Changeset 40305
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trunk/doc/release.2015/systematics.20140411/diffusion.tex
r40304 r40305 19 19 %\newcommand\newtext[1]{\textbf{\color{blue}#1}} 20 20 21 \newcommand\oldtext[1]{\textbf{\color{lightgray}#1} 22 \newcommand\newtext[1]{\textbf{\color{blue}#1} 23 \newcommand\fixtext[1]{\textbf{\color{red}#1} 21 \definecolor{light-gray}{gray}{0.50} 22 \newcommand\oldtext[1]{\textbf{\color{light-gray}#1}} 23 \newcommand\newtext[1]{\textbf{\color{blue}#1}} 24 \newcommand\fixtext[1]{\textbf{\color{red}#1}} 24 25 25 26 \usepackage[T1]{fontenc}% (2) specify encoding … … 514 515 of the PSF magnitude tree-rings would certainly have been obvious. 515 516 517 \newtext{Figure~\ref{fig:all.effects.rband} shows the complete set of 518 measured effects for the \rps\ filter. In addition to the PSF and 519 aperture photometry, this figure shows the astrometric residuals, 520 the high-frequency flat-field structures, along with two 521 measurements derived from the second moments: the ``smear'' and the 522 ``shear'', discussed below.} 523 516 524 \subsection{Astrometric Residuals} 517 525 … … 533 541 %% \end{figure*} 534 542 535 Figure~\ref{fig:astrom.by.filter} shows a similar type of measurement 543 \oldtext{Figure~3} \newtext{Figure~\ref{fig:all.effects.rband} (middle-left)} 544 shows a similar type of measurement 536 545 for astrometric residuals. To generate this plot, we use the same 537 546 selection of measurements for astrometry as for photometry. In this … … 550 559 : tangential component). 551 560 552 Figure~\ref{fig:astrom.by.filter} shows the 2D patterns of $\delta R$561 \oldtext{Figure~\ref{fig:astrom.by.filter} shows the 2D patterns of $\delta R$ 553 562 for each filter (\grizy). The dynamic range of the color scale is 554 from -20 to +20 milliarcseconds for all 5 plots. A tree-ring563 from -20 to +20 milliarcseconds for all 5 plots.} A tree-ring 555 564 pattern is visible for all five filters, with systematic structures 556 565 following a circular pattern centered on the chip corner; the finging 557 pattern is not apparent in the \yps\ astrometry. The per-pixel566 pattern is not apparent in the \yps\ astrometry. \oldtext{The per-pixel 558 567 standard deviations of these plots are listed in 559 Table~\ref{table:sigmas.by.filter}. The signal-to-noise of these568 Table~\ref{table:sigmas.by.filter}.} The signal-to-noise of these 560 569 structures is again somewhat weak, but the pattern is clearly visible 561 570 in these figures. … … 579 588 580 589 % 2012ApJ...750...99T = Tonry et al PS1 phot system 581 Figure~\ref{fig:flats.by.filter} shows the high-spatial-frequency 590 \oldtext{Figure~4} \newtext{Figure~\ref{fig:all.effects.rband} (middle-right)} 591 shows the high-spatial-frequency 582 592 structures in the flat-field images. For this measurement, we have 583 593 used a set of monochromatic flat-field images obtained with a tunable … … 597 607 pixels associated with each superpixel. 598 608 599 Figure~\ref{fig:flats.by.filter} shows the superpixel images for the600 flat-fields in the five filters. These flat-field images are609 \fixtext{Figure~\ref{fig:flats.by.filter} shows the superpixel images for the 610 flat-fields in the five filters.} These flat-field images are 601 611 displayed as fractional deviations relative to the median flat-field 602 612 image and can thus be compared to the magnitude residuals. When … … 699 709 PSF ellipticity from the $e_1$ term. 700 710 701 Figure~\ref{fig:smear.by.filter} shows the spatial trend of the smear, 711 \oldtext{Figure~5} \newtext{Figure~\ref{fig:all.effects.rband} (lower-left)} 712 shows the spatial trend of the smear, 702 713 $e_0$. The dynamic range of these images is -0.3 to +0.3 pixel$^2$. A 703 714 tree-ring pattern is visible for all 5 filters, though \yps\ is … … 705 716 spatial frequencies