129:
879:
is also conserved. In real systems, the étendue may increase (for example due to scattering) or the radiant flux may decrease (for example due to absorption) and, therefore, basic radiance may decrease. However, étendue may not decrease and radiant flux may not increase and, therefore, basic radiance
136:
Radiance is useful because it indicates how much of the power emitted, reflected, transmitted or received by a surface will be received by an optical system looking at that surface from a specified angle of view. In this case, the solid angle of interest is the solid angle subtended by the optical
331:
445:
refers to an area on the surface of the detector and Ω to the solid angle subtended by the source as viewed from that detector. When radiance is conserved, as discussed above, the radiance emitted by a source is the same as that received by a detector observing it.
666:
557:
768:
874:
183:
Spectral radiance expresses radiance as a function of frequency or wavelength. Radiance is the integral of the spectral radiance over all frequencies or wavelengths. For radiation emitted by the surface of an ideal
200:, so that its radiance is uniform with respect to angle of view, and is simply the Stefan–Boltzmann integral divided by π. This factor is obtained from the solid angle 2π steradians of a hemisphere decreased by
237:
1767:
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".
149:
are good indicators of how bright an object will appear. For this reason, radiance and luminance are both sometimes called "brightness". This usage is now discouraged (see the article
589:
176:
equal to the input, unless the index of refraction changes. As an example, if you form a demagnified image with a lens, the optical power is concentrated into a smaller area, so the
480:
100:
Historically, radiance was called "intensity" and spectral radiance was called "specific intensity". Many fields still use this nomenclature. It is especially dominant in
180:
is higher at the image. The light at the image plane, however, fills a larger solid angle so the radiance comes out to be the same assuming there is no loss at the lens.
1725:
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".
693:
804:
441:
refers to an area on the surface of the source, and Ω to the solid angle into which the light is emitted. When calculating radiance received by a detector,
2200:
1501:
per unit frequency or wavelength. This is sometimes also confusingly called "spectral intensity". Non-SI units of spectral flux density include
2156:
1648:
per unit frequency or wavelength. The latter is commonly measured in W⋅m⋅nm. This is sometimes also confusingly called "spectral intensity".
912:
168:. This means that for an ideal optical system in air, the radiance at the output is the same as the input radiance. This is sometimes called
231:("e" for "energetic", to avoid confusion with photometric quantities, and "Ω" to indicate this is a directional quantity), is defined as
201:
1072:
Radiant energy emitted, reflected, transmitted or received, per unit time. This is sometimes also called "radiant power", and called
326:{\displaystyle L_{\mathrm {e} ,\Omega }={\frac {\partial ^{2}\Phi _{\mathrm {e} }}{\partial \Omega \,\partial (A\cos \theta )}},}
1886:
per unit frequency or wavelength. The latter is commonly measured in J⋅m⋅nm. This is sometimes also called "spectral fluence".
2185:
794:
As the light travels through an ideal optical system, both the étendue and the radiant flux are conserved. Therefore,
2148:
905:
661:{\displaystyle L_{\mathrm {e} ,\Omega ,\lambda }={\frac {\partial L_{\mathrm {e} ,\Omega }}{\partial \lambda }},}
94:
55:
2215:
898:
192:, while the integral of its radiance, over the hemisphere into which its surface radiates, is given by the
1245:
Radiant intensity per unit frequency or wavelength. The latter is commonly measured in W⋅sr⋅nm. This is a
2118:
552:{\displaystyle L_{\mathrm {e} ,\Omega ,\nu }={\frac {\partial L_{\mathrm {e} ,\Omega }}{\partial \nu }},}
153:
for a discussion). The nonstandard usage of "brightness" for "radiance" persists in some fields, notably
47:
20:
193:
763:{\displaystyle L_{\mathrm {e} ,\Omega }=n^{2}{\frac {\partial \Phi _{\mathrm {e} }}{\partial G}},}
197:
1958:
1611:
1568:
996:
408:
78:
quantity: the radiance of a surface depends on the direction from which it is being observed.
2123:
1464:
1965:
should be denoted with suffix "e" (for "energetic") to avoid confusion with photometric or
1370:
per unit frequency or wavelength. The latter is commonly measured in W⋅sr⋅m⋅nm. This is a
1199:
Radiant flux emitted, reflected, transmitted or received, per unit solid angle. This is a
8:
2220:
1939:
161:
117:
1122:
Radiant flux per unit frequency or wavelength. The latter is commonly measured in W⋅nm.
2149:"Thermal insulation — Heat transfer by radiation — Physical quantities and definitions"
341:
43:
1844:
integrated over time of irradiation. This is sometimes also called "radiant fluence".
