108:
The brightness temperature is not a temperature as ordinarily understood. It characterizes radiation, and depending on the mechanism of radiation can differ considerably from the physical temperature of a radiating body (though it is theoretically possible to construct a device which will heat up by
88:
For radiation emitted by a non-thermal source such as a pulsar, synchrotron, maser, or a laser, the brightness temperature may be far higher than the actual temperature of the source. In this case, the brightness temperature is simply a measure of the intensity of the radiation as it would be
1381:
100:
of the surface. Since the emissivity is a value between 0 and 1, the real temperature will be greater than or equal to the brightness temperature. At high frequencies (short wavelengths) and low temperatures, the conversion must proceed through
1253:
899:
239:
1638:
In oceanography, the microwave brightness temperature, as measured by satellites looking at the ocean surface, depends on salinity as well as on the temperature and roughness (e.g. from wind-driven waves) of the water.
1629:
600:
1490:
1141:
1007:
1260:
703:
96:, with the intention of determining the real temperature. As detailed below, the real temperature of a surface can in some cases be calculated by dividing the brightness temperature by the
1153:
783:
120:
with a power of 1 mW, a frequency spread Δf = 1 GHz, an output aperture of 1 mm, and a beam dispersion half-angle of 0.56 mrad, the brightness temperature would be
1045:
740:
81:
emitted by an object simply by virtue of its temperature, then the actual temperature of the object will always be equal to or higher than the brightness temperature. Since the
1423:
142:
933:
634:
331:
485:
266:
1545:
762:
399:
302:
53:
1515:
1068:
447:
423:
375:
351:
1681:
1550:
490:
1428:
1073:
1985:
938:
643:
1656:
1942:
23:
is a measure of the intensity of electromagnetic energy coming from a source. In particular, it is the temperature at which a
1914:
1864:
1728:
1777:
92:
In some applications, the brightness temperature of a surface is determined by an optical measurement, for example using a
708:
1685:
109:
a source of radiation with some brightness temperature to the actual temperature equal to brightness temperature).
1828:
1376:{\displaystyle T_{b}={\frac {hc}{k\lambda }}\ln ^{-1}\left(1+{\frac {2hc^{2}}{I_{\lambda }\lambda ^{5}}}\right)}
1021:
1968:
1799:
2033:
1388:
1992:
1248:{\displaystyle I_{\lambda }={\frac {2hc^{2}}{\lambda ^{5}}}{\frac {1}{e^{\frac {hc}{kT\lambda }}-1}}}
28:
1707:
2028:
894:{\displaystyle T_{b}={\frac {h\nu }{k}}\ln ^{-1}\left(1+{\frac {2h\nu ^{3}}{I_{\nu }c^{2}}}\right)}
906:
607:
85:
is limited by 1, the brightness temperature is a lower bound of the object’s actual temperature.
307:
74:
The brightness temperature provides "a more physically recognizable way to describe intensity".
637:
470:
244:
117:
2023:
1523:
768:
it is the same at all frequencies. The brightness temperature can be used to calculate the
765:
1946:
747:
384:
287:
38:
8:
780:
The brightness temperature of a source with known spectral radiance can be expressed as:
269:
234:{\displaystyle I_{\nu }={\frac {2h\nu ^{3}}{c^{2}}}{\frac {1}{e^{\frac {h\nu }{kT}}-1}}}
1889:
1500:
1494:
For almost monochromatic radiation, the brightness temperature can be expressed by the
1053:
1016:
450:
432:
408:
360:
336:
1860:
1752:
1724:
461:
78:
64:
60:
1716:
1518:
378:
136:
102:
56:
1715:. Springer Theses. Berlin Heidelberg: Springer-Verlag Theses. pp. 171–174.
