297 research outputs found
Apodized Pupil Lyot Coronagraphs for Arbitrary Telescope Apertures
In the context of high dynamic range imaging, this study presents a
breakthrough for the understanding of Apodized Pupil Lyot Coronagraphs, making
them available for arbitrary aperture shapes. These new solutions find
immediate application in current, ground-based coronagraphic studies (Gemini,
VLT) and in existing instruments (AEOS Lyot Project). They also offer the
possiblity of a search for an on-axis design for TPF. The unobstructed aperture
case has already been solved by Aime et al. (2002) and Soummer et al. (2003).
Analytical solutions with identical properties exist in the general case and,
in particular, for centrally obscured apertures. Chromatic effects can be
mitigated with a numerical optimization. The combination of analytical and
numerical solutions enables the study of the complete parameter space (central
obstruction, apodization throughput, mask size, bandwidth, and Lyot stop size).Comment: 7 pages 4 figures - ApJL, accepte
Diffraction Analysis of 2-D Pupil Mapping for High-Contrast Imaging
Pupil-mapping is a technique whereby a uniformly-illuminated input pupil,
such as from starlight, can be mapped into a non-uniformly illuminated exit
pupil, such that the image formed from this pupil will have suppressed
sidelobes, many orders of magnitude weaker than classical Airy ring
intensities. Pupil mapping is therefore a candidate technique for coronagraphic
imaging of extrasolar planets around nearby stars. Unlike most other
high-contrast imaging techniques, pupil mapping is lossless and preserves the
full angular resolution of the collecting telescope. So, it could possibly give
the highest signal-to-noise ratio of any proposed single-telescope system for
detecting extrasolar planets. Prior analyses based on pupil-to-pupil
ray-tracing indicate that a planet fainter than 10^{-10} times its parent star,
and as close as about 2 lambda/D, should be detectable. In this paper, we
describe the results of careful diffraction analysis of pupil mapping systems.
These results reveal a serious unresolved issue. Namely, high-contrast pupil
mappings distribute light from very near the edge of the first pupil to a broad
area of the second pupil and this dramatically amplifies diffraction-based edge
effects resulting in a limiting attainable contrast of about 10^{-5}. We hope
that by identifying this problem others will provide a solution.Comment: 23 pages, 13 figures, also posted to
http://www.orfe.princeton.edu/~rvdb/tex/piaaFresnel/ms.pd
Predictability of band-limited, high-frequency, and mixed processes in the presence of ideal low-pass filters
Pathwise predictability of continuous time processes is studied in
deterministic setting. We discuss uniform prediction in some weak sense with
respect to certain classes of inputs. More precisely, we study possibility of
approximation of convolution integrals over future time by integrals over past
time. We found that all band-limited processes are predictable in this sense,
as well as high-frequency processes with zero energy at low frequencies. It
follows that a process of mixed type still can be predicted if an ideal
low-pass filter exists for this process.Comment: 10 page
Slepian functions and their use in signal estimation and spectral analysis
It is a well-known fact that mathematical functions that are timelimited (or
spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the
finite precision of measurement and computation unavoidably bandlimits our
observation and modeling scientific data, and we often only have access to, or
are only interested in, a study area that is temporally or spatially bounded.
In the geosciences we may be interested in spectrally modeling a time series
defined only on a certain interval, or we may want to characterize a specific
geographical area observed using an effectively bandlimited measurement device.
It is clear that analyzing and representing scientific data of this kind will
be facilitated if a basis of functions can be found that are "spatiospectrally"
concentrated, i.e. "localized" in both domains at the same time. Here, we give
a theoretical overview of one particular approach to this "concentration"
problem, as originally proposed for time series by Slepian and coworkers, in
the 1960s. We show how this framework leads to practical algorithms and
statistically performant methods for the analysis of signals and their power
spectra in one and two dimensions, and on the surface of a sphere.Comment: Submitted to the Handbook of Geomathematics, edited by Willi Freeden,
Zuhair M. Nashed and Thomas Sonar, and to be published by Springer Verla
Dynamic crossover in the global persistence at criticality
We investigate the global persistence properties of critical systems relaxing
from an initial state with non-vanishing value of the order parameter (e.g.,
the magnetization in the Ising model). The persistence probability of the
global order parameter displays two consecutive regimes in which it decays
algebraically in time with two distinct universal exponents. The associated
crossover is controlled by the initial value m_0 of the order parameter and the
typical time at which it occurs diverges as m_0 vanishes. Monte-Carlo
simulations of the two-dimensional Ising model with Glauber dynamics display
clearly this crossover. The measured exponent of the ultimate algebraic decay
is in rather good agreement with our theoretical predictions for the Ising
universality class.Comment: 5 pages, 2 figure
Classical capacity of the lossy bosonic channel: the exact solution
The classical capacity of the lossy bosonic channel is calculated exactly. It
is shown that its Holevo information is not superadditive, and that a
coherent-state encoding achieves capacity. The capacity of far-field,
free-space optical communications is given as an example.Comment: 4 pages, 2 figures (revised version
Information rate of waveguide
We calculate the communication capacity of a broadband electromagnetic
waveguide as a function of its spatial dimensions and input power. We analyze
the two cases in which either all the available modes or only a single
directional mode are employed. The results are compared with those for the free
space bosonic channel.Comment: 5 pages, 2 figures. Revised version (minor changes
Fourier Analytic Approach to Phase Estimation
For a unified analysis on the phase estimation, we focus on the limiting
distribution. It is shown that the limiting distribution can be given by the
absolute square of the Fourier transform of function whose support
belongs to . Using this relation, we study the relation between the
variance of the limiting distribution and its tail probability. As our result,
we prove that the protocol minimizing the asymptotic variance does not minimize
the tail probability. Depending on the width of interval, we derive the
estimation protocol minimizing the tail probability out of a given interval.
Such an optimal protocol is given by a prolate spheroidal wave function which
often appears in wavelet or time-limited Fourier analysis. Also, the minimum
confidence interval is derived with the framework of interval estimation that
assures a given confidence coefficient
Scalar and vector Slepian functions, spherical signal estimation and spectral analysis
It is a well-known fact that mathematical functions that are timelimited (or
spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the
finite precision of measurement and computation unavoidably bandlimits our
observation and modeling scientific data, and we often only have access to, or
are only interested in, a study area that is temporally or spatially bounded.
In the geosciences we may be interested in spectrally modeling a time series
defined only on a certain interval, or we may want to characterize a specific
geographical area observed using an effectively bandlimited measurement device.
It is clear that analyzing and representing scientific data of this kind will
be facilitated if a basis of functions can be found that are "spatiospectrally"
concentrated, i.e. "localized" in both domains at the same time. Here, we give
a theoretical overview of one particular approach to this "concentration"
problem, as originally proposed for time series by Slepian and coworkers, in
the 1960s. We show how this framework leads to practical algorithms and
statistically performant methods for the analysis of signals and their power
spectra in one and two dimensions, and, particularly for applications in the
geosciences, for scalar and vectorial signals defined on the surface of a unit
sphere.Comment: Submitted to the 2nd Edition of the Handbook of Geomathematics,
edited by Willi Freeden, Zuhair M. Nashed and Thomas Sonar, and to be
published by Springer Verlag. This is a slightly modified but expanded
version of the paper arxiv:0909.5368 that appeared in the 1st Edition of the
Handbook, when it was called: Slepian functions and their use in signal
estimation and spectral analysi
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