can also be seen. 706 717 707 Figure~\ref{fig:shear.by.filter} shows the spatial trend of the shear, 718 \oldtext{Figure~6} \newtext{Figure~\ref{fig:all.effects.rband} (lower-right)} 719 shows the spatial trend of the shear, 708 720 $e_2$. This value is positive definite and is plotted with a color 709 721 scale ranging from -0.02 to 0.22 pixel$^2$. Overlayed on 710 Figure~\ref{fig:shear.by.filter} is a set of vectors representing the 722 \oldtext{Figure~6} \newtext{Figure~\ref{fig:all.effects.rband} (lower-right)} 723 is a set of vectors representing the 711 724 ellipse orientation as a function of postion. The length of the 712 725 vectors corresponds to the value of $e_2$. The tree-ring structure is … … 729 742 much higher frequencies than the previous two effects. Aperture 730 743 magnitude (upper-right) and shear residuals (lower-right) do not 731 show a strong signal consistent with either of the two patterns.} \label{fig:all.effects.rband} 744 show a strong signal consistent with either of the two patterns.} 745 \label{fig:all.effects.rband} 732 746 \end{center} 733 747 \end{figure*} … … 778 792 For a given type of measurement, the systematic effect is strongly 779 793 correlated between filters. The strongest correlation is the smear 780 term : Figure~\ref{fig:smear.trends}shows the correlation of the smear781 pattern between \gps\ and the other four filters . Even \yps\ is794 term\oldtext{: Figure~8 shows the correlation of the smear 795 pattern between \gps\ and the other four filters}. Even \yps\ is 782 796 strongly correlated with \gps\ despite the presence of the fringe 783 797 pattern. PSF photometric residuals are also correlated between 784 filters , as shown in Figure~\ref{fig:psfmag.trends}. Here, the798 filters\oldtext{, as shown in Figure~9}. Here, the 785 799 \yps\ correlation with \gps\ is quite weak: the fringing pattern 786 800 dominates the tree rings for PSF photometry. The radial component of … … 792 806 pattern. 793 807 794 For all four types of measurements, the slope of the fitted lines are 795 listed in Table~\ref{table:correlation.by.filter}. There is a 796 consistency in the trend from \gps, with the strongest systematic 797 tree-ring effects to \yps, with the weakest effects. Note that the 798 second moment smear and astrometry terms have different relative 799 strength in \yps\ compared with \gps. 808 For all four types of measurements, the \oldtext{slope of the fitted 809 lines} \newtext{amplitudes relative to \gps} are listed in 810 Table~\ref{table:correlation.by.filter}. There is a consistency in 811 the trend from \gps, with the strongest systematic tree-ring effects 812 to \yps, with the weakest effects. Note that the second moment smear 813 and astrometry terms have different relative strength in 814 \yps\ compared with \gps. 800 815 801 816 % smear trends by filter … … 849 864 pattern between the different types of measurements. Different models 850 865 for the tree-ring structures make different predictions about the 851 correlations between different effects. Note the very different 866 correlations between different effects. 867 % 868 \newtext{Figure~\ref{fig:effects.vs.radius} shows the radial run of the 869 four effects which show clear tree rings (in \rps). Since the tree 870 rings are relatively narrow, this figure shows only the radial range 871 of 150 - 300 pixels to allow the reader to see the relationship 872 between structures in the different effects. } 873 % 874 Note the very different 852 875 spatial structure between the different measurements in a given 853 876 filter: the radial variations do not all follow the same patterns. … … 863 886 signal for \gps\ (upper-left), \rps\ (upper-right), \ips\ (lower-left), 864 887 \zps\ (lower-right). 