Image reconstruction with optical interferometers

This lecture is an introduction to image synthesis with emphasis set on the specific problems encountered in optical (visible/IR) interferometry. Image synthesis is first presented in the context of complex visibility data obtained with a known transfer function. This simple case is used to introduce the concept of regularization which is needed to lever degeneracies (due to missing spatial frequencies) of the image reconstruction problem. When the complex amplitude transmissions are unknown but vary slowly with respect to the exposure time, the self calibration method can recover both the amplitude transmissions and the image. When the complex amplitude transmissions vary too quickly, as it is generally the case in optical interferometry, the data consist in non-linear measurements such as the powerspectrum and the bispectrum which are insensitive to the fast varying aberrations set by the turbulence at the cost of some loss of Fourier phase information. We show how the inverse problem approach presented for the simpler cases can be extended to obtain effective image restoration algorithms.