J/A+A/660/A134         SEFD of stokes I,Q,U,V                    (Sutinjo, 2022)

System equivalent flux density of Stokes I, Q, U, V of a polarimetric interferometer. Sutinjo A.T., Ung D.C.X., Sokolowski M., Kovaleva M., McSweeney S. <Astron. Astrophys. 660, A134 (2022)> =2022A&A...660A.134S 2022A&A...660A.134S (SIMBAD/NED BibCode)
ADC_Keywords: Polarization Keywords: instrumentation: polarimeters - instrumentation: interferometers - techniques: interferometric - telescopes - techniques: polarimetric - methods: observational Abstract: This paper extends the treatment of system equivalent flux density (SEFD), discussed in our earlier paper to interferometric phased array telescopes. The objective is to develop an SEFD formula involving only the most fundamental assumptions that is readily applicable to phased array interferometer radio observations. Our aim is to compare the resultant SEFD expression against the often-used root-mean-square (rms) SEFD approximation, SEFDIrms=1/2*SQRT(SEFDXX2+SEFDYY2), to study the inaccuracy of the SEFDIrms. We take into account all mutual coupling and noise coupling within an array environment (intra-array coupling). This intra-array noise coupling is included in the SEFD expression through the realized noise resistance of the array, which accounts for the system noise. No assumption is made regarding the polarization (or lack thereof) of the sky nor the orthogonality of the antenna elements. The fundamental noise assumption is that, in phasor representation, the real and imaginary components of a given noise source are independent and equally distributed (iid) with zero mean. Noise sources that are mutually correlated and non-iid among themselves are allowed, provided the real and imaginary components of each noise source are iid. The system noise is uncorrelated between array entities separated by a baseline distance, which in the case of the Murchison Widefield Array (MWA) is typically tens of wavelengths or greater. By comparing the resulting SEFD formula to the SEFDIrms approximation, we proved that SEFDIrms always underestimates the SEFD, which leads to an overestimation of array sensitivity. We present the resulting SEFD formula that is generalized for the phased array, but has a similar form to the earlier result. Here, the physical meaning of the antenna lengths and the equivalent noise resistances have been generalized such that they are also valid in the array environment. The simulated SEFD was validated using MWA observation of a Hydra-A radio galaxy at 154.88MHz. The observed SEFDXX and SEFDI are on average higher by 9% and 4%, respectively, while the observed SEFDYY is lower by 4% compared to simulated values for all pixels within the -12dB beam width. The simulated and observed SEFD errors due to the rms SEFD approximation are nearly identical, with mean difference of images of virtually 0%. This