Post on 29-Sep-2020
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CS348B Lecture 4 Pat Hanrahan, 2005
Light
Visible electromagnetic radiation
Power spectrum
Polarization
Photon (quantum effects)
Wave (interference, diffraction)
1 102 104 106 108 1010 1012 1014 1016 1018 1020 1022 1024 1026
1016 1014 1012 1010 108 106 104 102 1 10-2 10-4 10-6 10-8
CosmicRays
GammaRays
X-RaysUltra-Violet
Infra-Red
RadioHeatPower
700 400600 500
IR R G B UV
Wavelength (NM)
From London and Upton
CS348B Lecture 4 Pat Hanrahan, 2005
Topics
Light sources and illumination
Radiometry and photometry
Quantify spatial energy distribution
Radiant intensity
Irradiance Inverse square law and cosine law
Radiance
Radiant exitance (radiosity)
Illumination calculations
Irradiance from environment
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Radiometry and Photometry
CS348B Lecture 4 Pat Hanrahan, 2005
Radiant Energy and Power
Power: Watts vs. Lumens
Energy efficiency
Spectral efficacy
Energy: Joules vs. Talbot
ExposureFilm response
Skin - sunburn
( ) ( )Y V L dλ λ λ= ∫Luminance
Φ
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CS348B Lecture 4 Pat Hanrahan, 2005
Radiometry vs. Photometry
Radiometry [Units = Watts]
Physical measurement of electromagnetic energy
Photometry and Colorimetry [Lumen]
Sensation as a function of wavelength
Relative perceptual measurement
Brightness [Brils]
Sensation at different brightness levels
Absolute perceptual measurement
Obeys Steven’s Power Law
13B Y=
CS348B Lecture 4 Pat Hanrahan, 2005
Blackbody Radiation
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CS348B Lecture 4 Pat Hanrahan, 2005
Tungsten Lamp
CS348B Lecture 4 Pat Hanrahan, 2005
Fluorescent Bulb
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CS348B Lecture 4 Pat Hanrahan, 2005
Sunlight
Radiant Intensity
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CS348B Lecture 4 Pat Hanrahan, 2005
Radiant Intensity
Definition: The radiant (luminous) intensity is the
power per unit solid angle emanating from
a point source.
( )d
Id
ωωΦ
≡
W lmcd candela
sr sr = =
CS348B Lecture 4 Pat Hanrahan, 2005
Angles and Solid Angles
Angle
Solid angle
l
rθ =
2
A
RΩ =
⇒ circle has 2π radians
⇒ sphere has 4π steradians
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CS348B Lecture 4 Pat Hanrahan, 2005
Differential Solid Angles
dφdθ
θ
φ
r
sinr θ
2
( )( sin )
sin
dA r d r d
r d d
θ θ φθ θ φ
=
=
2sin
dAd d d
rω θ θ φ= =
CS348B Lecture 4 Pat Hanrahan, 2005
Differential Solid Angles
dφdθ
θ
φ
r
sinr θ 2sin
dAd d d
rω θ θ φ= =
2
2
0 0
1 2
1 0
sin
cos
4
S
d
d d
d d
π π
π
ω
θ θ φ
θ φ
π−
Ω =
=
=
=
∫
∫ ∫
∫ ∫
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CS348B Lecture 4 Pat Hanrahan, 2005
Isotropic Point Source
2
4S
I d
I
ω
π
Φ =
=
∫
4I
πΦ
=
CS348B Lecture 4 Pat Hanrahan, 2005
Warn’s Spotlight
ω θ ω= = • ˆ( ) cos )s sI ( A
2 1
0 0
( ) cosI d dπ
ω θ ϕΦ = ∫ ∫
θ A
ω
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CS348B Lecture 4 Pat Hanrahan, 2005
Warn’s Spotlight
ω θ ω= = • ˆ( ) cos )s sI ( A
2 1 1
0 0 0
2( ) cos 2 cos cos
1sI d d d
s
π πω θ ϕ π θ θΦ = = =+∫ ∫ ∫
1( ) cos
2ss
I ω θπ+
= Φ
θ A
ω
CS348B Lecture 4 Pat Hanrahan, 2005
Light Source Goniometric Diagrams
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CS348B Lecture 4 Pat Hanrahan, 2005
PIXAR Light Source
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
Shadows
Shadow Matte
Projected Slide Texture
Radiance
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CS348B Lecture 4 Pat Hanrahan, 2005
Definition: The surface radiance (luminance) is
the intensity per unit area leaving a surface
Radiance
ωω
ωω
≡
Φ=
2
( , )( , )
( , )
dI xL x
dA
d x
d dA
= =
2 2 2
W cd lmnit
sr m m sr mdA
dω
( , )L x ω
CS348B Lecture 4 Pat Hanrahan, 2005
Typical Values of Luminance [cd/m2]
Surface of the sun 2,000,000,000 nit
Sunlight clouds 30,000
Clear day 3,000
Overcast day 300
Moon 0.03
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Irradiance
CS348B Lecture 4 Pat Hanrahan, 2005
The Invention of Photometry
Bouguer’s classic experimentCompare a light source and a candleIntensity is proportional to ratio of distances squared
Definition of a candelaOriginally a “standard”candleCurrently 550 nm laser w/ 1/683 W/sr1 of 6 fundamental SI units
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CS348B Lecture 4 Pat Hanrahan, 2005
Irradiance
Definition: The irradiance (illuminance) is thepower per unit area incident on a surface.
