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trunk/doc/release.2015/systematics.20140411/systematics.tex
r39833 r40096 104 104 \section{Pan-STARRS1} 105 105 106 The Pan-STARRS\,1 telescope (PS1) has recently completed observations 107 for its first survey mission (REF). PS1 is 1.8m telescope located on 108 the summit of Haleakala on the Hawaiian island of Maui (REF). This 109 wide-field telescope images a 3.3 degree field of view on a 1.4 110 gigapixel camera, with low distortion and generally good image quality 111 (median \approx \note{1.1 arcseconds} in all filters except for g, 112 with 1.3 arcseconds). Available filters are \gps,\rps,\ips with 113 bandpasses similar to the equivalent SDSS filters; \zps is somewhat 114 bluer than the SDSS $z$, while \yps is somewhat redder (see, REF, for 115 a complete specification). 116 117 The first PS1 science survey mission began 2010 May and completed 31 118 March 2014. The bulk of the observing time (56\%) goes to the 119 ``3$\pi$ Survey'', in which the \approx 30,000 square degrees 120 observable from Hawaii (north of Dec = -30) were repeatedly observed 121 over the nearly 4 year survey period. The typical coverage at the end 122 of the survey is \approx 10 observations per filter per point on the 123 sky in the 3$\pi$ region. The repeated observations allows for good 124 characterization of systematic sources of uncertainty. 125 126 The PS1 data will be released to the public in the Spring of 2015 via 127 the Mikulsky Archive to Space Telescopes (MAST) at the Space Telescope 128 Science Institute (STScI). 129 130 \subsection{GigaPixel Camera\,1} 131 132 The PS1 GigaPixel Camera\,1 (GPC1) was the largest astronomical camera 133 until HypersuprimeCam was completed. GPC1 is a mosaic camera 134 consisting of 60 detectors (``chips'') arranged in an 8x8 grid with 135 the 4 corners missing (FIGURE?). The detectors in this camera are 136 othogonal transfer array devices (REF), in which the single silicon 137 chip is sub-divided into a checkerboard of 64 sub-arrays (``cells''). 138 Each cell may be independently addressed and read, and the charge 139 accumulated in the pixels may be moved in either the $x$ or $y$ 140 directions (thus the term ``orthogonal transfer''). The full GPC1 141 thus consists of a total of 3840 cells, each \note{608 x 610} pixels. 142 143 \subsection{Data Processing} 144 145 Images obtained from PS1 are written to a set of computers located in 146 the observatory dome (``pixel servers''), and notification is then 147 sent via a web service to the Image Processing Pipeline (IPP) 148 computers in Kihei. The IPP cluster retrieves images from the summit 149 pixel servers as they are available, though no summit hand-shaking 150 takes place. The summit computers have a buffer for data from several 151 days' of observing so that data is not lost if the link to Kihei is 152 down or the IPP computer cluster is offline. 153 154 Raw images are saved on the IPP cluster and processed as needed. In 155 general, every science exposure is processed as soon as possible in a 156 stream called the ``nightly science processing''. As the survey has 157 proceeded and improvements have been made in the analysis software, 158 images have been reprocessed. To date (2015 Jan), there have been 2 159 complete reprocesssing runs (identified PV1 and PV2), and a third 160 (PV3) is in progress. As the software has been improved, the nightly 161 science processing software has been updated to reflect those 162 improvements. The nightly science processing thus is heterogenous in 163 the analysis and algorithms used. The software for the PVx 164 reprocessing is more homogenous. 165 166 Raw images are stored as multi-extension FITS images, with each cell 167 in a given chip stored as a separate image extension. The raw data are 168 generally stored with lossless compression applied to the pixel 169 arrays \note{CFITSIO REF}. The data for the 60 chips in a given 170 exposure are stored as separate FITS files. 171 172 The data processing system performs a number of steps distributed 173 across a cluster of linux-based computers. The first stage (``chip 174 processing'') is performed on individual chip image files 175 independently in parallel. At this stage, the images are detrended, 176 including overscan, bias, dark, flat-field, and (for $y$-band) 177 fringing corrections. Areas of bad data (e.g., regions of poor charge 178 transfer efficiency or non-linear dark glows) are masked. Within the 179 IPP processing code, masked pixels are identified as non-zero values 180 in a separate 16-bit mask image, which is then carried as part of the 181 processed image data products. The chip analysis also generates a 182 variance image which is used along with the signal image to specify 183 the noise properities as a function of pixel. Details of the 184 chip-stage processing can be found in \note{Waters et al REF}. 185 186 The chip-stage analysis also includes source detection and basic 187 characterization. After a sky background model is subtracted from the 188 image, individual sources are detected via cross-correlation with a 189 PSF model. Sources detected in the image are used to define the PSF 190 model. Simple aperture based measurements (total flux, 2nd and 191 higher-order moments, etc) are measured for all detections. An 192 estimate of the extendedness (non-PSF-nature) of the sources is used 193 to distinguish ``stellar'' detections from ``non-stellar'' detections. 194 Non-stellar detections above a minimum signal-to-noise \note{of 20} 195 are fitted with a galaxy surface brightness model, while remaining 196 sources are fitted with a PSF model, or a cluster of PSF models. The 197 end result of the chip-stage analysis is a collection of parameters 198 for each detection, including the positions ($X$, $Y$), PSF model 199 flux, aperture fluxes, 2nd moments. Details of the source analysis 200 and characterization can be found in \note{Magnier et al REF}. 