  In order for telescopes to obtain good and precise images they need to see
through atmospheric turbulence. To accomplish this and compensate for
atmospheric turbulence we use Adaptive Optics technologies. In this thesis we
analyze the variations in phase delays across phase plates which simulate
atmospheric turbulence in order to characterize them and determine how well
these phase plates reproduce the phase delay variation of the atmosphere. This
experiment was conducted using the Quadrature Polarization Interferometer (QPI)
testbed in the Lab of Adaptive Optics (LAO) at the University of California
Santa Cruz (UCSC). Using the QPI lab setup allowed us to be able to develop and
refine a final algorithm for determining the phase delay of the phase plates.
The characterization of the phase plates was accomplished by using the
interference patterns between a test and reference path and measuring their
pathlength variations. This was achieved by calculating the intensity of the
two paths of the Helium-Neon (HeNe) laser, modifying those values in order to
obtain phase values between the beam, and from the phase values we are able to
determine the path length variations, or phase delays, of the phase plates.
This allows us to determine Fried's parameter, $r_o$, by analyzing any given
separation on the phase plate and determining the path length variations
between those separations.
