147:
817:
50:
400:
254:
485:
The rate of energy flow through the surface fluctuates at the frequency of the radiation, but radiation detectors only respond to the average rate of flow. This is represented by replacing the
Poynting vector with the time average of its norm, giving
568:
802:
712:
146:
259:
1703:
per unit frequency or wavelength. The latter is commonly measured in W⋅m⋅nm. "Spectral emittance" is an old term for this quantity. This is sometimes also confusingly called "spectral intensity".
395:{\displaystyle {\begin{aligned}\Phi _{\mathrm {e} }&={\frac {dQ_{\mathrm {e} }}{dt}}\\Q_{\mathrm {e} }&=\int _{T}\int _{\Sigma }\mathbf {S} \cdot {\hat {\mathbf {n} }}\,dAdt\end{aligned}}}
489:
737:
625:
647:
1661:
per unit area. This is the emitted component of radiosity. "Radiant emittance" is an old term for this quantity. This is sometimes also confusingly called "intensity".
1437:
per unit frequency or wavelength. This is sometimes also confusingly called "spectral intensity". Non-SI units of spectral flux density include
2092:
1584:
per unit frequency or wavelength. The latter is commonly measured in W⋅m⋅nm. This is sometimes also confusingly called "spectral intensity".
848:
1008:
Radiant energy emitted, reflected, transmitted or received, per unit time. This is sometimes also called "radiant power", and called
1822:
per unit frequency or wavelength. The latter is commonly measured in J⋅m⋅nm. This is sometimes also called "spectral fluence".
2129:
114:
86:
2084:
841:
589:
133:
93:
71:
100:
191:
187:
150:
A flow chart describing the relationship of various physical quantities, including radiant flux and exitance.
67:
17:
2153:
834:
1181:
Radiant intensity per unit frequency or wavelength. The latter is commonly measured in W⋅sr⋅nm. This is a
563:{\displaystyle \Phi _{\mathrm {e} }\approx \int _{\Sigma }\langle |\mathbf {S} |\rangle \cos \alpha \ dA,}
797:{\displaystyle \Phi _{\mathrm {e} ,\lambda }={\frac {\partial \Phi _{\mathrm {e} }}{\partial \lambda }},}
82:
2117:
2059:
2148:
2163:
707:{\displaystyle \Phi _{\mathrm {e} ,\nu }={\frac {\partial \Phi _{\mathrm {e} }}{\partial \nu }},}
60:
1894:
1547:
1504:
932:
38:
1400:
1901:
should be denoted with suffix "e" (for "energetic") to avoid confusion with photometric or
1306:
per unit frequency or wavelength. The latter is commonly measured in W⋅sr⋅m⋅nm. This is a
1135:
Radiant flux emitted, reflected, transmitted or received, per unit solid angle. This is a
107:
8:
2158:
1875:
248:
1058:
Radiant flux per unit frequency or wavelength. The latter is commonly measured in W⋅nm.
2085:"Thermal insulation — Heat transfer by radiation — Physical quantities and definitions"
1780:
integrated over time of irradiation. This is sometimes also called "radiant fluence".
2125:
1898:
1267:
1144:
1095:
2122:
Radiometry and the
Detection of Optical Radiation (Pure & Applied Optics Series)
1785:
1742:
1666:
1623:
2054:
1450:
444:
440:
889:
425:
421:
167:
31:
816:
2142:
2044:
456:
1983:, not to be confused with a letter "v", indicating a photometric quantity.)
1353:
1310:
quantity. This is sometimes also confusingly called "spectral intensity".
1980:
2006:
1870:
1396:
1349:
1009:
183:
155:
1542:
per unit area. This is sometimes also confusingly called "intensity".
1391:
per unit area. This is sometimes also confusingly called "intensity".
2049:
1970:
1919:
1917:
1915:
1913:
1911:
1117:
1111:
179:
49:
1224:
1908:
1262:
quantity. This is sometimes also confusingly called "intensity".