869:{\displaystyle L_{\mathrm {e} ,\Omega }^{*}={\frac {L_{\mathrm {e} ,\Omega }}{n^{2}}}}
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42:
per unit projected area. Radiance is used to characterize diffuse emission and
128:
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2047:, not to be confused with a letter "v", indicating a photometric quantity.)
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1035:
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67:
35:
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quantity. This is sometimes also confusingly called "spectral intensity".
2113:
2044:
359:
39:
38:
emitted, reflected, transmitted or received by a given surface, per unit
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1413:
1073:
185:
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90:
27:
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per unit area. This is sometimes also confusingly called "intensity".
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per unit area. This is sometimes also confusingly called "intensity".
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quantity. This is sometimes also confusingly called "intensity".
113:
1966:
1502:
1318:
Radiant flux emitted, reflected, transmitted or received by a
1104:
1098:
973:
968:
172:. For real, passive, optical systems, the output radiance is
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160:
The radiance divided by the index of refraction squared is
59:
2201:
International
Lighting in Controlled Environments Workshop
2092:
2075:
2039:
1322:, per unit solid angle per unit projected area. This is a
188:
at a given temperature, spectral radiance is governed by
1929:
97:
is taken as a function of frequency or of wavelength.
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592:
483:
240:
2065:
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Comparison of photometric and radiometric quantities
2087:
2085:
437:When calculating the radiance emitted by a source,
868:
762:
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325:
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434:is isotropic (independent of viewing direction).
387:is a function of viewing direction, depending on
2207:
2091:Directional quantities are denoted with suffix "
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2023:
2021:
2019:
2017:
2143:
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1840:per unit area, or equivalently irradiance of a
1392:watt per steradian per square metre, per metre
202:integration over the cosine of the zenith angle
1351:watt per steradian per square metre per hertz
145:is an optical system, radiance and its cousin
2014:
906:
2136:
1952:
355:emitted, reflected, transmitted or received;
207:
1602:(emitted, reflected and transmitted by) a
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899:
2178:Introduction to Radiometry and Photometry
295:
112:. "Intensity" has many other meanings in
127:
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883:
85:is the radiance of a surface per unit
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1729:
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1207:
1080:
991:Energy of electromagnetic radiation.
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1987:Alternative symbols sometimes seen:
1303:watt per steradian per square metre
683:Radiance of a surface is related to
449:
2069:Spectral quantities given per unit
2033:Spectral quantities given per unit
13:
1904:joule per square metre, per metre
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2180:, Artech House, Boston, MA, 1994
1867:joule per square metre per hertz
1785:watt per square metre, per metre
1666:watt per square metre, per metre
1547:watt per square metre, per metre
790:is the étendue of the light beam.
1748:watt per square metre per hertz
1629:watt per square metre per hertz
1482:watt per square metre per hertz
1030:Radiant energy per unit volume.
570:Spectral radiance in wavelength
16:Physical quantity in radiometry
2170:
679:Conservation of basic radiance
461:Spectral radiance in frequency
314:
299:
123:
50:, and to quantify emission of
1:
2129:
1836:Radiant energy received by a
1267:watt per steradian per metre
1226:watt per steradian per hertz
116:, with the most common being
407:. For the special case of a
7:
2102:
1961:recommend that radiometric
212:
93:, depending on whether the
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54:and other particles. The
48:electromagnetic radiation
21:Radiance (disambiguation)
208:Mathematical definitions
170:conservation of radiance
2176:William Ross McCluney,
2119:Sakuma–Hattori equation
1959:Standards organizations
1821:joule per square metre
423:is proportional to cos
1882:Radiant exposure of a
1763:Radiant exitance of a
1702:watt per square metre
1583:watt per square metre
1432:watt per square metre
1011:joule per cubic metre
997:Radiant energy density
870:
764:
662:
553:
327:
133:
2124:Wien displacement law
2011:for radiant exitance.
1465:Spectral flux density
871:
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663:
554:
328:
131:
81:The related quantity
1995:for radiant energy,
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694:
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481:
238:
194:Stefan–Boltzmann law
19:For other uses, see
2216:Physical quantities
1461:Spectral irradiance
1335:Specific intensity
921:
893:SI radiometry units
884:SI radiometry units
830:
675:is the wavelength.
118:power per unit area
58:of radiance is the
2003:for radiant flux,
1612:Spectral radiosity
1209:Spectral intensity
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880:may not increase.
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566:is the frequency.
