Apodized apertures for solar coronagraphy

Astronomy and Astrophysics – Astrophysics

Scientific paper

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Sun: Corona, Instrumentation: High Angular Resolution, Telescopes

Scientific paper

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 ρ-1. 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.

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