Radiometry and Light Transport
FRS 123, Fall 2006
Overview
• Radiometry and photometry
• Illumination
• Shadows
• Light transport
• Global vs. local reflectance
Radiometric Units
• Light is a form of energy – measured in
Joules (J)
• Power: energy per unit time
– Measured in Joules/sec = Watts (W)
– Also called Radiant Flux (F)
Point Light Source in a Direction
• Total radiant flux in Watts
• How to define angular dependence?
– Solid angle
Solid angle dw
Digression – Solid Angle
• Angle in radians
Length l
Angle q = l/r
• Solid angle in steradians
Area A
Solid angle w = A/r2
Point Light Source in a Direction
• Total radiant flux in Watts
• How to define angular dependence?
– Solid angle
Area dA
Solid angle dw = dA/r2
• Radiant flux per unit solid angle
– Measured in Watts per steradian (W/sr)
Light Falling on a Surface
• Power per unit area – Irradiance (E)
– Measured in W/m2
• Move surface away from light
– Inverse square law: E ~ 1/r2
• Tilt surface away from light
– Cosine law: E ~ n · l
Light Emitted from a Surface
in A Direction
• Power per unit area per unit solid angle –
Radiance (L)
– Measured in W/m2/sr
– Projected area – perpendicular to given direction
dw
dA
dF
L
dA dw
• Cameras measure radiance!
Radiometry vs. Photometry
• These are all physical (radiometric) units
• Don’t take perception into account
• Eye sensitive to different colors
l (nm)
400
700
(blue)
(red)
Photometric Units
• Take human perception into account
• Original unit: candle
– Luminous intensity equal to a “standard candle”
• Today: one of the base SI units
– One candela (cd) is the luminous intensity of a
source producing 1/683 W/sr at 540  1012 Hz.
(555 nm., “green”)
Radiometric and Photometric Units
Radiant energy
Joule (J)
Radiant flux or power (F)
Watt (W) = J / sec
Radiant intensity (I)
W / sr
Irradiance (E)
W / m2
Radiance (L)
W / m2 / sr
Radiosity (B)
Luminous energy
Talbot
Luminous power
Lumen (lm) = talbot / sec = cd ·
sr
Luminous intensity
Candela (cd)
Illuminance
Lux = lm / m2
Luminance
Nit = lm / m2 / sr
Luminosity
Direct Illumination
F
E ?
A
A
Direct Illumination
F
E ?
A
F  Iw
I
w
A
Direct Illumination
I
n̂
l̂
r
A
F
E ?
A
F  Iw
A (nˆ  ˆl )
w
r2
I (nˆ  ˆl )
E
2
r
Diffuse vs. Specular Materials
• Diffuse surfaces reflect
light evenly
• Appearance solely
dependent on 1/r2 and
cosine law
Diffuse vs. Specular Materials
• Specular reflection
resembles mirror
reflection
• Maximum reflectance
along mirroring direction
• Reflectance dependent
on viewer
• Materials often mixtures
of diffuse and specular
Shadows
• What color has a shadow?
• Which shape has a shadow?
• What is a penumbra?
• Shadows depend on
– Shape and intensity of light source
– Shape of occluder
Shadows
• Point light source
illumination
– Hard shadow
– Perspective projection
of occluder
Shadows
• Directional
illumination
– Hard shadow
– Orthographic
projection of occluder
Shadows
• Hard shadows appear
nonnatural
• In reality, few directional
or point light sources
Shadows
• Real light sources have
a spatial extent
• Causes soft shadows:
umbra / penumbra
Shadows
Woo 1990
Shadows
Woo 1990
Light Transport
Ignoring area light sources
Jensen
Light Transport
added soft shadows
Jensen
Light Transport
added caustics
Jensen
Light Transport
added indirect diffuse illumination
Jensen
Light Path Types
Path Types?
Jensen
Path Types?
Debevec
Path Types?
Jensen
Path Types?
RenderPark
Global vs. Local Reflectance
• Two general classes of path types
• Direct reflection (local)
– Single reflective bounce toward camera
• Complex light path (global)
– Indirect illumination, specular interreflection,
subsurface scattering, participating media, …
• If we could separate these two in
photographs, we could learn more about light
transport…
Global vs. Local Illumination
[KRISHNAN 2006]
Global vs. Local Reflectance
• Photographic separation of both components
[KRISHNAN 2006]
Global vs. Local Reflectance
• Photographic separation of both components
[KRISHNAN 2006]
Global vs. Local Reflectance
Recipe:
• Spatially modulate light source (50% occlusion)
• Take many images with different modulation
• For each observed scene point:
consider Imax , Imin = maximum and minimum intensity
• Intensities due to global and local reflectance are:
– Iglobal = 2 Imin
– Ilocal = Imax – Imin
Global vs. Local Reflectance
• Many ways to structure illumination
Interreflection
[KRISHNAN 2006]
Interreflection
[KRISHNAN 2006]
Interreflection
[KRISHNAN 2006]
Subsurface Scattering
[KRISHNAN 2006]
Subsurface Scattering
[KRISHNAN 2006]
Subsurface Scattering
[KRISHNAN 2006]
Volumetric Scattering
[KRISHNAN 2006]
Volumetric Scattering
[KRISHNAN 2006]
Volumetric Scattering
[KRISHNAN 2006]
Diffuse Translucency
[KRISHNAN 2006]
Diffuse Translucency
[KRISHNAN 2006]
Diffuse Translucency
[KRISHNAN 2006]
Roses, …
[KRISHNAN 2006]
Roses, …
[KRISHNAN 2006]
Roses, …
[KRISHNAN 2006]
… Peppers, …
[KRISHNAN 2006]
… Peppers, …
[KRISHNAN 2006]
… Peppers, …
[KRISHNAN 2006]
… Skin, …
[KRISHNAN 2006]
… Skin, …
[KRISHNAN 2006]
… Skin, …
[KRISHNAN 2006]
… Bread, …
[KRISHNAN 2006]
… Bread, …
[KRISHNAN 2006]
… Bread, …
[KRISHNAN 2006]
… And A Complex Scene
[KRISHNAN 2006]
… And A Complex Scene
[KRISHNAN 2006]
… And A Complex Scene
[KRISHNAN 2006]
Summary and Outlook
• Scene appearance is determined by light
transport
• Light paths often utterly complex
• Computer graphics try to approximate
realistic light transport
• Painters rather use heuristics and careful
observation to obtain realism