Strategies for the deconvolution of hypertelescope images

¹ Université de Nice Sophia-Antipolis, Centre National de la Recherche Scientifique, Observatoire de la Côte d’Azur, UMR 7293 Lagrange, Parc Valrose, 06108 Nice, France
e-mail: claude.aime@unice.fr
² Princeton University, Mechanical & Aerospace Engineering, Olden street, Princeton, 08544 NJ, USA
e-mail: henri.lanteri@unice.fr megan_83@hotmail.fr acarlott@princeton.edu

Received: 24 June 2011
Accepted: 24 April 2012

Abstract

Aims. We study the possibility of deconvolving hypertelescope images and propose a procedure that can be used provided that the densification factor is small enough to make the process reversible.

Methods. We present the simulation of hypertelescope images for an array of cophased densified apertures. We distinguish between two types of aperture densification, one called FAD (full aperture densification) corresponding to Labeyrie’s original technique, and the other FSD (full spectrum densification) corresponding to a densification factor twice as low. Images are compared to the Fizeau mode. A single image of the observed object is obtained in the hypertelescope modes, while in the Fizeau mode the response produces an ensemble of replicas of the object. Simulations are performed for noiseless images and in a photodetection regime. Assuming first that the point spread function (PSF) does not change much over the object extent, we use two classical techniques to deconvolve the images, namely the Richardson-Lucy and image space reconstruction algorithms.

Results. Both algorithms fail to achieve satisfying results. We interpret this as meaning that it is inappropriate to deconvolve a relation that is not a convolution, even if the variation in the PSF is very small across the object extent. We propose instead the application of a redilution to the densified image prior to its deconvolution, i.e. to recover an image similar to the Fizeau observation. This inverse operation is possible only when the rate of densification is no more than in the FSD case. This being done, the deconvolution algorithms become efficient. The deconvolution brings together the replicas into a single high-quality image of the object. This is heuristically explained as an inpainting of the Fourier plane. This procedure makes it possible to obtain improved images while retaining the benefits of hypertelescopes for image acquisition consisting of detectors with a small number of pixels.