214:) and that of spectral flux in wavelength is the watt per metre (
170:
emitted, reflected, transmitted, or received per unit time, and
1902:
1438:
1254:
Radiant flux emitted, reflected, transmitted or received by a
1040:
1034:
909:
904:
207:
199:
206:), while that of spectral flux in frequency is the watt per
989:
984:
195:
2028:
2011:
1975:
1258:, per unit solid angle per unit projected area. This is a
190:
is taken as a function of frequency or of wavelength. The
239:
37:"Spectral power" redirects here. Not to be confused with
1865:
740:
650:
592:
492:
257:
2001:
1999:
1997:
1995:
1993:
1991:
1989:
820:
Comparison of photometric and radiometric quantities
2023:
2021:
74:. Unsourced material may be challenged and removed.
796:
706:
619:
562:
394:
1986:
2140:
2027:Directional quantities are denoted with suffix "
2018:
1965:
1963:
1961:
1959:
1957:
1955:
1953:
2079:
2077:
2075:
1776:per unit area, or equivalently irradiance of a
1328:watt per steradian per square metre, per metre
620:{\displaystyle \langle |\mathbf {S} |\rangle .}
1287:watt per steradian per square metre per hertz
247:('e' for "energetic", to avoid confusion with
1950:
842:
2072:
1888:
611:
593:
536:
518:
225:
1538:(emitted, reflected and transmitted by) a
849:
835:
375:
134:Learn how and when to remove this message
815:
145:
14:
2141:
811:
1784:
1665:
1546:
1395:
1266:
1143:
1016:
927:Energy of electromagnetic radiation.
869:
866:
863:
860:
2116:
1923:Alternative symbols sometimes seen:
1239:watt per steradian per square metre
72:adding citations to reliable sources
43:
2005:Spectral quantities given per unit
1969:Spectral quantities given per unit
218:)—commonly the watt per nanometre (
27:Measure of radiant energy over time
24:
2110:
1840:joule per square metre, per metre
782:
774:
769:
765:
747:
742:
692:
684:
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675:
657:
652:
513:
499:
494:
348:
320:
293:
268:
263:
25:
2175:
1803:joule per square metre per hertz
1721:watt per square metre, per metre
1602:watt per square metre, per metre
1483:watt per square metre, per metre
1684:watt per square metre per hertz
1565:watt per square metre per hertz
1418:watt per square metre per hertz
966:Radiant energy per unit volume.
629:
602:
527:
365:
354:
48:
230:
59:needs additional citations for
607:
597:
532:
522:
369:
13:
1:
2065:
1772:Radiant energy received by a
1203:watt per steradian per metre
1162:watt per steradian per hertz
178:is the radiant flux per unit
7:
2038:
1897:recommend that radiometric
722:Spectral flux in wavelength
481:represents the time period.
251:quantities), is defined as
186:, depending on whether the
10:
2180:
635:Spectral flux in frequency
36:
29:
2060:Radiosity (heat transfer)
2009:are denoted with suffix "
1973:are denoted with suffix "
1860:
1817:
1741:
1698:
1622:
1579:
1503:
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1348:
1301:
1223:
1180:
1094:
1057:
970:
931:
888:
883:
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874:
576:is the time average, and
226:Mathematical definitions
30:Not to be confused with
1895:Standards organizations
1757:joule per square metre
471:represents the area of
194:of radiant flux is the
2124:. Wiley-Interscience.
1818:Radiant exposure of a
1699:Radiant exitance of a
1638:watt per square metre
1519:watt per square metre
1368:watt per square metre
947:joule per cubic metre
933:Radiant energy density
821:
798:
708:
621:
564:
396:
151:
39:Spectral power density
1947:for radiant exitance.
1401:Spectral flux density
819:
799:
709:
622:
580:is the angle between
565:
397:
149:
1931:for radiant energy,
738:
648:
590:
490:
255:
68:improve this article
2154:Physical quantities
1397:Spectral irradiance
1271:Specific intensity
857:
829:SI radiometry units
812:SI radiometry units
808:is the wavelength.
443:, representing the
1939:for radiant flux,
1548:Spectral radiosity
1145:Spectral intensity
826:
822:
794:
718:is the frequency.
