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trunk/doc/release.2015/systematics.20140411/systematics.tex
r40105 r40108 94 94 $3\pi$ survey to characterize the behavior of the deep-depletion 95 95 devices used in the Pan-STARRS\,1 Gigapixel Camera. We have 96 identified systematic variations in the photometric behavior and97 stellar profiles which are similar to the so-called tree rings96 identified systematic spatial variations in the photometric behavior and 97 stellar profiles which are similar to the so-called Tree Rings 98 98 identified in devices used by other wide-field cameras (DECam and 99 Hypersuprime Camera). The tree-ring features identified in these99 Hypersuprime Camera). The Tree-Ring features identified in these 100 100 other cameras result from lateral electric fields which displace the 101 101 electrons as they are transported in the silicon to the pixel 102 102 location. In contrast, we show that the photometric and morphological 103 103 modifications observed in the GPC1 detectors are caused by variations 104 in the vertical charge transportation ra nge and resulting charge104 in the vertical charge transportation rate and resulting charge 105 105 diffusion variations. 106 106 \end{abstract} … … 110 110 111 111 \section{INTRODUCTION}\label{sec:intro} 112 113 \note{KCC says: note what is unique to GPC1 vs other cameras} 112 114 113 115 CCD detectors have evolved greatly since they were first introduced … … 148 150 1990s \citep{Holland.1996}, CCDs made from thick, high-resistivity ($ 149 151 > 10 k\Omega$-cm) silicon were developed for astronomical instruments 150 in the early 2000s \citep{Holland.2003}. The high-resistivity of the152 in the early 2000s \citep{Holland.2003}. The high-resistivity of the 151 153 silicon allows for depletion regions of hundreds of microns in depth, 152 154 compared to \approx 10\micron\ for the low-resistivity silicon. This … … 158 160 to be absorbed, increasing quantum efficiency in the red. Because 159 161 these thick, deep-depletion devices have near-unity quantum efficiency 160 across the whole a very wide spectral range, they have become the161 design of choice for many modern, large-scale CCD cameras (e.g., 162 Pan-STARRS GPC1, \citealt{2009amos.confE..40T}; Subaru Hypersuprime 163 Camera,\citealt{2010SPIE.7735E..3FK}; Dark Energy Survey Camera,162 across a very wide spectral range, they have become the design of 163 choice for many modern, large-scale CCD cameras (e.g., Pan-STARRS 164 GPC1, \citealt{2009amos.confE..40T}; Subaru Hypersuprime Camera, 165 \citealt{2010SPIE.7735E..3FK}; Dark Energy Survey Camera, 164 166 \citealt{2015AJ....150..150F}). 165 167 … … 174 176 175 177 The effects of lateral electric fields are likewise identified as the 176 cause of the so-called ``Tree -Rings'' observed in the flat-field,178 cause of the so-called ``Tree Rings'' observed in the flat-field, 177 179 astrometry, and photometry response of thick deep depletion detectors 178 \citep{2014PASP..126..750P}. These tree-ring patterns have been noted180 \citep{2014PASP..126..750P}. These Tree-Ring patterns have been noted 179 181 in the flat-field response of deep depletion devices since their early 180 182 testing \citep[see, e.g., Figure 2 in][]{2010SPIE.7735E..1RE} and were … … 219 221 March 2014, PS1 was run under the aegis of the Pan-STARRS Science 220 222 Consortium to perform a set of wide-field science surveys; since March 221 2014, the telescope has been operated by the Pan-STARRS New Science 222 Consortium (PSNSC). Under the PS1SC, the largest survey, both in 223 terms of area of the sky covered ($3\pi$ steradians) and fraction of 224 observing time (56\%), was the \TPS\ in which the entire sky north of 225 Declination $-30$\degrees\ was imaged up \approx 80 times over 4 226 years. These observations were distributed over five filters, \grizy, 227 and have been astrometrically and photometrically calibrated to good 228 precision \citep{magnier2017.calibration}. 223 2014, operations have been supported primarily by NASA's Near Earth 224 Object Observation program, see \cite{wainscoat.2015}. Under the 225 PS1SC, the largest survey, both in terms of area of the sky covered 226 ($3\pi$ steradians) and fraction of observing time (56\%), was the 227 \TPS\ in which the entire sky north of Declination $-30$\degrees\ was 228 imaged up \approx 80 times over 4 years. These observations were 229 distributed over five filters, \grizy, and have been astrometrically 230 and photometrically calibrated to good precision 231 \citep{magnier2017.calibration}. 