine the median of the residual second moments for each 644 superpixel, resulting in 3 images ($\delta M_{xx,xy,yy}$) for each 645 filter. 550 646 551 647 Using the second moment images, we can construct certain interesting … … 559 655 related to the shape of the elliptical contour as follows: 560 656 \begin{eqnarray} 561 e_0 & = & \sigma^2_ a + \sigma^2_b\\562 e_1 & = & (\sigma^2_ a - \sigma^2_b) \cos (2 \theta) \\563 e_2 & = & \sigma^2_ a - \sigma^2_b657 e_0 & = & \sigma^2_{\mbox{major}} + \sigma^2_{\mbox{minor}} \\ 658 e_1 & = & (\sigma^2_{\mbox{major}} - \sigma^2_{\mbox{minor}}) \cos (2 \theta) \\ 659 e_2 & = & \sigma^2_{\mbox{major}} - \sigma^2_{\mbox{minor}} 564 660 \end{eqnarray} 565 Where $\sigma_ a$ and $\sigma_b$ are the major and minor axis661 Where $\sigma_{\mbox{major}}$ and $\sigma_{\mbox{minor}}$ are the major and minor axis 566 662 dimensions of the ellipse and $\theta$ is the position angle. 567 663 Thus, $e_0$ is a measurement of the change in the size of the stellar … … 570 666 can determine the angle of the PSF ellipticity from the $e_1$ term. 571 667 572 Figure~\ref{fig:smear.by.filter} shows the spatial trend of the {\em 573 smear}, $\sigma^2_{major} + \sigma^2_{minor} = \delta M_{xx} + 574 \delta M_{yy}$. This value corresponds to the increase or decrease in 668 Figure~\ref{fig:smear.by.filter} shows the spatial trend of $e_0$, the {\em 669 smear}. This value corresponds to the increase or decrease in 575 670 the circularly-symmetric component of the image size. The dynamic 576 671 range of these images is -0.3 to +0.3 pixel$^2$. A tree-ring-like … … 579 674 can also be seen. 580 675 581 We can also construct a measurement of the change in ellipticity 582 $\sigma^2_{major} - \sigma^2_{minor} = (M_{xx} - M_{yy})^2 + 4 583 M_{xy}$. This value is plotted in Figure~\ref{fig:shear.by.filter}. 584 This value is positive definite and is plotted with a color scale 585 ranging from -0.02 to 0.22 pixel$^2$. We can also determine the 586 orientation of the corresponding ellipse. Overlayed on 676 Figure~\ref{fig:shear.by.filter} shows the spatial trend of $e_2$, the 677 {\em shear}. This value is positive definite and is plotted with a 678 color scale ranging from -0.02 to 0.22 pixel$^2$. We can also 679 determine the orientation of the corresponding ellipse. Overlayed on 587 680 Figure~\ref{fig:shear.by.filter} is a set of vectors representing the 588 681 ellipse orientation as a function of postion. The length of the 589 682 vectors corresponds to the value of $\sigma^2_{major} - 590 \sigma^2_{minor}$. The tree-ring-like structure is {\em not} apparent in this 591 figure for any filter. The spatial variations are low-frequency and 592 unrelated to the radial trend from the upper-left corner. 683 \sigma^2_{minor}$. The tree-ring-like structure is {\em not} apparent 684 in this figure for any filter. The spatial variations are 685 low-frequency and unrelated to the radial trend from the upper-left 686 corner. 593 687 594 688 \subsection{Correlations Between Tree-Ring-Like Patterns} … … 715 809 radial component of the astrometric residuals: $\frac{\partial 716 810 (\sigma^2_{major} + \sigma^2_{minor})}{\partial radius} \sim \delta 717 R$ (see Figure~\ref{fig:dsmear.vs.astrom} .811 R$ (see Figure~\ref{fig:dsmear.vs.astrom}). 718 812 719 813 Finally, the radial derivative of the radial component of the … … 730 824 residual values without a derivative. We are convinced that we have 731 825 the sense of the derivative correct by examination of specific 732 features in each imaage (e.g., \note{give example}).826 features in each imaage. 733 827 734 828 \begin{table} … … 781 875 782 876 \section{Discussion} 877 \label{sec:discussion} 783 878 784 879 These trends help to illuminate the underlying causes of these 785 880 different effects. 786 787 \note{summarize what pure lateral electric fields would do}788 881 789 882 First, if we consider the smear pattern … … 829 922 The slope of our relationship is \approx 0.5 in normalized units. 830 923 Thus the observed trends appear to be too weak by a factor of \approx 831 2. \note{looks like a slope of 1.0 would not be excluded by these 832 plots} 833 834 \note{I need to use the relationship between the astrometry and the 835 flat-field to calculate the amplitude of the lateral electric 836 fields.} 924 2, but otherwise exhibits the expected behavior. 837 925 838 926 The fact that the PSF ellipticity changes are {\em not} correlated … … 846 934 magnitudes. 847 935 936 Finally, the correlation between the smear structures and the 937 astrometry residuals shows that these two effects are connected. The 938 underlying connection is the pattern of the resistivity variations. 939 Regions with high (or low) resistivity show relatively high (or low) 940 amounts of smear; astrometric deviations follow the gradient between 941 these regions. 942 943 We interpret the changes in the {\em smear} term as changes in the 944 amount of charge diffusion. The blue filters exhibit the strongest 945 changes in the amount of smear. These are also the filters for which 946 the detected electrons have travelled the longest distance in the 947 silicon, and are thus most affected by diffusion effects. 948 949 \note{add more quantitative discussion of the variations in $E_y$ vs $E_x$?} 950 848 951 \section{Conclusion} 849 952 850 The tree rings are showing (at least?) two effects, though they must 851 be related. First, the images are experiencing circularly-symmetric 852 changes in the PSF size correlated with the tree-ring pattern. These 853 PSF size changes drive errors in the PSF photometry which the are also 854 correlated with the tree ring pattern on the scale of a few 855 millimagnitudes. These PSF size changes are consistent with changes 856 in the charge diffusion, which also introduces a circularly symmetric 857 smearing. 