704:
617:
560:
447:of radiant energy;
392:
390:
152:
2131:978-0-471-86188-1
1884:
1883:
1786:Spectral exposure
1667:Spectral exitance
1268:Spectral radiance
1096:Radiant intensity
789:
699:
573:⟨-⟩
550:
424:passing out of a
372:
308:
144:
143:
136:
118:
16:(Redirected from
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2135:
2104:
2103:
2101:
2100:
2081:
2032:
2025:
2016:
2003:
1984:
1979:" (Greek letter
1967:
1948:
1946:
1943:for irradiance,
1942:
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1926:
1921:
1906:
1892:
1837:
1800:
1754:
1743:Radiant exposure
1718:
1681:
1635:
1624:Radiant exitance
1599:
1562:
1516:
1480:
1464:
1460:
1456:
1448:
1444:
1433:Irradiance of a
1415:
1365:
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1284:
1236:
1200:
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1030:
981:
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901:
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801:
800:
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758:
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734:, is defined as
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717:
713:
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710:
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673:
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644:, is defined as
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2149:Power (physics)
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2111:Further reading
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2107:
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2095:catalogue. 1989
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2055:Power (physics)
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2019:
2004:
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1932:
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1790:
1753:
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1717:
1708:
1680:
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1628:
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1589:
1580:Radiosity of a
1561:
1552:
1515:
1509:
1479:
1470:
1462:
1458:
1454:
1451:solar flux unit
1446:
1442:
1414:
1405:
1399:
1364:
1358:
1352:
1324:
1315:
1283:
1274:
1270:
1235:
1229:
1199:
1190:
1158:
1149:
1106:
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1074:watt per metre
1070:
1063:
1029:
1022:
980:
976:
943:
937:
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856:
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828:
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773:
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764:
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691:
683:
682:
678:
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656:
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651:
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643:
632:
606:
601:
596:
591:
588:
587:
581:
577:
572:
571:
531:
526:
521:
512:
508:
498:
497:
493:
491:
488:
487:
478:
472:
466:
460:
450:
445:current density
441:Poynting vector
434:
428:
418:
412:
406:
389:
388:
364:
362:
361:
353:
347:
343:
337:
333:
326:
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314:
311:
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140:
129:
123:
120:
77:
75:
65:
53:
42:
35:
28:
23:
22:
15:
12:
11:
5:
2177:
2167:
2166:
2164:Temporal rates
2161:
2156:
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2136:
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2112:
2109:
2106:
2105:
2070:
2069:
2067:
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2052:
2047:
2040:
2037:
2034:
2033:
2017:
1985:
1949:
1907:
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1879:
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1873:
1868:
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1712:
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1704:
1697:
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1682:
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1651:
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1639:
1636:
1632:
1626:
1620:
1619:
1606:
1603:
1600:
1593:
1586:
1585:
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1569:
1566:
1563:
1556:
1550:
1544:
1543:
1532:
1523:
1520:
1517:
1513:
1507:
1501:
1500:
1487:
1484:
1481:
1474:
1467:
1466:
1459:10 W⋅m⋅Hz
1447:10 W⋅m⋅Hz
1431:
1422:
1419:
1416:
1409:
1403:
1393:
1392:
1381:
1372:
1369:
1366:
1362:
1356:
1346:
1345:
1332:
1329:
1326:
1319:
1312:
1311:
1302:Radiance of a
1300:
1291:
1288:
1285:
1278:
1272:
1264:
1263:
1252:
1243:
1240:
1237:
1233:
1227:
1221:
1220:
1207:
1204:
1201:
1194:
1187:
1186:
1179:
1166:
1163:
1160:
1153:
1147:
1141:
1140:
1133:
1120:
1114:
1108:
1104:
1098:
1092:
1091:
1078:
1075:
1072:
1065:
1060:
1059:
1056:
1043:
1037:
1031:
1024:
1020:
1014:
1013:
1012:in Astronomy.
