Radiometry

1
Radiometry

• Frank Dellaert
• Some slides by Jim Rehg

2
Outline

• Basic radiometry

3
Effect of Illumination
(Subject 8 from the Yale face database due to P.
Belhumeur et. al.)

• Light source strength and direction has a
  dramatic impact on distribution of brightness in
  the image (e.g. shadows, highlights, etc.)

4
Image formation

• Light source emits photons
• Absorbed, transmitted, scattered
• fluorescence

Camera
source
5
Surfaces receives and emits

• Incident light from lightfield
• Act as a light source
• How much light ?

6
Irradiance

• Irradiance amount of light falling on a surface
  patch
• symbolE, units W/m2

dA
7
Radiosity

• power leaving a point per area
• symbolB, units W/m2

dA
8
Light Directional

• Light emitted varies w. direction

9
Steradians (Solid Angle)

• 3D analogue of 2D angle

A
R
10
Steradians (contd)
11
Polar Coordinates
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Intensity

• Intensity amount of light emitted from a point
  per steradian
• symbolI, units W/sr

13
Irradiance and Intensity
dA
14
Radiance

• Radiance amount of light passing through an
  area dA and
• symbolL, units W x m-2 x sr-1

15
Radiance is important

• Response of camera/eye is proportional to
  radiance
• Pixel values
• Constant along a ray

16
Lightfield Gibson optic array !

• 5DOF Position 3DOF, 2 DOF for direction

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Lightfield Sampler
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Lightfield Sample
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Lambertian Emitters

• More photons emitted straight up
• Total power is proportional to wedge area
• Cosine law

20
Lambertian Constant Radiance

• Above see more photons
• Oblique see less photons, but area looks smaller
• Same brightness !

21
Example Our Sun

• Approximates Lambertian

Different angle Same brightness
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Counter-example

• Moon should be less bright at edges, as gets less
  light from sun.
• Reflects more light at grazing angles than a
  Lambertion reflector

23
Radiance Emitted/Reflected

• Radiance amount of light emitted from a surface
  patch per steradian per area
• foreshortened !

dA
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Calculating Radiosity
25
Example Sun

• Power 3.91 1026 W
• Surface Area6.07 1018 m2
• Power Radiance . Area . ?
• L 2.05 107 W/m2.sr
• Example from P. Dutre SIGGRAPH tutorial

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Irradiance (again)

• Integrate incoming radiance over hemisphere

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Example Sun
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BRDF
E
L
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BRDF Example
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Radiometry vs. Photometry
http//www.optics.arizona.edu/Palmer/rpfaq/rpfaq.h
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