Page 1 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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Light Sources and Illumination - Computer GraphicsEnergy Radiant Energy Luminous Energy Flux (Power) Radiant Power Luminous Power Flux Density Irradiance Radiosity Illuminance Luminosity
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Page 1
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
Page 2
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
Page 5
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