1006:
993:
987:
982:
978:
974:
968:
967:
964:
951:
948:
945:
941:
935:
929:
928:
925:
912:
907:
902:
898:
892:
890:Radiant energy
886:
885:
882:
879:
876:
872:
871:
868:
865:
862:
854:
853:
846:
839:
831:
827:
813:
810:
793:
787:
784:
776:
771:
767:
761:
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753:
749:
744:
727:
703:
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686:
681:
677:
671:
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659:
654:
638:
631:
628:
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613:
609:
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559:
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553:
547:
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541:
538:
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524:
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511:
507:
501:
496:
483:
482:
476:
464:
459:of a point on
448:
432:
426:closed surface
422:radiant energy
416:
410:
387:
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378:
371:
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261:
260:
242:
232:
229:
227:
224:
176:spectral power
168:radiant energy
142:
141:
83:"Radiant flux"
56:
54:
47:
32:Radiation flux
26:
9:
6:
4:
3:
2:
2176:
2165:
2162:
2160:
2157:
2155:
2152:
2150:
2147:
2146:
2144:
2133:
2127:
2123:
2119:
2115:
2114:
2094:
2090:
2089:ISO 9288:1989
2086:
2080:
2078:
2076:
2071:
2061:
2058:
2056:
2053:
2051:
2048:
2046:
2045:Luminous flux
2043:
2042:
2030:
2024:
2022:
2014:
2013:
2008:
2002:
2000:
1998:
1996:
1994:
1992:
1990:
1982:
1978:
1977:
1972:
1966:
1964:
1962:
1960:
1958:
1956:
1954:
1920:
1918:
1916:
1914:
1912:
1904:
1900:
1896:
1891:
1887:
1877:
1874:
1872:
1869:
1867:
1864:
1863:
1859:
1856:
1852:
1848:
1845:
1842:
1839:
1835:
1830:
1826:
1825:
1821:
1815:
1811:
1808:
1805:
1802:
1798:
1793:
1789:
1787:
1783:
1779:
1775:
1771:
1769:
1765:
1762:
1759:
1756:
1750:
1746:
1744:
1740:
1737:
1733:
1729:
1726:
1723:
1720:
1716:
1711:
1707:
1706:
1702:
1696:
1692:
1689:
1686:
1683:
1679:
1674:
1670:
1668:
1664:
1660:
1656:
1653:Radiant flux
1652:
1650:
1646:
1643:
1640:
1637:
1631:
1627:
1625:
1621:
1618:
1614:
1610:
1607:
1604:
1601:
1597:
1592:
1588:
1587:
1583:
1577:
1573:
1570:
1567:
1564:
1560:
1555:
1551:
1549:
1545:
1541:
1537:
1534:Radiant flux
1533:
1531:
1527:
1524:
1521:
1518:
1512:
1508:
1506:
1502:
1499:
1495:
1491:
1488:
1485:
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1478:
1473:
1469:
1468:
1452:
1440:
1436:
1430:
1426:
1423:
1420:
1417:
1413:
1408:
1404:
1402:
1398:
1394:
1390:
1386:
1383:Radiant flux
1382:
1380:
1376:
1373:
1370:
1367:
1361:
1357:
1355:
1351:
1347:
1344:
1340:
1336:
1333:
1330:
1327:
1323:
1318:
1314:
1313:
1309:
1305:
1299:
1295:
1292:
1289:
1286:
1282:
1277:
1273:
1269:
1265:
1261:
1257:
1253:
1251:
1247:
1244:
1241:
1238:
1232:
1228:
1226:
1222:
1219:
1215:
1211:
1208:
1205:
1202:
1198:
1193:
1189:
1188:
1184:
1178:
1174:
1170:
1167:
1164:
1161:
1157:
1152:
1148:
1146:
1142:
1138:
1134:
1132:
1128:
1124:
1121:
1119:
1115:
1113:
1109:
1103:
1099:
1097:
1093:
1090:
1086:
1082:
1079:
1076:
1073:
1069:
1062:
1061:
1055:
1051:
1047:
1044:
1042:
1038:
1036:
1032:
1028:
1021:
1019:
1018:Spectral flux
1015:
1011:
1007:
1005:
1001:
997:
994:
991:
988:
986:
983:
975:
973:
969:
965:
963:
959:
955:
952:
949:
946:
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936:
934:
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926:
924:
920:
916:
913:
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906:
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893:
891:
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859:
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845:
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832:
