Theoretical performance of solar coronagraphs using sharp-edged or apodized circular external occulters

Université de Nice Sophia-Antipolis, Centre National de la Recherche Scientifique, Observatoire de la Côte d’Azur, UMR7293 Lagrange, Parc Valrose, 06108 Nice, France
e-mail: claude.aime@unice.fr

Received: 17 July 2013
Accepted: 4 September 2013

Abstract

Context. This study focuses on an instrument able to monitor the corona close to the solar limb.

Aims. We study the performance of externally occulted solar coronagraphs. We compute the shape of the umbra and penumbra produced by the occulter at the entrance aperture of the telescope and compare levels of rejection obtained for a circular occulter with a sharp or smooth transmission at the edge.

Methods. We show that the umbral pattern in an externally occulted coronagraph can be written as a convolution product between the occulter diffraction pattern and an image of the Sun. We then focus on the analysis to circular symmetric occulters. We first derive an analytical expression using two Lommel series for the Fresnel diffraction pattern produced by a sharp-edged circular occulter. Two different expressions are used for inside and outside the occulter’s geometric shadow. We verify that a numerical approach that directly solves the Huygens-Fresnel integral gives the same result. This suggests that the numerical computation can be used for a circular occulter with any variable transmission.

Results. With the objective of observing the solar corona a few minutes from limb, a sharp-edged circular occulter of a few meters cannot produce an umbra darker than 10^-4 of the direct sunlight. The same occulter, having an apodization zone of a few percent of the diameter (3 cm for a 1.5 m occulter), darkers the umbra down to 10^-8 of the direct sunlight for linear transmission and to 10^-12 for Sonine or cosine bell transmissions. An investigation for an apodized occulter with manufacturing defaults is quickly performed.

Conclusions. It has been possible to numerically demonstrate the large superiority of apodized circular occulters with respect to the sharp-edged ones. These occulters allow the theoretical observation of the very limb-close corona with not yet obtained contrast ratios.