Changeset 39840
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trunk/doc/release.2015/ps1.calibration/calibration.tex
r39838 r39840 1 \documentclass[iop,floatfix]{emulateapj}1 % \documentclass[iop,floatfix]{emulateapj} 2 2 % \pdfoutput=1 3 3 4 4 % see latex.readme.txt for notes on using the PS1 template 5 %\documentclass[12pt,preprint]{aastex}5 \documentclass[12pt,preprint]{aastex} 6 6 %\documentclass[manuscript]{aastex} 7 7 %\documentclass[preprint2]{aastex} 8 8 %\documentclass[preprint2,longabstract]{aastex} 9 9 \RequirePackage{color} 10 % \input{astro.sty} 10 \RequirePackage{code} 11 \input{astro.sty} 11 12 12 13 % online version may use color, but print version needs b/w … … 86 87 87 88 % insert additional keywords as appropriate: 88 \keywords{Surveys:\PSONE }89 %\keywords{Surveys:\PSONE } 89 90 90 91 \section{Introduction}\label{sec:intro} … … 141 142 images are also corrected for fringing: a master fringe pattern is 142 143 scaled to match the observed fringing and subtracted. Mask and 143 variance image arrays are generated with the \changed{detrend 144 analysis} and carried forward at each stage of the IPP processing. 145 Source detection and photometry are performed for each chip 146 independently. As discussed below, preliminary astrometric and 147 photometric calibrations are performed for all chips in a single 148 exposure in a single analysis. 144 variance image arrays are generated with the detrend analysis and 145 carried forward at each stage of the IPP processing. Source detection 146 and photometry are performed for each chip independently. As 147 discussed below, preliminary astrometric and photometric calibrations 148 are performed for all chips in a single exposure in a single analysis. 149 149 150 150 Chip images are geometrically transformed based on the astrometric … … 266 266 A third form of the astrometry model is used in the context of the 267 267 calibration determined within the DVO database system. We retain the 268 two levels of transformations (chip $\r tarrow$ focal plane $\rtarrow$268 two levels of transformations (chip $\rightarrow$ focal plane $\rightarrow$ 269 269 tangent plane), but the relationship between the chip and focal plane 270 270 is represented with only the linear terms in the polynomial, … … 359 359 stars. For all possible pairs between the two lists, the values of 360 360 \[ 361 $\Delta X = X^{\rm ref}_{\rm chip} - X^{\rm obs}_{\rm chip}\\362 $\Delta Y = Y^{\rm ref}_{\rm chip} - Y^{\rm obs}_{\rm chip}361 \Delta X = X^{\rm ref}_{\rm chip} - X^{\rm obs}_{\rm chip}\\ 362 \Delta Y = Y^{\rm ref}_{\rm chip} - Y^{\rm obs}_{\rm chip} 363 363 \] 364 364 are generated. The collection of $\Delta X, \Delta Y$ values are … … 404 404 The astrometry solutions from the independent chip fits are used to 405 405 generate a single model for the camera-wide distortion terms. The 406 goal is to determine the two stage fit (chip $\r tarrow$ focal plane407 $\r tarrow$ tangent plane). There are a number of degenerate terms406 goal is to determine the two stage fit (chip $\rightarrow$ focal plane 407 $\rightarrow$ tangent plane). There are a number of degenerate terms 408 408 between these two levels of transformation, most obviously between the 409 409 parameters which define the constant offset from chip to focal plane … … 424 424 425 425 \note{describe the output smf file?} 426 427 \note{discuss the real-time photometric calibration} 426 428 427 429 \section{DVO Description} … … 522 524 contains 9 times as many rows as the Average table. The order of the 523 525 table is fixed in relation to the Average table: row $i$ of Average 524 defines the object with photometry contained in rows $9i \r tarrow 9i +526 defines the object with photometry contained in rows $9i \rightarrow 9i + 525 527 8$ ($i$ is zero counting). 526 528 … … 716 718 such as the instrumental variations and atmospheric attenuation. 717 719 \[ 718 M_{rel} & = & m_{inst} + ZP + M_{cal} \\720 M_{rel} = m_{inst} + ZP + M_{cal} 719 721 \] 720 722 … … 877 879 values for each GPC1 chip (40x40 pixels per point). \note{show the 878 880 flat-field residual images, discuss the features?}. We then used 879 \ node{setphot} to apply this new flat-field correction, as well as the881 \code{setphot} to apply this new flat-field correction, as well as the 880 882 ubercal flat-field corrections, to the data in the database. At this 881 883 point, we re-ran the entire relphot analysis to determine zero points … … 896 898 the bright end. \note{recommendation} 897 899 900 \section{PV3 DVO Master Database} 901 902 Data from the GPC1 chip images, the stack images, and the warp images 903 are loaded into DVO using the real-time analysis astrometric 904 calibration to guide the association of detections into objects. 