824:
818:
809:
791:
785:
759:
754:
751:
731:
723:
719:
701:
695:
669:
664:
661:
642:
636:
630:Spectral flux
627:
614:
584:
557:
554:
551:
545:
542:
539:
509:
505:
477:
469:
465:
458:
457:normal vector
453:
449:
446:
442:
437:
433:
427:
423:
415:
411:
405:
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403:
385:
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379:
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276:
250:
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237:
223:
209:
201:
197:
193:
189:
185:
181:
177:
173:
172:spectral flux
169:
165:
164:radiant power
161:
157:
148:
138:
135:
127:
124:December 2009
116:
113:
109:
106:
102:
99:
95:
92:
88:
85: –
84:
80:
79:Find sources:
73:
69:
63:
62:
57:This article
55:
51:
46:
45:
40:
33:
19:
18:Radiant power
2121:
2118:Boyd, Robert
2097:. Retrieved
2088:
2010:
1974:
1890:
1854:
1850:
1846:
1833:
1828:
1819:
1813:
1809:
1796:
1791:
1777:
1773:
1767:
1763:
1748:
1735:
1731:
1727:
1714:
1709:
1700:
1694:
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1658:
1654:
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1608:
1595:
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1539:
1535:
1529:
1525:
1510:
1497:
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1476:
1471:
1434:
1428:
1424:
1411:
1406:
1388:
1384:
1378:
1374:
1359:
1354:Flux density
1342:
1338:
1334:
1321:
1316:
1307:
1303:
1297:
1293:
1280:
1275:
1259:
1255:
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1230:
1217:
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1196:
1191:
1182:
1176:
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1168:
1155:
1150:
1136:
1130:
1126:
1122:
1101:
1088:
1084:
1080:
1067:
1053:
1049:
1045:
1026:
1017:
1003:
999:
995:
972:Radiant flux
971:
961:
957:
953:
938:
922:
918:
914:
895:
823:
729:
721:
720:
640:
634:
633:
582:
484:
467:
451:
435:
413:
409:is the time;
236:Radiant flux
235:
234:
231:Radiant flux
202:per second (
175:
171:
163:
160:radiant flux
159:
153:
130:
121:
111:
104:
97:
90:
78:
66:Please help
61:verification
58:
1905:quantities.
1308:directional
1260:directional
1183:directional
1137:directional
637:, denoted Φ
249:photometric
2159:Radiometry
2143:Categories
2099:2015-03-15
2066:References
2007:wavelength
1899:quantities
1876:Photometry
1871:Radiometry
1861:See also:
1463:10 Jy
1455:1 sfu
1350:Irradiance
1290:W⋅sr⋅m⋅Hz
1185:quantity.
1139:quantity.
1010:luminosity
867:Dimension
724:, denoted
238:, denoted
184:wavelength
156:radiometry
94:newspapers
2050:Heat flux
1971:frequency
1505:Radiosity
1443:1 Jy
1112:steradian
1110:watt per
1033:watt per
861:Quantity
786:λ
783:∂
770:Φ
766:∂
755:λ
743:Φ
696:ν
693:∂
680:Φ
676:∂
665:ν
653:Φ
612:⟩
594:⟨
546:α
543:
537:⟩
519:⟨
514:Σ
510:∫
506:≈
495:Φ
370:^
359:⋅
349:Σ
345:∫
335:∫
264:Φ
198:(W), one
180:frequency
2120:(1983).
2039:See also
1385:received
1225:Radiance
1165:W⋅sr⋅Hz
188:spectrum
1820:surface
1806:J⋅m⋅Hz
1778:surface
1774:surface
1701:surface
1687:W⋅m⋅Hz
1659:surface
1655:emitted
1582:surface
1568:W⋅m⋅Hz
1540:surface
1536:leaving
1435:surface
1421:W⋅m⋅Hz
1389:surface
1331:W⋅sr⋅m
1304:surface
1256:surface
1242:W⋅sr⋅m
1206:W⋅sr⋅m
884:Symbol
878:Symbol
455:is the
439:is the
420:is the
192:SI unit
166:is the
108:scholar
2128:
1903:photon
1449:) and
1439:jansky
992:= J/s
870:Notes
804:where
714:where
570:where
549:
473:Σ
461:Σ
429:Σ
402:where
110:
103:
96:
89:
81:
1657:by a
1387:by a
1035:hertz
905:joule
881:Name
875:Name
864:Unit
208:hertz
200:joule
115:JSTOR
101:books
2126:ISBN
1843:J/m
1760:J/m
1724:W/m
1641:W/m
1605:W/m
1522:W/m
1486:W/m
1371:W/m
1320:e,Ω,
1279:e,Ω,
1195:e,Ω,
1154:e,Ω,
1077:W/m
985:watt
950:J/m
586:and
220:W/nm
212:W/Hz
196:watt
87:news
2093:ISO
1935:or
1927:or
1465:).
