Introduction to Light Pollution
Lecture 2
prof. Željko Andreić
Faculty of Mining, Geology and Petroleum Engineering
University of Zagreb
[email protected]
http://rgn.hr/~zandreic/
Željko Andreić: Introduction to light pollution, P2
1
Contents
1. black body radiation
2. light in the nature
3. introduction to radiometry
4. introduction to photometry
Željko Andreić: Introduction to light pollution, P2
2
Black body radiation
W/(m2 ⋅m)
m
W/m2
c1 = 3,7418×10-16 Wm2
c2 = 0,014388 m ⋅ K
σ = 5,67×10−8 W m−2 K−4
Željko Andreić: Introduction to light pollution, P2
3
Black body radiation
Željko Andreić: Introduction to light pollution, P2
4
Black body radiation
cinder
match flame
candle flame
tungsten lightbulb
xenon arc
fluorescent lamp:
warm white
white
cold white
daylight
sunshine
daylight, sunny
daylight, cloudy
blue sky
Željko Andreić: Introduction to light pollution, P2
1 000 K
1 700 K
1 850 K
2 700 - 3 300 K
4 100 K
3 000 K
3 500 K
4 000 K
5 000 K
5 900 K
5 500 - 6 000 K
6 500 K
9 000 - 12 000 K
5
The Sun
solar constant: 1 390 W/m2
perihelium: 1 438 W/m2
aphelium: 1 345 W/m2
Sun in zenith, horizontal surface at sea-level: E = 1,24⋅105 lux
Željko Andreić: Introduction to light pollution, P2
6
Daylight
the height of the Sun
90o
E = 1,24⋅105 lux
65o
1,08⋅105
45o
7,59⋅105
25o
3,67⋅105
10o
1,09⋅105
5o
4 760
0o
732
-0,8o
453
-6o
3,4
-12o
0,0083
-18o
0,00065
Željko Andreić: Introduction to light pollution, P2
sunset or sunrise
end of civil twilight
end of nautical twilight
end of astronomical twilight
7
"nightlight"
The height of the Moon in culmination is between 25o - 70o
first quarter E = 10 - 30 mlx
full moon
80 - 250 mlx
last quarter
10 - 30 mlx
starry sky without the moon: 0,7 - 2 mlx
cloudy night:
0,03 - 0,1 mlx
Venus (max.):
Željko Andreić: Introduction to light pollution, P2
0,14 mlx
8
Introduction to radiometry
Radiometry: part of physics dealing with elektromagnetic radiation.
The electromagnetic spectrum is practically infinite.
visible
cosmic rays
ultraviolet
gama-rays
infra-red
x-rays
10-18
10-15
10-12
10-9
10-6
mikrowaves
10-3
radiowaves
1
103
low frequency electromagnetic radiation
(VLF, ELF, ULF...)
106
109
1012
wavelength (m)
Željko Andreić: Introduction to light pollution, P2
9
Radiometric quantities
Radiant energy, usual symbol Q, is like any other form of energy measured
in J.
Radiant flux is defined as the amount of energy carried away in unit time
by the electromagnetic radiation. Usual symbol is Φ, and standard unit is
W. It is defined as:
Φ=Q/t
Željko Andreić: Introduction to light pollution, P2
10
Radiometric quantities
Surface density of radiant flux is defined as flux of radiation passing
through, or falling upon a unit surface area:
E=Φ/A
It is measured in W/m2.
Depending on conditions, two different names are used for the radiant flux:
1. radiant exitance (Radiant emittance), if surface is the source of the
radiation . In this cas symol M is used instead of E.
2. Irradiance, the surface is irradiated by the radiation from some other
source.
Željko Andreić: Introduction to light pollution, P2
11
Radiometric quantities
Radiant intensity) is defined as radiant flux going into unit solid angle
(1 steradijan):
I=Φ/ω
It is measured in W/sr.
If radiant intensity is expressed per unit area, it is called radiance.
Radiance is defined as:
L=I/(A cosϕ)
i.e. unit area is always perpendicular to the direction of the emission.
Radiance is measured in Wsr-1m-2
Željko Andreić: Introduction to light pollution, P2
12
Radiometric quantities
All this quantities deal with all EM radiation present. If spectral distribution of
the radiation is important, the so called spectral functions are used. The
spectral functions are defined as derivatives of radiometric quantities over
wavelength (or frequency, as alternative). For instance, the spectral
density of radiant flux is defined as:
Eλ=E/λ
It is mesuared in Wm-2 µm-1. The other spectral radiometric functions are
defined in an analogous way.
Željko Andreić: Introduction to light pollution, P2
13
Radiometric constants
E
ρE
Radiometric constants are:
(they depend on the material!):
αE
absorption
α=Eapsorbed/Eincident
reflectivity
ρ=Ereflected/Eincident
transmission
τ=Etransmitted/Eincident
emissivity
ε=Esample/Eblack_body
τE
(at the same temperature)
Dimension of all coefficients is 1.
rule:
α+ρ+τ=1
Željko Andreić: Introduction to light pollution, P2
14
Lambert's surface
mirror reflection
diffuse reflection
Lambert's surface is idelly diffuse surface that produces constant radiance
regardless of the direction of the incoming radiation. The radiance of such
a surface is simply L=E/π, where E is the total radiant flux falling on the
surface.