201 202 \section{Photometry Analysis} 203 204 Lorem ipsum dolor sit amet, consectetur adipiscing elit. Vestibulum 205 bibendum nisi id tristique posuere. Duis eu mollis nulla. Maecenas est 206 turpis, mattis tempor urna vitae, placerat rhoncus sem. Lorem ipsum 207 dolor sit amet, consectetur adipiscing elit. Sed quis velit 208 nisl. Aliquam erat volutpat. Cras lacinia, nisl tristique auctor 209 molestie, dolor nulla rhoncus purus, ac accumsan nunc nunc ac 210 nibh. Maecenas vitae mollis mauris. Ut sollicitudin pulvinar purus, 211 eget luctus lorem tincidunt vitae. Vestibulum eu mattis neque. Nulla 212 in tortor id urna dapibus gravida a vel leo. 213 214 % refer back to refcat, ubercal, tonry 215 % discuss the PSF modeling 216 % what are the limitations of the current photometric precision 217 218 \section{Astrometry Analysis} 219 220 Astrometric calibration defines a transformation from the raw 221 instrumental positions (X,Y on a chip) to RA,DEC coordinates on the 222 sky. Astrometry calibration is performed at two separate stages in 223 the IPP analysis. First, every exposure is calibrated independently 224 during the processing by comparison to a reference catalog. This 225 astrometric analysis is performed as part of the second processing 226 stage, the ``camera'' analysis stage. The output from the chip stage 227 for all chips in an exposure are processed as a group in this 228 analysis. The initial guess for the astrometry comes from the 229 telescope coordinates provided in the image headers. 230 231 The RA, DEC, and position angle of the telescope boresite are provided 232 as part of the image metadata. The telescope and camera systems also 233 provide WCS header keywords for each chip separately. However, in the 234 early stages of the telescope commissioning, these values were not 235 reliable. Thus, within the IPP, and model for the camera layout is 236 used so that the single triplet (RA,DEC,PA) can be used to predict the 237 astrometric calibration of each chip. This guess is generally good to 238 10s of pixels, and need only be accurate to \approx 1/2 of a chip for 239 the software to discover the true coordinates. 240 241 The guess astrometry is used to select a set of likely reference stars 242 from the reference database. These stars are the cross-correlated 243 with the measured source positions to find the likely match between 244 stars in the reference catalog and detected sources in the image. 245 246 Once a reliable match has been determined, astrometric transformations 247 are determined to match the raw (X,Y) coordinates of the detections to 248 sky coordinates of the corresponding reference stars. 249 250 Within the IPP, two main classes of transformations may be used. For 251 single chips from non-mosaic cameras (or for the warp \& stack 252 skycells), the astrometry calibration consists of a projection from the 253 celestial sphere to a linearized coordinate system followed by a 254 transformation from the projection coordiante frame to the pixel 255 coordinate frame. The projection may be one of several possible 256 options (see Calabria et al REF), though in general the IPP uses the 257 SIN (or TAN) projection (define?). The transformation from the 258 projection coordiates to the pixel coordinate may use an afine 259 transformation or higher order polynomials (up to 3rd order). 260 261 For chips from a mosaic camera, the astrometric transformation is 262 defined as a multi-level operation. As in single-chip astrometry, a 263 projection (SIN or TAN) is used to convert the spherical celestial 264 coordiates to a local linear system (the 'tanget plane' coorinate 265 system). There are then two level of cartesian transformations: a 266 first set of polynomials (up to 3rd order) are used to transform the 267 tangent plane coordinates to the ``focal plane'' coordinates. This, 268 relatively low-order, correction accounts for rotation of the camera 269 and basic optical distortion coming from the optics and the 270 atmosphere. A second transformation is used to convert the focal 271 plane coordinate to the pixel coordinates for each chip. For the 272 on-the-fly calibration, these 273 transformations may consist of a set of polynomials up 274 to 3rd order in X and/or Y (i.e, $x^i y^j$ where $i + j <= 3$) 275 276 \note{add details on the transformation from focal-plane to tangent 277 plane: fit is done on the gradient}. 278 279 The on-the-fly astrometric calibration determines the astrometric 280 transformation to an accuracy of at least 0.3 arcsec (chips with worse 281 astrometry are rejected). Data from these images may now be ingested 282 into our internal database software for astronomical objects, the 283 Desktop Virtual Observatory \citep[DVO,][]{PS1.IPP}. This database 284 software associates detections from images together based on their 285 positions in the sky to define astrnomical ``objects''. The database 286 includes metadata to describe the links between objects and their 287 multiple detections as well as metadata defining the images and their 288 astrometric transformations. 289 290 After images have been ingested into the DVO software, calibration 291 improvements may be made within the database. A program called 292 ``relastro'' is used to improve the astrometry iterative. In one 293 mode, relastro loops between improving the mean positions of objects 294 and using the improved mean positions to improve the astrometric 295 calibrations of the images. In normal usage, relastro is only allowed 296 to update the chip-to-focal plane transformations; it is not normally 297 used to improve the focal-plane to tangent plane transformations. 298 Also, within relastro, the transformation from chip-to-focal plane may 299 be represented using either the polynomials as above or with a linear 300 transformation plus bilinear interpolation of a grid of correction 301 cells. In the latter case, the grid may be sampled as finely as 6x6 302 positions per chip. 303 304 % precision demonstration 305 % koppenhoefer effect 306 % MISSING: DCR! 307 308 \section{Systematic Residuals} 309 310 \subsection{Camera-Scale Trends} 311 312 \subsection{Tree-Rings : An Example Chip} 106 \note{tidy up this section} 107 108 The 1.8m Pan-STARRS\,1 telescope (PS1), located on the summit of 109 Haleakala on the Hawaiian island of Maui, has been surveying the sky 110 regularly since May 2010 \citep{chambers.2017}. From May 2010 through 111 March 2014, PS1 was run under the aegis of the Pan-STARRS Science 112 Consortium to perform a set of wide-field science surveys; since March 113 2014, the telescope is operated by the Pan-STARRS New Science 114 Consortium (PSNSC). Under the PS1SC, the largest survey, both in 115 terms of area of the sky covered and fraction of observing time 116 (56\%), was the \TPS\ in which the entire sky north of Declination 117 $-30$\degrees\ was imaged up \approx 80 times over the 4 years. These 118 observations were distributed over five filters, \grizy, and have been 119 astrometrically and photometrically calibrated to good precision 120 \citep{magnier.2017.calibration}. 