result suggests that the derived SEFD expression, as well as the simulation approach, is correct and may be applied to any pointing. As a result, this method permits identification of phased array telescope pointing angles where the rms approximation underestimates SEFD (overestimates sensitivity). For example, for Hydra-A observation with beam pointing (Az, ZA) = (81°, 46°), the underestimation in SEFD calculation using the rms expression is 7% within the -3dB beam width, but increases to 23% within the -12dB beam width. At 199.68MHz, for the simulated MWA pointing at (Az, ZA) = (45°, 56.96°), the underestimation reached 29% within the -3dB beam width and 36% within the -12dB beam width. This underestimation due to rms SEFD approximation at two different pointing angles and frequencies was expected and is consistent with the proof. Description: We present the system equivalent flux density (SEFD) expressions for all four Stokes parameters: I, Q, U, V. This dataset contains the tile parameters for an MWA tile evaluated at all sweetspot pointing for all coarse channels. File Summary: -------------------------------------------------------------------------------- FileName Lrecl Records Explanations -------------------------------------------------------------------------------- ReadMe 80 . This file rad_y.dat 991 218 Radiation efficiency (Y-pol) rad_x.dat 991 218 Radiation efficiency (X-pol) r_x.dat 1385 218 Array equivalent resistance (R factor X-pol) r_y.dat 1385 218 Array equivalent resistance (R factor Y-pol) trcv_x.dat 1582 218 Receiver noise temperature (X-pol) trcv_y.dat 1582 218 Receiver noise temperature (Y-pol) -------------------------------------------------------------------------------- Byte-by-byte Description of file: rad_y.dat -------------------------------------------------------------------------------- Bytes Format Units Label Explanations -------------------------------------------------------------------------------- 1- 6 F6.2 MHz Freq Frequency 8- 11 F4.2 --- gp000 Gridpoint 0 13- 16 F4.2 --- gp001 Gridpoint 1 18- 21 F4.2 --- gp002 Gridpoint 2 23- 26 F4.2 --- gp003 Gridpoint 3 28- 31 F4.2 --- gp004 Gridpoint 4 33- 36 F4.2 --- gp005 Gridpoint 5 38- 41 F4.2 --- gp006 Gridpoint 6 43- 46 F4.2 --- gp007 Gridpoint 7 48- 51 F4.2 --- gp008 Gridpoint 8 53- 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Gridpoint 192 1359-1364 F6.2 --- gp193 Gridpoint 193 1366-1371 F6.2 --- gp194 Gridpoint 194 1373-1378 F6.2 --- gp195 Gridpoint 195 1380-1385 F6.2 --- gp196 Gridpoint 196 -------------------------------------------------------------------------------- Byte-by-byte Description of file: r_y.dat -------------------------------------------------------------------------------- Bytes Format Units Label Explanations -------------------------------------------------------------------------------- 1- 6 F6.2 MHz Freq Frequency 8- 