905 After the full PV3 DVO database was constructed, including all of the 906 chip, stack, and warp detections, several external catalogs were 907 merged into the database. First, the complete 2MASS PSC was loaded 908 into a stand-alone DVO database, which was then merged into the PV3 909 master database. Next the DVO database of synthetic photometry in 910 the PS1 bands (see Section~\ref{sec:synthdb}) was merged in. Next, 911 the full Tycho database was added, followed by the AllWISE database. 912 After the Gaia release in August 2016, we generated a DVO database of 913 the Gaia positional and photometric information and merged that into 914 the master DVO database. 915 916 \note{need to describe the assignment of flags, etc, for the external 917 data sources}. 918 898 919 \section{Astrometry Analysis} 899 \begin{verbatim} 900 * initial astrometry based on real-time calibration 901 * relative astrometry calibration of images 902 * bright objects, images 903 * first pass to deter 904 \end{verbatim} 905 906 \section{Systematic Residuals} 907 908 \subsection{Camera-Scale Trends} 920 921 Once the full PV3 dataset loaded into the master PV3 DVO database, 922 along with supporting databases, and the photometric calibrations were 923 performed, relative astrometry could be performed on the database to 924 improve the overall astrometric calibration. 925 926 In many respects the relative astrometric analysis is similar to the 927 relative photometric analysis: the repeated measurements of the same 928 object in different images are used to determine a high quality 929 average position for the object. The new average positions are then 930 used to determine improved astrometric calibrations for each of the 931 images. These improved calibrations are used to set the observed 932 coordinates of the measurements from those images, which are in turn 933 used to improve the average positions of the objects. The whole 934 process is repeated for several iterations. Like the photometric 935 analysis, the astrometric analysis is performed in a parallel fashion 936 with the same concept that specific machines are responsible for 937 exposures and objects which land within their regions of 938 responsibility, defined on the basis of lines of constant RA and DEC. 939 Between iteration steps, the astrometric calibrations are shared 940 between the parallel machines as are the improved positions for 941 objects controlled by one machine but detect in images controlled by 942 another machine. Like the photometric analysis, the entire sky is 943 processed in one pass. However, there are some important differences 944 in the details. 945 946 \subsection{Systematic Effects} 947 948 First, the astrometric calibration has a larger number of systematic 949 effects which must be performed. These consist of: 1) the 950 Koppenh\"offer Effect, 2) Differential Chromatic Refraction, 3) Static 951 deviations in the camera. We discuss each of these in turn below. 952 953 \subsubsection{Koppenh\"offer Effect} 954 955 The Koppenh\"offer Effect was first identified (DATE) by Johannes 956 Koppenh\"offer (MPE) as part of the effort to search for planet 957 transists in the Stellar Transit Survey data. He noticed that the 958 astromety of bright stars and faint stars disagreed on overlapping 959 chips at the boundary between the STS fields. After some exploration, 960 it was determined that the X coordinate of the brightest stars was 961 offset from the expected location based on the faint stars for a 962 subset of the GPC1 chips. The essence of the effect was that the 963 bright stars were advanced along the serial register more quickly than 964 they should have been. The brighter the star, the more the charge 965 cloud was pushed ahead on the serial register. The amplitude of the 966 effect was at most \note{XXX}. Only the \note{2-phase} chips suffered 967 from this effect. By adjusting the \note{which?} voltages on the 968 camera, the effect was prevented in exposures after \note{DATE}. 969 However, this left \note{XXX,XXX exposures (XX\%)} already 970 contaminated by the effect. 971 972 We measured the Koppenh\"offer Effect by accumulating the residual 973 astrometry statistics for \note{how many} stars. For each chip, we 974 measured the mean X and Y displacements of the astrometric residuals 975 as function of the instrumental magnitude of the star divided by the 976 FWHM$^2$. \note{was there is significant difference using a surface 977 brightness version?} We measured the trend for all chips in a 978 number of different time ranges and found the effect to be quite 979 stable, in the period where it was present. The effect only appeared 980 in the serial direction. Figure~\ref{fig:koppenhoefer} shows the KE 981 trend for a typical affected chip both before and after the 982 correction. For the PV3 dataset, we re-measured the KE trends using 983 stars in the Galactic pole regions after an initial relative 984 astrometry calibration pass: the Galactic pole is necessary because 985 the real-time astrometric calibration relies largely on the fainter 986 stars which are not affected by the KE. The trend is then stored in a 987 form which can be applied to the database measurements. 