Biomedical Engineering Reference
In-Depth Information
FIGURE 9.3
Polarization images from the scanning device. The images through the three blue-filter alignments are
composited into a single image, mapped to red, green, and blue. The left image (a) was captured on a fine, clear morning.
The right image (b) was captured on a cloudy afternoon beside a lake.
indicating other promising applications of bio-
mimetic sensing for autonomous systems. A
partly cloudy sky still provides a strong polari-
zation signal in clear patches, even though the
location of the sun is not apparent in the image.
is predicted by the Rayleigh atmosphere model
[16]
. To a first-order approximation, the sun is
orthogonal to the direction of polarization of
any patch of sky. A
polarization sensor
measures
power and is directional but unsigned. In con-
trast, magnetometers provide an unambigu-
ous measurement of the magnetic field vector
that is also effectively constant for any given
location
[17]
.
Insects use the polarization patterns cast by
the sun and moon as an orientation reference
in preference to the actual angular position of
the celestial bodies on the eye
[18, 19]
. The
advantage of the polarization pattern is that it
is distributed across the sky. A measurement in
any direction gives a measurement of the direc-
tion of the sun from that point
[12]
. Many
insects use polarization in the blue region of the
spectrum, sensed with the dorsal rim area of
the compound eye
[20]
, shown in
Figure 9.1
. In
this region the ommatidia are arranged to
respond maximally to a series of polarization
directions. The radius of curvature of the dorsal
rim is significantly lower than for other parts
of the eye, ensuring that there is little variation
in the direction of view of dorsal rim omma-
tidia
[20]
. The population of ommatidia pro-
vides the information required to code the
direction of polarization.
Polarization compasses have been used for
human navigation, possibly by the Vikings a mil-
lennium ago, through the use of naturally occur-
ring dichroic crystals
[21]
. Scandinavian airlines
revived this form of navigation for commercial
9.3 AIRBORNE COMPASS BASED
ON SKY POLARIZATION
The sun is a clearly defined landmark in the sky
that can be used to determine bearings. When
the sky is partially occluded by cloud, foliage,
terrain, or dirt on the optical sensor, the sun may
be obscured. In conventional solar compasses,
significant effort is expended to ensure that the
sun is the landmark detected
[9]
rather than a
cloud.
The sky polarization pattern is the result of
Rayleigh scattering
of sunlight off molecules in
the atmosphere
[10]
, discussed in detail by Coul-
son
[11]
. The magnitude of the pattern is modi-
fied by atmospheric effects; however, the
direction of polarization vectors is reliable
[12]
.
Degree of polarization of reflected sunlight has
been used in the past as a remote measure of
atmospheric density on the planets. Measure-
ments taken by Dollfus
[13]
and others
[14]
in
the 1950s provided an estimate of the density of
the Martian atmosphere and later an indication
of the value of polarization compassing for
autonomous systems operating on Mars
[15]
.
The sky-polarization pattern relative to the
location of the sun, represented in
Figure 9.4
,