121 122 The wide-field PS1 telescope optics \citep{PS1.optics} image a 3.3 123 degree field of view on a 1.4 gigapixel camera \citep[GPC1][]{PS1.GPC1}, with 124 low distortion and generally good image quality. The median seeing 125 for the \TPS\ data vary somewhat by filter, with (\grizy) = (XXXX). 126 Routine observations are conducted remotely from the Advanced 127 Technology Research Center in Kula, the main facility of the 128 University of Hawaii's Institute for Astronomy operations on Maui. 129 130 GPC1 \citep{PS1.GPCA}, currently the largest astronomical camera in 131 terms of number of pixels, consists of a mosaic of 60 edge-abutted 132 $4800\times4800$ pixel detectors, with 10~$\mu$m pixels subtending 133 0.258~arcsec. These \note{OTA51} detectors, manufactured by Lincoln 134 Laboratory, are \note{75$\mu$m}-thick back-illuminated CCDs with a 135 readout time of 7 seconds for a full unbinned image. \note{details 136 about the voltages?} Initial performance assessments are presented 137 in \cite{PS1.GPCB}. The active, usable pixels cover $\sim 80$\% of the 138 FOV. 139 140 \subsection{Data Processing and Calibration} 141 142 Images obtained by PS1 are processed by the Pan-STARRS Image 143 Processing Pipeline (IPP; \citealp{PS1_IPP, 144 magnier.etal.2016.datasystem}). All observations are processed 145 nightly, with results sent to groups within the science consortium 146 (i.e., PS1SC during the \TPS) performing short-term science projects 147 (e.g., searching for transient and moving objects). In addition, the 148 \TPS\ dataset has been re-processed several times with improved 149 calibration and analysis techniques. To date (2017 July), 3 150 re-processings starting from raw pixel data have been performed. The 151 labels PV0, PV1, PV2, PV3 are used identify the nightly processing and 152 successive re-processing versions. PV3 has been used for the public 153 release of the Pan-STARRS \TPS\ data via the {\it Barbara A. Mikulski 154 Archive for Space Telescopes} (MAST) at the Space Telescope Science 155 Institute.\footnote{http//panstarrs.stci.edu} 156 157 The data processing and calibration operations are discussed in detail 158 in elsewhere 159 \citep{magnier.etal.2017.analysis,magnier.etal.2017.calibration,waters.2017}. 160 We re-visit here a number of points that are of significance to this 161 study. Images are processed following a fairly standard sequence of 162 image detrending, source detection, and initial calibration 163 (astrometric and photometric) of those detected sources. Additional 164 standard processing critical to PS1 science operations includes 165 geometric transformation (`warping') and image combinations (summed 166 stacks and differences). For the purposes of this analysis, we are 167 only considering the sources detected in the individual exposures from 168 the initial analysis steps. 169 170 As discussed in \cite{waters.2017}, image detrending includes 171 flat-field processing with a single epoch flat-field image for each 172 filter. The flat-field image used for this analysis has been 173 generated by median-combining dome flat-field images (after 174 pre-processing and pixel outlier rejections) and then multiplying by a 175 photometric flat-field correction image generated by the analysis of a 176 grid of images of a dense stellar field. The purpose of this second 177 step is to correct the basic flat-field image for errors arising from 178 the non-uniformity of the illumination, from non-pixel uniformity due 179 to the varying optical distorition across the field, and any other 180 factors which may make the flat-field image inconsistent with stellar 181 photometry, e.g., SED, filter band-pass variations, etc 182 \citep[see][]{waters.2017,magnier.cuillandre,magnier.belgium}. This 183 correction was made on a relatively coarse grid across the focal plane 184 in order to accumulate sufficient statistics from the stars in the 185 relatively small number of images available at the time. We have 186 found that a single flat-field set can be used for all PS1 187 observations to yield photometric consistency at the level of \approx 188 2\% \note{use the ubercal flat stdev as a statistic}. PS1 benefits in 189 this regard from the stability of having a single instrument which is 190 rarely removed. 191 192 Photometry of the PS1 images is performed using a 193 point-spread-function (PSF) model as well as multiple kinds of 194 apertures \citep{magnier.etal.2017.analysis}. In this analysis, we 195 refer to aperture photometry performed using an aperture defined based 196 on the image quality observed for a given chip. The aperture diameter 197 is set to be \note{XXX} times the FWHM for the image. 198 199 To improve the photometric systematic errors beyond the level achieved 200 with a single (photometrically corrected) flat-field set, the PS1 201 photometry is re-calibrated within the databasing system based on the 202 properties of the measured photometry. The calibration process is 203 discussed by \cite{ubercal,photladder,magnier.etal.2017.calibration}. 204 As part of this process, several flat-field corrections have been 205 determined. For the PV2 analysis discussed here, a flat-field 206 correction determined during the ubercal analysis 207 \citep[see][]{ubercal} consisted of an $8\times 8$ grid of corrections 208 for each GPC1 chip and filter for each of 4 seasons. The boundaries 209 of those seasons are \note{tentatively} identified with modifications 210 to the baffle structures or the system optics. The critical point 211 here is that the final effective flat-field image for the PV2 dataset 212 is based on a dome-flat at the highest resolution, with very low 213 resolution corrections based on photometry, resulting in photometric 214 calibration with roughly 1 millimag consistency for each measurement 215 \note{better number from ubercal?