769:
426:
1753:"Revised planet brightness temperatures using the Planck/LFI 2018data release"
1720:
2017:
277:
1150:
Spectral radiance of black-body radiation is expressed by wavelength as:
354:
281:
68:
1012:
465:
116:
the brightness temperature can reach 10 K. For the radiation of a
97:
82:
24:
1893:
1877:
402:
93:
32:
1495:
1048:
1624:{\displaystyle T_{b}={\frac {\pi I\lambda ^{2}L_{c}}{4kc\ln {2}}}}
112:
Nonthermal sources can have very high brightness temperatures. In
595:{\displaystyle T_{b}^{-1}={\frac {k}{h\nu }}\,{\text{ln}}\left}
273:
113:
1882:
Philosophical
Transactions: Physical Sciences and Engineering
1485:{\displaystyle T_{b}={\frac {I_{\lambda }\lambda ^{4}}{2kc}}}
1136:{\displaystyle T_{b}={\frac {Ic^{2}}{2k\nu ^{2}\Delta \nu }}}
705:
so that the brightness temperature can be simply written as:
1915:"Brightness Temperature of a Laser—C.E. Mungan, Spring 2010"
487:. That makes the reciprocal of the brightness temperature:
464:
is a portion of the black body radiance, determined by the
1800:"Emissivity, Energy Conservation, Brightness Temperature"
1002:{\displaystyle T_{b}={\frac {I_{\nu }c^{2}}{2k\nu ^{2}}}}
744:
In general, the brightness temperature is a function of
1553:
1526:
1503:
1431:
1391:
1263:
1257:
So, the brightness temperature can be calculated as:
1156:
1076:
1056:
1024:
941:
909:
786:
750:
711:
698:{\displaystyle I_{\nu }={\frac {2\nu ^{2}kT}{c^{2}}}}
646:
610:
493:
473:
435:
411:
387:
363:
339:
310:
290:
247:
145:
41:
27:
would have to be in order to duplicate the observed
1623:
1539:
1509:
1484:
1417:
1375:
1247:
1135:
1062:
1039:
1001:
927:
893:
756:
734:
697:
628:
594:
479:
441:
417:
393:
369:
345:
325:
296:
260:
233:
47:
1851:
1849:
772:of a body, in the case of non-thermal radiation.
2015:
1966:
1070:we can calculate the brightness temperature as:
77:When the electromagnetic radiation observed is
1855:Rybicki, George B., Lightman, Alan P., (2004)
1846:
604:At low frequency and high temperatures, when
1145:
1986:"Can you explain "brightness temperature"?"
775:
89:measured at the origin of that radiation.
1875:
731:
530:
1823:
1821:
2016:
1778:"AMSU Brightness Temperature-NOAA CDR"
1969:"Radiative Processes in Astrophysics"
1937:
1935:
1869:
1818:
1750:
1705:
1661:Lewis Center for Educational Research
1699:
1649:
1857:Radiative Processes in Astrophysics
1040:{\displaystyle \Delta \nu \ll \nu }
935:we can use the Rayleigh–Jeans law:
284:and in the frequency range between
13:
1932:
1633:
1124:
1025:
735:{\displaystyle T_{b}=\epsilon T\,}
14:
2045:
1806:. University of Wisconsin Madison
1418:{\displaystyle hc/\lambda \ll kT}
1015:radiation with very low relative
272:or Brightness) is the amount of
1978:
1960:
1907:
1876:Blandford, R.D. (15 Oct 1992).
1751:Maris, M.; et al. (2020).
1425:the brightness temperature is:
1792:
1770:
1744:
1674:
1:
1920:. United States Naval Academy
1642:
1757:Astronomy & Astrophysics
7:
928:{\displaystyle h\nu \ll kT}
629:{\displaystyle h\nu \ll kT}
10:
2050:
764:, and only in the case of
326:{\displaystyle \nu +d\nu }
55:. This concept is used in
1721:10.1007/978-3-642-19627-0
1146:Calculating by wavelength
480:{\displaystyle \epsilon }
1829:"brightness temperature"
1682:"Brightness Temperature"
1385:For long-wave radiation
776:Calculating by frequency
261:{\displaystyle I_{\nu }}
1709:The Transient Radio Sky
280:per unit time per unit
1991:. NASA. Archived from
1967:Jean-Pierre Macquart.
1780:. NOAA. 7 January 2021
1625:
1541:
1511:
1486:
1419:
1377:
1249:
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1041:
1003:
929:
895:
758:
736:
699:
630:
596:
481:
443:
419:
395:
371:
347:
327:
298:
262:
235:
49:
35:object at a frequency
17:Brightness temperature
1943:"Blackbody Radiation"
1878:"Pulsars and Physics"
1804:Satellite Meteorology
1626:
1542:
1540:{\displaystyle L_{c}}
1512:
1487:
1420:
1378:
1250:
1138:
1065:
1042:
1004:
930:
896:
759:
737:
700:
631:
597:
482:
444:
420:
396:
372:
348:
328:
299:
263:
236:
50:
1706:Keane, E.F. (2011).
