  Astronomical optical interferometers (OI) sample the Fourier transform of the
intensity distribution of a source at the observation wavelength. Because of
rapid atmospheric perturbations, the phases of the complex Fourier samples
(visibilities) cannot be directly exploited , and instead linear relationships
between the phases are used (phase closures and differential phases).
Consequently, specific image reconstruction methods have been devised in the
last few decades. Modern polychromatic OI instruments are now paving the way to
multiwavelength imaging. This paper presents the derivation of a
spatio-spectral ("3D") image reconstruction algorithm called PAINTER
(Polychromatic opticAl INTErferometric Reconstruction software). The algorithm
is able to solve large scale problems. It relies on an iterative process, which
alternates estimation of polychromatic images and of complex visibilities. The
complex visibilities are not only estimated from squared moduli and closure
phases, but also from differential phases, which help to better constrain the
polychromatic reconstruction. Simulations on synthetic data illustrate the
efficiency of the algorithm.
