Thesis (Ph. D.)--University of Rochester. Institute of Optics, 2010.
In image formation, the coherence properties of the illumination source are of great
importance. At the same time, the polarization properties of an optical system also
play a role in the quality of an imaging system, particularly those of high numerical
aperture (NA). Polarization-dependent coherence is therefore an important area of
study for any imaging system. In the past few years, while there has been a unification
of the ability to use coherence theory to describe vectorial fields through the use
of a construct called a correlation matrix, very little has been done experimentally
predicting or measuring the coherence properties of an illumination system comprised
of vectorial fields. In the work that follows, we explore several arrangements in which
a polarization vortex mode converter was placed in the pupil plane of an illumination
system. In these arrangements, we study both theoretically and experimentally
the spatially dependent coherence properties using a vectorial treatment of optical
coherence. Those properties were applied to imaging systems that then results in an
improvement in image contrast using polarization- and orientation-dependent coherence
properties of the illumination.
In this work, the main illumination systems we explored are a Gaussian Schellmodel
beam, a fully correlated and ‘collimated’ azimuthal vortex beam, a partially
correlated azimuthally-polarized vortex (PCAV) illumination system, and a partially
correlated radially-polarized vortex (PCRV) illumination system. For the case of
PCAV and PCRV illumination, we implemented critical and K¨ohler illumination systems
with a polarization orientation that has an azimuthal or radial symmetry in
the pupil plane. We demonstrated first theoretically and then experimentally that PCAV and PCRV illumination systems have a correlation matrix that describes the
correlation between electric fields as being only dependent on the separation of points
at a particular plane. Further, it was demonstrated that when comparing the fields
at two points in this plane separated by a certain distance, these fields are correlated
or in phase for one polarization orientation and anti-correlated or ! out of phase for
the orthogonal polarization.
In imaging systems, fields that are in phase constructively interfere while fields
that are ! out of phase destructively interfere. Thinking about a simple two-point
imaging experiment, destructive interference would result in a higher contrast and
constructive interference a lower contrast than that from an incoherent imaging system
with no interference of the fields. Therefore when using vortex illumination like
PCAV illumination, image fields polarized parallel to features in the image will produce
an image with higher contrast due to anti-correlated fields in the image plane.
In the following work, we theoretically and experimentally demonstrated polarization-
and orientation-dependent contrast enhancement in imaging systems with low
to moderate numerical apertures. Finally, a mathematical treatment of the correlation
properties of very high NA systems was also presented, in which we explored
the consequences of increasing the illumination system NA and changing the pupil
apodization function. For numerical apertures above about 0.4 it began to be apparent
that the longitudinal component of the illumination field at the object plane was
important to consider when trying to describe the correlation properties of PCRV
illumination. We found that PCAV illumination remains transverse for high NAs
and could be still described using a 2x2 correlation matrix. However, because PCRV
illumination has polarization components in three dimensions at the object plane, the
correlation properties had to be represented using a 3x3 correlation matrix.
By exploring the effects polarization has on the coherence properties of an illumination
system and consequentially on an imaging system, we continue the scientific
exploration of the important link between polarization and coherence. Having the ability to engineer specific polarization-dependent anti-correlations in an illumination
system or, more generally, the ability to determine the polarization and coherence
properties of any illuminator at some object plane experimentally will give optical
designers yet another tool to use when designing and optimizing imaging and even
non-imaging systems.