}. 216 217 For all objects, positions are measured from the PSF model for the 218 brighter sources (using a non-linear fitting process) and from a 219 simple centroid (1st moment) for the fainter source 220 \citep{magnier.etal.2017.analysis}. These position measurements are 221 used in the astrometric analysis. The astrometric calibration is 222 discussed by \cite{magnier.etal.2017.calibration}; for the PV2 223 dataset, the typical systematic floor is \approx 15 - 20 224 milliarcsecond for individual measurements of brighter stars. 225 226 \section{Tree-Ring-Like Patterns} 313 227 314 228 \begin{table} … … 331 245 \end{table} 332 246 333 We observe a number of low-level effects in different types of 334 measurements which have a similar spatial structure on individual 335 chips. These structures have a circular pattern centered one corner 336 of the affected chips. \note{do all chips show all effects? is the 337 amplitude very different from chip to chip?} We use measurements 338 from chip XY40 to illustrate the spatial patterns and relationships 339 between the different effects. For all effects, we are measuring the 340 mean value of the effect in 10x10 pixel boxes. The resulting images 341 are all constructed so that a given superpixel represents the same 342 range of true GPC1 XY40 pixels. Measurements were extracted from the 343 ``nightly science'' DVO database for observations covering the region 344 ($\alpha$,$\delta$) = (90\degree\ -- 150\degree, -25\degree\ -- 345 10\degree). This region avoids the Galactic Plane where astrometric 346 outliers have been more common. We limit the analysis to good 347 measurements (PSF\_QF $>$ 0.85) of likely stars ($|m_{psf} - m_{aper}| 348 < 0.2$). Only measurements with instrumental magnitude $< -8.0$ 349 ($-2.5\log \mbox{cts sec}^{-1} < -8.0$) are include to ensure 247 For many of the GPC1 OTA CCDs, we observe a pattern in the photometric 248 residuals which is similar in appearence to the Tree Rings described 249 in the Dark Energy Camera (DECam) by \cite{plazas.2014}. This pattern 250 consists of systematic deviations which are consistent in a set of 251 circular arcs centered on the corner of the CCD, as shown in 252 Figure~\ref{fig:psfmags.by.filter}. The details of the analysis used 253 to generate Figure~\ref{fig:psfmags.by.filter} are given below. For 254 now, we note that the GPC1 CCDs are constructed by dividing the 255 circular silicon wafer into 4 inscribed squares. Thus the corners of 256 the CCDs lie in the center of the silicon boule, just as the center of 257 the circular Tree Rings described by \cite{plazas.2014} match the 258 center of the boule from which they came. This gives the impression 259 that a similar mechanism is responsible for the pattern observed in 260 the PS1 photometry and the DECam photometry, namely the diffusive 261 effects of lateral electric field variations in the detectors. In the 262 next section, we will make the case that the patterns observed in the 263 PS1 residuals are {\em not} caused by this mechanism, but are instead 264 caused by variations in the {\em vertical} electric field (the field 265 direction perpendicular to the CCD surface). 266 267 First, in this section, we will describe how we have measured the 268 presence or absence of these tree-ring patterns in 5 types of data. 269 For all of these examples, we use a single GPC1 CCD (XY40) to 270 illustrate the effects in detail, but a similar set of effects are 271 seen in \note{many? most?} GPC1 detectors. First, we show the 272 residual PSF photometry. Second, we show the residual Aperture 273 photometry. Third, we show the astrometric residual patterns. 274 Fourth, we show the patterns observed in the flat-field images. 275 Finally, we show measurements derived from the second-moments of the 276 stars. 277 278 For all effects discussed below, we are measuring the mean value of 279 the effect in 10x10 pixel superpixels across the detector. The 280 resulting images are all constructed so that a given superpixel 281 represents the same range of true GPC1 XY40 pixels regardless of the 282 type of measurement. To generate the photometry, astrometry, or 283 second-moment measurements were extracted from the \note{PV0} DVO 284 database for observations covering the region ($\alpha$,$\delta$) = 285 (90\degree\ -- 150\degree, -25\degree\ -- 10\degree). This region of 286 the sky provides a fairly high density of stars, but avoids the 287 Galactic Plane where confusion may potentially contaminate the 288 measurement. We limit the analysis to good measurements 289 (\ippmisc{PSF_QF} $>$ 0.85) of likely stars ($|m_{psf} - m_{aper}| < 290 0.2$). Only measurements with instrumental magnitude $< -8.0$ 291 ($-2.5\log \mbox{cts sec}^{-1} < -8.0$) are included to ensure 350 292 reasonable signal-to-noise per measurement. We require at least 2 351 293 measurements in a given filter and 5 measurements total for any star 352 294 included in the analysis. 353 354 The following four different measurements show tree-ring structures355 (a) photometric residuals, (b) astrometric residuals, (c) a portion of356 the flat-field structure, and (d) variations in the second-moment of357 stars. In the following section, we show the spatial patterns for358 these features and measure their intensity as a function of the359 different filters. By comparing the spatial structures, we show that360 these effects are directly related. We defer for now discussion of361 any causes of the observed effects.362 295 363 296 \subsubsection{Photometric Residuals} … … 397 330 \end{figure*} 398 331 399 The tree-ring structure is clearly seen in the PSF magnitude 400 residuals. In this case, we select PSF magnitude measurements for 401 detections which fall in the given superpixel. We subtract each 402 measurement from the average magnitude for the object in the selected 403 f ilter ($\delta m_{psf} = \overline{m}_{psf} - m_{psf}$) to determine the404 residual magnitude, excluding as bad any measurement with $|\delta 405 m_{psf}| > 0.5$. For a given superpixel, we measure the median of the 406 $\delta m_{psf}$ distribution. Figure~\ref{fig:psfmags.by.filter} 407 shows the 2D patterns of $\delta m_{psf}$ for each filter (\grizy). 