229 232 230 233 % 2004SPIE.5489..667H == PS1.optics … … 310 313 the relatively small number of images available at the time. We have 311 314 found that a single flat-field set can be used for all PS1 312 observations to yield photometric consistencyat the level of \approx315 observations to yield photometric systematic errors at the level of \approx 313 316 2\%. PS1 benefits in this regard from the stability of having a 314 317 single instrument which is rarely removed. … … 319 322 aperture photometry performed using an aperture defined based on the 320 323 image quality observed for a given chip. The aperture diameter is set 321 to be \approx3.75 times the FWHM for the image.324 to be 3.75 times the FWHM for the image. 322 325 323 326 To improve the photometric systematic errors beyond the level achieved … … 331 334 correction determined during the ubercal analysis 332 335 \citep[see][]{2012ApJ...756..158S} consisted of an $8\times 8$ grid of 333 corrections for each GPC1 chip and filter for each of 4 seasons. The 334 boundaries of those seasons are tentatively identified with 335 modifications to the baffle structures or the system optics. The 336 critical point here is that the final effective flat-field image for 337 the PV2 dataset is based on a dome-flat at the highest resolution, 338 with very low resolution corrections based on photometry, resulting in 339 photometric systmatic uncertainties in the range 7 - 12 340 millimagnitudes, depending on the filter \citep{2013ApJS..205...20M}. 336 corrections for each GPC1 chip, corresponding to a correction for each 337 OTA ``cell'' and filter for each of 4 seasons. The boundaries of 338 those seasons are tentatively identified with modifications to the 339 baffle structures or the system optics. The critical point here is 340 that the final effective flat-field image for the PV2 dataset is based 341 on a dome-flat at the highest resolution, with very low resolution 342 corrections based on photometry, resulting in photometric systematic 343 uncertainties in the range 7 - 12 millimagnitudes, depending on the 344 filter \citep{2013ApJS..205...20M}. 341 345 342 346 For all objects, positions are measured from the PSF model for the … … 371 375 \end{table} 372 376 373 For many of the GPC1 OTA CCDs, we observe a pattern in the photometric374 residuals which is similar in appearence to the Tree Rings described 375 in the Dark Energy Camera (DECam) by \cite{2014PASP..126..750P}. This 376 pattern consists of systematic deviations which are consistent in a 377 set of circular arcs centered on the corner of the CCD, as shown in378 Figure~\ref{fig:psfmags.by.filter}. The details of the analysis used 379 to generate Figure~\ref{fig:psfmags.by.filter} are given below. For 380 now, we note that the GPC1 CCDs are constructed by dividing the381 circular silicon wafer into 4 inscribed squares. Thus the corners of 382 the CCDs lie in the center of the silicon boule, just as the center of 383 the c ircular Tree Rings described by \cite{2014PASP..126..750P} match384 the center of the boule from which they came. This gives the 385 impression that a similar mechanism is responsible for the pattern 386 observed in the PS1 photometry and the DECam photometry, namely the 387 diffusive effects of lateral electric field variations in the 388 detectors. In the next section, we will make the case that the 389 patterns observed in the PS1 photometry residuals are {\em not} caused 390 by this mechanism, but are instead caused by variations in the {\em 391 vertical} electric field (the field direction perpendicular tothe392 CCD surface).377 For many of the GPC1 OTA CCDs, we observe a spatial pattern in the 378 photometric residuals for each device which is similar in appearence 379 to the Tree Rings described in the Dark Energy Camera (DECam) by 380 \cite{2014PASP..126..750P}. This pattern consists of systematic 381 deviations which are consistent in a set of circular arcs centered on 382 the corner of the CCD, as shown in Figure~\ref{fig:psfmags.by.filter}. 