spectral power distributions “blackbody” planckian radiators

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Spectral Power Distributions “blackbody” Planckian radiators relative M (lam da) 0 1E+13 2E+13 3E+13 4E+13 5E+13 6E+13 7E+13 0 1000 2000 3000 4000 5000 Wavelength,nm spectral pow er M (lam da)norm alized 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

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Page 1: Spectral Power Distributions “blackbody” Planckian radiators

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

Page 2: Spectral Power Distributions “blackbody” Planckian radiators

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

Page 3: Spectral Power Distributions “blackbody” Planckian radiators

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

Page 4: Spectral Power Distributions “blackbody” Planckian radiators

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)

Page 5: Spectral Power Distributions “blackbody” Planckian radiators

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)

Page 6: 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

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)

Page 7: Spectral Power Distributions “blackbody” Planckian radiators

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)

Page 8: Spectral Power Distributions “blackbody” Planckian radiators

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

Page 9: Spectral Power Distributions “blackbody” Planckian radiators

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

Page 10: Spectral Power Distributions “blackbody” Planckian radiators

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

Page 11: Spectral Power Distributions “blackbody” Planckian radiators

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

Page 12: Spectral Power Distributions “blackbody” Planckian 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

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)

Page 13: Spectral Power Distributions “blackbody” Planckian radiators

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

Page 14: Spectral Power Distributions “blackbody” Planckian radiators

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

Page 15: Spectral Power Distributions “blackbody” Planckian radiators

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