#### Transcript Document

```Radiometry
Outline
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Quantities
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Spherical coordinates, foreshortening
Modeling surface properties: the BRDF
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Lambertian
Specular
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Geometry of perspective projection explains
location of scene point in image, but what about its
intensity and color?
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Radiometry is the measurement of electromagnetic
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Frequencies from infrared to visible to ultraviolet
Photometry quantifies camera/eye sensitivity
Measuring Light
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For now, ignore the fact that light has multiple
wavelengths; we’ll come back to this when we
discuss color
Fundamental quantities
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Radiant energy Q (measured in joules J)
 Proportional to number of photons (and photon frequency)
 Joules per second emitted
 Power per unit area through a surface (real or imaginary)
from all directions
Incoming and Outgoing
Light at a Surface
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Light arriving at a point on a surface from all
visible directions
 An image samples the irradiance
at the pinhole
-2
 Light leaving a surface in all
directions
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Power at a point in space in a given direction,
foreshortened
Can be incoming or outgoing
Does not attenuate with distance in vacuum
What is stored in a pixel—the light energy
arriving along a particular ray at a particular
point.
The more the surface is tilted away, the
larger an area the light energy is distributed
over.
Foreshortening
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Lines, patches tilted with respect to the
viewing direction present smaller apparent
lengths, areas, respectively, to the viewer
E.g., angle subtended
by differential line
segment in 2-D follows
from formula for arc
length
a
df
r
dl
Spherical Coordinate Terminology
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Local coordinates for patch of surface
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Colatitude/polar angle q (q
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Longitude/azimuth f
= 0 at normal n)
Solid angle w (steradians sr): Area of surface patch
on unit sphere (w = 4p for entire sphere)
w
3-D Foreshortening
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For patches, just extend 2-D argument to
areas:
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Foreshortening factor for light coming from (q,
f) is just cosq
Solid Angle in Spherical Coordinates
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Differential patch dqdf has smaller area
closer to pole due to shrinking width of df
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Circumference at a given polar angle q is
2prsinq, so the correct patch area is
dw = sinqdqdf
r
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Thus, irradiance from a particular direction is
Describing an
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5-dimensional function (3 position + 2 direction
variables)
Environment map: Radiance distribution at a given
point
Light field
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4-dimensional function: All positions on image planes of
all orthographic views of object
BRDF
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Bidirectional Reflectance Distribution
Function (BRDF): Ratio of outgoing radiance in
BRDF Properties
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Energy leaving · energy arriving
Symmetric in both directions (Helmholtz reciprocity)
Generally, only difference between incident and emitted angle f is
significant
Dependence on absolute f  Anisotropy
Can view BRDF as probability that incoming photon will leave in a
particular direction
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courtesy of S. Rusinkiewicz
Things the BRDF neglects
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Surface non-uniformity
Subsurface scattering
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Light moving under the
surface and emerging
elsewhere—e.g., marble,
skin
BRDF
Transmission
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Light going through to
other side
BSSRDF
courtesy of
H. Jensen
Reflectance Equation
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Radiance for a viewing direction given all
incoming light
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This is proportional to the pixel brightness
for that ray
Lambertian Surfaces
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surface does not depend on angle
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Albedo r: Ratio of light reflected by an object
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BRDF: f(.)
=r/p
Specular Surfaces
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Mirrorlike: Radiance only leaves along specular
direction (reflection of incoming direction)
BRDF:
Specular lobe models shiny
surface that is not perfect
mirror
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