408 The dynamic range of the color scale is from -20 to +20409 millimagnitudes for all 5 plots. 332 Figure~\ref{fig:psfmags.by.filter} shows the 2D patterns of PSF 333 photometric residuals. In this case, we select PSF magnitude 334 measurements for detections of stars which fall in the given 335 superpixel. We subtract each measurement from the average magnitude 336 for the object in the selected filter ($\delta m_{psf} = 337 \overline{m}_{psf} - m_{psf}$) to determine the residual magnitude, 338 excluding as an outlier any measurement with $|\delta m_{psf}| > 0.5$. 339 For a given superpixel, we measure the median of the $\delta m_{psf}$ 340 distribution. The figure shows $\delta m_{psf}$ for each filter 341 (\grizy). The dynamic range of the color scale is from -20 to +20 342 millimagnitudes for all 5 plots. 410 343 411 344 The tree-ring pattern is clearly visible for the four blue filters, … … 418 351 is comparable to the amplitude of the correlated structures, so we 419 352 need to integrate along the radial structures to make stronger 420 statements about these patterns. 421 422 We have also performed the same measurement for aperture magnitudes, 423 using the same selections. The 2D patterns for the aperture 424 magnitudes is shown in Figure~\ref{fig:apmags.by.filter}. The finging 353 statements about these patterns. \note{hanging statement?} 354 355 Figure~\ref{fig:apmags.by.filter} shows the equivalent measurement for 356 aperture photometry instead of PSF photometry. The finging 425 357 pattern again dominates the plot for \yps, but the tree-rings are not 426 358 seen in any of the filters. A diagonal pattern is visible in \gps … … 450 382 \end{figure*} 451 383 452 The tree-ring structure is also clearly seen in the astrometric 453 residuals. We use the same selection of measurements for astrometry 454 as for photometry. In this case, we extract the residual in both the 455 RA and DEC directions ($\delta RA = \overline{RA} - RA_i$, $\delta DEC 456 = \overline{DEC} - DEC_i$) and rotate these values to the chip 457 coordinate system ($\delta X,\delta Y$). We again exclude as bad any 458 measurement with $|\delta X|$ or $|\delta Y| > 0.5$ arcsec before 459 measuring the median values for each superpixel. We have determined 460 the approximate center of the circular tree-ring pattern as (-5,4960) 461 for this particular chip. Using this coordinate as the center, we 462 have converted the $\delta X,\delta Y$ offsets into $\delta R,\delta 463 \theta$ measurements ($\delta R$ : radial component away from the 464 center, $\delta \theta$ : tangential component). 384 Figure~\ref{fig:astrom.by.filter} shows a similar type of measurement 385 for astrometric residuals. To generate this plot, we use the same 386 selection of measurements for astrometry as for photometry. In this 387 case, we extract the residual in both the RA and DEC directions 388 ($\delta RA = \overline{RA} - RA_i$, $\delta DEC = \overline{DEC} - 389 DEC_i$) and rotate these values to the chip coordinate system ($\delta 390 X,\delta Y$) using our knowledge of the chip orientation on the sky. 391 We again exclude as bad any measurement with $|\delta X|$ or $|\delta 392 Y| > 0.5$ arcsec before measuring the median values for each 393 superpixel. We have determined the approximate center of the circular 394 tree-ring pattern as (-5,4960) for this particular chip. Using this 395 coordinate as the center of the pattern, we have converted the $\delta 396 X,\delta Y$ offsets into $\delta R,\delta \theta$ measurements 397 ($\delta R$ : radial component away from the center, $\delta \theta$ : 398 tangential component). 465 399 466 400 Figure~\ref{fig:astrom.by.filter} shows the 2D patterns of $\delta R$ 467 401 for each filter (\grizy). The dynamic range of the color scale is 468 from -20 to +20 milliarcseconds for all 5 plots. The tree-ring 469 pattern is visible for all five filters; the finging pattern is not 470 apparent in the \yps\ astrometry. \note{low-frequency structures? did 471 that take off fringing?} The per-pixel standard deviations of these 472 plots is listed in Table~\ref{table:sigmas.by.filter}. The 473 signal-to-noise of these structures is again somewhat weak, but the 474 pattern is clearly visible in these figures. 402 from -20 to +20 milliarcseconds for all 5 plots. A tree-ring-like 403 pattern is visible for all five filters, with systematic structures 404 following a circular pattern centered on the chip corner.; the finging 405 pattern is not apparent in the \yps\ astrometry. The per-pixel 406 standard deviations of these plots is listed in 407 Table~\ref{table:sigmas.by.filter}. The signal-to-noise of these 408 structures is again somewhat weak, but the pattern is clearly visible 409 in these figures. 475 410 476 411 \subsubsection{Flat-field Structures} … … 493 428 \end{figure*} 494 429 495 The tree-ring structure is also clearly seen in the flat-field 496 pattern. For this measurement, we have used a set of monochromatic 497 flat-field images obtained with a tunable laser. The laser is used to 498 illuminate our flat-field screen which is then observed by the PS1 499 telescope. These flat-field images were obtained 2011 Feb 09 as part 500 of a campaign to study the PS1 system response (Tonry et al REF). 501 Flats were obtain in a set of 4nm steps, with XXnm band-pass. To 502 enhance the signal-to-noise, we have combined a set of 6 flats at the 503 center of the corresponding filter. \note{high-pass filtering}. 430 Figure~\ref{fig:flats.by.filter} shows the high-spatial-frequency 431 structures in the flat-field images. For this measurement, we have 432 used a set of monochromatic flat-field images obtained with a tunable 433 laser. The laser is used to illuminate our flat-field screen which is 434 then observed by the PS1 telescope. These flat-field images were 435 obtained 2011 Feb 09 as part of a campaign to study the PS1 system 436 response \citep{tonry.phot}. Flats were obtain in a set of 4nm steps, 437 with \note{XXnm} band-pass. To enhance the signal-to-noise, we have 438 median-combined a set of 6 flats at the center of the corresponding filter. 