988 989 \subsubsection{Differential Chromatic Refraction} 990 991 Differential Chromatic Refraction (DCR) affects astrometry because the 992 reference stars used the calibrate the images are not the same color 993 (SED) as the rest of the stars in the image. For a given star of a 994 color different from the reference stars, as exposures are taken at 995 higher airmass, the apparent position of the star will be biased along 996 the parallactic angle. While it is possible to build a model for the 997 DCR impact based on the filter response functions and atmospheric 998 refraction, we have instead elected to use an empirical correction for 999 the DCR present in the PV3 database. We have measured the DCR trend 1000 using the astrometric residuals of millions of stars after performing 1001 an initial relative astrometry calibration. We define a blue DCR 1002 color ($g-i$) to be used when correcting the filters \gps,\rps,\ips, and a red 1003 DCR color ($z - y$) to be used when correcting the filters $zy$. In 1004 the process of performing the relative astrometry calibration, we 1005 record the median red and blue colors of the reference stars used to 1006 measure the astrometry calibration for each image. As we determine 1007 the astrometry parameters for each object in the database, we record 1008 the median red and blue reference star colors for all images used to 1009 determine the astrometry for a given object. For each star in the 1010 database, we know both the color of the star and the typical color of 1011 the reference stars used to calibrate the astrometry for that star. 1012 1013 We measure the mean deviation of the residuals in the parallactic 1014 angle direction and the direction perpendicular to the parallactic 1015 angle. For each filter, we determine the DCR trend as a function of 1016 the difference between the star color and the reference star color, 1017 using the red or blue color approriate to the particular filter, times 1018 the tangent of the zenith distance. Figure~\ref{fig:DCR} shows the 1019 DCR trend for the 5 filters \grizy, as well as the measured 1020 displacement in the direction perpendicular to the parallactic angle. 1021 We represent the trend with a spline fitted to this dataset. The DCR 1022 trend has an amplitude of \note{XXX - XXX} in the five filters. 1023 1024 \note{write down the DCR formalae for reference}. 1025 1026 \subsubsection{Astrometric Flat-field} 1027 1028 After correction for both KE and DCR, we observe persistent residual 1029 astrometric deviations which depend on the position in the camera. We 1030 construct an astrometric ``flat-field'' response by determining the 1031 mean residual displacement in the X and Y (chip) directions as a 1032 function of position in the focal plane. We have measured the 1033 astrometric flat using a sampling resolution of 40x40 pixels, matching 1034 the photometric flat-field correction images. 1035 Figure~\ref{fig:astroflat} shows the astrometric flat-field images for 1036 the five filters \grizy\ in each of the two coordinate directions. 1037 These plots show several types of features. 1038 1039 The dominant pattern in the astrometric residual is roughly a series 1040 of concentric rings. The pattern is similar to the pattern of the 1041 focal surface residuals measured by (REF), which also has a concentric 1042 series of rings with similar spacing. The ``tent'' in the center of 1043 the focal surface reflected in these astrometry residual plots. Our 1044 interpretation of the structure is that the deviations of the focal 1045 plane from the ideal focal surface introduces small-scale PSF changes, 1046 presumably coupled to the optical aberrations, which result in small 1047 changes in the centroid of the object relative to the PSF model at 1048 that location. Since the PSF model shape parameters are only able to 1049 vary at the level of a 6x6 grid per chips, the finer structures are 1050 not included in the PSF model. The PV2 analysis shows the ring 1051 structure more clearly, with a pattern much more closely following the 1052 focal surface deviations. In the PV2 analysis, the PSF model used at 1053 most a 3x3 grid per chip to follow the shape variations, so any 1054 changes caused by the optical aberrations would be less well modeled in 1055 the PV2 analysis, as we observe. 1056 1057 A second pattern which is weakly seen in several chips consists of 1058 consistent displacements in the X (serial) direction for certain 1059 cells. This effect can be seen most clearly in chips XY45 and XY46. 