1551:
1524:
1501:
1429:
1389:
1261:
1154:
1074:
1054:
1022:
939:
907:
784:
757:{\displaystyle \nu }
748:
709:
644:
608:
491:
471:
433:
409:
394:{\displaystyle \nu }
385:
361:
337:
308:
297:{\displaystyle \nu }
288:
245:
143:
48:{\displaystyle \nu }
39:
21:radiance temperature
766:blackbody radiation
511:
357:of the black body;
1657:"Brightness Units"
1621:
1537:
1507:
1482:
1415:
1373:
1245:
1133:
1060:
1037:
1017:spectral linewidth
999:
925:
891:
754:
732:
695:
638:Rayleigh–Jeans law
626:
592:
494:
477:
451:Boltzmann constant
439:
415:
391:
367:
343:
323:
294:
258:
231:
45:
2034:Planetary science
1888:(1660): 177–192.
1865:978-0-471-82759-7
1730:978-3-642-19626-3
1619:
1510:{\displaystyle I}
1480:
1366:
1295:
1243:
1233:
1200:
1131:
1063:{\displaystyle I}
997:
884:
813:
693:
636:, we can use the
585:
572:
534:
528:
462:spectral radiance
442:{\displaystyle k}
418:{\displaystyle c}
370:{\displaystyle h}
346:{\displaystyle T}
276:emitted per unit
229:
219:
189:
118:helium–neon laser
79:thermal radiation
65:materials science
61:planetary science
2041:
2008:
2007:
2005:
2003:
1997:
1990:
1982:
1976:
1975:
1973:
1964:
1958:
1957:
1955:
1954:
1945:. Archived from
1939:
1930:
1929:
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1925:
1919:
1911:
1905:
1904:
1902:
1900:
1873:
1867:
1853:
1844:
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1841:
1839:
1833:Oxford Reference
1825:
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1796:
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1763:
1748:
1742:
1741:
1739:
1737:
1714:
1703:
1697:
1696:
1694:
1693:
1684:. Archived from
1678:
1672:
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1667:
1653:
1630:
1628:
1627:
1622:
1620:
1618:
1617:
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1585:
1584:
1568:
1563:
1562:
1546:
1544:
1543:
1538:
1536:
1535:
1519:coherence length
1516:
1514:
1513:
1508:
1491:
1489:
1488:
1483:
1481:
1479:
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1234:
1232:
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1171:
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1123:
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1046:
1044:
1043:
1038:
1008:
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998:
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978:
977:
976:
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966:
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934:
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900:
898:
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892:
890:
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883:
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872:
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843:
827:
826:
814:
809:
801:
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739:
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127:
125:
54:
52:
51:
46:
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2038:
2029:Radio astronomy
2014:
2013:
2012:
2011:
2001:
1999:
1995:
1988:
1984:
1983:
1979:
1971:
1965:
1961:
1952:
1950:
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1691:
1689:
1680:
1679:
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1655:
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1650:
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1636:
1634:In oceanography
1613:
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1023:
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990:
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844:
842:
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791:
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647:
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549:
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498:
492:
489:
488:
472:
469:
468:
434:
431:
430:
410:
407:
406:
386:
383:
382:
379:Planck constant
362:
359:
358:
338:
335:
334:
309:
306:
305:
289:
286:
285:
252:
248:
246:
243:
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211:
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197:
196:
191:
183:
179:
172:
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140:
123:
121:
57:radio astronomy
40:
37:
36:
12:
11:
5:
2047:
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2010:
2009:
1998:on 17 May 2023
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1211:
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1121:
1117:
1113:
1110:
1103:
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1089:
1084:
1080:
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1033:
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1027:
993:
989:
985:
982:
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838:
834:
830:
825:
822:
818:
812:
808:
805:
799:
794:
790:
777:
774:
770:spectral index
753:
730:
727:
724:
719:
715:
690:
686:
681:
678:
673:
669:
665:
659:
654:
650:
625:
622:
619:
616:
613:
590:
584:
580:
577:
570:
567:
562:
559:
553:
546:
543:
539:
526:
523:
519:
514:
509:
506:
501:
497:
476:
438:
427:speed of light
414:
390:
366:
342:
322:
319:
316:
313:
293:
255:
251:
227:
224:
217:
214:
209:
206:
200:
195:
186:
182:
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167:
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158:
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149:
44:
9:
6:
4:
3:
2:
2046:
2035:
2032:
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2027:
2025:
2022:
2021:
2019:
1994:
1987:
1981:
1970:
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1949:on 2018-03-07
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1688:on 2017-06-11
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1953:2013-08-24
1692:2015-09-29
1643:References
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466:emissivity
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