Tech Briefs Magazine - May 2021 - PIT-26

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From left to right: An image developed of the cluster of reflective objects using single-point migration
of cross correlations, the rank-1 image, and Kirchhoff migration. The rank-1 and Kirchhoff migration
images are much better resolved than the image from single-point migration. (Courtesy of Matan
Leibovich, George Papanicolaou, and Chrysoula Tsogka)

However, the quick movement of the
imaging target relative to the receivers
can create an inverse synthetic aperture,
in which the signals that were detected
at multiple receivers as the target moved
throughout their field of view are synthesized coherently. This configuration
can effectively improve the resolution, as
if the imaging system had a wider aperture than the physical one.
Objects in LEO can spin on timescales
that range from a full rotation every few
seconds to every few hundred seconds,
which complicates the imaging process. It
is thus important to know - or at least be
able to estimate - some details about the
rotation before developing the image.
The authors therefore needed to estimate the parameters related to the
object's rotation before synthesizing the
data from different receivers. Though
simply checking all of the possible parameters to see which ones yield the sharpest
image is technically feasible, doing so
would require a lot of computational
power. Instead of employing this brute
force approach, the authors developed a
new algorithm that can analyze the imaging data to estimate the object's rotation
speed and the direction of its axis.

After accounting for the rotation, the
next step in the authors' imaging process
was to analyze the data to develop a picture of the space debris that would hopefully be as accurate and well-resolved as
possible. One method that researchers
often employ for this type of imaging of
fast-moving objects is the single-point
migration of cross correlations. Though
atmospheric fluctuations do not usually
significantly impair this technique, it
does not have a very high resolution. A
different, commonly used imaging
approach called Kirchhoff migration can
achieve a high resolution, as it benefits
from the inverse synthetic aperture configuration; however, the trade-off is that it
is degraded by atmospheric fluctuations.
With the goal of creating an imaging
scheme that is not too heavily affected by
atmospheric fluctuations but still maintains a high resolution, the authors proposed a third approach: an algorithm
whose result they call a rank-1 image.
" The introduction of the rank-1 image
and its resolution analysis for fast-moving
and rotating objects is the most novel
part of this study, " Leibovich said.
To compare the performance of the
three imaging schemes, the authors

gave simulated data of a rotating
object in LEO to each one and compared the images that they produced.
The rank-1 image was much more
accurate and well-resolved than the
result of single-point migration. It also
had similar qualities to the output of
the Kirchhoff migration technique.
But this result was not entirely surprising, given the problem's configuration. " It is important to note that the
rank-1 image benefits from the rotation of the object, " Papanicolaou said.
Though a rotating object generates
more complex data, one can actually
incorporate this additional information into the image processing technique to improve its resolution.
Rotation at certain angles can also
increase the size of the synthetic aperture, which significantly improves the
resolution for the Kirchhoff migration
and rank-1 images.
Further simulations revealed that the
rank-1 image is not easily muddled by
errors in the new algorithm for the estimation of rotation parameters. It is
also more robust to atmospheric effects
than the Kirchhoff migration image. If
receivers capture data for a full rotation of the object, the rank-1 image can
even achieve optimal imaging resolution. Due to its good performance, this
new imaging method could improve
the accuracy of imaging LEO satellites
and space debris. " Overall, this study
shed light on a new method for imaging fast-moving and rotating objects in
space, " Tsogka said. " This is of great
importance for ensuring the safety of
the LEO band, which is the backbone
of global remote sensing. "
For more information, contact Jillian
Kunze at kunze@siam.org.

New Electron Microscopy Technique Offers First Look at Previously
Hidden Processes
Northwestern University (Evanston, IL)
orthwestern researchers have developed a new microscopy method
that allows scientists to see the building
blocks of " smart " materials being
formed at the nanoscale. The chemical
process is set to transform the future of
clean water and medicines and for the
first time, people will be able to watch
the process in action.

Dispersion polymerization is a common scientific process used to make
medicines, cosmetics, latex and other
items, often on an industrial scale. And
at the nanoscale, polymerization can be
used to create nanoparticles with unique
and valuable properties.
These nanomaterials hold great
promise for the environment, where

they can be used to soak up oil spills or
other pollutants without harming
marine life. In medicine, as the foundation of " smart " drug delivery systems, it
can be designed to enter human cells
and release therapeutic molecules
under specified conditions.
There have been difficulties in scaling
up production of these materials.
Photonics & Imaging Technology, May 2021

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Tech Briefs Magazine - May 2021

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