introduction to light pollution lecture 2rgn.hr/~zandreic/students/introlp/lp_en_p2.pdf · xenon...

Željko Andreić: Introduction to light pollution, P2 1

Introduction to Light Pollution

Lecture 2

prof. Željko Andreić

Faculty of Mining, Geology and Petroleum EngineeringUniversity of Zagreb

[email protected]

http://rgn.hr/~zandreic/


Contents

1. black body radiation2. light in the nature3. introduction to radiometry4. introduction to photometry


Black body radiation

c1 = 3,7418×10-16 Wm2

c2 = 0,014388 m ⋅ K

σ = 5,67×10−8 W m−2 K−4

W/(m2 ⋅m)

W/m2

m


cinder 1 000 Kmatch flame 1 700 Kcandle flame 1 850 Ktungsten lightbulb 2 700 - 3 300 Kxenon arc 4 100 Kfluorescent lamp:

warm white 3 000 Kwhite 3 500 Kcold white 4 000 Kdaylight 5 000 K

sunshine 5 900 Kdaylight, sunny 5 500 - 6 000 Kdaylight, cloudy 6 500 Kblue sky 9 000 - 12 000 K



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


Daylight

the height of the Sun

90o E = 1,24⋅105 lux65o 1,08⋅105

45o 7,59⋅105

25o 3,67⋅105

10o 1,09⋅105

5o 4 7600o 732

-0,8o 453 sunset or sunrise-6o 3,4 end of civil twilight

-12o 0,0083 end of nautical twilight-18o 0,00065 end of astronomical twilight


"nightlight"

The height of the Moon in culmination is between 25o - 70o

first quarter E = 10 - 30 mlxfull moon 80 - 250 mlxlast quarter 10 - 30 mlx

starry sky without the moon: 0,7 - 2 mlxcloudy night: 0,03 - 0,1 mlx

Venus (max.): 0,14 mlx


Introduction to radiometry

Radiometry: part of physics dealing with elektromagnetic radiation.

The electromagnetic spectrum is practically infinite.

wavelength (m)

1 103 1012106 10910-310-12 10-9 10-610-18 10-15

mikro-

waves

radiowaves low frequency electromagnetic radiation

(VLF, ELF, ULF...)

infra-red

visible

x-rays

cosmic rays gama-rays

ultra-

violet


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


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.



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



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.



Radiometric constants are:

(they depend on the material!):

absorption α=Eapsorbed/Eincident

reflectivity ρ=Ereflected/Eincident

transmission τ=Etransmitted/Eincident

emissivity ε=Esample/Eblack_body (at the same temperature)

Dimension of all coefficients is 1.

rule: α + ρ + τ = 1

E

τE

αE

ρERadiometric constants


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.


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:

wavelength (nm)

700 800 104900 1000600300 400 50010 200

(near) infraredblue

middle

infrared

far

infrared

(near)

ultraviolet

far ultraviolet

ekstreme

ultraviolet

violet green y.

.

o. red


The human eye

Lens

Pupil

Cornea

Optic nerve

Iris

IrisRetina

Blind spot

Yellow spot


Cones

Rods

Light

The human eye


Day

Night

The human eye


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): above 0,035 cd/m2

transition (mesopic vision): around 0,035 cd/m2

night vision (photopic vision): below 0,035 cd/m2

The human eye


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

Introduction to photometry


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).

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.



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".



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.



Radiometric constants are:

(they depend on the material!):

absorption α=Eapsorbed/Eincident

reflectivity ρ=Ereflected/Eincident

transmission τ=Etransmitted/Eincident

emissivity ε=Esample/Eblack_body (at the same temperature)

Dimension of all coefficients is 1.

rule: α + ρ + τ = 1

E

τE

αE

ρEPhotometric constants


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.

introduction to light pollution lecture 2rgn.hr/~zandreic/students/introlp/lp_en_p2.pdf · xenon...

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