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409:Lambertian surface
342:partial derivative
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134:
1948:
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1850:Spectral exposure
1731:Spectral exitance
1332:Spectral radiance
1160:Radiant intensity
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450:Spectral radiance
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196:. Its surface is
83:spectral radiance
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1296:
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1279:
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1269:
1266:
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1234:
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1198:
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1188:
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1154:
1150:
1146:
1143:
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1133:
1126:
1125:
1119:
1115:
1111:
1108:
1106:
1102:
1100:
1096:
1092:
1085:
1083:
1082:Spectral flux
1079:
1075:
1071:
1069:
1065:
1061:
1058:
1055:
1052:
1050:
1047:
1039:
1037:
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1027:
1023:
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1016:
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984:
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977:
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937:
923:
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800:
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723:
719:
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540:
527:
518:
508:
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494:
485:
477:
476:
475:
470:
466:
462:
457:
447:
444:
440:
435:
430:
426:
420:
410:
398:
397:azimuth angle
394:
390:
383:
375:
371:
367:
364:
361:
357:
354:
346:
343:
339:
338:
337:
320:
311:
308:
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270:
259:
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242:
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219:
205:
203:
199:
195:
191:
187:
181:
179:
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171:
167:
163:
158:
156:
155:laser physics
152:
148:
144:
140:
130:
121:
119:
115:
111:
107:
103:
102:heat transfer
98:
96:
92:
88:
84:
79:
77:
69:
65:
61:
57:
53:
49:
45:
41:
37:
33:
29:
22:
2177:
2172:
2161:. Retrieved
2152:
2074:
2038:
1954:
1918:
1914:
1910:
1897:
1892:
1883:
1877:
1873:
1860:
1855:
1841:
1837:
1831:
1827:
1812:
1799:
1795:
1791:
1778:
1773:
1764:
1758:
1754:
1741:
1736:
1722:
1718:
1712:
1708:
1693:
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1676:
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1659:
1654:
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1603:
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1593:
1589:
1574:
1561:
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1540:
1535:
1498:
1492:
1488:
1475:
1470:
1452:
1448:
1442:
1438:
1423:
1418:Flux density
1406:
1402:
1398:
1385:
1380:
1371:
1367:
1361:
1357:
1344:
1339:
1323:
1319:
1313:
1309:
1294:
1288:
1281:
1277:
1273:
1260:
1255:
1246:
1240:
1236:
1232:
1219:
1214:
1200:
1194:
1190:
1186:
1165:
1152:
1148:
1144:
1131:
1117:
1113:
1109:
1090:
1067:
1063:
1059:
1036:Radiant flux
1025:
1021:
1017:
1002:
986:
982:
978:
959:
887:
878:
795:
793:
787:
777:
772:
682:
672:
670:
577:
573:
569:
568:
563:
561:
468:
464:
460:
459:
442:
438:
436:
428:
424:
418:
392:
391:through cos
388:
381:
379:
373:
369:
365:
353:radiant flux
335:
225:
221:
217:
216:
190:Planck's law
182:
173:
169:
159:
141:. Since the
135:
106:astrophysics
99:
80:
75:
68:square metre
36:radiant flux
31:
25:
2114:Light field
1969:quantities.
1372:directional
1324:directional
1247:directional
1201:directional
798:defined by
380:In general
360:solid angle
124:Description
76:directional
74:). It is a
40:solid angle
2221:Radiometry
2210:Categories
2163:2015-03-15
2130:References
2071:wavelength
1963:quantities
1940:Photometry
1935:Radiometry
1925:See also:
1527:10 Jy
1519:1 sfu
1414:Irradiance
1354:W⋅sr⋅m⋅Hz
1249:quantity.
1203:quantity.
1074:luminosity
931:Dimension
576:, denoted
467:, denoted
224:, denoted
198:Lambertian
186:black body
178:irradiance
151:Brightness
91:wavelength
44:reflection
28:radiometry
2035:frequency
1569:Radiosity
1507:1 Jy
1176:steradian
1174:watt per
1097:watt per
925:Quantity
850:Ω
827:∗
822:Ω
749:∂
736:Φ
732:∂
711:Ω
650:λ
647:∂
640:Ω
624:∂
613:λ
607:Ω
541:ν
538:∂
531:Ω
515:∂
504:ν
498:Ω
374:projected
358:Ω is the
340:∂ is the
312:θ
309:
297:∂
293:Ω
290:∂
277:Φ
267:∂
255:Ω
162:invariant
147:luminance
137:system's
110:astronomy
87:frequency
64:steradian
52:neutrinos
2103:See also
1449:received
1289:Radiance
1229:W⋅sr⋅Hz
399:through
218:Radiance
213:Radiance
95:spectrum
32:radiance
2109:Étendue
1884:surface
1870:J⋅m⋅Hz
1842:surface
1838:surface
1765:surface
1751:W⋅m⋅Hz
1723:surface
1719:emitted
1646:surface
1632:W⋅m⋅Hz
1604:surface
1600:leaving
1499:surface
1485:W⋅m⋅Hz
1453:surface
1395:W⋅sr⋅m
1368:surface
1320:surface
1306:W⋅sr⋅m
1270:W⋅sr⋅m
948:Symbol
942:Symbol
780:is the
685:étendue
574:surface
465:surface
372:is the
351:is the
344:symbol;
222:surface
174:at most
114:physics
56:SI unit
34:is the
2184:
1967:photon
1513:) and
1503:jansky
1056:= J/s
934:Notes
773:where
671:where
562:where
427:, and
417:/(∂Ω ∂
336:where
72:W·sr·m
1721:by a
1451:by a
1099:hertz
969:joule
945:Name
939:Name
928:Unit
581:e,Ω,λ
572:of a
472:e,Ω,ν
463:of a
376:area.
