Light
Visible electromagnetic radiation
Power spectrum
Freq uency (H er tz)
2 4 6 8 10 12 14 16 18 20 22 24 26
1 10 10 10 10 10 10 10 10 10 10 10 10 10
Pow er H ea t Ra d io Infra - Ultra - X -Ra y s Ga m m a Cosm ic
Red V iolet Ra y s Ra y s
16 14 12 10 8 6 4 2 -2 -4 -6 -8
10 10 10 10 10 10 10 10 1 10 10 10 10
W a velength (N M )
IR R G B UV
700 600 500 400
Polarization From London and Upton
Photon (quantum effects)
Wave (interference, diffraction)
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
Radiometry and Photometry
Radiant Energy and Power
Power: Watts vs. Lumens
Energy efficiency
Spectral efficacy
Energy: Joules vs. Talbot
Exposure Luminance
Film response
Y V ( ) L ( )d
Skin - sunburn
Radiometry vs. Photometry
Radiometry [Units = Watts]
Physical measurement of electromagnetic energy
Photometry and Colorimetry [Lumen]
Sensation as a function of wavelength
Relative perceptual measurement
1
Brightness [Brils] B Y 3
Sensation at different brightness levels
Absolute perceptual measurement
Obeys Steven’s Power Law
Radiant Intensity
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 candela
Originally a “standard” candle
Currently 550 nm laser w/ 1/683
W/sr
1 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
I ( )
d
W lm
sr sr cd candela
683 lumens/watt @ 555nm
Angles and Solid Angles
l
Angle
r
circle has 2p radians
A
Solid angle 2
R
sphere has 4p steradians
Differential Solid Angles
r sin
d dA (r d )(r sin d )
r
d r 2 sin d d
dA
d 2
sin d d
r
Differential Solid Angles
dA
r sin d 2
sin d d
r
d r
d d
S2
p 2p
sin d d
0 0
1 2p
d cos
1 0
d
4p
Isotropic Point Source
I d
S2
4p I
I
4p
Warn’s Spotlight
ˆ
A
ˆ )s
I ( ) cos ( A
s
2p 1
I ( ) d cos d
0 0
Warn’s Spotlight
ˆ
A
ˆ )s
I ( ) cos ( A
s
2p
2p
1 1
I ( ) d cos d 2p cos d cos
s
0 0 0
s 1
s 1 s
I ( ) cos
2p
Light Source Goniometric
Diagrams
Radiance
Radiance
Definition: The surface radiance (luminance) is
the intensity per unit (projected) area leaving a
surface
L ( x, ) dI ( x, )
L( x, )
dA
d d ( x, )
2
d dA
W cd lm
sr m2 m2 sr m 2 nit
dA
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 Miller and Hoffman, 1984
Maps all spherical directions to a to circle
Reflection direction indexed by normal
Resolution function of orientation
Irradiance
Irradiance
Definition: The irradiance (illuminance) is the
power per unit area incident on a surface.
d i
E( x)
dA
W lm
m2 m2 lux
Sometimes referred to as the radiant (luminous)
incidence.
Lambert’s Cosine Law
A
EA
E
A
Lambert’s Cosine Law
A A / cos
E cos
A / cos A
Irradiance: Isotropic Point Source
h
r I
4p
Irradiance: Isotropic Point Source
d
h
r I
4p
dA
d I d
Irradiance: Isotropic Point Source
d
h
r I
4p
dA
cos
d 2 dA
r
Irradiance: Isotropic Point Source
d
h
r I
4p
dA
cos
I d dA
4p r 2
Irradiance: Isotropic Point Source
d
h
r I
4p
dA
cos cos
I d dA E dA E
4p r 2
4p r 2
Irradiance: Isotropic Point Source
d
h r cos
r I
4p
dA
cos cos 3
E
4p r 2
4p h 2
Directional Power Arriving at a
Surface
Li ( x, )
d
dA
d i ( x, ) Li ( x, ) cos dAd
2
cos dAd dA d
d i ( x, )
2
Irradiance from the Environment
Li ( x, )
d 2 i ( x, ) Li ( x, )cos dA d dEdA
d
dE ( x, ) Li ( x, )cos d
dA
Light meter E( x) L ( x,)cos d
i
H2
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
L( , ) R
E( , ) N
Radiance Irradiance
Environment Map Environment Map
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.
d o
M ( x)
dA
W lm
m m
2 2
lux
In computer graphics, this quantity is often
referred to as the radiosity (B)
Directional Power Leaving a
Surface
Lo ( x , )
d
dA
d o ( x, ) Lo ( x, ) cos dAd
2
d o ( x, )
2
Uniform Diffuse Emitter
Lo ( x, )
M L o cos d
H2
d
Lo cos d
H2
dA
Projected Solid Angle
d
cos d
cos d p
H2
Uniform Diffuse Emitter
M L 2
o cos d
Lo ( x, )
H
Lo cos d d
H2
p Lo
M
Lo dA
p
Radiometry and Photometry
Summary
Radiometric and Photometric
Terms
Physics Radiometry Photometry
Energy Radiant Energy Luminous Energy
Flux (Power) Radiant Power Luminous Power
Flux Density Irradiance Illuminance
Radiosity 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 Lux Phot Footcandle
Luminosity
Luminance Nit Stilb
Apostilb, Blondel 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?”, James Kajiya