383 The details of the analysis used to generate 384 Figure~\ref{fig:psfmags.by.filter} are given below. For now, we note 385 that the GPC1 CCDs are constructed by dividing the circular silicon 386 wafer into 4 inscribed squares. Thus the corners of the CCDs lie in 387 the center of the silicon boule, just as the center of the circular 388 Tree Rings described by \cite{2014PASP..126..750P} match the center of 389 the boule from which they came. This gives the impression that a 390 similar mechanism is responsible for the pattern observed in the PS1 391 photometry and the DECam photometry, namely the diffusive effects of 392 lateral electric field variations in the detectors. In the next 393 section, we will make the case that the patterns observed in the PS1 394 photometry residuals are {\em not} caused by this mechanism, but are 395 instead caused by variations in the {\em vertical} electric field (the 396 field direction perpendicular to the CCD surface). 393 397 394 398 First, in this section, we will describe how we have measured the 395 presence or absence of these tree-ring patterns in 5 types of data.399 presence or absence of these Tree-Ring patterns in 5 types of data. 396 400 For all of these examples, we use a single GPC1 CCD (XY40) to 397 401 illustrate the effects in detail, but a similar set of effects are 398 402 seen in many of the GPC1 detectors. First, we show the residual PSF 399 photometry. Second, we show the residual Aperture photometry. Third,403 photometry. Second, we show the residual aperture photometry. Third, 400 404 we show the astrometric residual patterns. Fourth, we show the 401 405 patterns observed in the flat-field images. Finally, we show … … 408 412 type of measurement. To generate the photometry, astrometry, or 409 413 second-moment plots, measurements were extracted from the PV0 DVO 410 database for observations covering the region ($\alpha$,$\delta$) = 411 (90\degree\ -- 150\degree, -25\degree\ -- 10\degree). This region of 412 the sky provides a fairly high density of stars, but avoids the 413 Galactic Plane where confusion may potentially contaminate the 414 measurement. We limit the analysis to good measurements 415 (\ippmisc{PSF_QF} $>$ 0.85) of likely stars ($|m_{psf} - m_{aper}| < 416 0.2$). Only measurements with instrumental magnitude $< -8.0$ 417 ($-2.5\log \mbox{cts sec}^{-1} < -8.0$) are included to ensure 414 database \citep{magnier.2017.calibration} for observations covering 415 the region ($\alpha$,$\delta$) = (90\degree\ -- 150\degree, 416 -25\degree\ -- 10\degree). This region of the sky provides a fairly 417 high density of stars, but avoids the Galactic Plane where confusion 418 may potentially contaminate the measurement. We limit the analysis to 419 good measurements (\ippmisc{PSF_QF} $>$ 0.85, see 420 \citealt{magnier.2017.analysis}) of likely stars ($|m_{psf} - 421 m_{aper}| < 0.2$). Only measurements with instrumental magnitude $< 422 -8.0$ ($-2.5\log \mbox{cts sec}^{-1} < -8.0$) are included to ensure 418 423 reasonable signal-to-noise per measurement. We require at least 2 419 measurements in a given filter and 5 measurements total for any star420 included in the analysis.424 measurements in a given filter and at least 5 measurements total for 425 any star included in the analysis. 421 426 422 427 \subsection{Photometric Residuals} … … 428 433 \parbox{\figwidth}{\includegraphics[width=\figwidth]{\picdir/dmag.g.\plotext}} 429 434 \parbox{\figwidth}{ 430 \caption{PSF Magnitude residuals by Filter 431 } \label{fig:psfmags.by.filter}}435 \caption{PSF Magnitude residuals by Filter. \note{expand colorscale 436 bars, make clearer labels} } \label{fig:psfmags.by.filter}} 432 437 433 438 \includegraphics[width=\figwidth]{\picdir/dmag.r.\plotext} … … 468 473 millimagnitudes for all 5 plots. 