865 } \label{fig: smear.vs.psfmag}888 } \label{fig:effects.vs.radius} 866 889 \end{center} 867 890 \end{figure*} … … 876 899 signal for \gps\ (upper-left), \rps\ (upper-right), \ips\ (lower-left), 877 900 \zps\ (lower-right). 878 } \label{fig: smear.vs.psfmag}901 } \label{fig:dsmear.and.astrom} 879 902 \end{center} 880 903 \end{figure*} … … 889 912 signal for \gps\ (upper-left), \rps\ (upper-right), \ips\ (lower-left), 890 913 \zps\ (lower-right). 891 } \label{fig: smear.vs.psfmag}914 } \label{fig:dastrom.and.flat} 892 915 \end{center} 893 916 \end{figure*} … … 897 920 mean tend to have smaller measured PSF fluxes than the mean (note that 898 921 $\delta m_{psf}$ is defined so that positive values correspond to 899 larger fluxes). These trends are shown in 900 Figure~\ref{fig:smear.vs.psfmag}. 922 larger fluxes). \oldtext{These trends are shown in Figure 12.} 901 923 902 924 Second, the radial derivative of the smear is anti-correlated with the 903 radial component of the astrometric residuals: $\frac{\partial 904 (\sigma^2_{major} + \sigma^2_{minor})}{\partial radius} \sim \delta 905 R$ (see Figure~\ref{fig:dsmear.vs.astrom}). 925 radial component of the astrometric residuals 926 \newtext{Figure~\ref{fig:dsmear.and.astrom} shows the radial run of 927 $\frac{\partial (\sigma^2_{major} + \sigma^2_{minor})}{\partial radius}$ 928 and $\delta R$ together to illustrate this relationship.} 929 \oldtext{: $\frac{\partial(\sigma^2_{major} + \sigma^2_{minor})}{\partial radius} \sim \delta R$. (see Figure~13).} 906 930 907 931 Finally, the radial derivative of the radial component of the 908 astrometric residual is anti-correlated with the flat-field residual 909 errors: $\frac{\partial \delta R}{\partial radius} \sim \delta flat$ 910 (see Figure~\ref{fig:dastrom.vs.flat}). This last relationship is 911 somewhat weakly measured. Because of the periodic nature of the tree 912 rings, it is also difficult to be completely certain that the 913 flat-field is proportional to the derivative of the astrometry 914 residual, rather than the astrometry residual being proportional to 915 the derivative of the flat-field. The correlation is somewhat weaker 916 for derivative of the flat-field vs astrometry residual. The 917 correlation is very weak between the flat-field and the astrometry 918 residual values without a derivative. We are convinced that we have 919 the sense of the derivative correct by examination of specific 920 features in each image. 932 astrometric residual is correlated with the flat-field residual 933 errors. 934 \newtext{Figure~\ref{fig:dastrom.and.flat} shows the radial run of 935 $\frac{\partial \delta R}{\partial radius}$ and $\delta flat$ together 936 to illustrate this relationship.} 937 \oldtext{: $\frac{\partial \delta R}{\partial radius} \sim \delta flat$ (see Figure~14).} 938 939 This last relationship is somewhat weakly measured. Because of the 940 periodic nature of the tree rings, it is also difficult to be 941 completely certain that the flat-field is proportional to the 942 derivative of the astrometry residual, rather than the astrometry 943 residual being proportional to the derivative of the flat-field. 944 \newtext{Careful examination of Figures~\ref{fig:effects.vs.radius} 945 and \ref{fig:dastrom.and.flat} convince us that we have the sense of 946 the derivative correct.} 947 % 948 \oldtext{The correlation is somewhat weaker for derivative of the 949 flat-field vs astrometry residual. The correlation is very weak 950 between the flat-field and the astrometry residual values without a 951 derivative. We are convinced that we have the sense of the 952 derivative correct by examination of specific features in each 953 image.