spectral power distributions “blackbody” planckian radiators
Post on 19-Dec-2015
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Spectral Power Distributions
“blackbody” Planckian radiators
relative M(lamda)
0
1E+13
2E+13
3E+13
4E+13
5E+13
6E+13
7E+13
0 1000 2000 3000 4000 5000
Wavelength, nm
spec
tral
pow
er
M(lamda) normalized in visible @ T = 5500 K
0.00
0.20
0.40
0.60
0.80
1.00
400 450 500 550 600 650 700
Wavelength, nm
Planck’s Law
h = Planck’s constant
k = Boltzman constant
c = speed of light
λ = wavelength
T = absolute temperature
)1(
12)(
/5
2
kThce
hcM
Candle flame (1000K)
relative M(lamda)
0
2000000000
4000000000
6000000000
8000000000
10000000000
12000000000
14000000000
0 1000 2000 3000 4000 5000
Wavelength, nm
spec
tral
pow
erM(lamda) normalized in visible @ T = 1000 K
0.00
0.20
0.40
0.60
0.80
1.00
400 450 500 550 600 650 700
Wavelength, nm
relative M(lamda)
0
5E+11
1E+12
2E+12
2E+12
3E+12
3E+12
0 1000 2000 3000 4000 5000
Wavelength, nm
spec
tral
pow
erM(lamda) normalized in visible @ T = 2865 K
0.00
0.20
0.40
0.60
0.80
1.00
400 450 500 550 600 650 700
Wavelength, nm
100 W tungsten bulb (2856K)
relative M(lamda)
0
1E+12
2E+12
3E+12
4E+12
5E+12
6E+12
7E+12
0 1000 2000 3000 4000 5000
Wavelength, nm
spec
tral
pow
erM(lamda) normalized in visible @ T = 3400 K
0.00
0.20
0.40
0.60
0.80
1.00
400 450 500 550 600 650 700
Wavelength, nm
“Photoflood” 500 W bulb (3400K)
relative M(lamda)
0
1E+13
2E+13
3E+13
4E+13
5E+13
6E+13
7E+13
0 1000 2000 3000 4000 5000
Wavelength, nm
spec
tral
pow
erM(lamda) normalized in visible @ T = 5500 K
0.00
0.20
0.40
0.60
0.80
1.00
400 450 500 550 600 650 700
Wavelength, nm
Sunlight (5500K)
relative M(lamda)
0
5E+14
1E+15
1.5E+15
2E+15
2.5E+15
3E+15
3.5E+15
0 1000 2000 3000 4000 5000
Wavelength, nm
spec
tral
pow
erM(lamda) normalized in visible @ T = 12000 K
0.00
0.20
0.40
0.60
0.80
1.00
400 450 500 550 600 650 700
Wavelength, nm
Skylight (12000K)
Absolute vs. relative spectral power
M(lamda)
0
2E+13
4E+13
6E+13
8E+13
1E+14
1.2E+14
1.4E+14
1.6E+14
0 1000 2000 3000 4000 5000
Wavelength, nm
abso
lute
spe
ctra
l pow
er
6500K
5500K
2856K 0.0
0.2
0.4
0.6
0.8
1.0
400 450 500 550 600 650 700
Wavelength, nm
12000K
1000K
2856K
3400K
5500K
6500K
rela
tive
spec
tral
pow
er
Planck’s Law
h = Planck’s constant
k = Boltzman constant
c = speed of light
λ = wavelength
T = absolute temperature
)1(
12)(
/5
2
kThce
hcM
Stefan-Boltzman Law:
total power output
Total power = σ T 4
σ = Stefan-Boltzman constant
T = temperature Kelvins
M(lamda)
0
2E+13
4E+13
6E+13
8E+13
1E+14
1.2E+14
1.4E+14
1.6E+14
0 1000 2000 3000 4000 5000
Wavelength, nm
abso
lute
spe
ctra
l pow
er
6500K
5500K
2856K
Wein’s Displacement Law:wavelength at peak output
λmax = b/T
b = 2.898 x 10-3 (m K) T = temperature Kelvins
0.0
0.2
0.4
0.6
0.8
1.0
400 450 500 550 600 650 700
Wavelength, nm
12000K
1000K
2856K
3400K
5500K
6500K
rela
tive
spec
tral
pow
er
CIE 1988 V(wavelength) visibility function
0.00
0.25
0.50
0.75
1.00
350 450 550 650 750
wavelength, nm
Re
lati
ve
vis
ua
l eff
icie
nc
yCIE 1988 photopic visibility function V(λ)
380 0.0002
390 0.0008
400 0.0028
410 0.0074
420 0.0175
430 0.0273
440 0.0379
450 0.0468
460 0.0600
470 0.0910
480 0.1390
490 0.2080
500 0.3230
510 0.5030
520 0.7100
530 0.8620
540 0.9540
550 0.9950
560 0.9950
570 0.9520
580 0.8700
590 0.7570
600 0.6310
610 0.5030
620 0.3810
630 0.2650
640 0.1750
650 0.1070
660 0.0610
670 0.0320
680 0.0170
690 0.0082
700 0.0041
710 0.0021
720 0.0011
730 0.0005
740 0.0002
750 0.0001
760 0.0001
770 0.0000
nm V(λ) nm V(λ)
CIE 1988 photopic visibility function V(λ)with 2856K & 5500K blackbody radiators
CIE 1988 V(wavelength) visibility function
0.00
0.25
0.50
0.75
1.00
350 450 550 650 750
wavelength, nm
Re
lati
ve
vis
ua
l eff
icie
nc
y
V(λ)2856K
5500K
CIE 1988 photopic visibility function V(λ)with 2856K & 5500K blackbody radiators
CIE 1988 V(wavelength) visibility function
0.00
0.25
0.50
0.75
1.00
350 450 550 650 750
wavelength, nm
Re
lati
ve
vis
ua
l eff
icie
nc
y
V(λ)2856K
5500K
M(lamda)
0
2E+13
4E+13
6E+13
8E+13
1E+14
1.2E+14
1.4E+14
1.6E+14
0 1000 2000 3000 4000 5000
Wavelength, nm
abso
lute
spe
ctra
l pow
er
6500K
5500K
2856K
Radiometric constants: (ISO units, distance = meters)
Constants:
Planck's constant h 6.63E-34 J s
speed of light c 3.00E+08 m/s
Boltzman's constant k 1.38E-23 J/K
Wein's constant b 2.90E-03 m K
Stefan-Boltzman constant σ 5.670E-8 W/m2 K4