469 474 470 The tree-ring pattern is clearly visible for the four blue filters,475 The Tree-Ring pattern is clearly visible for the four blue filters, 471 476 but finging dominates the pattern for \yps. Small offsets of 472 477 individual cells are also apparent for \zps. While the patterns are … … 481 486 Figure~\ref{fig:apmags.by.filter} shows the equivalent measurement for 482 487 aperture photometry instead of PSF photometry. The finging 483 pattern again dominates the plot for \yps, but the tree-rings are not488 pattern again dominates the plot for \yps, but the Tree Rings are not 484 489 seen in any of the filters. A diagonal pattern is visible in \gps 485 490 which is not observed in the PSF magnitudes. While the per-pixel … … 518 523 Y| > 0.5$ arcsec before measuring the median values for each 519 524 superpixel. We have determined the approximate center of the circular 520 tree-ring pattern as (-5,4960) for this particular chip. Using this 521 coordinate as the center of the pattern, we have converted the $\delta 522 X,\delta Y$ offsets into $\delta R,\delta \theta$ measurements 523 ($\delta R$ : radial component away from the center, $\delta \theta$ : 524 tangential component).525 Tree-Ring pattern as (-5,4960) for this particular chip based on the 526 pattern of the X astrometry displacements. Using this coordinate as the center 527 of the pattern, we have converted the $\delta X,\delta Y$ offsets into 528 $\delta R,\delta \theta$ measurements ($\delta R$ : radial component 529 away from the center, $\delta \theta$ : tangential component). 525 530 526 531 Figure~\ref{fig:astrom.by.filter} shows the 2D patterns of $\delta R$ 527 532 for each filter (\grizy). The dynamic range of the color scale is 528 from -20 to +20 milliarcseconds for all 5 plots. A tree-ring-like533 from -20 to +20 milliarcseconds for all 5 plots. A Tree-Ring-like 529 534 pattern is visible for all five filters, with systematic structures 530 following a circular pattern centered on the chip corner .; the finging535 following a circular pattern centered on the chip corner; the finging 531 536 pattern is not apparent in the \yps\ astrometry. The per-pixel 532 537 standard deviations of these plots is listed in … … 562 567 obtained 2011 Feb 09 as part of a campaign to study the PS1 system 563 568 response \citep{2012ApJ...750...99T}. Flats were obtain in a set of 564 4nm steps. To enhance the signal-to-noise, we have median-combined a 565 set of 6 flats at the center of the corresponding filter. 566 567 In order to mask pixels which do not flatten well, we generate a 568 a copy of the image smoothed with a Gaussian kernel with 569 $\sigma = 1.5 pixels$. Any pixels in the smoothed image which deviate 570 from the median value in the image by more than 4 standard deviations 571 is masked. We generate the superpixel image by averaging the unmasked 572 pixels associated with each superpixel. We then high-pass filter the 573 superpixel image by subtracting a copy smoothed with a Gaussian of 574 $\sigma = 3.0$. 569 4nm steps sampling the spectral response curve of each filter. To 570 enhance the signal-to-noise, we have median-combined a set of 6 flats 571 at the wavelength center of the corresponding filter. 572 573 In order to mask pixels which do not flatten well, we generate a copy 574 of the image smoothed with a Gaussian kernel with $\sigma = 1.5$ 575 pixels. Any pixels in the smoothed image which deviate from the 576 median value in the image by more than 4 standard deviations are 577 masked. We generate the superpixel image by averaging the unmasked 578 pixels associated with each superpixel. In order to suppress 579 large-scale gradients in the flat-field response, we high-pass filter 580 the superpixel image by subtracting a copy smoothed with a Gaussian of 581 $\sigma = 3.0$. 575 582 576 583 Figure~\ref{fig:flats.by.filter} shows the remaining high-frequency … … 584 591 measured flux in those pixels, and thus a {\em negative} deviation in 585 592 $\delta m_{psf}$ as defined above. The dynamic range of the color 586 scale in these plots is -0.01 to +0.01. The tree-ring-like pattern is593 scale in these plots is -0.01 to +0.01. The Tree-Ring-like pattern is 587 594 strong in the (\gps,\rps,\ips) images, but nearly swamped by fringing 588 595 in \zps, and completely lost to finging in \yps. A diagonal banding 589 596 similar to the aperture residuals is seen in \gps. 597 598 \note{CZW asks about the blob in the flat-field response. KCC asks 599 about the brick-wall pattern. discuss these and fringing so we can 600 move on to the tree rings} 590 601 591 602 \subsection{Second Moments} … … 641 652 detection, we extract the values $M_{xx,xy,yy} = \sum F_i w_i (x^2, x 642 653 y, y^2) / \sum F_i w_i$. For each exposure, we find the median second 643 moments for PSF objects on this chip (XY40) and subtract th atmedian644 value from the instantaneous measurements of $M_{xx,xy,yy}$. We then654 moments for PSF objects on this chip (XY40) and subtract those median 655 values from the instantaneous measurements of $M_{xx,xy,yy}$. We then 645 656 determine the median of the residual second moments for each 646 657 superpixel, resulting in 3 images ($\delta M_{xx,xy,yy}$) for each … … 661 672 e_2 & = & \sigma^2_{\mbox{major}} - \sigma^2_{\mbox{minor}} 662 673 \end{eqnarray} 663 Where $\sigma_{\mbox{major}}$ and $\sigma_{\mbox{minor}}$ are the major and minor axis 664 dimensions of the ellipse and $\theta$ is the position angle. 