Sometimes referred to as the radiant (luminous) incidence.
Φ≡( ) id
E xdA
2 2
W lmlux
m m =
CS348B Lecture 4 Pat Hanrahan, 2005
Lambert’s Cosine Law
EAΦ =
EA
Φ=
A
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CS348B Lecture 4 Pat Hanrahan, 2005
Lambert’s Cosine Law
θ/ cosA
θ
Φ
cos/ cos
EA A
θθ
Φ Φ= =
A
CS348B Lecture 4 Pat Hanrahan, 2005
Irradiance: Isotropic Point Source
θ h
r
4I
πΦ
=
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CS348B Lecture 4 Pat Hanrahan, 2005
Irradiance: Isotropic Point Source
θ
r
4I
πΦ
=dω
dA
h
ωΦ =d I d
CS348B Lecture 4 Pat Hanrahan, 2005
Irradiance: Isotropic Point Source
θ
r
4I
πΦ
=
2
cosd dA
r
θω =
dω
dA
h
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CS348B Lecture 4 Pat Hanrahan, 2005
Irradiance: Isotropic Point Source
θ
r
4I
πΦ
=dω
dA
2
cos
4I d dA
r
θωπ
Φ=
h
CS348B Lecture 4 Pat Hanrahan, 2005
Irradiance: Isotropic Point Source
θ
r
4I
πΦ
=dω
dA
2
cos
4I d dA E dA
r
θωπ
Φ= =
2
cos
4E
r
θπ
Φ=
h
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CS348B Lecture 4 Pat Hanrahan, 2005
Irradiance: Isotropic Point Source
θ
r
4I
πΦ
=dω
dA
3
2 2
cos cos
4 4E
r h
θ θπ π
Φ Φ= =
cosh r θ=
CS348B Lecture 4 Pat Hanrahan, 2005
Directional Power Arriving at a Surface
ω ω θ ωΦ =2 ( , ) ( , )cosi id x L x dAd
ω( , )iL x
dAdω
θ
θ ω ω= icos dAd dA d2 ( , )id x ωΦ
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CS348B Lecture 4 Pat Hanrahan, 2005
Irradiance from the Environment
2
( ) ( , )cosi
H
E x L x dω θ ω= ∫
ω ω θ ωΦ = =2 ( , ) ( , )cosi id x L x dAd dEdA
( , ) ( , )cosidE x L x dω ω θ ω=
Light meter
ω( , )iL x
dA
θdω
CS348B Lecture 4 Pat Hanrahan, 2005
Typical Values of Illuminance [lm/m2]
Sunlight plus skylight 100,000 lux
Sunlight plus skylight (overcast) 10,000
Interior near window (daylight) 1,000
Artificial light (minimum) 100
Moonlight (full) 0.02
Starlight 0.0003
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CS348B Lecture 4 Pat Hanrahan, 2005
The Sky Radiance Distribution
From Greenler, Rainbows, halos and glories
CS348B Lecture 4 Pat Hanrahan, 2005
Gazing Ball ⇒ Environment Maps
Miller and Hoffman, 1984
Photograph of mirror ballMaps all spherical directions to a to circleReflection direction indexed by normalResolution function of orientation
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CS348B Lecture 4 Pat Hanrahan, 2005
Environment Maps
Interface, Chou and Williams (ca. 1985)
CS348B Lecture 4 Pat Hanrahan, 2005
Irradiance Environment Maps
Radiance Environment Map
Irradiance Environment Map
R N( , )L θ ϕ ( , )E θ ϕ
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CS348B Lecture 4 Pat Hanrahan, 2005
Irradiance Map or Light Map
Isolux contours
Radiant Exitance(Radiosity)
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CS348B Lecture 4 Pat Hanrahan, 2005
Radiant Exitance
Definition: The radiant (luminous) exitance is the energy per unit area leaving a surface.
In computer graphics, this quantity is oftenreferred to as the radiosity (B)
( ) odM x
dA
Φ≡
2 2
W lmlux
m m =
CS348B Lecture 4 Pat Hanrahan, 2005
Directional Power Leaving a Surface
ω ω θ ωΦ =2 ( , ) ( , )coso od x L x dAd
dAdω
θ
( , )oL x ω
2 ( , )od x ωΦ
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CS348B Lecture 4 Pat Hanrahan, 2005
Uniform Diffuse Emitter
ω( , )oL x
dA
θdω
θ ω
θ ω
=
=
∫
∫2
2
cos
cos
o
H
o
H
M L d
L d
CS348B Lecture 4 Pat Hanrahan, 2005
Projected Solid Angle
cos dθ ω
θ
θ ω πΩ = =∫2
cosH
d
dωcos dθ ω
Ω
Ω ≡ ∫
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CS348B Lecture 4 Pat Hanrahan, 2005
Uniform Diffuse Emitter
ω( , )oL x
dA
θdω
θ ω
θ ω
π
=
=
=
∫
∫2
2
cos
cos
o
H
o
H
o
M L d
L d
L
π=o
ML
Radiometry and PhotometrySummary
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CS348B Lecture 4 Pat Hanrahan, 2005
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 4 Pat Hanrahan, 2005
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 persteradian. Got it?”, James Kajiya