} 921 954 922 955 \begin{table} … … 987 1020 988 1021 First, if we consider the smear pattern 989 (Figure~\ref{fig:smear.by.filter}), the measurement shows that the 990 intrinsic sizes of the stellar images are varying in a radial sense 991 between the different tree-ring regions. Although images experience 992 an average image quality (due to seeing and focus) across the chip 993 which may vary substantially from exposure to exposure, stars landing 994 in the different tree-ring regions are consistently somewhat 1022 \oldtext{(Figure~5)}\newtext{(Figure~\ref{fig:all.effects.rband}, lower-left)}, 1023 the measurement shows that the intrinsic sizes of the stellar images 1024 are varying in a radial sense between the different tree-ring regions. 1025 Although images experience an average image quality \oldtext{(due to 1026 seeing and focus)} across the chip which may vary substantially from 1027 exposure to exposure \newtext{(due to seeing and focus)}, stars 1028 landing in the different tree-ring regions are consistently somewhat 995 1029 larger or somewhat smaller than that average. 996 1030 997 1031 Next, we can explain the correlation between the PSF photometry 998 residuals and the observed smear (Figure~\ref{fig:smear.vs.psfmag}). 1032 residuals and the observed smear 1033 \newtext{(Figure~\ref{fig:effects.vs.radius})}\oldtext{(Figure~12)}. 999 1034 In the photometry analysis, we model the PSF allowing for some spatial 1000 1035 variation in the shape. However, we have a limited number of stars to … … 1004 1039 interpolation between the $3 \times 3$ grid points. Thus, the spatial 1005 1040 scale on which we model PSF variations is much larger than the spatial 1006 scale on which PSF variations are actually occuring, as illustrated 1007 by the changes in the smear plot (Figure~\ref{fig:smear.by.filter}). 1041 scale on which PSF variations are actually occuring, as illustrated by 1042 the changes in the smear plot 1043 \oldtext{(Figure~5)}\newtext{(Figure~\ref{fig:all.effects.rband}, lower-left)}. 1008 1044 When the true PSF is larger than the model PSF, our model fits 1009 1045 systematically underestimate the amount of flux in a given object. 1010 Conversely, when the true PSF is smaller, we overestimate the flux -- this1011 t ype of offset is a typical effect when mis-estimating the PSF size.1012 The slope of the trend depends on the mean typical seeing for the 1013 given filter. For example, the \gps\ seeing is typically 1.3\arcsec, 1014 corresponding to a Gaussian $\sigma$ of 2.15 pixels. A smearing of 1015 $\sigma^2_{major} + \sigma^2_{minor} = 0.1$ pixels$^2$ would increase 1016 the size by about 0.02 pixels, or 1\%, roughly consistent with the 1017 observed photometric deviation of about 5 to 10 millimags for this 1018 amount of smearing.1046 Conversely, when the true PSF is smaller, we overestimate the flux -- 1047 this type of offset is a typical effect when mis-estimating the PSF 1048 size. The slope of the trend depends on the mean typical seeing for 1049 the given filter. For example, the \gps\ seeing is typically 1050 1.3\arcsec, corresponding to a Gaussian $\sigma$ of 2.15 pixels. A 1051 smearing of $\sigma^2_{major} + \sigma^2_{minor} = 0.1$ pixels$^2$ 1052 would increase the size by about 0.02 pixels, or 1\%, roughly 1053 consistent with the observed photometric deviation of about 5 to 10 1054 millimags for this amount of smearing. 1019 1055 1020 1056 The correlation between the flat-field structures and the radial 1021 1057 derivative of the astrometric residual displacements in the radial 1022 direction (Figure~\ref{fig:dastrom.vs.flat}) is consistent with radial 1023 variations in the plate-scale. The tree-rings observed by DES are 1024 completely attributed to effective plate scale changes. Effective 1025 plate scale changes result in flat-field deviations because the 1026 flat-field illumination is a source of constant surface brightness. 