Transcript 03_radiometry-1 - Computer Science and Engineering

Fundametals of Rendering Radiometry / Photometry
CIS 782
Advanced Computer Graphics
Raghu Machiraju
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Reading
• Chapter 5 of “Physically Based Rendering” by
Pharr&Humphreys
• Chapter 2 (by Hanrahan) “Radiosity and
Realistic Image Synthesis,” in Cohen and
Wallace.
• pp. 648 – 659 and Chapter 13 in “Principles of
Digital Image Synthesis”, by Glassner.
• Radiometry FAQ
http://www.optics.arizona.edu/Palmer/rpfaq/rp
faq.htm
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Realistic Rendering
• Determination of Intensity
• Mechanisms
– Emittance (+)
– Absorption (-)
– Scattering (+) (single vs. multiple)
Observer
Light
• Cameras or retinas record quantity of light
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Pertinent Questions
• Nature of light and how it is:
– Measured
– Characterized / recorded
• (local) reflection of light
• (global) spatial distribution of light
• Steady state light transport?
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What Is Light ?
• Light - particle model (Newton)
– Light travels in straight lines
– Light can travel through a vacuum
(waves need a medium to travel)
• Light – wave model (Huygens):
electromagnetic radiation: sinusiodal wave formed
coupled electric (E) and magnetic (H) fields
– Diffraction / Polarization
– Transmitted/reflected compoments
– Pink Floyd
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Electromagnetic spectrum
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Optics
• Three kinds
• Geometrical or ray
– Traditional graphics
– Reflection, refraction
– Optical system design
• Physical or wave
– Dispersion, interference
– Interaction of objects of size comparable to wavelength
• Quantum or photon optics
– Interaction of light with atoms and molecules
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Nature of Light
• Wave-particle duality – Wave packets which
emulate particle transport. Explain quantum
phenomena.
• Incoherent as opposed to laser. Waves are
multiple frequencies, and random in phase.
• Polarization – Ignore. Un-polarized light has many
waves summed all with random orientation
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Radiometry
• Science of measuring light
• Analogous science called photometry is
based on human perception.
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Radiometric Quantities
• Function of wavelength, time, position, direction,
polarization.
g(,t,r,, )
• Assume wavelength independence
– No phosphorescence
– Incident wavelength 1 exit 2
• Steady State

– Light travels fast
– No luminescence - Ignore it

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g(t,r,,  )
g(r,,  )
Result – five dimensions
• Adieu Polarization
– Would likely need wave optics to simulate
• Two quantities
– Position (3 components)
– Direction (2 components)

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g(r, )
Radiometry - Quantities
• Energy Q
• Power 
– Energy per time
• Irradiance E and Radiosity B
– Power per area
• Intensity I
– Power per solid angle
• Radiance L
– Power per projected area and solid angle
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Radiant Energy - Q
• Think of photon as carrying quantum of
energy hc/ = hf (photoelectric effect)
– c is speed of light
– h is Planck’s constant
– f is frequency of radiation
• Wave packets
• Total energy, Q, is then energy of the total
number of photons
• Units - joules or eV
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Radiation
Blackbody
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Tungsten
Consequence
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Fluorescent Lamps
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Power - 
•
•
•
•
•
•
Flow of energy (important for transport)
Also - radiant power or flux.
Energy per unit time (joules/s = eV/s)
Unit: W - watts
 = dQ/dt
Falls off with square
of distance
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Radiant Flux Area Density
• Area density of flux (W/m2)
• u = Energy arriving/leaving a surface per
unit time interval
• dA can be any 2D surface in space
• E.g. sphere:

u
2
4r
d
u
dA
dA
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Irradiance E
• Power per unit area incident on a surface
d
E
dA

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Radiosity or Radiant Exitance
B
• Power per unit area leaving surface
• Also known as Radiosity
• Same unit as irradiance, just direction
changes
d
B
dA

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Intensity I
• Flux density per unit solid angle
d
I
d
• Units – watts per steradian
• “intensity” is heavily overloaded. Why?
– Power of light source

– Perceived brightness
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Solid Angle
• Size of a patch, dA, is
dA  (r sin  d )( r d )
• Solid angle is
dA
d  2  sin dd
r
• Angle
l

r
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Solid Angle (contd.)
•
•
•
•
•
Solid angle generalizes angle!
Steradian
Sphere has 4 steradians! Why?
Dodecahedron – 12 faces, each pentagon.
One steradian approx equal to solid angle
subtended by a single face of dodecahedron
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
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QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
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Hemispherical Projection
• Use a hemisphere H over surface to
measure incoming/outgoing flux
• Replace objects and points with their
hemispherical projection

r
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Isotropic Point Source
d 
I

d 4
• Even distribution over sphere
• How do you get this?
• Quiz:
 Warn’s spot-light ? Determine flux
s
cos

I( ) 
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Other kinds of lights
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Other Lights
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Irradiance on Differential
Patch
d  cos
EI

2
dA 4 x  x s
• Inverse square Law
• How do you determine that ?
• Iso-lux contours
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x

xs
Radiance L
• Power per unit projected area per unit solid
2
angle.
d
L
2
• Units – watts per (steradian m )
dAp d
• We have now introduced projected area, a
cosine term.

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d
L
dAcosd
2
Projected Area
• Ap = A (N • V) = A cos 
V
N
V

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Why the Cosine Term?
• Foreshortening is by cosine of angle.
• Radiance gives energy by effective surface
area.
d cos

d
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Incident and Exitant Radiance
•
•
•
•
Incident Radiance: Li(p, )
Exitant Radiance: Lo(p, )
In general: Li  p,   Lo  p, 
p - no surface, no participating media
Li  p,   Lo  p, 


Li  p, 
Lo  p, 
p
p
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Irradiance from Radiance
E p,n  
 L p, cos d
i

• |cos|d is projection of a differential area
• We take |cos| in order to integrate over the
 whole sphere
n
Li  p, 

r
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p
Radiance
• Fundamental quantity, everything else
derived from it.
• Law 1: Radiance is invariant along a ray
• Law 2: Sensor response is proportional to
radiance
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Law1: Conservation Law !
d1
dA1
2
d

dA2
Total flux leaving one side = flux arriving other side, so
L1d1dA1  L2d2dA2
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Conservation Law !
d1
dA1
2
d

d1  dA2 /r

2
and
dA2
d 2  dA1 /r
therefore
L1 (dA2 / r ) dA1  L2 (dA1 / r ) dA2
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2

2
2
Conservation Law !
d1
dA1
2
so
d

dA2
L1 (dA2 / r 2 ) dA1  L2 (dA1 / r 2 ) dA2

L1  L2
Radiance doesn’t change with distance!
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Thus …
• Radiance doesn’t change with distance
– Therefore it’s the quantity we want to measure
in a ray tracer.
• Radiance proportional to what a sensor
(camera, eye) measures.
– Therefore it’s what we want to output.
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Photometry and Radiometry
• Photometry (begun 1700s by Bouguer) deals with
how humans perceive light.
• Bouguer compared every light with respect to
candles and formulated the inverse square law !
• All measurements relative to perception of
illumination
• Units different from radiometric but conversion is
scale factor -- weighted by spectral response of
eye (over about 360 to 800 nm).
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CIE curve
• Response is integral over all wavelengths
 v    V ( )d

350
400
450
Violet
500
550
600
Green
650
700
750
Red
© CIE, 1924, many more curves available, see http://cvision.ucsd.edu/lumindex.htm
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Radiometry vs. Photometry
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Next
SPD
XYZ
Display
Tone
Reproduction
RGB
Dither

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