TETRAHEDRAL GEOMETRY/TOPOLOGY SEMINAR
ANNOUNCEMENT
DATE: Friday, March 30,
2007
LOCATION: Hempfield
High School, Room 213 (directions at http://www.millersville.edu/~tgts/)
followed by
dinner at a place to be determined.
4:30 TALK: Andrew
Hicks,
“Direct
Methods of Optical Design”
The first
photograph was created in 1827 by Joseph Nicephore Niepce. In 1828,
William Rowan
Hamilton's founding papers on geometric optics began to appear.
This seems to be a
remarkable coincidence and one would think that the two siblings,
photography
and geometric optics, would each contribute to the growth of the other.
But this never
happened. Optical design in the 19th century was largely empirical,
and
today design in the geometric realm is often performed by optimizing a cost
function
which is defined via ray tracing. For example,
nowhere
in Rudolf Kinglslake's book "A History of the Photographic
Lens."
Recent advances in
machining, such as 5-axis diamond turning, have now made it
possible
to make high quality freeform optical surfaces, i.e. surfaces that do not have
rotational
symmetry. This opens up a whole new realm of design possibilities for
illumination
and imaging applications, but little theory exists for the design of such
surfaces.
I will describe methods that I have developed for this problem, based on
differential
geometry and partial differential equations. For some optical design
problems,
the surfaces may be modeled as integrals of distributions in Euclidean
space.
Hints of connections between Hamiltonian optics and these methods appear,
but
the full story remains unclear. Applications include the design of wide-angle
and
panoramic
imaging systems, and side view mirrors for motor vehicles without blind spots.
EVERYONE WELCOME
PLEASE FORWARD THIS ANNOUNCEMENT TO ANYONE
INTERESTED
The Tetrahedral Geometry/Topology Seminar is
sponsored jointly by