1060 In the PV2 analysis, this pattern is also more clearly seen. In this 1061 case, the fact that the astrometric model used polynomials with a 1062 maximum of 3rd order per chip means the deviation of individual cells 1063 cannot be followed by the astrometric model. 1064 1065 A third effect is seen at the edge of the chips, where there appears 1066 to be a tendency for the residual to follow the chip edge. The origin 1067 of this is unclear, but likely caused by the astrometry model failing 1068 to follow the underlying variations because of the need to extrapolate 1069 to the edge pixels. Finally, we also identify an interesting effect 1070 {\em not} visible at the resolution of these astrometric flat-field 1071 images. Fine structures are observed at the \approx 10 pixel scale 1072 similar to the ``tree rings'' reported by the DES team and others 1073 (G. Berstein REF \& REFS). We explore these tree rings in detail in 1074 \note{SECTION or REF?}. 1075 1076 After the initial analysis to measure the KE corrections, DCR 1077 corrections, and astrometric flat-field corrections, we applied these 1078 corrections to the entire database. Within the schema of the 1079 database, each measurement has the raw chip coordinates 1080 (\code{Measure.Xccd,Yccd}) as well as the offset for that object based on each of 1081 these three corrections: \code{Measure.XoffKH,YoffKH, 1082 Measure.XoffDCR,YoffDCR, Measure.XoffCAM,YoffCAM}. The offsets are 1083 calculated for each measurement based on the observed instrumental 1084 chip magnitudes and FWHM for the Koppenhoffer Effect, on the average 1085 chip colors and the altitude \& azimuth of each measurement for the 1086 DCR correction, and on the chip coordinates for the astrometric 1087 flat-field corrections. The corrections are combined and applied to 1088 the raw chip coordinates and saved back in the database in the fields 1089 \code{Measure.Xfix,Yfix}. At this point, we are ready to run the 1090 full astrometric calibration. 1091 1092 \subsection{Galactic Rotation and Solar Motion} 1093 1094 The initial analysis of the PV2 astrometry used the 2MASS positions as 1095 an inertial constraint: the 2MASS coordiates were included in the 1096 calculation of the mean positions for the objects in the database, 1097 with weight corresponding to the reported astrometric errors. In this 1098 analysis, the object positions used to determine the calibrations of 1099 the image parameters ignored proper motion and parallax. After the 1100 image calibrations were determined, then individual objects were 1101 fitted for proper motion and possibly parallax, as discussed in detail 1102 below. 1103 1104 Using the PV2 analysis of the astrometry calibration, we discovered 1105 large-scale systematic trends in the reported proper motions of 1106 background quasars. This motion had an amplitude of 10 - 15 1107 milliarcseconds per year and clear trends with Galactic longitude. We 1108 also observed systematic errors of the mean positions with respect to 1109 the ICRF milliarcsecond radio quasar positions, with an amplitude of 1110 \approx 60 milliarcseconds, again with trends associated with Galactic 1111 longitude. Since the 2MASS data were believed to have minimal average 1112 deviations relative to the ICRF quasars, this latter seemed to be a 1113 real effect. 1114 1115 We realized that both the proper motion and the mean position biases 1116 could be caused by a single common effect: the proper motion of the 1117 stars used as reference stars between the 2MASS epoch (\approx 2000) 1118 and PS1 epoch (\approx 2012). Since we are fitting the image 1119 calibrations without fitting for the proper motions of the stars, we 1120 are in essencence forcing those stars to have proper motions of 0.0. 1121 The background quasars would then be observed to have proper motions 1122 corresponding to the proper motions of the reference stars, but in the 1123 opposite direction. We demonstrated that the observed quasar proper 1124 motions agreed well with the distribution expected if the median 1125 distance to our reference stars was \approx 500 pc. 1126 1127 For PV3, we desired to address this bias by including our knowledge 1128 about the distances to the reference stars and the expected typical 1129 proper motions for stars at those distances. With some constraint on 1130 the distance to each star, we can determine the expected proper motion 1131 based on a model of the Galactic rotation and solar motions. We can 1132 then calculate the mean positions for the objects keeping the assumed 1133 proper motion fixed. When calibrating a specific image, the reference 1134 star mean position is then translated to the expected position at the 1135 epoch of that image. The image calibration is then performed relative 1136 to these predicted postions. This process naturally accounts for the 1137 proper motion of the reference stars. In order to make the 1138 calibrations consistent with the observed coordinates of an external 1139 inertial reference, we perform the iterative fits using the technique 1140 as described, but assign very high weights in the initial iterations 1141 to the inertial reference, and reduce the weights as the astrometric 1142 calibration iterations proceed. 