Željko Andreić: Introduction to light pollution, P2
15
Fotometry
Fotometry is dealing only with the visible light, taking into account the
spectral response of the human eye. Fotometric functions thus describe
the human vision and it's response to the light (brightness, color, etc.)
The visible light is a small part of the electromagnetic spectrum:
far
infrared
far ultraviolet
ekstreme
ultraviolet
violet
10
middle
infrared
(near)
ultraviolet
200
300
400
blue green
500
y. o. red
.
600
(near) infrared
700
800
900
1000
104
wavelength (nm)
Željko Andreić: Introduction to light pollution, P2
16
The human eye
Iris
Optic nerve
Cornea
Blind spot
Pupil
Yellow spot
Lens
Retina
Željko Andreić: Introduction to light pollution, P2
Iris
17
The human eye
Rods
Light
Cones
Željko Andreić: Introduction to light pollution, P2
18
The human eye
Day
Night
Željko Andreić: Introduction to light pollution, P2
19
The human eye
Željko Andreić: Introduction to light pollution, P2
20
The human eye
Field of view:
Monocular: 160 deg (h) x 175 deg (v)
Binocular: 200 deg (h) x 135 deg (v)
Binocular overlap (stereoscopic vision): 120 deg (h) x 135 deg (v)
day vision (scotopic vision):
transition (mesopic vision):
night vision (photopic vision):
Željko Andreić: Introduction to light pollution, P2
above 0,035 cd/m2
around 0,035 cd/m2
below 0,035 cd/m2
21
Introduction to photometry
The quantity of light (luminous energy), usual symbol Q, is measured in
lumen-seconds (lm·s or talbot).
The candela: luminous intensity of 1/60 cm2 of the projected area of a
black body radiator operating at the temperature of the solidification of
platinum (2045 K).
The lumen (lm) is defined in terms of candela. The luminous flux per
steradian from a source whose luminous intensity is 1 candela is 1 lumen.
The luminous flux, usual symbol Φ is measured in lumens (lm).
It is defined as:
Φ=∂Q/∂t
Željko Andreić: Introduction to light pollution, P2
22
Photometric quantities
Luminous flux density at a surface is defined as the luminous flux falling
on a unit surface area:
E=Φ/A
Two names are used for luminous flux density:
1. radiant exitance ili radiant emittance, if the surface in question is the
source of radiation. In this case the symbol M is used instead of E,
and the units used are lm/m2.
2. irradiance, if the surface in question is illuminated by light from some
other source. It is measured in lm/m2 (lux).
Željko Andreić: Introduction to light pollution, P2
23
Photometric quantities
The luminous intensity is defined as flux going itno a unit solid angle
(1 steradijan):
I=Φ/ω
It is measured in lm/sr = cd (candela).
If the light intensity is expressed per unit area, it is called luminance
or brigthness. The definition of brightness is:
L=I/(A cosϕ)
i.e. unit area is always perpendicular to the direction of the emission.
It is measured in nits (nt). 1 nt = 1 cd/m2.
Željko Andreić: Introduction to light pollution, P2
24
Photometric quantities
The luminous efficacy is defined as luminous flux per unit power of the light
source that produces the luminous flux:
K=Φv/Φe
It is measured in lm/w.
If radiometric and photometric functions are used simultaneusly, radiometric
functions are additionaly labelled with the subscript "e" and the
corresponding photometric functions with the subscript "v".
Željko Andreić: Introduction to light pollution, P2
25
Photometric quantities
All this quantities deal with all EM radiation present. If spectral distribution of
the radiation is important, the so called spectral functions are used. The
spectral functions are defined as derivatives of radiometric quantities over
wavelength (or frequency, as alternative). For instance, the spectral
density of luminous flux is defined as:
Eλ=∆E/∆λ
i mjeri se u lm·m-2 µm-1.
Željko Andreić: Introduction to light pollution, P2
26
Photometric constants
E
ρE
Radiometric constants are:
(they depend on the material!):
αE
absorption
α=Eapsorbed/Eincident
reflectivity
ρ=Ereflected/Eincident
transmission
τ=Etransmitted/Eincident
emissivity
ε=Esample/Eblack_body
τE
(at the same temperature)
Dimension of all coefficients is 1.
rule:
α+ρ+τ=1
Željko Andreić: Introduction to light pollution, P2
27
The standard light sources
The primary standard: black body at the temperature of solidification of
platinum (2045 K). A quite complicate laboratory device, used mainly
for calibration of secundary standard sources.
The secondary standard: a light bulb with tungsten wire or ribbon,
calibrated against the primary standard. Much smaller device,
and easier to use.
Željko Andreić: Introduction to light pollution, P2
28