Abstract. This paper generalizes to circular apertures the theoretical study of stellar coronagraphy with prolate apodized rectangular entrance apertures of Aime et al. (2002). The main difference between the two studies is that circular prolate spheroidal functions are used for a circular aperture instead of linear prolate spheroidal functions for rectangular apertures. Owing to the radial property of the problem, the solution to the general equation for coronagraphy is solved using a Hankel transform instead of a product of Fourier transforms in the rectangular case. This new theoretical study permits a better understanding of coronagraphy, stressing the importance of entrance pupil apodization. A comparison with the classical unapodized Lyot technique is performed: a typical gain of 10 4 to 10 6 can be obtained theoretically with this technique. Circular and rectangular apertures give overall comparable results: a total extinction of the star light is obtained for Roddier & Roddier's phase mask technique whilst optimal starlight rejections are obtained with a Lyot opaque mask. A precise comparison between a circular aperture and a square aperture of same surface favors the use of a circular aperture for detection of extrasolar planets.

Abstract. This paper presents a theoretical study of stellar coronagraphy with apodized entrance apertures. The study is restricted to a perfect telescope operating in space, and a monochromatic on-axis unresolved star. It is shown that linear prolate functions are the optimal apodizers for rectangular apertures in stellar coronagraphy. With the phase mask technique (Roddier & Roddier 1997), prolate functions can produce a total extinction of the star light. For Lyot's coronagraphy, the extinction is not complete, but prolate apodizations lead to an optimal star residual intensity with surprising interesting properties: the residual star light and the planet enjoy the same apodized intensity pattern (but different dynamic) with the optimal light concentration. With this technique, very high rejection rates can be obtained for Lyot's coronagraphy, with smaller mask sizes.

This paper is concerned with the theoretical properties of high-contrast coronagraphic images in the context of exoplanet searches. We derive and analyze the statistical properties of the residual starlight in coronagraphic images and describe the effect of a coronagraph on the speckle and photon noise. Current observations with coronagraphic instruments have shown that the main limitations to high-contrast imaging are due to residual quasi-static speckles. We tackle this problem in this paper and propose a generalization of our statistical model to include the description of static, quasi-static, and fast residual atmospheric speckles. The results provide insight into the effects on the dynamic range of wave front control, coronagraphy, active speckle reduction, and differential speckle calibration. The study is focused on ground-based imaging with extreme adaptive optics, but the approach is general enough to be applicable to space, with different parameters.

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In this paper, we propose a general method to devise maximum likelihood penalized (regularized) algorithms with positivity constraints. Moreover, we explain how to obtain ‘product forms’ of these algorithms. The algorithmic method is based on Kuhn–Tucker first-order optimality conditions. Its application domain is not restricted to the cases considered in this paper, but it can be applied to any convex objective function with linear constraints. It is specially adapted to the case of objective functions with a bounded domain, which completely encloses the domain of the (linear) constraints. The Poisson noise case typical of this last situation and the Gaussian additive noise case are considered and they are associated with various forms of regularization functions, mainly quadratic and entropy terms. The algorithms are applied to the deconvolution of synthetic images blurred by a realistic point spread function similar to that of Hubble Space Telescope operating in the far-ultraviolet and corrupted by noise. The effect of the relaxation on the convergence speed of the algorithms is analysed. The particular behaviour of the algorithms corresponding to different forms of regularization functions is described. We show that the ‘prior’ image is a key point in the regularization and that the best results are obtained with Tikhonov regularization with a Laplacian operator. The analysis of the Poisson process and of a Gaussian additive noise leads to similar conclusions. We bring to the fore the close relationship between Tikhonov regularization using derivative operators, and regularization by a distance to a ‘default image’ introduced by Horne (Horne K 1985 Mon. Not. R. Astron. Soc. 213 129–41).