Analysis & Optimal Design of Diffractive Optical Elements
Svetlana Rudnaya
Doctor of Philosophy (Applied & Industrial Mathematics), August 1999
ABSTRACT
The problem we study arose in an industrial application. For an optical system,
it is desired to produce a certain light intensity pattern on an image plan.
This can be realized by using a Diffractive Optics Element (DOE) placed between
the light source and the image plane. A DOE consists of an opaque screen with
an aperture covered by a thin transparent film. It is placed far from the light
source, so that an incoming light can be assumed to propagate as a plane wave.
As the light goes through the DOE, its properties (the phase and/or the amplitude)
are changed according to the principles of optics. The modified outgoing light,
which is not a plan wave anymore, produces a certain intensity pattern on the
image plan in the near field of the DOE. The problem of determining the intensity
pattern given a complete information about the DOE is called a Forward problem.
Of our particular interest is an optimal design of the DOE, also called an
Inverse problem. Given geometrical and physical parameters of the system
and a target pattern, we would like to determine the features, such as a thickness
variation, of the DOE that produces an intensity pattern that is as close to
the target one as possible. The Inverse problem can be complicated by specific
constraints coming from manufacturing capabilities. For example, the thickness
of the film may be restricted to be piecewise constant, satisfy a given resolution,
and take on only one of L ( > 2) given values. The smaller L is the
cheaper the manufacturing process will be. However, for small L, it may be more
difficult to solve the Inverse problem.
Research supported by the Minnesota Center for Industrial
Mathematics (MCIM)