1027 Pixels see a varying amount of flux depending on their effective area. 1028 This changing plate scale also affects the astrometry since these 1029 variations occur on spatial scales much smaller than the astrometric 1030 model. In this description of the tree rings, the flat-field 1031 deviations are $-1 \times \frac{\partial \delta R}{\partial r}$. The 1032 best-fit slopes of our correlations are \approx 0.5, but the 1033 signal-to-noise is rather low. A slope of -1 appears to be consistent 1034 with our measurements. 1058 direction 1059 \oldtext{(Figure~14)}\newtext{(Figure~\ref{fig:dastrom.and.flat})} 1060 is consistent with radial variations in the plate-scale. The 1061 tree-rings observed by DES are completely attributed to effective 1062 plate scale changes. Effective plate scale changes result in 1063 flat-field deviations because the flat-field illumination is a source 1064 of constant surface brightness. Pixels see a varying amount of flux 1065 depending on their effective area. This changing plate scale also 1066 affects the astrometry since these variations occur on spatial scales 1067 much smaller than the astrometric model. In this description of the 1068 tree rings, the flat-field deviations are $-1 \times \frac{\partial 1069 \delta R}{\partial r}$. The best-fit slopes of our correlations are 1070 \approx 0.5, but the signal-to-noise is rather low. A slope of -1 1071 appears to be consistent with our measurements. 1035 1072 1036 1073 The fact that the PSF ellipticity changes are {\em not} correlated 1037 with the tree-ring structure (Figure~\ref{fig:shear.by.filter}) tells us 1038 that, unlike the case for DES, the effective plate-scale changes seen 1039 in the flat-field and astrometry signals are not the dominant cause of 1040 the PSF photometry errors. Also, the fact that we do not measure 1041 significant aperture photometry errors correlated with the tree rings 1042 confirms this point. The amplitude of the flat-field errors are 1-2 1043 millimagnitudes, much smaller than the PSF photometry errors, and far 1044 below the pixel-to-pixel noise in the aperture magnitude residuals. 1045 It is likely in our opinion that the plate-scale changes causing the 1046 flat-field and astrometry effects are affecting both the ellipticity 1047 and the aperture magnitudes, but the level of the effect is too small 1048 to see given the other systematic structures (in the shear plot) and 1049 the noise level (in the aperture magnitudes). 1074 with the tree-ring structure 1075 \oldtext{(Figure~6)}\newtext{(Figure~\ref{fig:all.effects.rband})} 1076 tells us that, unlike the case for DES, the effective plate-scale 1077 changes seen in the flat-field and astrometry signals are not the 1078 dominant cause of the PSF photometry errors. Also, the fact that we 1079 do not measure significant aperture photometry errors correlated with 1080 the tree rings confirms this point. The amplitude of the flat-field 1081 errors are 1-2 millimagnitudes, much smaller than the PSF photometry 1082 errors, and far below the pixel-to-pixel noise in the aperture 1083 magnitude residuals. It is likely in our opinion that the plate-scale 1084 changes causing the flat-field and astrometry effects are affecting 1085 both the ellipticity and the aperture magnitudes, but the level of the 1086 effect is too small to see given the other systematic structures (in 1087 the shear plot) and the noise level (in the aperture magnitudes). 1050 1088 1051 1089 Finally, the correlation between the smear structures and the 1052 1090 astrometry residuals shows that these two effects are connected. 1053 Although the correlation is weak in Figure~\ref{fig:dsmear.vs.astrom}, 1091 Although the correlation is weak in 1092 \oldtext{Figure~13} \newtext{Figure~\ref{fig:effects.vs.radius}}, 1054 1093 careful inspection of the location of these two tree ring patterns 1055 1094 shows that the locations of the rings in the radial astrometric
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