The Fresnel Diffractive imager is an innovative concept of distributed space telescope, for high resolution (milli arc-seconds) spectro-imaging in the IR, visible and UV domains. This paper presents its optical principle and the science that can be done on potential astrophysical targets.The novelty lies in the primary optics: a binary Fresnel array, akin to a binary Fresnel zone plate. The main interest of this approach is the relaxed manufacturing and positioning constraints. While having the resolution and imaging capabilities of lens or mirrors of equivalent size, no optical material is involved in the focusing process: just vacuum. A Fresnel array consists of millions void subapertures punched into a large and thin opaque membrane, that focus light by diffraction into a compact and highly contrasted image. The positioning law of the aperture edges drives the image quality and contrast.This optical concept allows larger and lighter apertures than solid state optics, aiming to high angular resolution and high dynamic range imaging, in particular for UV applications. Diffraction focusing implies very long focal distances, up to dozens of kilometers, which requires at least a two-vessel formation flying in space.The first spacecraft, "the Fresnel Array spacecraft", holds the large punched foil: the Fresnel Array. The second, the "Receiver spacecraft" holds the field optics and focal instrumentation. A chromatism correction feature enables moderately large (20%) relative wavebands, and fields of a few to a dozen arc seconds.This Fresnel imager is adapted to high contrast stellar environments: dust disks, close companions and (we hope) exoplanets. Specific to the particular grid-like pattern of the primary focusing zone plate, is the very high dynamic range achieved in the images, in the case of compact objects.Large stellar photospheres may also be mapped with Fresnel arrays of a few meters opertaing in the UV. Larger and more complex fields can be imaged with a lesser dynamic range: galactic or extragalactic, or at the opposite distance scale: small solar system bodies. This paper will briefly address the optical principle, and in more detail the astrophysical missions and targets proposed for a 4-meter class demonstrator: -Exoplanet imaging, Exoplanet spectroscopic analysis in the visible and UV, -Stellar environments, young stellar systems, disks, -Galactic clouds, astrochemistry, -IR observation of the galactic center, -Small objects of our solar system.