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CS348B Lecture 5 Pat Hanrahan, Spring 2001
Light Sources and Illumination
Properties of light sources� Power Spectrum� Radiant and luminous intensity� Directional distribution – goniometric diagram� Shape
Illumination� Irradiance and illuminance� Area light sources
CS348B Lecture 5 Pat Hanrahan, Spring 2001
Blackbody
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CS348B Lecture 5 Pat Hanrahan, Spring 2001
Tungsten
CS348B Lecture 5 Pat Hanrahan, Spring 2001
Flourescent
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CS348B Lecture 5 Pat Hanrahan, Spring 2001
Sunlight
CS348B Lecture 5 Pat Hanrahan, Spring 2001
Radiant and Luminous Intensity
Definition: The radiant (luminous) intensity is the power per unit solid angle from a point.
( ) dId
ωωΦ≡
W lm cd candelasr sr
= =
2
( )S
I dω ωΦ = ∫
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CS348B Lecture 5 Pat Hanrahan, Spring 2001
The Invention of Photometry
Bouguer’s classic experiment� Compare a light source and a candle� Intensity is proportional to ratio of
distances squared
Definition of a standard candle� Originally “standard” candle� Currently 550 nm laser w/ 1/683 W/sr� 1 of 6 fundamental SI units
CS348B Lecture 5 Pat Hanrahan, Spring 2001
Goniometric Diagrams
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CS348B Lecture 5 Pat Hanrahan, Spring 2001
Warn’s Spotlight
ˆ ˆ( ) cos )s sI ω θ= = •(S A
12coscos2cos)(
1
0
2
0
1
0 +===Φ ∫∫ ∫ s
dddI s πθθπϕθωπ
θπ
ω ssI cos2
1)( +Φ=
θ A
S
CS348B Lecture 5 Pat Hanrahan, Spring 2001
PIXAR Standard Light Source
Ronen Barzel UberLight( ){
Clip to near/far planesClip to shape boundaryforeach superelliptical blocker
atten *= …foreach cookie texture
atten *= …foreach slide texture
color *= …foreach noise texture
atten, color *= …foreach shadow map
atten, color *= …Calculate intensity fall-offCalculate beam distribution
}
Inconsistent Shadows
Projected Shadow Matte
Projected Texture
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CS348B Lecture 5 Pat Hanrahan, Spring 2001
Irradiance and Illuminance
Definition: The irradiance (illuminance) is the power per unit area incident on a surface.
This is sometimes referred to as the radiant and luminous incidence.
2
( ) ( , ) cosi i iH
E x L x dω θ ω= ∫
)( iL ω
iθ
2
( ) ( , ) cosi i iddE x L x ddA
ω θ ωΦ≡ =
2 2
W lm luxm m
=
CS348B Lecture 5 Pat Hanrahan, Spring 2001
Isotropic Point Sources
� Note inverse square law fall off.� Note cosine dependency
πω
4)( Φ=I
dAh
dAr
dIdAEd 2
3
2
cos4
cos4
θπ
θπ
ω Φ=Φ===Φ
θ hr
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CS348B Lecture 5 Pat Hanrahan, Spring 2001
Distant or Directional Source
2
( ) cos cosH
E L d dω θ θ ϕ= ∫
)()cos(cos),( sssEL ϕϕδθθδϕθ −−=
2
2
( , ) cos cos
(cos cos ) ( ) cos cos
cos
H
s s sH
s s
L d d
E d d
E
θ ϕ θ θ ϕ
δ θ θ δ ϕ ϕ θ θ ϕ
θ
= − −
=
∫
∫
sθsE
CS348B Lecture 5 Pat Hanrahan, Spring 2001
Irradiance Distribution
Isolux contours
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CS348B Lecture 5 Pat Hanrahan, Spring 2001
