584 research outputs found
Optimal Asymmetric Apodizations and Shaped Pupils for Planet Finding Coronagraphy
The realization that direct imaging of extrasolar planets could be
technologically feasible within the next decade or so has inspired a great deal
of recent research into high-contrast imaging. We ourselves have contributed
several design ideas, all of which can be described as shaped pupil
coronagraphs. In this paper, we offer a complete and unified survey of
asymmetric shaped pupils designs, some of which have been published in our
previous papers. We also introduce a promising new design, which we call
barcode masks. These masks achieve the required contrast with a fairly large
discovery zone and throughput but most importantly they are perhaps the easiest
to manufacture and might therefore stand up best to a refined analysis based on
vector propogation techniques.Comment: 17 pages, 11 figures, submitted to Applied Optic
Local Warming
Using 55 years of daily average temperatures from a local weather station, I
made a least-absolute-deviations (LAD) regression model that accounts for three
effects: seasonal variations, the 11-year solar cycle, and a linear trend. The
model was formulated as a linear programming problem and solved using widely
available optimization software. The solution indicates that temperatures have
gone up by about 2 degrees Fahrenheit over the 55 years covered by the data. It
also correctly identifies the known phase of the solar cycle; i.e., the date of
the last solar minimum. It turns out that the maximum slope of the solar cycle
sinusoid in the regression model is about the same size as the slope produced
by the linear trend. The fact that the solar cycle was correctly extracted by
the model is a strong indicator that effects of this size, in particular the
slope of the linear trend, can be accurately determined from the 55 years of
data analyzed.
The main purpose for doing this analysis is to demonstrate that it is easy to
find and analyze archived temperature data for oneself. In particular, this
problem makes a good class project for upper-level undergraduate courses in
optimization or in statistics.
It is worth noting that a similar least-squares model failed to characterize
the solar cycle correctly and hence even though it too indicates that
temperatures have been rising locally, one can be less confident in this
result.
The paper ends with a section presenting similar results from a few thousand
sites distributed world-wide, some results from a modification of the model
that includes both temperature and humidity, as well as a number of suggestions
for future work and/or ideas for enhancements that could be used as classroom
projects.Comment: 12 pages, 5 figures, to appear in SIAM Revie
Laboratory Experiment of Checkerboard Pupil Mask Coronagraph
We present the results of the first laboratory experiment of checkerboard
shaped pupil binary mask coronagraphs using visible light, in the context of
the R&D activities for future mid-infrared space missions such as the 3.5 m
SPICA telescope. The primary aim of this work is to demonstrate the
coronagraphic performance of checkerboard masks down to a
peak-to-peak contrast, which is required to detect self-luminous extra-solar
planets in the mid-infrared region. Two masks, consisting of aluminum films on
a glass substrates, were manufactured using nano-fabrication techniques with
electron beam lithography: one mask was optimized for a pupil with a 30%
central obstruction and the other was for a pupil without obstruction. The
theoretical contrast for both masks was and no adaptive optics system
was employed. For both masks, the observed point spread functions were quite
consistent with the theoretical ones. The average contrast measured within the
dark regions was and . The
coronagraphic performance significantly outperformed the requirement
and almost reached the theoretical limit determined by the mask designs. We
discuss the potential application of checkerboard masks for mid-infrared
coronagraphy, and conclude that binary masks are promising for future
high-contrast space telescopes.Comment: 6 pages, 6 figure
A Parametric Simplex Algorithm for Linear Vector Optimization Problems
In this paper, a parametric simplex algorithm for solving linear vector
optimization problems (LVOPs) is presented. This algorithm can be seen as a
variant of the multi-objective simplex (Evans-Steuer) algorithm [12]. Different
from it, the proposed algorithm works in the parameter space and does not aim
to find the set of all efficient solutions. Instead, it finds a solution in the
sense of Loehne [16], that is, it finds a subset of efficient solutions that
allows to generate the whole frontier. In that sense, it can also be seen as a
generalization of the parametric self-dual simplex algorithm, which originally
is designed for solving single objective linear optimization problems, and is
modified to solve two objective bounded LVOPs with the positive orthant as the
ordering cone in Ruszczynski and Vanderbei [21]. The algorithm proposed here
works for any dimension, any solid pointed polyhedral ordering cone C and for
bounded as well as unbounded problems. Numerical results are provided to
compare the proposed algorithm with an objective space based LVOP algorithm
(Benson algorithm in [13]), that also provides a solution in the sense of [16],
and with Evans-Steuer algorithm [12]. The results show that for non-degenerate
problems the proposed algorithm outperforms Benson algorithm and is on par with
Evan-Steuer algorithm. For highly degenerate problems Benson's algorithm [13]
excels the simplex-type algorithms; however, the parametric simplex algorithm
is for these problems computationally much more efficient than Evans-Steuer
algorithm.Comment: 27 pages, 4 figures, 5 table
Identification and adaptive control of a high-contrast focal plane wavefront correction system
All coronagraphic instruments for exoplanet high-contrast imaging need
wavefront correction systems to reject optical aberrations and create
sufficiently dark holes. Since the most efficient wavefront correction
algorithms (controllers and estimators) are usually model-based, the modeling
accuracy of the system influences the ultimate wavefront correction
performance. Currently, wavefront correction systems are typically approximated
as linear systems using Fourier optics. However, the Fourier optics model is
usually biased due to inaccuracies in the layout measurements, the imperfect
diagnoses of inherent optical aberrations, and a lack of knowledge of the
deformable mirrors (actuator gains and influence functions). Moreover, the
telescope optical system varies over time because of instrument instabilities
and environmental effects. In this paper, we present an
expectation-maximization (E-M) approach for identifying and real-time adapting
the linear telescope model from data. By iterating between the E-step (a Kalman
filter and a Rauch smoother) and the M-step (analytical or gradient-based
optimization), the algorithm is able to recover the system even if the model
depends on the electric fields, which are unmeasurable hidden variables.
Simulations and experiments in Princeton's High Contrast Imaging Lab
demonstrate that this algorithm improves the model accuracy and increases the
efficiency and speed of the wavefront correction
New Orbits for the n-Body Problem
In this paper, we consider minimizing the action functional as a method for
numerically discovering periodic solutions to the -body problem. With this
method, we can find a large number of choreographies and other more general
solutions. We show that most of the solutions found, including all but one of
the choreographies, are unstable. It appears to be much easier to find unstable
solutions to the -body problem than stable ones. Simpler solutions are more
likely to be stable than exotic ones.Comment: 16 pages, 2 tables, 6 figure
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