Apodized apertures for solar coronagraphy

Université de Nice Sophia Antipolis, UMR 6525 Laboratoire Universitaire d'Astrophysique de Nice, Parc Valrose, 06108 Nice Cedex 2, France e-mail: Claude.Aime@unice.fr

Received: 22 November 2006
Accepted: 1 February 2007

Abstract

Aims.We propose the principle of a new solar telescope that makes it possible to observe the solar corona very close to the solar limb, without the help of a Lyot coronagraph. The result is obtained using a strongly apodized aperture.

Methods.We obtain the theoretical form of the diffraction halo produced by the solar disk at the level of the corona for a perfect diffraction-limited telescope, for raw and apodized apertures. The problem is first solved at one dimension for which a complete set of analytical expressions can be derived, including the effect of the center-to-limb solar variation. Formal equations are written for the two-dimensional case, and it is shown that the expression may take the form of a 1D integral. Nevertheless, the problem is difficult to solve. An analytic expression can be worked out using the line spread function, which is shown to give a valid approximation of the problem, in excellent agreement with a numerical computation that uses the exact integral.

Results.We show for the raw aperture that the diffraction halo is very strong and decreases slowly as . We propose as a solution to this problem an apodized aperture based on the generalized prolate spheroidal functions (GPSF). Such an apodized aperture may reduce the diffraction halo enough to permit a direct observation of the solar corona very close to the solar limb. A signal-to-noise ratio analysis is given.

Conclusions.Different strengths of apodization may be used, but very strong apodizations are indeed mandatory. A good choice seems to be a GPSF aperture with the prolate coefficient c on the order of 10. It could reduce the halo of diffraction by a factor 10⁵ (at the cost of an intensity throughput of 10% and a reduction in the classical resolution by a factor of about 1.6) and permit observation of the corona very close to the solar limb.