439 440 In order to mask pixels which do not flatten well, we generate a 441 a copy of the image smoothed with a Gaussian kernel with 442 $\sigma = 1.5 pixels$. Any pixels in the smoothed image which deviate 443 from the median value in the image by more than 4 standard deviations 444 is masked. We generate the superpixel image by averaging the unmasked 445 pixels associated with each superpixel. We then high-pass filter the 446 superpixel image by subtracting a copy smoothed with a Gaussian of 447 $\sigma = 3.0$. 504 448 505 449 Figure~\ref{fig:flats.by.filter} shows the remaining high-frequency … … 513 457 measured flux in those pixels, and thus a {\em negative} deviation in 514 458 $\delta m_{psf}$ as defined above. The dynamic range of the color 515 scale in these plots is -0.01 to +0.01. The tree-ring pattern is459 scale in these plots is -0.01 to +0.01. The tree-ring-like pattern is 516 460 strong in the (\gps,\rps,\ips) images, but nearly swamped by fringing 517 461 in \zps, and completely lost to finging in \yps. A diagonal banding … … 556 500 \end{figure*} 557 501 558 The tree-ring structure is also seen in the changes of the image size. 559 To measure this effect, we extract the second moments for all 560 detections, subject to the same selections as for the photometry and 561 astrometry residuals (good stars, multiple detections). The second 562 moments are measured with a Gaussian weighting function, with the 563 $\sigma_{w}$ scaled by the PSF size so that the $\sigma$ measured for 564 PSF stars is \approx 60\% of $\sigma_{w}$. (Note that, since the 565 measured $\sigma$ of stellar objects is biased down by the weighting 566 function, this is not quite the same as having $\sigma_{w} = 1.6$ 567 times the true PSF $\sigma$). For each detection, we measure 568 $M_{xx,xy,yy} = \sum F_i w_i (x^2, x y, y^2) / \sum F_i w_i$. For 569 each exposure, we find the mean second moments for PSF objects and 502 During the image analysis, the second moments are measured for all 503 stars. The values can be used to assess changes in the shape of stars 504 on the image. To measure changes in the shapes, we have extracted the 505 second moments for all stellar detections, subject to the same 506 selections as for the photometry and astrometry residuals (good stars, 507 multiple detections). The second moments are measured with a Gaussian 508 weighting function, with the $\sigma_{w}$ scaled by the PSF size so 509 that the $\sigma$ measured for PSF stars is \approx 60\% of 510 $\sigma_{w}$. (Note that, since the measured $\sigma$ of stellar 511 objects is biased down by the weighting function, this is not quite 512 the same as having $\sigma_{w} = 1.6$ times the true PSF $\sigma$, see 513 discussion in \citealt{magnier.etal.2017.analysis}). For each stellar 514 detection, we extract the values $M_{xx,xy,yy} = \sum F_i w_i (x^2, x 515 y, y^2) / \sum F_i w_i$. For each exposure, we find the mean second 516 moments ($\bar{M_{xx,xy,yy}}$) for PSF objects on this chip (XY40) and 570 517 subtract that mean value from the instantaneous measurements of 571 518 $M_{xx,xy,yy}$. We then determine the median of the residual second 572 moments for each superpixel. 519 moments for each superpixel, resulting in 3 images for each filter. 520 521 \note{write out this math, check out psLibADD} 522 523 Using the second moment images, we can construct certain interesting 524 combinations, inspired by discussions of lensing measurements \citep{kaiser.1995}: 525 \begin{eqnarray} 526 R^2 & = & \delta M_{xx} + \delta M_{yy} \\ 527 e_1 & = & \delta M_{xx} + \delta M_{yy} \\ 528 e_2 & = & 2 \delta M_{xy} 529 \end{eqnarray} 573 530 574 531 Figure~\ref{fig:smear.by.filter} shows the spatial trend of the {\em … … 576 533 \delta M_{yy}$. This value corresponds to the increase or decrease in 577 534 the circularly-symmetric component of the image size. The dynamic 578 range of these images is -0.3 to +0.3 pixel$^2$. The tree-ring pattern579 is visible for all 5 filters, though \yps is dominated by the fringing 580 pattern. Structures with relatively low spatial frequencies can also 581 be seen.535 range of these images is -0.3 to +0.3 pixel$^2$. A tree-ring-like 536 pattern is visible for all 5 filters, though \yps is dominated by the 537 fringing pattern. Structures with relatively low spatial frequencies 538 can also be seen. 582 539 583 540 We can also construct a measurement of the change in ellipticity … … 590 547 ellipse orientation as a function of postion. The length of the 591 548 vectors corresponds to the value of $\sigma^2_{major} - 592 \sigma^2_{minor}$. The tree-ring structure is notapparent in this549 \sigma^2_{minor}$. The tree-ring-like structure is {\em not} apparent in this 593 550 figure for any filter. The spatial variations are low-frequency and 594 551 unrelated to the radial trend from the upper-left corner. 595 552 596 \subsubsection{Correlations Between Systematic Trends}553 \subsubsection{Correlations Between Tree-Ring-Like Patterns} 597 554 598 555 \begin{table} … … 614 571 \end{table} 615 572 616 As discussed above, the signal-to-noise per pixel in the plots of the 617 systematic trends is relatively low (\approx 1.0). While the tree 618 rings are apparent in many of these figures, there are also 619 some other systematic structures which may degrade the signal 620 further. To quantatatively compare the tree-ring trends between 621 filters and between systematic effects, we need to measure the 573 Tree-ring-like patterns are clearly seen in 4 of the measurement types 574 above: the PSF photometry, the astrometry, the flat-field, and the 575 smear terms. As discussed above, the signal-to-noise per pixel in the 576 plots of the systematic trends is relatively low (\approx 1.0). While 577 the tree-ring-like patterns are apparent in many of these figures, 578 there are also some other systematic structures which may degrade the 579 signal further. 