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Light
Visible electromagnetic radiation Power spectrum
PolarizationPhoton (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
Topics
Light sources and illuminationRadiometry and photometryQuantify spatial energy distribution Radiant intensity Irradiance
Inverse square law and cosine law Radiance Radiant exitance (radiosity)
Illumination calculations Irradiance from environment
Radiometry and Photometry
Radiant Energy and Power
Power: Watts vs. Lumens Energy efficiency Spectral efficacy
Energy: Joules vs. Talbot Exposure
Film response Skin - sunburn
( ) ( )Y V L dλ λ λ=∫Luminance
Φ
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=
Radiant Intensity
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
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⎡ ⎤⎡ ⎤= =⎢ ⎥⎢ ⎥⎣ ⎦⎣ ⎦
683 lumens/watt @ 555nm
Angles and Solid Angles
Angle
Solid angle
l
rθ =
2
A
RΩ =
circle has 2 radians
sphere has 4 steradians
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= =
Differential Solid Angles
dφdθ
θ
φ
r
sinr θ2
sindA
d d dr
ω θ θ φ= =
2
2
0 0
1 2
1 0
sin
cos
4
S
d
d d
d d
ω
θ θ φ
θ φ
−
Ω =
=
=
=
∫
∫∫
∫∫
Isotropic Point Source
2
4S
I d
I
ω
Φ =
=
∫
4I
Φ
=
Warn’s Spotlight
ω θ ω= = •r ˆ( ) cos )s sI ( A
2 1
0 0
( ) cosI d d
ω θ ϕΦ =∫∫
θ A
ωr
Warn’s Spotlight
ω θ ω= = •r ˆ( ) cos )s sI ( A
2 1 1
0 0 0
2( ) cos 2 cos cos
1sI d d d
s
ω θ ϕ θ θΦ = = =+∫∫ ∫
1( ) cos
2ss
I ω θ+
=Φ
θ A
ωr
Light Source Goniometric Diagrams
Radiance
Definition: The surface radiance (luminance) is the intensity per unit (projected) 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
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
The Sky Radiance Distribution
From Greenler, Rainbows, halos and glories
Environment Maps
Interface, Chou and Williams (ca. 1985)
Gazing Ball Environment Maps
Photograph of mirror ball Maps all spherical directions to a to
circle Reflection direction indexed by normal Resolution function of orientation
Miller and Hoffman, 1984
Irradiance
Irradiance
Definition: The irradiance (illuminance) is the power 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⎡ ⎤ ⎡ ⎤=⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦
Lambert’s Cosine Law
EAΦ =
EA
Φ=
A
Lambert’s Cosine Law
θ/ cosA
θ
Φ
cos/ cos
EA A
θθ
Φ Φ= =
A
Irradiance: Isotropic Point Source
θ h
r 4I
Φ
=
Irradiance: Isotropic Point Source
4I
Φ
=θ
r
dω
dA
h
ωΦ =d I d
Irradiance: Isotropic Point Source
4I
Φ
=
2
cosd dA
r
θω =
θ
r
dω
dA
h
Irradiance: Isotropic Point Source
4I
Φ
=
2
cos
4I d dA
r
θωΦ
=
θ
r
dω
dA
h
Irradiance: Isotropic Point Source
4I
Φ
=
2
cos
4I d dA E dA
r
θωΦ
= =2
cos
4E
r
θΦ
=
θ
r
dω
dA
h
Irradiance: Isotropic Point Source
4I
Φ
=
3
2 2
cos cos
4 4E
r h
θ θ Φ Φ
= =
θ
r
dω
dA
cosh r θ=
Directional Power Arriving at a Surface
ω ω θ ωΦ =2 ( , ) ( , )cosi id x L x dAd
θ ω ω=r rgcos dAd dA d
ω( , )iL x
dAr dωr
θ
2 ( , )id x ωΦ
Irradiance from the Environment
2
( ) ( , )cosi
H
E x L x dω θ ω=∫
ω ω θ ωΦ = =2 ( , ) ( , )cosi id x L x dA d dEdA
( , ) ( , )cosidE x L x dω ω θ ω=
Light meter
ω( , )iL x
dA
θdω
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
Blackbody Radiation
Tungsten Lamp
Fluorescent Bulb
Sunlight
Irradiance Environment Maps
Radiance Environment Map
Irradiance Environment Map
R N( , )L θ ϕ ( , )E θ ϕ
Irradiance Map or Light Map
Isolux contours
Radiant Exitance(Radiosity)
Radiant Exitance
Definition: The radiant (luminous) exitance is the energy per unit area leaving a surface.
In computer graphics, this quantity is often referred to as the radiosity (B)
( ) odM x
dA
Φ≡
2 2
W lmlux
m m⎡ ⎤ ⎡ ⎤=⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦
Directional Power Leaving a Surface
ω ω θ ωΦ =2 ( , ) ( , )coso od x L x dAddAr dωr
θ
( , )oL x ω
2 ( , )od x ωΦ
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
Projected Solid Angle
cos dθ ω
θ
θ ω Ω = =∫%2
cosH
d
dω
Uniform Diffuse Emitter
ω( , )oL x
dA
θdω
θ ω
θ ω
=
=
=
∫
∫2
2
cos
cos
o
H
o
H
o
M L d
L d
L
=o
ML
Radiometry and PhotometrySummary
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
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 IntensityCandela (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