1234:e,Ω
1105:e,Ω
540:cos
222:).
216:W/m
204:J/s
182:or
174:or
162:or
154:In
70:by
2145::
2091:.
2087:.
2074:^
2031:".
2020:^
2015:".
1988:^
1981:nu
1952:^
1910:^
1866:SI
1832:e,
1795:e,
1713:e,
1676:e,
1594:e,
1557:e,
1475:e,
1461:=
1457:=
1445:=
1410:e,
1118:sr
1116:W/
1066:e,
1041:Hz
1039:W/
1025:e,
728:e,
639:e,
158:,
2134:.
2102:.
2029:Ω
2012:λ
1976:ν
1945:W
1941:I
1937:F
1933:P
1929:E
1925:W
1855:T
1853:⋅
1851:L
1849:⋅
1847:M
1834:λ
1829:H
1814:T
1812:⋅
1810:M
1797:ν
1792:H
1768:T
1766:⋅
1764:M
1752:e
1749:H
1736:T
1734:⋅
1732:L
1730:⋅
1728:M
1715:λ
1710:M
1695:T
1693:⋅
1691:M
1678:ν
1673:M
1649:T
1647:⋅
1645:M
1633:e
1630:M
1617:T
1615:⋅
1613:L
1611:⋅
1609:M
1596:λ
1591:J
1576:T
1574:⋅
1572:M
1559:ν
1554:J
1530:T
1528:⋅
1526:M
1514:e
1511:J
1498:T
1496:⋅
1494:L
1492:⋅
1490:M
1477:λ
1472:E
1453:(
1441:(
1429:T
1427:⋅
1425:M
1412:ν
1407:E
1379:T
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1375:M
1363:e
1360:E
1343:T
1341:⋅
1339:L
1337:⋅
1335:M
1322:λ
1317:L
1298:T
1296:⋅
1294:M
1281:ν
1276:L
1250:T
1248:⋅
1246:M
1231:L
1218:T
1216:⋅
1214:L
1212:⋅
1210:M
1197:λ
1192:I
1177:T
1175:⋅
1173:L
1171:⋅
1169:M
1156:ν
1151:I
1131:T
1129:⋅
1127:L
1125:⋅
1123:M
1102:I
1089:T
1087:⋅
1085:L
1083:⋅
1081:M
1068:λ
1064:Φ
1054:T
1052:⋅
1050:L
1048:⋅
1046:M
1027:ν
1023:Φ
1004:T
1002:⋅
1000:L
998:⋅
996:M
990:W
979:e
977:Φ
962:T
960:⋅
958:L
956:⋅
954:M
942:e
939:w
923:T
921:⋅
919:L
917:⋅
915:M
910:J
899:e
896:Q
850:e
843:t
836:v
806:λ
792:,
775:e
760:=
752:,
748:e
730:λ
726:Φ
716:ν
702:,
685:e
670:=
662:,
658:e
641:ν
615:.
608:|
603:S
598:|
583:n
578:α
558:,
555:A
552:d
533:|
528:S
523:|
500:e
479:T
475:;
468:A
463:;
452:n
436:S
431:;
417:e
414:Q
407:t
386:t
383:d
380:A
377:d
366:n
355:S
339:T
331:=
321:e
316:Q
305:t
302:d
294:e
289:Q
285:d
279:=
269:e
243:e
241:Φ
210:(
137:)
131:(
126:)
122:(
112:·
105:·
98:·
91:·
64:.
41:.
34:.
20:)
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