580 581 To quantatatively compare the tree-ring-like trends between 582 filters and between the types of measurements, we need to measure the 622 583 tree-ring structure explicitly and filter out the other effects if 623 584 possible. To do this, we have applied a high-pass filter to all of … … 630 591 the arc to minimize the error associated with the choice of the 631 592 pattern center and to avoid several bad cells near the bottom of the 632 chip. \note{draw the arcs?}633 634 For a given t rend, the systematic effect is strongly correlated635 between filters. The strongest correlation is the smear term: 636 Figure~\ref{fig:smear.trends} shows the correlation of the smear593 chip. 594 595 For a given type of measurement, the systematic effect is strongly 596 correlated between filters. The strongest correlation is the smear 597 term: Figure~\ref{fig:smear.trends} shows the correlation of the smear 637 598 pattern between \gps\ and the other four filters. Even \yps\ is 638 599 strongly correlated with \gps\ despite the presence of the fringe … … 645 606 flat-field residuals are generally correlated between filters, but 646 607 both \zps\ and \yps\ are affected by fringing. For \yps, the 647 correlation is completely washed out by the very strong fringing pattern. 648 649 For all four measurements, the slope of the fitted lines are listed in 650 Table~\ref{table:correlation.by.filter}. There is a consistency in 651 the trend from \gps, with the strongest systematic tree-ring effects 652 to \yps, with the weakest effects. Note that the second moment smear 653 and astrometry terms have different relative strength in 654 \yps\ compared with \gps. 608 correlation is completely washed out by the very strong fringing 609 pattern. 610 611 For all four types of measurements, the slope of the fitted lines are 612 listed in Table~\ref{table:correlation.by.filter}. There is a 613 consistency in the trend from \gps, with the strongest systematic 614 tree-ring effects to \yps, with the weakest effects. Note that the 615 second moment smear and astrometry terms have different relative 616 strength in \yps\ compared with \gps. 655 617 656 618 % smear trends by filter … … 694 656 \end{figure*} 695 657 696 An important question is the relationship between the different types 697 of systematic effects. Different models for the tree-ring structures 698 will make different predictions about the correlations between 699 different effects. We find the following relationships hold. First, 700 the PSF magnitude residuals and the second-moment smear trends are 701 strongly anti-correlated: regions which have larger PSFs than the mean 702 tend to have smaller measured PSF fluxes than the mean (note that 658 An important question is the relationship of the tree-ring-like 659 pattern between the different types of measurements. Different models 660 for the tree-ring structures make different predictions about the 661 correlations between different effects. Note the very different 662 spatial structure between the different measurements in a given 663 filter: the radial variations do not all follow the same patterns. 664 Instead, we find the following relationships hold: 665 666 First, the PSF magnitude residuals and the second-moment smear trends 667 are strongly anti-correlated: regions which have larger PSFs than the 668 mean tend to have smaller measured PSF fluxes than the mean (note that 703 669 $\delta m_{psf}$ is defined so that positive values correspond to 704 670 larger fluxes). These trends are shown in 705 Figure~\ref{fig:smear.vs.psfmag}. Second, the radial derivative of 706 the smear is anti-correlated with the radial component of the 707 astrometric residuals: $\frac{\partial (\sigma^2_{major} + 708 \sigma^2_{minor})}{\partial radius} \sim \delta R$ (see 709 Figure~\ref{fig:dsmear.vs.astrom}. Finally, the radial derivative of 710 the radial component of the astrometric residual is anti-correlated 711 with the flat-field residual errors: $\frac{\partial \delta 712 R}{\partial radius} \sim \delta flat$ (see 713 Figure~\ref{fig:dastrom.vs.flat}. This last relationship is somewhat 714 weakly measured. Because of the periodic nature of the tree rings, it 715 is also difficult to completely certain that the flat-field is 716 proportional to the derivative of the astrometry residual, and not the 717 other way around. The correlation is somewhat weaker for derivative 718 of the flat-field vs astrometry residual. The correlation is very 719 weak between the flat-field and the astrometry directly. We are 720 convinced that we have the sense of the derivative correct by the 721 details of specific features. 671 Figure~\ref{fig:smear.vs.psfmag}. 672 673 Second, the radial derivative of the smear is anti-correlated with the 674 radial component of the astrometric residuals: $\frac{\partial 675 (\sigma^2_{major} + \sigma^2_{minor})}{\partial radius} \sim \delta 676 R$ (see Figure~\ref{fig:dsmear.vs.astrom}. 677 678 Finally, the radial derivative of the radial component of the 679 astrometric residual is anti-correlated with the flat-field residual 680 errors: $\frac{\partial \delta R}{\partial radius} \sim \delta flat$ 681 (see Figure~\ref{fig:dastrom.vs.flat}. This last relationship is 682 somewhat weakly measured. Because of the periodic nature of the tree 683 rings, it is also difficult to be completely certain that the 684 flat-field is proportional to the derivative of the astrometry 685 residual, rather than the astrometry residual being proportional to 686 the derivative of the flat-field. The correlation is somewhat weaker 687 for derivative of the flat-field vs astrometry residual. The 688 correlation is very weak between the flat-field and the astrometry 689 residual values without a derivative. We are convinced that we have 690 the sense of the derivative correct by examination of specific 691 features in each imaage (e.g., \note{give example}). 