665 Thus, $e_0$ is a measurement of the change in the size of the stellar 666 PSFs as a function of position in the detector (``smear''), $e_2$ is a measurement 667 of the change in ellipticity of the stellar PSFs (``shear''), and we 668 can determine the angle of the PSF ellipticity from the $e_1$ term. 674 Where $\sigma_{\mbox{major}}$ and $\sigma_{\mbox{minor}}$ are the 675 major and minor axis dimensions of the ellipse and $\theta$ is the 676 position angle. Thus, $e_0$ is a measurement of the change in the 677 size of the stellar PSFs as a function of position in the detector 678 (``smear''), $e_2$ is a measurement of the change in ellipticity of 679 the stellar PSFs (``shear''), and we can determine the angle of the 680 PSF ellipticity from the $e_1$ term. 669 681 670 682 Figure~\ref{fig:smear.by.filter} shows the spatial trend of $e_0$, the {\em 671 683 smear}. This value corresponds to the increase or decrease in 672 684 the circularly-symmetric component of the image size. The dynamic 673 range of these images is -0.3 to +0.3 pixel$^2$. A tree-ring-like685 range of these images is -0.3 to +0.3 pixel$^2$. A Tree-Ring-like 674 686 pattern is visible for all 5 filters, though \yps is dominated by the 675 687 fringing pattern. Structures with relatively low spatial frequencies … … 683 695 ellipse orientation as a function of postion. The length of the 684 696 vectors corresponds to the value of $\sigma^2_{major} - 685 \sigma^2_{minor}$. The tree-ring-like structure is {\em not} apparent697 \sigma^2_{minor}$. The Tree-Ring-like structure is {\em not} apparent 686 698 in this figure for any filter. The spatial variations are 687 699 low-frequency and unrelated to the radial trend from the upper-left … … 692 704 \begin{table} 693 705 \caption{Systematic Trends : Correlations by filter\label{table:correlation.by.filter}} 706 \note{reconsider the column order} 694 707 % \tiny 695 708 \begin{center} … … 708 721 \end{table} 709 722 710 Tree- ring-like patterns are clearly seen in 4 of the measurement types723 Tree-Ring-like patterns are clearly seen in 4 of the measurement types 711 724 above: the PSF photometry, the astrometry, the flat-field, and the 712 725 smear terms. As discussed above, the signal-to-noise per pixel in the 713 726 plots of the systematic trends is relatively low (\approx 1.0). While 714 the tree-ring-like patterns are apparent in many of these figures,727 the Tree-Ring-like patterns are apparent in many of these figures, 715 728 there are also some other systematic structures which may degrade the 716 729 signal further. 717 730 718 To quantatatively compare the tree-ring-like trends between731 To quantatatively compare the Tree-Ring-like trends between 719 732 filters and between the types of measurements, we need to measure the 720 tree-ring structure explicitly and filter out the other effects if733 Tree-Ring structure explicitly and filter out the other effects if 721 734 possible. To do this, we have applied a high-pass filter to all of 722 the relevant images (PSF Photometry residuals, Astrometric residuals735 the relevant images (PSF photometry residuals, astrometric residuals 723 736 in the radial direction, flat-field residuals, and second moment smear 724 737 terms) to remove unrelated spatial structures. We have then measured … … 730 743 chip. 731 744 745 \note{include the arc on one of the figures?} 746 747 \note{do plots of all filter pairs in a triangle? is that interesting?