arXiv subjects

Céline Theys

Publications and source records attributed to Céline Theys.

3 recordsLinked to original sources

arXiv2024

A comparison of solar and stellar coronagraphs that make use of external occulters

Solar and stellar externally occulted coronagraphs share similar concepts, but are actually very different because of geometric characteristics. Solar occulters were first developed with a simple geometric model of diffraction perpendicular to the occulter edges. We apply this mere approach to starshades, and introduce a simple shifted circular integral of the occulter which allows to illustrate the influence of the number of petals on the extent of the deep central dark zone. We illustrate the reasons for the presence of an internal coronagraph in the solar case and its absence in the exoplanet case.

astro-ph.IM↗

arXiv2024

Computation of the Fresnel diffraction of starshades based on a polygonal approximation

The design of starshades, i.e. external occulters for stellar coronography, relies on the fast and precise computation of their associated diffraction patterns of incoming plane waves in the telescope aperture plane. We present here a method based on a polygonal approximation of the occulter's shape, that allows fast computation of their diffraction patterns in the Fresnel approximation, without aliasing artefacts. It is competitive with respect to methods based on direct 2D Fourier transforms, or Boundary Diffraction Wave algorithms.

astro-ph.IM↗

arXiv2013

A normalized scaled gradient method to solve non-negativity and equality constrained linear inverse problem - Application to spectral mixture analysis

This paper addresses the problem of minimizing a convex cost function under non-negativity and equality constraints, with the aim of solving the linear unmixing problem encountered in hyperspectral imagery. This problem can be formulated as a linear regression problem whose regression coefficients (abundances) satisfy sum-to-one and positivity constraints. A normalized scaled gradient iterative method (NSGM) is proposed for estimating the abundances of the linear mixing model. The positivity constraint is ensured by the Karush Kuhn Tucker conditions whereas the sum-to-one constraint is fulfilled by introducing normalized variables in the algorithm. The convergence is ensured by a one-dimensional search of the step size. Note that NSGM can be applied to any convex cost function with non negativity and flux constraints. In order to compare the NSGM with the well-known fully constraint least squares (FCLS) algorithm, this latter is reformulated in term of a penalized function, which reveals its suboptimality. Simulations on synthetic data illustrate the performances of the proposed algorithm in comparison with other unmixing algorithms and, more particulary, demonstrate its efficiency when compared to the popular FCLS. Finally, results on real data are given.

math.OC↗