858 859 In addition, there are radial plate-scale changes 860 correlated with the tree rings. These plate-scale changes introduce a 861 flat-field errors on the scale of \approx 1 millimagnitude and 862 astrometric errors in the scale of 2-3 milliarcseconds. The observed 863 relationship between the flat-field deviations and the radial 864 derivative of the astrometric deviations confirms that these two 865 measurements are caused by the same effect. 866 867 There must be some common cause for both the smearing (charge 868 diffusion) and the radial plate-scale changes since the astrometric 869 deviations are correlated with the radial derivative of the smearing. 953 The tree rings observed in the Pan-STARRS GPC1 data show (at least) 954 two effects, though they are related. First, the images are 955 experiencing circularly-symmetric changes in the PSF size correlated 956 with the tree-ring pattern. These PSF size changes drive errors in 957 the PSF photometry which the are also correlated with the tree ring 958 pattern on the scale of a few millimagnitudes. These PSF size changes 959 are consistent with changes in the charge diffusion, which also 960 introduces a circularly symmetric smearing. 961 962 In addition, there are radial plate-scale changes correlated with the 963 tree rings. These plate-scale changes introduce a flat-field errors 964 on the scale of \approx 1 millimagnitude and astrometric errors in the 965 scale of 2-3 milliarcseconds. The observed relationship between the 966 flat-field deviations and the radial derivative of the astrometric 967 deviations confirms this interpretation \citep[see discussion 968 in][]{2014PASP..126..750P}. 969 970 The vertical diffusion variations and the lateral charge migration are 971 both driven by the same variations in the doping structures. This 972 point is clear from the spatial correlation of the gradient in the 973 smear variations and the astrometric variations. 974 975 % The small-scale variations in the charge diffusion observed in these 976 % devices has not been reported for DECam, Hypersuprime Cam, or 977 % prototype LSST sensors. 978 979 The small-scale variations in the charge diffusion observed in the 980 Pan-STARRS detectors represents a new type of systematic effect in 981 deep depletion devices. This feature, if present in other detectors, 982 could manifest in systematic errors in several ways. Like in the 983 Pan-STARRS analysis example, the charge diffusion variations result in 984 fine-structure in the observed stellar point-spread functions. For 985 very precise photometry or morphological analysis, it will be 986 necessary for the PSF models to account for the extra charge 987 diffusion. Unlike the non-uniform pixel-size effects, correction of 988 the PSF photometry cannot simply be performed as an average flat-field 989 correction on the measurements after they have been processed. 990 The additional smearing acts as a convolution with a Gaussian kernel 991 of fixed size for a given filter. The photometry bias is a function 992 of the fractional change of the PSF size. Thus, the introduced error 993 depends on the average PSF for the image in question: an image with 994 good image quality will suffer larger PSF model errors than an image 995 with poor image quality. To account for this effect in a rigorous 996 way, the analysis should use the measured diffusion variations to 997 modify the model PSFs as a function of position before they are used 998 for the image analysis. 999 1000 The charge diffusion variations may also have an impact on 1001 spectroscopic measurements. Modern, precise spectroscopic 1002 measurements rely on precise measurements of the stellar line 1003 profiles. If such an analysis ignores variations in the charge 1004 diffusion, the measured line widths may be systematically biased. 1005 1006 This analysis points to the importance of careful instrumental 1007 characterization, especially for those instruments which are used for 1008 large-scale surveys with largely automatic data analysis systems and 1009 stringent precision goals. 870 1010 871 1011 \acknowledgments … … 893 1033 \end{document} 894 1034 895 Notes for paper re-work: 896 897 * Paper focus is now only on the diffusion variations 898 * strip out the discussion of other systematic effects 899 * strip down the PS1 introduction discussion 900 901 * tentative title: 902 Evidence for Small-Scale Charge-Diffusion Variations in Pan-STARRS CCDs 903 904 * outline 905 906 1. introduction 907 * thick CCDs 908 * tree rings == transverse field effects (see Plazas et al) 909 * we see something else 910 911 4 model : diffusion variations due to E|| field variations 912 913 5 discussion (how to treat in calibration / analysis) 914 915 6 conclusions 916 917 some possible refs to tree rings / charge diff: 918 919 * http://adsabs.harvard.edu/abs/2016SPIE.9904E..2CW (Woods et al 2016; TESS) 920 * https://arxiv.org/pdf/1605.01001.pdf : plazas et al 921 * http://ieeexplore.ieee.org/document/1225293/?part=1 Altmannshofer et al 2003 (about thick Si) 922 923 * plazas et al 2014 outline 924 925 1. intro: thick CCDs, transverse electric fields 926 2. DES / DECam 927 928 2.1 flat-field tree rings (discussion of flat-field tree rings 929 starting from the premise that they know the answer). 930 931 3 impact on astrometry and photometry 932 933 4 improving calibrations given tree rings 934 935 5 summary and conclusions 936 1035 %% Some refs to be added as appropriate: 1036 % Bernstein DEC astrometry : arxiv 1703.01679 1037 % Baumer et al arxiv 1706.07400 (Flat-fielding)
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