} 748 732 749 For a given type of measurement, the systematic effect is strongly 733 750 correlated between filters. The strongest correlation is the smear … … 738 755 filters, as shown in Figure~\ref{fig:psfmag.trends}. Here, the 739 756 \yps\ correlation with \gps\ is quite weak: the fringing pattern 740 dominates the tree-rings for PSF photometry. The radial component of757 dominates the Tree Rings for PSF photometry. The radial component of 741 758 the astrometric residual is also well correlated between filters, with 742 759 no loss of correlation due to fringing in \yps. Finally, the … … 749 766 listed in Table~\ref{table:correlation.by.filter}. There is a 750 767 consistency in the trend from \gps, with the strongest systematic 751 tree-ring effects to \yps, with the weakest effects. Note that the768 Tree-Ring effects to \yps, with the weakest effects. Note that the 752 769 second moment smear and astrometry terms have different relative 753 770 strength in \yps\ compared with \gps. … … 758 775 \begin{center} 759 776 \includegraphics[width=\figwidth]{\picdir/smear.trends.\plotext} 760 \caption{Smear : correlation between filters 777 \caption{Smear : correlation between filters \note{include trend slopes in plots?} 761 778 } \label{fig:smear.trends} 762 779 \end{center} … … 793 810 \end{figure*} 794 811 795 An important question is the relationship of the tree-ring-like812 An important question is the relationship of the Tree-Ring-like 796 813 pattern between the different types of measurements. Different models 797 for the tree-ring structures make different predictions about the814 for the Tree-Ring structures make different predictions about the 798 815 correlations between different effects. Note the very different 799 816 spatial structure between the different measurements in a given … … 817 834 errors: $\frac{\partial \delta R}{\partial radius} \sim \delta flat$ 818 835 (see Figure~\ref{fig:dastrom.vs.flat}. This last relationship is 819 somewhat weakly measured. Because of the periodic nature of the tree820 rings, it is also difficult to be completely certain that the836 somewhat weakly measured. Because of the periodic nature of the Tree 837 Rings, it is also difficult to be completely certain that the 821 838 flat-field is proportional to the derivative of the astrometry 822 839 residual, rather than the astrometry residual being proportional to … … 885 902 (Figure~\ref{fig:smear.by.filter}), the measurement shows that the 886 903 intrinsic size of the stellar images is varying in a radial sense 887 between the different tree-ring regions. Although images experience904 between the different Tree-Ring regions. Although images experience 888 905 an average image quality (due to seeing and focus) across the chip 889 906 which may vary substantially from exposure to exposure, stars landing 890 in the different tree-ring-like regions are consistently somewhat907 in the different Tree-Ring-like regions are consistently somewhat 891 908 larger or somewhat smaller than that average. 892 909 … … 895 912 the PSF, allowing for some spatial variation in the shape. However, 896 913 we have a limited number of stars to measure any spatial variation. 897 Thus the 2D variation are sampled on a very coarse (e.g., 3x3) grid 898 for each chip: the PSF parameters may vary smoothly across the chip 899 following the bilinear interpolation between the 3x3 grid points. 900 Thus, the spatial scale on which we model PSF variations is much 901 larger than the spatial scale on which PSF variations are apparently 902 occuring, as illustrated by the changes in the smear plot. When the 903 true PSF is larger than the model PSF, our model fits systematically 904 underestimate the amount of flux in a given object. Conversely, when 905 the PSF is smaller, we overestimate the flux -- this type of offset is 906 a typical effect when mis-estimating the PSF size. The slope of the 907 trend depends on the mean typical seeing for the given filter. For 908 example, the \gps\ seeing is typically 1.3\arcsec, corresponding to a 909 Gaussian $\sigma$ of 2.15 pixels. A smearing of $\sigma^2_{major} + 910 \sigma^2_{minor} = 0.1$ pixels$^2$ would increase the size by about 911 0.02 pixels, or 1\%, roughly consistent with the observed photometric 912 deviation of about 5 to 10 millimags for this amount of smearing. 914 Thus the 2D variation are sampled on a very coarse (e.g., $3 \times 915 3$) grid for each chip: the PSF parameters may vary smoothly across 916 the chip following the bilinear interpolation between the $3 \times 3$ 917 grid points. Thus, the spatial scale on which we model PSF variations 918 is much larger than the spatial scale on which PSF variations are 919 apparently occuring, as illustrated by the changes in the smear plot. 920 When the true PSF is larger than the model PSF, our model fits 921 systematically underestimate the amount of flux in a given object. 