13 F6.2 --- gp000 Gridpoint 0 15- 20 F6.2 --- gp001 Gridpoint 1 22- 27 F6.2 --- gp002 Gridpoint 2 29- 34 F6.2 --- gp003 Gridpoint 3 36- 41 F6.2 --- gp004 Gridpoint 4 43- 48 F6.2 --- gp005 Gridpoint 5 50- 55 F6.2 --- gp006 Gridpoint 6 57- 62 F6.2 --- gp007 Gridpoint 7 64- 69 F6.2 --- gp008 Gridpoint 8 71- 76 F6.2 --- gp009 Gridpoint 9 78- 83 F6.2 --- gp010 Gridpoint 10 85- 90 F6.2 --- gp011 Gridpoint 11 92- 97 F6.2 --- gp012 Gridpoint 12 99- 104 F6.2 --- gp013 Gridpoint 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-------------------------------------------------------------------------------- Byte-by-byte Description of file: trcv_x.dat -------------------------------------------------------------------------------- Bytes Format Units Label Explanations -------------------------------------------------------------------------------- 1- 6 F6.2 MHz Freq Frequency 8- 14 F7.2 --- gp000 Gridpoint 0 16- 22 F7.2 --- gp001 Gridpoint 1 24- 30 F7.2 --- gp002 Gridpoint 2 32- 38 F7.2 --- gp003 Gridpoint 3 40- 46 F7.2 --- gp004 Gridpoint 4 48- 54 F7.2 --- gp005 Gridpoint 5 56- 62 F7.2 --- gp006 Gridpoint 6 64- 70 F7.2 --- gp007 Gridpoint 7 72- 78 F7.2 --- gp008 Gridpoint 8 80- 86 F7.2 --- gp009 Gridpoint 9 88- 94 F7.2 --- gp010 Gridpoint 10 96- 102 F7.2 --- gp011 Gridpoint 11 104- 110 F7.2 --- gp012 Gridpoint 12 112- 118 F7.2 --- gp013 Gridpoint 13 120- 126 F7.2 --- gp014 Gridpoint 14 128- 134 F7.2 --- gp015 Gridpoint 15 136- 142 F7.2 --- gp016 Gridpoint 16 144- 150 F7.2 --- gp017 Gridpoint 17 152- 158 F7.2 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Gridpoint 125 1016-1022 F7.2 --- gp126 Gridpoint 126 1024-1030 F7.2 --- gp127 Gridpoint 127 1032-1038 F7.2 --- gp128 Gridpoint 128 1040-1046 F7.2 --- gp129 Gridpoint 129 1048-1054 F7.2 --- gp130 Gridpoint 130 1056-1062 F7.2 --- gp131 Gridpoint 131 1064-1070 F7.2 --- gp132 Gridpoint 132 1072-1078 F7.2 --- gp133 Gridpoint 133 1080-1086 F7.2 --- gp134 Gridpoint 134 1088-1094 F7.2 --- gp135 Gridpoint 135 1096-1102 F7.2 --- gp136 Gridpoint 136 1104-1110 F7.2 --- gp137 Gridpoint 137 1112-1118 F7.2 --- gp138 Gridpoint 138 1120-1126 F7.2 --- gp139 Gridpoint 139 1128-1134 F7.2 --- gp140 Gridpoint 140 1136-1142 F7.2 --- gp141 Gridpoint 141 1144-1150 F7.2 --- gp142 Gridpoint 142 1152-1158 F7.2 --- gp143 Gridpoint 143 1160-1166 F7.2 --- gp144 Gridpoint 144 1168-1174 F7.2 --- gp145 Gridpoint 145 1176-1182 F7.2 --- gp146 Gridpoint 146 1184-1190 F7.2 --- gp147 Gridpoint 147 1192-1198 F7.2 --- gp148 Gridpoint 148 1200-1206 F7.2 --- gp149 Gridpoint 149 1208-1214 F7.2 --- gp150 Gridpoint 150 1216-1222 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176 1424-1430 F7.2 --- gp177 Gridpoint 177 1432-1438 F7.2 --- gp178 Gridpoint 178 1440-1446 F7.2 --- gp179 Gridpoint 179 1448-1454 F7.2 --- gp180 Gridpoint 180 1456-1462 F7.2 --- gp181 Gridpoint 181 1464-1470 F7.2 --- gp182 Gridpoint 182 1472-1478 F7.2 --- gp183 