722 692 723 693 \begin{table} … … 772 742 773 743 These trends help to illuminate the underlying causes of these 774 different effects. First, we can easily explain the relationship 775 between the PSF photometry residuals and the observed smear. In the 776 photometry analysis, we model the PSF allowing for some spatial 777 variation in the shape. However, we limit the 2D variation to a 3x3 778 grid for each chip: the PSF parameters may vary smoothly across the 779 chip following the bilinear interpolation between the 3x3 grid points. 744 different effects. 745 746 \note{summarize what pure lateral electric fields would do} 747 748 First, if we consider the smear pattern 749 (Figure~\ref{fig:smear.by.filter}), the measurement shows that the 750 intrinsic size of the stellar images is varying in a radial sense 751 between the different tree-ring regions. Although images experience 752 an average image quality (due to seeing and focus) across the chip 753 which may vary substantially from exposure to exposure, stars landing 754 in the different tree-ring-like regions are consistently somewhat 755 larger or somewhat smaller than that average. 756 757 Next, we can explain the relationship between the PSF photometry 758 residuals and the observed smear: In the photometry analysis, we model 759 the PSF, allowing for some spatial variation in the shape. However, 760 we have a limited number of stars to measure any spatial variation. 761 Thus the 2D variation are sampled on a very coarse (e.g., 3x3) grid 762 for each chip: the PSF parameters may vary smoothly across the chip 763 following the bilinear interpolation between the 3x3 grid points. 780 764 Thus, the spatial scale on which we model PSF variations is much 781 765 larger than the spatial scale on which PSF variations are apparently 782 occuring . When the true PSF is larger than the model PSF, our model783 fits systematically underestimate the amount of flux in a given 784 object. Conversely, when the PSF is smaller, we overestimate the 785 flux. The slope of the trend depends on the mean typical seeing for 786 the given filter. For example, the \gps\ seeing is typically 787 1.3\arcsec, corresponding to a Gaussian $\sigma$ of 2.15 pixels. A 788 smearing of $\sigma^2_{major} + \sigma^2_{minor} = 0.1$ pixels$^2$ 789 would increase the size by about 0.02 pixels, or 1\%, so roughly 790 consistent with the observed photometric deviation of about 5 to 10 791 millimags for this amount of smearing. \note{model the 2D effect more 792 explicitly}.793 794 Second, the relationship between the flat-field residual and the 795 astrometric gradient is consistent with radial variations in the796 plate-scale. The tree-rings observed by DES are completely attributed 797 to effective plate scale changes. Effective plate scale changes would 798 result in flat-field deviations since the flat-field illumination is a 799 source of constant surface brightness. Pixels see a varying amount of 800 flux depending on their effective area. This changing plate scale 801 a lso affects the astrometry since these variations occur on spatial802 scalesmuch smaller than the astrometric model. In such a model, the766 occuring, as illustrated by the changes in the smear plot. When the 767 true PSF is larger than the model PSF, our model fits systematically 768 underestimate the amount of flux in a given object. Conversely, when 769 the PSF is smaller, we overestimate the flux -- this type of offset is 770 a typical effect when mis-estimating the PSF size. The slope of the 771 trend depends on the mean typical seeing for the given filter. For 772 example, the \gps\ seeing is typically 1.3\arcsec, corresponding to a 773 Gaussian $\sigma$ of 2.15 pixels. A smearing of $\sigma^2_{major} + 774 \sigma^2_{minor} = 0.1$ pixels$^2$ would increase the size by about 775 0.02 pixels, or 1\%, roughly consistent with the observed photometric 776 deviation of about 5 to 10 millimags for this amount of smearing. 777 778 The relationship between the flat-field residual and the astrometric 779 gradient is consistent with radial variations in the plate-scale. The 780 tree-rings observed by DES are completely attributed to effective 781 plate scale changes. Effective plate scale changes would result in 782 flat-field deviations since the flat-field illumination is a source of 783 constant surface brightness. Pixels see a varying amount of flux 784 depending on their effective area. This changing plate scale also 785 affects the astrometry since these variations occur on spatial scales 786 much smaller than the astrometric model. In such a model, the 803 787 flat-field deviations are $-1 \times \frac{\partial Pos}{\partial R}$. 804 788 The slope of our relationship is \approx 0.5 in normalized units. … … 806 790 2. \note{looks like a slope of 1.0 would not be excluded by these 807 791 plots} 792 793 \note{I need to use the relationship between the astrometry and the 794 flat-field to calculate the amplitude of the lateral electric 795 fields.} 808 796 809 797 The fact that the PSF ellipticity changes are {\em not} correlated … … 841 829 842 830 \end{document} 831 832 Notes for paper re-work: 833 834 * Paper focus is now only on the diffusion variations 835 * strip out the discussion of other systematic effects 836 * strip down the PS1 introduction discussion 837 838 * tentative title: 839 Evidence for Small-Scale Charge-Diffusion Variations in Pan-STARRS CCDs 840 841 * outline 842 843 1. introduction 844 * thick CCDs 845 * tree rings == transverse field effects (see Plazas et al) 846 * we see something else 847 848 4 model : diffusion variations due to E|| field variations 849 850 5 discussion (how to treat in calibration / analysis) 851 852 6 conclusions 853 854 some possible refs to tree rings / charge diff: 855 856 * http://adsabs.harvard.edu/abs/2016SPIE.9904E..2CW (Woods et al 2016; TESS) 857 * https://arxiv.org/pdf/1605.01001.pdf : plazas et al 858 * http://ieeexplore.ieee.org/document/1225293/?part=1 Altmannshofer et al 2003 (about thick Si) 859 860 * plazas et al 2014 outline 861 862 1. intro: thick CCDs, transverse electric fields 863 2. DES / DECam 864 865 2.1 flat-field tree rings (discussion of flat-field tree rings 866 starting from the premise that they know the answer). 867 868 3 impact on astrometry and photometry 869 870 4 improving calibrations given tree rings 871 872 5 summary and conclusions 873
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