220:of a
2182:ISBN
1907:J/m
1824:J/m
1788:W/m
1705:W/m
1669:W/m
1586:W/m
1550:W/m
1435:W/m
1384:e,Ω,
1343:e,Ω,
1259:e,Ω,
1218:e,Ω,
1141:W/m
1049:watt
1014:J/m
395:and
368:cos
108:and
66:per
62:per
60:watt
2157:ISO
1999:or
1991:or
1529:).
1298:e,Ω
1169:e,Ω
687:by
432:e,Ω
405:/∂Ω
385:e,Ω
306:cos
229:e,Ω
164:in
143:eye
89:or
46:of
26:In
2212::
2155:.
2151:.
2138:^
2095:".
2084:^
2079:".
2052:^
2045:nu
2016:^
1974:^
1930:SI
1896:e,
1859:e,
1777:e,
1740:e,
1658:e,
1621:e,
1539:e,
1525:=
1521:=
1509:=
1474:e,
1182:sr
1180:W/
1130:e,
1105:Hz
1103:W/
1089:e,
413:∂Φ
411:,
401:∂Φ
204:.
157:.
120:.
104:,
30:,
2166:.
2093:Ω
2076:λ
2040:ν
2009:W
2005:I
2001:F
1997:P
1993:E
1989:W
1919:T
1917:⋅
1915:L
1913:⋅
1911:M
1898:λ
1893:H
1878:T
1876:⋅
1874:M
1861:ν
1856:H
1832:T
1830:⋅
1828:M
1816:e
1813:H
1800:T
1798:⋅
1796:L
1794:⋅
1792:M
1779:λ
1774:M
1759:T
1757:⋅
1755:M
1742:ν
1737:M
1713:T
1711:⋅
1709:M
1697:e
1694:M
1681:T
1679:⋅
1677:L
1675:⋅
1673:M
1660:λ
1655:J
1640:T
1638:⋅
1636:M
1623:ν
1618:J
1594:T
1592:⋅
1590:M
1578:e
1575:J
1562:T
1560:⋅
1558:L
1556:⋅
1554:M
1541:λ
1536:E
1517:(
1505:(
1493:T
1491:⋅
1489:M
1476:ν
1471:E
1443:T
1441:⋅
1439:M
1427:e
1424:E
1407:T
1405:⋅
1403:L
1401:⋅
1399:M
1386:λ
1381:L
1362:T
1360:⋅
1358:M
1345:ν
1340:L
1314:T
1312:⋅
1310:M
1295:L
1282:T
1280:⋅
1278:L
1276:⋅
1274:M
1261:λ
1256:I
1241:T
1239:⋅
1237:L
1235:⋅
1233:M
1220:ν
1215:I
1195:T
1193:⋅
1191:L
1189:⋅
1187:M
1166:I
1153:T
1151:⋅
1149:L
1147:⋅
1145:M
1132:λ
1128:Φ
1118:T
1116:⋅
1114:L
1112:⋅
1110:M
1091:ν
1087:Φ
1068:T
1066:⋅
1064:L
1062:⋅
1060:M
1054:W
1043:e
1041:Φ
1026:T
1024:⋅
1022:L
1020:⋅
1018:M
1006:e
1003:w
987:T
985:⋅
983:L
981:⋅
979:M
974:J
963:e
960:Q
914:e
907:t
900:v
860:2
856:n
847:,
843:e
838:L
832:=
819:,
815:e
810:L
788:G
778:n
758:,
752:G
741:e
724:2
720:n
716:=
708:,
704:e
699:L
673:λ
656:,
637:,
633:e
628:L
618:=
610:,
604:,
600:e
595:L
578:L
564:ν
547:,
528:,
524:e
519:L
509:=
501:,
495:,
491:e
486:L
469:L
443:A
439:A
429:L
425:θ
421:)
419:A
415:e
403:e
393:θ
389:θ
382:L
370:θ
366:A
362:;
349:e
347:Φ
321:,
315:)
303:A
300:(
282:e
271:2
260:=
252:,
248:e
243:L
226:L
70:(
23:.
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