922 Conversely, when the PSF is smaller, we overestimate the flux -- this 923 type of offset is a typical effect when mis-estimating the PSF size. 924 The slope of the trend depends on the mean typical seeing for the 925 given filter. For example, the \gps\ seeing is typically 1.3\arcsec, 926 corresponding to a Gaussian $\sigma$ of 2.15 pixels. A smearing of 927 $\sigma^2_{major} + \sigma^2_{minor} = 0.1$ pixels$^2$ would increase 928 the size by about 0.02 pixels, or 1\%, roughly consistent with the 929 observed photometric deviation of about 5 to 10 millimags for this 930 amount of smearing. 913 931 914 932 The relationship between the flat-field residual and the astrometric 915 933 gradient is consistent with radial variations in the plate-scale. The 916 tree-rings observed by DES are completely attributed to effective934 Tree-Rings observed by DES are completely attributed to effective 917 935 plate scale changes. Effective plate scale changes would result in 918 936 flat-field deviations since the flat-field illumination is a source of … … 927 945 928 946 The fact that the PSF ellipticity changes are {\em not} correlated 929 with the tree ring structure tells us that the effective plate-scale930 changes seen in the flat-field and astrometry signals are not alsothe947 with the Tree-Ring structure tells us that the effective plate-scale 948 changes seen in the flat-field and astrometry signals are not the 931 949 dominant cause of the PSF photometry errors. Also, the fact that we 932 950 do not measure significant aperture photometry errors correlated with 933 the tree rings confirms this point. The amplitude of the flat-field951 the Tree Rings confirms this point. The amplitude of the flat-field 934 952 errors are 1-2 millimagnitudes, much smaller than the PSF photometry 935 953 errors, and far below the pixel-to-pixel noise in the aperture … … 953 971 \section{Conclusion} 954 972 955 The tree rings observed in the Pan-STARRS GPC1 data show (at least)973 The Tree Rings observed in the Pan-STARRS GPC1 data show (at least) 956 974 two effects, though they are related. First, the images are 957 975 experiencing circularly-symmetric changes in the PSF size correlated 958 with the tree-ring pattern. These PSF size changes drive errors in959 the PSF photometry which the are also correlated with the tree ring976 with the Tree-Ring pattern. These PSF size changes drive errors in 977 the PSF photometry which the are also correlated with the Tree-Ring 960 978 pattern on the scale of a few millimagnitudes. These PSF size changes 961 979 are consistent with changes in the charge diffusion, which also … … 963 981 964 982 In addition, there are radial plate-scale changes correlated with the 965 tree rings. These plate-scale changes introduce a flat-field errors983 Tree Rings. These plate-scale changes introduce a flat-field errors 966 984 on the scale of \approx 1 millimagnitude and astrometric errors in the 967 985 scale of 2-3 milliarcseconds. The observed relationship between the … … 970 988 in][]{2014PASP..126..750P}. 971 989 972 The vertical diffusion variations and the lateral charge migration are 973 both driven by the same variations in the doping structures. This 974 point is clear from the spatial correlation of the gradient in the 975 smear variations and the astrometric variations. 990 The spatial correlation of the gradient in the smear variations and 991 the astrometric variations imply that both of these two types of tree 992 ring effects are related, even though they manifest through different 993 mechanisms. We suspect that the variations in both the vertical charge 994 diffusion and the lateral charge migration are driven by changes 995 in the electric field structures in the silicon due to the same 996 variations in the doping structures in the silicon. 976 997 977 998 % The small-scale variations in the charge diffusion observed in these … … 1029 1050 Lorand University (ELTE) and the Los Alamos National Laboratory. 1030 1051 1052 \note{add NASA ops grant(s)} 1053 1031 1054 \bibliographystyle{apj} 1032 1055 \bibliography{lib}{}
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