In a 2013 American Journal of Physics paper, Lowell Wood proposed a method
for creating apodization and inverse apodization using the diffraction
patterns from slits. Apodization is a reduction in the amplitude of
the secondary maxima of diffracted light relative to the central peak,
while inverse
apodization is an enlargement of the secondary maxima. Both are
achieved by creating an aperture
function with tapered transmission from the edges to
the center of
the aperture. In apodization, the central diffraction peak
widens, while in inverse apodization, the central diffraction peak
thins, which is referred to as
super resolution. Super resolution is a technique which improves the
resolution of an imaging system beyond the diffraction limited value
and is useful in nanoparticle imaging. Much theoretical work
has
been done calculating the resulting diffraction patterns from
different aperture functions,
but little has been done to experimentally create aperture functions.
In this project, we extended Wood's method to circular apertures.
Wood's method for creating aperture functions involves filtering the
diffraction pattern from either a single- or double-slit, so that only
the desired portion of the diffraction pattern is transmitted. Using
this method, he was able to create a number of aperture functions for
the purpose of producing apodization and inverse apodization. We
improved the inverse apodization Wood achieved
using a circular aperture. When the Fresnel number [N] is even, the
on-axis intensity of the diffraction pattern from a circular aperture is
zero with intensity gradually increasing as you move away from
the axis. For our experiment, we passed light through a circular
aperture and then filtered the diffraction pattern in the near-field using
a second
circular aperture where N=2, so that only the desired portion of the
diffraction pattern was
transmitted. Using this method, we
hope to observe super resolution.
In a second part of the experiment, we
hope to
create improved optical vortices using a spiral phase plate. Currently,
the optical vortices we've made using our spiral phase plate exhibit
scattering from the center of the plate where the different thicknesses of glass
converge. We hope that by sending a beam with zero on-axis intensity
with gradually increasing intensity as you move away from the
axis,
we will be able to eliminate the unwanted scattering caused by the center
of the
plate.
This work was supported by the Laser Teaching
Center.