1143 1144 In order to perform this analysis, we need estimated distances for 1145 every reference star used in the analysis. Green et al (REF) 1146 performed SED fitting for 800M stars in the 3$\pi$ region using PV2 1147 data. The goal of this work was to determine the 3D structure of the 1148 dust in the galaxy. By fitting model SEDs to \note{all?} stars 1149 meeting a basic data quality cut \note{(describe)}, they determined 1150 the best spectral type, and thus $T_{\rm eff}$, absolute $r$-band 1151 magnitude, distance modulus, and extinction $A_V$ (the desired output 1152 and used to determine the dust extinction as a function of distance 1153 throughout the galaxy). We use the distance modulus determined in 1154 this analysis to predict the proper motions. 1155 1156 To convert the distances to proper motions, we use the Galactic 1157 rotation parameters ($A,B$) = (14.82,-12.37) km sec$^{-1}$ pc$^{-1}$ 1158 and Solar motion parameters ($U_{\rm sol}, V_{\rm sol}, W_{\rm sol}$) 1159 = (9.32, 11.18, 7.61) km sec$^{-1}$ as determined by Feast \& 1160 Whitelock (REF) using Hipparchos data. Proper motions are determined 1161 from the following: 1162 \begin{eqnarray} 1163 \mu^{\rm gal}_{l} & = & (A \cos (2 l) + B) \cos (b) \\ 1164 \mu^{\rm gal}_{b} & = & \frac{-A \sin (2 l) \sin (2 b)}{2} \\ 1165 \mu^{\rm sol}_{l} & = & \frac{U \sin(l) - V \cos(l)}{d} \\ 1166 \mu^{\rm sol}_{b} & = & \frac{(U \cos(l) + V \sin(l)) \sin(b) - W \cos(b)}{d} 1167 \end{eqnarray} 1168 where $d$ is the distance and $l,b$ are the Galactic coordintes of the 1169 star. \note{some reference?} Note that the proper motion induced by 1170 the Galactic rotation is independent of distance while the reflex 1171 motion induced by the solar motion decreases with increasing 1172 distance. Also note that this model assumes a flat rotation curve for 1173 objects in the thin disk; any reference stars which are part of 1174 the halo population will have proper motions which are not 1175 described by this model; the mostly random nature of the halo motions 1176 should act to increase the noise in the measurement, but should not 1177 introduce detectable motion biases. Also, if the distance modulus is 1178 not well determined, we can assume the object is simply following the 1179 Galactic rotation curve and set a fixed proper motion. If we do not 1180 have a distance modulus from the Green et al analysis, we assume a 1181 value of 500pc. 1182 1183 \note{plots to show how well this worked for PV3 pre Gaia} 1184 1185 \subsection{Gaia Constraint} 1186 1187 After the full relative astrometry analysis was performed for the PV3 1188 database, the Gaia Data Release 1 became available. This afforded us 1189 the opportunity to constrain the astrometry on the basis of the Gaia 1190 observations. Gaia DR1 objects which are bright enough to have proper 1191 motion and parallax solutions are in general saturated in the PS1 1192 observations. Thus, we are limited to using the Gaia mean positions 1193 reported for the fainter stars. We extracted all Gaia sources 1194 \note{not marked as a duplicate} from \note{where?} and generated a 1195 DVO database from this dataset. We then merged the Gaia DVO into the 1196 PV3 master DVO database. We re-ran the complete relative astrometry 1197 analysis using Gaia as an additional measurement. We applied the 1198 analysis described above, applying the estimated distances to 1199 determine preliminary proper motions. The Gaia mean epoch is reported 1200 as 2015.0, so all Gaia measurements were assigned this epoch. We 1201 wanted to ensure the Gaia measurements dominated the astrometric 1202 solutions, so we made the weight very high for the Gaia points: 1203 1000$\times$ the nominal weight in the initial fits (to lock down the 1204 reference frame), decreasing to 100$\times$ the nominal weight for the 1205 last fits. We also retained the 2MASS measurements in the analysis, 1206 but gave them somewhat lower weights than Gaia: while the 2MASS data 1207 does not have the accuracy of Gaia, the coverage is known to be quite 1208 complete, while the Gaia DR1 has clear gaps and holes. Having 2MASS, 1209 even at a lower weight, helps to tile over those gaps. 1210 1211 \note{Figures showing the Gaia residuals} 909 1212 910 1213 \section{Discussion}
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