Graphics Reference
In-Depth Information
v
y
u
,
v
(
)
x
,
y
(
)
u
x
Ray carrying
L
F
(
x
,
y
,
u
,
v
)
Main lens
Sensor plane
F
Figure 5.21
The in-camera light field. A point
(
x
,
y
)
on the sensor plane gets radiance from points on
the main lens parameterized by
(
s
,
t
)
. (After [Ng et al. 05] c
2005 ACM, Inc. Included
here by permission.)
path from an arbitrary point
(
u
,
v
)
on the lens to an arbitrary
(
x
,
y
)
, in which case
L
f
(
0.
The pixel value of the image formed inside a digital camera at a sensor pho-
tosite is ideally proportional to the time-integrated flux across the pixel photosite.
For sufficiently small pixels, the flux is essentially just the irradiance, which is
computed by integrating the incident radiance. Irradiance is obtained by integrat-
ing the incident radiance over the hemisphere of directions (See Equation (1.5)).
In camera computations it is more sensible to integrate across the lens, which re-
quires a change of variables to the lens parameters
u
and
v
analogous to the surface
integral transformation applied in the rendering equation (Equation (2.4)).
The actual integration depends on a number of intrinsic camera parameters,
as well as some extra geometry terms. However, under appropriate assumptions
the photosite irradiance can be approximated by
x
,
y
,
u
,
v
)=
F
2
L
F
1
cos
4
E
F
(
x
,
y
)=
(
x
,
y
,
u
,
v
)
A
(
u
,
v
)
θ
dudv
.
(5.6)
Here
A
is an “aperture” function that models the camera aperture: its value is
0 if the point
(
u
,
v
)
(
u
,
v
)
on the lens is outside the aperture, and 1 otherwise. The angle
θ
is the angle of incidence measured at the sensor surface; the fourth power comes
from the change of variables. When a sensor pixel corresponds to a
focused
point
in the scene, the irradiance comes from the radiance leaving that point in the scene
(located on the plane of focus in the scene). Assuming the radiance
L
F
is constant
over the pixel, the irradiance
E
F
on a focused pixel reduces in this case to
d
F
2
E
F
=
4
cos
4
θ
L
F
,
