3,347 research outputs found
The determinant of the Dirichlet-to-Neumann map for surfaces with boundary
For any orientable compact surface with boundary, we compute the regularized
determinant of the Dirichlet-to-Neumann (DN) map in terms of particular values
of dynamical zeta functions by using natural uniformizations, one due to
Mazzeo-Taylor, the other to Osgood-Phillips-Sarnak. We also relate in any
dimension the DN map for the Yamabe operator to the scattering operator for a
conformally compact related problem by using uniformization.Comment: 16 page
Spectral analysis of random walk operators on euclidian space
We study the operator associated to a random walk on endowed with a
probability measure. We give a precise description of the spectrum of the
operator near and use it to estimate the total variation distance between
the iterated kernel and its stationary measure. Our study contains the case of
Gaussian densities on .Comment: 19 page
Random walk on surfaces with hyperbolic cusps
We consider the operator associated to a random walk on finite volume
surfaces with hyperbolic cusps. We study the spectral gap (upper and lower
bound) associated to this operator and deduce some rate of convergence of the
iterated kernel towards its stationary distribution.Comment: 28 page
Active compensation of aperture discontinuities for WFIRST-AFTA: analytical and numerical comparison of propagation methods and preliminary results with a WFIRST-AFTA-like pupil
The new frontier in the quest for the highest contrast levels in the focal
plane of a coronagraph is now the correction of the large diffractive artifacts
effects introduced at the science camera by apertures of increasing complexity.
The coronagraph for the WFIRST/AFTA mission will be the first of such
instruments in space with a two Deformable Mirrors wavefront control system.
Regardless of the control algorithm for these multi Deformable Mirrors, they
will have to rely on quick and accurate simulation of the propagation effects
introduced by the out-of-pupil surface. In the first part of this paper, we
present the analytical description of the different approximations to simulate
these propagation effects. In Annex A, we prove analytically that, in the
special case of surfaces inducing a converging beam, the Fresnel method yields
high fidelity for simulations of these effects. We provide numerical
simulations showing this effect. In the second part, we use these tools in the
framework of the Active Compensation of Aperture Discontinuities technique
(ACAD) applied to pupil geometries similar to WFIRST-AFTA. We present these
simulations in the context of the optical layout of the High-contrast imager
for Complex Aperture Telescopes, which will test ACAD on a optical bench. The
results of this analysis show that using the ACAD method, an apodized pupil
lyot coronagraph and the performance of our current deformable mirrors, we are
able to obtain, in numerically simulations, a dark hole with an AFTA-like
pupil. Our numerical simulation shows that we can obtain contrast better than
in monochromatic light and better than 3.e-8 with 10% bandwidth
between 5 and 14 lambda/D.Comment: 16 pages, 5 figures, Accepted for publication (Oct. 23, 2015) in
Journal of Astronomical Telescopes, Instruments, and Systems, special
WFIRST-AFTA coronagrap
Active Beam Shaping System and Method Using Sequential Deformable Mirrors
An active optical beam shaping system includes a first deformable mirror arranged to at least partially intercept an entrance beam of light and to provide a first reflected beam of light, a second deformable mirror arranged to at least partially intercept the first reflected beam of light from the first deformable mirror and to provide a second reflected beam of light, and a signal processing and control system configured to communicate with the first and second deformable mirrors. The first deformable mirror, the second deformable mirror and the signal processing and control system together provide a large amplitude light modulation range to provide an actively shaped optical beam
Data Informativity for the Identication of MISO FIR Systems with Filtered White Noise Excitation
For Prediction Error Identication, there are two main ingredients to get a consistent estimate: one of them is the data informativity with respect to (w.r.t.) the considered model structure. One common criterion used for the informativity is the positive deniteness of the input density spectral power (DSP) matrix at all frequencies. This criterion is not appropriate for multisine excitation but can be used for ltered white noise excitation for many identication problems. However, this criterion is not necessary and its application for some identication problems might not be possible. In this paper, we propose a necessary and sucient condition for the data informativity in the case of multiple-inputs single-output (MISO) nite impulse response (FIR) model structure in open-loop
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