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.