Irradiance from Area Sources
2
cosΗ
dθ ω π=∫
2 2
( ) ( , ) cos cosi i i i iH H
E x L x d L dω θ ω θ ω= =∫ ∫
Projected Solid Angle
Radiosity formulation = Differential Form Factor
Note: Things are considerably complicated by shadows
iθ
CS348B Lecture 5 Pat Hanrahan, Spring 2001
Luminance of Common Light Sources
Surface of the sun 2,000,000,000. cd/m2
Sunlight clouds 30,000.Clear day 3,000.Overcast day 300.Moonlight 0.03Moonless 0.00003
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CS348B Lecture 5 Pat Hanrahan, Spring 2001
The Sky
From Greenler, Rainbows, halos and glories
CS348B Lecture 5 Pat Hanrahan, Spring 2001
Disk Source
r
R θ
cos 2
1 0cos2
12
2
2 2
cos cos
cos22
sin
d
d
d
E L d d
L
LrL
r R
θ π
θ
θ φ θ
θπ
π θ
π
=
=
=
=+
∫ ∫
Geometric Derivation Algebraic Derivation
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CS348B Lecture 5 Pat Hanrahan, Spring 2001
Spherical Source
2
2
2sin
cos
RrL
L
dLE
π
θπ
ωθ
=
=
= ∫rR
θ
Geometric Derivation Algebraic Derivation
CS348B Lecture 5 Pat Hanrahan, Spring 2001
The Sun
Solar constant (normal incidence at zenith)Irradiance 1353 W/m2
Illuminance 127,500 Lumen/m2 = 127.5 Kilo-LuxSolar angle
αααα = .25 degrees = .004 radians (half angle)ωωωω = ππππ sin2 αααα = 6 x 10-5 steradians
Radiance
Pluto (6 tera-meters) 50 Lux - read a newspaperDeep space -> 20 micro-lux (see, but not read!)
srmsrmWEL
⋅×=
××== − 2
75
23 W1025.2106
/10353.1ω
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CS348B Lecture 5 Pat Hanrahan, Spring 2001
Polygonal Source
CS348B Lecture 5 Pat Hanrahan, Spring 2001
Lambert’s Formula
1 1
n n
i i ii iA γ
= =
= •∑ ∑ N N� �
iiiA NN��
•=γ
iN�
iγ∑
=
3
1iiA
1A
2A−
3A−
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CS348B Lecture 5 Pat Hanrahan, Spring 2001
Radiosity and Luminosity
Definition: The radiosity (luminosity) is the energy per unit area leaving a surface.
This is officially referred to as the radiant and luminousexitance.
∫=2
cos)()(H
ooo dLxB ωθωoθ
)( oL ω
CS348B Lecture 5 Pat Hanrahan, Spring 2001
Uniform Diffuse Source
2 31 / ( 10 )foot lamberts cd ft glim foot lambertπ−− = = −
21 /lamberts cd cmπ=
2 31 1 / ( 10 )blondel apostilb nit cd m skot apostilbπ π−= = = =
cos
cos
B L d
L d
L
θ ω
θ ω
π
=
=
=
∫
∫ πBL =
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CS348B Lecture 5 Pat Hanrahan, Spring 2001
Radiometric and Photometric Terms
Physics Radiometry Photometry
Energy Radiant Energy Luminous Energy
Flux (Power) Radiant Power Luminous Power
Flux Density Irradiance
Radiosity
Illuminance
Luminosity
Angular Flux Density Radiance Luminance
Intensity Radiant Intensity Luminous Intensity
CS348B Lecture 5 Pat Hanrahan, Spring 2001
Photometric Units
Photometry Units
MKS CGS British
Luminous Energy Talbot
Luminous Power Lumen
Illuminance
Luminosity
Lux Phot Footcandle
Luminance Nit
Apostilb, Blondel
Stilb
Lambert Footlambert
Luminous Intensity Candela (Candle, Candlepower, Carcel, Hefner)
“Thus one nit is one lux per steradian is one candela per square meter is one lumen per square meter per steradian. Got it?” Kajiya