Gridpoint 183 1480-1486 F7.2 --- gp184 Gridpoint 184 1488-1494 F7.2 --- gp185 Gridpoint 185 1496-1502 F7.2 --- gp186 Gridpoint 186 1504-1510 F7.2 --- gp187 Gridpoint 187 1512-1518 F7.2 --- gp188 Gridpoint 188 1520-1526 F7.2 --- gp189 Gridpoint 189 1528-1534 F7.2 --- gp190 Gridpoint 190 1536-1542 F7.2 --- gp191 Gridpoint 191 1544-1550 F7.2 --- gp192 Gridpoint 192 1552-1558 F7.2 --- gp193 Gridpoint 193 1560-1566 F7.2 --- gp194 Gridpoint 194 1568-1574 F7.2 --- gp195 Gridpoint 195 1576-1582 F7.2 --- gp196 Gridpoint 196 -------------------------------------------------------------------------------- Byte-by-byte Description of file: trcv_y.dat -------------------------------------------------------------------------------- Bytes Format Units Label Explanations -------------------------------------------------------------------------------- 1- 6 F6.2 MHz Freq Frequency 8- 14 F7.2 --- gp000 Gridpoint 0 16- 22 F7.2 --- gp001 Gridpoint 1 24- 30 F7.2 --- gp002 Gridpoint 2 32- 38 F7.2 --- gp003 Gridpoint 3 40- 46 F7.2 --- gp004 Gridpoint 4 48- 54 F7.2 --- gp005 Gridpoint 5 56- 62 F7.2 --- gp006 Gridpoint 6 64- 70 F7.2 --- gp007 Gridpoint 7 72- 78 F7.2 --- gp008 Gridpoint 8 80- 86 F7.2 --- gp009 Gridpoint 9 88- 94 F7.2 --- gp010 Gridpoint 10 96- 102 F7.2 --- gp011 Gridpoint 11 104- 110 F7.2 --- gp012 Gridpoint 12 112- 118 F7.2 --- gp013 Gridpoint 13 120- 126 F7.2 --- gp014 Gridpoint 14 128- 134 F7.2 --- gp015 Gridpoint 15 136- 142 F7.2 --- gp016 Gridpoint 16 144- 150 F7.2 --- gp017 Gridpoint 17 152- 158 F7.2 --- gp018 Gridpoint 18 160- 166 F7.2 --- gp019 Gridpoint 19 168- 174 F7.2 --- gp020 Gridpoint 20 176- 182 F7.2 --- gp021 Gridpoint 21 184- 190 F7.2 --- gp022 Gridpoint 22 192- 198 F7.2 --- gp023 Gridpoint 23 200- 206 F7.2 --- gp024 Gridpoint 24 208- 214 F7.2 --- gp025 Gridpoint 25 216- 222 F7.2 --- gp026 Gridpoint 26 224- 230 F7.2 --- gp027 Gridpoint 27 232- 238 F7.2 --- gp028 Gridpoint 28 240- 246 F7.2 --- gp029 Gridpoint 29 248- 254 F7.2 --- gp030 Gridpoint 30 256- 262 F7.2 --- gp031 Gridpoint 31 264- 270 F7.2 --- gp032 Gridpoint 32 272- 278 F7.2 --- gp033 Gridpoint 33 280- 286 F7.2 --- gp034 Gridpoint 34 288- 294 F7.2 --- gp035 Gridpoint 35 296- 302 F7.2 --- gp036 Gridpoint 36 304- 310 F7.2 --- gp037 Gridpoint 37 312- 318 F7.2 --- gp038 Gridpoint 38 320- 326 F7.2 --- gp039 Gridpoint 39 328- 334 F7.2 --- gp040 Gridpoint 40 336- 342 F7.2 --- gp041 Gridpoint 41 344- 350 F7.2 --- gp042 Gridpoint 42 352- 358 F7.2 --- gp043 Gridpoint 43 360- 366 F7.2 --- gp044 Gridpoint 44 368- 374 F7.2 --- gp045 Gridpoint 45 376- 382 F7.2 --- gp046 Gridpoint 46 384- 390 F7.2 --- gp047 Gridpoint 47 392- 398 F7.2 --- gp048 Gridpoint 48 400- 406 F7.2 --- gp049 Gridpoint 49 408- 414 F7.2 --- gp050 Gridpoint 50 416- 422 F7.2 --- gp051 Gridpoint 51 424- 430 F7.2 --- gp052 Gridpoint 52 432- 438 F7.2 --- gp053 Gridpoint 53 440- 446 F7.2 --- gp054 Gridpoint 54 448- 454 F7.2 --- gp055 Gridpoint 55 456- 462 F7.2 --- gp056 Gridpoint 56 464- 470 F7.2 --- gp057 Gridpoint 57 472- 478 F7.2 --- gp058 Gridpoint 58 480- 486 F7.2 --- gp059 Gridpoint 59 488- 494 F7.2 --- gp060 Gridpoint 60 496- 502 F7.2 --- gp061 Gridpoint 61 504- 510 F7.2 --- gp062 Gridpoint 62 512- 518 F7.2 --- gp063 Gridpoint 63 520- 526 F7.2 --- gp064 Gridpoint 64 528- 534 F7.2 --- gp065 Gridpoint 65 536- 542 F7.2 --- gp066 Gridpoint 66 544- 550 F7.2 --- gp067 Gridpoint 67 552- 558 F7.2 --- gp068 Gridpoint 68 560- 566 F7.2 --- gp069 Gridpoint 69 568- 574 F7.2 --- gp070 Gridpoint 70 576- 582 F7.2 --- gp071 Gridpoint 71 584- 590 F7.2 --- gp072 Gridpoint 72 592- 598 F7.2 --- gp073 Gridpoint 73 600- 606 F7.2 --- gp074 Gridpoint 74 608- 614 F7.2 --- gp075 Gridpoint 75 616- 622 F7.2 --- gp076 Gridpoint 76 624- 630 F7.2 --- gp077 Gridpoint 77 632- 638 F7.2 --- gp078 Gridpoint 78 640- 646 F7.2 --- gp079 Gridpoint 79 648- 654 F7.2 --- gp080 Gridpoint 80 656- 662 F7.2 --- gp081 Gridpoint 81 664- 670 F7.2 --- gp082 Gridpoint 82 672- 678 F7.2 --- gp083 Gridpoint 83 680- 686 F7.2 --- gp084 Gridpoint 84 688- 694 F7.2 --- gp085 Gridpoint 85 696- 702 F7.2 --- gp086 Gridpoint 86 704- 710 F7.2 --- gp087 Gridpoint 87 712- 718 F7.2 --- gp088 Gridpoint 88 720- 726 F7.2 --- gp089 Gridpoint 89 728- 734 F7.2 --- gp090 Gridpoint 90 736- 742 F7.2 --- gp091 Gridpoint 91 744- 750 F7.2 --- gp092 Gridpoint 92 752- 758 F7.2 --- gp093 Gridpoint 93 760- 766 F7.2 --- gp094 Gridpoint 94 768- 774 F7.2 --- gp095 Gridpoint 95 776- 782 F7.2 --- gp096 Gridpoint 96 784- 790 F7.2 --- gp097 Gridpoint 97 792- 798 F7.2 --- gp098 Gridpoint 98 800- 806 F7.2 --- gp099 Gridpoint 99 808- 814 F7.2 --- gp100 Gridpoint 100 816- 822 F7.2 --- gp101 Gridpoint 101 824- 830 F7.2 --- gp102 Gridpoint 102 832- 838 F7.2 --- gp103 Gridpoint 103 840- 846 F7.2 --- gp104 Gridpoint 104 848- 854 F7.2 --- gp105 Gridpoint 105 856- 862 F7.2 --- gp106 Gridpoint 106 864- 870 F7.2 --- gp107 Gridpoint 107 872- 878 F7.2 --- gp108 Gridpoint 108 880- 886 F7.2 --- gp109 Gridpoint 109 888- 894 F7.2 --- gp110 Gridpoint 110 896- 902 F7.2 --- gp111 Gridpoint 111 904- 910 F7.2 --- gp112 Gridpoint 112 912- 918 F7.2 --- gp113 Gridpoint 113 920- 926 F7.2 --- gp114 Gridpoint 114 928- 934 F7.2 --- gp115 Gridpoint 115 936- 942 F7.2 --- gp116 Gridpoint 116 944- 950 F7.2 --- gp117 Gridpoint 117 952- 958 F7.2 --- gp118 Gridpoint 118 960- 966 F7.2 --- gp119 Gridpoint 119 968- 974 F7.2 --- gp120 Gridpoint 120 976- 982 F7.2 --- gp121 Gridpoint 121 984- 990 F7.2 --- gp122 Gridpoint 122 992- 998 F7.2 --- gp123 Gridpoint 123 1000-1006 F7.2 --- gp124 Gridpoint 124 1008-1014 F7.2 --- gp125 Gridpoint 125 1016-1022 F7.2 --- gp126 Gridpoint 126 1024-1030 F7.2 --- gp127 Gridpoint 127 1032-1038 F7.2 --- gp128 Gridpoint 128 1040-1046 F7.2 --- gp129 Gridpoint 129 1048-1054 F7.2 --- gp130 Gridpoint 130 1056-1062 F7.2 --- gp131 Gridpoint 131 1064-1070 F7.2 --- gp132 Gridpoint 132 1072-1078 F7.2 --- gp133 Gridpoint 133 1080-1086 F7.2 --- gp134 Gridpoint 134 1088-1094 F7.2 --- gp135 Gridpoint 135 1096-1102 F7.2 --- gp136 Gridpoint 136 1104-1110 F7.2 --- gp137 Gridpoint 137 1112-1118 F7.2 --- gp138 Gridpoint 138 1120-1126 F7.2 --- gp139 Gridpoint 139 1128-1134 F7.2 --- gp140 Gridpoint 140 1136-1142 F7.2 --- gp141 Gridpoint 141 1144-1150 F7.2 --- gp142 Gridpoint 142 1152-1158 F7.2 --- gp143 Gridpoint 143 1160-1166 F7.2 --- gp144 Gridpoint 144 1168-1174 F7.2 --- gp145 Gridpoint 145 1176-1182 F7.2 --- gp146 Gridpoint 146 1184-1190 F7.2 --- gp147 Gridpoint 147 1192-1198 F7.2 --- gp148 Gridpoint 148 1200-1206 F7.2 --- gp149 Gridpoint 149 1208-1214 F7.2 --- gp150 Gridpoint 150 1216-1222 F7.2 --- gp151 Gridpoint 151 1224-1230 F7.2 --- gp152 Gridpoint 152 1232-1238 F7.2 --- gp153 Gridpoint 153 1240-1246 F7.2 --- gp154 Gridpoint 154 1248-1254 F7.2 --- gp155 Gridpoint 155 1256-1262 F7.2 --- gp156 Gridpoint 156 1264-1270 F7.2 --- gp157 Gridpoint 157 1272-1278 F7.2 --- gp158 Gridpoint 158 1280-1286 F7.2 --- gp159 Gridpoint 159 1288-1294 F7.2 --- gp160 Gridpoint 160 1296-1302 F7.2 --- gp161 Gridpoint 161 1304-1310 F7.2 --- gp162 Gridpoint 162 1312-1318 F7.2 --- gp163 Gridpoint 163 1320-1326 F7.2 --- gp164 Gridpoint 164 1328-1334 F7.2 --- gp165 Gridpoint 165 1336-1342 F7.2 --- gp166 Gridpoint 166 1344-1350 F7.2 --- gp167 Gridpoint 167 1352-1358 F7.2 --- gp168 Gridpoint 168 1360-1366 F7.2 --- gp169 Gridpoint 169 1368-1374 F7.2 --- gp170 Gridpoint 170 1376-1382 F7.2 --- gp171 Gridpoint 171 1384-1390 F7.2 --- gp172 Gridpoint 172 1392-1398 F7.2 --- gp173 Gridpoint 173 1400-1406 F7.2 --- gp174 Gridpoint 174 1408-1414 F7.2 --- gp175 Gridpoint 175 1416-1422 F7.2 --- gp176 Gridpoint 176 1424-1430 F7.2 --- gp177 Gridpoint 177 1432-1438 F7.2 --- gp178 Gridpoint 178 1440-1446 F7.2 --- gp179 Gridpoint 179 1448-1454 F7.2 --- gp180 Gridpoint 180 1456-1462 F7.2 --- gp181 Gridpoint 181 1464-1470 F7.2 --- gp182 Gridpoint 182 1472-1478 F7.2 --- gp183 Gridpoint 183 1480-1486 F7.2 --- gp184 Gridpoint 184 1488-1494 F7.2 --- gp185 Gridpoint 185 1496-1502 F7.2 --- gp186 Gridpoint 186 1504-1510 F7.2 --- gp187 Gridpoint 187 1512-1518 F7.2 --- gp188 Gridpoint 188 1520-1526 F7.2 --- gp189 Gridpoint 189 1528-1534 F7.2 --- gp190 Gridpoint 190 1536-1542 F7.2 --- gp191 Gridpoint 191 1544-1550 F7.2 --- gp192 Gridpoint 192 1552-1558 F7.2 --- gp193 Gridpoint 193 1560-1566 F7.2 --- gp194 Gridpoint 194 1568-1574 F7.2 --- gp195 Gridpoint 195 1576-1582 F7.2 --- gp196 Gridpoint 196 -------------------------------------------------------------------------------- Acknowledgements: Daniel Ung, daniel.ung(at)curtin.edu.au
(End) Patricia Vannier [CDS] 10-Mar-2022
The document above follows the rules of the Standard Description for Astronomical Catalogues; from this documentation it is possible to generate f77 program to load files into arrays or line by line