Formation, Simulation and Restoration of Hypertelescopes Images

Abstract

This article first provides a historical and detailed introduction to the image formation models for diluted pupils array and their densified versions called hypertelescopes. We propose in particular an original derivation showing that densification using a periscopic setting like in Michelson’s 20 −  foot interferometer, or using inverted Galilean telescopes are fully equivalent. After a review based on previous reference studies (Tallon & Tallon-Bosc 1992; Labeyrie 1996; Aime 2008 and Aime et al. 2012), the introductory part ends with a tutorial section for simulating optical interferometric images produced by cophased arrays. We illustrate in details how the optical image formation model can be used to simulate hypertelescopes images, including sampling issues and their effects on the observed images.

In a second part of the article, we address the issue of restoring hypertelescope images and present numerical illustrations obtained for classical (constrained Maximum Likelihood) methods. We also provide a detailed survey of more recent deconvolution methods based on sparse representations and of their spread in interferometric image reconstruction.

The last part of the article is dedicated to two original and numerical studies. The first study shows by Monte Carlo simulations that the restoration quality achieved by constrained ML methods applied to photon limited images obtained from a diluted array on a square grid, or from a densified array (without spectral aliasing) on a grid, are essentially equivalent. The second study shows that it is possible to recover in hypertelescopes images quasi point sources that are not only far outside the clean field, but also superimposed on the replicas of other objects. This is true at least for the considered pupil array and in the limit of vanishing noise.