Transcript Document
Radiometry
Outline
What is Radiometry?
Quantities
Radiant energy, flux density
Irradiance, Radiance
Spherical coordinates, foreshortening
Modeling surface properties: the BRDF
Lambertian
Specular
Radiometry
Geometry of perspective projection explains
location of scene point in image, but what about its
intensity and color?
Radiometry is the measurement of electromagnetic
radiation, primarily optical
Frequencies from infrared to visible to ultraviolet
Photometry quantifies camera/eye sensitivity
Measuring Light
For now, ignore the fact that light has multiple
wavelengths; we’ll come back to this when we
discuss color
Fundamental quantities
Radiant energy Q (measured in joules J)
Proportional to number of photons (and photon frequency)
Radiant flux/power © of a light source (watts W)
Joules per second emitted
Radiant flux density (Wm-2)
Power per unit area through a surface (real or imaginary)
from all directions
Incoming and Outgoing
Light at a Surface
Irradiance E (Wm-2)
Light arriving at a point on a surface from all
visible directions
An image samples the irradiance
at the pinhole
-2
Radiosity B (Wm )
Light leaving a surface in all
directions
Radiance
Radiance L (Wm-2sr-1)
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
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
Local coordinates for patch of surface
Colatitude/polar angle q (q
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
For patches, just extend 2-D argument to
areas:
Foreshortening factor for light coming from (q,
f) is just cosq
Solid Angle in Spherical Coordinates
Differential patch dqdf has smaller area
closer to pole due to shrinking width of df
Circumference at a given polar angle q is
2prsinq, so the correct patch area is
dw = sinqdqdf
r
Computing Irradiance
Integrate radiance over the hemisphere
Thus, irradiance from a particular direction is
Describing an
Environment’s Radiance
Radiance distribution
5-dimensional function (3 position + 2 direction
variables)
Environment map: Radiance distribution at a given
point
Plenoptic function: Time variable added
Light field
Radiance distribution for an object
4-dimensional function: All positions on image planes of
all orthographic views of object
BRDF
Bidirectional Reflectance Distribution
Function (BRDF): Ratio of outgoing radiance in
one direction to incident irradiance
BRDF Properties
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
courtesy of S. Rusinkiewicz
Things the BRDF neglects
Surface non-uniformity
Subsurface scattering
Light moving under the
surface and emerging
elsewhere—e.g., marble,
skin
BRDF
Transmission
Light going through to
other side
BSSRDF
courtesy of
H. Jensen
Reflectance Equation
Radiance for a viewing direction given all
incoming light
This is proportional to the pixel brightness
for that ray
Lambertian Surfaces
Diffuse/matte reflectance: Radiance leaving
surface does not depend on angle
Albedo r: Ratio of light reflected by an object
to light received
BRDF: f(.)
=r/p
Specular Surfaces
Mirrorlike: Radiance only leaves along specular
direction (reflection of incoming direction)
BRDF:
Specular lobe models shiny
surface that is not perfect
mirror